SHELL is a NEW, GENERAL free energy minimization program for solids. It uses lattice statics and quasiharmonic lattice dynamics to calculate analytically the free energy of a crystal, AND its derivatives with respect to the dimensions of the unit cell (the external coordinates) AND the positions of the ions within the unt cell (the internal coordinates).

This is the first program to be able to perform efficient fully dynamic structure optimisation of unit cells of ionic and polar solids containing hundreds of ions.

Why lattice dynamics? Although neglected in recent years, lattice dynamics can be remarkably robust at elevated temperatures, while below the Debye temperature it scores importantly over classical Monte Carlo and molecular dynamics in that it takes account of zero-point energy and other quantum effects. It's cheap and precise, the results are easily interpreted and supply complementary information to that from MD. It also provides a very sensitive test for interatomic potentials.

Recently we have concentrated on the use of the program to model disordered solids and solid solutions by performing thermodynamic averages over the results of many individual free energy minimisations of particular configurations.

- Optimised geometries of unit cells at constant pressure or volume, at any specified temperature and pressure. Optimisation also can be carried out keeping any external or internal coordinate fixed.
- Internal energies, free energies and heat capacities,
- Phonon dispersion curves and vibrational densities of states.
- Thermodynamic Gruneisen functions (see the various bibles by Barron), and mode Gruneisen functions at any wave vector.
- Gradient of the free energy with respect to lattice parameters and/or internal coordinates.
- Elastic stiffnesses, generated in the static case by analytic calculation of the Hessian and in the dynamic case by numerical differentiation of the gradient.

To make the program easy to use, some external utilities are supplied for manipulation of Shell's input and output files. These include:

- Determining a set of symmetric internal coordinates given the full set of basis atoms
- Calculation of bond lengths and angles
- Conversion between units (kJ/mol and eV/ı for example - useful both for project students and their supervisors)
- Generation of a VRML (3d file format for visualisation) file for the unit cell.
- Plotting the forms of short-ranged potential vs. interatomic separation.

There is also an example input file and corresponding output file.

A related program for metals EAMLD is available from Dr. Barrera.

Full details of the theory explained simply:

Free energy derivatives and structure optimisation within quasiharmonic
lattice dynamics, M.B. Taylor, G.D. Barrera, N.L. Allan and T.H.K. Barron,
* Phys. Rev. B* **56**, 14380-14390 (1997)

(download
postscript
or
PDF file).

The program:

SHELL :
A code for lattice dynamics and structure optimisation of ionic
crystals, M.B. Taylor, G.D. Barrera, N.L. Allan, T.H.K. Barron and
W.C. Mackrodt, *Comput. Phys. Commun.* **109**, 135-143 (1998)

(download
postscript
or
PDF file).

Some more theory:

The zero static internal stress approximation in lattice dynamics and the
calculation of isotope effects on molar volumes, N.L. Allan, T.H.K. Barron
and J.A.O. Bruno,
*
J. Chem. Phys.*,
**105**, 8300-8303 (1996).

(download
postscript
or
PDF).

Application to defects:

The free energy of formation of defects in polar solids, M.B. Taylor,
G.D. Barrera, N.L. Allan, T.H.K. Barron and W.C. Mackrodt,
* Faraday
Discuss.*, **106**, 377-387 (1997)

(download postscript or
PDF).

Application to mixtures and disordered systems:

Free energy of solid solutions and phase diagrams via quasiharmonic lattice dynamics, N.L. Allan, G.D. Barrera, R.M. Fracchia, M. Yu. Lavrentiev, M.B. Taylor, I.T. Todorov and J.A. Purton,
* Phys. Rev. B * **63**, 094203 (2001)
(download PDF)

For related Monte Carlo work, see

*Ab initio* calculation of phase diagrams of oxides, M. Yu. Lavrentiev, N.L. Allan, G.D. Barrera, and J.A. Purton,
* J. Phys. Chem. B * **105**, 3594-3599 (2001)
(download PDF)

Overview:

Ionic solids at high temperatures and pressure: ab initio, lattice dynamics and Monte Carlo studies, N.L. Allan, G.D. Barrera, J.A. Purton, C.E. Sims
and M.B. Taylor,
*Phys. Chem., Chem. Phys.* **2**, 1099-1111 (2000) (feature article)
(download PDF).

gdb@quimica.unp.edu.ar Last update by NLA March 2004