cry (version 0.5.2)

sysabs: Locate systematic absences

Description

Given an mX3 matrix of Miller indices, this function returns those indices corresponding to valid reflections, i.e. to reflections which are not systematic absences.

Usage

sysabs(hkl, SG)

Value

idx A vector of integers corresponding to the position, in the array mhkl, in which the Miller indices ARE NOT systematically absent. The position of systematically-absent reflections can be found using !idx.

Arguments

hkl

An mX3 matrix or a data frame whose rows are the three integers corresponding to the Miller indices.

SG

A character. The extended Hermann-Mauguin symbol of the crystallographic space group.

Details

Crystallography symmetry forces constraints on data from x-ray diffraction. One of these constraints consists in the full cancellation of reflections with certain Miller indices. It is said that the reflection with that specific Miller index is systematically absent. For example, in data corresponding to a crystal with space group C 2, general reflections like (h,k,l) must obey h+k=2n (even number). Thus, the Miller indices (2,3,1) are a systematic absence because 2+3=5 (odd).

Examples

# C 2 monoclinic space group (special setting)
csym <- cryst_symm(15,set=5)
print(csym$SG)

# Create a full data frame of Miller indices
hkl <- expand.grid(H=-4:4,K=-4:4,L=-4:4)

# Index corresponding to valid reflections
# (not systematic absences)
idx <- sysabs(hkl,csym$SG)

# Indices for all reflections
fulldx <- 1:length(hkl[,1])

# Index corresponding to systematic absences
jdx <- fulldx[-idx]

# A couple of systematic absences
hkl[jdx[1:2],]