SPECIFIC HEATS OF CERTAIN SALTS OF IRON GROUP ELEMENTS FROM 65° TO 300°K.

1950 ◽  
Vol 28a (4) ◽  
pp. 367-376 ◽  
Author(s):  
H. D. Vasileff ◽  
H. Grayson-Smith
Keyword(s):  
Low Temperature ◽  
Specific Heat ◽  
Cobalt Nitrate ◽  
Second Order ◽  
Nickel Nitrate ◽  
Chromium Nitrate ◽  
Iron Group ◽  
Anhydrous Salt ◽  
Specific Heats ◽  
Entropy Changes

Using a new low temperature calorimeter, which is briefly described in the paper, the specific heats have been measured from 65° to 300°K. for the following salts: chromium sulphate (hydrated and anhydrous), chromium nitrate, cobalt nitrate, and nickel nitrate (hydrated). Hydrated chromium sulphate was found to have a transition of the second order at 195°K., while the specific heat of the anhydrous salt was quite regular. The hydrated nitrates all showed second order transitions in the neighborhood of 150°K. The entropy changes associated with these transitions have been estimated approximately, and vary from about 0.4 R for cobalt nitrate to 1.65 R for chromium nitrate, where R is the gas constant. Pending further evidence, it is tentatively suggested that the transitions are due to the onset of partial rotation of the H2O groups in the crystals.

Order?Disorder Transformations in Alloys. The Inclusion of Non-nearest Neighbour Interactions in Cluster Variation Methods. II. Low Temperature Specific Heats for Body Centred Cubic Lattices

1981 ◽  
Vol 34 (1) ◽  
pp. 75 ◽  
Author(s):  
Joan M Hanley ◽  
Thomas E Peacock
Keyword(s):  
Critical Temperature ◽  
Low Temperature ◽  
Specific Heat ◽  
Interaction Energy ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Nearest Neighbour ◽  
Specific Heats ◽  
Low Temperature Specific Heat ◽  
Cluster Variation

In Part I, the Sanchez and de Fontaine formulation of the cluster variation method was used to study the dependence of the critical temperature and the high temperature specific heat on the ratio of second neighbour to nearest neighbour interaction energy. This method can be extended to find solutions for the ordered state. The dependence of the low temperature specific heat on the interaction energy ratio is studied. As with the critical temperature and high T specific heat studies, it is found that both the sign and magnitude of ex affect the low temperature specific heat.

Low temperature specific heats of zinc alloyed with silver

1975 ◽  
Vol 343 (1634) ◽  
pp. 363-374 ◽  
Keyword(s):  
Low Temperature ◽  
Fermi Level ◽  
Specific Heat ◽  
Debye Temperature ◽  
Density Of States ◽  
Electronic Specific Heat ◽  
Pure Zinc ◽  
Specific Heats ◽  
Complete Breakdown ◽  
Specific Heat Coefficient

Measurements of the electronic specific heat coefficient and of the limiting Debye temperature are reported for pure zinc and for two n-phase alloys containing 2 at. % and 4 at. % silver in zinc, respectively. After a correction for electron-phonon enhancement the electronic specific heat coefficient for pure zinc differs by only a small percentage from the calculated value reported in the literature on the basis of a band calculation. The results for the alloys show a decreasing trend of the density of states at the Fermi level when silver is added to zinc. This is contrary to a prediction based on a rigid band approach. Hence, the results indicate a complete breakdown of the rigid band condition on alloying. The reasons for this are most likely associated with the influence of the d band electrons or with charge distribution effects between solute and solvent atoms.

LOW TEMPERATURE SPECIFIC HEAT OF INTERMETALLICS (Ti/Be)B2

2007 ◽  
Vol 21 (14) ◽  
pp. 885-891 ◽  
Author(s):  
NUPINDER KAUR ◽  
N. K. GAUR ◽  
R. K. SINGH
Keyword(s):  
Experimental Data ◽  
Thermal Properties ◽  
Low Temperature ◽  
Specific Heat ◽  
Debye Temperature ◽  
Cohesive Energy ◽  
Specific Heats ◽  
Molecular Force ◽  
Low Temperature Specific Heat ◽  
Rigid Ion Model

We have applied the Rigid Ion Model (RIM) to study the cohesive and thermal properties of binary intermetallic BeB 2 and TiB 2. The paper reports the calculated results on cohesive energy (ϕ), compressibility (β), molecular force constant (f), Restrahalen frequency (ν0), Debye temperature (Θ D ) and Gruneisen parameter (γ) for the temperature range 50 K ≤ T ≤ 300 K and the effect of van der Waal interaction on these properties are also shown. Our results on Debye temperature are closer to the experimental data. In addition, we have computed the specific heats for BeB 2 and TiB 2 and compared them with the available experimental data.

Experimental evidence for the Fermi surface overlap effect in ε-phase Ag—Zn alloys, obtained from low temperature specific heats

1975 ◽  
Vol 343 (1634) ◽  
pp. 375-387 ◽  
Keyword(s):  
Theoretical Model ◽  
Low Temperature ◽  
Specific Heat ◽  
Brillouin Zone ◽  
Band Gaps ◽  
Electronic Specific Heat ◽  
Specific Heats ◽  
Ε Phase ◽  
Specific Heat Coefficient ◽  
Zn Alloys

Measurements of the electronic specific heat coefficient and of the limiting Debye temperature are reported for ten Ag-Zn alloys in the range of the h.e.p. ε-phase. After a correction for the electron-phonon enhancement, the trend of the electronic specific heat coefficient is consistent with a nearly rigid band behaviour, showing a general decrease of the density of states at the Fermi level when the corners of the Brillouin zone are filled. A slight deviation from this trend occurs at electron concentration values exceeding approximately 1.85 5 , in agreement with other measured properties and confirming a theoretical model involving overlaps of electrons across the {00.2} planes of the Brillouin zone. The estimated band gaps are of the order of 2 eV. I t appears that whereas in the dilute rj-phase alloys of zinc with silver the rigid band condition is not valid the opposite is true in the concentrated ε-phase alloys.

The low temperature specific heats of some pure metals (Cu, Ag, Pt, Al, Ni, Fe, Co)

1965 ◽  
Vol 285 (1403) ◽  
pp. 561-580 ◽  
Keyword(s):  
Boundary Layer ◽  
Low Temperature ◽  
Specific Heat ◽  
Spin Wave ◽  
Vapour Pressure ◽  
Effective Field ◽  
Weighting Schemes ◽  
Specific Heats ◽  
Nuclear Contribution ◽  
Pure Metals

Details are given of the construction of a calorimeter to operate in the range 1.2 to 4.2 °K. Analyses of the results obtained for several pure metals (Cu, Ag, Pt, Al, Ni, Fe, Co) are given for various weighting schemes in reducing the results. The effects of errors due to the possible presence of a Kapitza boundary layer affecting the temperatures deduced from vapour pressure bulb measurements are considered. The results are analysed with a view to detecting further lattice contributions to the specific heat ( T 5 terms) and (in the case of ferromagnetics) spin wave contributions. The nuclear contribution and the effective field is evaluated for cobalt.

The interaction of lattice vibrations and free electrons in metals

1932 ◽  
Vol 28 (3) ◽  
pp. 367-385
Author(s):  
H. Jones
Keyword(s):  
Specific Heat ◽  
Second Order ◽  
Order Effects ◽  
Lattice Vibrations ◽  
Free Electrons ◽  
Thermoelectric Effects ◽  
Periodic Field ◽  
First Order ◽  
Specific Heats ◽  
Second Order Effects

The electron theory of metals, established in its present form mainly by Pauli, Sommerfeld and Bloch, makes it possible to classify the phenomena connected with metals into two main divisions, which may be called first order effects and second order effects, according to whether the effect depends on the first or second approximation to the energy of a degenerate electron gas at a given temperature. Examples of the first group are the constant paramagnetism of the alkalis and Volta contact potentials. Examples of the second group are the specific heat of the electrons and all thermoelectric effects. The temperature dependence of the electrical conductivity should be included in the group of first order effects, since here the temperature is introduced through the lattice wave motion. The limits of the existing theory are now easily described. First order effects are accounted for with success, second order effects are in the main far from being adequately covered by the theory. To see clearly the reason for this, one must examine briefly the basis of the existing theory. In the first approximation the metal is regarded as composed of two independent systems; a system of lattice vibrations, and a system of electrons free to move in a given space periodic field of potential. In this way by dealing with the two systems quite independently one can reproduce many properties of metals, for example, Debye's theory of specific heats. The theory of pure lattice heat conductivity is concerned only with the former system, while the constant paramagnetism of the alkalis, and the fact that the electrons contribute only a very small amount to the total specific heat of the metal can be accounted for by considering the latter system only.

Thermodynamic Aspects of the Glass-Rubber Transition

1968 ◽  
Vol 41 (3) ◽  
pp. 544-554 ◽  
Author(s):  
A. J. Staverman
Keyword(s):  
Specific Heat ◽  
Excess Entropy ◽  
Second Order ◽  
Order Transition ◽  
Transition Curve ◽  
Specific Heats ◽  
Glass Transformation ◽  
Internal Parameters ◽  
Second Order Transition ◽  
The Difference

Abstract In 1933 Ehrenfest defined transitions in which not only the thermodynamic potential but also the specific volume and entropy of the two states are equal. For these transitions he derived three relations, between the differences of the coefficients of dilatation and of compressibility and the specific heat on one hand and the slope of the transition curve in p-T-space on the other hand. Although it is beyond any doubt that the glass-rubber transition in polymers is not a second order transition as defined by Ehrenfest, yet the term “second order transition” is often applied to it. The confusion arising from this abuse of a physically well defined concept is enhanced by the fact that some of Ehrenfest's relations are under certain circumstances valid for the glass-rubber transition, although in those cases the physical background of these relations is quite different from that of a second order transition in Ehrenfest's sense. In fact, the essence of the glass transition was formulated clearly and correctly by Simon in 1931 and consists in the assumption that in a glass one or more internal parameters are not in equilibrium but are frozen in. Conditions required for the validity of each of Ehrenfest's relations are inspected. The equality of two functions of the dilatation and the compressibility coefficients and the specific heats of the two states depends on the condition that there is only one frozen parameter in the glass state. If there is more than one frozen parmeter, then the equality turns into an inequality and the physical meaning of the difference between the two sides is derived. Similar relations as those derived between the quantities mentioned, can be derived between specific heat, modulus of elasticity and temperature coefficient of that modulus. These new relations are more interesting for practical purposes and less subject to experimental errors than the older ones. Finally expressions for the slope of the transition curve are investigated. Validity of any one of the expressions depends on the physical condition required for a material to become a glass. Inversely from the validity of any of the possible expressions insight in the glass transformation can be derived. The scarce available data give the impression that a material turns into a glass whenever its excess entropy decreases below a critical value.

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