Thermodynamics of Crystals

Wallace, Duane C.; Callen, Herbert B.

doi:10.1119/1.1987046

Cited by 903 publications

(677 citation statements)

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“…Following a procedure similar to that described in Wallace (1998), but applying it to the unit-cell axes of a cubic crystal rather than to its volume, the following expression (to second order) for the behaviour of the a-axis may be obtained…”

Section: Thermal Expansionmentioning

confidence: 99%

“…Wallace, 1998), which also allow estimates of the Debye temperature of the material to be made. For data covering a wide temperature range, the second-order Grüneisen approximation is more appropriate than the first-order approximation (Vocadlo et al, 2002).…”

Section: Thermal Expansionmentioning

confidence: 99%

“…For data covering a wide temperature range, the second-order Grüneisen approximation is more appropriate than the first-order approximation (Vocadlo et al, 2002). This approximation, derived on the basis of a Taylor series expansion of (PV) to secondorder in ∆V (for details, see Wallace, 1998), takes the form…”

Section: Thermal Expansionmentioning

confidence: 99%

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Thermal expansion of CaIrO3 determined by X-ray powder diffraction

Lindsay-Scott

Wood

Dobson

2007

Physics of the Earth and Planetary Interiors

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Section: Thermal Expansionmentioning

confidence: 99%

Section: Thermal Expansionmentioning

confidence: 99%

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Thermal expansion of CaIrO3 determined by X-ray powder diffraction

Lindsay-Scott

Wood

Dobson

2007

Physics of the Earth and Planetary Interiors

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“…The adiabatic (C S ijkl ) and isothermal (C T ijkl ) second-order elastic constants can be defined as second derivatives of internal energy E and the Helmholtz free energy F, respectively, with respect to the homogeneous deformation of the unit cell 18 . …”

Section: Thermodynamic Definitions Of Elastic Constantsmentioning

confidence: 99%

Finite-temperature elasticity of fcc Al: Atomistic simulations and ultrasonic measurements

et al. 2011

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Though not very often, in literature there are cases where discrepancies exist in temperature dependence of elastic constants of materials. A particular example of this case is the behavior of C 12 coefficient of a simple metal, aluminum. Here, we attempt to provide insight into various contributions to temperature-dependence in elastic properties by investigating the thermo-elastic properties of fcc aluminum as a function of temperature through the use of two computational techniques and experiments. First, ab initio calculations based on density functional theory (DFT) are used in combination with quasi-harmonic theory to calculate the elastic constants at finite temperatures through a strain-free energy approach. Molecular dynamics (MD) calculations using tight-binding potentials are then used to extract the elastic constants through a fluctuation-based formalism. Through this dynamic approach, the different contributions (Born, kinetic and stress fluctuations) to the elastic constants are isolated and the underlying physical basis for the observed thermally-induced softening is elucidated. The two approaches are then used to shed light on the relatively large discrepancies in the reported temperature dependence of the elastic constants of fcc aluminum. Finally, the polycrystalline elastic constants (and their temperature dependence) of fcc aluminum are determined using Resonant Ultrasound Spectroscopy (RUS) and compared to previously published data as well as the atomistic calculations performed in this work.

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“…2 The equilibrium state of a mixed liquid/solid system, containing a liquid and a solid fraction, is completely fixed thermodynamically once the pure component properties and the excess Gibbs free energy, usually expressed in terms of a number of excess parameters, are known. [3][4][5] However, crystallization is a kinetic process, and the growth composition, i.e., the instantaneous composition of the solid phase being formed at the surface at large undercooling may deviate considerably from the composition according to the equilibrium phase diagram. Under batch conditions the composition of the mother phase will change, and thus also the growth composition will change during the crystallization, leading to composition gradients in the solid phase.…”

Section: Introductionmentioning

confidence: 99%

Effective Kinetic Phase Diagrams

Los

Matovic

2005

J. Phys. Chem. B

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The composition of a solid solution that is growing at conditions well away from equilibrium is not prescribed by equilibrium thermodynamics, but is determined kinetically. It depends both on the surface kinetics and on the transport of mass and heat to and away from the solidification front. In previous work, we have formulated a model for the kinetic or nonequilibrium segregation taking place at the solidification front enabling the construction of kinetic phase diagrams, which gives the growth composition of a solid solution as a function of the liquid composition and undercooling at the surface. In the present work, we extend this model to include both mass and heat transport, giving rise to effective kinetic phase diagrams. An overview of the tendencies in the calculated effective kinetic phase diagrams is given by scanning a large part of the parameter space, covering different types of materials, including metals, semiconductors, and molecular systems. We find striking and characteric differences in the relative contribution of the various processes to the effective segregation. For molecular mixtures, interfacial undercooling and heat transport limitation can be expected to be much more important than for metal and semiconductor mixtures where mass transport limitation is dominant.

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Thermodynamics of Crystals

Cited by 903 publications

References 0 publications

Thermal expansion of CaIrO3 determined by X-ray powder diffraction

Thermal expansion of CaIrO3 determined by X-ray powder diffraction

Finite-temperature elasticity of fcc Al: Atomistic simulations and ultrasonic measurements

Effective Kinetic Phase Diagrams

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