Some problems in the theory of equilibrium crystal shapes
Shi, An-Chang
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https://hdl.handle.net/2142/23929
Description
Title
Some problems in the theory of equilibrium crystal shapes
Author(s)
Shi, An-Chang
Issue Date
1989
Doctoral Committee Chair(s)
Wortis, M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
equilibrium crystal shapes
thermodynamics
NaCl crystals
atomic-scale interface fluctuations
Language
en
Abstract
"Recently, great progress has been made in the theory of equilibrium crystal
shapes, and a general thermodynamic framework of the problem has been developed.
Chapter 1 serves as a brief survey of the theory, in order to provide
basic background material of this thesis.
It has recently been observed that the shape of N aCl crystals in stable coexistence
with the vapor, while strictly cubical at low temperature, undergoes a
corner-rounding transition at T0 ~ 650°C. The theory developed in Chapter 2
takes proper account of the statistical mechanics of the atomic-scale interface
fluctuations by adopting a restricted solid- on- solid model of the interface. This
model is equivalent to an antiferromagnetic Ising model on a triangular lattice,
and its phase diagram provides a framework for understanding the qualitative
differences observed between the thermal evolution of NaCl and that of
metal crystals. Corner rounding occurs for N aCl via an energy- entropy crossover
mechanism. The role of the step-like excitations in building vicinal surfaces is
particularly emphasized. Estimates of To depend directly and sensitively on the
energy per unit length of steps. A detailed calculation of the atomic relaxation
effects on the edge and step energies per unit length is performed, which leads
to a value of T0 ~ 1000K, in good agreement with the experiments.
Gas adsorption at a crystal surface changes the interfacial free energy and,
therefore, modifies the corresponding equilibrium crystal shape. In Chapter 3,
the effects of adsorption on equilibrium crystal shapes are studied by two approaches.
First, a simple lattice-gas model of the adsorption process, including
both adatom- adatom and adatom-crystal-atom interactions, is solved exactly at
zero temperature. The dependence of the crystal shape on the adgas chemical
potential is calculated for the cubic crystals with a variety of crystal-atomcrystal-
atom interactions, and the shape- change systematics is given in terms
of crystal shape ""phase"" diagram. Secondly, a phenomenological theory of the
problem at nonzero temperature is developed. By using available experiment
data of the adsorption process, the theory is applied to the crystals of the practicely
important material Pt, and good correspondence between the theory and
experiments is obtained. Finally, a possible application of the theory to the
designing of more efficient metal catalysts is presented."
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