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In trying to better understand how spherical harmonics are implemented in GSAS-II, and think I may have found a bug.
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<div class="">When I choose a phase with cubic crystal symmetry (like space group 225), and texture model ‘rolling - mmm’, with harmonic order 4, I see the following spherical harmonic coefficients:</div>
<div class="">C(4,0,1) </div>
<div class="">C(4,2,1) </div>
<div class="">C(4,4,1) </div>
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<div class="">In digging through the code (GSASIIlattice.py, function GenSHCoeff), and comparing this convention to the GSAS technical manual (p 137), L corresponds to the order of spherical harmonics, M to the sample symmetry and N to the crystal symmetry
(as a note, N and M are transposed in the GSAS technical manual from what is done in the code, but that doesn’t seem to much of an issue). The appearance on the screen follows the C(L, M, N) convention. </div>
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<div class="">However, my understanding is that N=1 should constrained to be zero by the cubic symmetry, and it’s really ’N=0’ that should be listed. The preceding function (GSASIIlattice.py, function OdfChk) sets the permissible values for the symmetry, and
seems to do a integer division by 12 and adds 1 if the modulo of L%12 is not equal to 2. My understanding (following R.-J. Roe Journal of Applied Physics V37 1966) is that only values divisible by 4 are permitted for cubic symmetry. In addition, some of the
coefficients are linearly dependent on other coefficients, which isn’t reflected in the code. Table 15.2.4 in Bunge "Texture Analysis in Materials Science” 1982 seems to largely match with Table 1 of Roe 1966, with some additional terms added in Bunge when
L is odd that do not appear in Roe.</div>
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Dr. Adam Creuziger</div>
<div style="orphans: 2; widows: 2;" class="">National Institute of Standards and Technology (NIST)</div>
<div style="orphans: 2; widows: 2;" class="">Gaithersburg, MD USA 20899.8553</div>
<div style="orphans: 2; widows: 2;" class="">Office 301-975-6015</div>
<div style="orphans: 2; widows: 2;" class=""><a href="mailto:adam.creuziger@nist.gov" class="">adam.creuziger@nist.gov</a></div>
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