Elastic constants of cubic crystals

Jamal, M.; Jalali-Asadabadi, S.; Ahmad, Iftikhar; Aliabad, H. A. Rahnamaye

doi:10.1016/j.commatsci.2014.08.027

Cited by 436 publications

(130 citation statements)

References 49 publications

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“…Another type of response property that is highly temperature dependent is the elastic constants, which quantify a crystal's response to elastic deformation. The elastic constant matrix C of a molecular crystal can be obtained by a Taylor expansion around the equilibrium geometry:

E ((),, V, ε) = E_{0} + V_{0} ((), true {false\sum}_{i = 1}^{6} σ_{i} ε_{i} + \frac{1}{2} true {false\sum}_{i j = 1}^{6} C_{i j} ε_{i} ε_{j})

where ε is the strain applied to the unit cell and σ is the corresponding stress of the unit cell. The elastic constants can then be approximated by the second‐order derivatives of the energy with respect to the applied strain:

C_{i j} = \frac{1}{V_{0}} \frac{\partial^{2} E}{\partial ε_{i} \partial ε_{j}}

…”

Section: Addressing the Temperature And Pressure Gapmentioning

confidence: 99%

First‐principles modeling of molecular crystals: structures and stabilities, temperature and pressure

Hoja

Reilly

Tkatchenko

2016

WIREs Comput Mol Sci

162

222

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The understanding of the structure, stability, and response properties of molecular crystals at finite temperature and pressure is crucial for the field of crystal engineering and their application. For a long time, the field of crystal-structure prediction and modeling of molecular crystals has been dominated by classical mechanistic force-field methods. However, due to increasing computational power and the development of more sophisticated quantum-mechanical approximations, first-principles approaches based on density functional theory can now be applied to practically relevant molecular crystals. The broad transferability of first-principles methods is especially imperative for polymorphic molecular crystals. This review highlights the current status of modeling molecular crystals from first principles. We give an overview of current state-of-the-art approaches and discuss in detail the main challenges and necessary approximations. So far, the main focus in this field has been on calculating stabilities and structures without considering thermal contributions. We discuss techniques that allow one to include thermal effects at a first-principles level in the harmonic or quasi-harmonic approximation, and that are already applicable to realistic systems, or will be in the near future. Furthermore, this review also discusses how to calculate vibrational and elastic properties. Finally, we present a perspective on future uses of first-principles calculations for modeling molecular crystals and summarize the many remaining challenges in this field

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E ((),, V, ε) = E_{0} + V_{0} ((), true {false\sum}_{i = 1}^{6} σ_{i} ε_{i} + \frac{1}{2} true {false\sum}_{i j = 1}^{6} C_{i j} ε_{i} ε_{j})

C_{i j} = \frac{1}{V_{0}} \frac{\partial^{2} E}{\partial ε_{i} \partial ε_{j}}

…”

Section: Addressing the Temperature And Pressure Gapmentioning

confidence: 99%

First‐principles modeling of molecular crystals: structures and stabilities, temperature and pressure

Hoja

Reilly

Tkatchenko

2016

WIREs Comput Mol Sci

162

222

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“…The optimization of the relaxed structure is first achieved by PBE-GGA method and the same relaxed structure is used to calculate the elastic parameters by using the cubic elastic code. 22,23 To determine the variation of Debye temperature and Gruneisen parameter w.r.t. temperature, Gibbs2 code 23 is used.…”

Section: Computational Detailsmentioning

confidence: 99%

Electronic structure, thermomechanical and phonon properties of inverse perovskite oxide (Na₃OCl): An ab initio study

et al. 2020

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Summary Within first principles calculations, the electronic structure, thermodynamic, mechanical stability, magnetism, and phonon properties of the inverse perovskite (Na3OCl) have been summed up. The Birch‐Murnaghan derived lattice constant and bond‐lengths are identical, when compared to the experimental data. A direct energy gap of 2.18 eV observed from the band structure reveals the semiconducting nature of the present oxide. Also, the application of strain on electronic properties predicts the decrease in bandgap with respect to compressive strain and vice versa. The constituent nonmagnetic atoms in its crystal propose the total magnetic moment to be zero and the same is supported by susceptibility data. In addition to the negative Cauchy's pressure, the small bulk modulus compared to Young's modulus determined from elastic constants, possibly claims it as a brittle material. Also, the temperature dependent Gruneisen parameter (1.58) and Debye temperature (382.27 K) are determined to reveal the lattice thermal conductivity (κ = 6.48 W/mK) at room temperature.

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“…in the internal forces. The elastic constants here reported for the Ba2TiMnO6, cubic phase were calculated using the Wien2k Cubic-elastic package [13] by considering the second-order derivative (E(δ)) of a polynomial fit (E=E(δ)) of energy vs. strains (δ) at zero strain (δ =0).…”

Section: Ab-initio Calculationsmentioning

confidence: 99%

“…The Reuss (R), Voigt (V), and Hill (H) polycrystalline average values of the Young modulus (E), the shear modulus (G), and the Poisson ratio (ν) for the cubic Ba2TiMnO6 calculated by means of the expressions given in Ref. [13] are given in Table 3. Also indicated in Table 3 is the Zener´s anisotropy factor A = 2C44/(C11-C12).…”

Section: Elastic Propertiesmentioning

confidence: 99%

Ab-initio analysis of magnetic, structural, electronic and thermodynamic properties of the Ba2TiMnO6 manganite

Deluque-Toro

Téllez

Roa-Rojas

2018

DYNA

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Perovskite-like materials, which include magnetic elements, have relevance because their technological perspectives of applications in the spintronics industry. In this work, the magnetic, structural, electronic and thermodynamic properties of the Ba2TiMnO6 of the perovskite-like manganite are investigated. Calculations are carried out through the Full-Potential Linear Augmented Plane Wave method (FP-LAPW) within the framework of the Density Functional Theory (DFT) with exchange and correlation effects in the Generalized Gradient (GGA) and Local Density (LDA) approximations, including spin polarization. From the minimization of energy as a function of volume using the Murnaghan's state equation the equilibrium lattice parameter and cohesive properties of this compound were obtained. The study of the electronic structure was based in the analysis of the electronic density of states (DOS), and the band structure, showing that this compound evidences an effective magnetic moment of 3.0 µB. The pressure and temperature dependence of specific heat, entropy, thermal expansion coefficient, Debye temperature and Grüneisen parameter were calculated by DFT from the state equation using the quasi-harmonic model of Debye. A specific heat behavior CV≈CP was found at temperatures below T = 400 K, with Dulong-Petit limit values, which are quite higher than those, reported for simple perovskites.Keywords: perovskite material; electronic structure; thermodynamic properties; DFT.Análisis ab-initio de las propiedades magnéticas, estructurales, electrónicas y termodinámicas de la manganita Ba 2 TiMnO 6 Resumen Los materiales de tipo perovskita que incluyen elementos magnéticos son relevantes debido a sus perspectivas de aplicabilidad tecnológica en la industria de la espintrónica. En este trabajo fueron investigadas las propiedades magnéticas, estructurales, electrónicas y termodinámicas de la manganita de tipo perovskita Ba2TiMnO6. Los cálculos fueron realizados a través del método del potencial de ondas planas aumentadas y linealizadas (FP-LAPW), en el marco de la Teoría del Funcional Densidad (DFT), con efectos de intercambio y correlación en las aproximaciones de gradiente generalizado (GGA) y de densidad local (LDA), incluyendo polarización de espín. A partir de la minimización de la energía en función del volumen, usando la ecuación de estado de Murnaghan se obtuvieron los parámetros de equilibrio de la red las propiedades de cohesión de este compuesto. El estudio de la estructura electrónica se basó en el análisis de la densidad de estados (DOS) y la estructura de bandas, mostrando que este compuesto evidencia un momento magnético efectivo de 3.0 µB. la dependencia con la temperatura y la presión del calor específico, la entropía, el coeficiente de expansión térmica, la temperatura de Debye y el parámetro de Grüneisen fueron calculados mediante DFT a partir de la ecuación de estado, usando el modelo cuasi-armónico de Debye. Se encontró que el calor específico CV≈CP para temperaturas por debajo de T = 400 K, con un lí...

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Elastic constants of cubic crystals

Cited by 436 publications

References 49 publications

First‐principles modeling of molecular crystals: structures and stabilities, temperature and pressure

First‐principles modeling of molecular crystals: structures and stabilities, temperature and pressure

Electronic structure, thermomechanical and phonon properties of inverse perovskite oxide (Na₃OCl): An ab initio study

Ab-initio analysis of magnetic, structural, electronic and thermodynamic properties of the Ba2TiMnO6 manganite

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Elastic constants of cubic crystals

Cited by 436 publications

References 49 publications

First‐principles modeling of molecular crystals: structures and stabilities, temperature and pressure

First‐principles modeling of molecular crystals: structures and stabilities, temperature and pressure

Electronic structure, thermomechanical and phonon properties of inverse perovskite oxide (Na3OCl): An ab initio study

Ab-initio analysis of magnetic, structural, electronic and thermodynamic properties of the Ba2TiMnO6 manganite

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Electronic structure, thermomechanical and phonon properties of inverse perovskite oxide (Na₃OCl): An ab initio study