Interatomic Forces in Covalent Solids

A thesis presented

Martin Zdenek Bazant

The Department of Physics
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
in the subject of


Harvard University
Cambridge, Massachusetts

July, 1997

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(1 page postscript, 23K)

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.

Table of Contents

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

Table of Contents (4 pages postscript, 51K)


  1. Introduction (11 pages postscript, 102K)

  2. Models of Interatomic Forces in Covalent Solids (10 pages postscript, 112K)

  3. Elastic Constant Relations (24 pages postscript, 211K)

  4. Inversion of Cohesive Energy Curves (49 pages postscript, 772K)

  5. The Environment-Dependent Interatomic Potential (33 pages postscript, 376K)

  6. Molecular Dynamics Simulation of Disordered Phases (42 pages postscript, 455K)

  7. Conclusion (6 pages postscript, 59K)

  1. The Geometry of Strained Diamond and Graphite (6 pages postscript, 98K)

  2. Direct Inversion for Angular Forces (8 pages postscript, 115K)

  3. Recursion and the Mobius Inversion Formula (6 pages postscript, 103K)

Bibliography (11 pages postscript, 74K)


This is copyrighted material, intended for personal use only. Portions of this thesis were devoted to work in progress that would not appear in a journal article. Therefore, please contact the author before using or citing any results not included in the related published papers (at the time of thesis writing) or in the list of subsequent papers below. Specifically, in the case of Chapter 6, the difficulties in describing the liquid and amorphous phases have been corrected in the final version of EDIP (without sacrificing the desirable properties described in Chapter 5). In fact, EDIP is the first potential to predict a direct quench from liquid to amorphous, making it possible to simulate an experimentally relevant preparation method (e.g. laser quenching) as well as dynamics of the random tetrahedral network. For more details, see refs. 2 and 3 below.

Subsequent Publications Based on the Thesis (partial list)

  1. 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)

  2. 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)

  3. 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)

The EDIP Home Page (free software)