First principles phase diagram calculations for the wurtzite-structure systems AlN–GaN, GaN–InN, and AlN–InN

Burton, Benjamin P.; Walle, Axel van de; Kattner, Ursula R.

doi:10.1063/1.2372309

Cited by 59 publications

(52 citation statements)

References 42 publications

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“…As a consequence, the highest ⌬T C occurs in the system with the largest T C . This is in contrast to the wurtzitestructured nitrides 37 in which T C reductions due to F vib anticorrelate with %⌬R ij .…”

Section: Resultsmentioning

confidence: 41%

“…This suggests extensive miscibility gaps with high consolute temperatures for HfC-TiC and TiC-ZrC, comparable to AlN-InN. 37 Formation energies in HfC-ZrC are more like those in AlN-GaN, 37 i.e., consistent with complete miscibility at room temperature, also inferred from the thermodynamic assessment of the system. 14 The CEs were fit to a moderate number of structures to obtain a good CVS ͑Table I͒.…”

Section: Introductionmentioning

confidence: 56%

“…Excess volumes of mixing in these systems imply immiscibilities that would persist under pressure. In contrast, immiscibility with negative volumes of mixing, as in the wurtzitestructured nitrides, 37 implies decreased immiscibility under pressure.…”

Section: Introductionmentioning

confidence: 99%

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First-principles phase diagram calculations for the HfC–TiC, ZrC–TiC, and HfC–ZrC solid solutions

et al. 2009

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We report first-principles phase diagram calculations for the binary systems HfC-TiC, TiC-ZrC, and HfCZrC. Formation energies for superstructures of various bulk compositions were computed with a plane-wave pseudopotential method. They in turn were used as a basis for fitting cluster expansion Hamiltonians, both with and without approximations for excess vibrational free energies. Significant miscibility gaps are predicted for the systems TiC-ZrC and HfC-TiC, with consolute temperatures in excess of 2000 K. The HfC-ZrC system is predicted to be completely miscibile down to 185 K. Reductions in consolute temperature due to excess vibrational free energy are estimated to be ϳ7%, ϳ20%, and ϳ0%, for HfC-TiC, TiC-ZrC, and HfC-ZrC, respectively. Predicted miscibility gaps are symmetric for HfC-ZrC, almost symmetric for HfC-TiC and asymmetric for TiC-ZrC.

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Section: Resultsmentioning

confidence: 41%

Section: Introductionmentioning

confidence: 56%

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First-principles phase diagram calculations for the HfC–TiC, ZrC–TiC, and HfC–ZrC solid solutions

et al. 2009

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“…It may be difficult to use differences of electronegativity for quantitative estimates of the effects of vibrational entropy, especially for concentrated alloys, but it does seem that elements with large differences in electronegativity may show large effects of vibrational entropy in unmixing transformations. Burton, van de Walle and Kattner performed first principles computational studies of unmixing of three quasi-binary systems with the wurtzite structure, AlN-GaN, GaN-InN, and AlN-InN, using the bond-stiffness versus bond-length model [212]. With similar structures, there is a general expectation that the solubility should depend on differences in the ionic size of the metal atoms.…”

Section: Computational Studies Of Unmixingmentioning

confidence: 99%

Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

557

428

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Abstract. The literature on vibrational thermodynamics of materials is reviewed. The emphasis is on metals and alloys, especially on the progress over the last decade in understanding differences in the vibrational entropy of different alloy phases and phase transformations. Some results on carbides, nitrides, oxides, hydrides and lithium-storage materials are also covered.Principles of harmonic phonons in alloys are organized into thermodynamic models for unmixing and ordering transformations on an Ising lattice, and extended for non-harmonic potentials. Owing to the high accuracy required for the phonon frequencies, quantitative predictions of vibrational entropy with analytical models prove elusive. Accurate tools for such calculations or measurements were challenging for many years, but are more accessible today. Ab-initio methods for calculating phonons in solids are summarized. The experimental techniques of calorimetry, inelastic neutron scattering, and inelastic x-ray scattering are explained with enough detail to show the issues of using these methods for investigations of vibrational thermodynamics. The explanations extend to methods of data analysis that affect the accuracy of thermodynamic information.It is sometimes possible to identify the structural and chemical origins of the differences in vibrational entropy of materials, and the number of these assessments is growing. There has been considerable progress in our understanding of the vibrational entropy of mixing in solid solutions, compound formation from pure elements, chemical unmixing of alloys, order-disorder transformations, and martensitic transformations. Systematic trends are available for some of these phase transformations, although more examples are needed, and many results are less reliable at high temperatures. Nanostructures in materials can alter sufficiently the vibrational dynamics to affect thermodynamic stability. Internal stresses in polycrystals of anisotropic materials also contribute to the heat capacity. Lanthanides and actinides show a complex interplay of vibrational, electronic, and magnetic entropy, even at low temperatures.A "quasiharmonic model" is often used to extend the systematics of harmonic phonons to high temperatures by accounting for the effects of thermal expansion against a bulk modulus. Non-harmonic effects beyond the quasiharmonic approximation originate from the interactions of thermally-excited phonons with other phonons, or with the interactions of phonons with electronic excitations. In the classical high temperature limit, the adiabatic electron-phonon coupling can have a surprisingly large effect in metals when temperature causes significant changes in the electron density near the Fermi level. There are useful similarities in how temperature, pressure, and composition alter the conduction electron screening and the interatomic force constants. Phononphonon "anharmonic" interactions arise from those non-harmonic parts of the interatomic potential that cannot be accounted for by the quasiharmonic ...

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“…The transition temperature from our simulation is about 1150 K, which is higher than the experimental value of 735 K 22 . This type of overestimation of order-disorder transition temperatures from first-principles is common in calculations of bulk alloy phase diagrams, particularly in cases where vibrational entropy ignored 25,26 . A previous study of the MR reconstruction using embedded atom potentials has pointed to the importance of both atomic relaxation as well as vibrational entropy in describing these transitions 27 .…”

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confidence: 99%

First-principles cluster expansion study of missing-row reconstructions of fcc (110) surfaces

et al. 2011

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First principles phase diagram calculations for the wurtzite-structure systems AlN–GaN, GaN–InN, and AlN–InN

Cited by 59 publications

References 42 publications

First-principles phase diagram calculations for the HfC–TiC, ZrC–TiC, and HfC–ZrC solid solutions

First-principles phase diagram calculations for the HfC–TiC, ZrC–TiC, and HfC–ZrC solid solutions

Vibrational thermodynamics of materials

First-principles cluster expansion study of missing-row reconstructions of fcc (110) surfaces

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