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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:
2720in;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
276href="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> 
280Exercise 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:
2850in;line-height:115%'>Introduction</h2>
286
287<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Texture
288analysis using GSAS-II employs spherical harmonics modeling, as described by
289Bunge, &quot;Texture Analysis in Materials Science&quot; (1982), and
290implemented by Von Dreele, J. Appl. Cryst., <b>30</b>, 517-525 (1997) in GSAS.
291The even part of the orientation distribution function (ODF) via the general
292axis equation</p>
293
294<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
295style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=357
296height=56
297src="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;
300margin-left:0in;line-height:115%'>is used to give the intensity corrections due
301to texture. The two harmonic terms, <span
302style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
303top:3.0pt'><img width=43 height=35
304src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image002.png"></span> and
305<span
306style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
307top:3.0pt'><img width=40 height=35
308src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image003.png"></span>,
309take on values according to the crystal and sample symmetries, respectively,
310and thus the two inner summations are over only the resulting unique, nonzero
311harmonic terms. These unique terms are automatically selected by GSAS-II
312according to the space group symmetry and the user chosen sample symmetry. The
313available sample symmetries are cylindrical symmetry, 2/m, mmm and no symmetry.
314The choice of sample symmetry profoundly affects the selection of harmonic
315coefficients. For example, in the case of cylindrical sample symmetry (fiber
316texture) only <span
317style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
318top:3.0pt'><img width=39 height=35
319src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"></span> terms
320are nonzero so the rest are excluded from the summations and the set of <span
321style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
322top:3.0pt'><img width=28 height=35
323src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png"></span>coefficients
324is sufficient to describe the effect on the diffraction patterns due to
325texture. The crystal harmonic factor, <span
326style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
327top:3.0pt'><img width=43 height=35
328src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"></span>,
329is defined for each reflection, h, <i>via</i> polar and azimuthal coordinates (<span
330style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
331of a unit vector coincident with h relative to the reciprocal lattice. For most
332crystal symmetries, <span style='font-family:Symbol'>f</span> is the angle
333between h and the n-th order major rotation axis of the space group (usually
334the c-axis) and <span style='font-family:Symbol'>b</span> is the angle between
335the projections of h and any secondary axis (usually the a-axis) onto the
336normal plane.  In a similar way the sample harmonic factor, <span
337style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
338top:3.0pt'><img width=40 height=35
339src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image003.png"></span>,
340is defined according to polar and azimuthal coordinates (<span
341style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
342of a unit vector coincident with the diffraction vector relative to a
343coordinate system attached to the external form of the sample. For example, in
344the case of a rolled steel plate having mmm symmetry, the polar angle, <span
345style='font-family:Symbol'>y</span>, is frequently measured from the normal
346direction (ND) and <span style='font-family:Symbol'>g</span> is then measured
347from the rolling direction (RD) in the TD (transverse direction) - RD plane. 
348Thus, the general axis equation becomes</p>
349
350<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
351margin-left:0in;line-height:115%'><span
352style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=428
353height=72
354src="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
359diffraction experiment the crystal reflection coordinates (<span
360style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
361are 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>)
363are 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;
366margin-left:0in;line-height:115%'>To define the sample coordinates (<span
367style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>),
368we have defined an instrument coordinate system (I, J, K) such that K is
369parallel to the diffraction vector and J is coincident with the direction of
370the incident radiation beam toward the source. We further define a standard set
371of 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>)
373so that <span style='font-family:Symbol'>W</span> and <span style='font-family:
374Symbol'>F</span> are rotations about K and <span style='font-family:Symbol'>C</span>
375is a rotation about J when <span style='font-family:Symbol'>W</span> <span
376style='font-family:Symbol'> </span>= 0.  Finally, as the sample may be mounted
377so that the sample coordinate system (I<sub>s</sub>, J<sub>s</sub>, K<sub>s</sub>)
378does not coincide with the instrument coordinate system (I, J, K), we define
379three 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:
381Symbol'>F</span><sub>s</sub>) that describe the rotation from (I<sub>s</sub>, J<sub>s</sub>,
382K<sub>s</sub>) to (I, J, K).  The sample rotation angles are defined so that
383with the goniometer angles at zero <span style='font-family:Symbol'>W</span><sub>s</sub>
384and <span style='font-family:Symbol'>F</span><sub>s</sub> are rotations about K
385and <span style='font-family:Symbol'>C</span><sub>s</sub> is a rotation about
386J.  The zeros of these three sample rotation angles can be refined as part of
387the Rietveld analysis to accommodate any angular offset in sample mounting.
388After including the diffraction angle, <span style='font-family:Symbol'>Q</span>,
389and 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;
392margin-left:0in;line-height:115%'><b>M = -</b><b><span style='font-family:Symbol'>Q</span>A</b><b><span
393style='font-family:Symbol'>WC</span>(</b><b><span style='font-family:Symbol'>F</span>+</b><b><span
394style='font-family:Symbol'>F</span><sub>s</sub>)</b><b><span style='font-family:
395Symbol'>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;
398margin-left:0in;line-height:115%'>By transformation of unit Cartesian vectors
399(100, 010 and 001) with this rotation matrix, the sample orientation
400coordinates (<span style='font-family:Symbol'>y</span>, <span style='font-family:
401Symbol'>g</span>) are given by</p>
402
403<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
404margin-left:0in;line-height:115%'><i>cos</i>(<span style='font-family:Symbol'>y</span>)
405= <span
406style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
407top:15.0pt'><img width=45 height=67
408src="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
410style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
411top:15.0pt'><img width=107 height=67
412src="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;
415margin-left:0in;line-height:115%'>The harmonic terms, <span
416style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
417top:3.0pt'><img width=62 height=35
418src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image010.png"></span> and
419<span
420style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
421top:3.0pt'><img width=57 height=35
422src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image011.png"></span>,
423are developed from</p>
424
425<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
426margin-left:0in;line-height:115%'><span
427style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=220
428height=56
429src="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;
432margin-left:0in;line-height:115%'>where the normalized associated Legendre
433functions, <span
434style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
435top:3.0pt'><img width=44 height=35
436src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image013.png"></span>,
437are defined via a Fourier expansion as</p>
438
439<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
440margin-left:0in;line-height:115%'><span
441style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=206
442height=70
443src="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;
446margin-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;
449margin-left:0in;line-height:115%'><span
450style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=211
451height=70
452src="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;
455margin-left:0in;line-height:115%'>for m odd.  Each sum is only over either the
456even or odd values of s, respectively, because of the properties of the Fourier
457coefficients, <span
458style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
459top:3.0pt'><img width=33 height=35
460src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.png"></span>
461These 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;
464margin-left:0in;line-height:115%'><span
465style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=565
466height=74
467src="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;
470margin-left:0in;line-height:115%'>is satisfied.  Terms of the form <span
471style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
472top:3.0pt'><img width=148 height=35
473src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.png"></span> and
474<span
475style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
476top:3.0pt'><img width=134 height=35
477src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png"></span> are
478combined depending on the symmetry and the value of m along with appropriate
479normalization coefficients to give the harmonic terms <span
480style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
481top:3.0pt'><img width=64 height=35
482src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"></span> and
483<span
484style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
485top:3.0pt'><img width=60 height=35
486src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png"></span>
487For cubic crystal symmetry, the term <span
488style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
489top:3.0pt'><img width=64 height=35
490src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"></span> is
491obtained directly from the Fourier expansion</p>
492
493<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
494margin-left:0in;line-height:115%'><span
495style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=258
496height=70
497src="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;
500margin-left:0in;line-height:115%'>using the coefficients, <span
501style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
502top:3.0pt'><img width=30 height=35
503src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.png"></span>,
504as tabulated by Bunge (1982). </p>
505
506<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
507margin-left:0in;line-height:115%'>The Rietveld refinement of texture then proceeds
508by constructing derivatives of the profile intensities with respect to the
509allowed harmonic coefficients, <span
510style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
511top:3.0pt'><img width=29 height=35
512src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"></span>,
513and 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:
515Symbol'>F</span><sub>s</sub>, all of which can be adjustable parameters of the
516refinement. Once the refinement is complete, pole figures for any reflection
517may be constructed by use of the general axis equation, the refined values for <span
518style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
519top:3.0pt'><img width=29 height=35
520src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"></span> and
521the 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:
523Symbol'>F</span><sub>s</sub>. </p>
524
525<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
526margin-left:0in;line-height:115%'>The magnitude of the texture is evaluated
527from the texture index by</p>
528
529<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
530margin-left:0in;line-height:115%'><span
531style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=241
532height=72
533src="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;
536margin-left:0in;line-height:115%'>If the texture is random then J = 1,
537otherwise J &gt; 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;
541margin-left:0in;line-height:115%'>In GSAS-II the texture is defined in two ways
542to accommodate the two possible uses of this correction. In one, a suite of
543spherical harmonics coefficients is defined for the texture of a phase in the
544sample; this can have any of the possible sample symmetries and is the usual
545result desired for texture analysis. The other is the suite of spherical
546harmonics terms for cylindrical sample symmetry with the cylinder axis parallel
547to K for each phase in each powder pattern (“histogram”) and is usually used to
548accommodate preferred orientation effects in a Rietveld refinement. The former
549description allows refinement of the sample orientation zeros, <span
550style='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
552description does not (they are assumed to be zero and not refinable). The
553sample orientation angles, (<span style='font-family:Symbol'>W</span>, <span
554style='font-family:Symbol'>C</span>, <span style='font-family:Symbol'>F) </span>are
555specified in the Sample Parameters table in the GSAS-II data tree structure and
556are applied for either description.</p>
557
558<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
559margin-left:0in;line-height:115%'>In this tutorial we will use both of these
560descriptions to determine the texture of the two phases in a NiTi shape memory
561alloy sample with cylindrical symmetry (wire texture) as collected at APS on
562beam line 1ID-C (data kindly provided by Paul Paradise &amp; Aaron Stebner of
563Colo. School of Mines). Thus, there are three ways within GSAS-II that can be
564used for this texture analysis all beginning with the same 2D area detector
565image. Each will be described in turn after the initial setup of the GSAS-II
566project, image input &amp; integration.</p>
567
568<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
5690in;line-height:115%'>Step 1. Image input &amp; integration</h2>
570
571<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you have
572not done so already, <u><span style='color:#0070C0'><a
573href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none'>start
574GSAS-II</span></a></span></u>. Note that menu entries are listed in <b><span
575style='font-family:"Calibri",sans-serif'>bold face</span></b> below as <b><span
576style='font-family:"Calibri",sans-serif'>Help/About GSAS-II</span></b>, which
577lists first the name of the menu (here <b><span style='font-family:"Calibri",sans-serif'>Help</span></b>)
578and 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
582style='font-family:"Calibri",sans-serif'>Import/Image/from GE image file</span></b>
583menu item to read the data file into the current GSAS-II project. A file
584selection dialog will be shown; its appearance will depend on your OS. Change
585the 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>.
587An image will appear</p>
588
589<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
590width=624 height=535 id="Picture 58"
591src="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
594style='font-family:"Calibri",sans-serif'>Image Controls</span></b> data page
595will show</p>
596
597<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
598width=624 height=389 id="Picture 59"
599src="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
602was previously calibrated and the coefficients are stored in a file found by
603doing <b><span style='font-family:"Calibri",sans-serif'>Parms/Load Controls</span></b>
604from the <b><span style='font-family:"Calibri",sans-serif'>Image Controls</span></b>
605menu. 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
607style='font-family:"Calibri",sans-serif'>Open</span></b>. The <b><span
608style='font-family:"Calibri",sans-serif'>Image Controls</span></b> window will
609be 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
612width=624 height=389 id="Picture 60"
613src="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
616the image can be enhanced by lowering the <b><span style='font-family:"Calibri",sans-serif'>Max
617intensity</span></b> (<b><span style='font-family:"Calibri",sans-serif'>15000</span></b>
618is suitable) and shows that the diffraction rings show the effect of texture
619and that the image has a fairly high background. Placing the cursor in the
620corners or inside the inner ring shows a background &gt;1700. This can be
621suppressed by adjusting the <b><span style='font-family:"Calibri",sans-serif'>Flat
622Bkg</span></b> (I chose <b><span style='font-family:"Calibri",sans-serif'>1700</span></b>
623for 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
626width=624 height=522 id="Picture 61"
627src="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
630analysis we will need to integrate the image into a number of slices sampling
631the changing ring intensity with azimuthal angle. Also note that the image
632seems to have <b><span style='font-family:"Calibri",sans-serif'>mm</span></b>
633symmetry so that the unique part of this intensity variation covers 0-90° of
634azimuth. In addition the ring intensity variation is such that using 10° slices
635will capture it reasonably well. However, we want to include both 0° and 90° as
636slice centers. Thus there will be 10 slices beginning at -5° and ending at 95°.
637Check the <b><span style='font-family:"Calibri",sans-serif'>Show integration
638limits?</span></b> box and uncheck the <b><span style='font-family:"Calibri",sans-serif'>Do
639full integration? </span></b>box, enter <b><span style='font-family:"Calibri",sans-serif'>10</span></b>
640in the <b><span style='font-family:"Calibri",sans-serif'>No. azimuth bins</span></b>,
641enter <b><span style='font-family:"Calibri",sans-serif'>-5</span></b> in the <b><span
642style='font-family:"Calibri",sans-serif'>Start azimuth</span></b> box (it will
643change to 355) and enter <b><span style='font-family:"Calibri",sans-serif'>455</span></b>
644in the <b><span style='font-family:"Calibri",sans-serif'>End azimuth</span></b>
645box. In addition, recall that the sample was mounted vertically and thus is
646aligned with the defined laboratory I axis. Thus, the sample coordinate system
647needs to be rotated by 90° to match the sample axis with the K axis; this can
648be done by making the <b><span style='font-family:"Calibri",sans-serif'>Sample
649goniometer axis Chi</span></b> = <b><span style='font-family:"Calibri",sans-serif'>90</span></b>.
650The 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
653width=624 height=522 id="Picture 62"
654src="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
657style='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
660width=624 height=389 id="Picture 63"
661src="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
664that the image contains a number of “picked bits” (very high count “zingers”);
665these can be mostly eliminated by setting the upper threshold in Masks. Select <b><span
666style='font-family:"Calibri",sans-serif'>Masks</span></b> and the following
667should appear</p>
668
669<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
670width=624 height=191 id="Picture 64"
671src="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
674style='font-family:"Calibri",sans-serif'>Upper threshold</span></b> to <b><span
675style='font-family:"Calibri",sans-serif'>2500</span></b>; the image will be
676redrawn reflecting this mask. By zooming in you may see isolated red pixels;
677these are excluded points. Make sure the diffraction rings do not have any
678excluded 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
681width=624 height=522 id="Picture 65"
682src="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.
685This level is too low. Return to the <b><span style='font-family:"Calibri",sans-serif'>Image
686Controls</span></b> item in the data tree.</p>
687
688<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
689ready to integrate the image; do <b><span style='font-family:"Calibri",sans-serif'>Integration/Integrate</span></b>
690from the <b><span style='font-family:"Calibri",sans-serif'>Image Controls</span></b>
691menu. 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
694width=624 height=522 id="Picture 66"
695src="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:
6980in;line-height:115%'>Step 2. Enter NiTi phases</h2>
699
700<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This NiTi
701alloy consists of two phases, cubic B2 and monoclinic B19’. Their parameters
702are:<br>
703B2: <b><span style='font-family:"Calibri",sans-serif'>P m 3 m</span></b>, a=<b><span
704style='font-family:"Calibri",sans-serif'>3.0240</span></b>, Ni <b><span
705style='font-family:"Calibri",sans-serif'>0,0,0</span></b>, Ti <b><span
706style='font-family:"Calibri",sans-serif'>œ,œ,œ</span></b>, U<sub>iso</sub>=<b><span
707style='font-family:"Calibri",sans-serif'>0.005 </span></b>for both.<br>
708B19’:  <b><span style='font-family:"Calibri",sans-serif'>P 1 1 21/m</span></b>,
709a=<b><span style='font-family:"Calibri",sans-serif'>2.8853</span></b>, b=<b><span
710style='font-family:"Calibri",sans-serif'>4.6353</span></b>, c=<b><span
711style='font-family:"Calibri",sans-serif'>4.1368</span></b>, &#947;=<b><span
712style='font-family:"Calibri",sans-serif'>96.821</span></b>, Ti <b><span
713style='font-family:"Calibri",sans-serif'>0.5787,0.2841,Œ</span></b>, Ni <b><span
714style='font-family:"Calibri",sans-serif'>0.9700,0.8209,Œ</span></b>, U<sub>iso</sub>=<b><span
715style='font-family:"Calibri",sans-serif'>0.005</span></b> for both.<br>
716Use the <b><span style='font-family:"Calibri",sans-serif'>Data/Add new phase</span></b>
717to enter the <b><span style='font-family:"Calibri",sans-serif'>B2</span></b>
718and <b><span style='font-family:"Calibri",sans-serif'>B19’</span></b> phases;
719then for each enter the information given above on their respective <b><span
720style='font-family:"Calibri",sans-serif'>General</span></b> and <b><span
721style='font-family:"Calibri",sans-serif'>Atoms</span></b> tabs. Don’t forget
722the spaces between the axial fields for the space group symbols. On the <b><span
723style='font-family:"Calibri",sans-serif'>Atoms</span></b> tab begin by doing <b><span
724style='font-family:"Calibri",sans-serif'>Edit Atoms/Append atom</span></b>
725twice then fill in the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
726and coordinates boxes. A double click of the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
727entry will show a popup of the Periodic Table; select the element as
728appropriate. NB: GSAS-II happily takes “1/2” &amp; “1/4” for coordinate values;
729these get converted to their decimal equivalent upon entry. Note the use of a
730nonstandard space group designation for B19’. When done the B2 Atoms table
731should look like</p>
732
733<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
734width=624 height=176 id="Picture 68"
735src="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’
738Atoms table should be</p>
739
740<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
741width=624 height=176 id="Picture 69"
742src="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
746phase; there will be a message indicating the lack of data for each. Do <b><span
747style='font-family:"Calibri",sans-serif'>Edit Phase/Add powder histograms</span></b>,
748do <b><span style='font-family:"Calibri",sans-serif'>Set All</span></b> on the
749popup selection window and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>.
750The window for B2 will change to</p>
751
752<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
753width=624 height=434 id="Picture 70"
754src="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
757B19’ will be</p>
758
759<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
760width=624 height=455 id="Picture 71"
761src="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
764save the project file (I used <b><span style='font-family:"Calibri",sans-serif'>NiTi</span></b>
765for a name); we will use this as a starting point for three different texture
766determinations. Do a <b><span style='font-family:"Calibri",sans-serif'>File/Save
767project as…</span></b> and give it a new name (I used <b><span
768style='font-family:"Calibri",sans-serif'>NiTi-A</span></b>); this will become
769the 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:
7720in;line-height:115%'>Method A. Full refinement</h2>
773
774<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
7750in;line-height:115%'>Introduction</h3>
776
777<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In this method
778we will do a full Rietveld refinement of the texture, profile parameters, peak
779position variables and crystal structure parameters. This is suitable in this
780case because of the relatively small number of histograms (10 in this case)
781needed for the texture determination; do recall that each phase in each
782histogram has a set of parameters (e.g. phase fraction, size, mustrain &amp;
783hydrostatic strain) in addition to the ones for each histogram (e.g. background
784&amp; scale factor). Consequently the total number of parameters can build up
785very quickly in this method of analysis. The other two methods seek to reduce
786this problem by splitting the fitting into a sequential refinement (histogram
787by 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:
7900in;line-height:115%'>Step 1. Initial refinement</h3>
791
792<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In the initial
793refinement we need to vary the phase fraction for each phase/histogram and the
794background 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
796select <b><span style='font-family:"Calibri",sans-serif'>Sample Parameters</span></b>
797for it. Note that Goniometer chi is set to 90; that came from the same entry in
798the Image Controls during integration. Also, if you chose other than the 1<sup>st</sup>
799PWDR data set the Detector azimuth will be some nonzero value; that is also
800reflected in the name assigned to the histogram (e.g. <b><span
801style='font-family:"Calibri",sans-serif'>PWDR NDC5_01588_1.ge2 Azm= 40.00</span></b>).
802Uncheck the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale
803factor</span></b> box and then do <b><span style='font-family:"Calibri",sans-serif'>Command/Copy
804flags</span></b>; select <b><span style='font-family:"Calibri",sans-serif'>Set
805All</span></b> and then press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>.
806That will clear the scale factor refinement flag for all histograms; we will be
807varying the phase fractions instead.</p>
808
809<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select
810the 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
813width=624 height=471 id="Picture 72"
814src="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
817style='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>,
819select <b><span style='font-family:"Calibri",sans-serif'>Set All</span></b>
820&amp; press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b> to
821copy 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
823ready for the first refinement; do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>
824from the main GSAS-II data tree window. A progress bar popup will appear and
825when done a <b><span style='font-family:"Calibri",sans-serif'>Refinement results</span></b>
826popup will show with Rw~32%. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
827to load this result; GSAS-II will return you to the last window you were using
828and display (NB: pick the 1<sup>st</sup> PWDR entry) the 1<sup>st</sup> powder
829pattern showing you the fit</p>
830
831<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
832width=624 height=535 id="Picture 73"
833src="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
836poor. You can survey the fit successively by 1<sup>st</sup> selecting say the 1<sup>st</sup>
837PWDR entry from the tree and then using the up/down arrow keys to step to the
838next one; the plot will redraw at each step (NB: at the same scale as the 1<sup>st</sup>
839one selected) and the data window will show statistics of the fit. There is a
840substantial intensity discrepancy; this is due to the texture. It is also
841evident that some of the peaks are out of place relative to the reflection
842markers; this is due to macroscopic strain in the drawn wire. For the <span
843style='font-family:"Calibri",sans-serif'>B2</span> phase select the <b><span
844style='font-family:"Calibri",sans-serif'>Texture</span></b> tab; it should look
845like</p>
846
847<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
848width=624 height=219 id="Picture 74"
849src="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
852model is <b><span style='font-family:"Calibri",sans-serif'>cylindrical</span></b>
853by default; that is what we want. Change the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
854order</span></b> to <b><span style='font-family:"Calibri",sans-serif'>8</span></b>
855and check both <b><span style='font-family:"Calibri",sans-serif'>Refine texture</span></b>
856and <b><span style='font-family:"Calibri",sans-serif'>Show coeff</span></b>.
857The window should look like</p>
858
859<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
860width=624 height=232 id="Picture 75"
861src="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
865style='font-family:"Calibri",sans-serif'>D11</span></b>; the <b><span
866style='font-family:"Calibri",sans-serif'>Data</span></b> window should look
867like (any PWDR item will do)</p>
868
869<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
870width=624 height=321 id="Picture 76"
871src="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
874style='font-family:"Calibri",sans-serif'>Edit Phase/Copy flags</span></b> to
875have <b><span style='font-family:"Calibri",sans-serif'>D11</span></b> refined
876for all PWDR data sets.</p>
877
878<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select
879the <b><span style='font-family:"Calibri",sans-serif'>B19’</span></b> phase <b><span
880style='font-family:"Calibri",sans-serif'>Texture</span></b> tab. Then select <b><span
881style='font-family:"Calibri",sans-serif'>6</span></b> for the <b><span
882style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> and check
883the two boxes as before.</p>
884
885<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
886width=624 height=303 id="Picture 77"
887src="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
891style='font-family:"Calibri",sans-serif'>B19’</span></b> phase and check all 4
892of the <b><span style='font-family:"Calibri",sans-serif'>Dij</span></b> boxes
893and do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy flags</span></b>
894as before. The tab will look like</p>
895
896<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
897width=624 height=360 id="Picture 78"
898src="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
901style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
902main menu. The refinement will finish with Rw ~27%; the 1<sup>st</sup> PWDR
903pattern looks like</p>
904
905<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
906width=624 height=535 id="Picture 79"
907src="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
910peaks for both phases are too sharp. It is likely that this is a microstrain
911effect. Select <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
912for the <b><span style='font-family:"Calibri",sans-serif'>B2 </span></b>phase
913and select the <b><span style='font-family:"Calibri",sans-serif'>microstrain</span></b>
914box. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy
915flags</span></b> to set it for the other PWDR data sets. Do the same for the <b><span
916style='font-family:"Calibri",sans-serif'>B19’</span></b> phase. Then do <b><span
917style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
918main 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:
9210in;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
924individual 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
927width=624 height=535 id="Picture 80"
928src="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
931that there remains intensity differences due to texture. We can increase the
932harmonic order to more closely fit these, however one should only do this
933carefully. 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
936width=624 height=257 id="Picture 81"
937src="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
940of the 001 pole figure will be drawn. This is the very typical “bulls eye” for
941cylindrical texture; of much more use is an inverse pole figure. Select that
942from 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
945width=624 height=535 id="Picture 82"
946src="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
949probability of reflection vectors coinciding with the sample wire axis the high
950spots are the 111 family of reflections. We should try the next higher Harmonic
951order (10). </p>
952
953<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
954Texture tab for the B19’ phase. Again a bullseye pole figure is drawn; change
955that to an Inverse pole figure.</p>
956
957<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
958width=624 height=535 id="Picture 83"
959src="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
962strongly textured (the cursor shows 12-13 MRD at the peaks) along the -140
963direction. Again we want to increment the Harmonic order to the next higher
964level (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
966the 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
968is very strongly textured!) to 10 and the B2 phase to 12; the final refinement
969converged 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’
973coefficients</p>
974
975<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
976width=624 height=317 id="Picture 84"
977src="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
980pole figure</p>
981
982<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
983width=624 height=535 id="Picture 85"
984src="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
987coefficients</p>
988
989<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
990width=624 height=224 id="Picture 86"
991src="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
994pole figure</p>
995
996<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
997width=624 height=535 id="Picture 87"
998src="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
1001the tutorial on Method A for doing texture analysis. It is useful for a case like
1002this one where there are very few data sets required for the texture analysis.
1003However, for the case of lower sample symmetry one must several dozen or even a
1004few hundred histograms and then the suite of parameters can easily be &gt; 1000
1005of which only a few dozen describe the texture. This leads to the next Methods
1006for texture analysis in GSAS-II.</p>
1007
1008<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
10090in;line-height:115%'>Method B. Sequential refinement &amp; texture analysis
1010from result</h2>
1011
1012<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
10130in;line-height:115%'>Introduction</h3>
1014
1015<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
1016the texture analysis in much the same way as Method A except that all the
1017initial refinements are done “sequentially”, that is refinements are done for
1018the parameters associated with each powder pattern to convergence in a serial
1019fashion. In this case where there are 10 PWDR data sets, there will be 10
1020refinements done in sequence. Parameters that span all the data (e.g. lattice
1021parameters, atom parameters &amp; texture) are not varied in this sequence
1022refinement. The effect of texture is modeled as a Preferred Orientation
1023correction to each histogram. To begin do <b><span style='font-family:"Calibri",sans-serif'>File/Open
1024project…</span></b> for the <b><span style='font-family:"Calibri",sans-serif'>NiTi.gpx</span></b>
1025file created in the first step and then do a <b><span style='font-family:"Calibri",sans-serif'>File/Save
1026project as…</span></b> to save it as <b><span style='font-family:"Calibri",sans-serif'>NiTi-B</span></b>.
1027This renames the project and it should have one IMG, 10 PWDR entries and two
1028phases of NiTi (B2 and B19’).</p>
1029
1030<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
10310in;line-height:115%'>Step 1. Initial refinement</h3>
1032
1033<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
1034the same way as Method A so I’ll 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1038</span>Select any <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b>
1039entry, go to <b><span style='font-family:"Calibri",sans-serif'>Sample Parameters</span></b>
1040and uncheck <b><span style='font-family:"Calibri",sans-serif'>Histogram scale
1041factor</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1045</span>Select the <b><span style='font-family:"Calibri",sans-serif'>B2</span></b>
1046phase <b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab and
1047check the <b><span style='font-family:"Calibri",sans-serif'>Phase fraction</span></b>
1048box and change the <b><span style='font-family:"Calibri",sans-serif'>Preferred
1049orientation model</span></b> to <b><span style='font-family:"Calibri",sans-serif'>Spherical
1050harmonics</span></b>. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit
1051Phase/Copy data</span></b> to copy both the flag and the model to the other
1052PWDR entries.</p>
1053
1054<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;text-indent:-.25in;
1055line-height:115%'>3)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1056</span>Select the <b><span style='font-family:"Calibri",sans-serif'>B19’</span></b>
1057phase <b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab and
1058check the <b><span style='font-family:"Calibri",sans-serif'>Phase fraction box</span></b>
1059and change the <b><span style='font-family:"Calibri",sans-serif'>Preferred
1060orientation model</span></b> to <b><span style='font-family:"Calibri",sans-serif'>Spherical
1061harmonics</span></b>. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit
1062Phase/Copy data</span></b> to copy both the flag and the model to the other
1063PWDR entries.</p>
1064
1065<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select <b><span
1066style='font-family:"Calibri",sans-serif'>Controls</span></b> from the GSAS-II
1067data tree</p>
1068
1069<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1070width=624 height=191 id="Picture 88"
1071src="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
1074style='font-family:"Calibri",sans-serif'>Select Data</span></b> button for <b><span
1075style='font-family:"Calibri",sans-serif'>Sequential Refinement</span></b>; a
1076file selection popup will appear. Do <b><span style='font-family:"Calibri",sans-serif'>Set
1077All</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>.
1078The <b><span style='font-family:"Calibri",sans-serif'>Controls</span></b> page
1079will be repainted indicating that 10 data sets are selected for sequential
1080refinement.</p>
1081
1082<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1083width=624 height=199 id="Picture 89"
1084src="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
1087choice of starting at the last one and for copying results from one to the
1088next. We won’t 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>)
1090as controls. We are now ready to do the 1<sup>st</sup> sequential refinement.
1091Do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Sequential
1092refine</span></b> from the main menu. A progress bar popup will appear showing
1093residuals as it processes each of 10 data sets. After a few seconds the <b><span
1094style='font-family:"Calibri",sans-serif'>Refinement results</span></b> popup
1095will appear; press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1096to accept them. The data window displays the <b><span style='font-family:"Calibri",sans-serif'>Sequential
1097refinement results</span></b> as a table.</p>
1098
1099<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1100width=624 height=176 id="Picture 90"
1101src="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
1104for each data set and columns for all refined parameters and some derived ones along
1105with residual and convergence indicators. The residuals are not very good (we
1106haven’t really refined much) but the &#916;&#967;<sup>2</sup> column shows that
1107convergence was achieved (NB: poor convergence will be highlighted in yellow or
1108red depending on how bad it is).</p>
1109
1110<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you examine
1111one of the PWDR entries, you’ll see that just in this point in Method A much of
1112the misfit is texture and perhaps peak position.</p>
1113
1114<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1115width=624 height=535 id="Picture 91"
1116src="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
1119parameters, 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
1122width=508 height=500 id="Picture 5"
1123src="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
1126style='font-family:"Calibri",sans-serif'>D11</span></b> box under
1127Hydrostatic/elastic strain, set the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
1128order</span></b> to <b><span style='font-family:"Calibri",sans-serif'>6</span></b>
1129and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1130box for it (Preferred orientation). Then in two steps, do <b><span
1131style='font-family:"Calibri",sans-serif'>Edit Phase/Copy flags</span></b> and <b><span
1132style='font-family:"Calibri",sans-serif'>Set All</span></b> for the file
1133selection. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit
1134Phase/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
1137width=322 height=390 id="Picture 92"
1138src="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
1141you to select which parameters to copy data and flags. Select <b><span
1142style='font-family:"Calibri",sans-serif'>Pref. Ori.</span></b> And press <b><span
1143style='font-family:"Calibri",sans-serif'>OK</span></b>; the file selection is
1144next. Do <b><span style='font-family:"Calibri",sans-serif'>Set All</span></b>
1145and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b> to do this
1146copy. That copies the full spherical harmonics model to the other data sets.
1147Select one to check if you’d like.</p>
1148
1149<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next do the
1150same 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
1152use spherical harmonics order <b><span style='font-family:"Calibri",sans-serif'>4</span></b>.
1153When done that Data window will look like</p>
1154
1155<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1156width=624 height=421 id="Picture 93"
1157src="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
1160ready for the next refinement; do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Sequential
1161refine</span></b>. Be careful not (by habit say) pick Refine; a warning popup
1162will appear. After it completes the Sequential refinement results shows that
1163the fit is better but convergence wasn’t quite complete.</p>
1164
1165<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1166width=624 height=204 id="Picture 95"
1167src="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
1170best to do another round of sequential refinement (I had to do two) to get
1171convergence. A plot of one PWDR entry gives</p>
1172
1173<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1174width=624 height=535 id="Picture 96"
1175src="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
1178experience in Method A, the calculated peaks are too sharp. We need to vary the
1179mustrain parameters for both phases. Go to the Data tab for each phase, check
1180the <b><span style='font-family:"Calibri",sans-serif'>microstrain</span></b>
1181box and do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy
1182flags</span></b> for all the data sets. Then do another <b><span
1183style='font-family:"Calibri",sans-serif'>Calculate/Sequential refine</span></b>.
1184My Sequential refinement results showed great improvement but incomplete
1185refinement</p>
1186
1187<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1188width=624 height=204 id="Picture 97"
1189src="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
1192sequential refinement (twice) gave convergence.</p>
1193
1194<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1195width=624 height=204 id="Picture 98"
1196src="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
1199the PWDR data sets showed a fairly good fit but some discrepancies (especially
1200for Azm=20.00)</p>
1201
1202<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1203width=624 height=535 id="Picture 99"
1204src="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
1207perhaps the B19’ phase needs high order spherical harmonics. Select the Data
1208tab for the B19’ phase and change the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
1209order</span></b> to <b><span style='font-family:"Calibri",sans-serif'>6</span></b>.
1210Then do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy
1211selected data</span></b> for <b><span style='font-family:"Calibri",sans-serif'>Pref.Ori.</span></b>
1212to the other data sets. This (after few repeats) gives a further improvement in
1213the fit</p>
1214
1215<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1216width=624 height=204 id="Picture 100"
1217src="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
1220now sufficient for us to proceed to the next step and determine the texture of
1221the two phases.</p>
1222
1223<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
12240in;line-height:115%'>Step 2. Texture analysis</h3>
1225
1226<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>During the
1227sequential refinements done in Step 1, we fitted the profiles allowing strain
1228parameters (Dij) for peak position shifts and microstrain for peak shape. We
1229modeled the intensity variation with a spherical harmonics preferred
1230orientation correction. If you select any PWDR entry from the GSAS-II data tree
1231and pick the Reflection List subentry (at the bottom) you can see the magnitude
1232of 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
1235phase we see</p>
1236
1237<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1238width=624 height=204 id="Picture 101"
1239src="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
1242B19’ phase we see</p>
1243
1244<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1245width=624 height=204 id="Picture 102"
1246src="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
1249orientation correction is Prfo; notice a few entries in red. These are
1250nonphysical correction values (the correction can’t be negative) but by in
1251large these are small. This next step uses these corrections as input data for
1252a texture refinement. To start select the Texture tab for the B2 phase; you’ll
1253see</p>
1254
1255<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1256width=608 height=290 id="Picture 16"
1257src="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
1260sample has wire texture, we’ll use the default Texture model (<b><span
1261style='font-family:"Calibri",sans-serif'>cylindrical</span></b>). Then set the <b><span
1262style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> to <b><span
1263style='font-family:"Calibri",sans-serif'>12</span></b> (what we used earlier)
1264and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1265and <b><span style='font-family:"Calibri",sans-serif'>Show coeff</span></b>
1266boxes. 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
1269width=624 height=225 id="Picture 103"
1270src="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
1273style='font-family:"Calibri",sans-serif'>Texture/Refine texture</span></b> from
1274the 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
1277width=624 height=225 id="Picture 104"
1278src="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
1281style='font-family:"Calibri",sans-serif'>Texture plot type</span></b> to <b><span
1282style='font-family:"Calibri",sans-serif'>Inverse pole figure</span></b> to get
1283a more useful plot</p>
1284
1285<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1286width=624 height=535 id="Picture 105"
1287src="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
1290essentially the same as we obtained earlier in Method A (maybe not quite as
1291strong here).</p>
1292
1293<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the
1294Texture 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
1296A. After setting the two flags and doing <b><span style='font-family:"Calibri",sans-serif'>Texture/Refine
1297texture</span></b> we get</p>
1298
1299<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1300width=624 height=324 id="Picture 106"
1301src="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
1304pole 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
1307width=624 height=535 id="Picture 107"
1308src="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
1311very similar to what we found in Method A but again not quite as strong (max
1312MRD ~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
1315style='font-family:"Calibri",sans-serif'>File/Save project</span></b> from the
1316main menu; this saves the final texture results done in Step 2 (you also will
1317need it for Method C).</p>
1318
1319<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
13200in;line-height:115%'>Method C. Sequential refinement &amp; full texture
1321refinement</h2>
1322
1323<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
13240in;line-height:115%'>Introduction</h3>
1325
1326<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This uses the
1327same approach as Method B except that after the sequential refinements are
1328finished we then fix almost all the parameters and then do a final texture
1329refinement with all the data. Thus, this is a replacement for Step 2 in Method
1330B. To begin do <b><span style='font-family:"Calibri",sans-serif'>File/Open
1331project…</span></b> for the <b><span style='font-family:"Calibri",sans-serif'>NiTi-B.gpx</span></b>
1332file created in Method B and then do a <b><span style='font-family:"Calibri",sans-serif'>File/Save
1333project as…</span></b> to save it as <b><span style='font-family:"Calibri",sans-serif'>NiTi-C</span></b>.
1334This renames the project and it should have one IMG, 10 PWDR entries and two
1335phases of NiTi (B2 and B19’).</p>
1336
1337<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
13380in;line-height:115%'>Step 1. Clearing unwanted variables from sequential
1339refinement</h3>
1340
1341<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Here we want
1342to clear refinement flags for all parameters that need not be varied in a
1343texture analysis refinement. The general rule is to not refine any parameter
1344unless 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1348</span><b><span style='font-family:"Calibri",sans-serif'>Background</span></b>:
1349as the background was fit during the sequential refinement we should fix it
1350here. Select any <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b>
1351entry and choose the <b><span style='font-family:"Calibri",sans-serif'>Background</span></b>
1352subentry for it. Clear the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1353flags and the do <b><span style='font-family:"Calibri",sans-serif'>File/Copy
1354flags</span></b> selecting all data sets. This will clear all background
1355refinement 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1359</span><b><span style='font-family:"Calibri",sans-serif'>B2</span></b> phase:
1360we do not want to refine either the microstrain, D<sub>11</sub>, or preferred
1361orientation coefficients. Select the <b><span style='font-family:"Calibri",sans-serif'>B2</span></b>
1362phase and its <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1363tab. 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>
1366boxes. Also set the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
1367order</span></b> to zero (this will avoid a lot of nasty (but harmless)
1368messages 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
1370clear all the flags and an <b><span style='font-family:"Calibri",sans-serif'>Edit
1371Phase/Copy selected data</span></b> for <b><span style='font-family:"Calibri",sans-serif'>Pref.Ori</span></b>
1372to copy the zeroed out harmonic coefficients.</p>
1373
1374<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;text-indent:-.25in;
1375line-height:115%'>3)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1376</span><b><span style='font-family:"Calibri",sans-serif'>B19’</span></b>: we do
1377not want to refine either the microstrain, Dij, or preferred orientation
1378coefficients. Select the <b><span style='font-family:"Calibri",sans-serif'>B19’</span></b>
1379phase and its <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1380tab. Clear the <b><span style='font-family:"Calibri",sans-serif'>microstrain</span></b>,
1381four <b><span style='font-family:"Calibri",sans-serif'>Dij</span></b> and <b><span
1382style='font-family:"Calibri",sans-serif'>Preferred orientation</span></b>
1383boxes. Also set the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
1384order</span></b> to zero (this will avoid a lot of nasty (but harmless)
1385messages 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
1387clear all the flags and an <b><span style='font-family:"Calibri",sans-serif'>Edit
1388Phase/Copy selected data</span></b> for <b><span style='font-family:"Calibri",sans-serif'>Pref.Ori</span></b>
1389to copy the zeroed out harmonic coefficients.</p>
1390
1391<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1392margin-left:.25in;line-height:115%'>&nbsp;</p>
1393
1394<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1395margin-left:.25in;line-height:115%'>Notice that we have allowed refinement of
1396the <b><span style='font-family:"Calibri",sans-serif'>Phase fractions</span></b>;
1397these may change during the texture refinement. Now select the <b><span
1398style='font-family:"Calibri",sans-serif'>Texture</span></b> tab for the <b><span
1399style='font-family:"Calibri",sans-serif'>B2</span></b> phase (it may still have
1400values from the Method B).</p>
1401
1402<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1403margin-left:.25in;line-height:115%'><img border=0 width=624 height=236
1404id="Picture 108"
1405src="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;
1408margin-left:.25in;line-height:115%'>You can clear these by setting the <b><span
1409style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> to zero and
1410then back to <b><span style='font-family:"Calibri",sans-serif'>12</span></b>.
1411Leave the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1412&amp; <b><span style='font-family:"Calibri",sans-serif'>Show</span></b> boxes
1413checked.</p>
1414
1415<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1416margin-left:.25in;line-height:115%'><img border=0 width=624 height=236
1417id="Picture 109"
1418src="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;
1421margin-left:.25in;line-height:115%'>Then do the same for the <b><span
1422style='font-family:"Calibri",sans-serif'>B19’</span></b> phase. Select the <b><span
1423style='font-family:"Calibri",sans-serif'>B19’</span></b> phase and its <b><span
1424style='font-family:"Calibri",sans-serif'>Texture</span></b> tab. Set the <b><span
1425style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> to zero and
1426then back to <b><span style='font-family:"Calibri",sans-serif'>10</span></b>.
1427Leave the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1428and <b><span style='font-family:"Calibri",sans-serif'>Show</span></b> boxes
1429checked. 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:
14320in;line-height:115%'>Step 2. Texture refinement</h3>
1433
1434<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do <b><span
1435style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
1436main menu; you will see the warning message</p>
1437
1438<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1439width=562 height=130 id="Picture 110"
1440src="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
1443you do want to do a nonsequential full refinement, so press the <b><span
1444style='font-family:"Calibri",sans-serif'>OK</span></b> button. A quick look at
1445the console will show that there are 61 variables in this refinement. If yours
1446shows more then you didn’t clear all the flags in Step 1. The <b><span
1447style='font-family:"Calibri",sans-serif'>Sequential results</span></b> entry is
1448deleted from the GSAS-II data tree. A progress bar will show giving the
1449residuals during the refinement. When finished, select the <b><span
1450style='font-family:"Calibri",sans-serif'>B2</span></b> phase and its <b><span
1451style='font-family:"Calibri",sans-serif'>Texture</span></b> tab; if the Texture
1452plot type is still <b><span style='font-family:"Calibri",sans-serif'>Inverse
1453pole 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
1456width=624 height=535 id="Picture 111"
1457src="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
1460almost 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
1463width=624 height=236 id="Picture 112"
1464src="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
1469inverse pole figure is</p>
1470
1471<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
1472width=624 height=535 id="Picture 113"
1473src="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
1476almost 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
1479width=624 height=323 id="Picture 114"
1480src="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
1483Method you can add parameters (atom coordinates &amp; thermal motion
1484parameters) that could not be refined in method B. It should be clear from this
1485tutorial that in more complex textures where the data set may consist of slices
1486obtained from a suite of 2D images collected as the sample is rotated, Method C
1487will give a relatively fast determination of the texture without resorting to
1488large matrix least-squares refinements.</p>
1489
1490</div>
1491
1492</body>
1493
1494</html>
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