1 citations · 1 across the 7 of their papers we have counts for
7 papers
Delone lattice studies in C3, the space of three complex variables
Lawrence C. Andrews, Herbert J. Bernstein
The Delone (Selling) scalars, which are used in unit cell reduction and in lattice type determination, are studied in , the space of three complex variables. The thre…
SELLA -- A Program for Determining Bravais Lattice Types
Lawrence C. Andrews, Herbert J. Bernstein, Nicholas K. Sauter
We introduce a new Bravais lattice determination algorithm. SELLA is a straight-forward algorithm and a program for determining Bravais lattice type based on Selling (Delone) reduc…
Measuring Lattices
Lawrence C. Andrews, Herbert J. Bernstein
Unit cells are used to represent crystallographic lattices. Calculations measuring the differences between unit cells are used to provide metrics for measuring meaningful distances…
An Invertible Seven-Dimensional Dirichlet Cell Characterization of Lattices
Herbert J. Bernstein, Lawrence C. Andrews, Mario Xerri
Characterization of crystallographic lattices is an important tool in structure solution, crystallographic database searches and clustering of diffraction images in serial crystall…
The Geometry of Niggli Reduction III: SAUC -- Search of Alternate Unit Cells
Keith J. McGill, Mojgan Asadi, Maria Toneva Karakasheva +2
A crystallographic cell is a representation of a lattice, but each lattice can be represented just as well by any of an infinite number of such unit cells. Searching for matches to…
The Geometry of Niggli Reduction II: BGAOL -- Embedding Niggli Reduction
Lawrence C. Andrews, Herbert J. Bernstein
Niggli reduction can be viewed as a series of operations in a six-dimensional space derived from the metric tensor. An implicit embedding of the space of Niggli-reduced cells in a…
The Geometry of Niggli Reduction I: The Boundary Polytopes of the Niggli Cone
Lawrence C. Andrews, Herbert J. Bernstein
Correct identification of the Bravais lattice of a crystal is an important step in structure solution. Niggli reduction is a commonly used technique. We investigate the boundary po…