Content
Problem
Meng sees a problem with interpretation of data. She observes in data large sample of events which have 2-peaks in the qH around two most probable positions 1.1 and 1.7 1/Å. In contrast, our model of lattice does not show these peaks simultaneously.
There may be different explanation of this problem:
- errors in generation of lattice,
- errors in generation of look-up table,
- errors in indexing - association of data with look-up table,
- wrong lattice model.
A few cross-check are presented below in order to address this issue.
Lattice
We use a few methods from pyimgalgos.FiberIndexing to generate lattice:
triclinic_primitive_vectors - generates triclinic crystal cell primitive vectors:
a= 18.55 # Angstrom
b, c = 1.466*a, 0.262*a # Angstrom
alpha, beta, gamma = 90, 90, 78.47 # 180 - 101.53 degree
a1, a2, a3 = triclinic_primitive_vectors(a, b, c, alpha, beta, gamma)
Test print shows that everything looks as expected:
# Triclinic crystal cell parameters: # a = 18.55 A # b = 27.19 A # c = 4.86 A # alpha = 90.00 deg # beta = 90.00 deg # gamma = 78.47 deg # 3-d space primitive vectors: # a1 = (18.55, 0.0, 0.0) # a2 = (-5.435623727109098, 26.645523961582906, 0.0) # a3 = (0.0, 0.0, 4.8601)
b1, b2, b3 = reciprocal_from_bravias(a1, a2, a3) - converts 3-d primitive vectors to reciprocal space primitive vectors.
Test print shows that everything looks as expected:
# reciprocal space primitive vectors: # b1 = [ 0.05390836 0.01099718 -0. ] # b2 = [ 0. 0.03752976 0. ] # b3 = [ 0. -0. 0.20575708]
Then, call to method
x, y, z, r, h, k, l = lattice(b1, b2, b3, hmax, kmax, lmax, cdtype)
returns 2-d (or 3-d if lmax>0) arrays. They are tested by
hmax, kmax, lmax = 4, 6, 0 # size of lattice to consider
# 2-d lattice test
test_lattice (b1, b2, b3, hmax, kmax, lmax, cdtype=np.float32)
lattice_node_radius(b1, b2, b3, hmax, kmax, lmax, cdtype=np.float32)
Output of this 2-d test looks as expected:
h.shape: (13, 9) row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 k.shape: (13, 9) row: -6 -6 -6 -6 -6 -6 -6 -6 -6 row: -5 -5 -5 -5 -5 -5 -5 -5 -5 row: -4 -4 -4 -4 -4 -4 -4 -4 -4 row: -3 -3 -3 -3 -3 -3 -3 -3 -3 row: -2 -2 -2 -2 -2 -2 -2 -2 -2 row: -1 -1 -1 -1 -1 -1 -1 -1 -1 row: 0 0 0 0 0 0 0 0 0 row: 1 1 1 1 1 1 1 1 1 row: 2 2 2 2 2 2 2 2 2 row: 3 3 3 3 3 3 3 3 3 row: 4 4 4 4 4 4 4 4 4 row: 5 5 5 5 5 5 5 5 5 row: 6 6 6 6 6 6 6 6 6 l.shape: (13, 9) row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 x coords.shape: (13, 9) row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 y coords.shape: (13, 9) row: -0.2692 -0.2582 -0.2472 -0.2362 -0.2252 -0.2142 -0.2032 -0.1922 -0.1812 row: -0.2316 -0.2206 -0.2096 -0.1986 -0.1876 -0.1767 -0.1657 -0.1547 -0.1437 row: -0.1941 -0.1831 -0.1721 -0.1611 -0.1501 -0.1391 -0.1281 -0.1171 -0.1061 row: -0.1566 -0.1456 -0.1346 -0.1236 -0.1126 -0.1016 -0.0906 -0.0796 -0.0686 row: -0.1190 -0.1081 -0.0971 -0.0861 -0.0751 -0.0641 -0.0531 -0.0421 -0.0311 row: -0.0815 -0.0705 -0.0595 -0.0485 -0.0375 -0.0265 -0.0155 -0.0045 0.0065 row: -0.0440 -0.0330 -0.0220 -0.0110 0.0000 0.0110 0.0220 0.0330 0.0440 row: -0.0065 0.0045 0.0155 0.0265 0.0375 0.0485 0.0595 0.0705 0.0815 row: 0.0311 0.0421 0.0531 0.0641 0.0751 0.0861 0.0971 0.1081 0.1190 row: 0.0686 0.0796 0.0906 0.1016 0.1126 0.1236 0.1346 0.1456 0.1566 row: 0.1061 0.1171 0.1281 0.1391 0.1501 0.1611 0.1721 0.1831 0.1941 row: 0.1437 0.1547 0.1657 0.1767 0.1876 0.1986 0.2096 0.2206 0.2316 row: 0.1812 0.1922 0.2032 0.2142 0.2252 0.2362 0.2472 0.2582 0.2692 z coords.shape: (13, 9) row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 r of lattice nodes.shape: (13, 9) row: 0.3449 0.3046 0.2697 0.2423 0.2252 0.2209 0.2300 0.2512 0.2817 row: 0.3165 0.2736 0.2357 0.2058 0.1876 0.1847 0.1977 0.2238 0.2591 row: 0.2901 0.2443 0.2031 0.1699 0.1501 0.1492 0.1675 0.1997 0.2403 row: 0.2665 0.2176 0.1724 0.1348 0.1126 0.1150 0.1408 0.1803 0.2263 row: 0.2463 0.1945 0.1451 0.1015 0.0751 0.0837 0.1202 0.1671 0.2179 row: 0.2305 0.1764 0.1232 0.0725 0.0375 0.0601 0.1089 0.1618 0.2157 row: 0.2201 0.1651 0.1100 0.0550 0.0000 0.0550 0.1100 0.1651 0.2201 row: 0.2157 0.1618 0.1089 0.0601 0.0375 0.0725 0.1232 0.1764 0.2305 row: 0.2179 0.1671 0.1202 0.0837 0.0751 0.1015 0.1451 0.1945 0.2463 row: 0.2263 0.1803 0.1408 0.1150 0.1126 0.1348 0.1724 0.2176 0.2665 row: 0.2403 0.1997 0.1675 0.1492 0.1501 0.1699 0.2031 0.2443 0.2901 row: 0.2591 0.2238 0.1977 0.1847 0.1876 0.2058 0.2357 0.2736 0.3165 row: 0.2817 0.2512 0.2300 0.2209 0.2252 0.2423 0.2697 0.3046 0.3449
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