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+ - + - + - + - + - + - + - + - + - + - + - + - + + + + + - - + + - + + + + - + - 1/23 + 15/26 @@ -2346,36 +2908,36 @@ - - + + Ri - - + + Ri - - + + −1 - - + + +1 - - + + −3 - - + + +3 - - + + ±3 - + /9j/4AAQSkZJRgABAQEBLAEsAAD//gATQ3JlYXRlZCB3aXRoIEdJTVD/2wBDAAEBAQEBAQEB AQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEB AQH/2wBDAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEBAQEB @@ -92164,61 +92726,68 @@ + + SasView Tutorials + + Basic 1D Data Fitting + in SasView Version 5 - SasView Tutorials - - Basic 1D Data Fitting - in SasView Version 5 - - - www.sasview.org - - - - - - - Preamble + + www.sasview.org + + + + + + + Preamble - 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 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: 21 August 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 +92796,34 @@ - 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 +93002,24 @@ - ( + ( - ( + ( I - ( + ( Q - ) + ) meas @@ -92456,17 +93028,17 @@ - ( + ( Q - ) + ) calc - ) + ) 2 @@ -92475,22 +93047,22 @@ - ( + ( Q - ) + ) 2 - ) + ) / - ( + ( @@ -92504,7 +93076,7 @@ - ) + ) @@ -92512,150 +93084,154 @@ - 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. 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 @@ -92663,14 +93239,14 @@ V - ( + ( Δ ρ - ) + ) 2 @@ -92679,154 +93255,154 @@ - VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAfoLAAAu - AgAAXAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAPkLAAAtAgAAlQAB - AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv - biBTZXJpZgAAAAAAAKYBAAAAAAAAAAAFAAAAAAACAP8DAAAAAAAAAAEA/wMAAAAAAIgAAQAC - AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAABuAAAAugEAAAEASY0AAAAA - AAEAAQBJAIwAAQAAAAAAiwABAAIAAAAfAIoAAQA8AAAAAwA2AAAACgBPcGVuU3ltYm9sAAAA - AAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAQD/AwAAAAAAiAABAAIAAAABAIcAAQAF - AAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAEsBAAC6AQAAAQAAACgAjwAAAAAAAQABACgA - 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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 +93410,11 @@ - ( + ( Q - ) + ) meas @@ -92847,11 +93423,11 @@ - ( + ( Q - ) + ) calc @@ -92860,66 +93436,68 @@ - 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 +94140,20622 @@ - 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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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. Click the Compute/Plot button. + + + + + + Tip: Upto and including SasView 5.0.4 the Compute/Plot button was labelled Show Plot. - - 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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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. 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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. + + + iVBORw0KGgoAAAANSUhEUgAAB4AAAAQ4CAIAAABnsVYUAAAgAElEQVR4nOzde3xU930n/O/v + 3Oaqy+h+AckCSYAkzB2MZIfYNcYC2yFpA9v22TptY3i6fXZhd5/k9Wodb/e1jp+28bOvB7pJ + di13k9ImTaF1QhKDwCRNiI0M5maMECDJgLhJQpcZ3eZ6zu/3/HE0o5E0MxrdEIbPO3nZo3PO + /H6/GR1h6aMv3x8TQhAAAAAA3Bfsz67M9RIm7e5/SJvrJQDMpPz8/LleAgAAAMAjhCGABgAA + AAAAAAAAAIDZIM31AgAAAAAAAAAAAADg4YQAGgAAAAAAAAAAAABmBQJoAAAAAAAAAAAAAJgV + CKABAAAAAAAAAAAAYFYo8U4MDg41X225dfuud8jLGEtJcc6fX7iwdIHDYb+f6wMAAAAAAAAA + AACAz6jYAfTVqy0H9v/k2qc3BgYGucFlRbbZrS5X+sKFJS++VFtSUnyfVwkAAAAAAAAAAAAA + nzlMCDHm0KlTZ77113/j9/s0VbNaLZqmqaoiyzIRCSKH3fbHX/2DqqUVc7FaAAAAAAAAAAAA + gAcLYyzB2fEB7BxijJ05c2bVqlUxz549e3b16tUzu+CxPaCvXG7+1l//jd/vd9jtaWmp6elp + 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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. 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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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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 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. 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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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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 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 +118754,23405 @@ - 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). - - Example 2 - + + 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. + 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. And in the absence of electrolyte SDS micelles are reported to be approximately spherical. - - To start with, select the sphere model. - - - iVBORw0KGgoAAAANSUhEUgAABBEAAAOGCAYAAAC6PwgeAAAACXBIWXMAAA7EAAAOwwHaapjc - AAJrWklEQVR4nOydB2AURRfH/9cvvfeQUELvvTcLvYlIB+mgUkREBVSkKPoBilhAulRBUUA6 - Kr1K7x1CIKT3crn67du7Sy6VAIGAvB+u2dudfTM7uzu7782bN/I6deqYwDAMwzAMwzAMwzAM - 8wDkQz5bVNxlYBiGYRiGYRiGYRjmOUBe3AVgGIZhGIZhGIZhmGcNmUyGlMR43Lp6BbHR0ZBK - pY8t02g0wMPLG6XKlYeTqzuSE+KemHx3Hz9k3L6GVWOGQiLIlskVjy2fkEsgKRJBDMMwDMMw - DMMwDPNfIT42HvdvXUWLupVQt25N6PX6x5Ypl8vw77+nsf/4JQRVqIo7156cfF2qBheW/4Qd - /24FmSe0Wt1jyxfzyGlDMBmNuHH2X1w/fQzalES4e/uj8RsDIVcqYdAVTaYMwzAMwzAMwzAM - 8yyj1eugVsrh6+eDG+EJkEkfvwPezcVJlKdWXoNOr3+i8jXp6VDIpVBEhiE6LAySIvNEkJgL - KpEIwlUq/LlgNhIjwuDs4gpvb29hux4X/voDZeq3hLOXH/TajCLJmGEYhmEYhmEYhmGeVURd - WfjPZAKMwiIpgikJSA7JI7nSQshXCjr6nm1bcPzgfmi1WiiVysy/IydNhtrODtqMjDzlS8go - QbINBpiMBmFFKv4mbLOSWMpga8IwWbbDJMlKbVnNNCKoHRwQH3kfSZF34eXtDWcXZ3h6uEMm - lyM5MQERF/6FsnZzKNR2edeG0hlu0hgMb18bsWnAsJ9PoHElT5hikpCX/4Is/hx2//oFLrsO - 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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. + + + iVBORw0KGgoAAAANSUhEUgAABpAAAAP7CAYAAABcKM3/AAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXgU55nv/W9V9aZ9QYgdsUiyzWIHcGIscMAYHAPzToiTQOKZhGxA4lkg + M7Hnndg+c2XAmXfiLDDnHOc1JDNxJhvMOIckA4rHBoMDMrbjXQZHEggJmx2hXWp1d9X5oxe1 + pJbU2lic3+e6+lKruup57qqublX3red+DMdxHEREREREJCnG379ztUMYktN/nXW1QxC5qsaN + G3e1QxARERERuS4YSiCJiIiIiIiIiIiIiIhIPPNqByAiIiIiIiIiIiIiIiLXFiWQRERERERE + REREREREpAslkERERERERERERERERKQLV28PtLS08sunfs3Bg4c5f+4iLrfFxInj+fCHF7Dy + T+4mJSXlSsYpIiIiIiIiIiIiIiIyZIZh9Pm44zhXKJLkGIbB73//e+bNm5fw8VdeeYVbb711 + 2OM2nAQt1tac4utf38zlusukpKTg8/nweNyYponjOOTl5bLpb/6CcePGDGswIiIiIiIiIiIi + IiIiI8kwjF6TLX09drW88sor3L5gIS8cPtQjidTXY0PVo4RdS0srX//7f6SxoZHs7Czy8nIZ + MyaPcWPzGT9+LOPHjcFxYPv//2+0t7f330PpBgzDiNw2UDrAAEs3GCzYVtWzzQ2lULWNBcYC + uj88VFXbFvQfc9x+9Yivy2rRdoY/ThERERERERERERERSU70O/34+/G3a9W8efN44fAhbl+w + 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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 respective empirical formulae and densities in the relevant boxes and click Calculate (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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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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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. 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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. + + + iVBORw0KGgoAAAANSUhEUgAABo4AAAP9CAYAAACzFp+5AAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXxU53n//c85ZzbtC0LsSIAk2yx2ACfGAgcbg2OgT0KcBBK3CdmAxPk1 + kDZ2n8b2r68WnD6Ns0Dbx3mMkyZOsxRa50eSguLaYHBAxk68y+BIAiFhsyO0S6OZOef5YxaN + pJE02lic7/v1kpHOnHPf11lGHp3r3NdtOI7jICIiIiIiSTH+9u0rHcKwnPpq1pUOQeSKmjBh + wpUOQURERETkqmYocSQiIiIiIiIiIiIiIiIA5pUOQERERERERERERERERK4OShyJiIiIiIiI + iIiIiIgIoMSRiIiIiIiIiIiIiIiIRLj6eqG1tY1fPvVrDhw4xLmzF3C5LSZPnsgHP7iQlX92 + FykpKZczThERERERERERERERkWEzDKPf1x3HuUyRJMcwDP7whz8wf/78hK+//PLL3HzzzSMW + t+EkaKmu9iTf+MZmLtVfIiUlBZ/Ph8fjxjRNHMchLy+XTX/1FSZMGDciQYiIiIiIiIiIiIiI + iFwOhmH0mWTp77Ur5eWXX+bWhYt44dDBXsmj/l4bql6l6lpb2/jG3/4DTY1NZGdnkZeXy7hx + 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Also note that the volfraction parameter has dropped to ~1 %. - - So how might the fit be improved further? 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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. + + 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 data to button to create a 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. + + + + + iVBORw0KGgoAAAANSUhEUgAABo4AAAP7CAYAAABlT3ykAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXxU5333/c85ZzbtC0LsiEWSbRY7gBNjgYNNwDHQJ3GcFBK3CdmAxF2g + bew+je27rxacPo2zQO/7dh5D0sZplkLr3iQpKK4NBgdk7MS7DI4kEBI2O0K7NNs59x+zaCSN + pNHG4nzfr9e8NDpzznX9zpkzozPz0/W7DMdxHEREREREJCXG37xztUMYltN/nnO1QxC5qiZM + mHC1QxARERERuaYZShyJiIiIiIiIiIiIiIgIgHm1AxAREREREREREREREZFrgxJHIiIiIiIi + IiIiIiIiAihxJCIiIiIiIiIiIiIiIlGuvh5oa2vnP5/+BQcPHub8uYu43BaTJ0/kwx9exKo/ + uJu0tLQrGaeIiIiIiIiIiIiIiMiwGYbR7+OO41yhSFJjGAa//e1vWbBgQdLHX3nlFW699dYR + 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- - Indeed this does improve the fit further. 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. But this time set the volfraction and charge parameters to the values determined from the fit to the sphere model; 0.017 and 20, respectively. - - Check radius_polar and run the fit. + + 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 1:1.1. 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. + + + - 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. - - iVBORw0KGgoAAAANSUhEUgAABA0AAAMeCAYAAAB2mP1WAAAACXBIWXMAAA7EAAAOwwHaapjc - AALS8klEQVR4nOydB2BURRPH/9cvl94TEiD03rt0FKkiitIEEaRZEAUUBZVPULAhKgpSlSLS - FFAQEJWi9N47CSW9X9rl6vdm7y65FCB0kPmFx72yb3bfvjqzs7PKhg0b2sAwDMMwDMMwDMMw - DFMI5eD/zb3XZWAYhmEYhmEYhmEY5j5Eea8LwDAMwzAMwzAMwzD3AplMBrlcjqN7dyE5MYHW - iOVbwWq1Sv/b0LB5S3j6+CEjLQWRZ04L+XK54pbLTPL9AwNRrnIVuPv6wxYThT2L5+P8/j1Q - 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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 - + + + + + + + + + + + + + + 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 (Vidulich et al, J Phys Chem, 1967) - - Enter these values and click Show Plot. - - - iVBORw0KGgoAAAANSUhEUgAABBEAAAMgCAYAAAB1evrtAAAACXBIWXMAAA7EAAAOwwHaapjc - AAKDJklEQVR4nOydB2AURRfH/9cvl0vvnRZ6L1KUJkoRVGx0EBAFCyBNRFQUVPRDBBHpTZqK - IkU6SpEivUuHEFJISL9ccv3u25nLXS4FCCUQ4P1wzZbZmdnZvd19b1+RNmzY0AaCIAiCIAiC - 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Increase it to 150 Å. + + Now check the background, radius, volfraction, and charge parameters and click Fit. + + + + iVBORw0KGgoAAAANSUhEUgAABpAAAAP7CAYAAABcKM3/AAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXxU553n+885pzbtC0LsiEWSbRY7gBNjgYNNwDHQN3GcNCSeTsgGJM5M + Q3pi953Ynr7d4PTtOAv0zDjXkEzH6SwNPe4hSYPiscHggIzteJfBkQRCwmZHaJdKVXXO/aMW + VUklqbSxON/361UvlU6d8zy/c+pU6VT99Pwew3EcBxERERERSYnxX9692iEMy+m/zLnaIYhc + VRMmTLjaIYiIiIiIXBcMJZBEREREREREREREREQknnm1AxAREREREREREREREZFrixJIIiIi + IiIiIiIiIiIikkAJJBEREREREREREREREUng6uuBtrZ2/u3p33Dw4GHOn7uIy20xefJEPvrR + Raz6s7tJS0u7knGKiIiIiIiIiIiIiIgMm2EY/T7uOM4ViiQ1hmHwhz/8gQULFiR9/NVXX+XW + W28d8bgNJ0mL9XWn+Pa3N3O54TJpaWn4fD48HjemaeI4DgUF+Wz6q28wYcK4EQ1GRERERERE + RERERERkNBmG0Weypb/HrpZXX32V2xct5sXDh3olkfp7bLh6lbBra2vn2//l72huaiY3N4eC + gnzGjStgwvhCJk4cz8QJ43Ac2P7//ROdnZ0D91C+AcMwIrcNlA8ywPINBou21fRuc0M51Gxj + kbGIng8PV822RQPHHLdfveJLWC3azsjHKSIiIiIiIiIiIiIiqYl+px9/P/52rVqwYAEvHj7E + 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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 +142167,5458 @@ - 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. + + + iVBORw0KGgoAAAANSUhEUgAABpAAAAP8CAYAAABBLf1HAAAACXBIWXMAAA7DAAAOwwHHb6hk + AAAgAElEQVR4nOzdeXxU553n+885pzbtC0LsiEWSbRY7gBNjgYNNwDHQN3GcNCSeTsgGJM5M + Q3pi953Ynr7d4PTtOAv0zDjXkEzH6SwNPe4hSYPiscHggIzteJfBkQRCwmZHaJdKVXXO/aMW + VUklqbSxON/361UvlU6d8zy/c+pU6VT99Pwew3EcBxERERERSYnxX9692iEMy+m/zLnaIYhc + VRMmTLjaIYiIiIiIXBcMJZBEREREREREREREREQknnm1AxAREREREREREREREZFrixJIIiIi + IiIiIiIiIiIikkAJJBEREREREREREREREUng6uuBtrZ2/u3p33Dw4GHOn7uIy20xefJEPvrR + Raz6s7tJS0u7knGKiIiIiIiIiIiIiIgMm2EY/T7uOM4ViiQ1hmHwhz/8gQULFiR9/NVXX+XW + W28d8bgNJ0mL9XWn+Pa3N3O54TJpaWn4fD48HjemaeI4DgUF+Wz6q28wYcK4EQ1GRERERERE + RERERERkNBmG0Weypb/HrpZXX32V2xct5sXDh3olkfp7bLh6lbBra2vn2//l72huaiY3N4eC + gnzGjStgwvhCJk4cz8QJ43Ac2P7//ROdnZ0D91C+AcMwIrcNlA8ywPINBou21fRuc0M51Gxj + 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IIAAEgAAAAAAAAAAAAL+P4cZHAeIq8cpAAAAAElFTkSuQmCC - Whilst this looks like a good fit, notice that the Reduced Chi2 is 4780, and the residuals are quite poor. 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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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: 21 August 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 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 + + + + + + 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 respective empirical formulae and densities in the relevant boxes and click Calculate (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. 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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. + + 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 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. 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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. + + 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 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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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