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Unit Cell Computations with NIST*LATTICE

This page performs various computations on lattices using NIST*LATTICE, "A Program to Analyze Lattice Relationships" (Version of Spring, 1991) by Vicky Lynn Karen and Alan D. Mighell, National Institute of Standards and Technology, Materials Science and Engineering Laboratory, Gaithersburg, Maryland 20899. [V. L. Karen and A. D. Mighell, NIST Technical Note 1290 (1991); V. L. Karen & A. D. Mighell, U.S. Patent 5,235,523].

Compute reduced cell from a unit cell

This computes a reduced cell from the input cell. Optionally, derivative cells (subcells and supercells generated from the reduced cell), can be computed as well.

Relate two unit cells

Input two unit cells to compare, as well as tolerances on these parameters. The input unit cells will be reduced prior to their comparison using the Converse-Transform method (V. L. Karen & A. D. Mighell, U.S. Patent 5,235,523).

Centering (see below)
a b c alpha beta gamma P I F A B C R
Cell 1
Cell 2
Tolerance
Computation Mode: Integer Matrices Integer & Fraction Matrices.
Matrix Range: Allowed Range for Integer Matrices: 1-40;
for Integer & Fraction Matrices: 1-10

Search for higher symmetry unit cells

Input a unit cell, as well as tolerances on these parameters. The input unit cell will be reduced and then a search will be performed for higher symmetry lattices using Converse-Transform analysis (V. L. Karen & A. D. Mighell, U.S. Patent 5,235,523). Optionally, the search can include subcells and/or supercells generated from the reduced cell.

Centering (see below)
a b c alpha beta gamma P I F A B C R
Unit Cell
Tolerance

Convert reduced cell to conventional cell

Multiply unit cell by a matrix

a: b: c:
alpha: beta: gamma:
    Matrix

or form to default values.

Invert a 3x3 matrix

Multiply two 3x3 matrices

Matrix 1Matrix 2
 times

Centering options:

June 2003
Brian Toby, Camille Y. Jones and Vicky Lynn Karen