Possible bug: non-cubic definitions

[Lil Read]

Dear Ralf,

I have been working with calcite with the crystal symmetry (-3m1). This uses the four-number notation of Miller indices. It follows that for this crystal symmetry (hkil) direction is equivalent to (khil), for example. However, when I use such identities, for example in my twinning, and project these to the fundamental region, these do not project to the same point in the fundamental region. i.e. (1 0 -1 4) does not project to the same point as (0 1 -1 4).  See the attached figure.

CS = {...

  'notIndexed',...

  crystalSymmetry('-3m1', [4.99 4.99 17.061], 'X||a', 'Z||c*', 'mineral', 'Calcite')};

twinning012 = orientation('axis',Miller(0,1,-1,2,CS{2}),'uvw','angle',180*degree,CS{2},CS{2});

twinning102 = orientation('axis',Miller(1,0,-1,2,CS{2}),'uvw','angle',180*degree,CS{2},CS{2});
figure
plot(twinning012.project2FundamentalRegion('antipodal'),'MarkerColor','m','MarkerSize',20)
hold on

plot(twinning102.project2FundamentalRegion('antipodal'),'MarkerColor','y','MarkerSize',20)

Have I misunderstood something in the code or definitions or is this a bug?

Best wishes,

Lil

[ruediger Kilian]

Hi Lil,
for ‘-3m’ there are 6 equivalent Millers for <10-12> and the are not identical to the the <01-12>. You can use the ‘==‘ to check for crystallographically equivalent directions.
More notably, I think you have a bracket wrong and accordingly your twin definition. I guess you’d like to specify Miller(0,1,-1,2,CS{2},'uvw’) not ,Miller(0,1,-1,2,CS{2}), that makes a difference.
Cheers,
Rüdiger

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> <Possible_bug_non_cubic_directions.jpg>