The Role of Phonon Dispersion in Controlling Atomic Rearrangement in Solid Solutions
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THE ROLE OF PHONON DISPERSION SOLUTIONS
IN CONTROLLING ATOMIC REARRANGEMENT
T.B. Wu Dept. of Materials Science & Engineering, University, Hsinchu, Taiwan, R.O.C.
IN SOLID
National Tsing Hua
ABSTRACT The elastic energy of a solid solution of atoms of different sizes can be written as a Fourier sum with coefficients as a function of position in reciprocal space. Each coefficient is made up of three components. The first one is an energy associated with taking atoms of the pure elements and placing them randomly on the average lattice of the alloy. The second one is an elastic gradient energy associated with composition fluctuations and which is proportional to the second derivative of the dispersion curve. The third is the relaxation energy concerned with the motion of atoms away from the average lattice to more comfortable positions. Because of the contribution of the elastic gradient energy, it is shown that the shape of the phonon dispersion curve can affect precipitation or ordering in a solid solution.
INTRODUCTION Following Matsubara [1], Kanzaki [2], Krivoglaz and Tikhovova [3], Cook and deFontaine [4,5] reformulated the elastic energy contribution due to atomic size differences in a crystalline solid solution. Their results indicate that the elastic energy of the solution depends not only on crystallographic direction but also on the wave length of the composition modulation or fluctuation; if this energy is large enough it can determine the morphology of any transformation. The Cook-deFontaine theory involves three types of coupling parameters between atoms to describe the (microscopic) thermodynamics of the system. These are the lattice coupling parameters (which are a set of force constants that can be obtained from measurement of phonon dispersion), the solute-lattice coupling parameters (which are a set of constants representing the forces produced on neighbor atoms due to the composition variation at the origin site), and solute coupling parameters (which represent the initial energy of the random solution without lattice distortion). However, the theory is ambiguous as to the contribution of the initial energy. It is the purpose of this paper to examine this problem. As a result, the role of phonon dispersion in controlling atomic rearrangement in a solid solution will become apparent.
REMARKS ON COOK-DEFONTAINE THEORY In a perfect crystal of a pure element (or stoichiometric compound) each atom sits on an ideal site in the crystal (neglecting thermal vibrations). When an alloy is formed by replacing atoms in the solvent crystal with solute atoms of a different size, this ideal structure is disturbed by local displacements around solute atoms. A higher energy state is thus expected for atoms in this distorted structure if the electronic interaction between solute and solvent atoms is not taken into consideration, positive energy (heat absorption) has to be introduced for alloy formation.
Mat.
Res.
soc.
Symp.
Proc.
Vol.
21
(1984)
Published by Elsevier Science Publishing Co.,
Inc.
20
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