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A long-standing limitation of first-principles calculations of substitutional alloy phase diagrams is the difficulty in accounting for lattice vibrations. A survey of the theoretical and experimental literature seeking to quantify the effect of lattice vibrations on phase stability indicates that they can be significant. Typical vibrational entropy differences between phases are of the order of 0.1 to 0.2kB/atom, which is comparable to the typical values of configurational entropy differences in binary alloys (at most 0.693kB/atom). This article presents the basic formalism underlying ab initio phase diagram calculations, along with the generalization required to account for lattice vibrations. The authors review 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.
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Read moreA first-principles investigation of the phase stability in the O2-LiCoO2 system is performed to better understand the unusual layered phases obtained upon Li deintercalation (i.e., T#2 and O6). First-principles pseudopotential calculations within the local density approximation and thermodynamic models extracted from these calculations both show that two tetrahedral sites for the Li ions need to be considered in the T#2 structure for qualitative agreement with experiment to be obtained...
Read moreIn this study, the native point defects including oxygen vacancy and interstitial, metal (La, Al) vacancy and interstitial, and metal antisite in perovskite LAO are studied. Defect formation energies are studied as a function of the external chemical potentials and Fermi level. The stable defects are identified under different external chemical potentials and Fermi levels. The effect of image charge corrections is also investigated. Finally, based on results in this study, optimal growth conditions can be proposed to achieve better defect engineering for LAO gate dielectrics.
Read moreExtensive experimental work has been carried out to characterize the stable Na-vacancy ordering patterns at various compositions of layered NaxCoO2. However, contradictions and debates prevail in the literature, particularly at high Na concentrations x>0.5. Understanding of the exotic electronic properties in this system requires a thorough understanding of the Na-vacancy structural orderings. Using density functional theory in the generalized gradient approximation (GGA), combined with a cluster expansion structure prediction algorithm we have found an intricate set of Na-vacancy ordered ground states in NaxCoO2 (0.5⩽x⩽1). We demonstrate a newly predicted ordering pattern between 0.67⩽x⩽0.71. By comparing the first principles electronic structure methods within the GGA and GGA+U (Hubbard U correction) approximations, we demonstrate that at certain Na concentration the stable ordering is affected by charge localization on the Co layer through coupling between the Na and Co lattices.
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