Thermo-Elasticity of Materials from Quasi-Harmonic Calculations

Destefanis, Maurizio; Ravoux, Corentin; Cossard, Alessandro; Erba, Alessandro

doi:10.3390/min9010016

Cited by 29 publications

(41 citation statements)

References 58 publications

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“…We note that a full quasi-harmonic description of thermo-elasticity, as recently outlined in Ref. 65, is still rather challenging for MOFs. The single-crystal elastic constants of MOF-5 were computed, both with B3LYP and B3LYP-D3, at six dierent pressures (0.0, 0.1, 0.2, 0.3, 0.4 and 0.5 GPa), 66,67 which allowed us to determine the pressure dependence of a variety of mechanical properties.…”

Section: Resultsmentioning

confidence: 96%

Quasi-Harmonic Lattice Dynamics of a Prototypical Metal-Organic Framework

Ryder

Maul²,

Civalleri³

et al. 2019

Preprint

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Quasi-harmonic lattice-dynamical calculations are performed to investigate the combined effect of temperature and pressure on the structural and mechanical properties of a prototypical metal-organic framework material: MOF-5. The softening upon compression of an A2g phonon mode at the gamma point in the high-symmetry Fm3m structure is identified, which leads to a symmetry reduction and a group subgroup phase transition to a low-symmetry Fm3 phase for compressions larger than 0.8%. The effect of the symmetry reduction on the equation-of-state of MOF-5 is investigated, which provides a static bulk modulus K reducing from 17 to 14 GPa and a corresponding change of K0 (pressure derivative of K) from positive to negative. The effect of pressure on the negative thermal expansion of the framework and on its mechanical response is analysed. The evolution of the mechanical anisotropy of MOF-5 as a function of pressure is also determined, which allows us to identify the occurrence of a shear-induced mechanical instability at 0.45 GPa.<br>

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Section: Resultsmentioning

confidence: 96%

Quasi-Harmonic Lattice Dynamics of a Prototypical Metal-Organic Framework

Ryder

Maul²,

Civalleri³

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We note that a full quasi‐harmonic description of thermo‐elasticity, as recently outlined in ref. [], is still rather challenging for MOFs. The single‐crystal elastic constants of MOF‐5 were computed, both with B3LYP and B3LYP‐D3, at six different pressures (0.0, 0.1, 0.2, 0.3, 0.4, and 0.5 GPa), which allowed us to determine the pressure dependence of a variety of mechanical properties.…”

Section: Resultsmentioning

confidence: 99%

Quasi‐Harmonic Lattice Dynamics of a Prototypical Metal–Organic Framework

Ryder

Maul

Civalleri

et al. 2019

Advcd Theory and Sims

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Quasi-harmonic lattice-dynamical calculations are performed to investigate the combined effect of temperature and pressure on the structural and mechanical properties of a prototypical metal-organic framework material: MOF-5. The softening upon compression of an A 2g phonon mode at the point in the high-symmetry Fm3m structure is identified, which leads to a symmetry reduction and a group-subgroup phase transition to a low-symmetry Fm3 phase for compressions larger than 0.8%. The effect of the symmetry reduction on the equation-of-state of MOF-5 is investigated, which provides a static bulk modulus K reducing from 17 to 14 GPa and a corresponding change of K (pressure derivative of K ) from positive to negative. The effect of pressure on the negative thermal expansion of the framework and on its mechanical response is analyzed. The evolution of the mechanical anisotropy of MOF-5 as a function of pressure is also determined, which allows identifying the occurrence of a shear-induced mechanical instability at 0.45 GPa.

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“…Within the harmonic approximation to the lattice dynamics (i.e., if only second-order interatomic force constants are evaluated at a single volume), thermal expansion would be null, 12 as well as the thermal dependence of the elastic moduli. 35 The zero-pressure volumetric thermal expansion of a solid is often described in terms of a thermal expansion coefficient αV (T), which is defined as…”

Section: B Thermal Expansionmentioning

confidence: 99%

Negative thermal expansion of Cu2O studied by quasi-harmonic approximation and cubic force-constant method

Linnera

Erba

Karttunen

2019

The Journal of Chemical Physics

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Cubic cuprous oxide, Cu 2 O, is characterized by a peculiar structural response to temperature: it shows a relatively large negative thermal expansion below 250 K, then followed by a positive thermal expansion at higher temperatures. The two branches of its thermal expansion (negative and positive) are almost perfectly symmetric at low temperatures, with the minimum of its lattice parameter at about 250 K and with the lattice parameter at 500 K almost coinciding with that at 0 K. We perform lattice-dynamical quantum-mechanical calculations to investigate the thermal expansion of Cu 2 O. Phonon mode-specific Grüneisen parameters are computed, which allows us to identify different spectral regions of atomic vibrations responsible for the two distinct regimes of thermal expansion. Two different computational approaches are explored, their results compared, and their numerical aspects critically assessed: a well-established method based on the quasiharmonic approximation, where harmonic frequencies are computed at different lattice volumes, and an alternative approach, where quadratic and cubic interatomic force-constants are computed at a single volume. The latter scheme has only recently become computationally feasible in the context of lattice thermal conductivity simulations. When proper numerical parameters are used (phonon sampling, tolerances, etc.), the two approaches are here shown to provide a very consistent description, yet at a rather different computational cost. All of the experimentally observed features of the complex thermal expansion of Cu 2 O are correctly reproduced up to 500 K, with a slight overall underestimation of the volume contraction.

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Thermo-Elasticity of Materials from Quasi-Harmonic Calculations

Cited by 29 publications

References 58 publications

Quasi-Harmonic Lattice Dynamics of a Prototypical Metal-Organic Framework

Quasi-Harmonic Lattice Dynamics of a Prototypical Metal-Organic Framework

Quasi‐Harmonic Lattice Dynamics of a Prototypical Metal–Organic Framework

Negative thermal expansion of Cu2O studied by quasi-harmonic approximation and cubic force-constant method

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