Elastic constants of beryllium: a first-principles investigation

Corso, Andrea Dal

doi:10.1088/0953-8984/28/7/075401

Cited by 136 publications

(84 citation statements)

References 45 publications

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“…This is also consistent with the fact that LDA tends to overbind in crystals. We perform elastic-constant calculations 42,43 to obtain the elastic constants (C 11 , C 12 , C 13 , C 33 , C 44 −54 GPa and C 13 = 23 GPa), which may be due to the fact these two values are not directly determined in experiment, as discussed in Ref. [44].…”

Section: Resultsmentioning

confidence: 99%

Direct calculation of the linear thermal expansion coefficients ofMoS2via symmetry-preserving deformations

Gan

Liu

2016

Phys. Rev. B

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Using density-functional perturbation theory and the Grüneisen formalism, we directly calculate the linear thermal expansion coefficients (TECs) of a hexagonal bulk system MoS2 in the crystallographic a and c directions. The TEC calculation depends critically on the evaluation of a temperature-dependent quantity Ii(T ), which is the integral of the product of heat capacity and Γi(ν), of frequency ν and strain type i, where Γi(ν) is the phonon density of states weighted by the Grüneisen parameters. We show that to determine the linear TECs we may use minimally two uniaxial strains in the z direction, and either the x or y direction. However, a uniaxial strain in either the x or y direction drastically reduces the symmetry of the crystal from a hexagonal one to a base-centered orthorhombic one. We propose to use an efficient and accurate symmetry-preserving biaxial strain in the xy plane to derive the same result for Γ(ν). We highlight that the Grüneisen parameter associated with a biaxial strain may not be the same as the average of Grüneisen parameters associated with two separate uniaxial strains in the x and y directions due to possible preservation of degeneracies of the phonon modes under a biaxial deformation. Large anisotropy of TECs is observed where the linear TEC in the c direction is about 1.8 times larger than that in the a or b direction at high temperatures. Our theoretical TEC results are compared with experiment. The symmetry-preserving approach adopted here may be applied to a broad class of two lattice-parameter systems such as hexagonal, trigonal, and tetragonal systems, which allows many complicated systems to be treated on a first-principles level.

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Section: Resultsmentioning

confidence: 99%

Direct calculation of the linear thermal expansion coefficients ofMoS2via symmetry-preserving deformations

Gan

Liu

2016

Phys. Rev. B

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“…To study the linear thermal expansion coefficient α L (T), we employ the thermodynamic theory as implemented in thermo-pw package [41]. We consider the anharmonic effect, in which the volume dependence of the phonon frequencies in a solid at finite temperature is included.…”

Section: Methods Of Calculationsmentioning

confidence: 99%

“…Generally speaking, the longitudinal vibration for longitudinal acoustic (LA) modes is along the bond direction which favors the crystal volume expansion, whereas the transverse vibration in the TA modes is associated with the bond-angle-bending (perpendicular to the bond) which tends to reduce the crystal volume [15,20,22,45,46]. This effect can be identified from the dimensionless mode Grüneisen parameter: [41,47,48]…”

Section: Mode-dependent Grüneisen Parametersmentioning

confidence: 99%

A systematic study of the negative thermal expansion in zinc-blende and diamond-like semiconductors

et al. 2019

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Upon heating, almost all zinc-blende (ZB) and diamond-like semiconductors undergo volume contraction at low temperature, i.e. negative thermal expansion (NTE), instead of commonly expected expansion. Specifically, CuCl has the largest NTE among these semiconductors with a coefficient comparable with the record value of ZrW 2 O 8 . So far, underlying physical mechanism remains ambiguous. Here, we present a systematic and quantitative study of the NTE in ZB and diamond-like semiconductors using first-principles calculations. We clarified that the material ionicity, which renders the softening of the bond-angle-bending and thus, the enhancement of excitation of the transverse acoustic (TA) phonon, is responsible for the NTE of ZB and diamond-like semiconductors. With the increase in the ionicity from the groups IV, III-V, IIB-VI to IB-VII ZB semiconductors, the coefficient of the maximum NTE increases due to the weakness in bond-rotation effect, which makes the relative motion between cation and anion transverse to the direction of the bond more feasible and the mode Grüneisen parameters of the TA modes more negative. Since CuCl has the highest ionicity among all ZB and diamond-like semiconductors, it is expected to have the largest NTE, in good agreement with the experimental observation. This understanding would be beneficial for tetrahedral materials with specific applications.

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“…The dynamical matrices are calculated on a 4 × 4 × 6, 2 × 2 × 6, 3 × 3 × 4, and 8 × 8 × 3 q-points for (4, 8 2 ), (3,12 2 ), (6 3 ), and (4 4 ) 3D-Cs, respectively. To examine the mechanically stable of the 3D-C ALs, we use the Thermo-pw code [32] to calculate the elastic constants C i j . The calculated elastic constants are derived from the finite difference approach and are by default averaged over the entire unit cell volumes.…”

Section: Calculation Methodsmentioning

confidence: 99%

“…According to the Born criteria, the elastic constants of the tetragonal and hexagonal crystals have to satisfy the following conditions [46]: C 11 > |C 12 |, 2C 2 13 < C 33 (C 11 + C 12 ), C 44 > 0, and C 66 > 0 (the condition for C 66 is redundant in the hexagonal case). The elastic constants can be derived by fitting the strain-stress curves associated with uniaxial and equibiaxial strains, as implemented in Thermo-pw code [32]. The calculated C i j values of the 3D-C ALs are listed in Table 2 at the neutral charge.…”

Section: Dynamical and Mechanical Stabilitymentioning

confidence: 99%

Three-dimensional carbon Archimedean lattices for high-performance electromechanical actuators

Hung

Nugraha

Saito

2017

Carbon

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We propose three-dimensional carbon (3D-C) structures based on the Archimedean lattices (ALs) by combining sp 2 bonding in the polygon edges and sp 3 bonding in the polygon vertices. By first-principles calculations, four types of 3D-C ALs: (4, 8 2 ), (3, 12 2 ), (6 3 ), and (4 4 ) 3D-Cs are predicted to be stable both dynamically and mechanically among 11 possible ALs, in which the notations (p 1 , p 2 , . . .) are the indices of the AL structures. Depending on their indices, the 3D-C ALs show distinctive electronic properties: the (4, 8 2 ) 3D-C is an indirect band-gap semiconductor, the (3, 12 2 ) 3D-C is semimetal, while the (6 3 ) and (4 4 ) 3D-Cs are metals. Considering the structural deformation due to the changes in their electronic energy bands, we discuss the electromechanical properties of the 3D-C ALs as a function of charge doping. We find a semiconductor-to-metal and semimetallic-to-semiconductor transitions in the (4, 8 2 ) and (3, 12 2 ) 3D-Cs as a function of charge doping, respectively. Moreover, the (3, 12 2 ) 3D-C exhibits a sp 2 -sp 3 phase transformation at high charge doping, which leads to a huge 30% irreversible strain, while the reversible strain in the (4, 8 2 ) 3D-C is up to 9%, and thus they are quite promising for electromechanical actuators.

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Elastic constants of beryllium: a first-principles investigation

Cited by 136 publications

References 45 publications

Direct calculation of the linear thermal expansion coefficients ofMoS2via symmetry-preserving deformations

Direct calculation of the linear thermal expansion coefficients ofMoS2via symmetry-preserving deformations

A systematic study of the negative thermal expansion in zinc-blende and diamond-like semiconductors

Three-dimensional carbon Archimedean lattices for high-performance electromechanical actuators

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