Changeset f40f743 in sasview for sansmodels/src/sans/models/media/model_functions.html
- Timestamp:
- Aug 24, 2012 12:49:46 PM (12 years ago)
- Branches:
- master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
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sansmodels/src/sans/models/media/model_functions.html
r17574ae rf40f743 8 8 <li style="line-height: 115%;"><a href="#Introduction"><strong>Introduction</strong></a></li> 9 9 <li style="line-height: 115%;"><a href="#Shapes"><strong>Shapes</strong></a>: <a href="#SphereModel">SphereModel</a>, <a href="#BinaryHSModel">BinaryHSModel</a>, <a href="#FuzzySphereModel">FuzzySphereModel</a>, <a href="#RaspBerryModel">RaspBerryModel</a>, <a href="#CoreShellModel">CoreShellModel</a>, <a href="#Core2ndMomentModel">Core2ndMomentModel</a>, <a href="#CoreMultiShellModel">CoreMultiShellModel</a>, <a href="#VesicleModel">VesicleModel</a>, <a href="#MultiShellModel">MultiShellModel</a>, <a href="#OnionExpShellModel">OnionExpShellModel</a>, <a href="#SphericalSLDModel">SphericalSLDModel</a>, <a href="#LinearPearlsModel">LinearPearlsModel</a>, <a href="#PearlNecklaceModel">PearlNecklaceModel</a> , <a href="#CylinderModel">CylinderModel</a>, <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>, <a href="#CoreShellBicelleModel">CoreShellBicelleModel</a>,<a href="#HollowCylinderModel">HollowCylinderModel</a>, <a href="#FlexibleCylinderModel">FlexibleCylinderModel</a>, <a href="#FlexibleCylinderModel">FlexCylEllipXModel</a>, <a href="#StackedDisksModel">StackedDisksModel</a>, <a href="#ParallelepipedModel">ParallelepipedModel</a>, <a href="#CSParallelepipedModel">CSParallelepipedModel</a>, <a href="#EllipticalCylinderModel">EllipticalCylinderModel</a>, <a href="#BarBellModel">BarBellModel</a>, <a href="#CappedCylinderModel">CappedCylinderModel</a>, <a href="#EllipsoidModel">EllipsoidModel</a>, <a href="#CoreShellEllipsoidModel">CoreShellEllipsoidModel</a>, <a href="#TriaxialEllipsoidModel">TriaxialEllipsoidModel</a>, <a href="#LamellarModel">LamellarModel</a>, <a href="#LamellarFFHGModel">LamellarFFHGModel</a>, <a href="#LamellarPSModel">LamellarPSModel</a>, <a href="#LamellarPSHGModel">LamellarPSHGModel</a>, <a href="#LamellarPCrystalModel">LamellarPCrystalModel</a>, <a href="#SCCrystalModel">SCCrystalModel</a>, <a href="#FCCrystalModel">FCCrystalModel</a>, <a href="#BCCrystalModel">BCCrystalModel</a>.</li> 10 <li style="line-height: 115%;"><a href="#Shape-Independent"><strong>Shape-Independent</strong></a>: <a href="#Absolute%20Power_Law">AbsolutePower_Law</a>, <a href="#BEPolyelectrolyte">BEPolyelectrolyte</a>, <a href="#BroadPeak">BroadPeak,<span><span style="text-decoration: underline;"><span style="color: blue;">CorrLength</span></span></span><span>,</span></a> <a href="#DAB_Model">DAB_Model</a>, <a href="#Debye">Debye</a>, <a href="#Number_Density_Fractal">FractalModel</a>, <a href="#FractalCoreShell">FractalCoreShell</a>, <a href="#GaussLorentzGel">GaussLorentzGel</a>, <a href="#Guinier">Guinier</a>, <a href="#GuinierPorod">GuinierPorod</a>, <a href="#Lorentz">Lorentz</a>, <a href="#Mass_Fractal">MassFractalModel</a>, <a href="#MassSurface_Fractal">MassSurfaceFractal</a>, <a href="#Peak%20Gauss%20Model">PeakGaussModel</a>, <a href="#Peak%20Lorentz%20Model">PeakLorentzModel</a>, <a href="#Poly_GaussCoil">Poly_GaussCoil</a>, <a href="#PolymerExclVolume">PolyExclVolume</a>, <a href="#PorodModel">PorodModel</a>, <a href="#RPA10Model">RPA10Model</a>, <a href="#StarPolymer">StarPolymer</a>, <a href="#Surface_Fractal">SurfaceFractalModel</a>, <a href="#Teubner%20Strey">Teubner Strey</a>, <a href="#TwoLorentzian">TwoLorentzian</a>, <a href="#TwoPowerLaw">TwoPowerLaw</a>, <a href="#UnifiedPowerRg">UnifiedPowerRg</a>, <a href="#LineModel">LineModel</a>, <a href="#ReflectivityModel">ReflectivityModel</a>, <a href="#ReflectivityIIModel">ReflectivityIIModel</a>, <a href="#GelFitModel">GelFitModel</a> , <a href="#FractalO_Z">FractalO_Z</a>.</li>10 <li style="line-height: 115%;"><a href="#Shape-Independent"><strong>Shape-Independent</strong></a>: <a href="#Absolute%20Power_Law">AbsolutePower_Law</a>, <a href="#BEPolyelectrolyte">BEPolyelectrolyte</a>, <a href="#BroadPeak">BroadPeak,<span><span style="text-decoration: underline;"><span style="color: blue;">CorrLength</span></span></span><span>,</span></a> <a href="#DAB_Model">DAB_Model</a>, <a href="#Debye">Debye</a>, <a href="#Number_Density_Fractal">FractalModel</a>, <a href="#FractalCoreShell">FractalCoreShell</a>, <a href="#GaussLorentzGel">GaussLorentzGel</a>, <a href="#Guinier">Guinier</a>, <a href="#GuinierPorod">GuinierPorod</a>, <a href="#Lorentz">Lorentz</a>, <a href="#Mass_Fractal">MassFractalModel</a>, <a href="#MassSurface_Fractal">MassSurfaceFractal</a>, <a href="#Peak%20Gauss%20Model">PeakGaussModel</a>, <a href="#Peak%20Lorentz%20Model">PeakLorentzModel</a>, <a href="#Poly_GaussCoil">Poly_GaussCoil</a>, <a href="#PolymerExclVolume">PolyExclVolume</a>, <a href="#PorodModel">PorodModel</a>, <a href="#RPA10Model">RPA10Model</a>, <a href="#StarPolymer">StarPolymer</a>, <a href="#Surface_Fractal">SurfaceFractalModel</a>, <a href="#Teubner%20Strey">Teubner Strey</a>, <a href="#TwoLorentzian">TwoLorentzian</a>, <a href="#TwoPowerLaw">TwoPowerLaw</a>, <a href="#UnifiedPowerRg">UnifiedPowerRg</a>, <a href="#LineModel">LineModel</a>, <a href="#ReflectivityModel">ReflectivityModel</a>, <a href="#ReflectivityIIModel">ReflectivityIIModel</a>, <a href="#GelFitModel">GelFitModel</a>.</li> 11 11 <li style="line-height: 115%;"><a href="#Model"><strong>Customized Models</strong></a>: <a href="#testmodel">testmodel</a>, <a href="#testmodel_2">testmodel_2</a>, <a href="#sum_p1_p2">sum_p1_p2</a>, <a href="#sum_Ap1_1_Ap2">sum_Ap1_1_Ap2</a>, <a href="#polynomial5">polynomial5</a>, <a href="#sph_bessel_jn">sph_bessel_jn</a>.</li> 12 12 <li style="line-height: 115%;"><a href="#Structure_Factors"><strong>Structure Factors</strong></a>: <a href="#HardsphereStructure">HardSphereStructure</a>, <a href="#SquareWellStructure">SquareWellStructure</a>, <a href="#HayterMSAStructure">HayterMSAStructure</a>, <a href="#StickyHSStructure">StickyHSStructure</a>.</li> … … 5426 5426 <p> </p> 5427 5427 <p style="margin-left: 0.55in; text-indent: -0.3in;"><strong><span style="font-size: 14pt;">3.11.</span></strong><strong><span style="font-size: 7pt;"> </span></strong><strong><span style="font-size: 14pt;"><a name="MassSurface_Fractal"></a><a name="MassSurfaceFractal"></a>MassSurfaceFractal</span></strong></p> 5428 <p style="margin-left: 0.25in;">Calculates the scattering based on the Schmidt/Hurd references (below). </p> 5428 <p> A number of natural and commercial processes form high-surface area materials as a result of the vapour-phase aggregation of primary particles. Examples of such materials include soots, aerosols, and ‘fume’ or pyrogenic silicas. These are all characterised by cluster mass distributions (sometimes also cluster size distributions) and internal surfaces that are fractal in nature. The scattering from such materials displays two distinct breaks in log-log representation, corresponding to the radius-of-gyration of the primary particles, rg, and the radius-of-gyration of the clusters (aggregates), Rg. Between these boundaries the scattering follows a power law related to the mass fractal dimension, Dm, whilst above the high-Q boundary the scattering follows a power law related to the surface fractal dimension of the primary particles, Ds.</p> 5429 <p style="margin-left: 0.55in;">The scattered intensity I(Q) is then calculated using a modified Ornstein-Zernicke equation:</p> 5429 5430 <p style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 85pt;"><br /> </span></p> 5430 5431 <p style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/masssurface_fractal_eq1.jpg" alt="" /></span><span style="font-size: 14pt;"> </span></p> … … 7030 7031 <p style="margin-left: 0.25in; text-indent: 0.25in;">H. Benoit, J. Polymer Science., 11, 596-599 (1953)</p> 7031 7032 <p> </p> 7032 <p style="margin-left: 0.55in; text-indent: -0.3in;"><strong><span style="font-size: 14pt;">3.30.</span></strong><strong><span style="font-size: 7pt;"> </span></strong><a name="FractalO_Z"></a><strong><span style="font-size: 14pt;">FractalO_Z</span></strong></p>7033 <p> A number of natural and commercial processes form high-surface area materials as a result of the vapour-phase aggregation of primary particles. Examples of such materials include soots, aerosols, and ‘fume’ or pyrogenic silicas. These are all characterised by cluster mass distributions (sometimes also cluster size distributions) and internal surfaces that are fractal in nature. The scattering from such materials displays two distinct breaks in log-log representation, corresponding to the radius-of-gyration of the primary particles, rg, and the radius-of-gyration of the clusters (aggregates), Rg. Between these boundaries the scattering follows a power law related to the mass fractal dimension, Dm, whilst above the high-Q boundary the scattering follows a power law related to the surface fractal dimension of the primary particles, Ds.</p>7034 <p style="margin-left: 0.55in;">The scattered intensity I(Q) is then calculated using a modified Ornstein-Zernicke equation:</p>7035 <p><img src="img/image236.gif" alt="" /></p>7036 <p style="margin-left: 0.55in;">Where:</p>7037 <p><span><img src="img/image237.gif" alt="" /></span></p>7038 <p> </p>7039 <p> This example dataset was produced using 300 data points, qmin=0.001 Å-1, qmax=0.3 Å-1 and the default values:</p>7040 <p style="margin-left: 0.25in; text-align: center;" align="center"><strong>Default input parameter values</strong></p>7041 <div align="center">7042 <table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0">7043 <tbody>7044 <tr style="height: 19.25pt;">7045 <td style="border: 1pt solid width: 107pt; height: 19.25pt;" valign="top" width="143">7046 <p>Parameter name</p>7047 </td>7048 <td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7049 <p>Units</p>7050 </td>7051 <td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7052 <p>Default value</p>7053 </td>7054 </tr>7055 <tr style="height: 19.25pt;">7056 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">7057 <p>Background</p>7058 </td>7059 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7060 <p>cm-1</p>7061 </td>7062 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7063 <p>0.01</p>7064 </td>7065 </tr>7066 <tr style="height: 19.25pt;">7067 <td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 19.25pt;">7068 <p>Scale</p>7069 </td>7070 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7071 <p>cm-1</p>7072 </td>7073 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7074 <p>10000.0</p>7075 </td>7076 </tr>7077 <tr style="height: 19.25pt;">7078 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">7079 <p>Cluster Rg</p>7080 </td>7081 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7082 <p>Å</p>7083 </td>7084 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7085 <p>3520.0</p>7086 </td>7087 </tr>7088 <tr style="height: 19.25pt;">7089 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">7090 <p>Mass fractal exponent</p>7091 </td>7092 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143"> </td>7093 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7094 <p>1.8</p>7095 </td>7096 </tr>7097 <tr style="height: 19.25pt;">7098 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">7099 <p>Primary particle Rg</p>7100 </td>7101 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7102 <p>Å</p>7103 </td>7104 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7105 <p>82.0</p>7106 </td>7107 </tr>7108 <tr style="height: 19.25pt;">7109 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 19.25pt;" valign="top" width="143">7110 <p>Surface fractal exponent</p>7111 </td>7112 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7113 <p>cm-1</p>7114 </td>7115 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143">7116 <p>2.5</p>7117 </td>7118 </tr>7119 </tbody>7120 </table>7121 </div>7122 <p style="margin-left: 0.5in;"> </p>7123 <p style="margin-left: 0.5in;"> </p>7124 <p style="margin-left: 0.5in; text-align: center;" align="center"><img id="Picture 11" src="img/image238.gif" alt="" width="470" height="336" /></p>7125 <p style="text-align: center;" align="center"><strong>Figure. 1D plot using the default values (w/300 data points, qmin=0.001, and qmax=0.3).</strong></p>7126 <p style="margin-left: 0.5in; text-align: center;" align="center"> </p>7127 <p style="margin-left: 0.25in;"> REFERENCES</p>7128 <p style="margin-left: 0.25in;">PW Schmidt, J Appl Cryst, (1991), 24, 414-435.</p>7129 <p style="margin-left: 0.25in;">AJ Hurd, DW Schaefer, JE Martin, Phys Rev A, (1987), 35, 2361-2364.</p>7130 7033 <p> </p> 7131 7034 <p style="margin-left: 0.25in; text-indent: -0.25in;"><strong><span style="font-size: 16pt;">4.</span></strong><strong><span style="font-size: 7pt;"> </span></strong><a name="Model"></a><strong><span style="font-size: 16pt;">Customized Models </span></strong></p>
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