Thermionic constants of metals and semiconductors - IV. Monovalent metals (continued)

1954 ◽  
Vol 225 (1161) ◽  
pp. 159-172
Keyword(s):  
Thermal Expansion ◽  
Work Function ◽  
Temperature Variation ◽  
Condensed Phase ◽  
Energy Barrier ◽  
External Pressure ◽  
Detailed Calculation ◽  
Free Electrons ◽  
Saturation Vapour Pressure ◽  
Thermal Oscillations

In a monovalent metal, in which the valency electrons may be regarded as forming a free-electron assemblage, the assumption of a temperature-independent energy barrier at the surface of the metal is shown to be equivalent to taking the free electrons in the condensed phase, namely, the metal, and the electrons in the gaseous phase in thermal equilibrium with it, as forming a homogeneous single component system . The temperature variation of the work function is then determined by the temperature variation of the therm odynamic potential of the electrons in the condensed phase, when the external pressure is kept constant a t the value of the saturation vapour pressure of the electrons, which is equivalent to keeping the pressure of the electron assemblage in the condensed phase also constant, since the energy barrier at the surface is independent of temperature. It is further shown that for a degenerate, or nearly degenerate, electron assemblage the specific heat at constant pressure is the same as that at constant volume, and it is easily calculated. The temperature coefficient of the work function calculated therefrom corresponds to an apparent lowering of about 8 to 10% in the value of the A coefficient in therm ionic emission. This agrees with observation. On the other hand, the thermal expansion of the lattice is found to be about 25 to 50 times that to be expected thermodynamically for the electron assemblage in the condensed phase. This result, when viewed against the nearly normal observed value of the A coefficient, shows that the energy barrier at the surface of the metal should decrease with increase of temperature by the same amount by which the thermodynamic potential of the electrons in the condensed phase decreases as a result of the thermal expansion of the lattice. A detailed calculation is made of the effect of both the thermal expansion of the lattice, and the increased thermal oscillations of the atoms in the lattice, associated with the rise in temperature, on the energy of the barrier at the surface. The net effect is found to be a lowering of this energy of the required magnitude.

A Generalized Model for Residual Stress Caused by Thermal Mismatch in Multilayer Structures

2011 ◽  
Vol 704-705 ◽  
pp. 1284-1290
Author(s):  
Yu Mei Bai ◽  
Ying Qiang Xu ◽  
Tao Zhang
Keyword(s):  
Residual Stress ◽  
Thermal Expansion ◽  
Temperature Variation ◽  
Analytical Model ◽  
Layer Structure ◽  
Engineering Application ◽  
Effect Of Temperature ◽  
Multilayer Structures ◽  
Coating System ◽  
Thermal Expansion Mismatch

An analytical model based on multilayer structure with thermal expansion mismatch caused by temperature gradients was established to predict the residual stress in the system. The solution obtained from the model is independent of the number of layers. Three simplified models: bi-layer structure, coating system and film system with great compatibility are developed considering different engineering application. And the bilayer structure is verified by Stoney’s equation under the same conditions. Tri-layer coating system ZrO2/ Al2O3/1Cr18Ni9Ti is established in order to research the effect of temperature variations on the residual stress between different layers. The results suggested the stress has obvious mutation in coating interface with different temperature variation. And the residual stress with different temperature variation in different layers is larger than that with identical temperature variation. Key words: multilayer structures; residual stress; analytical model; thermal expansion mismatch; temperature variation

Thermal expansion coefficients and Gruneisen parameters of quartz at high temperature by X-ray method

1994 ◽  
Vol 9 (2) ◽  
pp. 148-150
Author(s):  
Nabil N. Rammo ◽  
Saad B. Farid
Keyword(s):  
Thermal Expansion ◽  
High Temperature ◽  
Ambient Temperature ◽  
Least Squares ◽  
Temperature Variation ◽  
Ray Method ◽  
X Ray ◽  
Least Squares Fitting ◽  
Thermal Expansion Coefficients ◽  
Expansion Coefficients

The temperature variation of the interplanar spacings (101), (112), and (211) of 325 mesh quartz was determined in the range 300–966 °K using X-ray powder diffractometry. The measured lattice parameters have been found to increase nonlinearly with temperature, and the dependence has been expressed by a polynomial of second degree from the least-squares fitting of the data, the results of which are presented herein. Values are given for the thermal expansion coefficients and Gruneisen parameter in the range 300 to 768 °K. In the range 768–966 °K, the expansion is zero. The derivatives dαa/dT, dαc/dT, and dαv/dT at ambient temperature are also given.

The electronic capacitor at a metal–electrolyte interface

1984 ◽  
Vol 62 (6) ◽  
pp. 1145-1158 ◽  
Author(s):  
G. A. Martynov ◽  
R. R. Salem
Keyword(s):  
Surface Tension ◽  
Work Function ◽  
Mercury Electrode ◽  
Electron Work Function ◽  
Potential Drop ◽  
Free Electrons ◽  
Left Hand ◽  
Zero Charge ◽  
Wide Range ◽  
The Right

A model for the dense part of electrical double layer is proposed using the concept that conduction electrons penetrate into a solution to form an electronic capacitor on the metal surface. The potential drop between the metal and solution, the charge of the metal, its surface tension, and the electron work function for a metal–solution interface are calculated within the framework of the model, and the formulae derived are compared with experiment. It is shown that for a metal–vacuum interface of 38 metals in the left-hand subgroups of the Mendeleev table the discrepancy between the theoretical and experimental values of surface tension and work function does not exceed the experimental error (i.e. it is less than 10%); for six metals in the right-hand subgroups and especially for semimetals the theoretical error is two to three times higher. The density of free electrons in a metal determined in terms of the concepts of the model is shown to vary monotonously with the element number for all 54 metals with available experimental data.A relationship, previously unknown, between surface tension and zero-charge potential is established, which enabled one to calculate the electronic capacitor charge for mercury (the theoretical value is 33 C/cm2, and the experimental value is 36–38 C/cm2). This paper also reports the calculated values of the integral capacity of a mercury electrode in water: the experimental value is 29 F/cm2 (at the zero-charge point), and the theoretical value is 28 F/cm2. The model predicts an increase of the capacity in the anodic region and a decrease in the cathodic region, in a good agreement with experiment. It should be stressed that although the theory includes only one fitting parameter, the density of free electrons in the metal, it correctly explains a wide range of phenomena.

scholarly journals Temperature Variation of the Work Function of the Oxide Superconductor, YBa2Cu3O7.

Shinku ◽  
1992 ◽  
Vol 35 (3) ◽  
pp. 183-186
Author(s):  
Shigeru SAITO ◽  
Masamichi OHKI ◽  
Tatsuo TANI ◽  
Takao MAEDA ◽  
Masahiro ISHIHARA ◽  
...  
Keyword(s):  
Work Function ◽  
Temperature Variation ◽  
Oxide Superconductor

Buckling Thresholds for Pre-Loaded Spherical Shells Subject to Localized Blasts

2019 ◽  
Vol 87 (3) ◽  
Author(s):  
Jan Sieber ◽  
John W. Hutchinson ◽  
J. Michael T. Thompson
Keyword(s):  
Impact Energy ◽  
Energy Barrier ◽  
Threshold Energy ◽  
External Pressure ◽  
Extensive Study ◽  
Energy Threshold ◽  
Integration Scheme ◽  
Spherical Shells ◽  
Buckling Mode ◽  
The Impact

Abstract This paper investigates the robustness against localized impacts of elastic spherical shells pre-loaded under uniform external pressure. We subjected a pre-loaded spherical shell that is clamped at its equator to axisymmetric blast-like impacts applied to its polar region. The resulting axisymmetric dynamic response is computed for increasing amplitudes of the blast. Both perfect shells and shells with axisymmetric geometric imperfections are analyzed. The impact energy threshold causing buckling is identified and compared with the energy barrier that exists between the buckled and unbuckled static equilibrium states of the energy landscape associated with the pre-loaded pressure. The extent to which the impact energy of the threshold blast exceeds the energy barrier depends on the details of its shape and width. Targeted blasts that approximately replicate the size and shape of the energy barrier buckling mode defined in the paper have an energy threshold that is only modestly larger than the energy barrier. An extensive study is carried out for more realistic Gaussian-shaped blasts revealing that the buckling threshold energy for these blasts is typically in the range of at least 10–40% above the energy barrier, depending on the pressure pre-load and the blast width. The energy discrepancy between the buckling threshold and energy barrier is due to elastic waves spreading outward from the impact and dissipation associated with the numerical integration scheme. Buckling is confined to the vicinity of the pole such that, if the shell is not shallow, the buckling thresholds are not strongly dependent on the location of the clamping boundary, as illustrated for a shell clamped halfway between the pole and the equator.

Some aspects of thermal and elastic properties of yttrium

1979 ◽  
Vol 57 (2) ◽  
pp. 120-127 ◽  
Author(s):  
R. Ramji Rao ◽  
A. Rajput
Keyword(s):  
Thermal Expansion ◽  
Temperature Variation ◽  
Elastic Constants ◽  
Temperature Limit ◽  
Third Order ◽  
Thermal Expansion Data ◽  
Systematic Calculation ◽  
Limit Formula ◽  
Third Order Elastic Constants ◽  
Good Agreement

A systematic calculation of the lattice heat capacity, third-order elastic constants and the temperature variation of the effective Grüneisen functions of the hexagonal close-packed metal yttrium is carried out using the approach of Keating. The normalized frequency distribution function employed for specific heat calculations is obtained using 50 880 frequencies. Good agreement is found between the calculated and experimental Cv1 values. The l0 third-order elastic constants are evaluated using two anharmonic parameters and these, in turn, are utilized to calculate the low-temperature limit [Formula: see text] of thermal expansion, the Anderson–Güneisen (A–G) parameter δ, and the second Grüneisen constant q of yttrium. The temperature dependence of the volume Grüneisen function and its high-temperature limit [Formula: see text] are determined. The theoretical values of [Formula: see text] and [Formula: see text] are in excellent agreement with those estimated from the experimental thermal expansion data of Meyerhoff and Smith obtained for this metal. The calculated value of the A–G parameter δ is used in Anderson's equation to determine the temperature variation of the bulk modulus of yttrium and it is found that the change in Bs from 4 to 400 K calculated in this manner shows good agreement with that estimated from the experimental results of Smith and Gjevre. The variation of the lattice parameters of yttrium with hydrostatic pressure is also investigated using its third-order elastic constants and Thurston's extrapolation formulae.

scholarly journals The temperature variation of the work function of clean and of thoriated tungsten

1937 ◽  
Vol 163 (915) ◽  
pp. 499-510 ◽  
Keyword(s):  
Work Function ◽  
Temperature Variation ◽  
Transmission Coefficient ◽  
Electron Emission ◽  
Universal Constant ◽  
Absolute Temperature ◽  
Theoretical Equation ◽  
Restricted Range ◽  
Thoriated Tungsten ◽  
The Mean

It is well known that the relation between the electron emission i from a hot body and its absolute temperature T may be expressed empirically by the equation i = AT 2 e -ψ/ kT , in which A and ψ are constants characteristic of the emitting surface, and k is Boltzmann’s constant. This is of the same form as the theoretical equation i = A 0 D - T 2 e -x/ kT , in which A 0 is a universal constant having the numerical value of 120 amp. cm. -2 degree -2 , D - is the mean transmission coefficient, and X is the work function of the emitter. This quantity is not necessarily constant with temperature, and if we assume its temperature variation to be linear, as we may do within a sufficiently restricted range of temperatures, setting X = ω+α KT , Where ω and α are Constants, we may rewrite(2) thus: i = A 0 D - T 2 e -ω/ kT . It may be shown (cf. Reimann 1934a, p. 265) that in such cases as occur in nature D - probably never varies appreciably with temperature, and so, assuming this, and comparing (1) with (4), we may write A = A 0 D - e-α, ψ = ψ .

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