Study of Temperature Dependence of Volume Thermal Expansion of Nanomaterials Using New Integral Form of Equation of State (IFEOS)

2021 ◽  
pp. 90-98
Author(s):  
Mahipal Singh ◽  
Madan Singh
Keyword(s):  
Thermal Expansion ◽  
Equation Of State ◽  
Temperature Dependence ◽  
Integral Form

A neutron powder diffraction determination of the thermal expansion tensor of crocoite (PbCrO4) between 60 K and 290 K

1996 ◽  
Vol 60 (403) ◽  
pp. 963-972 ◽  
Author(s):  
Kevin S. Knight
Keyword(s):  
Thermal Expansion ◽  
Temperature Dependence ◽  
Powder Diffraction ◽  
Maximum Expansion ◽  
Lattice Constants ◽  
Thermal Expansion Tensor ◽  
Diffraction Determination ◽  
Line Passing ◽  
Neutron Time

AbstractThe thermal expansion tensor of crocoite has been determined from high-resolution neutron time-of-flight powder diffraction data. The temperature dependence of the lattice constants between 4.5 K and 290 K have been fitted to a quasi-harmonic Einstein model, and the temperature dependence of the thermal expansion tensor has been calculated for 60 K ≤ T ≤ 290 K. The magnitudes of the principal expansivities and their orientation exhibit saturation behaviour for temperatures above 300 K. The predicted saturated expansion coefficients are α11 = 33.1(1) × 10−6K−1, α22 = 15.72(3) × 10−6K−1, α33 = 3.36(1) × 10−6K−1, with α22 parallel to b and α11 lying at an angle of −37.86(5)° to c for the P21/n setting of the crystal structure. The direction of maximum expansion is approximately parallel to both and the least-squares line passing through the projection of the chromium atoms on (010). The direction of minimum expansion lies approximately parallel to [101]. No evidence was found for either a structural or magnetic phase transition between 4.5 K and 300 K.

Phonon Decay in GaN and AlN and Self-Heating in III-N Devices

2006 ◽  
Vol 955 ◽  
Author(s):  
Mark Holtz ◽  
D. Y. Song ◽  
S. A. Nikishin ◽  
V. Soukhoveev ◽  
A. Usikov ◽  
...  
Keyword(s):  
Thermal Expansion ◽  
Temperature Dependence ◽  
High Quality ◽  
Self Heating ◽  
Phonon Emission ◽  
Decay Properties ◽  
Phonon Properties

ABSTRACTWe report studies of the temperature dependence of Raman lines in high quality GaN and AlN. The temperature dependence of the phonon energies and linewidths are used to produce consistent phonon decay properties of zone center optic phonons. In GaN we observe the E22 phonon to decay into three phonons, while the A1(LO) phonon is well described according to the so-called Ridley process – one TO and one LA phonon. For AlN the E22 phonon decays by two phonon emission and the A1(LO) line also exhibits a dependence consistent with the Ridley process. Along with the phonon decay processes, it is important in each case to take into account the contribution of the thermal expansion, including the temperature dependence, to describe observed temperature shifts in the phonon properties.

Algorithms for Density, Potential Temperature, Conservative Temperature, and the Freezing Temperature of Seawater

2006 ◽  
Vol 23 (12) ◽  
pp. 1709-1728 ◽  
Author(s):  
David R. Jackett ◽  
Trevor J. McDougall ◽  
Rainer Feistel ◽  
Daniel G. Wright ◽  
Stephen M. Griffies
Keyword(s):  
Thermal Expansion ◽  
Equation Of State ◽  
Thermodynamic Potential ◽  
Potential Temperature ◽  
Inverse Function ◽  
Freezing Temperature ◽  
Ocean Models ◽  
The Difference ◽  
New Equation ◽  
Density Equation

Abstract Algorithms are presented for density, potential temperature, conservative temperature, and the freezing temperature of seawater. The algorithms for potential temperature and density (in terms of potential temperature) are updates to routines recently published by McDougall et al., while the algorithms involving conservative temperature and the freezing temperatures of seawater are new. The McDougall et al. algorithms were based on the thermodynamic potential of Feistel and Hagen; the algorithms in this study are all based on the “new extended Gibbs thermodynamic potential of seawater” of Feistel. The algorithm for the computation of density in terms of salinity, pressure, and conservative temperature produces errors in density and in the corresponding thermal expansion coefficient of the same order as errors for the density equation using potential temperature, both being twice as accurate as the International Equation of State when compared with Feistel’s new equation of state. An inverse function relating potential temperature to conservative temperature is also provided. The difference between practical salinity and absolute salinity is discussed, and it is shown that the present practice of essentially ignoring the difference between these two different salinities is unlikely to cause significant errors in ocean models.

scholarly journals Analysis of Equation of State for Carbon Nanotubes

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Jeewan Chandra ◽  
Pooja Kapri Bhatt ◽  
Kuldeep Kholiya
Keyword(s):  
Experimental Data ◽  
Carbon Nanotubes ◽  
Thermal Expansion ◽  
Carbon Nanotube ◽  
Equation Of State ◽  
Compression Behavior ◽  
Nanotube Bundles ◽  
The Individual

Compression behavior of carbon nanotube bundles and individual carbon nanotubes within the bundle has been studied by using the Suzuki, Shanker, and usual Tait formulations. It is found that the Suzuki formulation is not capable of explaining the compression behavior of nanomaterials. Shanker formulation slightly improves the results obtained by the Suzuki formulation, but only usual Tait’s equation (UTE) of state gives results in agreement to the experimental data. The present study reveals that the product of bulk modules and the coefficient of volume thermal expansion remain constant for carbon nanotubes. It has also been found that the individual carbon nanotubes are less compressible than bundles of carbon nanotubes.

Few-Parameter Equation of State of the Shock Adiabat with Allowance for Melting

2008 ◽  
Vol 3 (4) ◽  
pp. 52-63
Author(s):  
Evgeny I. Kraus
Keyword(s):  
Solid State ◽  
Equation Of State ◽  
Temperature Dependence ◽  
Thermodynamic Functions ◽  
Melting Curve ◽  
Shock Adiabat ◽  
Elastic Component ◽  
Configuration Entropy ◽  
Model Equations ◽  
State Body

The model equations for thermodynamic functions of liquid status based on volume and temperature dependence of Gruneisen coefficient are offered. Thermal components are described by the Debye’s model. Despite the perfect analogy to solid-state body the distinction in an elastic component of energy and pressures is taken into consideration when deriving the equations. The configuration entropy is embedded into thermodynamic functions of liquid. It describes a disorderliness measure of liquid and results in the final values of the entropy when temperature formally amounts to zero. The melting curve as the boundary between phases is constructed.

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