Evaluation of the Grüneisen Constant

Bansigir, K. G.

doi:10.1063/1.1656895

Cited by 17 publications

(6 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Altogether, this relation (Eq. 8) provides a simple physical justification for the chemist's intuition that the anharmonicity of solids is related to the type of bond and atomic coordination (density) 9,36,37 . Nor would it be surprising if more intricate connections were found between elasticity, atomic structure and anharmonicity through modern machine learning methods.…”

Section: Resultsmentioning

confidence: 99%

Inherent anharmonicity of harmonic solids

Agne¹,

Anand²,

Snyder³

2022

Preprint

View full text Add to dashboard Cite

Atomic vibrations, in the form of phonons, are foundational in describing the thermal behavior of materials. The possible frequencies of phonons in materials are governed by the complex bonding between atoms, which is physically represented by a spring-mass model that can account for interactions (spring forces) between the atoms (masses). The lowest order, harmonic, approximation only considers linear forces between atoms and is thought incapable of explaining phenomena like thermal expansion and thermal conductivity, which are attributed to non-linear, anharmonic, interactions. Here we show that the kinetic energy of atoms in a solid produces a pressure much like the kinetic energy of atoms in a gas does. This vibrational or phonon pressure naturally increases with temperature, as it does in a gas, and therefore results in a thermal expansion. Because thermal expansion thermodynamically defines a Grüneisen parameter, which is a typical metric of anharmonicity, we show that even a harmonic solid will necessarily have some anharmonicity. A consequence of this phonon pressure model is a harmonic estimation of the Grüneisen parameter from the ratio of the transverse and longitudinal speeds of sound. We demonstrate the immediate utility of this model by developing a high-throughput harmonic estimate of lattice thermal conductivity that is comparable to other state-of-the-art estimations. By linking harmonic and anharmonic properties explicitly, this study provokes new ideas about the fundamental nature of anharmonicity, while also providing a basis for new materials engineering design metrics.

show abstract

Section: Resultsmentioning

confidence: 99%

Inherent anharmonicity of harmonic solids

Agne¹,

Anand²,

Snyder³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Перша спроба визначення середнього значення параметра Грюнайзена γ для групи додекаборидів була проведена авторами (Vadets et al, 1998). За методом Банзігіра (Bansigir, 1968) при кімнатній температурі за співвідношенням…”

Section: вступunclassified

Estimation of the Gruneisen parameter and an explicit measure of anharmonicity of dodecaborides

Fedyshyn¹,

Vadets²,

Гаращенко³

et al. 2018

SMLNUVMBF

View full text Add to dashboard Cite

In previous works on the ratio (θД – the characteristic temperature of Debye, was calculated according to the Lindemann formula; V – molar volume of hypothetical lattice atoms; γ is the Gruneisen parameter) for the group of dodecaborides (TbB12, DyB12, HoB12, ErB12, TuB12, LaB12, UB12) the average value of γ = 1.3 was determined. However, due to the ambiguity of the coefficient of proportionality in the Lindemann formula by definition θD, the authors selected an independent high-temperature X-ray method for determining the dependence θr (T). Taking into account the immutability of the structure and type of interatomic connection in the temperature interval of the search (293–973 K), the authors evaluated the value and temperature dependence of γ (T) of each dodecaboride separately. The results of the search showed that the value of γ for each given dodecaboride is different, but practically independent from temperature. For some dodecaborides, the parameter γ is about 2–3 units, and for others it is overestimated. The values of γ made it possible to estimate the magnitude of the implicit γβ and the explicit parts of the universal measure of anharmonicity of dodecaborides , where β – real coefficient of volumetric expansion of the crystalline lattice. Because (n – dimensionless coefficient of proportionality), then the temperature change n(T) is also determined.

show abstract

“…За наявності значень θ Д і V, побудувавши залежність з використанням (3), за методом Банзігіра (Bansigir, 1968) знаходять середнє значення параметра Грюнайзена γ для ізоструктурних кристалів з однаковим типом зв'язків між атомами.…”

Section: вступunclassified

The estimation of the parameter Gruneisen metal hexaborides

et al. 2018

View full text Add to dashboard Cite

The basis for the estimation of the Gruneisen parameter γ is laid (θД – Debye’s characteristic temperature, V– molar volume) from which the mathematical expression follows . In previous publications in order to determine θД the Lindemann formula was used. However, due to the ambiguity of the dimensional coefficient C in the Lindemann formula, the authors used the method of high-temperature roentgenography within the limits of 293–973 K. On the basis of analisys of the intensity of one maximum interference (hkl) at different temperatures, was determined by Chipman’s method X-ray characteristic temperature θр(Т) groups of hexaboard type CaB6, namely CaB6, YB6, LaB6, CeB6, PrB6 , NdB6, ErB6, ThB6, YbB6. Considering, that neither the structure nor the interatomic connections within the temperature search of hexaborides does not change, the value of the parameter γ is determined. Its value was obtained within 2.5–4.7 for CeB6, NdB6, ErB6, YbB6, ThB6 and order 5.5–6.6 for CaB6, YB6, LaB6, PrB6. The parameters of Gruneisen proved to be practically independent of temperature. The presence of the meanings of γ made it possible to divide the implicit and explicit parts of the anagrammonism into a calming measure. The generalizing measure of anharmonism is mainly exhausted by the product γβ (β – the coefficient of the volumetric expansion of the crystalline lattice.

show abstract

Evaluation of the Grüneisen Constant

Cited by 17 publications

References 8 publications

Inherent anharmonicity of harmonic solids

Inherent anharmonicity of harmonic solids

Estimation of the Gruneisen parameter and an explicit measure of anharmonicity of dodecaborides

The estimation of the parameter Gruneisen metal hexaborides

Contact Info

Product

Resources

About