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267	<body lang=EN-US link=blue vlink=purple style='word-wrap:break-word'>
268
269	<div class=WordSection1>
270
271	<h1 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
272	0in;line-height:115%'>Texture analysis of 2D data in GSAS-II</h1>
273
274	<p class=MsoNormal style='margin-bottom:0in'><BL><span style='font-family:Symbol'>·</span>
275	<b>A video version of this tutorial is available at <a
276	href="https://anl.box.com/v/Textureanalysisof2DdatainGSAS-" target="_blank">https://anl.box.com/v/Textureanalysisof2DdatainGSAS-</a></b>
277	</p>
278
279	<p class=MsoNormal style='margin-bottom:0in'><span style='font-family:Symbol'>·</span>
280	Exercise files are found <a href="data/" target="_blank">here</a> </p>
281
282	</BL>
283
284	<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
285	0in;line-height:115%'>Introduction</h2>
286
287	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Texture
288	analysis using GSAS-II employs spherical harmonics modeling, as described by
289	Bunge, "Texture Analysis in Materials Science" (1982), and
290	implemented by Von Dreele, J. Appl. Cryst., <b>30</b>, 517-525 (1997) in GSAS.
291	The even part of the orientation distribution function (ODF) via the general
292	axis equation</p>
293
294	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
295	style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=357
296	height=56
297	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image001.png"></span></p>
298
299	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
300	margin-left:0in;line-height:115%'>is used to give the intensity corrections due
301	to texture. The two harmonic terms, <span
302	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
303	top:3.0pt'><img width=43 height=35
304	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image002.png"></span> and
305	<span
306	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
307	top:3.0pt'><img width=40 height=35
308	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image003.png"></span>,
309	take on values according to the crystal and sample symmetries, respectively,
310	and thus the two inner summations are over only the resulting unique, nonzero
311	harmonic terms. These unique terms are automatically selected by GSAS-II
312	according to the space group symmetry and the user chosen sample symmetry. The
313	available sample symmetries are cylindrical symmetry, 2/m, mmm and no symmetry.
314	The choice of sample symmetry profoundly affects the selection of harmonic
315	coefficients. For example, in the case of cylindrical sample symmetry (fiber
316	texture) only <span
317	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
318	top:3.0pt'><img width=39 height=35
319	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"></span> terms
320	are nonzero so the rest are excluded from the summations and the set of <span
321	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
322	top:3.0pt'><img width=28 height=35
323	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png"></span>coefficients
324	is sufficient to describe the effect on the diffraction patterns due to
325	texture. The crystal harmonic factor, <span
326	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
327	top:3.0pt'><img width=43 height=35
328	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"></span>,
329	is defined for each reflection, h, <i>via</i> polar and azimuthal coordinates (<span
330	style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
331	of a unit vector coincident with h relative to the reciprocal lattice. For most
332	crystal symmetries, <span style='font-family:Symbol'>f</span> is the angle
333	between h and the n-th order major rotation axis of the space group (usually
334	the c-axis) and <span style='font-family:Symbol'>b</span> is the angle between
335	the projections of h and any secondary axis (usually the a-axis) onto the
336	normal plane. In a similar way the sample harmonic factor, <span
337	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
338	top:3.0pt'><img width=40 height=35
339	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image003.png"></span>,
340	is defined according to polar and azimuthal coordinates (<span
341	style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
342	of a unit vector coincident with the diffraction vector relative to a
343	coordinate system attached to the external form of the sample. For example, in
344	the case of a rolled steel plate having mmm symmetry, the polar angle, <span
345	style='font-family:Symbol'>y</span>, is frequently measured from the normal
346	direction (ND) and <span style='font-family:Symbol'>g</span> is then measured
347	from the rolling direction (RD) in the TD (transverse direction) - RD plane.
348	Thus, the general axis equation becomes</p>
349
350	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
351	margin-left:0in;line-height:115%'><span
352	style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=428
353	height=72
354	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image007.png"></span><br>
355	<br>
356	</p>
357
358	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In a
359	diffraction experiment the crystal reflection coordinates (<span
360	style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
361	are determined by the choice of reflection index (hkl) while the sample coordinates
362	(<span style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
363	are determined by the sample orientation on the diffractometer.</p>
364
365	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
366	margin-left:0in;line-height:115%'>To define the sample coordinates (<span
367	style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>),
368	we have defined an instrument coordinate system (I, J, K) such that K is
369	parallel to the diffraction vector and J is coincident with the direction of
370	the incident radiation beam toward the source. We further define a standard set
371	of right-handed goniometer eulerian angles (<span style='font-family:Symbol'>W</span>,
372	<span style='font-family:Symbol'>C</span>, <span style='font-family:Symbol'>F</span>)
373	so that <span style='font-family:Symbol'>W</span> and <span style='font-family:
374	Symbol'>F</span> are rotations about K and <span style='font-family:Symbol'>C</span>
375	is a rotation about J when <span style='font-family:Symbol'>W</span> <span
376	style='font-family:Symbol'> </span>= 0. Finally, as the sample may be mounted
377	so that the sample coordinate system (I<sub>s</sub>, J<sub>s</sub>, K<sub>s</sub>)
378	does not coincide with the instrument coordinate system (I, J, K), we define
379	three eulerian sample rotation offset angles (<span style='font-family:Symbol'>W</span><sub>s</sub>,
380	<span style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:
381	Symbol'>F</span><sub>s</sub>) that describe the rotation from (I<sub>s</sub>, J<sub>s</sub>,
382	K<sub>s</sub>) to (I, J, K). The sample rotation angles are defined so that
383	with the goniometer angles at zero <span style='font-family:Symbol'>W</span><sub>s</sub>
384	and <span style='font-family:Symbol'>F</span><sub>s</sub> are rotations about K
385	and <span style='font-family:Symbol'>C</span><sub>s</sub> is a rotation about
386	J. The zeros of these three sample rotation angles can be refined as part of
387	the Rietveld analysis to accommodate any angular offset in sample mounting.
388	After including the diffraction angle, <span style='font-family:Symbol'>Q</span>,
389	and a detector azimuthal angle, A, the full rotation matrix, <b>M</b>, is </p>
390
391	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
392	margin-left:0in;line-height:115%'><b>M = -</b><b><span style='font-family:Symbol'>Q</span>A</b><b><span
393	style='font-family:Symbol'>WC</span>(</b><b><span style='font-family:Symbol'>F</span>+</b><b><span
394	style='font-family:Symbol'>F</span><sub>s</sub>)</b><b><span style='font-family:
395	Symbol'>C</span><sub>s</sub></b><b><span style='font-family:Symbol'>W</span><sub>s</sub></b></p>
396
397	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
398	margin-left:0in;line-height:115%'>By transformation of unit Cartesian vectors
399	(100, 010 and 001) with this rotation matrix, the sample orientation
400	coordinates (<span style='font-family:Symbol'>y</span>, <span style='font-family:
401	Symbol'>g</span>) are given by</p>
402
403	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
404	margin-left:0in;line-height:115%'><i>cos</i>(<span style='font-family:Symbol'>y</span>)
405	= <span
406	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
407	top:15.0pt'><img width=45 height=67
408	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image008.png"></span> and
409	<i>tan</i>(<span style='font-family:Symbol'>g</span>) = <span
410	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
411	top:15.0pt'><img width=107 height=67
412	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image009.png"></span></p>
413
414	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
415	margin-left:0in;line-height:115%'>The harmonic terms, <span
416	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
417	top:3.0pt'><img width=62 height=35
418	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image010.png"></span> and
419	<span
420	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
421	top:3.0pt'><img width=57 height=35
422	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image011.png"></span>,
423	are developed from</p>
424
425	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
426	margin-left:0in;line-height:115%'><span
427	style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=220
428	height=56
429	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image012.png"></span></p>
430
431	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
432	margin-left:0in;line-height:115%'>where the normalized associated Legendre
433	functions, <span
434	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
435	top:3.0pt'><img width=44 height=35
436	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image013.png"></span>,
437	are defined via a Fourier expansion as</p>
438
439	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
440	margin-left:0in;line-height:115%'><span
441	style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=206
442	height=70
443	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image014.png"></span></p>
444
445	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
446	margin-left:0in;line-height:115%'>for m even and</p>
447
448	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
449	margin-left:0in;line-height:115%'><span
450	style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=211
451	height=70
452	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image015.png"></span></p>
453
454	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
455	margin-left:0in;line-height:115%'>for m odd. Each sum is only over either the
456	even or odd values of s, respectively, because of the properties of the Fourier
457	coefficients, <span
458	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
459	top:3.0pt'><img width=33 height=35
460	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.png"></span>.
461	These Fourier coefficients are determined so that the definition</p>
462
463	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
464	margin-left:0in;line-height:115%'><span
465	style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=565
466	height=74
467	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image017.png"></span></p>
468
469	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
470	margin-left:0in;line-height:115%'>is satisfied. Terms of the form <span
471	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
472	top:3.0pt'><img width=148 height=35
473	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.png"></span> and
474	<span
475	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
476	top:3.0pt'><img width=134 height=35
477	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png"></span> are
478	combined depending on the symmetry and the value of m along with appropriate
479	normalization coefficients to give the harmonic terms <span
480	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
481	top:3.0pt'><img width=64 height=35
482	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"></span> and
483	<span
484	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
485	top:3.0pt'><img width=60 height=35
486	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png"></span>.
487	For cubic crystal symmetry, the term <span
488	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
489	top:3.0pt'><img width=64 height=35
490	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"></span> is
491	obtained directly from the Fourier expansion</p>
492
493	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
494	margin-left:0in;line-height:115%'><span
495	style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=258
496	height=70
497	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.png"></span></p>
498
499	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
500	margin-left:0in;line-height:115%'>using the coefficients, <span
501	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
502	top:3.0pt'><img width=30 height=35
503	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.png"></span>,
504	as tabulated by Bunge (1982). </p>
505
506	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
507	margin-left:0in;line-height:115%'>The Rietveld refinement of texture then proceeds
508	by constructing derivatives of the profile intensities with respect to the
509	allowed harmonic coefficients, <span
510	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
511	top:3.0pt'><img width=29 height=35
512	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"></span>,
513	and the three sample orientation angles, <span style='font-family:Symbol'>W</span><sub>s</sub>,
514	<span style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:
515	Symbol'>F</span><sub>s</sub>, all of which can be adjustable parameters of the
516	refinement. Once the refinement is complete, pole figures for any reflection
517	may be constructed by use of the general axis equation, the refined values for <span
518	style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
519	top:3.0pt'><img width=29 height=35
520	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"></span> and
521	the sample orientation angles <span style='font-family:Symbol'>W</span><sub>s</sub>,
522	<span style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:
523	Symbol'>F</span><sub>s</sub>. </p>
524
525	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
526	margin-left:0in;line-height:115%'>The magnitude of the texture is evaluated
527	from the texture index by</p>
528
529	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
530	margin-left:0in;line-height:115%'><span
531	style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=241
532	height=72
533	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image025.png"></span></p>
534
535	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
536	margin-left:0in;line-height:115%'>If the texture is random then J = 1,
537	otherwise J > 1; for a single crystal J = <span style='font-family:Symbol'>¥.</span>
538	</p>
539
540	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
541	margin-left:0in;line-height:115%'>In GSAS-II the texture is defined in two ways
542	to accommodate the two possible uses of this correction. In one, a suite of
543	spherical harmonics coefficients is defined for the texture of a phase in the
544	sample; this can have any of the possible sample symmetries and is the usual
545	result desired for texture analysis. The other is the suite of spherical
546	harmonics terms for cylindrical sample symmetry with the cylinder axis parallel
547	to K for each phase in each powder pattern (histogram) and is usually used to
548	accommodate preferred orientation effects in a Rietveld refinement. The former
549	description allows refinement of the sample orientation zeros, <span
550	style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
551	<span style='font-family:Symbol'>F</span><sub>s</sub>, but the latter
552	description does not (they are assumed to be zero and not refinable). The
553	sample orientation angles, (<span style='font-family:Symbol'>W</span>, <span
554	style='font-family:Symbol'>C</span>, <span style='font-family:Symbol'>F) </span>are
555	specified in the Sample Parameters table in the GSAS-II data tree structure and
556	are applied for either description.</p>
557
558	<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
559	margin-left:0in;line-height:115%'>In this tutorial we will use both of these
560	descriptions to determine the texture of the two phases in a NiTi shape memory
561	alloy sample with cylindrical symmetry (wire texture) as collected at APS on
562	beam line 1ID-C (data kindly provided by Paul Paradise & Aaron Stebner of
563	Colo. School of Mines). Thus, there are three ways within GSAS-II that can be
564	used for this texture analysis all beginning with the same 2D area detector
565	image. Each will be described in turn after the initial setup of the GSAS-II
566	project, image input & integration.</p>
567
568	<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
569	0in;line-height:115%'>Step 1. Image input & integration</h2>
570
571	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you have
572	not done so already, <u><span style='color:#0070C0'><a
573	href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none'>start
574	GSAS-II</span></a></span></u>. Note that menu entries are listed in <b><span
575	style='font-family:"Calibri",sans-serif'>bold face</span></b> below as <b><span
576	style='font-family:"Calibri",sans-serif'>Help/About GSAS-II</span></b>, which
577	lists first the name of the menu (here <b><span style='font-family:"Calibri",sans-serif'>Help</span></b>)
578	and second the name of the entry in the menu (here <b><span style='font-family:
579	"Calibri",sans-serif'>About GSAS-II</span></b>). </p>
580
581	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Use the <b><span
582	style='font-family:"Calibri",sans-serif'>Import/Image/from GE image file</span></b>
583	menu item to read the data file into the current GSAS-II project. A file
584	selection dialog will be shown; its appearance will depend on your OS. Change
585	the search directory to <b><span style='font-family:"Calibri",sans-serif'>2DTexture/data
586	</span></b>and then select the file <b><span style='font-family:"Calibri",sans-serif'>NDC5_01588_1.ge2</span></b>.
587	An image will appear</p>
588
589	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
590	width=624 height=535 id="Picture 58"
591	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image026.png"></p>
592
593	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and the <b><span
594	style='font-family:"Calibri",sans-serif'>Image Controls</span></b> data page
595	will show</p>
596
597	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
598	width=624 height=389 id="Picture 59"
599	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image027.png"></p>
600
601	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detector
602	was previously calibrated and the coefficients are stored in a file found by
603	doing <b><span style='font-family:"Calibri",sans-serif'>Parms/Load Controls</span></b>
604	from the <b><span style='font-family:"Calibri",sans-serif'>Image Controls</span></b>
605	menu. A file selection popup will appear showing <b><span style='font-family:
606	"Calibri",sans-serif'>NDC5.imctrl</span></b>; select it and press <b><span
607	style='font-family:"Calibri",sans-serif'>Open</span></b>. The <b><span
608	style='font-family:"Calibri",sans-serif'>Image Controls</span></b> window will
609	be repainted with the new values and the image will be redrawn.</p>
610
611	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
612	width=624 height=389 id="Picture 60"
613	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image028.png"></p>
614
615	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detail in
616	the image can be enhanced by lowering the <b><span style='font-family:"Calibri",sans-serif'>Max
617	intensity</span></b> (<b><span style='font-family:"Calibri",sans-serif'>15000</span></b>
618	is suitable) and shows that the diffraction rings show the effect of texture
619	and that the image has a fairly high background. Placing the cursor in the
620	corners or inside the inner ring shows a background >1700. This can be
621	suppressed by adjusting the <b><span style='font-family:"Calibri",sans-serif'>Flat
622	Bkg</span></b> (I chose <b><span style='font-family:"Calibri",sans-serif'>1700</span></b>
623	for this). The image will now show the rings much more clearly.</p>
624
625	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
626	width=624 height=522 id="Picture 61"
627	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image029.png"></p>
628
629	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For texture
630	analysis we will need to integrate the image into a number of slices sampling
631	the changing ring intensity with azimuthal angle. Also note that the image
632	seems to have <b><span style='font-family:"Calibri",sans-serif'>mm</span></b>
633	symmetry so that the unique part of this intensity variation covers 0-90° of
634	azimuth. In addition the ring intensity variation is such that using 10° slices
635	will capture it reasonably well. However, we want to include both 0° and 90° as
636	slice centers. Thus there will be 10 slices beginning at -5° and ending at 95°.
637	Check the <b><span style='font-family:"Calibri",sans-serif'>Show integration
638	limits?</span></b> box and uncheck the <b><span style='font-family:"Calibri",sans-serif'>Do
639	full integration? </span></b>box, enter <b><span style='font-family:"Calibri",sans-serif'>10</span></b>
640	in the <b><span style='font-family:"Calibri",sans-serif'>No. azimuth bins</span></b>,
641	enter <b><span style='font-family:"Calibri",sans-serif'>-5</span></b> in the <b><span
642	style='font-family:"Calibri",sans-serif'>Start azimuth</span></b> box (it will
643	change to 355) and enter <b><span style='font-family:"Calibri",sans-serif'>455</span></b>
644	in the <b><span style='font-family:"Calibri",sans-serif'>End azimuth</span></b>
645	box. In addition, recall that the sample was mounted vertically and thus is
646	aligned with the defined laboratory I axis. Thus, the sample coordinate system
647	needs to be rotated by 90° to match the sample axis with the K axis; this can
648	be done by making the <b><span style='font-family:"Calibri",sans-serif'>Sample
649	goniometer axis Chi</span></b> = <b><span style='font-family:"Calibri",sans-serif'>90</span></b>.
650	The plot will change with each entry and at the end should look like</p>
651
652	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
653	width=624 height=522 id="Picture 62"
654	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image030.png"></p>
655
656	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The <b><span
657	style='font-family:"Calibri",sans-serif'>Image Controls</span></b> should be</p>
658
659	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
660	width=624 height=389 id="Picture 63"
661	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image031.png"></p>
662
663	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It turns out
664	that the image contains a number of picked bits (very high count zingers);
665	these can be mostly eliminated by setting the upper threshold in Masks. Select <b><span
666	style='font-family:"Calibri",sans-serif'>Masks</span></b> and the following
667	should appear</p>
668
669	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
670	width=624 height=191 id="Picture 64"
671	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image032.png"></p>
672
673	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the <b><span
674	style='font-family:"Calibri",sans-serif'>Upper threshold</span></b> to <b><span
675	style='font-family:"Calibri",sans-serif'>2500</span></b>; the image will be
676	redrawn reflecting this mask. By zooming in you may see isolated red pixels;
677	these are excluded points. Make sure the diffraction rings do not have any
678	excluded points. For example with the level set to 2200 the plot shows</p>
679
680	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
681	width=624 height=522 id="Picture 65"
682	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.png"></p>
683
684	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>for one ring.
685	This level is too low. Return to the <b><span style='font-family:"Calibri",sans-serif'>Image
686	Controls</span></b> item in the data tree.</p>
687
688	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
689	ready to integrate the image; do <b><span style='font-family:"Calibri",sans-serif'>Integration/Integrate</span></b>
690	from the <b><span style='font-family:"Calibri",sans-serif'>Image Controls</span></b>
691	menu. When done the last powder pattern in the tree will be displayed</p>
692
693	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
694	width=624 height=522 id="Picture 66"
695	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image034.png"></p>
696
697	<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
698	0in;line-height:115%'>Step 2. Enter NiTi phases</h2>
699
700	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This NiTi
701	alloy consists of two phases, cubic B2 and monoclinic B19. Their parameters
702	are:<br>
703	B2: <b><span style='font-family:"Calibri",sans-serif'>P m 3 m</span></b>, a=<b><span
704	style='font-family:"Calibri",sans-serif'>3.0240</span></b>, Ni <b><span
705	style='font-family:"Calibri",sans-serif'>0,0,0</span></b>, Ti <b><span
706	style='font-family:"Calibri",sans-serif'>œ,œ,œ</span></b>, U<sub>iso</sub>=<b><span
707	style='font-family:"Calibri",sans-serif'>0.005 </span></b>for both.<br>
708	B19: <b><span style='font-family:"Calibri",sans-serif'>P 1 1 21/m</span></b>,
709	a=<b><span style='font-family:"Calibri",sans-serif'>2.8853</span></b>, b=<b><span
710	style='font-family:"Calibri",sans-serif'>4.6353</span></b>, c=<b><span
711	style='font-family:"Calibri",sans-serif'>4.1368</span></b>, γ=<b><span
712	style='font-family:"Calibri",sans-serif'>96.821</span></b>, Ti <b><span
713	style='font-family:"Calibri",sans-serif'>0.5787,0.2841,Œ</span></b>, Ni <b><span
714	style='font-family:"Calibri",sans-serif'>0.9700,0.8209,Œ</span></b>, U<sub>iso</sub>=<b><span
715	style='font-family:"Calibri",sans-serif'>0.005</span></b> for both.<br>
716	Use the <b><span style='font-family:"Calibri",sans-serif'>Data/Add new phase</span></b>
717	to enter the <b><span style='font-family:"Calibri",sans-serif'>B2</span></b>
718	and <b><span style='font-family:"Calibri",sans-serif'>B19</span></b> phases;
719	then for each enter the information given above on their respective <b><span
720	style='font-family:"Calibri",sans-serif'>General</span></b> and <b><span
721	style='font-family:"Calibri",sans-serif'>Atoms</span></b> tabs. Dont forget
722	the spaces between the axial fields for the space group symbols. On the <b><span
723	style='font-family:"Calibri",sans-serif'>Atoms</span></b> tab begin by doing <b><span
724	style='font-family:"Calibri",sans-serif'>Edit Atoms/Append atom</span></b>
725	twice then fill in the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
726	and coordinates boxes. A double click of the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
727	entry will show a popup of the Periodic Table; select the element as
728	appropriate. NB: GSAS-II happily takes 1/2 & 1/4 for coordinate values;
729	these get converted to their decimal equivalent upon entry. Note the use of a
730	nonstandard space group designation for B19. When done the B2 Atoms table
731	should look like</p>
732
733	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
734	width=624 height=176 id="Picture 68"
735	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image035.png"></p>
736
737	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and the B19
738	Atoms table should be</p>
739
740	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
741	width=624 height=176 id="Picture 69"
742	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image036.png"></p>
743
744	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
745	<b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab for each
746	phase; there will be a message indicating the lack of data for each. Do <b><span
747	style='font-family:"Calibri",sans-serif'>Edit Phase/Add powder histograms</span></b>,
748	do <b><span style='font-family:"Calibri",sans-serif'>Set All</span></b> on the
749	popup selection window and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>.
750	The window for B2 will change to</p>
751
752	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
753	width=624 height=434 id="Picture 70"
754	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image037.png"></p>
755
756	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and that for
757	B19 will be</p>
758
759	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
760	width=624 height=455 id="Picture 71"
761	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image038.png"></p>
762
763	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You should now
764	save the project file (I used <b><span style='font-family:"Calibri",sans-serif'>NiTi</span></b>
765	for a name); we will use this as a starting point for three different texture
766	determinations. Do a <b><span style='font-family:"Calibri",sans-serif'>File/Save
767	project as</span></b> and give it a new name (I used <b><span
768	style='font-family:"Calibri",sans-serif'>NiTi-A</span></b>); this will become
769	the new project name for the next part of this tutorial.</p>
770
771	<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
772	0in;line-height:115%'>Method A. Full refinement</h2>
773
774	<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
775	0in;line-height:115%'>Introduction</h3>
776
777	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In this method
778	we will do a full Rietveld refinement of the texture, profile parameters, peak
779	position variables and crystal structure parameters. This is suitable in this
780	case because of the relatively small number of histograms (10 in this case)
781	needed for the texture determination; do recall that each phase in each
782	histogram has a set of parameters (e.g. phase fraction, size, mustrain &
783	hydrostatic strain) in addition to the ones for each histogram (e.g. background
784	& scale factor). Consequently the total number of parameters can build up
785	very quickly in this method of analysis. The other two methods seek to reduce
786	this problem by splitting the fitting into a sequential refinement (histogram
787	by histogram) step followed by a texture fitting step.</p>
788
789	<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
790	0in;line-height:115%'>Step 1. Initial refinement</h3>
791
792	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In the initial
793	refinement we need to vary the phase fraction for each phase/histogram and the
794	background in each histogram. To start select any <b><span style='font-family:
795	"Calibri",sans-serif'>PWDR</span></b> entry from the GSAS-II data tree and
796	select <b><span style='font-family:"Calibri",sans-serif'>Sample Parameters</span></b>
797	for it. Note that Goniometer chi is set to 90; that came from the same entry in
798	the Image Controls during integration. Also, if you chose other than the 1<sup>st</sup>
799	PWDR data set the Detector azimuth will be some nonzero value; that is also
800	reflected in the name assigned to the histogram (e.g. <b><span
801	style='font-family:"Calibri",sans-serif'>PWDR NDC5_01588_1.ge2 Azm= 40.00</span></b>).
802	Uncheck the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale
803	factor</span></b> box and then do <b><span style='font-family:"Calibri",sans-serif'>Command/Copy
804	flags</span></b>; select <b><span style='font-family:"Calibri",sans-serif'>Set
805	All</span></b> and then press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>.
806	That will clear the scale factor refinement flag for all histograms; we will be
807	varying the phase fractions instead.</p>
808
809	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select
810	the B2 phase and pick the Data tab; you will see</p>
811
812	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
813	width=624 height=471 id="Picture 72"
814	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"></p>
815
816	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Select the <b><span
817	style='font-family:"Calibri",sans-serif'>Phase fraction</span></b> box. Then do
818	<b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy data</span></b>,
819	select <b><span style='font-family:"Calibri",sans-serif'>Set All</span></b>
820	& press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b> to
821	copy these to the other histograms. Next select the <b><span style='font-family:
822	"Calibri",sans-serif'>B19</span></b> phase and repeat this process. We are now
823	ready for the first refinement; do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>
824	from the main GSAS-II data tree window. A progress bar popup will appear and
825	when done a <b><span style='font-family:"Calibri",sans-serif'>Refinement results</span></b>
826	popup will show with Rw~32%. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
827	to load this result; GSAS-II will return you to the last window you were using
828	and display (NB: pick the 1<sup>st</sup> PWDR entry) the 1<sup>st</sup> powder
829	pattern showing you the fit</p>
830
831	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
832	width=624 height=535 id="Picture 73"
833	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"></p>
834
835	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is quite
836	poor. You can survey the fit successively by 1<sup>st</sup> selecting say the 1<sup>st</sup>
837	PWDR entry from the tree and then using the up/down arrow keys to step to the
838	next one; the plot will redraw at each step (NB: at the same scale as the 1<sup>st</sup>
839	one selected) and the data window will show statistics of the fit. There is a
840	substantial intensity discrepancy; this is due to the texture. It is also
841	evident that some of the peaks are out of place relative to the reflection
842	markers; this is due to macroscopic strain in the drawn wire. For the <span
843	style='font-family:"Calibri",sans-serif'>B2</span> phase select the <b><span
844	style='font-family:"Calibri",sans-serif'>Texture</span></b> tab; it should look
845	like</p>
846
847	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
848	width=624 height=219 id="Picture 74"
849	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png"></p>
850
851	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The texture
852	model is <b><span style='font-family:"Calibri",sans-serif'>cylindrical</span></b>
853	by default; that is what we want. Change the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
854	order</span></b> to <b><span style='font-family:"Calibri",sans-serif'>8</span></b>
855	and check both <b><span style='font-family:"Calibri",sans-serif'>Refine texture</span></b>
856	and <b><span style='font-family:"Calibri",sans-serif'>Show coeff</span></b>.
857	The window should look like</p>
858
859	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
860	width=624 height=232 id="Picture 75"
861	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image042.png"></p>
862
863	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the
864	<b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab, select <b><span
865	style='font-family:"Calibri",sans-serif'>D11</span></b>; the <b><span
866	style='font-family:"Calibri",sans-serif'>Data</span></b> window should look
867	like (any PWDR item will do)</p>
868
869	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
870	width=624 height=321 id="Picture 76"
871	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image043.png"></p>
872
873	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then do <b><span
874	style='font-family:"Calibri",sans-serif'>Edit Phase/Copy flags</span></b> to
875	have <b><span style='font-family:"Calibri",sans-serif'>D11</span></b> refined
876	for all PWDR data sets.</p>
877
878	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select
879	the <b><span style='font-family:"Calibri",sans-serif'>B19</span></b> phase <b><span
880	style='font-family:"Calibri",sans-serif'>Texture</span></b> tab. Then select <b><span
881	style='font-family:"Calibri",sans-serif'>6</span></b> for the <b><span
882	style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> and check
883	the two boxes as before.</p>
884
885	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
886	width=624 height=303 id="Picture 77"
887	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image044.png"></p>
888
889	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the
890	<b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab for the <b><span
891	style='font-family:"Calibri",sans-serif'>B19</span></b> phase and check all 4
892	of the <b><span style='font-family:"Calibri",sans-serif'>Dij</span></b> boxes
893	and do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy flags</span></b>
894	as before. The tab will look like</p>
895
896	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
897	width=624 height=360 id="Picture 78"
898	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image045.png"></p>
899
900	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do <b><span
901	style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
902	main menu. The refinement will finish with Rw ~27%; the 1<sup>st</sup> PWDR
903	pattern looks like</p>
904
905	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
906	width=624 height=535 id="Picture 79"
907	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image046.png"></p>
908
909	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The calculated
910	peaks for both phases are too sharp. It is likely that this is a microstrain
911	effect. Select <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
912	for the <b><span style='font-family:"Calibri",sans-serif'>B2 </span></b>phase
913	and select the <b><span style='font-family:"Calibri",sans-serif'>microstrain</span></b>
914	box. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy
915	flags</span></b> to set it for the other PWDR data sets. Do the same for the <b><span
916	style='font-family:"Calibri",sans-serif'>B19</span></b> phase. Then do <b><span
917	style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
918	main menu. The fit will be substantially improved with Rw ~10%.</p>
919
920	<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
921	0in;line-height:115%'>Step 2. Finish refinement and examine texture</h3>
922
923	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Looking at the
924	individual PWDR data sets (e.g. the one for Azm=20.00)</p>
925
926	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
927	width=624 height=535 id="Picture 80"
928	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"></p>
929
930	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is evident
931	that there remains intensity differences due to texture. We can increase the
932	harmonic order to more closely fit these, however one should only do this
933	carefully. Select the Texture tab for the B2 phase; the Texture tab will show</p>
934
935	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
936	width=624 height=257 id="Picture 81"
937	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"></p>
938
939	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a drawing
940	of the 001 pole figure will be drawn. This is the very typical bulls eye for
941	cylindrical texture; of much more use is an inverse pole figure. Select that
942	from the Texture plot type; the plot will be redrawn</p>
943
944	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
945	width=624 height=535 id="Picture 82"
946	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.png"></p>
947
948	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This shows the
949	probability of reflection vectors coinciding with the sample wire axis the high
950	spots are the 111 family of reflections. We should try the next higher Harmonic
951	order (10). </p>
952
953	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
954	Texture tab for the B19 phase. Again a bullseye pole figure is drawn; change
955	that to an Inverse pole figure.</p>
956
957	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
958	width=624 height=535 id="Picture 83"
959	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"></p>
960
961	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This phase is very
962	strongly textured (the cursor shows 12-13 MRD at the peaks) along the -140
963	direction. Again we want to increment the Harmonic order to the next higher
964	level (8). Again do Calculate/Refine from the main menu; the Rwp has dropped to
965	~8.9%. One can add the atom Uiso for the Ni and Ti atoms in the B2 phase and
966	the coordinates and Uiso for the B19 phase. The Rw drops a bit further to
967	~8.4%. Finally, we can increase the harmonic order again for the B19 phase (it
968	is very strongly textured!) to 10 and the B2 phase to 12; the final refinement
969	converged to Rw ~7.8% and the B19 inverse pole figure has peaks at ~18 MRD
970	(Multiple of Random Distribution) and the B2 phase peaks are ~7MRD.</p>
971
972	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B19
973	coefficients</p>
974
975	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
976	width=624 height=317 id="Picture 84"
977	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"></p>
978
979	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and inverse
980	pole figure</p>
981
982	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
983	width=624 height=535 id="Picture 85"
984	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"></p>
985
986	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B2
987	coefficients</p>
988
989	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
990	width=624 height=224 id="Picture 86"
991	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"></p>
992
993	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and inverse
994	pole figure</p>
995
996	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
997	width=624 height=535 id="Picture 87"
998	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"></p>
999
1000	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This completes
1001	the tutorial on Method A for doing texture analysis. It is useful for a case like
1002	this one where there are very few data sets required for the texture analysis.
1003	However, for the case of lower sample symmetry one must several dozen or even a
1004	few hundred histograms and then the suite of parameters can easily be > 1000
1005	of which only a few dozen describe the texture. This leads to the next Methods
1006	for texture analysis in GSAS-II.</p>
1007
1008	<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
1009	0in;line-height:115%'>Method B. Sequential refinement & texture analysis
1010	from result</h2>
1011
1012	<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
1013	0in;line-height:115%'>Introduction</h3>
1014
1015	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
1016	the texture analysis in much the same way as Method A except that all the
1017	initial refinements are done sequentially, that is refinements are done for
1018	the parameters associated with each powder pattern to convergence in a serial
1019	fashion. In this case where there are 10 PWDR data sets, there will be 10
1020	refinements done in sequence. Parameters that span all the data (e.g. lattice
1021	parameters, atom parameters & texture) are not varied in this sequence
1022	refinement. The effect of texture is modeled as a Preferred Orientation
1023	correction to each histogram. To begin do <b><span style='font-family:"Calibri",sans-serif'>File/Open
1024	project</span></b> for the <b><span style='font-family:"Calibri",sans-serif'>NiTi.gpx</span></b>
1025	file created in the first step and then do a <b><span style='font-family:"Calibri",sans-serif'>File/Save
1026	project as</span></b> to save it as <b><span style='font-family:"Calibri",sans-serif'>NiTi-B</span></b>.
1027	This renames the project and it should have one IMG, 10 PWDR entries and two
1028	phases of NiTi (B2 and B19).</p>
1029
1030	<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
1031	0in;line-height:115%'>Step 1. Initial refinement</h3>
1032
1033	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
1034	the same way as Method A so Ill be brief. Do the following steps:</p>
1035
1036	<p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;text-indent:
1037	-.25in;line-height:115%'>1)<span style='font:7.0pt "Times New Roman"'>
1038	</span>Select any <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b>
1039	entry, go to <b><span style='font-family:"Calibri",sans-serif'>Sample Parameters</span></b>
1040	and uncheck <b><span style='font-family:"Calibri",sans-serif'>Histogram scale
1041	factor</span></b>. Then copy the flags to the other PWDR entries.</p>
1042
1043	<p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;text-indent:
1044	-.25in;line-height:115%'>2)<span style='font:7.0pt "Times New Roman"'>
1045	</span>Select the <b><span style='font-family:"Calibri",sans-serif'>B2</span></b>
1046	phase <b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab and
1047	check the <b><span style='font-family:"Calibri",sans-serif'>Phase fraction</span></b>
1048	box and change the <b><span style='font-family:"Calibri",sans-serif'>Preferred
1049	orientation model</span></b> to <b><span style='font-family:"Calibri",sans-serif'>Spherical
1050	harmonics</span></b>. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit
1051	Phase/Copy data</span></b> to copy both the flag and the model to the other
1052	PWDR entries.</p>
1053
1054	<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;text-indent:-.25in;
1055	line-height:115%'>3)<span style='font:7.0pt "Times New Roman"'>
1056	</span>Select the <b><span style='font-family:"Calibri",sans-serif'>B19</span></b>
1057	phase <b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab and
1058	check the <b><span style='font-family:"Calibri",sans-serif'>Phase fraction box</span></b>
1059	and change the <b><span style='font-family:"Calibri",sans-serif'>Preferred
1060	orientation model</span></b> to <b><span style='font-family:"Calibri",sans-serif'>Spherical
1061	harmonics</span></b>. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit
1062	Phase/Copy data</span></b> to copy both the flag and the model to the other
1063	PWDR entries.</p>
1064
1065	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select <b><span
1066	style='font-family:"Calibri",sans-serif'>Controls</span></b> from the GSAS-II
1067	data tree</p>
1068
1069	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1070	width=624 height=191 id="Picture 88"
1071	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"></p>
1072
1073	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Press the <b><span
1074	style='font-family:"Calibri",sans-serif'>Select Data</span></b> button for <b><span
1075	style='font-family:"Calibri",sans-serif'>Sequential Refinement</span></b>; a
1076	file selection popup will appear. Do <b><span style='font-family:"Calibri",sans-serif'>Set
1077	All</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>.
1078	The <b><span style='font-family:"Calibri",sans-serif'>Controls</span></b> page
1079	will be repainted indicating that 10 data sets are selected for sequential
1080	refinement.</p>
1081
1082	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1083	width=624 height=199 id="Picture 89"
1084	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"></p>
1085
1086	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You have the
1087	choice of starting at the last one and for copying results from one to the
1088	next. We wont do either here. Each refinement will use the other controls
1089	(e.g. <b><span style='font-family:"Calibri",sans-serif'>Max cycles</span></b>)
1090	as controls. We are now ready to do the 1<sup>st</sup> sequential refinement.
1091	Do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Sequential
1092	refine</span></b> from the main menu. A progress bar popup will appear showing
1093	residuals as it processes each of 10 data sets. After a few seconds the <b><span
1094	style='font-family:"Calibri",sans-serif'>Refinement results</span></b> popup
1095	will appear; press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1096	to accept them. The data window displays the <b><span style='font-family:"Calibri",sans-serif'>Sequential
1097	refinement results</span></b> as a table.</p>
1098
1099	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1100	width=624 height=176 id="Picture 90"
1101	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"></p>
1102
1103	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>There is a row
1104	for each data set and columns for all refined parameters and some derived ones along
1105	with residual and convergence indicators. The residuals are not very good (we
1106	havent really refined much) but the Δχ<sup>2</sup> column shows that
1107	convergence was achieved (NB: poor convergence will be highlighted in yellow or
1108	red depending on how bad it is).</p>
1109
1110	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you examine
1111	one of the PWDR entries, youll see that just in this point in Method A much of
1112	the misfit is texture and perhaps peak position.</p>
1113
1114	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1115	width=624 height=535 id="Picture 91"
1116	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"></p>
1117
1118	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>To set these
1119	parameters, select the Data tab for the B2 phase</p>
1120
1121	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1122	width=508 height=500 id="Picture 5"
1123	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image117.png"></p>
1124
1125	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Check the <b><span
1126	style='font-family:"Calibri",sans-serif'>D11</span></b> box under
1127	Hydrostatic/elastic strain, set the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
1128	order</span></b> to <b><span style='font-family:"Calibri",sans-serif'>6</span></b>
1129	and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1130	box for it (Preferred orientation). Then in two steps, do <b><span
1131	style='font-family:"Calibri",sans-serif'>Edit Phase/Copy flags</span></b> and <b><span
1132	style='font-family:"Calibri",sans-serif'>Set All</span></b> for the file
1133	selection. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit
1134	Phase/Copy selected data</span></b>; that will bring up a new popup</p>
1135
1136	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1137	width=322 height=390 id="Picture 92"
1138	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image118.png"></p>
1139
1140	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This allows
1141	you to select which parameters to copy data and flags. Select <b><span
1142	style='font-family:"Calibri",sans-serif'>Pref. Ori.</span></b> And press <b><span
1143	style='font-family:"Calibri",sans-serif'>OK</span></b>; the file selection is
1144	next. Do <b><span style='font-family:"Calibri",sans-serif'>Set All</span></b>
1145	and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b> to do this
1146	copy. That copies the full spherical harmonics model to the other data sets.
1147	Select one to check if youd like.</p>
1148
1149	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next do the
1150	same thing for the B19 phase; here there are 4 <b><span style='font-family:
1151	"Calibri",sans-serif'>Dij </span></b>parameters to check (do all of them) and
1152	use spherical harmonics order <b><span style='font-family:"Calibri",sans-serif'>4</span></b>.
1153	When done that Data window will look like</p>
1154
1155	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1156	width=624 height=421 id="Picture 93"
1157	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"></p>
1158
1159	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
1160	ready for the next refinement; do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Sequential
1161	refine</span></b>. Be careful not (by habit say) pick Refine; a warning popup
1162	will appear. After it completes the Sequential refinement results shows that
1163	the fit is better but convergence wasnt quite complete.</p>
1164
1165	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1166	width=624 height=204 id="Picture 95"
1167	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"></p>
1168
1169	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is probably
1170	best to do another round of sequential refinement (I had to do two) to get
1171	convergence. A plot of one PWDR entry gives</p>
1172
1173	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1174	width=624 height=535 id="Picture 96"
1175	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"></p>
1176
1177	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>As our
1178	experience in Method A, the calculated peaks are too sharp. We need to vary the
1179	mustrain parameters for both phases. Go to the Data tab for each phase, check
1180	the <b><span style='font-family:"Calibri",sans-serif'>microstrain</span></b>
1181	box and do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy
1182	flags</span></b> for all the data sets. Then do another <b><span
1183	style='font-family:"Calibri",sans-serif'>Calculate/Sequential refine</span></b>.
1184	My Sequential refinement results showed great improvement but incomplete
1185	refinement</p>
1186
1187	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1188	width=624 height=204 id="Picture 97"
1189	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"></p>
1190
1191	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Repeating the
1192	sequential refinement (twice) gave convergence.</p>
1193
1194	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1195	width=624 height=204 id="Picture 98"
1196	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"></p>
1197
1198	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Examination of
1199	the PWDR data sets showed a fairly good fit but some discrepancies (especially
1200	for Azm=20.00)</p>
1201
1202	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1203	width=624 height=535 id="Picture 99"
1204	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"></p>
1205
1206	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Showing that
1207	perhaps the B19 phase needs high order spherical harmonics. Select the Data
1208	tab for the B19 phase and change the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
1209	order</span></b> to <b><span style='font-family:"Calibri",sans-serif'>6</span></b>.
1210	Then do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy
1211	selected data</span></b> for <b><span style='font-family:"Calibri",sans-serif'>Pref.Ori.</span></b>
1212	to the other data sets. This (after few repeats) gives a further improvement in
1213	the fit</p>
1214
1215	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1216	width=624 height=204 id="Picture 100"
1217	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"></p>
1218
1219	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This fit is
1220	now sufficient for us to proceed to the next step and determine the texture of
1221	the two phases.</p>
1222
1223	<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
1224	0in;line-height:115%'>Step 2. Texture analysis</h3>
1225
1226	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>During the
1227	sequential refinements done in Step 1, we fitted the profiles allowing strain
1228	parameters (Dij) for peak position shifts and microstrain for peak shape. We
1229	modeled the intensity variation with a spherical harmonics preferred
1230	orientation correction. If you select any PWDR entry from the GSAS-II data tree
1231	and pick the Reflection List subentry (at the bottom) you can see the magnitude
1232	of this correction for each reflection in each phase.</p>
1233
1234	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For the B2
1235	phase we see</p>
1236
1237	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1238	width=624 height=204 id="Picture 101"
1239	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"></p>
1240
1241	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and for the
1242	B19 phase we see</p>
1243
1244	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1245	width=624 height=204 id="Picture 102"
1246	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"></p>
1247
1248	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The preferred
1249	orientation correction is Prfo; notice a few entries in red. These are
1250	nonphysical correction values (the correction cant be negative) but by in
1251	large these are small. This next step uses these corrections as input data for
1252	a texture refinement. To start select the Texture tab for the B2 phase; youll
1253	see</p>
1254
1255	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1256	width=608 height=290 id="Picture 16"
1257	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image137.png"></p>
1258
1259	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Since this
1260	sample has wire texture, well use the default Texture model (<b><span
1261	style='font-family:"Calibri",sans-serif'>cylindrical</span></b>). Then set the <b><span
1262	style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> to <b><span
1263	style='font-family:"Calibri",sans-serif'>12</span></b> (what we used earlier)
1264	and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1265	and <b><span style='font-family:"Calibri",sans-serif'>Show coeff</span></b>
1266	boxes. The data window will be redrawn (and an orange blank plot will appear).</p>
1267
1268	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1269	width=624 height=225 id="Picture 103"
1270	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"></p>
1271
1272	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do <b><span
1273	style='font-family:"Calibri",sans-serif'>Texture/Refine texture</span></b> from
1274	the menu; the window will be repainted and a bullseye pole figure will appear. </p>
1275
1276	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1277	width=624 height=225 id="Picture 104"
1278	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"></p>
1279
1280	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the <b><span
1281	style='font-family:"Calibri",sans-serif'>Texture plot type</span></b> to <b><span
1282	style='font-family:"Calibri",sans-serif'>Inverse pole figure</span></b> to get
1283	a more useful plot</p>
1284
1285	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1286	width=624 height=535 id="Picture 105"
1287	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"></p>
1288
1289	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is
1290	essentially the same as we obtained earlier in Method A (maybe not quite as
1291	strong here).</p>
1292
1293	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the
1294	Texture tab for the B19 phase and do the same; use <b><span style='font-family:
1295	"Calibri",sans-serif'>Harmonic order 10</span></b> as we did earlier in Method
1296	A. After setting the two flags and doing <b><span style='font-family:"Calibri",sans-serif'>Texture/Refine
1297	texture</span></b> we get</p>
1298
1299	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1300	width=624 height=324 id="Picture 106"
1301	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"></p>
1302
1303	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a bullseye
1304	pole figure; change that to Inverse pole figure to see the texture</p>
1305
1306	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1307	width=624 height=535 id="Picture 107"
1308	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"></p>
1309
1310	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Again this is
1311	very similar to what we found in Method A but again not quite as strong (max
1312	MRD ~10 instead of ~18) and a bit choppier.</p>
1313
1314	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do a <b><span
1315	style='font-family:"Calibri",sans-serif'>File/Save project</span></b> from the
1316	main menu; this saves the final texture results done in Step 2 (you also will
1317	need it for Method C).</p>
1318
1319	<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
1320	0in;line-height:115%'>Method C. Sequential refinement & full texture
1321	refinement</h2>
1322
1323	<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
1324	0in;line-height:115%'>Introduction</h3>
1325
1326	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This uses the
1327	same approach as Method B except that after the sequential refinements are
1328	finished we then fix almost all the parameters and then do a final texture
1329	refinement with all the data. Thus, this is a replacement for Step 2 in Method
1330	B. To begin do <b><span style='font-family:"Calibri",sans-serif'>File/Open
1331	project</span></b> for the <b><span style='font-family:"Calibri",sans-serif'>NiTi-B.gpx</span></b>
1332	file created in Method B and then do a <b><span style='font-family:"Calibri",sans-serif'>File/Save
1333	project as</span></b> to save it as <b><span style='font-family:"Calibri",sans-serif'>NiTi-C</span></b>.
1334	This renames the project and it should have one IMG, 10 PWDR entries and two
1335	phases of NiTi (B2 and B19).</p>
1336
1337	<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
1338	0in;line-height:115%'>Step 1. Clearing unwanted variables from sequential
1339	refinement</h3>
1340
1341	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Here we want
1342	to clear refinement flags for all parameters that need not be varied in a
1343	texture analysis refinement. The general rule is to not refine any parameter
1344	unless we expect it to affect the peak intensities. These are listed below:</p>
1345
1346	<p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;text-indent:
1347	-.25in;line-height:115%'>1)<span style='font:7.0pt "Times New Roman"'>
1348	</span><b><span style='font-family:"Calibri",sans-serif'>Background</span></b>:
1349	as the background was fit during the sequential refinement we should fix it
1350	here. Select any <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b>
1351	entry and choose the <b><span style='font-family:"Calibri",sans-serif'>Background</span></b>
1352	subentry for it. Clear the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1353	flags and the do <b><span style='font-family:"Calibri",sans-serif'>File/Copy
1354	flags</span></b> selecting all data sets. This will clear all background
1355	refinement flags.</p>
1356
1357	<p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;text-indent:
1358	-.25in;line-height:115%'>2)<span style='font:7.0pt "Times New Roman"'>
1359	</span><b><span style='font-family:"Calibri",sans-serif'>B2</span></b> phase:
1360	we do not want to refine either the microstrain, D<sub>11</sub>, or preferred
1361	orientation coefficients. Select the <b><span style='font-family:"Calibri",sans-serif'>B2</span></b>
1362	phase and its <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1363	tab. Clear the <b><span style='font-family:"Calibri",sans-serif'>microstrain</span></b>,
1364	<b><span style='font-family:"Calibri",sans-serif'>D<sub>11</sub></span></b> and
1365	<b><span style='font-family:"Calibri",sans-serif'>Preferred orientation</span></b>
1366	boxes. Also set the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
1367	order</span></b> to zero (this will avoid a lot of nasty (but harmless)
1368	messages at the start of the refinement). Then do <b><span style='font-family:
1369	"Calibri",sans-serif'>Edit Phase/Copy flags</span></b> selecting all data to
1370	clear all the flags and an <b><span style='font-family:"Calibri",sans-serif'>Edit
1371	Phase/Copy selected data</span></b> for <b><span style='font-family:"Calibri",sans-serif'>Pref.Ori</span></b>
1372	to copy the zeroed out harmonic coefficients.</p>
1373
1374	<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;text-indent:-.25in;
1375	line-height:115%'>3)<span style='font:7.0pt "Times New Roman"'>
1376	</span><b><span style='font-family:"Calibri",sans-serif'>B19</span></b>: we do
1377	not want to refine either the microstrain, Dij, or preferred orientation
1378	coefficients. Select the <b><span style='font-family:"Calibri",sans-serif'>B19</span></b>
1379	phase and its <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1380	tab. Clear the <b><span style='font-family:"Calibri",sans-serif'>microstrain</span></b>,
1381	four <b><span style='font-family:"Calibri",sans-serif'>Dij</span></b> and <b><span
1382	style='font-family:"Calibri",sans-serif'>Preferred orientation</span></b>
1383	boxes. Also set the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
1384	order</span></b> to zero (this will avoid a lot of nasty (but harmless)
1385	messages at the start of the refinement). Then do <b><span style='font-family:
1386	"Calibri",sans-serif'>Edit Phase/Copy flags</span></b> selecting all data to
1387	clear all the flags and an <b><span style='font-family:"Calibri",sans-serif'>Edit
1388	Phase/Copy selected data</span></b> for <b><span style='font-family:"Calibri",sans-serif'>Pref.Ori</span></b>
1389	to copy the zeroed out harmonic coefficients.</p>
1390
1391	<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1392	margin-left:.25in;line-height:115%'> </p>
1393
1394	<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1395	margin-left:.25in;line-height:115%'>Notice that we have allowed refinement of
1396	the <b><span style='font-family:"Calibri",sans-serif'>Phase fractions</span></b>;
1397	these may change during the texture refinement. Now select the <b><span
1398	style='font-family:"Calibri",sans-serif'>Texture</span></b> tab for the <b><span
1399	style='font-family:"Calibri",sans-serif'>B2</span></b> phase (it may still have
1400	values from the Method B).</p>
1401
1402	<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1403	margin-left:.25in;line-height:115%'><img border=0 width=624 height=236
1404	id="Picture 108"
1405	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"></p>
1406
1407	<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1408	margin-left:.25in;line-height:115%'>You can clear these by setting the <b><span
1409	style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> to zero and
1410	then back to <b><span style='font-family:"Calibri",sans-serif'>12</span></b>.
1411	Leave the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1412	& <b><span style='font-family:"Calibri",sans-serif'>Show</span></b> boxes
1413	checked.</p>
1414
1415	<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1416	margin-left:.25in;line-height:115%'><img border=0 width=624 height=236
1417	id="Picture 109"
1418	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"></p>
1419
1420	<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1421	margin-left:.25in;line-height:115%'>Then do the same for the <b><span
1422	style='font-family:"Calibri",sans-serif'>B19</span></b> phase. Select the <b><span
1423	style='font-family:"Calibri",sans-serif'>B19</span></b> phase and its <b><span
1424	style='font-family:"Calibri",sans-serif'>Texture</span></b> tab. Set the <b><span
1425	style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> to zero and
1426	then back to <b><span style='font-family:"Calibri",sans-serif'>10</span></b>.
1427	Leave the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1428	and <b><span style='font-family:"Calibri",sans-serif'>Show</span></b> boxes
1429	checked. This completes the setup for the full texture refinement.</p>
1430
1431	<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
1432	0in;line-height:115%'>Step 2. Texture refinement</h3>
1433
1434	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do <b><span
1435	style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
1436	main menu; you will see the warning message</p>
1437
1438	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1439	width=562 height=130 id="Picture 110"
1440	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image152.png"></p>
1441
1442	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In this case
1443	you do want to do a nonsequential full refinement, so press the <b><span
1444	style='font-family:"Calibri",sans-serif'>OK</span></b> button. A quick look at
1445	the console will show that there are 61 variables in this refinement. If yours
1446	shows more then you didnt clear all the flags in Step 1. The <b><span
1447	style='font-family:"Calibri",sans-serif'>Sequential results</span></b> entry is
1448	deleted from the GSAS-II data tree. A progress bar will show giving the
1449	residuals during the refinement. When finished, select the <b><span
1450	style='font-family:"Calibri",sans-serif'>B2</span></b> phase and its <b><span
1451	style='font-family:"Calibri",sans-serif'>Texture</span></b> tab; if the Texture
1452	plot type is still <b><span style='font-family:"Calibri",sans-serif'>Inverse
1453	pole figure</span></b> (from Method B) you should see</p>
1454
1455	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1456	width=624 height=535 id="Picture 111"
1457	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"></p>
1458
1459	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>which is
1460	almost identical to that from Method A. The coefficients are seen in</p>
1461
1462	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1463	width=624 height=236 id="Picture 112"
1464	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"></p>
1465
1466	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the
1467	<b><span style='font-family:"Calibri",sans-serif'>B19</span></b> phase and its
1468	<b><span style='font-family:"Calibri",sans-serif'>Texture</span></b> tab; the
1469	inverse pole figure is</p>
1470
1471	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1472	width=624 height=535 id="Picture 113"
1473	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"></p>
1474
1475	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and also
1476	almost identical to what was obtained in Method A; the coefficients are seen in</p>
1477
1478	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1479	width=624 height=323 id="Picture 114"
1480	src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"></p>
1481
1482	<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>With this
1483	Method you can add parameters (atom coordinates & thermal motion
1484	parameters) that could not be refined in method B. It should be clear from this
1485	tutorial that in more complex textures where the data set may consist of slices
1486	obtained from a suite of 2D images collected as the sample is rotated, Method C
1487	will give a relatively fast determination of the texture without resorting to
1488	large matrix least-squares refinements.</p>
1489
1490	</div>
1491
1492	</body>
1493
1494	</html>

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