Changeset 5bf0331 in sasview for src/sans/models/media/model_functions.html
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- May 5, 2014 9:21:47 AM (11 years ago)
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src/sans/models/media/model_functions.html
r6771d94 r0089be3 8 8 <li><a href="#Introduction"><b>Introduction</b></a></li> 9 9 <li><a href="#Shapes"><b>Shapes</b></a>: 10 <ul> 11 <li>Sphere based:<br/> 12 <a href="#SphereModel">SphereModel (Magnetic 2D Model)</a>, 13 <a href="#BinaryHSModel">BinaryHSModel</a>, 14 <a href="#FuzzySphereModel">FuzzySphereModel</a>, 15 <a href="#RaspBerryModel">RaspBerryModel</a>, 16 <a href="#CoreShellModel">CoreShellModel (Magnetic 2D Model)</a>, 17 <a href="#Core2ndMomentModel">Core2ndMomentModel</a>, 18 <a href="#CoreMultiShellModel">CoreMultiShellModel (Magnetic 2D Model)</a>, 19 <a href="#VesicleModel">VesicleModel</a>, 20 <a href="#MultiShellModel">MultiShellModel</a>, 21 <a href="#OnionExpShellModel">OnionExpShellModel</a>, 22 <a href="#SphericalSLDModel">SphericalSLDModel</a>, 23 <a href="#LinearPearlsModel">LinearPearlsModel</a>, 24 <a href="#PearlNecklaceModel">PearlNecklaceModel</a> 25 </li> 26 <li>Cylinder based:<br/> 27 <a href="#CylinderModel">CylinderModel (Magnetic 2D Model)</a>, 28 <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>, 29 <a href="#CoreShellBicelleModel">CoreShellBicelleModel</a>, 30 <a href="#HollowCylinderModel">HollowCylinderModel</a>, 31 <a href="#FlexibleCylinderModel">FlexibleCylinderModel</a>, 32 <a href="#FlexibleCylinderModel">FlexCylEllipXModel</a>, 33 <a href="#StackedDisksModel">StackedDisksModel</a>, 34 <a href="#EllipticalCylinderModel">EllipticalCylinderModel</a>, 35 <a href="#BarBellModel">BarBellModel</a>, 36 <a href="#CappedCylinderModel">CappedCylinderModel</a>, 37 <a href="#PringleModel">PringleModel</a> 38 </li> 39 <li>Parallelpipeds:<br/> 40 <a href="#ParallelepipedModel">ParallelepipedModel (Magnetic 2D Model)</a>, 41 <a href="#CSParallelepipedModel">CSParallelepipedModel</a> 42 </li> 43 <li>Ellipsoids:<br/> 44 <a href="#EllipsoidModel">EllipsoidModel</a>, 45 <a href="#CoreShellEllipsoidModel">CoreShellEllipsoidModel</a>, 46 <a href="#TriaxialEllipsoidModel">TriaxialEllipsoidModel</a> 47 </li> 48 <li>Lamellar:<br/> 49 <a href="#LamellarModel">LamellarModel</a>, 50 <a href="#LamellarFFHGModel">LamellarFFHGModel</a>, 51 <a href="#LamellarPSModel">LamellarPSModel</a>, 52 <a href="#LamellarPSHGModel">LamellarPSHGModel</a> 53 </li> 54 <li>Paracrystals:<br/> 55 <a href="#LamellarPCrystalModel">LamellarPCrystalModel</a>, 56 <a href="#SCCrystalModel">SCCrystalModel</a>, 57 <a href="#FCCrystalModel">FCCrystalModel</a>, 58 <a href="#BCCrystalModel">BCCrystalModel</a> 59 </li> 60 </ul> 10 <ul> 11 <li>Sphere based:<br/> 12 <a href="#SphereModel">SphereModel (Magnetic 2D Model)</a>, 13 <a href="#BinaryHSModel">BinaryHSModel</a>, 14 <a href="#FuzzySphereModel">FuzzySphereModel</a>, 15 <a href="#RaspBerryModel">RaspBerryModel</a>, 16 <a href="#CoreShellModel">CoreShellModel (Magnetic 2D Model)</a>, 17 <a href="#Core2ndMomentModel">Core2ndMomentModel</a>, 18 <a href="#CoreMultiShellModel">CoreMultiShellModel (Magnetic 2D Model)</a>, 19 <a href="#VesicleModel">VesicleModel</a>, 20 <a href="#MultiShellModel">MultiShellModel</a>, 21 <a href="#OnionExpShellModel">OnionExpShellModel</a>, 22 <a href="#SphericalSLDModel">SphericalSLDModel</a>, 23 <a href="#LinearPearlsModel">LinearPearlsModel</a>, 24 <a href="#PearlNecklaceModel">PearlNecklaceModel</a> 25 </li> 26 <li>Cylinder based:<br/> 27 <a href="#CylinderModel">CylinderModel (Magnetic 2D Model)</a>, 28 <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>, 29 <a href="#CoreShellBicelleModel">CoreShellBicelleModel</a>, 30 <a href="#HollowCylinderModel">HollowCylinderModel</a>, 31 <a href="#FlexibleCylinderModel">FlexibleCylinderModel</a>, 32 <a href="#FlexibleCylinderModel">FlexCylEllipXModel</a>, 33 <a href="#StackedDisksModel">StackedDisksModel</a>, 34 <a href="#EllipticalCylinderModel">EllipticalCylinderModel</a>, 35 <a href="#BarBellModel">BarBellModel</a>, 36 <a href="#CappedCylinderModel">CappedCylinderModel</a>, 37 <a href="#PringleModel">PringleModel</a> 38 </li> 39 <li>Parallelpipeds:<br/> 40 <a href="#ParallelepipedModel">ParallelepipedModel (Magnetic 2D Model)</a>, 41 <a href="#CSParallelepipedModel">CSParallelepipedModel</a>, 42 <a href="#RectangularHollowPrismInfThinWallsModel">RectangularHollowPrismInfThinWallsModel</a>, 43 <a href="#RectangularPrismModel">RectangularPrismModel</a>, 44 <a href="#RectangularHollowPrismModel">RectangularHollowPrismModel</a> 45 </li> 46 <li>Ellipsoids:<br/> 47 <a href="#EllipsoidModel">EllipsoidModel</a>, 48 <a href="#CoreShellEllipsoidModel">CoreShellEllipsoidModel</a>, 49 <a href="#CoreShellEllipsoidXTModel">CoreShellEllipsoidXTModel</a>, 50 <a href="#TriaxialEllipsoidModel">TriaxialEllipsoidModel</a> 51 </li> 52 <li>Lamellar:<br/> 53 <a href="#LamellarModel">LamellarModel</a>, 54 <a href="#LamellarFFHGModel">LamellarFFHGModel</a>, 55 <a href="#LamellarPSModel">LamellarPSModel</a>, 56 <a href="#LamellarPSHGModel">LamellarPSHGModel</a> 57 </li> 58 <li>Paracrystals:<br/> 59 <a href="#LamellarPCrystalModel">LamellarPCrystalModel</a>, 60 <a href="#SCCrystalModel">SCCrystalModel</a>, 61 <a href="#FCCrystalModel">FCCrystalModel</a>, 62 <a href="#BCCrystalModel">BCCrystalModel</a> 63 </li> 64 </ul> 61 65 <li><a href="#Shape-Independent"><b>Shape-Independent</b></a>: 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 66 <a href="#Absolute%20Power_Law">AbsolutePower_Law</a>, 67 <a href="#BEPolyelectrolyte">BEPolyelectrolyte</a>, 68 <a href="#BroadPeakModel">BroadPeakModel</a>, 69 <a href="#CorrLength">CorrLength</a>, 70 <a href="#DABModel">DABModel</a>, 71 <a href="#Debye">Debye</a>, 72 <a href="#Number_Density_Fractal">FractalModel</a>, 73 <a href="#FractalCoreShell">FractalCoreShell</a>, 74 <a href="#GaussLorentzGel">GaussLorentzGel</a>, 75 <a href="#Guinier">Guinier</a>, 76 <a href="#GuinierPorod">GuinierPorod</a>, 77 <a href="#Lorentz">Lorentz</a>, 78 <a href="#Mass_Fractal">MassFractalModel</a>, 79 <a href="#MassSurface_Fractal">MassSurfaceFractal</a>, 80 <a href="#Peak%20Gauss%20Model">PeakGaussModel</a>, 81 <a href="#Peak%20Lorentz%20Model">PeakLorentzModel</a>, 82 <a href="#Poly_GaussCoil">Poly_GaussCoil</a>, 83 <a href="#PolymerExclVolume">PolyExclVolume</a>, 84 <a href="#PorodModel">PorodModel</a>, 85 <a href="#RPA10Model">RPA10Model</a>, 86 <a href="#StarPolymer">StarPolymer</a>, 87 <a href="#Surface_Fractal">SurfaceFractalModel</a>, 88 <a href="#TeubnerStreyModel">Teubner Strey</a>, 89 <a href="#TwoLorentzian">TwoLorentzian</a>, 90 <a href="#TwoPowerLaw">TwoPowerLaw</a>, 91 <a href="#UnifiedPowerRg">UnifiedPowerRg</a>, 92 <a href="#LineModel">LineModel</a>, 93 <a href="#ReflectivityModel">ReflectivityModel</a>, 94 <a href="#ReflectivityIIModel">ReflectivityIIModel</a>, 95 <a href="#GelFitModel">GelFitModel</a>.</li> 96 93 97 <li><a href="#Model"><b>Customized Models</b></a>: 94 95 96 97 98 99 100 98 <a href="#testmodel">testmodel</a>, 99 <a href="#testmodel_2">testmodel_2</a>, 100 <a href="#sum_p1_p2">sum_p1_p2</a>, 101 <a href="#sum_Ap1_1_Ap2">sum_Ap1_1_Ap2</a>, 102 <a href="#polynomial5">polynomial5</a>, 103 <a href="#sph_bessel_jn">sph_bessel_jn</a>.</li> 104 101 105 <li><a href="#Structure_Factors"><b>Structure Factors</b></a>: 102 103 104 105 106 106 <a href="#HardsphereStructure">HardSphereStructure</a>, 107 <a href="#SquareWellStructure">SquareWellStructure</a>, 108 <a href="#HayterMSAStructure">HayterMSAStructure</a>, 109 <a href="#StickyHSStructure">StickyHSStructure</a>.</li> 110 107 111 <li><a href="#References"><b>References</b></a></li> 108 112 </ul> … … 3575 3579 3576 3580 3577 3578 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.27.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="EllipsoidModel"></a><b><span style="font-size: 14pt;">Ellipsoid Model</span></b></p> 3581 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.27.</span></b><b><span style="font-size: 7pt;"> </span></b><b><span style="font-size: 14pt;"><a name="RectangularHollowPrismInfThinWallsModel"></a>RectangularHollowPrismInfThinWallsModel</span></b></p> 3582 3583 <p>This model provides the form factor, P( <em>q</em>), for a hollow rectangular prism 3584 with infinitely thin walls.</p> 3585 <p><em>Definition</em></p> 3586 <p>The 1D scattering intensity for this model is calculated according to the equations given by 3587 Nayuk and Huber (Nayuk, 2012).</p> 3588 <p>Assuming a hollow parallelepiped with infinitely thin walls, edge lengths A ≤ B ≤ C 3589 <span class="formula"><i>A</i>â 3590 â€â 3591 <i>B</i>â 3592 â€â 3593 <i>C</i></span> 3594 3595 and presenting an orientation with respect to the scattering vector given by θ and φ, 3596 where θ is the angle between the <em>z</em> axis and the longest axis of the parallelepiped <em>C</em>, and φ 3597 is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis, 3598 the form factor is given by:</p> 3599 3600 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_1.png" alt="" /></span></p> 3601 3602 <p>where</p> 3603 3604 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_2.png" alt="" /></span></p> 3605 3606 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_3.png" alt="" /></span></p> 3607 3608 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_4.png" alt="" /></span></p> 3609 3610 <p>and</p> 3611 3612 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_5.png" alt="" /></span></p> 3613 3614 <p>The 1D scattering intensity is calculated as:</p> 3615 3616 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrismInfThinWalls_6.png" alt="" /></span></p> 3617 3618 <p>where <em>V</em> is the volume of the rectangular prism, <span class="formula"><i>ρ</i><sub><span class="mbox">pipe</span></sub></span> 3619 is the scattering length of the 3620 parallelepiped, <span class="formula"><i>ρ</i><sub><span class="mbox">solvent</span></sub></span> 3621 is the scattering length of the solvent, and 3622 (if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p> 3623 <p>The 2D scattering intensity is not computed by this model.</p> 3624 <p>The returned value is scaled to units of cm<sup>-1</sup> and the parameters of the RectangularHollowPrismInfThinWallModel 3625 are the following:</p> 3626 <table border="1" class="docutils"> 3627 <colgroup> 3628 <col width="40%" /> 3629 <col width="23%" /> 3630 <col width="37%" /> 3631 </colgroup> 3632 <thead valign="bottom"> 3633 <tr><th class="head">Parameter name</th> 3634 <th class="head">Units</th> 3635 <th class="head">Default value</th> 3636 </tr> 3637 </thead> 3638 <tbody valign="top"> 3639 <tr><td>scale</td> 3640 <td>None</td> 3641 <td>1</td> 3642 </tr> 3643 <tr><td>short_side</td> 3644 <td>Å</td> 3645 <td>35</td> 3646 </tr> 3647 <tr><td>b2a_ratio</td> 3648 <td>None</td> 3649 <td>1</td> 3650 </tr> 3651 <tr><td>c2a_ratio</td> 3652 <td>None</td> 3653 <td>1</td> 3654 </tr> 3655 <tr><td>sldPipe</td> 3656 <td>Å<sup>-2</sup></td> 3657 <td>6.3e-6</td> 3658 </tr> 3659 <tr><td>sldSolv</td> 3660 <td>Å<sup>-2</sup></td> 3661 <td>1.0e-6</td> 3662 </tr> 3663 <tr><td>background</td> 3664 <td>cm<sup>-1</sup></td> 3665 <td>0</td> 3666 </tr> 3667 </tbody> 3668 </table> 3669 <p>REFERENCES</p> 3670 <ol class="upperalpha simple" start="18"> 3671 <li>Nayuk and K. Huber, <em>Z. Phys. Chem.</em> 226 (2012) 837-854.</li> 3672 </ol> 3673 <p><em>Validation of the RectangularHollowPrismInfThinWallsModel</em></p> 3674 <p>Validation of the code was done qualitatively by comparing the output of the 1D model to the curves 3675 shown in (Nayuk, 2012).</p> 3676 3677 3678 3679 3680 3681 3682 3683 3684 3685 3686 3687 3688 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.28.</span></b><b><span style="font-size: 7pt;"> </span></b><b><span style="font-size: 14pt;"><a name="RectangularPrismModel"></a>RectangularPrismModel</span></b></p> 3689 <p>This model provides the form factor, P( <em>q</em>), for a rectangular prism.</p> 3690 <p>Note that this model is almost totally equivalent to the existing 3691 ParallelepipedModel. The only difference is that the way the 3692 relevant parameters are defined here (<em>a</em>, <em>b/a</em>, <em>c/a</em> instead of <em>a</em>, <em>b</em>, <em>c</em>) 3693 allows to use polydispersity with this model while keeping the shape 3694 of the prism (e.g. setting <em>b/a</em> = 1 and <em>c/a</em> = 1 and applying polydispersity 3695 to <em>a</em> will generate a distribution of cubes of different sizes).</p> 3696 <p><em>Definition</em></p> 3697 <p>The 1D scattering intensity for this model was calculated by Mittelbach and Porod (Mittelbach, 1961), 3698 but the implementation here is closer to the equations given by Nayuk and Huber (Nayuk, 2012).</p> 3699 <p>The scattering from a massive parallelepiped with an orientation with respect to the scattering vector 3700 given by θ and φ is given by:</p> 3701 3702 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularPrism_1.png" alt="" /></span></p> 3703 3704 <p>where <em>A</em>, <em>B</em> and <em>C</em> are the sides of the parallelepiped and must fulfill <span class="formula"><i>A</i>â 3705 ≤â 3706 <i>B</i>â 3707 ≤â 3708 <i>C</i></span> 3709 , 3710 θ is the angle between the <em>z</em> axis and the longest axis of the parallelepiped <em>C</em>, and φ 3711 is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis.</p> 3712 <p>The normalized form factor in 1D is obtained averaging over all possible orientations:</p> 3713 3714 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularPrism_2.png" alt="" /></span></p> 3715 3716 <p>The 1D scattering intensity is calculated as:</p> 3717 3718 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularPrism_3.png" alt="" /></span></p> 3719 3720 <p>where <em>V</em> is the volume of the rectangular prism, <span class="formula"><i>ρ</i><sub><span class="mbox">pipe</span></sub></span> 3721 is the scattering length of the 3722 parallelepiped, <span class="formula"><i>ρ</i><sub><span class="mbox">solvent</span></sub></span> 3723 is the scattering length of the solvent, and 3724 (if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p> 3725 <p>The 2D scattering intensity is not computed by this model.</p> 3726 <p>The returned value is scaled to units of cm<sup>-1</sup> and the parameters of the RectangularPrismModel are the following:</p> 3727 <table border="1" class="docutils"> 3728 <colgroup> 3729 <col width="40%" /> 3730 <col width="23%" /> 3731 <col width="37%" /> 3732 </colgroup> 3733 <thead valign="bottom"> 3734 <tr><th class="head">Parameter name</th> 3735 <th class="head">Units</th> 3736 <th class="head">Default value</th> 3737 </tr> 3738 </thead> 3739 <tbody valign="top"> 3740 <tr><td>scale</td> 3741 <td>None</td> 3742 <td>1</td> 3743 </tr> 3744 <tr><td>short_side</td> 3745 <td>Å</td> 3746 <td>35</td> 3747 </tr> 3748 <tr><td>b2a_ratio</td> 3749 <td>None</td> 3750 <td>1</td> 3751 </tr> 3752 <tr><td>c2a_ratio</td> 3753 <td>None</td> 3754 <td>1</td> 3755 </tr> 3756 <tr><td>sldPipe</td> 3757 <td>Å<sup>-2</sup></td> 3758 <td>6.3e-6</td> 3759 </tr> 3760 <tr><td>sldSolv</td> 3761 <td>Å<sup>-2</sup></td> 3762 <td>1.0e-6</td> 3763 </tr> 3764 <tr><td>background</td> 3765 <td>cm<sup>-1</sup></td> 3766 <td>0</td> 3767 </tr> 3768 </tbody> 3769 </table> 3770 <p>REFERENCES</p> 3771 <ol class="upperalpha simple" start="16"> 3772 <li>Mittelbach and G. Porod, <em>Acta Physica Austriaca</em> 14 (1961) 185-211.</li> 3773 </ol> 3774 <ol class="upperalpha simple" start="18"> 3775 <li>Nayuk and K. Huber, <em>Z. Phys. Chem.</em> 226 (2012) 837-854.</li> 3776 </ol> 3777 <p><em>Validation of the RectangularPrismModel</em></p> 3778 <p>Validation of the code was done by comparing the output of the 1D model to the output of the existing 3779 parallelepiped model.</p> 3780 3781 3782 3783 3784 3785 3786 3787 3788 3789 3790 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.29.</span></b><b><span style="font-size: 7pt;"> </span></b><b><span style="font-size: 14pt;"><a name="RectangularHollowPrismModel"></a>RectangularHollowPrismModel</span></b></p> 3791 <p>This model provides the form factor, P( <em>q</em>), for a hollow rectangular parallelepiped 3792 with a wall thickness Î.</p> 3793 <p><em>Definition</em></p> 3794 <p>The 1D scattering intensity for this model is calculated by forming the difference of the 3795 amplitudes of two massive parallelepipeds differing in their outermost dimensions in 3796 each direction by the same length increment 2 Δ (Nayuk, 2012).</p> 3797 <p>As in the case of the massive parallelepiped, the scattering amplitude is computed for a particular 3798 orientation of the parallelepiped with respect to the scattering vector and then averaged over all 3799 possible orientations, giving:</p> 3800 3801 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_1.png" alt="" /></span></p> 3802 3803 <p>where θ is the angle between the <em>z</em> axis and the longest axis of the parallelepiped, φ 3804 is the angle between the scattering vector (lying in the <em>xy</em> plane) and the <em>y</em> axis, and:</p> 3805 3806 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_2.png" alt="" /></span></p> 3807 3808 <p>where <em>A</em>, <em>B</em> and <em>C</em> are the external sides of the parallelepiped fulfilling <span class="formula"><i>A</i>â 3809 ≤â 3810 <i>B</i>â 3811 ≤â 3812 <i>C</i></span> 3813 , 3814 and the volume <em>V</em> of the parallelepiped is:</p> 3815 3816 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_3.png" alt="" /></span></p> 3817 3818 <p>The 1D scattering intensity is calculated as:</p> 3819 3820 <p style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="img/RectangularHollowPrism_4.png" alt="" /></span></p> 3821 3822 <p>where <span class="formula"><i>ρ</i><sub><span class="mbox">pipe</span></sub></span> 3823 is the scattering length of the 3824 parallelepiped, <span class="formula"><i>ρ</i><sub><span class="mbox">solvent</span></sub></span> 3825 is the scattering length of the solvent, and 3826 (if the data are in absolute scale) scale represents the volume fraction (which is unitless) .</p> 3827 <p>The 2D scattering intensity is not computed by this model.</p> 3828 <p>The returned value is scaled to units of cm<sup>-1</sup> and the parameters of the RectangularHollowPrismModel 3829 are the following:</p> 3830 <table border="1" class="docutils"> 3831 <colgroup> 3832 <col width="40%" /> 3833 <col width="23%" /> 3834 <col width="37%" /> 3835 </colgroup> 3836 <thead valign="bottom"> 3837 <tr><th class="head">Parameter name</th> 3838 <th class="head">Units</th> 3839 <th class="head">Default value</th> 3840 </tr> 3841 </thead> 3842 <tbody valign="top"> 3843 <tr><td>scale</td> 3844 <td>None</td> 3845 <td>1</td> 3846 </tr> 3847 <tr><td>short_side</td> 3848 <td>Å</td> 3849 <td>35</td> 3850 </tr> 3851 <tr><td>b2a_ratio</td> 3852 <td>None</td> 3853 <td>1</td> 3854 </tr> 3855 <tr><td>c2a_ratio</td> 3856 <td>None</td> 3857 <td>1</td> 3858 </tr> 3859 <tr><td>thickness</td> 3860 <td>Å</td> 3861 <td>1</td> 3862 </tr> 3863 <tr><td>sldPipe</td> 3864 <td>Å<sup>-2</sup></td> 3865 <td>6.3e-6</td> 3866 </tr> 3867 <tr><td>sldSolv</td> 3868 <td>Å<sup>-2</sup></td> 3869 <td>1.0e-6</td> 3870 </tr> 3871 <tr><td>background</td> 3872 <td>cm<sup>-1</sup></td> 3873 <td>0</td> 3874 </tr> 3875 </tbody> 3876 </table> 3877 <p>REFERENCES</p> 3878 <ol class="upperalpha simple" start="18"> 3879 <li>Nayuk and K. Huber, <em>Z. Phys. Chem.</em> 226 (2012) 837-854.</li> 3880 </ol> 3881 <p><em>Validation of the RectangularHollowPrismModel</em></p> 3882 <p>Validation of the code was done qualitatively by comparing the output of the 1D model to the curves 3883 shown in (Nayuk, 2012).</p> 3884 3885 3886 3887 3888 3889 3890 3891 3892 3893 3894 3895 3896 3897 3898 3899 3900 3901 3902 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.30.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="EllipsoidModel"></a><b><span style="font-size: 14pt;">Ellipsoid Model</span></b></p> 3579 3903 <p>This model provides the form factor for an ellipsoid (ellipsoid of revolution) with uniform scattering length density. The form factor is normalized by the particle volume.</p> 3580 3904 <p style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;"> </span>Definition</b></p> … … 3710 4034 <p><a name="_Ref173223004"></a>Figure 6: Comparison of the intensity for uniformly distributed ellipsoids calculated from our 2D model and the intensity from the NIST SANS analysis software. The parameters used were: Scale=1.0, Radius_a=20 Å, Radius_b=400 Å, Contrast=3e-6 Å -2, and Background=0.0 cm -1.</p> 3711 4035 <p> </p> 3712 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2. 28.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="CoreShellEllipsoidModel"></a><b><span style="font-size: 14pt;">CoreShellEllipsoidModel </span></b></p>4036 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.31.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="CoreShellEllipsoidModel"></a><b><span style="font-size: 14pt;">CoreShellEllipsoidModel </span></b></p> 3713 4037 <p>This model provides the form factor, P(<em>q</em>), for a core shell ellipsoid (below) where the form factor is normalized by the volume of the cylinder. P(q) = scale*<f^2>/V+background where the volume V= 4pi/3*rmaj*rmin2 and the averaging < > is applied over all orientation for 1D. </p> 3714 4038 <p style="text-align: center;" align="center"> <img id="Picture 41" src="img/image125.gif" alt="" width="335" height="179" /></p> … … 3849 4173 3850 4174 3851 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.29.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="TriaxialEllipsoidModel"></a><b><span style="font-size: 14pt;">TriaxialEllipsoidModel</span></b></p> 4175 4176 4177 4178 4179 4180 4181 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.32.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="CoreShellEllipsoidXTModel"></a><b><span style="font-size: 14pt;">CoreShellEllipsoidXTModel </span></b></p> 4182 4183 <p>An alternative version of P( *q*) for the core plus shell ellipsoid (see 4184 CoreShellEllipsoidModel), having as 4185 parameters the core axial ratio X and a shell thickness, which are more often 4186 what we would like to determine and behave better when polydispersity is 4187 applied than the four independent radii in the original model.</p> 4188 4189 <p>The geometric parameters are: equat_core = equatorial core radius = Rminor_core, 4190 X_core = polar_core/equat_core = Rmajor_core/Rminor_core 4191 T_shell = equat_outer - equat_core = Rminor_outer - Rminor_core, 4192 XpolarShell = Tpolar_shell/T_shell = (Rmajor_outer - Rmajor_core)/(Rminor_outer - Rminor_core)</p> 4193 4194 <p>In terms of the original radii: 4195 polar_core = equat_core * X_core, equat_shell = equat_core + T_shell 4196 polar_shell = equat_core * X_core + T_shell*XpolarShell 4197 (where we note that "shell" perhaps confusingly, relates to the outer radius).</p> 4198 4199 <p>When X_core < 1 the core is oblate, when X_core > 1 it is prolate, 4200 X_core =1 is a spherical core. For a fixed shell thickness XpolarShell = 1, to scale the 4201 shell thickness pro-rata with the radius XpolarShell = X_core.</p> 4202 4203 <p>When including and S(Q), the radius in S(Q) is calculated to be that of a 4204 sphere with the same 2nd virial coefficient of the outr surface of the ellipsoid. 4205 This may have some undesirable effects if the aspect ratio of the ellipsoid is 4206 large ( X<<1 or X>>1), when the S(Q) which assumes spheres wil not in any case be valid.</p> 4207 4208 <p>If SANS data are in absolute units, and sld's are correct, then "scale" should be the total 4209 volume fraction of the "outer particle". When S(Q) is introduced this moves to the S(Q) 4210 volume fraction, and "scale" should then be 1.0, or contain some ther units conversion factor 4211 if you have say Xray data.</p> 4212 4213 4214 <div align="center"> 4215 <table style="border-collapse: collapse;" border="2" cellspacing="0" cellpadding="0"> 4216 <tbody> 4217 <tr style="height: 18.8pt;"> 4218 <td style="border: 1pt solid width: 107pt; height: 18.8pt;" valign="top" width="143"> 4219 <p>Parameter name</p> 4220 </td> 4221 <td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4222 <p>Units</p> 4223 </td> 4224 <td style="border-width: 1pt 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4225 <p>Default value</p> 4226 </td> 4227 </tr> 4228 <tr style="height: 18.8pt;"> 4229 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4230 <p>background</p> 4231 </td> 4232 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4233 <p>cm-1</p> 4234 </td> 4235 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4236 <p>0.001</p> 4237 </td> 4238 </tr> 4239 <tr style="height: 18.8pt;"> 4240 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4241 <p>equat_core</p> 4242 </td> 4243 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4244 <p>Å</p> 4245 </td> 4246 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4247 <p>20</p> 4248 </td> 4249 </tr> 4250 <tr style="height: 18.8pt;"> 4251 <td style="border-width: medium 1pt 1pt; vertical-align: top; width: 107pt; height: 18.8pt;"> 4252 <p>scale</p> 4253 </td> 4254 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4255 <p></p> 4256 </td> 4257 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4258 <p>0.05</p> 4259 </td> 4260 </tr> 4261 <tr style="height: 18.8pt;"> 4262 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4263 <p>sld_core</p> 4264 </td> 4265 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4266 <p>Å -2</p> 4267 </td> 4268 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4269 <p>2.0e-6</p> 4270 </td> 4271 </tr> 4272 <tr style="height: 18.8pt;"> 4273 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4274 <p>sld_shell</p> 4275 </td> 4276 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4277 <p>Å -2</p> 4278 </td> 4279 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4280 <p>1.0e-6</p> 4281 </td> 4282 </tr> 4283 <tr style="height: 18.8pt;"> 4284 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4285 <p>sld_solv</p> 4286 </td> 4287 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4288 <p>Å -2</p> 4289 </td> 4290 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4291 <p>6.3e-6</p> 4292 </td> 4293 </tr> 4294 <tr style="height: 18.8pt;"> 4295 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4296 <p>T_shell</p> 4297 </td> 4298 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4299 <p>Å</p> 4300 </td> 4301 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4302 <p>30</p> 4303 </td> 4304 </tr> 4305 <tr style="height: 18.8pt;"> 4306 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4307 <p>X_core</p> 4308 </td> 4309 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4310 <p></p> 4311 </td> 4312 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4313 <p>3.0</p> 4314 </td> 4315 </tr> 4316 <tr style="height: 18.8pt;"> 4317 <td style="border-width: medium 1pt 1pt; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4318 <p>XpolarShell</p> 4319 </td> 4320 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"></td> 4321 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 18.8pt;" valign="top" width="143"> 4322 <p>1.0</p> 4323 </td> 4324 </tr> 4325 </tbody> 4326 </table> 4327 </div> 4328 4329 4330 4331 4332 4333 4334 4335 4336 4337 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.33.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="TriaxialEllipsoidModel"></a><b><span style="font-size: 14pt;">TriaxialEllipsoidModel</span></b></p> 3852 4338 <p>This model provides the form factor, P(<em>q</em>), for an ellipsoid (below) where all three axes are of different lengths, i.e., Ra =< Rb =< Rc (Note that users should maintains this inequality for the all calculations). P(q) = scale*<f^2>/V+background where the volume V= 4pi/3*Ra*Rb*Rc, and the averaging < > is applied over all orientation for 1D. </p> 3853 4339 <p style="text-align: center;" align="center"> <img id="Picture 42" src="img/image128.jpg" alt="" width="376" height="226" /></p> … … 3970 4456 3971 4457 3972 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.3 0.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="LamellarModel"></a><b><span style="font-size: 14pt;">LamellarModel</span></b></p>4458 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.34.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="LamellarModel"></a><b><span style="font-size: 14pt;">LamellarModel</span></b></p> 3973 4459 <p>This model provides the scattering intensity, I(<em>q</em>), for a lyotropic lamellar phase where a uniform SLD and random distribution in solution are assumed. The ploydispersion in the bilayer thickness can be applied from the GUI.</p> 3974 4460 <p>The scattering intensity I(q) is:</p> … … 4057 4543 <p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p> 4058 4544 <p> also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p> 4059 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.31.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="LamellarFFHGModel"></a><b><span style="font-size: 14pt;">LamellarFFHGModel</span></b></p> 4060 <p>This model provides the scattering intensity, I(<em>q</em>), for a lyotropic lamellar phase where a random distribution in solution are assumed. The SLD of the head region is taken to be different from the SLD of the tail region.</p> 4061 <p>The scattering intensity I(q) is:</p> 4545 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.35.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="LamellarFFHGModel"></a><b><span style="font-size: 14pt;">LamellarFFHGModel</span></b></p> 4546 <p>This model calculates the form factor from a lyotropic lamellar phase. The intensity calculated is for lamellae of two-layer scattering length density that are randomly distributed in solution (a powder average). The scattering length density of the tail region, headgroup region, and solvent are taken to be different. 4547 No inter-lamellar structure factor is calculated. Other models are available where S(q) is calculated.</p> 4548 <p>The returned value is scale*I(q) + background, and is in units of [cm<sup>-1</sup>]:</p> 4062 4549 <p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image136.PNG" alt="" /></span></p> 4063 <p> The form factor is,</p>4550 <p>where the form factor is given by:</p> 4064 4551 <p style="text-align: center;" align="center"><img src="img/image137.jpg" alt="" width="432" height="46" /></p> 4065 <p>where <span style="font-family: Symbol;">dT</span> = tail length (or t_length), <span style="font-family: Symbol;">dH</span> = heasd thickness (or h_thickness) , <span style="font-family: Symbol;">Dr</span>H = SLD (headgroup) - SLD(solvent), and <span style="font-family: Symbol;">Dr</span>T = SLD (tail) - SLD(headgroup).</p> 4066 <p>The 2D scattering intensity is calculated in the same way as 1D, where the <em>q</em> vector is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" width="111" height="23" /></span><span style="font-size: 14pt;">.</span></p> 4067 <p><span style="font-size: 14pt;"> </span></p> 4068 <p>The returned value is in units of [cm-1], on absolute scale. In the parameters, sld_tail = SLD of the tail group, and sld_head = SLD of the head group.</p> 4552 <p>where δ<sub>T</sub> = tail length (or t_length), δ<sub>H</sub> = head thickness (or h_thickness), Δρ<sub>H</sub> = SLD (headgroup) - SLD(solvent), and Δρ<sub>T</sub> = SLD (tail) - SLD(solvent). 4553 <br>(sld_tail = SLD of the tail group, and sld_head = SLD of the head group)</p> 4554 <p>The 2D scattering intensity is calculated in the same way as 1D, where the q vector is defined as:</p> 4555 <p><img src="img/image040.gif" alt="" width="111" /></p> 4556 <p>NOTE: The total bilayer thickness = 2(δ<sub>H</sub> + δ<sub>T</sub>)</p> 4557 <p>The meaning of the multiplicative scale factor is not well-defined, but should be on the order of the volume fraction of solution occupied by the lamellar crystallites. Please see the original references for clarification.</p> 4069 4558 <p> </p> 4070 4559 <div align="center"> … … 4166 4655 <p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p> 4167 4656 <p> also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p> 4168 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.3 2.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="LamellarPSModel"></a><b><span style="font-size: 14pt;">LamellarPSModel</span></b></p>4657 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.36.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="LamellarPSModel"></a><b><span style="font-size: 14pt;">LamellarPSModel</span></b></p> 4169 4658 <p>This model provides the scattering intensity (<b>form factor</b> <b>*</b> <b>structure factor</b>), I(<em>q</em>), for a lyotropic lamellar phase where a random distribution in solution are assumed.</p> 4170 4659 <p>The scattering intensity I(q) is:</p> … … 4279 4768 <p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p> 4280 4769 <p> also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p> 4281 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.3 3.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="LamellarPSHGModel"></a><b><span style="font-size: 14pt;">LamellarPSHGModel</span></b></p>4770 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.37.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="LamellarPSHGModel"></a><b><span style="font-size: 14pt;">LamellarPSHGModel</span></b></p> 4282 4771 <p>This model provides the scattering intensity (<b>form factor</b> <b>*</b> <b>structure factor</b>), I(<em>q</em>), for a lyotropic lamellar phase where a random distribution in solution are assumed. The SLD of the head region is taken to be different from the SLD of the tail region.</p> 4283 4772 <p>The scattering intensity I(q) is:</p> … … 4426 4915 <p>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502.</p> 4427 4916 <p> also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p> 4428 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.3 4.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="LamellarPCrystalModel"></a><b><span style="font-size: 14pt;">LamellarPCrystalModel</span></b></p>4917 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.38.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="LamellarPCrystalModel"></a><b><span style="font-size: 14pt;">LamellarPCrystalModel</span></b></p> 4429 4918 <p>Lamella ParaCrystal Model: Calculates the scattering from a stack of repeating lamellar structures. The stacks of lamellae (infinite in lateral dimension) are treated as a paracrystal to account for the repeating spacing. The repeat distance is further characterized by a Gaussian polydispersity. This model can be used for large multilamellar vesicles.</p> 4430 4919 <p>The scattering intensity I(q) is calculated as:</p> … … 4542 5031 <p>REFERENCE</p> 4543 5032 <p>M. Bergstrom, J. S. Pedersen, P. Schurtenberger, S. U. Egelhaaf, J. Phys. Chem. B, 103 (1999) 9888-9897.</p> 4544 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.3 5.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="SCCrystalModel"></a><b><span style="font-size: 14pt;">SC(Simple Cubic Para-)CrystalModel</span></b></p>5033 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.39.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="SCCrystalModel"></a><b><span style="font-size: 14pt;">SC(Simple Cubic Para-)CrystalModel</span></b></p> 4545 5034 <p>Calculates the scattering from a simple cubic lattice with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution.</p> 4546 5035 <p>The returned value is scaled to units of [cm-1sr-1], absolute scale.</p> … … 4666 5155 <p style="text-align: center;" align="center"><b><img src="img/image157.jpg" alt="" width="447" height="322" /></b></p> 4667 5156 <p style="text-align: center;" align="center"><b>Figure. 2D plot using the default values (w/200X200 pixels).</b></p> 4668 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2. 36.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="FCCrystalModel"></a><b><span style="font-size: 14pt;">FC(Face Centered Cubic Para-)CrystalModel</span></b></p>5157 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.40.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="FCCrystalModel"></a><b><span style="font-size: 14pt;">FC(Face Centered Cubic Para-)CrystalModel</span></b></p> 4669 5158 <p>Calculates the scattering from a face-centered cubic lattice with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution. </p> 4670 5159 <p>The returned value is scaled to units of [cm-1sr-1], absolute scale.</p> … … 4791 5280 <p style="text-align: center;" align="center"><img src="img/image166.jpg" alt="" width="473" height="352" /></p> 4792 5281 <p style="text-align: center;" align="center"><b>Figure. 2D plot using the default values (w/200X200 pixels).</b></p> 4793 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2. 37.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="BCCrystalModel"></a><b><span style="font-size: 14pt;">BC(Body Centered Cubic Para-)CrystalModel</span></b></p>5282 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.41.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="BCCrystalModel"></a><b><span style="font-size: 14pt;">BC(Body Centered Cubic Para-)CrystalModel</span></b></p> 4794 5283 <p>Calculates the scattering from a body-centered cubic lattice with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution.The returned value is scaled to units of [cm-1sr-1], absolute scale.</p> 4795 5284 <p>The scattering intensity I(q) is calculated as:</p> … … 5239 5728 <p style="margin-left: 0.25in;">The parameter L is referred to as the correlation length.</p> 5240 5729 <p style="margin-left: 0.25in;">For 2D plot, the wave transfer is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" /></span><span style="font-size: 14pt;">.</span></p> 5730 <p style="text-indent: 0.25in;">Note: If I(Q) is in absolute units (cm-1) scale must divided by 10^8 to convert it to Å-1.</p> 5241 5731 <p style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 5242 5732 <div align="center"> … … 5259 5749 </td> 5260 5750 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143"> 5261 <p> None</p>5751 <p>Å-4 </p> 5262 5752 </td> 5263 5753 <td style="border-width: medium 1pt 1pt medium; width: 107pt; height: 19.25pt;" valign="top" width="143"> … … 5296 5786 <p style="margin-left: 0.5in;"> </p> 5297 5787 <p style="margin-left: 0.5in;">Debye, Bueche, "Scattering by an Inhomogeneous Solid", J. Appl. Phys. 20, 518 (1949).</p> 5298 <p style="margin-left: 0.25in;"><i>2013/09/09 - Description reviewed by King, S. and Parker, P.</i></p>5788 <p style="margin-left: 0.25in;"><i>2013/09/09, 2014/04/22 - Description reviewed by King, S. and Parker, P.</i></p> 5299 5789 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.6.</span></b><b><span style="font-size: 7pt;"> </span></b><b><span style="font-size: 14pt;"> <a name="Absolute Power_Law"></a>Absolute Power_Law </span></b></p> 5300 5790 <p style="margin-left: 0.25in;">This model describes a power law with background.</p>
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