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The Effect of Lattice Vibrations on Substitutional Alloy Thermodynamics
A longstanding limitation of first-principles calculations of substitutional
alloy phase diagrams is the difficulty to account for lattice vibrations. A
survey of the theoretical and experimental literature seeking to quantify the
impact of lattice vibrations on phase stability indicates that this effect can
be substantial. Typical vibrational entropy differences between phases are of
the order of 0.1 to 0.2 k_B/atom, which is comparable to the typical values of
configurational entropy differences in binary alloys (at most 0.693 k_B/atom).
This paper describes the basic formalism underlying ab initio phase diagram
calculations, along with the generalization required to account for lattice
vibrations. We overview the various techniques allowing the theoretical
calculation and the experimental determination of phonon dispersion curves and
related thermodynamic quantities, such as vibrational entropy or free energy. A
clear picture of the origin of vibrational entropy differences between phases
in an alloy system is presented that goes beyond the traditional bond counting
and volume change arguments. Vibrational entropy change can be attributed to
the changes in chemical bond stiffness associated with the changes in bond
length that take place during a phase transformation. This so-called ``bond
stiffness vs. bond length'' interpretation both summarizes the key phenomenon
driving vibrational entropy changes and provides a practical tool to model
them.Comment: Submitted to Reviews of Modern Physics 44 pages, 6 figure