Elastic Constants of LiF from 4.2°K to 300°K by Ultrasonic Methods

Briscoe, C. V.; Squire, Ch̀arles F.

doi:10.1103/physrev.106.1175

Cited by 142 publications

(29 citation statements)

References 11 publications

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“…In terms of ionic solids, the TMTPSS functional is more accurate than TM on LiCl, LiF, and MgO, while less accurate on the other three. When it comes to the three transition The experimental values used for error calculation are from these references: Li, 36 K, 37 Al, 38 C 39 , Si, 40 SiC, 41 Ge, 40 BP, 42 AlP, 43 AlAs, 43 GaN, 44 GaP, 43 GaAs, 40 NaCl, 45 NaF, 45 LiCl, 45 LiF, 46 MgO, 47 MgS, 48 Cu, 49 Pd, 50 and Ag. 51 The smallest and largest MAEs are in bold blue and red, respectively.…”

Section: Bulk Modulimentioning

confidence: 99%

Comparative study of semilocal density functionals on solids and surfaces

Tian

Tao

2017

Chemical Physics Letters

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Recently, Tao and Mo (TM) proposed an accurate all-purpose nonempirical meta-generalized gradient approximation (meta-GGA). The exchange part was derived from the density matrix approximation, while the correlation part is based on a modification of TPSS correlation in the low-density or strong-interaction limit. To further understand this density functional, we combine the TM exchange part with the original TPSS correlation and make a comprehensive assessment of this combination, which we call TMTPSS functional, on solids and solid surfaces.Our test includes 22 lattice constants and bulk moduli, 30 band gaps of semiconductors, 7 cohesive energies, and surface exchange-correlation energies for r s ranging from 2 to 3 bohr. Our calculations show that TMTPSS functional is quite competitive to the TM meta-GGA functional, improving upon the nonempirical functionals LSDA, PBE GGA, and TPSS meta-GGA for most properties considered. In particular, it significantly improves the surface exchange-correlation energy calculation, with a mean absolute error of only 1 erg/cm 2 .

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Section: Bulk Modulimentioning

confidence: 99%

Comparative study of semilocal density functionals on solids and surfaces

Tian

Tao

2017

Chemical Physics Letters

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“…As will be shown in Figure 8, for a very strong Debye boson-phonon interaction phonons can assume the linear dispersion of the Debye bosons up to zone boundary. [13] [14]. The low temperature portion can be fitted by ~ T 2.5 function.…”

Section: Figure 2 Extends the Dispersion Of The Debye Bosons With Tramentioning

confidence: 99%

“…The dispersion of the Debye bosons therefore becomes slightly weaker than linear. Figure 2 includes the calculated dispersion of the Debye bosons using the known data for the temperature dependence of the sound velocity vT(T) [7,14].…”

Section: Figure 2 Extends the Dispersion Of The Debye Bosons With Tramentioning

confidence: 99%

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On the Distinction between Debye Bosons and Phonons

Köbler¹

2015

Int. J. Thermo

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A method is described that allows one to construct the dispersion of the Debye bosons (sound waves) from the known temperature dependence of the sound velocities. The method simply assumes that the sound velocity measured at temperature T gives the slope of the dispersion relation at excitation energy E = kBT. The associated reduced wave vector is set equal to q/q0 = a0kBT/hvL/T. In this way the dispersion of the Debye bosons can be constructed for all thermal energies for which sound velocities vL/T(T) are known. This can be up to melting temperature. Surprisingly, for metals and for insulators the dispersion of the Debye bosons can continue up to wave vector values of several times the zone boundary. At melting temperature the wavelength of the Debye bosons is of the order of the atomic diameters. The sources of the Debye bosons therefore must have atomic dimensions. Spontaneous generation of Debye bosons by individual atoms is, however, a completely unexplored process. Interactions with the atomistic background of phonons or lattice defects provide damping to the Debye bosons and make the material specific sound velocity vL/T(T) additionally sample and temperature dependent. For practically all solids it is observed that elastic constants and vL/T(T) decrease as a function of increasing temperature. For high energies the dispersion relation of the Debye bosons therefore becomes visibly lower than linear. Interactions between Debye bosons and phonons can modify the dispersion of the acoustic phonons appreciably. Because of their different symmetries the dispersion relations of Debye bosons and acoustic phonons can attract each other. It is observed that for low wave vector values the dispersion of the acoustic phonons can assume the linear wave vector dependence of the Debye bosons. At the end of the linear section a functional crossover to a sine-like function of wave vector occurs.

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“…Figure 2 shows deviations of the LSDA, PBE, TPSS, PBEsol, TM, HSE06, and optB86b-vdW bulk moduli from the experimental data for these solids. The TM functional is less accurate than PBEsol and nonlocal functionals HSE06 and optB86b-vdW, but outperforms all-purpose functionals 48 SiC, 49 Ge, 48 BP, 50 AlP, 51 AlAs, 51 GaN, 52 GaP, 51 GaAs, 48 NaCl, 53 NaF, 53 LiCl, 53 LiF, 54 MgO, 55 MgS, 56 Cu, 57 Pd, 58 and Ag. 59 The smallest and largest MAEs for semilocal functionals are in bold blue and red, respectively.…”

Section: Bulk Modulimentioning

confidence: 97%

Assessment of the Tao-Mo nonempirical semilocal density functional in applications to solids and surfaces

Car

Staroverov

et al. 2017

Phys. Rev. B

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Recently, Tao and Mo developed a new semilocal exchange-correlation density functional. The exchange part of this functional is derived from a density matrix expansion corrected to reproduce the fourth-order gradient expansion in the slowly-varying-density limit, while the correlation part is based on the TPSS correlation functional with a modification for the low-density limit. In the present work, the Tao-Mo functional is assessed by computing various properties of solids and jellium surfaces. This includes 22 lattice constants and bulk moduli, 30 band gaps, 7 cohesive energies, and jellium surface exchange and correlation energies for the density parameter r s in the range from 2 to 3 bohrs. Our calculations show that the Tao-Mo meta-generalized gradient approximation can yield consistently high accuracy for most properties considered here, with mean absolute errors of 0.025 Å for lattice constants, 7.0 GPa for bulk moduli, 0.08 eV/atom for cohesive energies, and 35 erg/cm 2 for surface exchange-correlation energies.The mean absolute error in band gaps is larger than that of TPSS, but slightly smaller than the errors of LSDA, PBE, and revTPSS. However, band gaps are still underestimated, particularly for large-gap semiconductors, compared to the HSE06 nonlocal screened hybrid functional.

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Elastic Constants of LiF from 4.2°K to 300°K by Ultrasonic Methods

Cited by 142 publications

References 11 publications

Comparative study of semilocal density functionals on solids and surfaces

Comparative study of semilocal density functionals on solids and surfaces

On the Distinction between Debye Bosons and Phonons

Assessment of the Tao-Mo nonempirical semilocal density functional in applications to solids and surfaces

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