Changeset 7d0563e in sasview for sansview/doc/model_functions.html


Ignore:
Timestamp:
Sep 28, 2009 1:11:34 PM (15 years ago)
Author:
Jae Cho <jhjcho@…>
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
Children:
f0ff8d65
Parents:
beaaa8b
Message:

updated and fixed some incorrectness of model description.

File:
1 edited

Legend:

Unmodified
Added
Removed

  • sansview/doc/model_functions.html

    rbeaaa8b r7d0563e  
    51625162src="../images/html/image073.png"></span></p> 
    51635163 
     5164 
     5165 
     5166<p class=MsoNormal>The form factor is,</p> 
     5167 
     5168<p class=MsoNormal>&nbsp;</p> 
     5169 
     5170<p class=MsoNormal align=center style='text-align:center'><span 
     5171style='position:relative;top:15.0pt'><img border=0 width=398 height=46 
     5172src="../images/html/image078.png"></span></p> 
     5173 
     5174<p class=MsoNormal align=center style='text-align:center'><span 
     5175style='position:relative;top:16.0pt'>&nbsp;</span></p> 
     5176 
     5177<p class=MsoNormal>where delta<sub>T</sub> 
     5178= tail length (or t_length), delta<sub>H</sub> 
     5179= head thickness (or h_thickness) , <i><span style='font-family:"Arial","sans-serif"'>&#916;</span>&#961;</i><sub>H</sub> 
     5180= SLD (headgroup) - SLD(solvent), and <i><span style='font-family:"Arial","sans-serif"'>&#916;</span>&#961;</i><sub>T</sub> 
     5181= SLD (tail) - SLD(headgroup).</p> 
     5182 
     5183<p class=MsoNormal>The 2D scattering intensity is calculated in the same way as 
     51841D, where the <i>q</i> vector is defined as<span style='font-size:14.0pt; 
     5185position:relative;top:8.0pt'><img border=0 width=103 height=33 
     5186src="../images/html/image010.png"></span><span style='font-size:14.0pt; 
     5187position:relative;top:6.0pt'>.</span></p> 
     5188 
     5189<p class=MsoNormal><span style='font-size:14.0pt;position:relative;top:6.0pt'>&nbsp;</span></p> 
     5190 
     5191<p class=MsoNormal>The returned value is in units of [cm<sup>-1</sup>], on 
     5192absolute scale. In the parameters, sld_tail = SLD of the tail group, and 
     5193sld_head = SLD of the head group.</p> 
     5194 
     5195<p class=MsoNormal>&nbsp;</p> 
     5196 
     5197<p class=MsoNormal><sub>&nbsp;</sub></p> 
     5198 
     5199<div align=center> 
     5200 
     5201<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 
     5202 style='border-collapse:collapse;border:none'> 
     5203 <tr style='height:18.8pt'> 
     5204  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     5205  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5206  <p class=MsoBodyText>Parameter name</p> 
     5207  </td> 
     5208  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     5209  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5210  <p class=MsoBodyText>Units</p> 
     5211  </td> 
     5212  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     5213  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5214  <p class=MsoBodyText>Default value</p> 
     5215  </td> 
     5216 </tr> 
     5217 <tr style='height:18.8pt'> 
     5218  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     5219  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5220  <p class=MsoBodyText>background</p> 
     5221  </td> 
     5222  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5223  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5224  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5225  <p class=MsoBodyText>cm<sup>-1</sup></p> 
     5226  </td> 
     5227  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5228  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5229  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5230  <p class=MsoBodyText>0.0</p> 
     5231  </td> 
     5232 </tr> 
     5233 <tr style='height:18.8pt'> 
     5234  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     5235  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5236  <p class=MsoBodyText>sld_head</p> 
     5237  </td> 
     5238  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5239  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5240  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5241  <p class=MsoBodyText>Å<sup> -2</sup></p> 
     5242  </td> 
     5243  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5244  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5245  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5246  <p class=MsoBodyText>3e-006</p> 
     5247  </td> 
     5248 </tr> 
     5249 <tr style='height:18.8pt'> 
     5250  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     5251  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5252  <p class=MsoBodyText>scale</p> 
     5253  </td> 
     5254  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5255  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5256  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5257  <p class=MsoBodyText>&nbsp;</p> 
     5258  </td> 
     5259  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5260  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5261  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5262  <p class=MsoBodyText>1</p> 
     5263  </td> 
     5264 </tr> 
     5265 <tr style='height:18.8pt'> 
     5266  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     5267  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5268  <p class=MsoBodyText>sld_solvent</p> 
     5269  </td> 
     5270  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5271  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5272  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5273  <p class=MsoBodyText>Å<sup> -2</sup></p> 
     5274  </td> 
     5275  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5276  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5277  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5278  <p class=MsoBodyText>6e-006</p> 
     5279  </td> 
     5280 </tr> 
     5281 <tr style='height:18.8pt'> 
     5282  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     5283  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5284  <p class=MsoBodyText>h_thickness</p> 
     5285  </td> 
     5286  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5287  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5288  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5289  <p class=MsoBodyText>Å</p> 
     5290  </td> 
     5291  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5292  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5293  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5294  <p class=MsoBodyText>10</p> 
     5295  </td> 
     5296 </tr> 
     5297 <tr style='height:18.8pt'> 
     5298  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     5299  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5300  <p class=MsoBodyText>t_length</p> 
     5301  </td> 
     5302  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5303  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5304  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5305  <p class=MsoBodyText>Å</p> 
     5306  </td> 
     5307  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5308  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5309  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5310  <p class=MsoBodyText>15</p> 
     5311  </td> 
     5312 </tr> 
     5313 <tr style='height:18.8pt'> 
     5314  <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
     5315  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5316  <p class=MsoBodyText>sld_tail</p> 
     5317  </td> 
     5318  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5319  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5320  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5321  <p class=MsoBodyText>Å<sup> -2</sup></p> 
     5322  </td> 
     5323  <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
     5324  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
     5325  padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
     5326  <p class=MsoBodyText>0</p> 
     5327  </td> 
     5328 </tr> 
     5329</table> 
     5330 
     5331</div> 
     5332 
     5333<p class=MsoNormal>&nbsp;</p> 
     5334 
     5335<p class=MsoNormal>&nbsp;</p> 
     5336 
     5337<p class=MsoNormal align=center style='text-align:center'><img border=0 
     5338width=444 height=343 src="../images/html/image079.png"></p> 
     5339 
     5340<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure. 
     53411D plot using the default values (w/1000 data point).</b></p> 
     5342 
     5343<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p> 
     5344 
     5345<p class=MsoNormal align=center style='text-align:center'>&nbsp;</p> 
     5346 
     5347<p class=MsoNormal>Our model uses the form factor calculations implemented in a 
     5348c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p> 
     5349 
     5350<p class=MsoNormal>&nbsp;</p> 
     5351 
     5352<p class=MsoBodyText>REFERENCE</p> 
     5353 
     5354<p class=MsoNormal>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 
     5355487-502.</p> 
     5356 
     5357<p class=MsoNormal>            also in J. Phys. Chem. B, 105, (2001) 
     535811081-11088.</p> 
     5359 
     5360<p class=MsoNormal>&nbsp;</p> 
     5361 
     5362<p class=MsoNormal>&nbsp;</p> 
     5363<p class=MsoNormal>&nbsp;</p> 
     5364 
     5365<p class=MsoNormal><b>&nbsp;</b></p> 
     5366 
     5367<p class=MsoNormal><b>&nbsp;</b></p> 
     5368 
     5369 
     5370<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
     5371style='font-size:14.0pt'>2.18.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     5372</span></span></b><b><span style='font-size:14.0pt'><a name="LamellarPSModel">LamellarPSModel</a></span></b></p> 
     5373 
     5374<p class=MsoNormal>&nbsp;</p> 
     5375 
     5376<p class=MsoNormal>This model provides the scattering intensity (<b>form factor</b> 
     5377<b>*</b> <b>structure factor</b>), I(<i>q</i>), for a lyotropic lamellar phase where 
     5378a random distribution in solution are assumed.  </p> 
     5379 
     5380<p class=MsoNormal>&nbsp;</p> 
     5381 
     5382<p class=MsoNormal>The scattering intensity I(q) is:</p> 
     5383 
     5384<p class=MsoNormal>&nbsp;</p> 
     5385 
     5386<p class=MsoNormal align=center style='text-align:center'><span 
     5387style='position:relative;top:15.0pt'><img border=0 width=133 height=46 
     5388src="../images/html/image077.png"></span></p> 
     5389 
     5390<p class=MsoNormal align=center style='text-align:center'><span 
     5391style='position:relative;top:16.0pt'>&nbsp;</span></p> 
     5392 
     5393 
     5394 
    51645395<p class=MsoNormal>The form factor is</p> 
    51655396 
    … …  
    52025433style='position:relative;top:16.0pt'>&nbsp;</span></p> 
    52035434 
    5204 <p class=MsoNormal>Here d= (repeat) spacing, <span style='font-family:Symbol'>d</span> 
    5205 = bilayer thickness, the contrast <span style='font-family:Symbol'>Dr</span> = 
     5435<p class=MsoNormal>Here d= (repeat) spacing, delta 
     5436= bilayer thickness, the contrast <i><span style='font-family:"Arial","sans-serif"'>&#916;</span>&#961;</i> = 
    52065437SLD (headgroup) - SLD(solvent), K=smectic bending elasticity, B=compression 
    52075438modulus, and N = number of lamellar plates (n_plates).</p> 
    … …  
    53915622<p class=MsoNormal>&nbsp;</p> 
    53925623 
     5624 
     5625 
    53935626<p class=MsoNormal>&nbsp;</p> 
    53945627 
    … …  
    53995632 
    54005633<p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    5401 style='font-size:14.0pt'>2.18.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    5402 </span></span></b><b><span style='font-size:14.0pt'><a name="LamellarPSModel">LamellarPSModel</a></span></b></p> 
     5634style='font-size:14.0pt'>2.19.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     5635</span></span></b><b><span style='font-size:14.0pt'><a name="LamellarPSHGModel">LamellarPSHGModel</a></span></b></p> 
    54035636 
    54045637<p class=MsoNormal>&nbsp;</p> 
    … …  
    54335666style='position:relative;top:16.0pt'>&nbsp;</span></p> 
    54345667 
    5435 <p class=MsoNormal>where <span style='font-family:Symbol'>d<sub>T</sub></span> 
    5436 = tail length (or t_length), <span style='font-family:Symbol'>d<sub>H</sub></span> 
    5437 = heasd thickness (or h_thickness) , <span style='font-family:Symbol'>Dr</span><sub>H</sub> 
    5438 = SLD (headgroup) - SLD(solvent), and <span style='font-family:Symbol'>Dr</span><sub>T</sub> 
    5439 = SLD (tail) - SLD(headgroup).</p> 
    5440  
    5441 <p class=MsoNormal>The 2D scattering intensity is calculated in the same way as 
    5442 1D, where the <i>q</i> vector is defined as<span style='font-size:14.0pt; 
    5443 position:relative;top:8.0pt'><img border=0 width=103 height=33 
    5444 src="../images/html/image010.png"></span><span style='font-size:14.0pt; 
    5445 position:relative;top:6.0pt'>.</span></p> 
    5446  
    5447 <p class=MsoNormal><span style='font-size:14.0pt;position:relative;top:6.0pt'>&nbsp;</span></p> 
    5448  
    5449 <p class=MsoNormal>The returned value is in units of [cm<sup>-1</sup>], on 
    5450 absolute scale. In the parameters, sld_tail = SLD of the tail group, and 
    5451 sld_head = SLD of the head group.</p> 
    5452  
    5453 <p class=MsoNormal>&nbsp;</p> 
    5454  
    5455 <p class=MsoNormal><sub>&nbsp;</sub></p> 
    5456  
    5457 <div align=center> 
    5458  
    5459 <table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 
    5460  style='border-collapse:collapse;border:none'> 
    5461  <tr style='height:18.8pt'> 
    5462   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
    5463   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5464   <p class=MsoBodyText>Parameter name</p> 
    5465   </td> 
    5466   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
    5467   border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5468   <p class=MsoBodyText>Units</p> 
    5469   </td> 
    5470   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
    5471   border-left:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5472   <p class=MsoBodyText>Default value</p> 
    5473   </td> 
    5474  </tr> 
    5475  <tr style='height:18.8pt'> 
    5476   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
    5477   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5478   <p class=MsoBodyText>background</p> 
    5479   </td> 
    5480   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5481   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5482   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5483   <p class=MsoBodyText>cm<sup>-1</sup></p> 
    5484   </td> 
    5485   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5486   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5487   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5488   <p class=MsoBodyText>0.0</p> 
    5489   </td> 
    5490  </tr> 
    5491  <tr style='height:18.8pt'> 
    5492   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
    5493   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5494   <p class=MsoBodyText>sld_head</p> 
    5495   </td> 
    5496   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5497   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5498   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5499   <p class=MsoBodyText>Å<sup> -2</sup></p> 
    5500   </td> 
    5501   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5502   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5503   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5504   <p class=MsoBodyText>3e-006</p> 
    5505   </td> 
    5506  </tr> 
    5507  <tr style='height:18.8pt'> 
    5508   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
    5509   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5510   <p class=MsoBodyText>scale</p> 
    5511   </td> 
    5512   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5513   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5514   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5515   <p class=MsoBodyText>&nbsp;</p> 
    5516   </td> 
    5517   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5518   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5519   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5520   <p class=MsoBodyText>1</p> 
    5521   </td> 
    5522  </tr> 
    5523  <tr style='height:18.8pt'> 
    5524   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
    5525   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5526   <p class=MsoBodyText>sld_solvent</p> 
    5527   </td> 
    5528   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5529   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5530   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5531   <p class=MsoBodyText>Å<sup> -2</sup></p> 
    5532   </td> 
    5533   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5534   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5535   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5536   <p class=MsoBodyText>6e-006</p> 
    5537   </td> 
    5538  </tr> 
    5539  <tr style='height:18.8pt'> 
    5540   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
    5541   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5542   <p class=MsoBodyText>h_thickness</p> 
    5543   </td> 
    5544   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5545   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5546   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5547   <p class=MsoBodyText>Å</p> 
    5548   </td> 
    5549   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5550   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5551   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5552   <p class=MsoBodyText>10</p> 
    5553   </td> 
    5554  </tr> 
    5555  <tr style='height:18.8pt'> 
    5556   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
    5557   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5558   <p class=MsoBodyText>t_length</p> 
    5559   </td> 
    5560   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5561   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5562   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5563   <p class=MsoBodyText>Å</p> 
    5564   </td> 
    5565   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5566   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5567   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5568   <p class=MsoBodyText>15</p> 
    5569   </td> 
    5570  </tr> 
    5571  <tr style='height:18.8pt'> 
    5572   <td width=143 valign=top style='width:107.0pt;border:solid windowtext 1.0pt; 
    5573   border-top:none;padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5574   <p class=MsoBodyText>sld_tail</p> 
    5575   </td> 
    5576   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5577   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5578   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5579   <p class=MsoBodyText>Å<sup> -2</sup></p> 
    5580   </td> 
    5581   <td width=143 valign=top style='width:107.0pt;border-top:none;border-left: 
    5582   none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; 
    5583   padding:0in 5.4pt 0in 5.4pt;height:18.8pt'> 
    5584   <p class=MsoBodyText>0</p> 
    5585   </td> 
    5586  </tr> 
    5587 </table> 
    5588  
    5589 </div> 
    5590  
    5591 <p class=MsoNormal>&nbsp;</p> 
    5592  
    5593 <p class=MsoNormal>&nbsp;</p> 
    5594  
    5595 <p class=MsoNormal align=center style='text-align:center'><img border=0 
    5596 width=444 height=343 src="../images/html/image079.png"></p> 
    5597  
    5598 <p class=MsoNormal align=center style='text-align:center;text-autospace:none'><b>Figure. 
    5599 1D plot using the default values (w/1000 data point).</b></p> 
    5600  
    5601 <p class=MsoNormal align=center style='text-align:center'>&nbsp;</p> 
    5602  
    5603 <p class=MsoNormal align=center style='text-align:center'>&nbsp;</p> 
    5604  
    5605 <p class=MsoNormal>Our model uses the form factor calculations implemented in a 
    5606 c-library provided by the NIST Center for Neutron Research (Kline, 2006):</p> 
    5607  
    5608 <p class=MsoNormal>&nbsp;</p> 
    5609  
    5610 <p class=MsoBodyText>REFERENCE</p> 
    5611  
    5612 <p class=MsoNormal>Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 
    5613 487-502.</p> 
    5614  
    5615 <p class=MsoNormal>            also in J. Phys. Chem. B, 105, (2001) 
    5616 11081-11088.</p> 
    5617  
    5618 <p class=MsoNormal>&nbsp;</p> 
    5619  
    5620 <p class=MsoNormal>&nbsp;</p> 
    5621  
    5622 <p class=MsoNormal>&nbsp;</p> 
    5623  
    5624 <p class=MsoNormal><b>&nbsp;</b></p> 
    5625  
    5626 <p class=MsoNormal><b>&nbsp;</b></p> 
    5627  
    5628  
    5629 <p class=MsoNormal style='margin-left:.55in;text-indent:-.3in'><b><span 
    5630 style='font-size:14.0pt'>2.19.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    5631 </span></span></b><b><span style='font-size:14.0pt'><a name="LamellarPSHGModel">LamellarPSHGModel</a></span></b></p> 
    5632  
    5633 <p class=MsoNormal>&nbsp;</p> 
    5634  
    5635 <p class=MsoNormal>This model provides the scattering intensity (<b>form factor</b> 
    5636 <b>*</b> <b>structure factor</b>), I(<i>q</i>), for a lyotropic lamellar phase where 
    5637 a random distribution in solution are assumed.  The SLD of the head region is 
    5638 taken to be different from the SLD of the tail region.</p> 
    5639  
    5640 <p class=MsoNormal>&nbsp;</p> 
    5641  
    5642 <p class=MsoNormal>The scattering intensity I(q) is:</p> 
    5643  
    5644 <p class=MsoNormal>&nbsp;</p> 
    5645  
    5646 <p class=MsoNormal align=center style='text-align:center'><span 
    5647 style='position:relative;top:15.0pt'><img border=0 width=133 height=46 
    5648 src="../images/html/image077.png"></span></p> 
    5649  
    5650 <p class=MsoNormal align=center style='text-align:center'><span 
    5651 style='position:relative;top:16.0pt'>&nbsp;</span></p> 
    5652  
    5653 <p class=MsoNormal>The form factor is,</p> 
    5654  
    5655 <p class=MsoNormal>&nbsp;</p> 
    5656  
    5657 <p class=MsoNormal align=center style='text-align:center'><span 
    5658 style='position:relative;top:15.0pt'><img border=0 width=398 height=46 
    5659 src="../images/html/image078.png"></span></p> 
    5660  
    5661 <p class=MsoNormal align=center style='text-align:center'><span 
    5662 style='position:relative;top:16.0pt'>&nbsp;</span></p> 
    5663  
    56645668<p class=MsoNormal>The structure factor is</p> 
    56655669 
    … …  
    56915695<p class=MsoNormal>&nbsp;</p> 
    56925696 
    5693 <p class=MsoNormal>where <span style='font-family:Symbol'>d<sub>T</sub></span> 
    5694 = tail length (or t_length), <span style='font-family:Symbol'>d<sub>H</sub></span> 
    5695 = heasd thickness (or h_thickness) , <span style='font-family:Symbol'>Dr</span><sub>H</sub> 
    5696 = SLD (headgroup) - SLD(solvent), and <span style='font-family:Symbol'>Dr</span><sub>T</sub> 
     5697<p class=MsoNormal>where delta<sub>T</sub> 
     5698= tail length (or t_length), delta<sub>H</sub> 
     5699= head thickness (or h_thickness) , <i><span style='font-family:"Arial","sans-serif"'>&#916;</span>&#961;</i><sub>H</sub> 
     5700= SLD (headgroup) - SLD(solvent), and <i><span style='font-family:"Arial","sans-serif"'>&#916;</span>&#961;</i><sub>T</sub> 
    56975701= SLD (tail) - SLD(headgroup). Here d= (repeat) spacing, K=smectic bending 
    56985702elasticity, B=compression modulus, and N = number of lamellar plates 
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