Debye temperature in the high-temperature limit and anharmonic component of the heat capacity of vanadium

1986 ◽  
Vol 51 (2) ◽  
pp. 962-964 ◽  
Author(s):  
Zh. M. Tomilo
Keyword(s):  
Heat Capacity ◽  
High Temperature ◽  
Debye Temperature ◽  
Temperature Limit ◽  
High Temperature Limit

scholarly journals Effects of Vacancy Cluster Defects on Electrical and Thermodynamic Properties of Silicon Crystals

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Pei-Hsing Huang ◽  
Chi-Ming Lu
Keyword(s):  
Heat Capacity ◽  
Debye Temperature ◽  
Density Functional ◽  
Phonon Dispersion ◽  
Vacancy Cluster ◽  
Temperature Limit ◽  
Phase Changes ◽  
Hexagonal Ring ◽  
High Temperature Limit ◽  
Silicon Crystals

A first-principle plane-wave pseudopotential method based on the density function theory (DFT) was employed to investigate the effects of vacancy cluster (VC) defects on the band structure and thermoelectric properties of silicon (Si) crystals. Simulation results showed that various VC defects changed the energy band and localized electron density distribution of Si crystals and caused the band gap to decrease with increasing VC size. The results can be ascribed to the formation of a defect level produced by the dangling bonds, floating bonds, or high-strain atoms surrounding the VC defects. The appearance of imaginary frequencies in the phonon spectrum of defective Si crystals indicates that the defect-region structure is dynamically unstable and demonstrates phase changes. The phonon dispersion relation and phonon density of state were also investigated using density functional perturbation theory. The obtained Debye temperatureθDfor a perfect Si crystal had a minimum value of 448 K atT= 42 K and a maximum value of 671 K at the high-temperature limit, which is consistent with the experimental results reported by Flubacher. Moreover, the Debye temperature decreased with increases in the VC size. VC defects had minimal effects on the heat capacity (Cv) value when temperatures were below 150 K. As the temperature was higher than 150 K, the heat capacity gradually increased with increasing temperature until it achieved a constant value of 11.8 cal/cell·K. The heat capacity significantly decreased as the VC size increased. For a 2 × 2 × 2 superlattice Si crystal containing a hexagonal ring VC (HRVC10), the heat capacity decreased by approximately 17%.

scholarly journals A 4d $$ \mathcal{N} $$ = 1 Cardy Formula

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Jaewon Song
Keyword(s):  
Black Holes ◽  
Free Energy ◽  
Asymptotic Behavior ◽  
High Temperature ◽  
Gauge Theory ◽  
Chemical Potential ◽  
Temperature Limit ◽  
Superconformal Index ◽  
High Temperature Limit ◽  
Cardy Formula

Abstract We study the asymptotic behavior of the (modified) superconformal index for 4d $$ \mathcal{N} $$ N = 1 gauge theory. By considering complexified chemical potential, we find that the ‘high-temperature limit’ of the index can be written in terms of the conformal anomalies 3c − 2a. We also find macroscopic entropy from our asymptotic free energy when the Hofman-Maldacena bound 1/2 < a/c < 3/2 for the interacting SCFT is satisfied. We study $$ \mathcal{N} $$ N = 1 theories that are dual to AdS5 × Yp,p and find that the Cardy limit of our index accounts for the Bekenstein-Hawking entropy of large black holes.

scholarly journals Equations of viscous flow of silicate liquids with different approaches for universality of high temperature viscosity limit

2014 ◽  
Vol 8 (2) ◽  
pp. 59-68
Author(s):  
Ana Kozmidis-Petrovic
Keyword(s):  
High Temperature ◽  
Viscous Flow ◽  
Temperature Limit ◽  
High Temperature Limit ◽  
Viscosity Parameter ◽  
General Rules ◽  
Viscosity Limit ◽  
Dependent Parameter ◽  
Silicate Liquids ◽  
The Difference

The Vogel-Fulcher-Tammann (VFT), Avramov and Milchev (AM) as well as Mauro, Yue, Ellison, Gupta and Allan (MYEGA) functions of viscous flow are analysed when the compositionally independent high temperature viscosity limit is introduced instead of the compositionally dependent parameter ??. Two different approaches are adopted. In the first approach, it is assumed that each model should have its own (average) hightemperature viscosity parameter ??. In that case, ?? is different for each of these three models. In the second approach, it is assumed that the high-temperature viscosity is a truly universal value, independent of the model. In this case, the parameter ?? would be the same and would have the same value: log ?? = ?1.93 dPa?s for all three models. 3D diagrams can successfully predict the difference in behaviour of viscous functions when average or universal high temperature limit is applied in calculations. The values of the AM functions depend, to a greater extent, on whether the average or the universal value for ?? is used which is not the case with the VFT model. Our tests and values of standard error of estimate (SEE) show that there are no general rules whether the average or universal high temperature viscosity limit should be applied to get the best agreement with the experimental functions.

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