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Participating facilities include (in alphabetical order): the Australian National Science & Technology Centre for Neutron Scattering, the Diamond Light Source, the European Spallation Source, the Federal Institute for Materials Research and Testing, the Institut Laue Langevin, the ISIS Pulsed Neutron & Muon Source, the National Institute of Standards & Technology Center for Neutron Research, the Oak Ridge National Laboratory Neutron Sciences Directorate, and the Technical University Delft Reactor Institute. - + SasView was originally developed by the University of Tennessee as part of the Distributed Data Analysis of Neutron Scattering Experiments (DANSE) project funded by the US National Science Foundation (NSF), but is currently being developed as an Open Source project hosted on GitHub and managed by a consortium of scattering facilities. Participating facilities include (in alphabetical order): the Australian National Science & Technology Centre for Neutron Scattering, the Diamond Light Source, the European Spallation Source, the Federal Institute for Materials Research and Testing, the Institut Laue Langevin, the ISIS Pulsed Neutron & Muon Source, the National Institute of Standards & Technology Center for Neutron Research, the Oak Ridge National Laboratory Neutron Sciences Directorate, and the Technical University Delft Reactor Institute. + SasView is distributed under a 'Three-clause' BSD licence which you may read here: https://github.com/SasView/sasview/blob/master/LICENSE.TXT SasView is free to download and use, including for commercial purposes. - - © 2009-2018 UMD, UTK, NIST, ORNL, ISIS, ESS, ANSTO, ILL, TUD, DLS,. BAM - - - - If you make use of SasView + + © 2009-2024 UMD, UTK, NIST, ORNL, ISIS, ESS, ANSTO, ILL, TUD, DLS,. BAM + + + + If you make use of SasView - If you use SasView to do productive scientific research that leads to a publication, we ask that you acknowledge use of the program with the following text: - - This work benefited from the use of the SasView application, originally developed under NSF Award DMR-0520547. SasView also contains code developed with funding from the EU Horizon 2020 programme under the SINE2020 project Grant No 654000. - - - - Contributors to this Tutorial - + If you use SasView to do productive scientific research that leads to a publication, we ask that you acknowledge use of the program with the following text: + + This work benefited from the use of the SasView application, originally developed under NSF Award DMR-0520547. SasView also contains code developed with funding from the EU Horizon 2020 programme under the SINE2020 project Grant No 654000. + + + + Contributors to this Tutorial + Steve King (stephen.king@stfc.ac.uk) - Piotr Rozyczko (piotr.rozyczko@esss.se) - Wojciech Potrzebowski (wojciech.potrzebowski@esss.se) - - Last revised: 19 May 2019 + Piotr Rozyczko (piotr.rozyczko@esss.se) + Wojciech Potrzebowski (wojciech.potrzebowski@esss.se) + Susana Teixeira (susana.marujoteixeira@nist.gov) + Paul Butler (butlerpd@udel.edu) + + + Last revised: 2 September 2024 + - Learning Objective + Acknowledgements + + SK would like to thank Adrian Rennie for constructive comments on an earlier version of this tutorial. + Learning Objective - This tutorial will demonstrate how to fit individual 1D (‘intensity’ versus Q) datasets in SasView and showcase some of the associated functionality of the program. Simultaneous or batch fitting of multiple 1D datasets, and the fitting of 2D datasets, are considered in separate tutorials. + This tutorial will demonstrate how to fit individual 1D (‘intensity’ versus Q) datasets in SasView and showcase some of the associated functionality of the program. Simultaneous or batch fitting of multiple 1D datasets, and the fitting of 2D datasets, are considered in separate tutorials. - It is assumed that the reader has some familiarity with the purpose and principles of data fitting. If not, these Wikipedia articles provide an overview: - - + It is assumed that the reader has some familiarity with the purpose and principles of data fitting. If not, these Wikipedia articles provide an overview: + + - https://en.wikipedia.org/wiki/Curve_fitting + https://en.wikipedia.org/wiki/Curve_fitting - https://en.wikipedia.org/wiki/Mathematical_optimization + https://en.wikipedia.org/wiki/Mathematical_optimization @@ -92227,34 +92830,34 @@ - The program interface shown in this tutorial is SasView Version 5.0 running on a Windows platform but, apart from a few small differences in look and functionality, this tutorial is generally applicable to any earlier version of SasView on any platform. However, there is a separate tutorial for using the old program interface released with SasView 4.x. + The program interface shown in this tutorial is SasView Version 5.0.6 running on a Windows platform but, apart from a few small differences in look and functionality, this tutorial is generally applicable to any earlier version of SasView on any platform. However, there is a separate tutorial for using the old program interface released with SasView 4.x. - - - - Glossary - + + + + Glossary + - a priori information + a priori information - Known facts about the system whose datasets are being modelled that can guide the selection of model or model parameters. + Known facts about the system whose datasets are being modelled that can guide the selection of model or model parameters. - Chi-square (Χ 2, ‘Chi2’) + Chi-square (Χ 2, ‘Chi2’) - A statistical test of how well a chosen model fits the data with a given set of model parameters. In SasView this means - - + A statistical test of how well a chosen model fits the data with a given set of model parameters. 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Clearly, as Χ 2→0, the better the model fit is. - - NB: The SasView interface actually reports a variation of chi-square called the reduced chi-square, sometimes referred to as the ‘goodness-of-fit’ - - + + where I is the scattering intensity and E is the error on the intensity value. Clearly, as Χ 2→0, the better the model fit is. + + NB: The SasView interface actually reports a variation of chi-square called the reduced chi-square, sometimes referred to as the ‘goodness-of-fit’ + + @@ -92430,24 +93036,24 @@ - ( + ( - ( + ( I - ( + ( Q - ) + ) meas @@ -92456,17 +93062,17 @@ - ( + ( Q - ) + ) calc - ) + ) 2 @@ -92475,22 +93081,22 @@ - ( + ( Q - ) + ) 2 - ) + ) / - ( + ( @@ -92504,7 +93110,7 @@ - ) + ) @@ -92512,150 +93118,154 @@ - VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAARonAABP - AgAA/QAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAABknAABOAgAAlQAB - AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv - biBTZXJpZgAAAAAAAKYBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAIgAAQAC - AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAACKAAAAugEAAAEAWAIBAAAA - AAEAAQBYAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9uIFNl - cmlmAAAAAAAA/QAAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAQD/AwAAAAAAiAABAAIAAAAB - 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formula - - where Npts is the number of data points in the dataset and Nparams is the number of model parameters being optimised (which may be less than the total number of parameters in the model!). As ΧR 21, the better the model fit is. + + where Npts is the number of data points in the dataset and Nparams is the number of model parameters being optimised (which may be less than the total number of parameters in the model!). As ΧR 21, the better the model fit is. - Compute [button] + Compute/Plot [button] - Perform a direct calculation of the model with the current parameters but without any optimisation + Perform a direct calculation of the model with the current parameters but without any optimisation - Correlated parameters + Correlated parameters - To obtain the best solutions the optimiser needs to explore the widest possible parameter space. That is best achieved if every parameter can be considered independent of every other parameter. However, there will be instances where this is not the case and one or more parameters may be correlated. In such cases the best approach is to fix the values of some of correlated parameters using a priori information and then optimise the remaining values. - - A particularly common instance of correlated parameters encountered when model-fitting SAS data is when the components of the forward scattering intensity - - + To obtain the best solutions the optimiser needs to explore the widest possible parameter space. That is best achieved if every parameter can be considered independent of every other parameter. However, there will be instances where this is not the case and one or more parameters may be correlated. 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- where Φ is the volume fraction of scatterers, V is the volume of one scatterer (and so dependent on size parameters), and Δρ is the contrast (difference in SLDs), are separated out as individual parameters in a model. - - Correlated parameters often manifest themselves in the SasView interface as having very large uncertainties. + + where Φ is the volume fraction of scatterers, V is the volume of one scatterer (and so dependent on size parameters), and Δρ is the contrast (difference in SLDs), are separated out as individual parameters in a model. Optimizing two or more of these parameters will cause them to be correlated. + + Correlated parameters often manifest themselves in the SasView interface as having very large uncertainties. - Fit [button] + Fit [button] - Perform a calculation of the model optimising the selected parameters + Perform a calculation of the model optimising the selected parameters - Model-fitting + Model-fitting - The process of finding a good yet physically-realistic mathematical description (‘solution’) for a dataset or collection of datasets. The procedure employed to achieve this is called optimisation. + The process of finding a good yet physically-realistic mathematical description (‘solution’) for a dataset or collection of datasets. The procedure employed to achieve this is called optimisation. - OpenCL + OpenCL - A low-level software framework that allows calculations to be distributed between any compatible processors (eg, GPUs as well as CPUs) on the host computer. OpenCL can speed up demanding model-fits if suitable hardware is available. + A low-level software framework that allows calculations to be distributed between any compatible processors (eg, GPUs as well as CPUs) on the host computer. OpenCL can speed up demanding model-fits if suitable hardware is available. - OpenMP + OpenMP - A software framework that permits shared-memory multi-processing (ie, parallelisation) of calculations. OpenMP can speed up demanding model-fits if suitable hardware is available. + A software framework that permits shared-memory multi-processing (ie, parallelisation) of calculations. OpenMP can speed up demanding model-fits if suitable hardware is available. - Optimiser + Optimiser - The mathematical algorithm used to perform the model-fitting. + The mathematical algorithm used to perform the model-fitting. - Polydispersity + (Poly)dispersity - Where one or more model parameters have a distribution of values. - - SasView allows for 2 types of polydispersity: - + Where one or more model parameters have a distribution of values. + + SasView allows for 2 types of (poly)dispersity: + - Size + Size - where, for example, the radii and/or lengths of the scatterers have a distribution of values - - This will apply in most instances + where, for example, the radii and/or lengths of the scatterers have a distribution of values + This will apply in most instances - Angular + Angular - where the scatterers are anisometric in shape (eg, cylinders) and exhibit preferred orientations with respect to Q, for example, in under shear or in a magnetic field + where the scatterers are anisometric in shape (eg, cylinders) and exhibit preferred orientations with respect to Q, for example, under shear or in a magnetic field - + - Reduced Chi2 + Reduced Chi2 - See Chi-square + See Chi-square - Residual + Residual - The difference between the measured and calculated values of a function at a given point. In SasView this means: - - + The difference between the measured and calculated values of a function at a given point. In SasView this means: + + R - ( + ( Q - ) + ) = I @@ -92834,11 +93444,11 @@ - ( + ( Q - ) + ) meas @@ -92847,11 +93457,11 @@ - ( + ( Q - ) + ) calc @@ -92860,66 +93470,68 @@ - VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAboRAAAd - AgAAeAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAALkRAAAcAgAAlQAB - AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv - biBTZXJpZgAAAAAAAKYBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAIgAAQAC - AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAABuAAAAgwEAAAEAUgIBAAAA - AAEAAQBSAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA8AAAAAwA2AAAACgBPcGVuU3ltYm9sAAAA - AAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAiAABAAIAAAABAIcAAQAF - AAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAJ4BAACDAQAAAQAAACgAjwAAAAAAAQABACgA - jAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24gU2VyaWYAAAAA - AACmAQAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAABAP8DAAAAAACIAAEAAgAAAAEAhwABAAUA - AAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAARAIAAIMBAAABAFExAQAAAAABAAEAUQCMAAEA 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the number of standard deviations between the measured value and the calculated value. Thus, for a good fit, 68% of the values will lie within -1 < R(Q)Normalised < +1, and 95% within +/-2. - - Residuals larger than +/-3 indicate significant problems with either the input data or the choice of model or model parameters. + + where E is the error on the intensity value. + + A normalised residual can be thought of as the number of standard deviations between the measured value and the calculated value. Thus, for a good fit, 68% of the values will lie within -1 < R(Q)Normalised < +1, and 95% within +/-2. + + Residuals larger than +/-3 indicate significant problems with either the input data or the choice of model or model parameters. - SLD + SLD - Abbreviation for Scattering Length Density, a measure of the ability of a molecule to scatter. Strictly speaking, SLD is a SANS quantity, so if fitting SAXS data use electron density values in their place. - - SLD values (neutron and X-ray) can be calculated with the SLD Calculator Tool in SasView. + Abbreviation for Scattering Length Density, a measure of the ability of a molecule to scatter. Strictly speaking, SLD is a SANS quantity, so if fitting SAXS data use electron density values in their place. + + SLD values (neutron and X-ray) can be calculated with the SLD Calculator Tool in SasView. - Smearing + Smearing - Sometimes the instrumental geometry used to acquire the experimental data has an impact on the clarity of features in the scattering curve. For example, peaks or fringes might be slightly broadened. This is known as Q-resolution smearing. - - To compensate for this effect SasView can add a resolution contribution into a model calculation (which by definition will be exact) to make it more representative of what has been measured experimentally. - - SasView provides 4 smearing options: - + Sometimes the instrumental geometry used to acquire the experimental data has an impact on the clarity of features in the scattering curve. For example, peaks or fringes might be slightly broadened. This is known as Q-resolution smearing. + + To compensate for this effect SasView can add a resolution contribution into a model calculation (which by definition will be exact) to make it more representative of what has been measured experimentally. + + SasView provides 4 smearing options: + - None + None - no smearing correction is applied + no smearing correction is applied - Use dQ Data + Use dQ Data - the measured Q-resolution for each data point is used to apply a smearing correction - This is the default if dQ data is present + the measured Q-resolution for each data point is used to apply a smearing correction + This is the default if dQ data is present - Custom Pinhole + Custom Pinhole - SasView will apply a smearing correction suitable for data measured on ‘pinhole geometry’ instruments (eg, most SAXS/SANS instruments) + SasView will apply a smearing correction suitable for data measured on ‘pinhole geometry’ instruments (eg, most SAXS/SANS instruments) - Custom Slit + Custom Slit - SasView will apply a smearing correction suitable for data measured on ‘slit geometry’ instruments (eg, most USAXS/USANS instruments) + SasView will apply a smearing correction suitable for data measured on ‘slit geometry’ instruments (eg, most USAXS/USANS instruments) - + - Theory + Theory - The name SasView gives to a model calculation. + The name SasView gives to a model calculation. - Uncertainties + Uncertainties - Every experimental measurement, including the measurement of I(Q), is subject to some degree of error (which will, ideally, be included in the dataset). Similarly, the parameters returned by optimisation will have some associated range of uncertainty. - - Parameters with uncertainties that are more than 95% of the parameter value should be viewed with deep suspicion. - - NB: Unhelpfully, but for reasons of space, the SasView interface actually labels parameter uncertainties as errors. + Every experimental measurement, including the measurement of I(Q), is subject to some degree of error (which will, ideally, be included in the dataset). Similarly, the parameters returned by optimisation will have some associated range of uncertainty. + + Parameters with uncertainties that are more than 95% of the parameter value should be viewed with deep suspicion. + + NB: Unhelpfully, but for reasons of space, the SasView interface actually labels parameter uncertainties as errors. - Weighting + Weighting - An optimiser can be instructed to pay less or more attention to data points in a dataset by changing the weighting of those data points. - - SasView provides 4 weighting options: - + An optimiser can be instructed to pay less or more attention to data points in a dataset by changing the weighting of those data points. + + SasView provides 4 weighting options: + - No Weighting + No Weighting - all data points will be weighted equally + all data points will be weighted equally - Use dI Data + Use dI Data - the data points will be inversely weighted according to their measured intensity errors (ie, less prominence will be given to data points with large errors) - This is the default if dI data is present + the data points will be inversely weighted according to their measured intensity errors (ie, less prominence will be given to data points with large errors) + This is the default if dI data is present - Use sqrt |(I Data)| + Use sqrt |(I Data)| - the data points will be inversely weighted according to the square root of their intensity values + the data points will be inversely weighted according to the square root of their intensity values - Use |(I Data)| + Use |(I Data)| - the data points will be inversely weighted according to their intensity values + the data points will be inversely weighted according to their intensity values - - - - Running SasView - - Windows - Either select SasView from ‘Start> ‘All Programs’ or, if you asked the installer to create one, double-click on the SasView desktop icon. - - + + + + Running SasView + + Windows + Either select SasView from ‘Start> ‘All Programs’ or, if you asked the installer to create one, double-click on the SasView desktop icon. + + iVBORw0KGgoAAAANSUhEUgAAAMAAAADuCAYAAABveghBAAAACXBIWXMAABcSAAAXEgFnn9JS AABIhklEQVR4nO29OYAkSXIdah5ZZ3d1T81AoYam9JfS7y/91bYoEZTQkAhIHErElziQSEpY SNgv/aUEUOJQ4lJCUyIpoSlxNTYlLrXCHnN1T091dd1VGfHj2eFu7hF51NFZR4b1xGRkRFRk @@ -93560,19702 +94174,17236 @@ - Mac OS - Go in to your ‘Applications’ folder and select SasView. + Mac OS + Go in to your ‘Applications’ folder and select SasView. - - iVBORw0KGgoAAAANSUhEUgAABZwAAAOGCAIAAADnKMI4AADLVklEQVR4nOzdCUAWZf7A8Wc4 - xDtTUFPxBFJ0Ky21wCPvfbF2tU3UsugEO3bBbalcsRO7rL/QWgntVra1qV22rbB5pFbQmpXZ - IhngwXrkleaRqRzvf473fud9ecEXXga+n4pmnnmumXfgfef3PvNMyBVXXCEAAAAAAACMJuSO - R/4a6D4AAAAAAADUWkigOwAAAAAAADw6e/pUafG248eO+bfaCy68MDp2YFjrtg3TRMsTR9a9 - lL3/u23+bSJEEpJ/awQAAAAAAP5S9OWX1197dUx0X/9WW1K6850PN1wxakzDNPH+I3Pv+VNy - 3FUP+7eJEN2YRslXhbuLv/nl+LHgkOALw7tGDrik58Ah/m0YAAAAAADU6Ny5szHRffce+dm/ - 1cp1njv3kRYTaIAmTh398arhl/5c/I1/mwiRJKeoxumTxz9e9rfKX061atXqwg4XtGgRGiQq - 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\test\1d_data folder in the SasView installation directory. + + Select the ISIS_Polymer_Blend_RT2.xml dataset and click the Open button. + + + iVBORw0KGgoAAAANSUhEUgAABpAAAAP7CAYAAABcKM3/AAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXxc9X3v/9c5Zzats1hesRnJssVibCNTwhpsME4CuZcQauKkaes0DU5C + c9v0d3PbR0Ny215Cb29v2jQtTX8x7W3cX9OUQLiGFkhq7NiOzVoiZBYTYy3jfZNmRvss55zf + HzOSR9JIGi1egPfz8dDD0pnv+X4/58yMosyHz+druK7rIiIiIiIiJTH+4O0LHcK0HPvt4IUO + QeSCmj9//oUOQURERETkXcFQAklEREREREREREREREQKmRc6ABEREREREREREREREbm4KIEk + IiIiIiIiIiIiIiIiwyiBJCIiIiIiIiIiIiIiIsN4xnqgt7ePJ370FLt27eXUyTN4vBYLFy7g + lltu4qP/6UOUlZWdzzhFRERERERERERERESmbfPmzeM+vmnTpvMUSWk2b97MPffcQ01NTdHH + z5w5wxNPPDHjcRdNIB2KHearX32QeGecsrIyqqur8Pm89PX28+wz23jl5Vf58v/zW8yfP3dG + gxERERERERERERERETnXxkq2TJRcuhDuuecetj75JHd/7GOjkkhnzpxh65NPcs8998z4uobr + um7hgd7ePj5/3+/Q1dVNVVUlVVWVVFSUE/D7sTweXMchlc5QUVHO7//BlwkEAuOv0Ladzdta + 8j/Us27TWuomEWDb9s28GrmX9Y3h4XO2LmbTqgSPP9ZC/b3rKXx4uuJNj/PYK53jx1xwXZFr + 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To assist us in this task we have the a priori knowledge that this sample is a (solid) polymer blend (as it happens, of h8-polystyrene and d8-polystyrene). In the absence of solvent molecules the conformational characteristics of the polymer chains in the sample are described by a 3D random walk mediated by excluded volume constraints. Polymer physics tells us that this results in a Gaussian distribution of chain density about the centre-of-mass. The scattering from such a structure was formulated by Debye (1947) and is implemented in SasView as the mono_gauss_coil model. - + + + + + + + Tip: Notice that the name of the data that appears in the Data Explorer is different to the name of the file that was just loaded. What is being displayed is the title of the data read from within the file. Prior to SasView 5.0.4 the file name would have been displayed. Obviously, this feature depends on the file containing suitable metadata in the first place! The CanSAS1D (.xml) and NXcanSAS (.h5) standard formats are suitably compatible. + + From SasView 5.0.4 it is possible to assign custom names to the data by right-clicking on a data set in the Data Explorer and selecting Change Name. + + iVBORw0KGgoAAAANSUhEUgAAAWAAAAE1CAYAAADZIjoIAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nO3df2xb530u8EdSstoW0hBpqdJduFvTjqzSNjEwDZHYG2QnIg3HaGEFoAs1 + yL1sMCdhFdAMAnXmzdg/wmX04hWWiah0kqHlFqRCzEEyNiitTfrKXGEnUC0BUyw2UmQanbtr + XbLNmP1I6jYR7x+HpA7Jc8hD/Xol8/kAgiOe9z3nJRU9es/3HPJtyuVyORARrUPXrl3D1q1b + 6+ozMzODL33pS6rbdTodcrkcYpMZoKl0Wy4HfGXDv6O9vb3uYyr1aa5rL0REtGwYwEREgjCA + iYgEYQATEQnCACYiEoQBTEQkyB1qGwLHT63mOIiIAAD+Y0dFD2H15FS8GOxX27SsxudW9usL + X/gC/+W//Hed/Ftv7szOztadOdPT07lsNqv6VYjF8/+Szp2fLP069y/p3PT09KKOqaQpl1N+ + I0bg+KlV+Us08f9Wbt+OHV/E+alfr9wBiGhZjfyovtzhGzHWMIYv0frg2PFF0UMQQrUGLMJT + B7+2pP6vjVwp+Z4zYKL1oVF/T9dUAAPAlStXajdS8LWvVYZ3o/5QidabRp0sLUsJ4rPPPluO + 3Sy7Rj2tIVpvGjF8gWUI4Pfeew/nzp3DrVu3lmM8y0r+Q73U14T7+36i2vZSXxPuN8i+vn4K + 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To assist us in this task we have the a priori knowledge that this sample is a (solid) polymer blend (as it happens, of h8-polystyrene and d8-polystyrene). In the absence of solvent molecules the conformational characteristics of the polymer chains in the sample are described by a 3D random walk mediated by excluded volume constraints. Polymer physics tells us that this results in a Gaussian distribution of chain density about the centre-of-mass. The scattering from such a structure was formulated by Debye (1947) and is implemented in SasView as the mono_gauss_coil model. + - Tip: The names of several models changed between SasView 3.x and SasView 4.x. For example, the mono_gauss_coil model was previously called the Debye model. + Tip: The names of several models changed between SasView 3.x and SasView 4.x. For example, the mono_gauss_coil model was previously called the Debye model. - - In the FitPage, select the model Category called shape-independent and then from the drop-down box below select the mono_gauss_coil model. 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Click the Compute/Plot button. + + + + + + Tip: Upto and including SasView 5.0.4 the Compute/Plot button was labelled Show Plot. + + + + The model loads with some default parameters, the calculated (not optimised at this stage) scattering from which is shown as the orange line on the upper graph. 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A separate Data Info window will appear. 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To change this, right-click on a graph and select Change Scale. For this example, linear I-axes are better. + If you want to examine the contents of the dataset, right-click on the upper graph, select ISIS_Polymer_Blend_RT2.xml and then DataInfo. A separate Data Info window will appear. + + The amount of information presented by DataInfo will depend on the file format of the dataset (CanSAS-standard xml files contain the most information) and the compliance of the data reduction program that wrote them. + + + iVBORw0KGgoAAAANSUhEUgAAAf8AAAOICAIAAABXK2+5AAAgAElEQVR4nOzdfYzkaH4f9oec + 3nmf2dmd3Z3Z23vb2+JIV2q9nO5k41ixBViBAVYjTv9hNc5IjL6zY5b27rxFA2nglDQQwGpA + F/cfYRmR7KKBJG04sdIJnM4fU/w7BpqWo1spOpV675q8N0l3e/btaXd2dnZn563yB1nFh+8P + WWTx7fv5Z3eqyIcPWV2/Yj1kPV/utddeIwAA0DJrhJDRaFR2NwAAYHWGwyFfdh8AAKAEqP4A + AG2E6g8A0Eao/gAAbcTfu3ev7D4AAMCq8a+//o2y+wAAAKvGP378uOw+AADAqmHcHwCgjfin + nnqq7D4AAMCqrX3uc7+SaoX33rt3+m3zz//iR+/fe5/juCtXLn/sYy+90vnUpUsXC+oiAADk + bu38+fPsS3/72+bh//5/ffc73797970nj5+cWTtz4eL5Z5659sorL/9nf0t6+eVPFNdRAADI + UYpx/3//77/x3/zmb/3+7//BO+/ceeqptStXLz/99JUL58/f/+D+dPrGP1X/2fRPTorrKABA + KhyDsvvowXHc66+/HvXs66+/nm+H+TfeeINluW+9cfpP/vt/ev/+/UsXLz799NVr155+9tln + 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values. We can exclude these points from the fitting using the Q range boxes in the Fit Options tab of the FitPage. - - Change the Q-limits by typing values in the boxes. 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We can exclude these points from the fitting using the Q range boxes in the Fit Options tab of the FitPage. + + Change the Q-limits by typing values in the boxes. For this example, set the maximum-Q value to 0.19 Å-1. The outer limit bar (the vertical black line on the right of the plot) moves inward to the new Q limit. + + + iVBORw0KGgoAAAANSUhEUgAABpAAAAP9CAYAAACKcS7iAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXxU933v/9c5s2gkoRUhdsQiyTaLMeDEIHDA2CQG7k2dxIY4XUjTGBIn + t9DbJv01ttvbGue2dZpA6yTXOLmJ86ubmta9JC0org0BB2TwjQ3YMtiSWMS+aV9nOefcP2bR + jDSSRhtg5/18PBRLZ875fj/nzIxymI8+n6/hOI6DiIiIiIikxPiz9250CENy4Q9zbnQIIjfU + +PHjb3QIIiIiIiIfCIYSSCIiIiIiIiIiIiIiIhLPvNEBiIiIiIiIiIiIiIiIyM1FCSQRERER + ERERERERERFJoASSiIiIiIiIiIiIiIiIJHD39kBbWzv/9tLP2bfvAFcuX8PtcTFp0gQ+9rHF + rP4vHyc9Pf16xikiIiIiIiIiIiIiIjJkhmH0+bjjONcpktQYhsGvf/1rFixYkPTxN998kzvv + vHPY4zacJCOeqT3LN77xJA31DaSnp+Pz+fB6PZimieM4FBTks+m/f4Xx48cOazAiIiIiIiIi + IiIiIiIjyTCMXpMtfT12o7z55pssWryE1w/s75FE6uuxoerRwq6trZ1v/Nlf0dzUTG5uDgUF + +YwdW8D4cYVMmDCOCePH4jiw7X/9iM7Ozv5nKN+AYRiRrw2UDzDA8g0Gi7fW9BxzQznUbGWx + sZjuDw9VzdbF/cccd1494kvYLTrO8McpIiIiIiIiIiIiIiKpiX6mH/99/NfNasGCBbx+YD+L + 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AGgIjgAAAAAAAEgiOAIAAAAAAKAhOAIAAAAAACCJ4AgAAAAAAICG4AgAAAAAAIAkgiMAAAAA + AAAa/wPrTcN3k1HRbwAAAABJRU5ErkJggg== - - Several things happen very quickly: - - + + Several things happen very quickly: + + + + The progression of the fit is displayed in the Status Bar at the bottom of the SasView window + + + Parameters and their uncertainties update in the FitPage + - The progression of the fit is displayed in the Status Bar at the bottom of the SasView window + The Reduced Chi2 (chi-squared) value updates in the FitPage - Parameters and their uncertainties update in the FitPage + The orange line on the upper graph updates its position and shape - The Reduced Chi2 (chi-squared) value updates in the FitPage + The residuals plot in the lower graph updates - The orange line on the upper graph updates its position and shape + Optimiser output appears in the Log Explorer* - The residuals plot in the lower graph updates + A Results Panel appears* - Finally, Fitting completed successfully appears in the Status Bar + Finally, Fitting completed successfully appears in the Status Bar - - What do you think of the solution? It looks good, right? The model calculation (‘theory’ curve) is running through the measured datapoints, the normalised residuals are all within +/-2 standard deviations, and the Reduced Chi2 is a very respectable 0.70. - - But, look closely at the model parameters and their uncertainties. Two of the parameters, scale and i_zero, have nonsensical uncertainties. Why? - - To understand this it is instructive to examine the help documentation for the model. Click the Help button on the FitPage (not in the Menu Bar) alongside the model name. The documentation tells us that the function that SasView is fitting is - - + + + + + + + Tip: The outputs denoted with a * above only appear in SasView 5.0.5 and later. + + + + + What do you think of the solution? It looks good, right? The model calculation (‘theory’ curve) is running through the measured datapoints, the normalised residuals are all within +/-2 standard deviations, and the Reduced Chi2 is close to 1 (more on this shortly!). + + But, look closely at the model parameters and their uncertainties. Two of the parameters, scale and i_zero, have uncertainties (the Error) that make no sense. Why? + + To understand this it is instructive to examine the help documentation for the model. Click the Help button on the FitPage (not in the Menu Bar) alongside the model name. 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- So, in this model scale and i_zero are correlated parameters; changing one of them affects the other and the optimiser is unable to home in on a robust solution. To fit the data with this model we only need one of these parameters. - + + So, in this model scale and i_zero are correlated parameters; changing one of them affects the other and the optimiser is unable to home in on a robust solution. To fit the data with this model we only need one of these parameters. + - Tip: SasView adds an overall scale factor (scale) and a Q-independent background to all its models for consistency, even though some models might not need one or other of these parameters. If in doubt, consult the model help documentation. + Tip: SasView adds an overall scale factor (scale) and a Q-independent background to all its models for consistency, even though some models might not need one or other of these parameters. If in doubt, consult the model help documentation. - - Uncheck the scale parameter and set its value to 1.0. 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(for output suitable for Excel or LaTeX) - + If you want the parameter values and their uncertainties, go to the Menu Bar and select Edit and either Copy Params (for output suitable for a text editor) or Copy Params as... (for output suitable for Excel or LaTeX) + - If you want a copy of the graphs, right-click on a graph and select either Save Image (as .ps/eps, .jpg, .pdf, .png, .raw, .svg, or .tif), Print Image, or Copy to Clipboard - + If you want a copy of the graphs, right-click on a graph and select either Save Image (as .ps/eps, .jpg, .pdf, .png, .raw, .svg, or .tif), Print Image, or Copy to Clipboard + - If you want a file of the model function (the green line) and/or residuals, right-click on the appropriate graph and select either M1 [ISIS_Polymer_Blend_RT2.xml] or Residuals for M1 [ISIS_Polymer_Blend_RT2.xml] and then Save Points as a File (as plain ASCII text: .txt, or in CanSAS1D format: .xml) - + If you want a file of the model function (the orange line) and/or residuals, right-click on the appropriate graph and select either M1 [LOQ Standard RT2_SANS.xml] or Residuals for M1 [LOQ Standard RT2_SANS.xml] and then Save Points as a File (as plain ASCII text: .txt, or in CanSAS1D format: .xml) + - If you want a two-page pdf report containing all pertinent information including copies of the graphs, go to the Menu Bar and select Edit and Report Results + If you want a two-page pdf report containing all pertinent information including copies of the graphs, go to the Menu Bar and select Edit and Report Results - - and finally - + + and finally + + - A SasView session can be saved and reloaded as an ‘Analysis’ (an individual model fit), or as a ‘Project’ (everything done since starting your SasView session) by going to the Menu Bar and selecting File and either Save Analysis or Save Project. + A SasView session can be saved and reloaded as an ‘Analysis’ (an individual model fit), or as a ‘Project’ (everything done since starting your SasView session) by going to the Menu Bar and selecting File and either Save Analysis or Save Project. - - We shall now examine some additional aspects of model-fitting this dataset. - - Return to the FitPage and change the Instrumental Smearing to None. Then run the Fit again. Notice anything? The parameter values and the Reduced Chi2 value have all subtly changed. This is to be expected; Q-resolution affects the measured data, so it must have a bearing on the model fit. - - Now change the model to the one called poly_gauss_coil. This model is an extension of Debye’s original scattering law to include a Schulz-Zimm molecular weight distribution. This model has one extra parameter: the polydispersity of the polymer (Mw/Mn). Set the polydispersity to 1.03 (but leave it unchecked; this is more a priori information) and run the Fit again. - - The parameter values change again, but there is a marked improvement (decrease) in the Reduced Chi2 value. - - Lastly, reset Instrumental Smearing to Use dQ Data and run the Fit one last time. - - Here is a summary of the fit results: - + + We shall now examine some additional aspects of model-fitting this dataset. + + Return to the FitPage and change the Instrumental Smearing to None. Then run the Fit again. Notice anything? The parameter values and the Reduced Chi2 value have all subtly changed. This is to be expected; Q-resolution affects the measured data, so it must have a bearing on the model fit. + Now change the model to the one called poly_gauss_coil. This model is an extension of Debye’s original scattering law to include a Schulz-Zimm molecular weight distribution. This model has one extra parameter: the polydispersity of the polymer (Mw/Mn). Set the polydispersity to 1.03 (but leave it unchecked; this is more a priori information) and run the Fit again. + + The parameter values change again, but there is a marked improvement (decrease) in the Reduced Chi2 value. + + Lastly, reset Instrumental Smearing to Use dQ Data and run the Fit one last time. + + Here is a summary of the fit results: + @@ -116407,26249 +114165,23216 @@ - Param: - - Model + Param: + + Model - scale + scale - bckgrd + bckgrd - bckgrd _err + bckgrd _err - i_zero + i_zero - i_zero _err + i_zero _err - rg + rg - rg _err + rg _err - poly disp + poly disp - reduced chi2 + reduced chi2 - mono - use dQ + mono + use dQ - 1 + 1 - 0.0777 + 0.0777 - 0.0076 + 0.0076 - 49.75 + 49.75 - 0.169 + 0.169 - 56.57 + 56.57 - 0.146 + 0.146 - n/a + n/a - 0.780 + 0.780 - mono none + mono none - 1 + 1 - 0.0758 + 0.0758 - 0.0076 + 0.0076 - 49.65 + 49.65 - 0.169 + 0.169 - 56.44 + 56.44 - 0.146 + 0.146 - n/a + n/a - 0.771 + 0.771 - poly none + poly none - 1 + 1 - 0.0676 + 0.0676 - 0.0077 + 0.0077 - 50.07 + 50.07 - 0.172 + 0.172 - 57.36 + 57.36 - 0.150 + 0.150 - 1.03 + 1.03 - 0.659 + 0.659 - poly - use dQ + poly + use dQ - 1 + 1 - 0.0695 + 0.0695 - 0.0077 + 0.0077 - 50.17 + 50.17 - 0.172 + 0.172 - 57.50 + 57.50 - 0.150 + 0.150 - 1.03 + 1.03 - 0.669 + 0.669 + + + + + So for this dataset (sample) allowing for even a tiny amount of molecular weight polydispersity – thereby maximising our use of a priori information - gives rise to a significant improvement in the quality of the fit! And though it does appear that including the Q-resolution smearing slightly degrades the quality of the fit in this example, it should be remembered that instrumental smearing is always present (and so should be handled) and this dataset was devoid of any fine structure (peaks, fringes). + + + + + + Aside: You may have noticed that all of the Reduced Chi2 values in the summary table above are slightly less than 1. Whilst values >1 are indicative of a poor fit, Reduced Chi2 values <1 are usually an indication that the data is being ‘over-fit’; for example, because the uncertainties on the data have been over-estimated (and the fact that most of the Residuals in the earlier screen shot lie within the ±1 band is also suspicious). It is not unusual for uncertainties to be incorrect, but it is more common for them to be under-estimated, not over-estimated. - - So for this dataset (sample) allowing for even a tiny amount of molecular weight polydispersity – thereby maximising our use of a priori information - gives rise to a significant improvement in the quality of the fit! And though it does appear that including the Q-resolution smearing slightly degrades the quality of the fit in this example, it should be remembered that instrumental smearing is always present (and so should be handled) and this dataset was devoid of any fine structure (peaks, fringes). - - Example 2 - + + + + + + + + + + Example 2 + - This demonstrates a fit requiring a structure factor and introduces the use of multiple FitPages. + This demonstrates a fit requiring a structure factor and introduces the use of multiple FitPages. + + + + + From the \test\1d_data folder in the SasView installation directory, load the hSDS_D2O_2p0_percent.xml dataset and send the data for fitting. + + + + + + Tip: You can either: i) restart SasView, ii) click the Delete Data button in the Data Explorer before loading the new dataset to remove all traces of Example 1, or simply uncheck the LOQ Standard RT2 dataset in the Data Explorer and have SasView create a new FitPage when you click the Send to button, as illustrated below. - - From the \test\1d_data folder in the SasView installation directory, load the hSDS_D2O_2p0_percent.xml dataset and send the data for fitting. - - This dataset is the SANS from a 2 %w/w solution of the widely-studied surfactant h25-sodium dodecyl sulphate (SDS) in heavy water (D2O). So let us consider the available a priori information. - - The critical micelle concentration for SDS is about 0.2 %w/w, so the scattering must represent a concentrated micellar solution (though not too concentrated else the scattering would show diffraction peaks from a liquid crystalline lattice). SDS is also an anionic surfactant, so the micelles will be charged. Interactions between the charged micelles can be expected to manifest themselves in the scattering as a structure factor. 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So let us consider the available a priori information. + + The critical micelle concentration for SDS is about 0.2 %w/w, so the scattering must represent a concentrated micellar solution (though not too concentrated else the scattering would show diffraction peaks from a liquid crystalline lattice). SDS is also an anionic surfactant, so the micelles will be charged. Interactions between the charged micelles can be expected to manifest themselves in the scattering as a structure factor. And in the absence of electrolyte SDS micelles are reported to be approximately spherical. + + To start with, select the sphere model and compute it. + + + iVBORw0KGgoAAAANSUhEUgAABo4AAAP7CAYAAABlT3ykAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXxU5333/c85ZzbtC0LsiEWSbRY7gBNjgQPGYBvokxAnhcRtQjYgcdtA + 2th9Wtt3Xy04fRpngd737TyGpI3TLIXWuUlSUFwbDA7I2I53GRxJICRsdoR2aTQz59x/zKKR + NJJGG4vzfb9e89LozDnX9TtnzozOzE/X7zIcx3EQEREREZGkGH/z7tUOYUhOfy3raocgclWN + GzfuaocgIiIiInJNM5Q4EhEREREREREREREREQDzagcgIiIiIiIiIiIiIiIi1wYljkRERERE + RERERERERARQ4khEREREREREREREREQiXL090NLSyi+e/hUHDx7m/LmLuNwWEyeO56MfXcDK + P7qblJSUKxmniIiIiIiIiIiIiIjIkBmG0efjjuNcoUiSYxgGv/vd75g3b17Cx1999VVuvfXW + YYvbcBK0VFtzir/9281crrtMSkoKPp8Pj8eNaZo4jkNeXi6b/vLPGDduzLAEISIiIiIiIiIi + IiIiciUYhtFrkqWvx66WV199ldsXLOTFw4d6JI/6emywepSqa2lp5W//5h9obGgkOzuLvLxc + xozJY9zYfMaPH8v4cWNwHNj+//8r7e3t/fdQugHDMCK3DZQOMMDSDQYLtlX1bHNDKVRtY4Gx + gO4PD1XVtgX9xxy3Xz3i67JatJ3hj1NERERERERERERERJIT/U4//n787Vo1b948Xjx8iNsX + 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Two of them, sld (for the SDS) and sld_solvent (for the D2O), can be calculated explicitly. - - Go to the Menu Bar, select Tools, and then SLD Calculator. Enter the respective empirical formulae and densities in the relevant boxes and click Calculate (leave the neutron wavelength as 6 Å): - - + This model has 5 parameters. Two of them, sld (for the SDS) and sld_solvent (for the D2O), can be calculated explicitly. + + Go to the Menu Bar, select Tools, and then SLD Calculator. Enter the following empirical formulae and densities in the relevant boxes (leave the neutron wavelength as 6 Å): + + - SDS:Na1C12H25S1O4; density 1.01 g/cm3 + SDS:Na1C12H25S1O4; density 1.01 g/cm3 - D2O:D2O1; density 1.11 g/cm3 + D2O:D2O1; density 1.11 g/cm3 - Hopefully you got values of sld = 0.337x10-6 Å-2 and sld_solvent = 6.39x10-6 Å-2? - - Enter these values in the FitPage. 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/iWXWBPh381LGSdP6OCOa3V3gJlDMHmXntK+b3br88xRmhDgkoNPJwAAAAAA8LPzH04iFKtV - 37s1Z4PMrzMUG6f3CfDRb64K1+KD3fT46rUqczDdAAAAAACAn6P/cBKhJvdbB3bN+jxTsyr2 - sOghAAAAAAA/Tz9xEgEAAAAAAPx/QRIBAAAAAABYQhIBAAAAAABYQhIBAAAAAABYQhIBAAAA - AABY8k+K3WlotCeRPwAAAABJRU5ErkJggg== + + Hopefully you got values of sld = 0.337x10-6 Å-2 and sld_solvent = 6.39x10-6 Å-2? + + Enter these values in the FitPage (they are not auto-populated from the SLD Calculator). 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The orange theory curve now represents the scattering from non-interacting, monodisperse, spherical micelles ~13 Å in radius. And the scale parameter in this case represents the volume fraction of micelles (encouragingly, about 2 %!). 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And the scale parameter in this case represents the volume fraction of micelles (encouragingly, about 2 %!). But to fit the broad peak – from the interacting micelles – we need to incorporate a structure factor – an S(Q) - into the model. + + Click on the Structure factor drop-down box just to the right of the P(Q) Model name drop-down and select the hayter_msa S(Q). + + + + + iVBORw0KGgoAAAANSUhEUgAABpAAAAP7CAYAAABcKM3/AAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXxU933v/9c5s2gkoRUhdsQiyTaLMeDEIHDA2MQGblMnscFOF9I0hsTJ + LfTeJvfX2G5va9zbW6cN9DrJNU5u4vzqpqZ1LkkLimtDwAEZ3DiALYMtiUXsm/Z1lnPO/WMW + zUgjabQBdt7Px0OxdOac7/dzzswoh/no8/kajuM4iIiIiIhISow/ff9GhzAkF/4o50aHIHJD + jR8//kaHICIiIiLyoWAogSQiIiIiIiIiIiIiIiLxzBsdgIiIiIiIiIiIiIiIiNxclEASERER + ERERERERERGRBEogiYiIiIiIiIiIiIiISAJ3bw+0tbXzk1d+xr59B7hy+Rpuj4tJkybwiU8s + ZvV/+iTp6enXM04REREREREREREREZEhMwyjz8cdx7lOkaTGMAx+9atfsWDBgqSPv/3229x5 + 553DHrfhJBnxTO1ZvvGNp2mobyA9PR2fz4fX68E0TRzHoaAgn03/5SuMHz92WIMRERERERER + EREREREZSYZh9Jps6euxG+Xtt99m0eIlvHlgf48kUl+PDVWPFnZtbe1840//kuamZnJzcygo + 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know the values of several of them: - - + + This adds 5 new parameters, but fortunately we know the values of several of them: + + - volfraction:2 %w/w is approximately (2/1.01) %v/v = 0.019 + volfraction:2 %w/w is approximately (2/1.01) %v/v = 0.0198 - charge: + charge: - temperature:298 K + temperature:298 K - concentration_salt:0 M + concentration_salt:8.5e-3 M - dielectconst:78.06 (Vidulich et al, J Phys Chem, 1967) + dielectconst:78.06 (Vidulich et al, J Phys Chem, 1967) - - However, the volfraction parameter now duplicates the scale parameter. So set scale=1.0 and uncheck it, and check the volfraction parameter instead. 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If the micelles are in equilibrium with dissolved surfactant that is not micellised, at the critical micelle concentration the minimum ionic concentration in this particular system will likely be around 8 9 mM. + + + + + However, the volfraction parameter now duplicates the scale parameter. So set scale=1.0 and uncheck it, and check the volfraction parameter instead. Also check the charge parameter. + + And also exclude some of the noisy data at high-Q by bringing the maximum fitting limit in to Q~0.2 Å-1. + + Run the fit again. + + + + + + + + iVBORw0KGgoAAAANSUhEUgAABo8AAAP7CAYAAACKjReaAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXgU55nv/W9V9aZ9QYgdsUiyzWIHcGIscMAYHAPzToiTQOKZhGxA4lkg + M7Hnndg+c2XAmXfiLDDnHOc1JDNxJhvMOIckA4rHBoMDMrbjXQZHEggJmx2hXWp1d9X5oxe1 + pJbU2lic3+e6+lKruup57qqublX3red+DMdxHEREREREJCnG379ztUMYktN/nXW1QxC5qsaN + G3e1QxARERERueYZSh6JiIiIiIiIiIiIiIhIlHm1AxAREREREREREREREZFrh5JHIiIiIiIi + IiIiIiIiEqPkkYiIiIiIiIiIiIiIiMS4enugpaWVXz71aw4ePMz5cxdxuS0mThzPhz+8gJV/ + cjcpKSlXMk4REREREREREREREZEhMwyjz8cdx7lCkSTHMAx+//vfM2/evISPv/LKK9x6663D + GrfhJGittuYUX//6Zi7XXSYlJQWfz4fH48Y0TRzHIS8vl01/8xeMGzdm2AIRERERERERERER + EREZaYZh9Jpo6euxq+WVV17h9gULeeHwoR4JpL4eG4oeZetaWlr5+t//I40NjWRnZ5GXl8uY + MXmMG5vP+PFjGT9uDI4D2///f6O9vb3/Hko3YBhG5LaB0gEGWLrBYMG2qp5tbiiFqm0sMBbQ + 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for improvement: the Reduced Chi2 is still 6.35 and the residuals range between +/- 4. Also note that the volfraction parameter has dropped to ~1 %. - - So how might the fit be improved further? 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Also note that the volfraction parameter has dropped to ~1 %. + + So how might the fit be improved further? One possibility is that water molecules are mixed in with the surfactant sulphate head groups, thereby increasing the effective SLD of the surfactant molecules (and reducing the scattering contrast; ie, sldsld_solvent). + + To test this, check the sld parameter and run the fit again. + + + iVBORw0KGgoAAAANSUhEUgAABo8AAAP8CAYAAACXiCciAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXgU55nv/W9V9aZ9QYgdsUiyzWIHcGIscMAYHAPzToiTQOKZhGxA4lkg + M7Hnndg+c2XAmXfiLDDnHOc1JDNxJhvMOIckA4rHBoMDMrbjXQZHEggJmx2hXWp1d9X5oxe1 + pJbU2lic3+e6+lKruup57qqublX3red+DMdxHEREREREJCnG379ztUMYktN/nXW1QxC5qsaN + G3e1QxARERERueYZSh6JiIiIiIiIiIiIiIhIlHm1AxAREREREREREREREZFrh5JHIiIiIiIi + IiIiIiIiEqPkkYiIiIiIiIiIiIiIiMS4enugpaWVXz71aw4ePMz5cxdxuS0mThzPhz+8gJV/ + cjcpKSlXMk4REREREREREREREZEhMwyjz8cdx7lCkSTHMAx+//vfM2/evISPv/LKK9x6663D + GrfhJGittuYUX//6Zi7XXSYlJQWfz4fH48Y0TRzHIS8vl01/8xeMGzdm2AIRERERERERERER + EREZaYZh9Jpo6euxq+WVV17h9gULeeHwoR4JpL4eG4oeZetaWlr5+t//I40NjWRnZ5GXl8uY + 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The Reduced Chi2 has dropped to 0.855, the residuals are within +/- 2, and the volfraction parameter has increased to almost 1.7 %. - - But is there scope for an even better fit? Maybe. There is published evidence that suggests SDS micelles are actually slightly ellipsoidal. - - To test this, use the Send To button to create a second FitPage and then select the ellipsoid model. Do not select an S(Q) for the time being. - - Set sld and sld_solvent to their calculated values. - - We know from the fit to the sphere model that the micelles have a radius ~20 Å so set radius_polar=20 and radius_equatorial=40 (ie, to give the ellipsoids an intial axial ratio of 1:2; a sphere would be 1:1 of course). Check the scale and background parameters and run the fit. - - Now select the hayter_msa S(Q) as before and set the known values you used previously. And just like before, set scale=1.0 and uncheck it. 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The Reduced Chi2 has dropped to ~2, the residuals are within +/- 2, and the volfraction parameter has increased to almost 1.5 %, which is close to the 1.78 % expected from the solution concentration (2 %) minus the cmc (0.2 %) = 1.8 % / 1.01. + + This fit is, to all intents and purposes, as good a fit as one might reasonably expect to achieve. However, there is published evidence that suggests SDS micelles are actually slightly ellipsoidal (see, for example, DOI 10.1016/j.colsurfa.2024.134394 and the references therein). Can SasView confirm or refute this? + + Use the Send data to button to create another FitPage and then select the ellipsoid model. Do not select an S(Q) for the time being. + + Set sld and sld_solvent to their calculated values. + + We know from the fit to the sphere model that the micelles have a radius ~20 Å so set radius_polar=20 and radius_equatorial=40 (ie, to give the ellipsoids an intial axial ratio of 1:2; a sphere would be 1:1 of course). Limit the maximum Q of the fit again. Check the scale and background parameters and run the fit. + + Now select the hayter_msa S(Q) as before and set the known values you used previously. And just like before, set scale=1.0 and uncheck it. But this time set the volfraction and charge parameters to the values determined from the fit to the sphere model; 0.015 and 42, respectively. + + Also set the radius_effective_mode to ‘equivalent_volume_sphere’. + + Check radius_polar and run the fit. + + Uncheck radius_polar, check radius_equatorial and run the fit. + + Now also check radius_polar and run the fit. + + Now check volfraction and charge and run the fit. + + Finally, check sld and run the fit. + + + + + + iVBORw0KGgoAAAANSUhEUgAABpAAAAP7CAYAAABcKM3/AAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXwU553v+09V9aZ9QYgdsUiyzWIHcGIscLAxJAbOnThOBhJnEpJMgMRz + zqDMiT33xPbJKwPO3ImTGGbmOtc4OTPOyTIw4zkkGVA8Ntg4IGMn3mVwJLFI2OwI7VKru6vu + H72oW2pJrQ2B832/XjJSLc/zq+pquap/en6P4TiOg4iIiIiIpMT4H++OdQjDcvovc8Y6BJEx + NWnSpLEOQURERETkmmAogSQiIiIiIiIiIiIiIiLxzLEOQERERERERERERERERK4uSiCJiIiI + iIiIiIiIiIhIAiWQREREREREREREREREJIGrrxVtbe38+9O/4sCBQ5w/dxGX22Lq1Ml89KNL + WPNfPkZaWtqVjFNERERERERERERERGTYDMPod73jOFcoktQYhsHvf/97Fi1alHT9q6++ys03 + 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So the SasView fitting is certainly consistent with the literature reports. But unambiguously distinguishing between the two cases would require more precise measurements and higher quality data. - - Example 3 - + + A fit at least as good as the one to the sphere model is obtained, suggesting that the micelles are ellipsoids with an axial ratio of 1:1.2. So the SasView fitting is certainly consistent with the literature reports. But unambiguously distinguishing between the two cases would require more precise measurements and higher quality data. + + One could also explore the extent to which size polydispersity (see Example 3) impacts both models, or whether more nuanced models, for example, the core_shell_sphere or the core_shell_ellipsoid, allowing for a difference in SLD between the head and tail regions of the micelles, are better descriptions of the data. + + + + + + + + + + + + + + + + + + + + Example 3 + - This demonstrates a fit requiring a structure factor and polydispersity. + This demonstrates a fit requiring a structure factor and polydispersity. - - From the \test\1d_data folder in the SasView installation directory, load the Ludox_silica.xml dataset and send the data for fitting. - - This dataset is the SANS from a concentrated dispersion of Ludox® silica nanoparticles in light water (H2O), so there will once again be an S(Q) contribution from charged spheres. - - Select the sphere P(Q) model and the hayter_msa S(Q) model. - - Once again, we have a lot of a priori information: - - + + From the \test\1d_data folder in the SasView installation directory, load the Ludox_silica.xml dataset and send the data for fitting. + + This dataset is the SANS from a concentrated dispersion of Ludox® silica nanoparticles in light water (H2O), so there will once again be an S(Q) contribution from charged spheres. + + Select the sphere P(Q) model and the hayter_msa S(Q) model. + + Once again, we have a lot of a priori information: + + - sld: 3.4 x10-6 Å-2 (calculated) + sld: 3.4 x10-6 Å-2 (calculated) - sld_solvent:-0.56x10-6 Å-2 (calculated) + sld_solvent:-0.56x10-6 Å-2 (calculated) - volfraction:18 %v/v (based on the manufacturers data sheet; 40 %w/w) + volfraction:18 %v/v (based on the manufacturers data sheet; 40 %w/w) - temperature:298 K + temperature:298 K - concentration_salt:0 M + concentration_salt:0 M - dielectconst:78.39 (Vidulich et al, J Phys Chem, 1967) + dielectconst:78.06 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Increase it to 150 Å. + + Now check the background, radius, volfraction, and charge parameters and click Fit. + + + + + iVBORw0KGgoAAAANSUhEUgAABpAAAAP9CAYAAACKcS7iAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXxU5333/c85ZzbtC0LsiEWSbRY7gBNjgYONwTHQJ3GcFBK3CVkMJE5b + 1DZ2n7u27z4tOH0aZ4H2vp3HkLRxGieF1r1JUlBcGwwOyNiOdxkcSSAkbHaEdmk0M+c8f8yi + kTSSRhuL832/XnpJOnPOdf3OMtKZ+c31uwzHcRxERERERCQpxv9470qHMCyn/izrSocgckVN + mDDhSocgIiIiInJNMJRAEhERERERERERERERkXjmlQ5AREREREREREREREREri5KIImIiIiI + iIiIiIiIiEg3SiCJiIiIiIiIiIiIiIhIN66+HmhtbeM/n/klBw4c4tzZC7jcFpMnT+TjH1/E + qj+4i5SUlMsZp4iIiIiIiIiIiIiIyLAZhtHv447jXKZIkmMYBr/97W9ZsGBBwsdfe+01br75 + 5hGP23AStFhXe5K//utNXKq/REpKCj6fD4/HjWmaOI5DXl4upX/xDSZMGDeiwYiIiIiIiIiI + iIiIiIwmwzD6TLb099iV8tprr3HrosW8dOhgryRSf48NV68Sdq2tbfz1//g7mhqbyM7OIi8v + l3Hj8pgwPp+JE8czccI4HAe2/X//QkdHx8A9lG3AMIzI1wbKBhlg2QaDRVure7e5oQyqt7LI + WETPh4ereuuigWOO269e8XVbLdrOyMcpIiIiIiIiIiIiIiLJib6nH/9z/NfVasGCBbx06CC3 + 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In Example 2 we managed to obtain a good solution without having to specifically address polydispersity, most likely because the size of the micelles meant any fringes in the scattering curve were beyond the range of the data. + + In the lower part of FitPage, click on the checkbox named Polydispersity. 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If you need a different distribution, select it before you set any distribution parameters. The SasView help documentation provides some guidance on appropriate use cases for different distributions. + Tip: By default SasView always selects a Gaussian distribution. If you need a different distribution, select it before you set any distribution parameters. The SasView help documentation provides some guidance on appropriate use cases for different distributions. - - The width of the chosen polydispersity distribution is determined by the PD parameter and the definition of this changes depending on the distribution. For the Log-Normal distribution: - - + + The width of the chosen polydispersity distribution is determined by the PD parameter and the definition of this changes depending on the distribution. For the Log-Normal distribution: + + @@ -142664,3062 +137389,5440 @@ - VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAa0IAAAT - AgAAJAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAKwIAAASAgAAlQAB - AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv - biBTZXJpZgAAAAAAAKYBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAIgAAQAC - AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABuAAAAgwEAAAIAUEQyAgAA - AAACAAIAUABEAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA8AAAAAwA2AAAACgBPcGVuU3ltYm9s - AAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAiAABAAIAAAABAIcA - AQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAM4CAACDAQAAAQAAAD0ATwEAAAAAAQAB - AD0AjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5TeW1ib2wAAAAAAACm - AQAA//8AAAAABQAAAAAAAgD/AwAAAAAAAAABAP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/ - ////AIYAAQAEAAAAAAAAAHIAAgAaAAAAGQQAAIMBAAABAAAAwwP+AAAAAAABAAEAwwOMAAEA - AAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAP0A - AAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAIgAAQACAAAAAQCHAAEABQAAAP// - //8AhgABAAQAAAAAAAAAcgACACYAAABkBQAA1QEAAAYAbm9ybWFs3AIAAAAABgAGAG4AbwBy - AG0AYQBsAIwAAQAAAAAAlQABAAQAAAAAAAAAlgABAAIAAAAJAIwAAQAAAAAA + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAe4HAAAU + AgAAJAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAO0HAAATAgAAlQAB + AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJhdGlv + biBTZXJpZgAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAA + AIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAAAaAAAAcgEAAAIA + UEQ0AgAAAAACAAIAUABEAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8AAAACgBPcGVu + U3ltYm9sAAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAA + iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAGECAAByAQAAAQAA + AD0AUAEAAAAAAQABAD0AjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAAFADwAAAAKAE9wZW5T + eW1ib2wAAAAAAACnAQAA//8AAAAABQAAAAAAAgD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACI + AAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAuQMAAHIBAAABAAAA + wwP/AAAAAAABAAEAwwOMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJh + dGlvbiBTZXJpZgAAAAAAAP0AAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAA + AAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACACYAAAAQBQAA3AEA + AAYAbm9ybWFs3AIAAAAABgAGAG4AbwByAG0AYQBsAIwAAQAAAAAAlQABAAQAAAAAAAAAlgAB + AAIAAAAJAIwAAQAAAAAA - - where σnormal is the width of the underlying Normal distribution. 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But whatever the distribution, PD=0 represents monodispersity (a very sharp distribution) and PD=1 represents an extremely broad distribution. + + Enter PD=0.15 and click Fit. + + Now check Distribution of radius and click Fit again. + + + iVBORw0KGgoAAAANSUhEUgAABo4AAAP8CAYAAAB4SkwcAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXxU553n+885pzbtC0LsiEWSbRY7gBNjgYONwTHQN3GcNCSeTshiIHFm + Gron9txp29O3G5y+HWeB7rnONU6m43ScNPS4hyQNiscGgwMytuNdBkcSCAmbHaFdKlXVOfNH + LSpJJalUklic7/v10kulU+c8z++cOlU6Vb96fo/hOI6DiIiIiIgkxfiv71/pEIbl1J/nXOkQ + RK6oCRMmXOkQRERERESuaoYSRyIiIiIiIiIiIiIiIgJgXukARERERERERERERERE5OqgxJGI + iIiIiIiIiIiIiIgAShyJiIiIiIiIiIiIiIhIhKu/O9ra2vm3Z3/NgQOHOHf2Ai63xeTJE/nk + Jxex6k/uIi0t7XLGKSIiIiIiIiIiIiIiMmyGYQx4v+M4lymS5BiGwe9//3sWLFiQ8P7XX3+d + m2++ecTiNpwELdXXneSv/mozlxoukZaWhs/nw+NxY5omjuNQUJDPpr/8FhMmjBuRIERERERE + RERERERERC4HwzD6TbIMdN+V8vrrr3ProsW8fOhgn+TRQPelqk+pura2dv7qv/4tzU3N5Obm + UFCQz7hxBUwYX8jEieOZOGEcjgPb//9/orOzc/AeyjdgGEbkZwPlQwywfIPBom01fdvcUA41 + 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The volfraction parameter is also higher than we would like. - - Optimising the sld value reduces its value slightly from 3.4x10-6 to 3.2x10-6 but also improves the Reduced Chi2 to 3250 with minimal effect on the other parameters. But this is as good a fit as is likely to be achieved in this instance. The reasons are beyond the scope of this tutorial. - - - - Further Information - - For further information, please consult the - - SasView Tutorial Series - - or - - http://www.sasview.org - - or email - - help@sasview.org - + Whilst there is certainly room for improvement in both the Reduced Chi2 and Residuals, this is nonetheless a promising fit to the data. The radius is within the size range typical of this material, but the volfraction is higher than anticipated. Seeming inconsitencies like this should always trigger a re-evaluation of the priors. For example, although Ludox® dispersions are described as being in water, is the dispersion medium truly water? Or does it contain residual components from the manufacturing process which may make the assumptions used about the values of sld_solvent, concentration_salt and dielectconst less valid? + Also notice that an additional graph window has appeared depicting the actual form of the Log-Normal size distribution used in the model calculation. + + Another nice feature is that it is also possible to see the separate contributions that the P(Q) and S(Q) make to the overall result. + + In the Data Explorer, click the > symbol to expand the Ludox® entry. + + + Data + + Model calculation + + + P(Q) + S(Q) + + + iVBORw0KGgoAAAANSUhEUgAAATcAAAGtCAYAAABz3zMXAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nO2df3gb9Z3n3yM7CYRfAboNXkqdNJIoXkM3uJStVGJyJdxJoWzwtc5eCHWa + I1Lb52mkO848lyfO+knjPNmnPliJ9qG1QlP72KYPoU19u1haYmjq7FkcPwK34DW1pBD70j6B + dlmyDxy9ksRzf8yMPBrNSCNZtkaj9+t5FEea73e+3xlJb30+3+/M9y2cO3dOBCGE2IzGF198 + sdp9IISQiiMwciOE2Inh4WEAjNwIITXO7bffrvt6IwCsXr16UTtDCCGV4PTp07qv/+xnP4Nj + 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managed by a consortium of scattering facilities. Participating facilities include (in alphabetical order): the Australian National Science & Technology Centre for Neutron Scattering, the Diamond Light Source, the European Spallation Source, the Federal Institute for Materials Research and Testing, the Institut Laue Langevin, the ISIS Pulsed Neutron & Muon Source, the National Institute of Standards & Technology Center for Neutron Research, the Oak Ridge National Laboratory Neutron Sciences Directorate, and the Technical University Delft Reactor Institute. + + SasView is distributed under a 'Three-clause' BSD licence which you may read here: + https://github.com/SasView/sasview/blob/master/LICENSE.TXT + + SasView is free to download and use, including for commercial purposes. + + © 2009-2024 UMD, UTK, NIST, ORNL, ISIS, ESS, ANSTO, ILL, TUD, DLS,. BAM + + + + If you make use of SasView + + If you use SasView to do productive scientific research that leads to a publication, we ask that you acknowledge use of the program with the following text: + + This work benefited from the use of the SasView application, originally developed under NSF Award DMR-0520547. SasView also contains code developed with funding from the EU Horizon 2020 programme under the SINE2020 project Grant No 654000. + + + + Contributors to this Tutorial + + Steve King (stephen.king@stfc.ac.uk) + Piotr Rozyczko (piotr.rozyczko@esss.se) + Wojciech Potrzebowski (wojciech.potrzebowski@esss.se) + Susana Teixeira (susana.marujoteixeira@nist.gov) + Paul Butler (butlerpd@udel.edu) + + + Last revised: 2 September 2024 + + + Acknowledgements + + SK would like to thank Adrian Rennie for constructive comments on an earlier version of this tutorial. + Learning Objective + + This tutorial will demonstrate how to fit individual 1D (‘intensity’ versus Q) datasets in SasView and showcase some of the associated functionality of the program. Simultaneous or batch fitting of multiple 1D datasets, and the fitting of 2D datasets, are considered in separate tutorials. + + It is assumed that the reader has some familiarity with the purpose and principles of data fitting. If not, these Wikipedia articles provide an overview: + + + + https://en.wikipedia.org/wiki/Curve_fitting + + + https://en.wikipedia.org/wiki/Mathematical_optimization + + + + + + + + + The program interface shown in this tutorial is SasView Version 6.0.0 running on a Windows platform but, apart from a few small differences in look and functionality, this tutorial is generally applicable to any version of SasView Version 6.x on any platform. However, there are separate tutorials for SasView 5.x and for using the old program interface released with SasView 4.x. + + + + + + + Glossary + + + + + + + a priori information + + + Known facts about the system whose datasets are being modelled that can guide the selection of model or model parameters. + + + + + Chi-square (Χ 2, ‘Chi2’) + + + A statistical test of how well a chosen model fits the data with a given set of model parameters. 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Clearly, as Χ 2→0, the better the model fit is. + + NB: The SasView interface actually reports a variation of chi-square called the reduced chi-square, sometimes referred to as the ‘goodness-of-fit’ + + + + + + + X + Reduced + 2 + + = + + + + + ( + + + + + + ( + + + I + + + + ( + + Q + + ) + + meas + + + I + + + + ( + + Q + + ) + + calc + + + + ) + + 2 + + / + E + + + + ( + + Q + + ) + + 2 + + + + ) + + + / + + ( + + + + N + pts + + + + N + params + + + + ) + + + + X_Reduced^{2} = sum ( (I(Q)_{meas}-I(Q)_{calc})^{2} / E(Q)^2 ) / ( N_pts - N_params ) + + + + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAUwmAABQ + AgAA/QAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAEsmAABPAgAAlQAB + AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJhdGlv + biBTZXJpZgAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAA + AIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAAaAAAAwgEAAAEA + 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+ formula + + + where Npts is the number of data points in the dataset and Nparams is the number of model parameters being optimised (which may be less than the total number of parameters in the model!). As ΧR 21, the better the model fit is. + + + + + Compute/Plot [button] + + + Perform a direct calculation of the model with the current parameters but without any optimisation + + + + + + Correlated parameters + + + To obtain the best solutions the optimiser needs to explore the widest possible parameter space. That is best achieved if every parameter can be considered independent of every other parameter. However, there will be instances where this is not the case and one or more parameters may be correlated. In such cases the best approach is to fix the values of some of correlated parameters using a priori information and then optimise the remaining values. + + A particularly common instance of correlated parameters encountered when model-fitting SAS data is when the components of the forward scattering intensity + + + + + + I + + + ( + + 0 + + ) + + = + ϕ + + V + + + ( + + + Δ + ρ + + + ) + + 2 + + + I(0)= %phi V (%DELTA%rho)^2 + + + + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAARMLAAAw + AgAAXAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAABILAAAvAgAAlQAB + AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJhdGlv + biBTZXJpZgAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAA + AIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAAaAAAAwgEAAAEA + SY0AAAAAAAEAAQBJAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8AAAACgBPcGVuU3lt + Ym9sAAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAAB + AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAO4AAADCAQAAAQAAACgA + kAAAAAAAAQABACgAjAABAAAAAACLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQAExpYmVyYXRp + b24gU2VyaWYAAAAAAACnAQAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAABAP8DAAAAAAAAAAAA + AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAjQEAAMIBAAAB + ADDUAAAAAAABAAEAMACMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAUAPAAAAAoAT3BlblN5 + bWJvbAAAAAAAAKcBAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgA + AQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAAB7AgAAwgEAAAEAAAAp + AJAAAAAAAAEAAQApAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8AAAACgBPcGVuU3lt + Ym9sAAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAAB + AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAP8CAADCAQAAAQAAAD0A + UAEAAAAAAQABAD0AjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAAFADwAAAAKAE9wZW5TeW1i + b2wAAAAAAACnAQAA//8AAAAABQAAAAAAAgD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACIAAEA + AgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAVwQAAMIBAAABAAAA1QPc + AAAAAAABAAEA1QOMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJhdGlv + biBTZXJpZgAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAA + AIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAACVBQAAwgEAAAEA + VgIBAAAAAAEAAQBWAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8AAAACgBPcGVuU3lt + Ym9sAAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAAB + AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAO0GAADCAQAAAQAAACgA + kAAAAAAAAQABACgAjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAAFADwAAAAKAE9wZW5TeW1i + b2wAAAAAAACnAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACIAAEA + AgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAiwcAAMIBAAABAAAAlAMD + AQAAAAABAAEAlAOMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAUAPAAAAAoAT3BlblN5bWJv + bAAAAAAAAKcBAAD//wAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgAAQAC + AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAADjCAAAwgEAAAEAAADBA+gA + AAAAAAEAAQDBA4wAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8AAAACgBPcGVuU3ltYm9s + AAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAABAAIA + AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAAYKAADCAQAAAQAAACkAkAAA + AAAAAQABACkAjAABAAAAAACLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQAExpYmVyYXRpb24g + U2VyaWYAAAAAAAD9AAAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACI + AAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAiwoAAO4AAAABADJ/ + AAAAAAABAAEAMgCMAAEAAAAAAJUAAQAEAAAAAAAAAJYAAQACAAAACQCMAAEAAAAAAA== + + + + + where Φ is the volume fraction of scatterers, V is the volume of one scatterer (and so dependent on size parameters), and Δρ is the contrast (difference in SLDs), are separated out as individual parameters in a model. Optimizing two or more of these parameters will cause them to be correlated. + + Correlated parameters often manifest themselves in the SasView interface as having very large uncertainties. + + + + + Fit [button] + + + Perform a calculation of the model optimising the selected parameters + + + + + Model-fitting + + + The process of finding a good yet physically-realistic mathematical description (‘solution’) for a dataset or collection of datasets. The procedure employed to achieve this is called optimisation. + + + + + OpenCL + + + A low-level software framework that allows calculations to be distributed between any compatible processors (eg, GPUs as well as CPUs) on the host computer. OpenCL can speed up demanding model-fits if suitable hardware is available. + + + + + OpenMP + + + A software framework that permits shared-memory multi-processing (ie, parallelisation) of calculations. OpenMP can speed up demanding model-fits if suitable hardware is available. + + + + + Optimiser + + + The mathematical algorithm used to perform the model-fitting. + + + + + (Poly)dispersity + + + Where one or more model parameters have a distribution of values. + + SasView allows for 2 types of (poly)dispersity: + + + + + + + Size + + + where, for example, the radii and/or lengths of the scatterers have a distribution of values + This will apply in most instances + + + + + Angular + + + where the scatterers are anisometric in shape (eg, cylinders) and exhibit preferred orientations with respect to Q, for example, under shear or in a magnetic field + + + + + + + + + Reduced Chi2 + + + See Chi-square + + + + + Residual + + + The difference between the measured and calculated values of a function at a given point. In SasView this means: + + + + + + R + + + ( + + Q + + ) + + = + I + + + + + ( + + Q + + ) + + meas + + + I + + + + ( + + Q + + ) + + calc + + + R(Q) = I(Q)_{meas}-I(Q)_{calc} + + + + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAe0QAAAd + AgAAeAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAOwQAAAcAgAAlQAB + AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJhdGlv + biBTZXJpZgAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAA + AIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAAaAAAAjQEAAAEA + UgIBAAAAAAEAAQBSAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8AAAACgBPcGVuU3lt + Ym9sAAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAAB + AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAD4BAACNAQAAAQAAACgA + kAAAAAAAAQABACgAjAABAAAAAACLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQAExpYmVyYXRp + b24gU2VyaWYAAAAAAACnAQAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAABAP8DAAAAAAAAAAAA + AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAA3AEAAI0BAAAB + AFExAQAAAAABAAEAUQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAUAPAAAAAoAT3BlblN5 + bWJvbAAAAAAAAKcBAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgA + AQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAAA0AwAAjQEAAAEAAAAp + AJAAAAAAAAEAAQApAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8AAAACgBPcGVuU3lt + Ym9sAAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAAB + AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAALkDAACNAQAAAQAAAD0A + UAEAAAAAAQABAD0AjAABAAAAAACLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQAExpYmVyYXRp + b24gU2VyaWYAAAAAAACnAQAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAABAP8DAAAAAAAAAAAA + AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAKwUAAI0BAAAB + AEmNAAAAAAABAAEASQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAUAPAAAAAoAT3BlblN5 + bWJvbAAAAAAAAKcBAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgA + AQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAAD/BQAAjQEAAAEAAAAo + AJAAAAAAAAEAAQAoAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBIAAAABQBCAAAAEABMaWJlcmF0 + aW9uIFNlcmlmAAAAAAAApwEAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAQD/AwAAAAAAAAAA + AAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAJ0GAACNAQAA + AQBRMQEAAAAAAQABAFEAjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAAFADwAAAAKAE9wZW5T + eW1ib2wAAAAAAACnAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACI + AAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAA9QcAAI0BAAABAAAA + KQCQAAAAAAABAAEAKQCMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJh + dGlvbiBTZXJpZgAAAAAAAP0AAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAA + AAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACACAAAAB6CAAA3AEA + AAQAbWVhcwgCAAAAAAQABABtAGUAYQBzAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8 + AAAACgBPcGVuU3ltYm9sAAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAA + AAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAIsK + AACNAQAAAQAAABIiUAEAAAAAAQABABIijAABAAAAAACLAAEAAgAAAB8AigABAEgAAAAFAEIA + AAAQAExpYmVyYXRpb24gU2VyaWYAAAAAAACnAQAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAAB + AP8DAAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAX + AAAA/QsAAI0BAAABAEmNAAAAAAABAAEASQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAUA + PAAAAAoAT3BlblN5bWJvbAAAAAAAAKcBAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAEA/wMA + AAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAADR + DAAAjQEAAAEAAAAoAJAAAAAAAAEAAQAoAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBIAAAABQBC + AAAAEABMaWJlcmF0aW9uIFNlcmlmAAAAAAAApwEAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAA + AQD/AwAAAAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIA + FwAAAHANAACNAQAAAQBRMQEAAAAAAQABAFEAjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAAF + ADwAAAAKAE9wZW5TeW1ib2wAAAAAAACnAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAABAP8D + AAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAA + rQ4AAI0BAAABAAAAKQCQAAAAAAABAAEAKQCMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUA + QgAAABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAP0AAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAA + AAEA/wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgAC + ACAAAAAxDwAA3AEAAAQAY2FsY6YBAAAAAAQABABjAGEAbABjAIwAAQAAAAAAlQABAAQAAAAA + AAAAlgABAAIAAAAJAIwAAQAAAAAA + + + formula + + + where I is the scattering intensity. + + NB: The SasView interface actually reports a variation of the residual called the normalised residual + + + + + + R + + + + ( + + Q + + ) + + Normalised + + = + + + ( + + + I + + + + ( + + Q + + ) + + meas + + + I + + + + ( + + Q + + ) + + calc + + + + ) + + / + E + + + + ( + + Q + + ) + + + R(Q)_Normalised = ( I(Q)_{meas}-I(Q)_{calc} ) / E(Q) + + + + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAUkbAAAd + AgAAsAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAEgbAAAcAgAAlQAB + AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJhdGlv + biBTZXJpZgAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAA + AIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAAaAAAAjQEAAAEA + 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AAQAYwBhAGwAYwCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAUAPAAAAAoAT3BlblN5bWJv + bAAAAAAAAKcBAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgAAQAC + AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABTFgAAjQEAAAEAAAApAJAA + AAAAAAEAAQApAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8AAAACgBPcGVuU3ltYm9s + AAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAABAAIA + AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAPIWAACNAQAAAQAAAC8AdgAA + AAAAAQABAC8AjAABAAAAAACLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQAExpYmVyYXRpb24g + U2VyaWYAAAAAAACnAQAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACI + AAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAkRcAAI0BAAABAEUC + AQAAAAABAAEARQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAUAPAAAAAoAT3BlblN5bWJv + bAAAAAAAAKcBAAD//wAAAAAFAAAAAAAAAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgAAQAC + AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAADOGAAAjQEAAAEAAAAoAJAA + AAAAAAEAAQAoAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBIAAAABQBCAAAAEABMaWJlcmF0aW9u + IFNlcmlmAAAAAAAApwEAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAA + iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAG0ZAACNAQAAAQBR + MQEAAAAAAQABAFEAjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAAFADwAAAAKAE9wZW5TeW1i + b2wAAAAAAACnAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACIAAEA + AgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAxRoAAI0BAAABAAAAKQCQ + AAAAAAABAAEAKQCMAAEAAAAAAJUAAQAEAAAAAAAAAJYAAQACAAAACQCMAAEAAAAAAA== + + + formula + + + where E is the error on the intensity value. + + A normalised residual can be thought of as the number of standard deviations between the measured value and the calculated value. Thus, for a good fit, 68% of the values will lie within -1 < R(Q)Normalised < +1, and 95% within +/-2. + + Residuals larger than +/-3 indicate significant problems with either the input data or the choice of model or model parameters. + + + + + SLD + + + Abbreviation for Scattering Length Density, a measure of the ability of a molecule to scatter. Strictly speaking, SLD is a SANS quantity, so if fitting SAXS data use electron density values in their place. + + SLD values (neutron and X-ray) can be calculated with the SLD Calculator Tool in SasView. + + + + + Smearing + + + Sometimes the instrumental geometry used to acquire the experimental data has an impact on the clarity of features in the scattering curve. For example, peaks or fringes might be slightly broadened. This is known as Q-resolution smearing. + + To compensate for this effect SasView can add a resolution contribution into a model calculation (which by definition will be exact) to make it more representative of what has been measured experimentally. + + SasView provides 4 smearing options: + + + + + + + None + + + no smearing correction is applied + + + + + Use dQ Data + + + the measured Q-resolution for each data point is used to apply a smearing correction + This is the default if dQ data is present + + + + + Custom Pinhole + + + SasView will apply a smearing correction suitable for data measured on ‘pinhole geometry’ instruments (eg, most SAXS/SANS instruments) + + + + + Custom Slit + + + SasView will apply a smearing correction suitable for data measured on ‘slit geometry’ instruments (eg, most USAXS/USANS instruments) + + + + + + + + + Theory + + + The name SasView gives to a model calculation. + + + + + Uncertainties + + + Every experimental measurement, including the measurement of I(Q), is subject to some degree of error (which will, ideally, be included in the dataset). Similarly, the parameters returned by optimisation will have some associated range of uncertainty. + + Parameters with uncertainties that are more than 95% of the parameter value should be viewed with deep suspicion. + + NB: Unhelpfully, but for reasons of space, the SasView interface actually labels parameter uncertainties as errors. + + + + + Weighting + + + An optimiser can be instructed to pay less or more attention to data points in a dataset by changing the weighting of those data points. + + SasView provides 4 weighting options: + + + + + + + No Weighting + + + all data points will be weighted equally + + + + + Use dI Data + + + the data points will be inversely weighted according to their measured intensity errors (ie, less prominence will be given to data points with large errors) + This is the default if dI data is present + + + + + Use sqrt |(I Data)| + + + the data points will be inversely weighted according to the square root of their intensity values + + + + + Use |(I Data)| + + + the data points will be inversely weighted according to their intensity values + + + + + + + + + + Running SasView + + Windows + Either select SasView from ‘Start> ‘All Programs’ or, if you asked the installer to create one, double-click on the SasView desktop icon. + + + iVBORw0KGgoAAAANSUhEUgAAAG4AAACACAIAAABld8teAAAgAElEQVR4nO19a4xd13Xet9Y+ + 59x758XH8C1RomiSlmRJjhTbUkauFMtOHEWpHSupW6RxmyIA1RRFC7RAgaLor/ZPf5VGi6J1 + gAJt4jSNDdtpYMqxY8upZcqWbFmiJEri8E2RHD6H87r3nsdeqz/23uece2fI4QyHpJxyYUDe + ex777P3tbz322nufS6qK27ISEt3qCiwgqmrFqigAEAMgosjwLa7WYnLroVTVvLBW7MSlyffO + nreiE5cuvnP0+OTULHGTk1Gh1qrBxiM7Nz92/50b1wzd6vpeUehWKXhe2MnZ2bdPnBo/NfGd + n7y+//Dxbp6laQHAFnmaQmg9RasAhhCzRsw7t679l59//HMfv4+Jbkmdry43G8rC2kszs99/ + 492/ePm1V4+8N9XuWkG7m3XTjEBEgCjZBuyIUkOVAIGoqIqIqt2yduTffOHJ5/72R9+HYN4k + KFV1tpv+ePzYV1/62UvvHrs00+lkNissgZnZsCEQQQEUaVR0E7WsEEAhKiIAABGraZrv2Dr6 + H3b/6rNP3H8Tqr0kueG2UoHzUzNf//H+r7y0/+TFy+3UZrllSlrNaJgYgCp8Z4p2O2RTgoBI + 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What is being displayed is the title of the data read from within the file. Prior to SasView 5.0.4 the file name would have been displayed. Obviously, this feature depends on the file containing suitable metadata in the first place! The CanSAS1D (.xml) and NXcanSAS (.h5) standard formats are suitably compatible. + + From SasView 5.0.4 it is possible to assign custom names to the data by right-clicking on a data set in the Data Explorer and selecting Change Name. + + iVBORw0KGgoAAAANSUhEUgAAAWAAAAE1CAYAAADZIjoIAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nO3df2xb530u8EdSstoW0hBpqdJduFvTjqzSNjEwDZHYG2QnIg3HaGEFoAs1 + yL1sMCdhFdAMAnXmzdg/wmX04hWWiah0kqHlFqRCzEEyNiitTfrKXGEnUC0BUyw2UmQanbtr + XbLNmP1I6jYR7x+HpA7Jc8hD/Xol8/kAgiOe9z3nJRU9es/3HPJtyuVyORARrUPXrl3D1q1b + 6+ozMzODL33pS6rbdTodcrkcYpMZoKl0Wy4HfGXDv6O9vb3uYyr1aa5rL0REtGwYwEREgjCA + iYgEYQATEQnCACYiEoQBTEQkyB1qGwLHT63mOIiIAAD+Y0dFD2H15FS8GOxX27SsxudW9usL + X/gC/+W//Hed/Ftv7szOztadOdPT07lsNqv6VYjF8/+Szp2fLP069y/p3PT09KKOqaQpl1N+ + I0bg+KlV+Us08f9Wbt+OHV/E+alfr9wBiGhZjfyovtzhGzHWMIYv0frg2PFF0UMQQrUGLMJT + B7+2pP6vjVwp+Z4zYKL1oVF/T9dUAAPAlStXajdS8LWvVYZ3o/5QidabRp0sLUsJ4rPPPluO + 3Sy7Rj2tIVpvGjF8gWUI4Pfeew/nzp3DrVu3lmM8y0r+Q73U14T7+36i2vZSXxPuN8i+vn4K + 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To assist us in this task we have the a priori knowledge that this sample is a (solid) polymer blend (as it happens, of h8-polystyrene and d8-polystyrene). In the absence of solvent molecules the conformational characteristics of the polymer chains in the sample are described by a 3D random walk mediated by excluded volume constraints. Polymer physics tells us that this results in a Gaussian distribution of chain density about the centre-of-mass. The scattering from such a structure was formulated by Debye (1947) and is implemented in SasView as the mono_gauss_coil model. + + + + + + Tip: The names of several models changed between SasView 3.x and SasView 4.x. For example, the mono_gauss_coil model was previously called the Debye model. + + + + + In the FitPage, select the model Category called shape-independent and then from the drop-down box below select the mono_gauss_coil model. Click the Compute/Plot button. + + + + + + Tip: Upto and including SasView 5.0.4 the Compute/Plot button was labelled Show Plot. + + + + The model loads with some default parameters, the calculated (not optimised at this stage) scattering from which is shown as the orange line on the upper graph. 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To change this, right-click on a graph and select Change Scale. For this example, linear I-axes are better. + + If you want to examine the contents of the dataset, right-click on the upper graph, select ISIS_Polymer_Blend_RT2.xml and then DataInfo. A separate Data Info window will appear. + + The amount of information presented by DataInfo will depend on the file format of the dataset (CanSAS-standard xml files contain the most information) and the compliance of the data reduction program that wrote them. + + + iVBORw0KGgoAAAANSUhEUgAAAf8AAAOICAIAAABXK2+5AAAgAElEQVR4nOzdfYzkaH4f9oec + 3nmf2dmd3Z3Z23vb2+JIV2q9nO5k41ixBViBAVYjTv9hNc5IjL6zY5b27rxFA2nglDQQwGpA + F/cfYRmR7KKBJG04sdIJnM4fU/w7BpqWo1spOpV675q8N0l3e/btaXd2dnZn563yB1nFh+8P + WWTx7fv5Z3eqyIcPWV2/Yj1kPV/utddeIwAA0DJrhJDRaFR2NwAAYHWGwyFfdh8AAKAEqP4A + AG2E6g8A0Eao/gAAbcTfu3ev7D4AAMCq8a+//o2y+wAAAKvGP378uOw+AADAqmHcHwCgjfin + nnqq7D4AAMCqrX3uc7+SaoX33rt3+m3zz//iR+/fe5/juCtXLn/sYy+90vnUpUsXC+oiAADk + bu38+fPsS3/72+bh//5/ffc73797970nj5+cWTtz4eL5Z5659sorL/9nf0t6+eVPFNdRAADI + UYpx/3//77/x3/zmb/3+7//BO+/ceeqptStXLz/99JUL58/f/+D+dPrGP1X/2fRPTorrKABA + KhyDsvvowXHc66+/HvXs66+/nm+H+TfeeINluW+9cfpP/vt/ev/+/UsXLz799NVr155+9tln + 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We can exclude these points from the fitting using the Q range boxes in the Fit Options tab of the FitPage. + + Change the Q-limits by typing values in the boxes. For this example, set the maximum-Q value to 0.19 Å-1. 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Finally, Fitting completed successfully appears in the Status Bar + + + + + + + + + Tip: To open the Log Explorer, select View > Show Log Explorer. + + + + + What do you think of the solution? It looks good, right? The model calculation (‘theory’ curve) is running through the measured datapoints, the normalised residuals are all within +/-2 standard deviations, and the Reduced Chi2 is close to 1 (more on this shortly!). + + But, look closely at the model parameters and their uncertainties. Two of the parameters, scale and i_zero, have uncertainties (the Error) that make no sense. Why? + + To understand this it is instructive to examine the help documentation for the model. Click the Help button on the FitPage (not in the Menu Bar) alongside the model name. The documentation tells us that the function that SasView is fitting is + + + + + + I + + + ( + + Q + + ) + + = + scale + + . + + I + 0 + + . + P + + + ( + + Q + + ) + + + + background + + + I(Q)=scale . I_0 . 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To fit the data with this model we only need one of these parameters. + + + + + + Tip: SasView adds an overall scale factor (scale) and a Q-independent background to all its models for consistency, even though some models might not need one or other of these parameters. If in doubt, consult the model help documentation. + + + + + Uncheck the scale parameter and set its value to 1.0. 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you want to record the solution you have a number of options: + + + + If you want the parameter values and their uncertainties, go to the Menu Bar and select Edit and either Copy Params (for output suitable for a text editor) or Copy Params as... (for output suitable for Excel or LaTeX) + + + + If you want a copy of the graphs, right-click on a graph and select either Save Image (as .ps/eps, .jpg, .pdf, .png, .raw, .svg, or .tif), Print Image, or Copy to Clipboard + + + + If you want a file of the model function (the orange line) and/or residuals, right-click on the appropriate graph and select either M1 [LOQ Standard RT2_SANS.xml] or Residuals for M1 [LOQ Standard RT2_SANS.xml] and then Save Points as a File (as plain ASCII text: .txt, or in CanSAS1D format: .xml) + + + + If you want a two-page pdf report containing all pertinent information including copies of the graphs, go to the Menu Bar and select Edit and Report Results + + + + and finally + + + + A SasView session can be saved and reloaded as an ‘Analysis’ (an individual model fit), or as a ‘Project’ (everything done since starting your SasView session) by going to the Menu Bar and selecting File and either Save Analysis or Save Project. + + + + We shall now examine some additional aspects of model-fitting this dataset. + + Return to the FitPage and change the Instrumental Smearing to None. Then run the Fit again. Notice anything? The parameter values and the Reduced Chi2 value have all subtly changed. This is to be expected; Q-resolution affects the measured data, so it must have a bearing on the model fit. + Now change the model to the one called poly_gauss_coil. This model is an extension of Debye’s original scattering law to include a Schulz-Zimm molecular weight distribution. This model has one extra parameter: the polydispersity of the polymer (Mw/Mn). Set the polydispersity to 1.03 (but leave it unchecked; this is more a priori information) and run the Fit again. + + The parameter values change again, but there is a marked improvement (decrease) in the Reduced Chi2 value. + + Lastly, reset Instrumental Smearing to Use dQ Data and run the Fit one last time. + + Here is a summary of the fit results: + + + + + + + + + + + + + + + Param: + + Model + + + scale + + + bckgrd + + + bckgrd _err + + + i_zero + + + i_zero _err + + + rg + + + rg _err + + + poly disp + + + reduced chi2 + + + + + mono + use dQ + + + 1 + + + 0.0777 + + + 0.0076 + + + 49.75 + + + 0.169 + + + 56.57 + + + 0.146 + + + n/a + + + 0.780 + + + + + mono none + + + 1 + + + 0.0758 + + + 0.0076 + + + 49.65 + + + 0.169 + + + 56.44 + + + 0.146 + + + n/a + + + 0.771 + + + + + poly none + + + 1 + + + 0.0676 + + + 0.0077 + + + 50.07 + + + 0.172 + + + 57.36 + + + 0.150 + + + 1.03 + + + 0.659 + + + + + poly + use dQ + + + 1 + + + 0.0695 + + + 0.0077 + + + 50.17 + + + 0.172 + + + 57.50 + + + 0.150 + + + 1.03 + + + 0.669 + + + + + So for this dataset (sample) allowing for even a tiny amount of molecular weight polydispersity – thereby maximising our use of a priori information - gives rise to a significant improvement in the quality of the fit! And though it does appear that including the Q-resolution smearing slightly degrades the quality of the fit in this example, it should be remembered that instrumental smearing is always present (and so should be handled) and this dataset was devoid of any fine structure (peaks, fringes). + + + + + + Aside: You may have noticed that all of the Reduced Chi2 values in the summary table above are slightly less than 1. Whilst values >1 are indicative of a poor fit, Reduced Chi2 values <1 are usually an indication that the data is being ‘over-fit’; for example, because the uncertainties on the data have been over-estimated (and the fact that most of the Residuals in the earlier screen shot lie within the ±1 band is also suspicious). It is not unusual for uncertainties to be incorrect, but it is more common for them to be under-estimated, not over-estimated. + + + + + Example 2 + + + + + + This demonstrates a fit requiring a structure factor and introduces the use of multiple FitPages. + + + + + From the \example_data\1d_data folder in the SasView installation directory, load the hSDS_D2O_2p0_percent.xml dataset and send the data for fitting. + + + + + + Tip: You can either: i) restart SasView, ii) click the Delete Data button in the Data Explorer before loading the new dataset to remove all traces of Example 1, or simply uncheck the LOQ Standard RT2 dataset in the Data Explorer and have SasView create a new FitPage when you click the Send to button, as illustrated below. + + + + + This dataset is the SANS from a 2 %w/w solution of the widely-studied surfactant h25-sodium dodecyl sulphate (SDS) in heavy water (D2O). 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Two of them, sld (for the SDS) and sld_solvent (for the D2O), can be calculated explicitly. + + Go to the Menu Bar, select Tools, and then SLD Calculator. Enter the following empirical formulae and densities in the relevant boxes (leave the neutron wavelength as 6 Å): + + + + SDS:Na1C12H25S1O4; density 1.01 g/cm3 + + + D2O:D2O1; density 1.11 g/cm3 + + + + Hopefully you got values of sld = 0.337x10-6 Å-2 and sld_solvent = 6.39x10-6 Å-2? + + Enter these values in the FitPage (they are not auto-populated from the SLD Calculator). 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And the scale parameter in this case represents the volume fraction of micelles (encouragingly, about 2 %!). 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Also note that the volfraction parameter has dropped to ~1 %. + + So how might the fit be improved further? One possibility is that water molecules are mixed in with the surfactant sulphate head groups, thereby increasing the effective SLD of the surfactant molecules (and reducing the scattering contrast; ie, sldsld_solvent). + + To test this, check the sld parameter and run the fit again. + + + iVBORw0KGgoAAAANSUhEUgAABpAAAAP8CAYAAABBLf1HAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzde3QU953n/XdVdbdaV4QQN2PMTZJtLsaAHWOBg03sxMLz7JDLwJPMZJhk + Ysh4Zways/acHZt9nllDnrPxJIGZPc4BzyVkksmYXc+SmQXFg02wjWTsxDa2ZXAkcZGwuQvd + pb5V1fNHq1vdUktqtSQEzud1Th2k6qrf71fVXU11f/X9/gzXdV1EREREREREREREREREepjj + PQARERERERERERERERG5viiAJCIiIiIiIiIiIiIiIkk8gz0YCIU5+uFJTn3cxITciXzx0/Ov + 1bhERERERERERERERERknKQMIHUGw/zg39/kx6+9R3NLgOaLYcLBEN3BML/30OJrPUYRERER + ERERERERERG5hvqVsDvX3MHXdh3gf779MWZ2MeFAFpYZjTP98MCvrvkARURERERERERERERE + RothGIMu1xvDMHjrrbcGfPytt94ak3EnBZA6AiH+y/NHaA1aTMjOJ8uxMGyDFQtm8K3fXsz0 + olx+fbZp1AchIiIiIiIiIiIiIiJyrbium3K5Hv3qV7/i3hUrUwaR3nrrLe5dsZJf/Wr0E4CS + 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The Reduced Chi2 has dropped to ~1, the residuals are within +/- 2, and the volfraction parameter has increased to almost 1.7 %, which is very close to the 1.78 % expected from the solution concentration (2 %) minus the cmc (0.2 %) = 1.8 % / 1.01. + + This fit is, to all intents and purposes, as good a fit as one might reasonably expect to achieve. However, there is published evidence that suggests SDS micelles are actually slightly ellipsoidal (see, for example, DOI 10.1016/j.colsurfa.2024.134394 and the references therein). Can SasView confirm or refute this? + + Use the Send to button to create another FitPage and then select the ellipsoid model. Do not select an S(Q) for the time being. + + Set sld and sld_solvent to their calculated values. + + We know from the fit to the sphere model that the micelles have a radius ~20 Å so set radius_polar=20 and radius_equatorial=40 (ie, to give the ellipsoids an intial axial ratio of 1:2; a sphere would be 1:1 of course). Limit the maximum Q of the fit again. Check the scale and background parameters and run the fit. + + Now select the hayter_msa S(Q) as before and set the known values you used previously. And just like before, set scale=1.0 and uncheck it. 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So the SasView fitting is certainly consistent with the literature reports. But unambiguously distinguishing between the two cases would require more precise measurements and higher quality data. Just because a model fits the experimental data is not always proof that it is the correct model! + + One could also explore the extent to which size polydispersity (see Example 3) impacts both models, or whether more nuanced models, for example, the core_shell_sphere or the core_shell_ellipsoid, allowing for a difference in SLD between the head and tail regions of the micelles, are better descriptions of the data. + + + + + + + + + + + + + + + + Example 3 + + + + + + This demonstrates a fit requiring a structure factor and polydispersity. + + + + + From the \example_data\1d_data folder in the SasView installation directory, load the Ludox_silica.xml dataset and send the data for fitting. + + This dataset is the SANS from a concentrated dispersion of Ludox® silica nanoparticles in light water (H2O), so there will once again be an S(Q) contribution from charged spheres. + + Select the sphere P(Q) model and the hayter_msa S(Q) model. + + Once again, we have a lot of a priori information: 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In Example 2 we managed to obtain a good solution without having to specifically address polydispersity, most likely because the size of the micelles meant any fringes in the scattering curve were beyond the range of the data. + + In the lower part of FitPage, click on the checkbox named Polydispersity. 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selects a Gaussian distribution. If you need a different distribution, select it before you set any distribution parameters. The SasView help documentation provides some guidance on appropriate use cases for different distributions. + + + + + The width of the chosen polydispersity distribution is determined by the PD parameter and the definition of this changes depending on the distribution. For the Log-Normal distribution: + + + + + + PD + = + + σ + normal + + + PD= %sigma_normal + + + + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAe4HAAAU + AgAAJAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAO0HAAATAgAAlQAB + AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJhdGlv + biBTZXJpZgAAAAAAAKcBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAA + AIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAAAaAAAAcgEAAAIA + UEQ0AgAAAAACAAIAUABEAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8AAAACgBPcGVu + U3ltYm9sAAAAAAAApwEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAA + iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAGECAAByAQAAAQAA + AD0AUAEAAAAAAQABAD0AjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAAFADwAAAAKAE9wZW5T + eW1ib2wAAAAAAACnAQAA//8AAAAABQAAAAAAAgD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACI + AAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAuQMAAHIBAAABAAAA + wwP/AAAAAAABAAEAwwOMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJh + dGlvbiBTZXJpZgAAAAAAAP0AAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAA + AAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACACYAAAAQBQAA3AEA + AAYAbm9ybWFs3AIAAAAABgAGAG4AbwByAG0AYQBsAIwAAQAAAAAAlQABAAQAAAAAAAAAlgAB + AAIAAAAJAIwAAQAAAAAA + + + + + where σnormal is the width of the underlying Normal distribution. 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/vzvT/T8j7r+9wc8/6empPSrPv/dNzCg/of//P//fhMLujD7FogAAAAASUVORK5CYII= + + + + Whilst there is certainly room for improvement in both the Reduced Chi2 and Residuals, this is nonetheless a promising fit to the data. The radius is within the size range typical of this material, but the volfraction is higher than anticipated. Seeming inconsitencies like this should always trigger a re-evaluation of the priors. For example, although Ludox® dispersions are described as being in water, is the dispersion medium truly water? Or does it contain residual components from the manufacturing process which may make the assumptions used about the values of sld_solvent, concentration_salt and dielectconst less valid? + Also notice that an additional graph window has appeared depicting the actual form of the Log-Normal size distribution used in the model calculation. + + Another nice feature is that it is also possible to see the separate contributions that the P(Q) and S(Q) make to the overall result. + + In the Data Explorer, click the > symbol to expand the Ludox® entry. + + + Data + + Model calculation + + + P(Q) + S(Q) + + + iVBORw0KGgoAAAANSUhEUgAAATcAAAGtCAYAAABz3zMXAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nO2df3gb9Z3n3yM7CYRfAboNXkqdNJIoXkM3uJStVGJyJdxJoWzwtc5eCHWa + I1Lb52mkO848lyfO+knjPNmnPliJ9qG1QlP72KYPoU19u1haYmjq7FkcPwK34DW1pBD70j6B + dlmyDxy9ksRzf8yMPBrNSCNZtkaj9+t5FEea73e+3xlJb30+3+/M9y2cO3dOBCGE2IzGF198 + sdp9IISQiiMwciOE2Inh4WEAjNwIITXO7bffrvt6IwCsXr16UTtDCCGV4PTp07qv/+xnP4Nj + 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Experiments (DANSE) project funded by the US National Science Foundation (NSF), but is currently being developed as an Open Source project hosted on GitHub and managed by a consortium of scattering facilities. Participating facilities include (in alphabetical order): the Australian National Science & Technology Centre for Neutron Scattering, the Diamond Light Source, the European Spallation Source, the Federal Institute for Materials Research and Testing, the Institut Laue Langevin, the ISIS Pulsed Neutron & Muon Source, the National Institute of Standards & Technology Center for Neutron Research, the Oak Ridge National Laboratory Neutron Sciences Directorate, and the Technical University Delft Reactor Institute. + + SasView is distributed under a 'Three-clause' BSD licence which you may read here: + https://github.com/SasView/sasview/blob/master/LICENSE.TXT + + SasView is free to download and use, including for commercial purposes. + + © 2009-2025 UMD, UTK, NIST, ORNL, ISIS, ESS, ANSTO, ILL, TUD, DLS, BAM + + + + If you make use of SasView + + If you use SasView to do productive scientific research that leads to a publication, we ask that you acknowledge use of the program with the following text: + + This work benefited from the use of the SasView application, originally developed under NSF Award DMR-0520547. SasView also contains code developed with funding from the EU Horizon 2020 programme under the SINE2020 project Grant No 654000. + + + + Contributors to this Tutorial + + Steve King (stephen.king@stfc.ac.uk) + Piotr Rozyczko (piotr.rozyczko@esss.se) + Wojciech Potrzebowski (wojciech.potrzebowski@esss.se) + + + + Revisions + + Last revised: 27 May 2025 + + + + Acknowledgements + + The correlation function analysis used in earlier versions of SasView was originally coded by Adam Washington at Sheffield University, UK and released on GitHub under an MIT License (https://github.com/rprospero/corfunc-py). It was incorporated into SasView by ISIS Summer Student Lewis O’Driscoll in 2016. However, the inspiration for that code lies in a much earlier piece of software, CORFUNC, developed by Tom Nye (then an undergraduate mathematician at Cambridge University, UK) in 1994 at the request of (now Prof) Tony Ryan (whilst seconded to the Daresbury SRS). CORFUNC was later released as part of the CCP13 software suite for Fibre & Polymer Diffraction. The source code for CORFUNC is available at https://github.com/scattering-central/CCP13. + + In SasView 6.x the correlation function analysis has been completely refactored from first principles by Lucas Wilkins at ISIS. It may not, therefore, nor should it necessarily be expected to, exactly reproduce the output from the earlier codes. + + SK would like to thank Elliot Gilbert (ANSTO) for prompting a more careful analysis of the data in Example 1. + + + + + Learning Objective + + This tutorial will demonstrate how to perform correlation function analysis on 1D (‘intensity’ versus Q) datasets in SasView 6.x. This analysis was not available before Version 4.1.0. + + It is assumed that the reader has some familiarity with the purpose and principles of correlation function analysis. If not, these references provide an overview: + + + + Ruland, W. Coll. Polym. Sci. (1977), 255, 417-427 + + + Strobl, G.R.; Schneider, M. J. Polym. Sci. (1980), 18, 1343-1359 + + + Koberstein, J.; Stein R. J. Polym. Sci. Phys. Ed. (1983), 21, 2181-2200 + + + Baltá Calleja, F.J.; Vonk, C.G. X-ray Scattering of Synthetic Poylmers, Elsevier. Amsterdam (1989), 247-270 + + + Göschel, U.; Urban, G. Polymer (1995), 36, 3633-3639 + + + Stribeck, N. X-ray Scattering of Soft Matter, Springer-Verlag. Berlin Heidelberg (2007), Section 8.5 + + + https://www.diamond.ac.uk/Instruments/Soft-Condensed-Matter/small-angle/SAXS-Software/CCP13/Fibre-Diffraction-Review.html (Issue 3) + + + https://www.sasview.org/docs/user/qtgui/Perspectives/Corfunc/corfunc-theory.html + + + + + + + + + Also note that the integrals applied by the correlation function analysis in SasView (see page 15) assume that the data being transformed was either collected on a pinhole-collimated instrument or, if it was instead collected on a slit-collimated instrument, that it has been suitably Lorentz-corrected. Transforming slit-smeared data directly will generate invalid output. + + + + + + + + + + The program interface shown in this tutorial is SasView Version 6.0.1 running on Windows 11 but, apart from a few small differences in look and functionality, this tutorial is generally applicable to SasView 6.x running on any platform. However, there are separate tutorials for using the old program interface released with SasView 4.x and SasView 5.x. + + + + + + + + Glossary + + + + + + + a priori information + + + Known facts about the system/datasets being analysed. + + + + + Correlation function + + + A real-space function that describes spatial relations in the system whose datasets are being analysed. The greater the degree of structural order in the system, the more periodicity the correlation function will display. In essence, the correlation function is a density probability function. + + + + + Correlation length + + + A measure of the periodicity of a correlation function. + + + + + Extrapolation + + + A mathematical process for inferring unknown values, or extending a function beyond known limits, using trends in known data or established dependencies. + + + + + Fourier Transform + + + A mathematical ‘tool’ that decomposes a measured signal into a sum of sine or cosine functions. + + + + + Invariant + + + Also called the Porod Invariant, the Scattering Invariant, and the Total Scattering: + + + + + + Invariant + = + + + + 0 + + + I + + + + ( + + Q + + ) + + + Q + 2 + + dQ + + Invariant= int from{0} to{infinity} I(Q) Q^2 dQ + + + + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAkAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAYoJAABX + AgAAXAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAIkJAABWAgAAiwAB + AAIAAAAAGJUAAQAEAAAAAAAAAJYAAQACAAAACQCLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQ + AExpYmVyYXRpb24gU2VyaWYAAAAAAADwAAAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAABAP8D + AAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAvAAAA + DQAAAFIBAAAJAEludmFyaWFudH0DAAAAAAkACQBJAG4AdgBhAHIAaQBhAG4AdACMAAEAAAAA + AIsAAQACAAAAHwCKAAEAQgAAAAUAPAAAAAoAT3BlblN5bWJvbAAAAAAAAPAAAAD//wAAAAAF + AAAAAAAAAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8A + hgABAAQAAAAAAAAAcgACABoAAACjAwAAUgEAAAEAAAA9AL8AAAAAAAEAAQA9AIwAAQAAAAAA + iwABAAIAAAAfAIoAAQBCAAAABQA8AAAACgBPcGVuU3ltYm9sAAAAAAAAXgEAAP//AAAAAAUA + AAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCG + AAEABAAAAAAAAAByAAIAGgAAAFQEAAByAQAAAQAAACsiygAAAAAAAQABACsijAABAAAAAACL + AAEAAgAAAB8AigABAEgAAAAFAEIAAAAQAExpYmVyYXRpb24gU2VyaWYAAAAAAACQAAAAAAAA + AAAABQAAAAAAAAD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/ + ////AIYAAQAEAAAAAAAAAHIAAgAXAAAAlQQAADcCAAABADBIAAAAAAABAAEAMACMAAEAAAAA + AIsAAQACAAAAHwCKAAEAQgAAAAUAPAAAAAoAT3BlblN5bWJvbAAAAAAAAJAAAAD//wAAAAAF + AAAAAAAAAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8A + hgABAAQAAAAAAAAAcgACABoAAACCBAAASwAAAAEAAAAeImwAAAAAAAEAAQAeIowAAQAAAAAA + iwABAAIAAAAfAIoAAQBIAAAABQBCAAAAEABMaWJlcmF0aW9uIFNlcmlmAAAAAAAA8AAAAAAA + AAAAAAUAAAAAAAIA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA + /////wCGAAEABAAAAAAAAAByAAIAFwAAAEgFAABSAQAAAQBJUAAAAAAAAQABAEkAjAABAAAA + AACLAAEAAgAAAB8AigABAEIAAAAFADwAAAAKAE9wZW5TeW1ib2wAAAAAAADwAAAA//8AAAAA + BQAAAAAAAAD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD///// + AIYAAQAEAAAAAAAAAHIAAgAaAAAAvwUAAFIBAAABAAAAKABSAAAAAAABAAEAKACMAAEAAAAA + AIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAPAAAAAA + AAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAA + AP////8AhgABAAQAAAAAAAAAcgACABcAAAAcBgAAUgEAAAEAUa0AAAAAAAEAAQBRAIwAAQAA + AAAAiwABAAIAAAAfAIoAAQBCAAAABQA8AAAACgBPcGVuU3ltYm9sAAAAAAAA8AAAAP//AAAA + AAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA//// + /wCGAAEABAAAAAAAAAByAAIAGgAAANwGAABSAQAAAQAAACkAUgAAAAAAAQABACkAjAABAAAA + AACLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQAExpYmVyYXRpb24gU2VyaWYAAAAAAADwAAAA + AAAAAAAABQAAAAAAAgD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUA + AAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAPwcAAFIBAAABAFGtAAAAAAABAAEAUQCMAAEA + AAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAJAA + AAAAAAAAAAAFAAAAAAAAAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEA + BQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAD2BwAA2gAAAAEAMkgAAAAAAAEAAQAyAIwA + AQAAAAAAiwABAAIAAAAfAIoAAQBIAAAABQBCAAAAEABMaWJlcmF0aW9uIFNlcmlmAAAAAAAA + 8AAAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAABAAIAAAABAIcA + AQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAFwIAABSAQAAAgBkUSUBAAAAAAIAAgBk + AFEAjAABAAAAAACMAAEAAAAAAIwAAQAAAAAA + + + + + + + + Inverse-space + + + See reciprocal-space + + + + + Long Period + + + In a lamellar system, the distance from one face of a lamellae to the same face of the adjacent lamellae. + + + + + Real-space + + + Real world coordinates. The opposite of inverse-space or reciprocal space. + + + + + Reciprocal-space + + + The Fourier Transform of real world coordinates. The opposite of real-space. In scattering measurements, Q is the reciprocal-space equivalent of a real world length scale. + + + + + SLD + + + Abbreviation for Scattering Length Density, a measure of the ability of a molecule to scatter. Strictly speaking, SLD is a SANS quantity, so if fitting SAXS data use electron density values in their place. + + SLD values (neutron and X-ray) can be calculated with the SLD Calculator Tool in SasView. + + + + + Total Scattering + + + See Invariant + + + + + Transformation + + + A mathematical process for converting between real-space and inverse-space. + + + + + Uncertainties + + + Every experimental measurement, including the measurement of I(Q), is subject to some degree of error (which will, ideally, be included in the dataset). Similarly, the parameters returned by any analysis will have some associated range of uncertainty. + + Parameters with uncertainties that are more than 95% of the parameter value should be viewed with deep suspicion. + + + + Running SasView + + Windows + Either select SasView from ‘Start> ‘All Programs(if using Windows 10), or click on the magnifying glass icon in the toolbar and type ‘SasView’ into the search box (if using Windows 11) or, if you asked the installer to create one, double-click on the SasView desktop icon. + + + iVBORw0KGgoAAAANSUhEUgAAAG4AAACACAIAAABld8teAAAgAElEQVR4nO19a4xd13Xet9Y+ + 59x758XH8C1RomiSlmRJjhTbUkauFMtOHEWpHSupW6RxmyIA1RRFC7RAgaLor/ZPf5VGi6J1 + gAJt4jSNDdtpYMqxY8upZcqWbFmiJEri8E2RHD6H87r3nsdeqz/23uece2fI4QyHpJxyYUDe + ex777P3tbz322nufS6qK27ISEt3qCiwgqmrFqigAEAMgosjwLa7WYnLroVTVvLBW7MSlyffO + nreiE5cuvnP0+OTULHGTk1Gh1qrBxiM7Nz92/50b1wzd6vpeUehWKXhe2MnZ2bdPnBo/NfGd + n7y+//Dxbp6laQHAFnmaQmg9RasAhhCzRsw7t679l59//HMfv4+Jbkmdry43G8rC2kszs99/ + 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Figure reprinted from “Use of scattering methods in chemical + industry - SAXS and SANS from fibers and films”. Chapter 21, in “Neutrons, X-rays and Light: + Scattering Methods Applied to Soft Condensed Matter”. Lindner & Zemb (editors), North-Holland. 2002. + + This periodicity in the nanostructure manifests itself as a peak in the scattering data. + + At the bottom of the Data Explorer panel, click the drop-down that currently says ‘Fitting’ and select Corfunc. 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axis scales or to alter the appearance of the plot, click on the ‘rising arrow’ arrow icon (“Edit axis, curve and image parameters”) in the plot toolbar. + + + + + + The correlation function is computed by taking the (cosine) Fourier Transform of the scattering data. However, this requires performing an integration between Q=0 and Q=, and quite clearly the measured data do not extend to those limits (and nor could they)! The prerequisite, therefore, is to extrapolate the measured data towards those limits. + + The three vertical bars represent the limits of the measured data that will be used to construct the extrapolation functions. In the case of the low-Q extrapolation, all data to the left of the leftmost vertical bar is used. In the case of the high-Q extrapolation, data between the two rightmost vertical bars is used. + + + Aside: At the present time, SasView extrapolates the measured data with the following functions: + + + + + + + Low-Q + + + High-Q + + + + + Guinier function + + + Porod function + + + + + + + + + I + + + ( + + Q + + ) + + = + + e + + ( + + + + A + + + B + + . + + Q + 2 + + + + ) + + + + + I(Q)=e^( A + B . 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A and K are just scale factors with ln(A) = I(Q=0). + + Though the Guinier function may be a dubious description of the low-angle scattering from some systems, because of the transformation from reciprocal-space to real-space any artefacts that the use of this function introduces only manifest themselves in the region of the correlation function where the density probability is close to zero anyhow. + + Conversely, the quality of the high-Q extrapolation is much more important, so consider carefully which data points to include between the limit bars. Do not include any data points within the peak itself. In lieu of infinity, SasView computes the high-Q extrapolation out to 100 times the largest Q value in the measured dataset. + + + The default positions of the limit bars need adjustment. In particular, the high-Q limits span a break of slope which the Porod extrapolation procedure will struggle with. + + + + + + + Tip: You can change the default extrapolation ranges in the Corfunc Perspective page either by typing appropriate Q-values in the “Guinier End”, “Porod Start” and “Porod End” boxes, or by grabbing and moving the black bars in the multicolour “Adjust” tool (the grey bars represent the data limits). + + You cannot grab and move the limit bars on the plot itself, but their positions will update on the plot in response to your inputs above. + + + + + + For this example, first change the low-Q extrapolation limit to 0.011. This should give three data points for the Guinier fit. + + Now make the upper limit for the high-Q extrapolation (the rightmost vertical bar) to be the penultimate data point (Q=0.283), as the last data point has a large uncertainty. In fact, if you try setting Q=0.285 the box will turn red as a warning it is the last data point! + + The positioning of the lower limit for the high-Q extrapolation is more arbitrary but, as explained above, also more important. We need to encompass sufficient data points to give a good extrapolation but not so many that the extrapolation is impacted by the tail of the peak in the data. 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+ + + + + + Aside: In SasView 4.x the program automatically subtracts the background level from the displayed data. In SasView 5.x and SasView 6.x the data are always displayed with the background still present. + + + Aside: Smoothing is applied to prevent the joins between the extrapolations and the measured dataset generating ‘ripples’ in the correlation function. At the same time it provides a means of giving the concatenated dataset equally spaced Q points which facilitates the Fourier Transform. + + The algorithm used is described in more detail in the SasView documentation at: https://www.sasview.org/docs/user/qtgui/Perspectives/Corfunc/corfunc-technical.html#merging + + + Unlike SasView 4.x/5.x, SasView 6.x also gives additional control over how the correlation function is interpreted. + + + iVBORw0KGgoAAAANSUhEUgAAAkMAAAA8CAYAAABl0r6mAAAACXBIWXMAAA7DAAAOxQGRNQ/i + AAAbc0lEQVR4nO2dTWzb2LXH/9PJzEToZEK4s5h00Qwo2cBAGXRKlJkCDeJkQcADdWEF4GLw + NkQ3brQw1EWFlsVDF0WZQishBZQaXZSbrghYs6gwLrioHWQTEFBnEW1kizNdpW9Rl5MBqiCf + b0FSvKQoidSHHVvnBwiJTery8N5zzz33nEP6NcdxXoIgCIIgCGJB+dZxC0AQBEEQBHGckDNE + EARBEMRCQ84QQRAEQRALDTlDBEEQBEEsNOQMEQRBEASx0JAzRBAEQRDEQnPmuAUgiKR0u13c + vXsXBwcH6PV6yGQyyOVyuHr1KrLZ7HGLR5xCSOeIWXLv4BHu7D3Evf1v8HXvGc5nzuDK8jnc + XL2AK7l3jlu8heY1es8QcRJoNBpot9u4du0aLl++jEwmg8PDQxwcHODzzz/HpUuXsL6+ftxi + 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For now, leave both methods on the automatic setting. + + We are now ready to compute the correlation function. So click the Go button. + + After a few seconds, several things happen: + + + + SasView computes the low-Q and high-Q extrapolation functions; the values of A, B, K, σ, and Background are returned in the Extrapolation Parameters section of the Corfunc Perspective. + + + + The graph window updates to show an orange line; this is a smoothed concatenation of the low-Q extrapolation (from 0 Q < Qmin), the measured dataset (from Qmin Q ≤ Qmax), and the high-Q extrapolation (from Qmax < Q 100 x Qmax). Note that the full Q-range of the extrapolated data is not displayed for clarity! + + + + Unseen, correlation functions are computed from the extrapolated data. + + + + The correlation functions are interpreted assuming the presence of a quasi-lamellar structure and the resulting parameters are displayed in the Lamellar Parameters section of the Corfunc Perspective. + + + + + iVBORw0KGgoAAAANSUhEUgAAB3wAAAQHCAYAAAAXjxgsAAAACXBIWXMAAA7EAAAOxQGMMD9a + AAAgAElEQVR4nOzde3xU5Z0/8M85Z2YyScg93IUk5III4WorQRRBUEPdiq7AWltLrQRbd7ek + v7L9lUpri2VtbQVd3f4IVqld2xLdlrY22ZaLgJBEtirIJSUJ5ML9knsymes5vz9m5mTut0yu + fN6v1yiZOed5nnPmJJmZT57vIxg6WxQAgP2//UsYgD7CMhAHPfQ4jzrUp8PfWfK3vxLCeQ3W + t2cLQ+7SGRDhn/nQOPcf/te/57UmBLlSgl2bnvuHci0PVeFeJeH+PIjW92S0xtNn/fUDMRoU + j06FMDvz3D9c4R4bf4ATEVHYXH9Z9OUXyQh6/RzuaRhmL1v5fpD6ari836EQ9PUbvr9//t3s + F0Ow8xvO+9OB/F3FXzQRGpknItjTHe7j0RXsN1qkjw9PwX6PR/p4aEL5wTGyznfkwj3joT6D + fRfuNTDC3mZBHOwBEBERERERERERERERERFRZBj4EhERERERERERERERERENU5pADxrNVhyt + 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If this is not the case, manually adjust the Background and re-extrapolate. If the high-Q data are noisy then this may require several iterations. + + + + + + The background value returned, 0.305, represents the background at 100 x Qmax. To check how well it represents the background level within the range of the experimental data, click on the magnifying glass icon at the bottom of the plot window and drag the cursor to expand just the high-Q region of the data. + + iVBORw0KGgoAAAANSUhEUgAAA8gAAAL+CAYAAABxBj0GAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeVyU9f7//+ewDMgqqaiYK6IFmpiKx8olUdFKc2n5lKeUfuXpHAyXMmkz + tY2yculwKrOoT6fPyU/CKT9WipK2mImVmGn5VdLsuKMiiwoC1++PgZFhAJFtBnjcbzduznXN + tbznYtTrOe/X+z2mrKwsQwAAAAAANHMujm4AAAAAAADOwK30QWFhoQoKCmQYdChfLpPJJLPZ + LDc3t0tvDAAAAABwStZEV1BQoICAALm40Kl8uYqLi3X69GkCMgAAAAA0YtZEZxgG4biGXFxc + ZBiG8vLyHN2UZqO01z4/P9/RTUET0tjeV1SvAAAA1C3uquqQn5+fo5vQbBiGodzcXK456lRj + e1+VtpeADAAAUDfoMkajZDKZGC+POtfY3leNrb0AAADOjoAMAAAAAIAIyAAAAAAASCIgAwAA + AAAgiYAMAAAAAICkugrI62Lk4eFR5meIlu2rxn77lmlITfYDAAAAAKCO1Togr4vxkMc4aXV+ + vvJLf1b31pwwDw2pKu2ui5FH2Crdtst2vz0ZtW1R45AS6ytfX9ufyIS6evEZSoi81PFSFFvu + /LEpdXR6J5eREGl37X19Y+WsL9/S3kjV2duj4pMo0u6a+MrX7k1R8r5pLm+Wy5ASa/t3rqK/ + 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The background value increases slightly to 0.311. + + + Now click on the plot tab labelled ‘Real Space’. Two functions are displayed: + + + + Γ1(z); the 1D Correlation Function + + + Γ3(z); the 3D-averaged (or ‘Radial’) Correlation Function + + + + iVBORw0KGgoAAAANSUhEUgAAA8sAAAL+CAYAAACaMYYFAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzde3iT9f3/8Vd6SgukLVhajlIsghPQKq4MD6DCqIowB8zT5qEIyqgWD3Pi + FDqdInzZVJgV56l44Ht5oH5ZpwhVFFF/zs4DTpkiraAMaTn2QEvP9++PNHeTND2kSZumPB/X + lavpnfvwTkhLX/mcLCUlJYYAAAAAAIApJNAFAAAAAADQ3YQFuoBgV1dXp5qaGhkGDfSBYrFY + FBERobAw3s4AAAAA/IN04aOamhr17dtXISE00gdKQ0ODjhw5QlgGAAAA4Dce0wWtpd4hKAdW + SEiIDMNQRUVFoEtBD+DoqVBdXR3oUtqFnhUAAACdw+NfVzU1NerTp48sFktX1xN0ysrKAl0C + GkVHRwe6BPQAhmHo6NGjQfN+ctRLWAYAAPAvj02ihmEQlAEclywWS1D1qgm2egEAAIIF/YcB + AAAAAHBDWAYAAAAAwA1hGQAAAAAAN4RlAAAAAADcEJYDaFO6VVar623iqgI/nb1Aqya2db5N + Sne7fvomP10eAAAAAIKY/8JyXoZsNpvTbbKyCttxXGGWJnfkuB5i/Irtqq6ubrzlauydo/0Y + mFtRsEoTrTOk3Oqm629fIe3ogmt3A4VZk93erzbZbBnKC3RhLbDX28k/G81+FhtvGe6vSp4y + PG5HXoZNk53+kfIyPLyenv4dPb72x9fvQgAAgO7GL2E5L8Mm2ywpp7xc5Y5bzmgtSnb9w9HD + 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But notice that less structure is evident in Γ3(z) because of the orientational averaging. + + The reader may be familiar with pair distribution functions (usually abbreviated to PDF’s) from Total Scattering measurements. In the same way PDF’s describe the probability of finding two atoms separated by a given distance in a material, these correlation functions reflect the separation of similar SLD (and by inference, similar density). + + + + + + + + + + + + + Now click on the plot tab labelled ‘IDFto see the Interface Distribution Function, g1(z). + + + iVBORw0KGgoAAAANSUhEUgAAA8gAAAL+CAYAAABxBj0GAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXxU9b3/8fdMQhISkrAEEtYQwyaLphdMhCLYEgk+8LYBXO+jAqlKq0i0 + VDSigKC3LNVbRKJI/d3wqEtRhIteijQUW71WSqSKVloRIpvBhATIQgIJyZzfH5OZZLIOIZMz + k3k9H495YGa+58znnDnxkfd8l2MpLi42BAAAAACAnws0uwAA8AbV1dWqqqqSYfjWd4YWi0VB + QUEKDOR/5wAAAFeKv6gAQFJVVZV69Oghq9VqdimXxWaz6dy5cwRkAACAduDyF5Wv9qCYwdFr + U1lZaXYpfodzD0/xtXAs2Wvm/9kAAADtwyUgV1VVqVu3brJYLGbV4zMMw9D58+cVERFhdil+ + h3MPTygtLTW7BAAAAJjMpbvEMAzCsZssFgu9Nibh3AMAAADwBN8bTwgAAAAAgAcQkAEAAAAA + EAEZAAAAAABJBGQAAAAAACQRkAHgiv1xfrAmrTvi8nNwcMPHJNVrYndknSa50w4AAAAd4soD + 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+ Γ + 1 + + + + ( + + z + + ) + + dz + + %GAMMA_3 = {1} over {r} int from{ 0 } to{ r } %GAMMA_1 ( z ) dz + + + + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAkAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAVYGAACs + AgAAcwAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAFUGAACrAgAAiwAB + AAIAAAAAGJUAAQAEAAAAAAAAAJYAAQACAAAACQCLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQ + AExpYmVyYXRpb24gU2VyaWYAAAAAAADwAAAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAABAP8D + AAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAA + BgAAAKcBAAABAD+LAAAAAAABAAEAkwOMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAA + ABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAJAAAAAAAAAAAAAFAAAAAAAAAP8DAAAAAAAAAAEA + /wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcA + AACYAAAA3wEAAAEAM0gAAAAAAAEAAQAzAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8 + AAAACgBPcGVuU3ltYm9sAAAAAAAA8AAAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAA + AAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAOkA + 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AAAFAAAAAAAAAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP// + //8AhgABAAQAAAAAAAAAcgACABoAAAAwBAAApwEAAAEAAAAoAFIAAAAAAAEAAQAoAIwAAQAA + AAAAiwABAAIAAAAfAIoAAQBIAAAABQBCAAAAEABMaWJlcmF0aW9uIFNlcmlmAAAAAAAA8AAA + AAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAQD/AwAAAAAAAAAAAAAAiAABAAIAAAABAIcAAQAF + AAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAJwEAACnAQAAAQB6XQAAAAAAAQABAHoAjAAB + AAAAAACLAAEAAgAAAB8AigABAEIAAAAFADwAAAAKAE9wZW5TeW1ib2wAAAAAAADwAAAA//8A + AAAABQAAAAAAAAD/AwAAAAAAAAABAP8DAAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/ + ////AIYAAQAEAAAAAAAAAHIAAgAaAAAADgUAAKcBAAABAAAAKQBSAAAAAAABAAEAKQCMAAEA + AAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAAABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAPAA + AAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEA + BQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAAB2BQAApwEAAAIAZHrVAAAAAAACAAIAZAB6 + AIwAAQAAAAAAjAABAAAAAACMAAEAAAAAAA== + + + formula + + + which is equivalent to computing: + + + + + Γ + 3 + + + + ( + + z + + ) + + = + + 1 + Invariant + + + + + + 0 + + + I + + + ( + + Q + + ) + + + Q + 2 + + + + sin + + ( + + Qz + + ) + + + Qz + + dQ + + %GAMMA_3 ( z ) = {1} over {Invariant} int from{0} to{ infinity } I( Q) Q^2 {sin(Qz)} over {Qz} dQ + + + + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAkAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAATIPAAB8 + AgAAuwAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAADEPAAB7AgAAiwAB + AAIAAAAAGJUAAQAEAAAAAAAAAJYAAQACAAAACQCLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQ + AExpYmVyYXRpb24gU2VyaWYAAAAAAADwAAAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAABAP8D + AAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAA + BgAAAHcBAAABAD+LAAAAAAABAAEAkwOMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAA + ABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAJAAAAAAAAAAAAAFAAAAAAAAAP8DAAAAAAAAAAEA + /wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcA + AACYAAAArwEAAAEAM0gAAAAAAAEAAQAzAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8 + AAAACgBPcGVuU3ltYm9sAAAAAAAA8AAAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAA + 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AAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAABNCgAA + 6AAAAAEANEgAAAAAAAEAAQA0AIwAAQAAAAAAiwABAAIAAAAfAIoAAQBIAAAABQBCAAAAEABM + aWJlcmF0aW9uIFNlcmlmAAAAAAAA8AAAAAAAAAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAA + AAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAALYK + AABgAQAAAwBjb3NAAQAAAAADAAMAYwBvAHMAjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAAF + ADwAAAAKAE9wZW5TeW1ib2wAAAAAAADwAAAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAABAP8D + AAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAA + CwwAAGABAAABAAAAKABSAAAAAAABAAEAKACMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUA + QgAAABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAPAAAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAA + AAEA/wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgAC + ABoAAABoDAAAYAEAAAIAUXoLAQAAAAACAAIAUQB6AIwAAQAAAAAAiwABAAIAAAAfAIoAAQBC + AAAABQA8AAAACgBPcGVuU3ltYm9sAAAAAAAA8AAAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAA + AQD/AwAAAAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIA + 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But because the features of interest in the transforms are all at much smaller distances only a reduced range out to 390 Å is shown for clarity. + + Having obtained the correlation functions it is always advisable to inspect them for artefacts from the Fourier Transform procedure: + + + + Do Γ1(z) & Γ3(z) smoothly curve into the ordinate at z=0? (sometimes overly small values of σ can cause the functions to meet the ordinate at a sharp angle) + + + This example: Yes + + + + + Does Γ1(0) = Γ3(0) = 1? + + + This example: Yes + + + + + Do Γ1(z) & Γ3(z) tend to 0 as z tends to ? + + + This example: Yes + + + + + Are there ‘ripples’ in Γ1(z) & Γ3(z) with a period of + + + + 2 + + π + / + + ( + + + 100 + + Q + max + + + + ) + + + + 2%pi / ( 100 Q_max ) + + + + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAkAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAXQFAAA0 + AQAAQAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAHMFAAAzAQAAiwAB + AAIAAAAAGJUAAQAEAAAAAAAAAJYAAQACAAAACQCLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQ + AExpYmVyYXRpb24gU2VyaWYAAAAAAADwAAAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAABAP8D + AAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAA + AgAAANwAAAABADJ4AAAAAAABAAEAMgCMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAA + ABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAPAAAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA + /wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcA + AACdAAAA3AAAAAEAP3gAAAAAAAEAAQDAA4wAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8 + AAAACgBPcGVuU3ltYm9sAAAAAAAA8AAAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAA + AAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAADoB + AADcAAAAAQAAAC8AQwAAAAAAAQABAC8AjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAAFADwA + AAAKAE9wZW5TeW1ib2wAAAAAAADwAAAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAABAP8DAAAA + AAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAiAEA + ANwAAAABAAAAKABSAAAAAAABAAEAKACMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAA + ABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAPAAAAAAAAAAAAAFAAAAAAAAAP8DAAAAAAAAAAEA + /wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0A + AADlAQAA3AAAAAMAMTAwaAEAAAAAAwADADEAMAAwAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBI + AAAABQBCAAAAEABMaWJlcmF0aW9uIFNlcmlmAAAAAAAA8AAAAAAAAAAAAAUAAAAAAAIA/wMA + AAAAAAAAAQD/AwAAAAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAA + AAByAAIAFwAAAGkDAADcAAAAAQBRrQAAAAAAAQABAFEAjAABAAAAAACLAAEAAgAAAB8AigAB + AEgAAAAFAEIAAAAQAExpYmVyYXRpb24gU2VyaWYAAAAAAACQAAAAAAAAAAAABQAAAAAAAgD/ + AwAAAAAAAAABAP8DAAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAA + AAAAAHIAAgAdAAAAIQQAABQBAAADAG1hePAAAAAAAAMAAwBtAGEAeACMAAEAAAAAAIsAAQAC + AAAAHwCKAAEAQgAAAAUAPAAAAAoAT3BlblN5bWJvbAAAAAAAAPAAAAD//wAAAAAFAAAAAAAA + AP8DAAAAAAAAAAEA/wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQA + AAAAAAAAcgACABoAAAAiBQAA3AAAAAEAAAApAFIAAAAAAAEAAQApAIwAAQAAAAAAjAABAAAA + AACMAAEAAAAAAA== + + + ? (ie, corresponding to the truncation point of the Fourier Transform) + + + This example: No (Qmax for this dataset was 0.285 Å-1 so the period of these ripples would be ~0.2 Å) + + + + + Are there ‘ripples’ in Γ1(z) & Γ3(z) with a period of + + + + 2 + + π + / + + Q + max + + + + 2%pi / Q_max + + + + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAkAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAT8DAAAv + AQAAKwAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAD4DAAAuAQAAiwAB + AAIAAAAAGJUAAQAEAAAAAAAAAJYAAQACAAAACQCLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQ + AExpYmVyYXRpb24gU2VyaWYAAAAAAADwAAAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAABAP8D + AAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAA + AgAAANcAAAABADJ4AAAAAAABAAEAMgCMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAA + ABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAPAAAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA + /wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcA + AACdAAAA1wAAAAEAP3gAAAAAAAEAAQDAA4wAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8 + AAAACgBPcGVuU3ltYm9sAAAAAAAA8AAAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAA + AAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAADoB + AADXAAAAAQAAAC8AQwAAAAAAAQABAC8AjAABAAAAAACLAAEAAgAAAB8AigABAEgAAAAFAEIA + AAAQAExpYmVyYXRpb24gU2VyaWYAAAAAAADwAAAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAAB + AP8DAAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAX + AAAAkAEAANcAAAABAFGtAAAAAAABAAEAUQCMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUA + QgAAABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAJAAAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAA + AAEA/wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgAC + AB0AAABIAgAADwEAAAMAbWF48AAAAAAAAwADAG0AYQB4AIwAAQAAAAAAjAABAAAAAACMAAEA + AAAAAA== + + + formula + ? (ie, corresponding to the point at which the measured dataset was extrapolated to high-Q) + + + This example: Not obviously (Qmax for the extrapolation was 0.279 Å so the period of these ripples would be ~22 Å) + + + + + Are there ‘ripples’ in Γ1(z) & Γ3(z) with a period of + + + + 2 + + π + / + + Q + min + + + + 2%pi / Q_min + + + + VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAkAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAASMDAAAv + AQAAKwAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAACIDAAAuAQAAiwAB + AAIAAAAAGJUAAQAEAAAAAAAAAJYAAQACAAAACQCLAAEAAgAAAB8AigABAEgAAAAFAEIAAAAQ + AExpYmVyYXRpb24gU2VyaWYAAAAAAADwAAAAAAAAAAAABQAAAAAAAAD/AwAAAAAAAAABAP8D + AAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAA + AgAAANcAAAABADJ4AAAAAAABAAEAMgCMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUAQgAA + ABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAPAAAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA + /wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcA + AACdAAAA1wAAAAEAP3gAAAAAAAEAAQDAA4wAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAABQA8 + AAAACgBPcGVuU3ltYm9sAAAAAAAA8AAAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAA + AAAAAAAAAAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAADoB + AADXAAAAAQAAAC8AQwAAAAAAAQABAC8AjAABAAAAAACLAAEAAgAAAB8AigABAEgAAAAFAEIA + AAAQAExpYmVyYXRpb24gU2VyaWYAAAAAAADwAAAAAAAAAAAABQAAAAAAAgD/AwAAAAAAAAAB + AP8DAAAAAAAAAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAX + AAAAkAEAANcAAAABAFGtAAAAAAABAAEAUQCMAAEAAAAAAIsAAQACAAAAHwCKAAEASAAAAAUA + QgAAABAATGliZXJhdGlvbiBTZXJpZgAAAAAAAJAAAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAA + AAEA/wMAAAAAAAAAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgAC + AB0AAABIAgAADwEAAAMAbWlu2AAAAAAAAwADAG0AaQBuAIwAAQAAAAAAjAABAAAAAACMAAEA + AAAAAA== + + + formula + ? (ie, corresponding to the point at which the measured dataset was extrapolated to low-Q) + + + This example: No (Qmin for this dataset was 0.007 Å so the period of these ripples would be ~900 Å) + + + + + + and lastly: + + + + Do the principle peaks in Γ1(z) & Γ3(z) seem to correspond to expectations?!!! + + + This example: It is well-established that the quasi-lamellar repeat distance between the crystalline regions in hydrated nylon-6 is about 84±4 Å (see for example, King, S.M.; Bucknall, D.G. Polymer (2005), 46, 11424-11434). As can be seen the first prominent maximum in Γ1(z) is around 74 Å, but the fact that it is not a sharp or symmetrical peak bears testament to an underlying distribution of imperfectly ordered spacings. So in general Γ1(z) does seem believable. The maximum in Γ3(z) is around 99 Å. + + + + + + + + + + + Tip: To save the data points for Γ1(z), Γ3(z) or g1(z), simply click the Export Transformed button and they will be written to a text file. The format of this file is described in the Appendix. It is similarly possible to save the extrapolated dataset by clicking the Export Extrapolated button. A dialog window will appear requesting the Q-range and Q-interval, but note that this is pre-populated with the values from the loaded dataset (ie, without the extrapolations). + + + + + + + + As we have the a priori information that this sample possesses a quasi-lamellar structure the final part of the analysis is to inspect the physical parameters SasView has derived from Γ1(z). These are the values displayed in the Lamellar Parameters section of the Corfunc Perspective. + + + + + + + WARNING! + The Lamellar Parameters are garbage unless it is known that the scattering they are derived from is from a lamellar or quasi-lamellar nanostructure! So use them with caution! + + + + + + Before we look at the values themselves it is first instructive to understand how they are derived. + + + Aside: Various procedures have been proposed to extract structural parameters from Γ1(z). SasView uses the positions of the first local minima (with Γ1(z) < 0) and local maxima (with Γ1(z) > 0), along with the extrapolated intercept and gradient of the linear section between the ordinate at z=0 and the first local minima, as shown below. Note that in this figure x represents z. + + + iVBORw0KGgoAAAANSUhEUgAAAgkAAAHICAIAAABLXO4jAAA/GElEQVR4nO3de1CTd74/8IQ7 + iiCIl07Pzu6eA92ejn/smdmdOnittEC4KBe5KCKiGBQv4G6ta8ejq8df1657KqhVAeutihYV + qHJRFOoN3O05M+vs8fTsVJ06te3SagEJGK7J75M88BieXEhCkueS9+uPTHh4knzzJPm+n+/3 + +zzP10ur1coAAAAMePFdAAAAEBxkAwAAcCEbAACAC9kAAABcyAYAAOBCNgAAABeyAQAAuJAN + AADAhWwAAAAuZAMAAHAhGwAAgAvZAAAAXMgGAADgQjYAAAAXsgEAALiQDQAAwIVsAAAALmQD + AABwIRsAAIAL2QAAAFzIBgAA4EI2AAAAF2/Z8KB4Znhhi8l/RRTdby4IM/2w+jz5rtcs/jtW + VqctUTiolAAAbom3bAgraNbGFeeFF3KqcsqMbLMPelC8q1S5VWsmGIhiU1FEeHV9iQLhAABg + P177lMJeMbGsYGtasZn1H9RWtCi3Wqz2w+LSIgoRDgAAYyLA8QZFQYHpf+iiISIt3PKjw16Z + LkM4AACMiQCzwaz7X7TIpm8d6lDSjSzcGx6YMBxmUCQqZbu+fCBTmO95AgAAi0SUDQ++vCd7 + 0WxQlNQp5bHZxXHNBffzYkuVdVqDhkLLF/epBcFLKQEAJEBE2aBrNsjSXvw9lA4zK1paRiRD + +GsRsgo0HAAA7CfobBjRb2SC/qikwpaIohMYXAAAcCDBZoPu/Icv0ooi7rFLdO2BeyNXyS5s + USqVpYX6rqXhABkxLAEAALbjNRsefEk390x3/+jOf9AFRMWLJa9MNxxIYJKhrrlEkSgbGngI + 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Nye. 1994. + + + + From which: + + Long PeriodLp + Average Hard Block ThicknessLc + Average Core ThicknessD0 + Average Interface ThicknessDtr + Local CrystallinityLc / Lp = Φc + + Eeckhaut PolydispersityΓmin / Γmax + Stribeck PolydispersityLc / ((Lc – Lp) Γmax) + + and: + + Average Soft Block ThicknessLpLc = La + Average Chord Length((1/Lc) + (1/La))-1 + Average Crystalline Chord Length((1/Lc) + (1/La))-1 / Φc + Non-Ideality(Lp – Lp*)2 / Lp2 + + “hard block” = crystalline, “soft block” = amorphous + + + For more information the reader is referred to the references provided at the start of this tutorial. But from the box above it should be clear that this is a semi-quantitative approach! The programmatic challenge then lies in devising robust algorithms to correctly identify the first local minima and maxima, Dtr, D0 and Lc. Clearly, if Γ1(z) exhibits too much noise/distortion incorrect interpretations will result. + + To allow you gauge the confidence you can place in the lamellar parameters, SasView 6.x actually generates a plot of how it is interpreting Γ1(z). 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And the derived lamellar parameters are: + + iVBORw0KGgoAAAANSUhEUgAAAmEAAACxCAYAAACMVGpNAAAACXBIWXMAAA7DAAAOxAGILj6j + AAAgAElEQVR4nO3dv2vb+B8/8Ke/ZGl7cOLoP3BKnaOYLAYN6fKdBE1yQzO4Y9Fkg4eiDJfB + 0KmgITdUdBA4k/jALfXgDrUT0PRdmkHgpYRysaPbbiqcDi7QodTfQbL9liz/diIneT7A0EQ/ + /Jbs9zsvvV8vqRnf97sgIiIiomv1f9JuABEREdFdxCCMiIiIKAUMwoiIiIhSwCCMiIiIKAUM + woiIiIhSwCCMiIiIKAUMwoiIiIhSsHgQ5uiQVAveEhqzOAe6JEF3gp88S1162xxdgiRFX733 + IyIiIpoWZ8LmoBgt+L4fvFoGzgo3LBBbqcCZiIjobmIQtii5jKqhwG7cpCiMiIiI0nbFQZgH + SxVTdzqc2DLVcoR1VFgegpma3jYJMzbRlKC4z0nNsaCKqURx+sqzoEoqLCdcZ9aZorN2sL7Y + dkmCagl7cfSgvb11wvf3LHVkerOXUnWEdYJ9BqnXyHlDbLuE5Y4uQSrYgFtBPnYORm0z/FmF + y2LnU403goiIiEa62iDMO8H53iB1V9NsFGJ5O7dyCFR7y11U8hKkww20fB++X4PmVlAS/rg7 + uoQCav19towzFKYMmLyTc+y1wjSiX4NmF2JpRBdBc3z4ThnylId5ce4CuSxkAE4DqAmpSlRK + sQDJRqGxGyw3VQAeTs73wuP14dc02IVYYOlWcIhqf7lbyUOSDrHREs5baXAOPEtFvi7uM4dK + Ptinagb7gGIEy0114jbDn5WDsuxAz1eQqw3O596U54uIiIiAtaRffvnyZexGDx8+nG7vchlm + efCjuqsBh214UPsBjmJUUQ5/UF8aUOw69qq9AEjFS0NB/vwCgAx4Fg5tDTVfFd7iAFrlECde + ub+f0c0xMWiOiqA5HqAONtQOpg++AACOjoKtwGgFbVJNU3jDp9hTKug1PzxiGC9VYQcyytGT + BA2HiDRLMVAdnCQYio36Xuy85c8RvI2DtxXAaAnHob6EoeTRcEyo4lsPDmK6bbSD2DlWsLHe + 3wDlMiImfY+IiIjuknj8lBiEJa04N0cP0l89ijFhgxyyo6Kgi3O4sFGQ7KFFWiTQGdccCaOb + IwYVo7mVPKRK/51R8x0MYhsPlppHxRXaFtk66fgc6FIBg2YpmHiWRp0kr40zuLDzEiqxRUos + 4Jx+m/DfkZOjYlcroJCXUNFq/Rk10dK+Q0RERDdc0sTElaYjg/ojIT1X05awV22wP+GVEAPE + WwNdiqYy521O5O5I3xwEYJ4FVcqj3k/BtmAok5qlQwpO0iBNOl+zxBbCaA2fI2fsVOHs26hm + eIxnBT6qg4iIaEZXGIQ5aNgKjJYQpCxqfQMKztCep/7bacBWDLQmR2tz807qcLXahGAn3iwb + itGaIoickpxFDm6QAr3KbQYbo+yEtWyHfOwFERHRtK4wCFvHhuKiftL7s+xAF/OA85DLOIgV + oQMeLH2KP/7rG1DcOgbN0bFoc4aal80BdqNfzO5ZpUhaMrlZCtz6CQbNEtOS8wjq6OLF/Y4e + L/YPashm2kbkWdCFOw689tlCrSYiIrprlhOE9R53EHm8gYxy1QAq+fB3DewuIR2pmi0YEN8v + j/PdKYrp5TKC5oTbNXbnTkeOaVxwB2jYthIOJqYj5XI1cjyN3cXTkXLZibRDkiQcbrwczEiG + xf0F4REVE7cZepOs8NlKwZ2VM9xRSkREdNdlfN/vxn/55csXFlUTERERLUlSbMUn5hMRERGl + 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Responsibility for correctly reporting these parameters therefore lies with the user! + + As mentioned at the start, for this particular example it is known that the peak in the SANS data, and therefore the peak in the correlation functions, comes from the ‘soft’ (amorphous) regions. This can be easily proven by hydrating the nylon fibres with a water mixture matched to the SLD of nylon; the peak then disappears! + + + + + + In SasView 6.x two measures of the polydispersity are offered; one proposed by Guy Eeckhaut, the other proposed by Norbert Stribeck. Only the former value is reported by SasView 4.x/5.x. + + + + + + + It is then highly-recommended to conduct a ‘sensitivity check’ to see how Γ1(z), Γ3(z), g1(z) and the extracted parameters change as the value of Bg is altered. To do this, simply untick Fit Background, change the value of the Background parameter, and then click Go. + + + + + + Below we can see the effect of changing Bg from 0.31128 (the value above) to 0.3000 (ie, 3.6% less). Visually, only a very keen eye would spot the change in Γ1(z) and Γ3(z), but there is quite a dramatic change in g1(z) around 45 Å. + + + + iVBORw0KGgoAAAANSUhEUgAAB3wAAAQFCAYAAABaR7knAAAACXBIWXMAAA7EAAAOwgHDcamd + AAAgAElEQVR4nOzde3xU5Z0/8M85Z2YyScg93C9JIInK1YBVCCiKoIJdi67Aqu2ytQJWdwt2 + q72g1VbZVm01WGt/gtWyXdsFXaW1kLVcBIQQWRWQmyaBXLhfck8mczvn/P6YzMnc58xkcv+8 + X69RMnPO8zznmZO5nG++30ewNNWp6C5Ct/WkU/cdem/iPmq9T0ewWQq2v6pjXsP17dtCrzt1 + ukXkM6+Pe/++f/77nmtCmDMl3Lnpu7+ec7m3ivQsifT1IFa/k7EaT6d11QtiLKg+nQoRdua7 + f6QiPTa+gBMRUcQ83yw680bSjz4/RzoNfexjK78PUmf1le87pENnf+G7+vVvoJ8M4eY3ku+n + 3flexTeaKPXPiQj3dEf6eGyFe0eL9vG+Kdz7eLSP66PnhaN/zXf0Ip1xvc9g50V6DvSzr1kQ + e3oAREREREREREREREREREQUHQZ8iYiIiIiIiIiIiIiIiIj6KEOoB612Jw6UV6HqfAOSE1Kx + sDC3u8ZFRERERERERERERERERERhBAz4ttqdeGPXF/jv0q9Q32hD/UUHHDY72uwO3HfzNd09 + RiIiIiIiIiIiIiIiIiIiCsCvpPP5Rgu++8eP8f7RWogJg+GwxkESXXHh/9p2pNsHSERERERE + RERERERERET0vZXfR2JSutctY/BwPPLIv8Fiaevp4fmZNOU67Pl4b9DH93y8F5Ov/Vqn+/EK + 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the importance of having good data in the high-Q region in order to allow a sensible background subtraction prior to calculating the correlation functions. + + But in summary, we can see that the Correlation Function analysis suggests that most of the quasi-lamellar nanostructure in the nylon fibres is actually amorphous polymer (~28% crystallinity, soft block thickness of ~53 Å). And certainly nylon fibres are highly flexible and extensible. + + + As a further check, a SasView model-fit to the same dataset is shown below. The model used (lamellar_stack_paracrystal) describes a sandwich of regular repeating lamellae of infinite lateral dimensions where the lamellar repeat distance is subject to Gaussian polydispersity. The model fit also incorporates 10% instrumental resolution smearing (as the data were collected with pinhole collimation). + + The SLD of the hard blocks has been fixed at the SLD for nylon, whilst the SLD of the matrix has been fixed at the SLD of heavy water. + + + iVBORw0KGgoAAAANSUhEUgAAB3wAAAQGCAYAAADc08uJAAAACXBIWXMAAA7EAAAOwQHoXPpe + AAAgAElEQVR4nOzde3hU1b0//vfae2YyuRKSkHARkkASlauACgQQRLCC51vv8LUey9EKtPYi + nlbP7ylwTnuAfr+tVcF67CNYLVrbA9Uear+Q9gAREAJoj9xBk5AbyD0h98xt7/37YzKTuc+e + ySSZwPv1PPshzOy91tpr7z23z16fJdqbGzT0FtFrNenUe7seT1x7rfdwBOulYNtrOvo1XN2+ + JcTdqdMrIu95fVzb9//z3/dcE2HOlHDnpu/2es7leBXpWRLp60GsrslYtafbeuoFMRY0n0pF + hJX5bh+pSPeNL+BERBQxzzeL7ryRXEefnyPthn72sZXfB6m7+sv3HdKhuxd8T7/+3egnQ7j+ + jeT7aW++V/GNJkrXZ0eEO9yRPh9b4d7Ron2+fwr3Ph7t8/roeeG4vvo7epH2uN4j2H2RngPX + 2dcsSH3dACIiIiIiIiIiIiIiIiIiig4DvkRERERERERERERERERE/ZQh1JMWmwOfVtSg5kIj + 0pLS8WBxQW+1i4iIiIiIiIiIiIiIiIiIwggY8G2zOfDW7mP4z4Nf4lqTFdcu2WG32tBhs+Px + 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AAAAAAAA9RSBLwAAAAAAAAAAAADUUwS+AAAAAAAAAAAAAFBPsYcvAAAAAAAO4Hv4rLNLAAAA + AAA0QC6SlJOT4+w6AAAAAABo0E707+zsEgAAAAAADZBL8+bNnV0DAAAAAAANWlJSkrNLAAAA + AAA0UIaLFy9anF0EAAAAAAAAAAAAAKDqGjm7AAAAAAAAAAAAAABA9RD4AgAAAAAAAAAAAEA9 + ReALAAAAAAAAAAAAAPUUgS8AAAAAAAAAAAAA1FMEvgAAAAAAAAAAAABQTxH4AgAAAAAAAAAA + AEA9ReALAAAAAAAAAAAAAPUUgS8AAAAAAAAAAAAA1FMEvgAAAAAAAAAAAABQTxH4AgAAAAAA + AAAAAEA9ReALAAAAAAAAAAAAAPUUgS8AAAAAAAAAAAAA1FMEvgAAAAAAAAAAAABQTxH4AgAA + AAAAAAAAAEA9ReALAAAAAAAAAAAAAPUUgS8AAAAAAAAAAAAA1FMEvgAAAAAAAAAAAABQTxH4 + AgAAAAAAAAAAAEA9ReALAAAAAAAAAAAAAPUUgS8AAAAAAAAAAAAA1FMEvgAAAAAAAAAAAABQ + TxH4AgAAAAAAAAAAAEA9ReALAAAAAAAAAAAAAPUUgS8AAAAAAAAAAAAA1FMEvgAAAAAAAAAA + AABQTxH4AgAAAAAAAAAAAEA9ReALAAAAAAAAAAAAAPUUgS8AAAAAAAAAAAAA1FMEvgAAAAAA + AAAAAABQTxH4AgAAAAAAAAAAAEA99f8B5zl+raQvqCMAAAAASUVORK5CYII= + + + + Although the fit is not very good, it nonetheless returns a lamellar repeat distance of ~87 Å with ~24% polydispersity (one standard deviation). The comparable values from the correlation function analysis were 74 Å and 7.5-11.5%, respectively. There is, however, quite a large discrepancy on the layer thickness. One additional piece of information the fit returns, that is not accessible by correlation function analysis, is the number of lamellae in each stack; here Nlayers: ~30. + + So which analysis is more correct? That very much depends on the system being studied. In this example, the amorphous/crystalline regions in a nylon fibre are certainly not regular infinite lamellar sheets of uniform thickness. The fitting model is therefore describing a very idealised structure. In contrast, the correlation function analysis is completely model-independent as far as the computation of Γ1(z), Γ3(z), and g1(z) are concerned, but the interpretation of those functions is then less precise. It also assumes that the water molecules are completely penetrating all of the amorphous regions. + + + Going Manual + + The ‘Automatic’ settings will attempt to use the most appropriate of each of the two procedures shown, based on the quality of the computed correlation function. + + + iVBORw0KGgoAAAANSUhEUgAAAjoAAAA/CAYAAADpGmJaAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAWoElEQVR4nO2dP2zb2B3Hv3fJ5SL0kgjuDZcOTUDpYJyTQ69CwSvQIEoGyTi4gxlAQzai + k3mDoQ4KSnToVLCIF8EFSgMdyqWTAOuGChebQ60gSzioN8QCjEi8dEo71NXlgCrI3w7UH5Li + X1GyJfr3AYxA4fN7v/fel+/9+Ps9Wu90Op23IAiCIAiCiCHvHrcBBEEQBEEQ04IcHYIgCIIg + Ygs5OgRBEARBxBZydAiCIAiCiC3k6BAEQRAEEVvI0SEIgiAIIraQo0MQBEEQRGwhR4cgCIIg + iNhCjg5BEARBELHl9HEbQBBetNtt3L9/H61WC91uF4lEAul0GtevX0cqlTpu84iYQXojJsmD + 1jPI9ad48Ph7fNd9hQuJ07j28TkI2Yu4lj5/3OadGN6hr4AgZpVqtYr9/X3cuHEDLMsikUjg + 8PAQrVYLX3/9Na5evYrV1dXjNpOICaQ3YpL8ZvsJtur/cr0u3LgIibt0hBadXGY+daUWk0gm + XX6K6nGbNxGMPuYh664lUIzcXx1yPolpDJku5yc+F9VqFS9evMCdO3eQzWaRSCQAAAsLC2BZ + 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The alternatives are then: + + + + Tangent Method: in circumstances where the form of the initial decay of the correlation function makes it difficult to establish a true tangent, the midpoint of the initial decay can be used instead; + + + + Long Period Method: in circumstances where the computed correlation function exhibits oscillations between the first minimum and the subsequent true maximum, it may be more appropriate to compute the Long Period as twice the distance of the first minimum. + + + + + + Optional + + The dataset \example_data\1d_data\ISIS_83404.txt is SANS from the same fibres but after exposure to sulphuric acid, a reagent known to degrade the amide linkage. If you wish, use correlation function analysis to examine how this changes the nanostructure. + + + Example 2 + + + + + + This example is actually a demonstration of correlation function analysis from a nanostructure that does not exhibit lamellar order. It is included here to highlight the potential applications of correlation function analysis in other fields. + + + + + The data in question is from a parametric survey, using a variety of techniques but including SANS, of how different heat treatments affect the nanostructure of Fe-Cr binary alloys. The work is described in Xu et al, Acta Mat., (2017) available at https://doi.org/10.1016/j.actamat.2017.12.008. This material undergoes spinodal decomposition on thermal ageing, resulting in Fe-rich and Cr-rich domains and a characteristic ‘spinodal peak’ in the SANS. + + + iVBORw0KGgoAAAANSUhEUgAAA38AAAKhCAIAAABvloAzAAMek0lEQVR4nOz953scV57nC57w + 6X0mvPeGAAEQ9JRoJVEqSVVSSSrTVW1mpuc+z9wXO3v32b9iX+zsPHfnmbvdPV1dpWqpquS9 + ISmSojcAARLee5PIRPrMsHtOnMxgEjSSKIlgkedbLCgyMuyJiDyf+J2fYTVNA0REREREP4JU + VYW/sTRNUxSF5+CfXOOjJEkcxymKIssywzBwSbgA/BZObNpBP0jBxqA2+xiIiIgeuNjNPgAi + IiKiR0oYH/H0N0IkRE9IqHB5nufzCTV/I4+yHoNTJCIiul2EPomIiIh+YG0wcGKaxCR6O1Pi + +XABiKH442PBnURERI+xCH0SERER/ZC6nR3hnNt9nAxCxWZOLOIKRURE9DiI0CcRERHRjy6a + prFpE1Nm/lf5H/E0ZFBFUViW/D4TERE9miK/bkREREQ/pPKH3fOnMYAaDp354/K3j9ET9CQi + InqERX7giIiIiH5I3T7ybvClYQG9ffn88fcHc5xEREREm6VHmT6R1QHbGIxff01FnygK//yj + 71Q4H/7JBgQoKuwejChMlAvE6DZ0GwZaGC4NaEZRFIZhwK22DVVfWFPVDYGuqirrc6ibEZ5o + I6SPISJ6xHW3GKNvsyQRERHRo6pHkz5lWWZZFv6a4xR64ObPOp2f4ANioqZqcAHEpTo4Mnq/ + kANKlKsPdxW5CX1lGn17O3riCQSYuQhWcHPEDS5MQWA10vipQEObIf0NERERERER0WOmR5M+ + 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Figure reproduced from Fig 6 in Xu et al, Acta Mat., (2017). + + + iVBORw0KGgoAAAANSUhEUgAABusAAAJOCAIAAAAxk621ABcupklEQVR4nGz9a68k25Ydhq1n + RGTm3ruqzvN23+5W89FNNiCSIC3KIGxIH2z4owDDMGDAP8p/yID9hZJlybRoWSKpFsnuvn3v + edZjPzIzItbLc4y5Vu46TdfNW6dq196ZESvWmo8xxxwztNKMNc20Zqqz1shf5Fctxnj5j7Gb + scG0qVhTzDqVRf5d/lzxI8aOV8HvTb7s8I/yyzbj5GXMxZpg8HL8hmb0V/P4FvzB9q/YbEwu + ZrL9q3I9+O7Kf4vyN6vfOb6/VvmW5GO/Bv1u0y+ovv6Rb4eX/JaDifxC5hflkhy+tZnim339 + /n6R/ClnfvlW+quMv96+OG4s8Ts//2T9aL1Pjxu/XSf+RVdL/pt51ZPehzO7Lpr+LFePN81P + bnzpjfYbaLGvuqkND0c/yxl75pt4vnSd8IZBfkr+FV/sz+EXd66XbW9PQL416N/l+6y9fVOx + +KLVR8Mbqvh8eVjO6dI6o2/Af5bN0Zy3levHT262fzpu9pcLevtldb31jrhWBmvFR6NPp902 + Y+K9y/s6XKfrW0N+WV2y9tkd4n338U282Motqgvh9KMrPqKN1+2efF8kfYjYi36s1XhQ+EDv + ceW+vd5KGbe085tkLSwfbnD8gYzFMber5IXZz/be39iGstIFP871r7enJduoZBzb/kxlrbLj + ozMl6jU31z4/wc0k3Ve3W9J3si06GgdeKjarb9W2WhzOnesrgJut3Efct/ITXp/T7WJb+2wN + blvOjAf4uuvGMS5ev7dhj/QftJ/9YBtPvfWdYcZl6xr48faZn2E/e3PHc7G2fp1+LFGFGTBz + 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Figure reproduced from Fig 9 in Xu et al, Acta Mat., (2017). + + Thin sections of the alloy specimens were examined by STEM-EELS and the resulting images processed to generate the 2D auto-correlation maps of the Fe/Cr distribution shown above. These maps were in turn radially-integrated to yield an averaged (auto)correlation function as shown below. + + + iVBORw0KGgoAAAANSUhEUgAABuoAAAH1CAIAAACftD+gAAUfw0lEQVR4nOz9Z3QkV3YuCoZN + 7xPeexTKoLz3xSrapjfdTaoNJbWkK+lKM2/NWm/+zdx/s+57T6O5sq027G5671me5b2D9x5I + IDOR3psws885mYEsVBVYJIuiyI4tNoRKREacOHFif/vbZxtOlmVKlXsngUDgf/2v//UP//AP + 0WgU/mm1Wrdv375161aLxZLJZOLxOEw4y7IMwwiCQNP0tz3e77BIkgTTaLPZ4He3233kyJGe + np50Os1xnNls3rdvH0w7z/Mw59ls9tse7PdKYOZhYWu1Wpj2Y8eOXb16FT6BxQwf7t69GxY8 + PJdIJFK41L/tIX9XhagIURThJyxmo9Go1+sHBwePHz/e29sLcwtru7y8/MEHH1y1ahUck0ql + QM/AL/An+CljUfXMVxOYN5hejUZTUlIC/7x27drnn38+MTFBNE9zc/P+/fvb2tqSyWQoFIID + QPN80+MBIW8T/AKYAu/gwMDA6dOnYUnAc4dR2e32xx577Nlnn62srARl+I2O549NiJYjOi0c + Dh8+fPi1116D9QCfwIN4+OGH/+RP/qSuro68rapl9TWlcAKJBoNpB8T58MMPDx06NDMzA48D + Fjmovqeffhp0IEw7HEYmv/BbqnwFgSUN00seAYAOTPunn3763nvvjY2NwScOh2Pv3r2w2uvr + 6+GfKr5/NbmTiiDrFh7B7Ozs+++///HHH3s8Hlj8tbW1Dz300BNPPFFaWgq6HT6BI4lS+kbH + 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Figure reproduced from Fig 10 in Xu et al, Acta Mat., (2017). + + For comparison, here are the (replotted) correlation functions as computed using SasView 5.x: + + + iVBORw0KGgoAAAANSUhEUgAAA+UAAAC9CAIAAABalEvaAAB6pklEQVR4nO3dBVwUTRsA8L1u + OLq7S1CQUMFubEEMDGzFLuzuxlbs7sJ67W4MVFRURLo7rt+5WzwRC6kDfP6/7/Pd25vbnTt2 + Zp7ZnZ0lSyQSDAAAAAAAAFAtkRWdAQAAAAAAAMAvQbwOAAAAAABA9QXxOgAAAAAAANVXeeP1 + hLDQa9HKbTt6qpLk6/KenNtz5WWOhmf3gY1My7l9AAAAAAAA/mXlidcFr8+ePHFox6mcho4t + Gqhy8IBd+PH8oY2b7up4qFyfGWyzb2kDPVrF5BQAAAAAAIB/T3nidZKWTZ0eI/smHsolCMXo + pXRdQcrD548NBwXP6ax6gzjo9IMvDbpZVFBWAQAAAAAA+OeUJ14nqptbq6t8IfBSv00JKRII + aQS2pvScOlOfUcjj/erD8fHx0dHRGRkZIpGoHHkAAFQuKpVap04dHR0dtFxQUJCampqXlycQ + CBSdLwDA79DpdENDQxqt6BI3Krbp6em5ublCoVCxGQMA/J6Ghoa2tnaJleW+31QgwogIoegl + AZNIJASi9Fw7gSARi3/5uV27dk2fPr1jx46qqqrlzQMAoNJ8+fIFxeurV69Gy+fPn+/du7ez + s7O6urqi8wUA+J3o6OgxY8YMGDAAf3ngwIFRo0a5u7srKysrNmMAgN/Lyso6efKkiopK8ZXl + i9clEpFQyOcLhCKx7JUEo3LUCaywa0/y3EyfXck17a/2q4+iGB/9u3nzZvy8HQCgerpz586m + 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reasonable! But the important point here is that the SANS-derived correlation functions are averaged over a far larger gauge volume (mm3) compared to that from the STEM-EELS measurements (nm3). + + + + Further Information + + For further information, please consult the + + SasView Tutorial Series + + or + + http://www.sasview.org + + or email + + help@sasview.org + + + Appendix + + Clicking the Export Transformed button in the Corfunc Perspective window writes a comma-separated text file with the extension .csv. + + + iVBORw0KGgoAAAANSUhEUgAAA34AAAO6CAYAAADAUIW2AAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOy9f4wc13Xv+a0ms8/Oo21GQWxGC4R6Di3iuevN9E4S27v/RLuQlQdTSdMm + vNGO0g0tdhyE+zZZZRPOQMt1mhMbUbqjJEISW/LbyS7RoxkocJh0ezlZrCQ+E4i8Cg2/ecNB + tZPRTqSxOc9QAqwjeGn9sMi5+0f/qu6uuudW3aqunuH3AxQg8dS599xzzzm3bvftGmd7e1t9 + 6Utfwvnz5/G+970Pu7u7IHcWv/M7v4PHH388azMIIYQQQgghKXG4+x/dTd8HXvpvsrSHZMBH + PzqHxx57jJs/QgghhBBCDii5rA0ghBBCCCGEEJIuOaVU1jYQQgghhBBCCEkRfuNHCCGEEEII + 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GkiEt8lhvqmWKsDQXWVUSxWMu2N31TGyTbEHj57PUYTHimXZT9rwDahcEsbNuwmGdursOtA6 + I3eMoyiojtvuJyyyK0TcD/Hw5ObmZn55eYlXr15lWzghZO95//49nj59ut5CTB3Fowmas/V2 + 9IyGgkF51ReWbO6ZDxXqKpqN+Bt5ABhoKAOU1xwzyXZ5NPFgsS9t7ft3Q4WwU6zTTyruer3F + W/EjhJA1YZy3/N/OWk8p4s8r7NwzHyrUFSGEEAFqHReVPo62mDFnNI4eTYr1h9sWgBDy2DCh + F4/Qcvbw1tCbrXumT0NnlvWoYx3PfKhQV4QQQsSo9WvMtli+1plttfxNwoEfIWTDWK9Lr29b + DEII2Us4kUIIWQ2mehJCCCGEEELIA+d3T5482bYMhJAdZZc3KBPy0KC/EUIWMB7sJ7teb/8H + mfIg2hCwrN4AAAAASUVORK5CYII= + + + + The columns in this file are, in order of occurrence: + + + + The real-space distance (in the inverse of the units of the input data) + + + The value of Γ1(z) + + + The value of Γ3(z) + + + The value of g1(z) + + + + + + + + WARNING! + SasView will load this file but it will incorrectly interpret the second & third columns (because it will be expecting dI and dQ values, not Γ3(z) and g1(z) values)! + + + + + + + + \ No newline at end of file diff --git a/correlation_function_analysis_in_sasview_v6.pdf b/correlation_function_analysis_in_sasview_v6.pdf new file mode 100644 index 0000000..55e77e5 Binary files /dev/null and b/correlation_function_analysis_in_sasview_v6.pdf differ