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Triclinic crystal cell parameters
Triclinic crystal cell in 3-d is described by cell edge lengthes, a, b, c, and associated angles between edges, alpha, beta, and gamma, as shown in the plot.
| Code Block |
|---|
*----------*
/ \ / \
/ \ / \
/ \ gamma \
/ *----------*
/ / / /
/alpha / / /
*-------/--* c
\ / \beta /
a / \ /
\ / \ /
*-----b----* |
As a starting point in this analysis we use parameters from previous study
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a = 18.36 A b = 26.65 A c = 4.81 A alpha = 90.00 deg beta = 90.00 deg gamma = 102.83 deg |
See: Crystal structure, Bravais lattice, Crystal system, Primitive cell, Lattice constant
3-d space primitive vectors
Crystal cell parameters can be transformed to 3-d primitive vectors
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a1 = (18.36, 0.0, 0.0) a2 = (5.917873795354449, 25.984635262829016, 0.0) a3 = (0.0, 0.0, 4.81) |
Reciprocal space primitive vectors
See: Reciprocal lattice, Surface diffraction, Miller index3-d primitive vectors can be converted in reciprocal space primitive vectors
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b1 = [ 0.05446623 0.01240442 0. ] b2 = [ 0. 0.03848428 0. ] b3 = [ 0. 0. 0.20790021] |
See: Reciprocal lattice, Surface diffraction, Miller index
Table of lattice nodes sorted by radius
Lattice nodes in reciprocal space can be evaluated from primitive vectors and associated Muller indexes h,k,l. Lattice nodes ordered by ascending R(h,k,l) - distance between (h,k,l) and (0,0,0) points, is presented in table
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2-d case 3-d case ( h, k) R(h,k)[1/A] ( h, k, l) R(h,k,l)[1/A] ___________________ ________________________ ( 0, 0) 0.0000 ( 0, 0, 0) 0.0000 ( 0, 1) 0.0385 ( 0, 1, 0) 0.0385 ( 1, 0) 0.0559 ( 1, 0, 0) 0.0559 (-1, 1) 0.0604 (-1, 1, 0) 0.0604 ( 1, 1) 0.0745 ( 1, 1, 0) 0.0745 ( 0, 2) 0.0770 ( 0, 2, 0) 0.0770 (-1, 2) 0.0845 (-1, 2, 0) 0.0845 ( 1, 2) 0.1047 ( 1, 2, 0) 0.1047 (-2, 1) 0.1098 (-2, 1, 0) 0.1098 ( 2, 0) 0.1117 ( 2, 0, 0) 0.1117 ( 0, 3) 0.1155 ( 0, 3, 0) 0.1155 (-1, 3) 0.1166 (-1, 3, 0) 0.1166 (-2, 2) 0.1208 (-2, 2, 0) 0.1208 ( 2, 1) 0.1260 ( 2, 1, 0) 0.1260 ( 1, 3) 0.1390 ( 1, 3, 0) 0.1390 (-2, 3) 0.1417 (-2, 3, 0) 0.1417 ( 2, 2) 0.1491 ( 2, 2, 0) 0.1491 (-1, 4) 0.1517 (-1, 4, 0) 0.1517 ( 0, 4) 0.1539 ( 0, 4, 0) 0.1539 (-3, 1) 0.1634 (-3, 1, 0) 0.1634 ( 3, 0) 0.1676 ( 3, 0, 0) 0.1676 (-3, 2) 0.1682 (-3, 2, 0) 0.1682 (-2, 4) 0.1689 (-2, 4, 0) 0.1689 ( 1, 4) 0.1750 ( 1, 4, 0) 0.1750 ( 2, 3) 0.1776 ( 2, 3, 0) 0.1776 ( 3, 1) 0.1801 ( 3, 1, 0) 0.1801 (-3, 3) 0.1812 (-3, 3, 0) 0.1812 (-1, 5) 0.1881 (-1, 5, 0) 0.1881 ( 0, 5) 0.1924 ( 0, 5, 0) 0.1924 ( 3, 2) 0.1993 ( 3, 2, 0) 0.1993 (-2, 5) 0.1999 (-2, 5, 0) 0.1999 (-3, 4) 0.2008 (-3, 4, 0) 0.2008 ( 2, 4) 0.2093 ( 0, 0, 1) 0.2079 1st contributing index with l=1 ( 1, 5) 0.2119 ( 2, 4, 0) 0.2093 (-4, 1) 0.2181 ( 0, 1, 1) 0.2114 (-4, 2) 0.2196 ( 1, 5, 0) 0.2119 ( 4, 0) 0.2234 ( 1, 0, 1) 0.2153 ( 3, 3) 0.2236 (-1, 1, 1) 0.2165 (-3, 5) 0.2254 (-4, 1, 0) 0.2181 (-4, 3) 0.2276 (-4, 2, 0) 0.2196 ( 4, 1) 0.2350 ( 1, 1, 1) 0.2209 (-4, 4) 0.2416 ( 0, 2, 1) 0.2217 ( 2, 5) 0.2430 ( 4, 0, 0) 0.2234 ( 3, 4) 0.2515 ( 3, 3, 0) 0.2236 ( 4, 2) 0.2520 (-1, 2, 1) 0.2244 (-4, 5) 0.2605 (-3, 5, 0) 0.2254 (-5, 2) 0.2727 (-4, 3, 0) 0.2276 ( 4, 3) 0.2733 ( 1, 2, 1) 0.2328 (-5, 1) 0.2733 ( 4, 1, 0) 0.2350 (-5, 3) 0.2775 (-2, 1, 1) 0.2351 ( 5, 0) 0.2793 ( 2, 0, 1) 0.2360 ( 3, 5) 0.2818 ( 0, 3, 1) 0.2378 (-5, 4) 0.2874 (-1, 3, 1) 0.2383 ( 5, 1) 0.2903 (-2, 2, 1) 0.2404 ( 4, 4) 0.2982 (-4, 4, 0) 0.2416 (-5, 5) 0.3019 ( 2, 5, 0) 0.2430 ( 5, 2) 0.3057 ( 2, 1, 1) 0.2431 ( 5, 3) 0.3251 ( 1, 3, 1) 0.2501 ( 4, 5) 0.3257 ( 3, 4, 0) 0.2515 ( 5, 4) 0.3476 (-2, 3, 1) 0.2516 ( 5, 5) 0.3727 ( 4, 2, 0) 0.2520 |
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This makes event selection more complicated and in result the same matching algorithm finds 4× less peaks. 
References
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