Thermodynamics of high temperature, Mie–Gruneisen solids

Lemons, Don S.; Lund, C.M.

doi:10.1119/1.19091

Cited by 33 publications

(17 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The family of isotherms is depicted on the Figure 6. The physical meaning has parts of isotherms to the right side of the top, where condition of stability 0 f q    is fulfilled [17]. In the top of the curves the transition in other phase takes place, but the structure of new phase is not described by the present considerations.…”

Section: Isotherms Of the Atomic Chainmentioning

confidence: 92%

“…By rising of the temperature the roots and the top coincide on the abscissa axis, and farther the chain can exist only under the action of negative (compressing) force. As it was noted in [17], the solid corps must resist to the action of stretching force, otherwise it is not a solid corps. The family of isotherms is depicted on the Figure 6.…”

Section: Isotherms Of the Atomic Chainmentioning

confidence: 99%

“…We undertake now a mathematical investigation of this equation for the purpose to receive equations for isotherms and isobars and analyse their behaviour in order to discover transitions. As was noticed [17] the calculations are most simple for values n = 12, m = 6 that we introduce in above expressions and use the notation…”

Section: The Minimum Energy Is Displaced On Distancementioning

confidence: 99%

See 2 more Smart Citations

To the Question of Validity Grüneisen Solid State Equation

Kozlovskiy¹

2012

WJCMP

View full text Add to dashboard Cite

The first justified theory of solid state was proposed by Grüneisen in the year 1912 and was based on the virial theorem. The forces of interaction between two atoms were assumed as changing with distance between them according to inverse power laws. But only virial theorem is insufficient to deduce the equation of state, so this author has introduced some relations, which are correct, when the forces linearly depend on displacement of atoms. But with such law of interaction the phase transitions cannot take place. Debye received Grüneisen equation in another way. He deduced the expression for thermocapacity, using Plank formula for energy of harmonic vibrator. Taking into account the dependence of atomic vibration frequency from distance between atoms, when the forces of interaction are anharmonic, he received the equation of state, which in classical limit turns to Grüneisen equation. The question, formulated by Debye is-How can we come to phase transitions, when Plank formula for harmonic vibrator was used? Debye solved this question not perfectly, because he was born to small anharmonicity. In the presented work a chain of atoms is considered, and their movement is analysed by means of relations, equivalent to virial theorem and theorem of Lucas (disappearing of mean force). Both are the results of variation principle of Hamilton. The Grüneisen equation for low temperature (not very low, where quantum expression for energy is essential) was obtained, and a family of isotherms and isobars are drown, which show the existence of spinodals, where phase transitions occur. So, Grüneisen equation is an equation of state for low temperatures.

show abstract

Section: Isotherms Of the Atomic Chainmentioning

confidence: 92%

Section: Isotherms Of the Atomic Chainmentioning

confidence: 99%

Section: The Minimum Energy Is Displaced On Distancementioning

confidence: 99%

See 1 more Smart Citation

To the Question of Validity Grüneisen Solid State Equation

Kozlovskiy¹

2012

WJCMP

View full text Add to dashboard Cite

show abstract

“…During the Lagrangian phase, we thus have to solve systems (27), (31), (32), (33), (34), and (35). This system is implicit due to Equations (34)-(35) and couples all connecting mixed cells together.…”

Section: Corrections Due To Velocity Enrichmentmentioning

confidence: 99%

Modelling complex high speed multimaterial evolutions using a single mesh multivelocity strategy

Folzan

Tallec

Perlat

2015

Numerical Meth Engineering

View full text Add to dashboard Cite

International audienceIn the present paper, we propose another space discretization of the kinematic constraint for a single grid multi velocity formulation leading to a better approximation of the interface physics. The paper is organized as follows. In the next section, we will briefly review the problem to solve and the single mesh multi-velocity discretization strategy. In Section 3, we will then introduce our new cell-based discretization of the normal velocity continuity constraint on the interface, develop the proper velocity enrichment, and analyse its stability. A generic time discretization is next introduced in Section 4 and adapted to the specific space discretization proposed herein. The proposed methodology is finally validated on a few numerical examples

show abstract

“…As these are derived from free energy, they are closely linked to the thermodynamic properties of the material. They can be related to the specific heat, the Debye temperature and parameter Grüneisen [14,18]. Thus, there are many methods to study the characterization of materials.…”

Section: Fig 1 Uv-vis Spectrum Of the Materials Pltmentioning

confidence: 99%

Estudio de las modificaciones estructurales en un material ferroeléctrico por medio de dos métodos ópticos

Valbuena-Niño¹,

Joya

Barba-Ortega³

2017

ITECKNE Innovación E Investigación en Ingeniería

View full text Add to dashboard Cite

Resumen− Las intensidades de las líneas Raman del cerámico complejo (titanato de plomo) se han investigado como una función de la relación de las áreas de los modos Raman de baja frecuencia E (1TO) y silenciosos. Un cambio de fase tetragonal dentro del material cúbi-co fue observado por espectroscopía Raman. Las muestras fueron sometidas a las mismas condiciones en el momento de realizar las mediciones de Raman. Los espectros UV-vis de absorción sugirieron un cambio en los niveles de energía al aumentar la concentración del elemento de lantano (La). La intención de este estudio es observar cambios estructurales en el material mediante intensidades Raman sin utilizar la posición central tradicional del ancho máximo en las bandas.Palabras Clave− Espectroscopía Raman, material ferroeléctrico, métodos ópticos Abstract− The intensities of the Raman lines of the ceramic complex (lead titanate) have been investigated as a function of the relation of the areas of the low Raman frequency modes E(1TO) and silent. A change of tetragonal phase into cubic material was observed by Raman spectrjky. The samples were subjected to the same conditions at the time of making the Raman measurements. The UV-vis spectra of absorption suggested a change in energy levels with increasing concentration of lanthanum element (La). This study's intention is to observe structural changes in the material by means of Raman intensities without using the traditional central position of the peak width in the bands.

show abstract

Thermodynamics of high temperature, Mie–Gruneisen solids

Abstract: An inexpensive and easy experiment to measure the electrical resistance of high-T c superconductors as a function of temperature Am.

Cited by 33 publications

References 2 publications

To the Question of Validity Grüneisen Solid State Equation

To the Question of Validity Grüneisen Solid State Equation

Modelling complex high speed multimaterial evolutions using a single mesh multivelocity strategy

Estudio de las modificaciones estructurales en un material ferroeléctrico por medio de dos métodos ópticos

Contact Info

Product

Resources

About

Thermodynamics of high temperature, Mie–Gruneisen solids

Abstract: An inexpensive and easy experiment to measure the electrical resistance of high-T c superconductors as a function of temperature Am.

Cited by 33 publications

References 2 publications

To the Question of Validity Gr&#252;neisen Solid State Equation

To the Question of Validity Gr&#252;neisen Solid State Equation

Modelling complex high speed multimaterial evolutions using a single mesh multivelocity strategy

Estudio de las modificaciones estructurales en un material ferroeléctrico por medio de dos métodos ópticos

Contact Info

Product

Resources

About

To the Question of Validity Grüneisen Solid State Equation

To the Question of Validity Grüneisen Solid State Equation