A thesis presented

by

Martin Zdenek Bazant

to

The Department of Physics

in partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

in the subject of

Physics

Harvard University

Cambridge, Massachusetts

July, 1997

**Download all 225 pages:**
postscript, 1,872K or
gzipped postscript, 548K.

One of the outstanding unsolved problems in the physics of
materials is that of designing a transferable interatomic potential
for covalently bonded solids, such as Si, Ge and C. In spite of
intense efforts which have produced over thirty fitted potentials for
the prototypical covalent solid, Si, realistic simulations are still
problematic for important bulk phenomena such as plastic deformation,
diffusion, crystallization and melting. In this thesis, innovative
analytic techniques are used to extract concrete information regarding
the functional form of interatomic potentials directly from *ab
initio* energy calculations. By deriving elastic constant relations
we study forces mediated by sp^3 and sp^2 hybrid covalent bonds,
and by inversion of cohesive energy curves we explore the covalent to
metallic transition and angular forces. This body of results provides
a reliable foundation upon which to build empirical potentials and
develop our intuition about chemical bonding. These theoretical
predictions can be captured using a new functional form with only a
few adjustable parameters called the Environment-Dependent Interatomic
Potential (EDIP). Efforts to fit an EDIP for Si have already led to
unprecedented transferability for bulk defects. Work in extending the
model to disordered bulk phases (liquid and amorphous) is underway,
and extensions to related materials should be possible. The speed of
force evaluation with the new model is comparable to the most
efficient existing potentials, making possible large-scale atomistic
simulations of covalently bonded materials with heightened realism.

Title Page, Acknowledgements,
Citations to Previously Published Work
(5 pages postscript, 54K)

Table of Contents (4 pages postscript, 51K)

Chapters

- Introduction
(11 pages postscript, 102K)
- Models of Interatomic Forces in Covalent Solids
(10 pages postscript, 112K)
- Elastic Constant Relations
(24 pages postscript, 211K)
- Inversion of Cohesive Energy Curves
(49 pages postscript, 772K)
- The Environment-Dependent Interatomic Potential
(33 pages postscript, 376K)
- Molecular Dynamics Simulation of Disordered Phases
(42 pages postscript, 455K)
- Conclusion
(6 pages postscript, 59K)

- The Geometry of Strained Diamond and Graphite
(6 pages postscript, 98K)
- Direct Inversion for Angular Forces
(8 pages postscript, 115K)
- Recursion and the Mobius Inversion Formula
(6 pages postscript, 103K)

- M. Z. Bazant, E. Kaxiras, J. F. Justo,
Environment-Dependent Interatomic Potential for bulk silicon,
Phys. Rev. B
**56**, 8542 (1997). ( Los Alamos XXX E-Print Archive) - M. Z. Bazant, E. Kaxiras and J. F. Justo, The Environment-Dependent
Interatomic Potential applied to silicon disordered structures and phase transitions,
Mat. Res. Soc. Proc.
**491**, 339 (1997). (7 pages ps, 1.78M, 383K gzipped) - J. F. Justo, M. Z. Bazant, E. Kaxiras, V. V. Bulatov,
and S. Yip, Interatomic potential for silicon defects and disordered phases,
Phys. Rev. B
**58**, 2539 (1998). ( Los Alamos XXX E-Print Archive)

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