BVC --- a Bond Valence Calculator for TI-85 and TI-86


Prof. Dr. Richard Dronskowski
Department of Chemistry
Aachen University of Technology (RWTH)
52074 Aachen, Germany
email: drons@HAL9000.ac.rwth-aachen.de


THEORY

Within bond valence (or bond length-bond strength) theory, there is a one-to-one
correspondence between an atoms valence and this atoms individual bond lengths to
its neighbors. The concept, very well established within solid-state and crystal
chemistry, goes back to by Pauling [1] but has been refined by many others. A very
good account has been given by Brown [2]. 

While the bond valence v is the sum of all individual bond strengths s_i

                           ---|
                       v = \    s_i,
                           /__|
                             i 

the bond strength s_i itself may be calculated using the most commonly adopted
expression

                       s_i = exp{r_0 - r_i)/37 pm},

where r_0, the bond valence parameter, and r_i, the bond length, are provided in
picometers. Two reliable sources for r_0 parameters are the 1985 paper by Brown and
Altermatt [3] and the 1991 paper by Brese and O'Keeffe [4].


PROGRAM

The BVC program performs all bond valence calculations needed to successfully work
through an inorganic crystal structure in terms of atomic valences (oxidation
states), bond strengths, comparisons with idealized structures, etc.

Upon start, the program will ask for the individual bond lengths, typically taken
from an X-ray or neutron crystal structure determination. Enter all bond lengths and
close the list using "0" pm. If a bond valence parameter r_0 is already stored in
the calculator, the bond valence will automatically be calculated. If not, choose
"r0" in the menu and provide a parameter. As an alternative, you may specify a
chosen valence ("val" menu item) such that an appropriate r_0 parameter can be
calculated. For a given r_0 parameter and a given valence, the program will
calculate an optimal bond length to fit a perfectly symmetrical polyhedron of an
arbitrary coordination number; try the "coord" menu item. Finally, item "bonds" will
allow you to enter a set of new bond lengths, "EXIT" will stop the program, and
"INIT" (TI-86 version only) will re-initialize the program. Have fun!


HISTORY

1992: early version (1.0), unpublished, written at the Max-Planck-Institute for 
      Solid State Research; helpful in writing a couple of scientific papers :-)
1999: improved, updated, documented version (2.0)


LITERATURE

[1] L. Pauling, J. Am. Chem. Soc. 69 (1947) 542.
[2] I. D. Brown, in "Structure and Bonding in Crystals", Vol. 2,
                 edited by M. O'Keeffe and A. Navrotsky;
                 Academic Press, NY 1981.
[3] I. D. Brown, D. Altermatt, Acta Crystallogr. B 41 (1985) 244.
[4] N. E. Brese, M. O'Keeffe, Acta Crystallogr. B 47 (1991) 192.
  
