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G6 Bravais Lattice Determination Interface

by

Lawrence C. Andrews
and

Herbert J. Bernstein, Bernstein+Sons, yaya@bernstein-plus-sons.com


Please read the NOTICE below before use of this web page


Output Style:

Select the crystal lattice centering:

Specify the cell edge lengths and angles:


_cell.length_a _cell.angle_alpha
_cell.length_b _cell.angle_beta
_cell.length_c _cell.angle_gamma

Specify the cell edge length esd's and angle esd's:


_cell.length_a_esd _cell.angle_alpha_esd
_cell.length_b_esd _cell.angle_beta_esd
_cell.length_c_esd _cell.angle_gamma_esd

NOTICE

Some of the software and documents included within this software package are the intellectual property of various parties, and placement in this package does not in anyway imply that any such rights have in any way been waived or diminished.

With respect to any software or documents for which a copyright exists, ALL RIGHTS ARE RESERVED TO THE OWNERS OF SUCH COPYRIGHT.

Even though the authors of the various documents and software found here have made a good faith effort to ensure that the documents are correct and that the software performs according to its documentation, and we would greatly appreciate hearing of any problems you may encounter, the programs and documents any files created by the programs are provided **AS IS** without any warrantee as to correctness, merchantability or fitness for any particular or general use.

THE RESPONSIBILITY FOR ANY ADVERSE CONSEQUENCES FROM THE USE OF PROGRAMS OR DOCUMENTS OR ANY FILE OR FILES CREATED BY USE OF THE PROGRAMS OR DOCUMENTS LIES SOLELY WITH THE USERS OF THE PROGRAMS OR DOCUMENTS OR FILE OR FILES AND NOT WITH AUTHORS OF THE PROGRAMS OR DOCUMENTS.

Access to the source of ITERATE

This program and related scripts are available as a self-extracting shell-script archive or as a self-extracting C-shell-script archive.

What Does This Web Page Do?

In simple terms, what this page does is to find the cells which are "close" to the cell given, in order to help find the Bravais lattice of highest symmetry consistent with the cell.

A central problem in the solution of every crystal structure is to determine the correct Bravais lattice of the crystal. The Bravais lattices as they are usually listed are:

aP triclinic (anorthic) primitive
mP monoclinic primitive
mS monoclinic side-centered (usually C-centered)
oP orthorhombic primitive
oS orthorhombic side-centered
oF orthorhombic face-centered
oI orthorhombic body-centered
hP hexagonal primitive
hR hexagonal rhombohedrally-centered
tP tetragonal primitive
tI tetragonal body-centered
cP cubic primitive
cF cubic face-centered
cI cubic body-centered

Failure to find the highest correct symmetry has several consequences, the worst of which is that the structure may not be solved. The least of the consequences is that Richard Marsh may publish a paper that points out the error, corrects it, and finds a better solution to the structure. Many methods have been described for finding the correct Bravais lattice. A summary of the published methods was published in the paper that described the G6 formalism (which is used in the program on this web page).

"Lattices and Reduced Cells as Points in 6-Space and Selection of Bravais Lattice Type by Projections." Lawrence C. Andrews and Herbert J. Bernstein, Acta Crystallographica, A44, 1009-1018 (1988).

The program on this Web page implements a search in G6 for the various Bravais lattices that the user's cell may fit. For each lattice type, the best metric match is reported. If the higher symmetry type is actually correct, then that is likely to be the best cell from which to start further refinement. However, the possibility exists that one of the rejected cells (which did not match as well) was actually the correct one to use. The reason for this ambiguity is experimental error and its propagation in the transformations of the lattices in the program. Fortunately, the rejected cells are usually quite similar to the accepted one.

A note on standard deviations: First, even in the best of circumstances, standard deviations of unit cell dimensions from 4-circle diffractometer data are always underestimated (by at least a factor of 2). In addition, the points chosen for the determination are often not well distributed (for example all in the first octant of orthorhombic lattices). These less than optimal choices cause substantial systematic error. The experimental errors are amplified in the mathematical conversions between various lattices that any lattice search program must perform. It is not a rare occurrence for angles to be incorrect by 0.5 degrees in initial unit cell determinations.

Note: Even in most well determined unit cells, the actual errors in the edge lengths is 0.2 to 0.5 parts per thousand. (Note that reproducibility of the measurements is substantially better, leading to the illusion that diffractometers produce excellent unit cell parameters). Use of standard deviations that are too small is a common reason for failure of Bravais lattice searches. For small molecules, 0.1 Angstroms is a reasonable error for the edge lengths, for proteins, 0.4 to 0.5 (or even more for preliminary measurements). Accurate unit cell parameters must by determined by a number of more complex methods and must include extrapolation to remove systematic effects. For an excellent summary, see "Xray Structure Determination", G.H.Stout and L.H.Jensen, Wiley, 1989.