Surface specific heats of metal nanocrystals at low temperatures

Nanoscale ◽  
2015 ◽  
Vol 7 (15) ◽  
pp. 6762-6766 ◽  
Author(s):  
Haile Lei ◽  
Jun Li ◽  
Jiangshan Luo
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Spatial Dimension ◽  
Analytical Expression ◽  
Metal Nanocrystals ◽  
Specific Heats ◽  
The Core ◽  
2D And 3D

In order to quantitatively explain the enhanced specific heat of metal nanocrystals measured from 4.2 K to 80 K, an analytical expression has been deduced to determine the surface specific heat in nanocrystals, which is proportional to T2.5 at low temperatures. The effectively spatial dimension of surfaces should be neither pure 2D nor 3D, but between 2D and 3D, due to the effect of atoms in the core of nanocrystals.

The Specific Heat of Carbon Dioxide—Correction

1928 ◽  
Vol 24 (2) ◽  
pp. 290-290
Author(s):  
W. H. McCrea
Keyword(s):  
Carbon Dioxide ◽  
Specific Heat ◽  
Low Temperatures ◽  
Molecular Form ◽  
Specific Heats ◽  
Heat Curve

In a recent paper in these Proceedings the writer suggested the possibility of a transition from one molecular form to another in CO2. The suggestion is embodied in the equation (10) and the resulting specific heats for low temperatures given. He greatly regrets that it was not till after those results were published that he found they gave a high and altogether impossible maximum in the specific heat curve for higher temperatures before it returns to the neighbourhood of the unmodified curve Cv′.

scholarly journals Atomic specific heats between the boiling points of liquid nitrogen and hydrogen. I.—The mean atomic specific heats at 50° absolute of the elements a periodic function of the atomic weights

1913 ◽  
Vol 89 (609) ◽  
pp. 158-169 ◽  
Keyword(s):  
Periodic Function ◽  
Specific Heat ◽  
Liquid Nitrogen ◽  
Low Temperatures ◽  
Liquid Hydrogen ◽  
Specific Heats ◽  
Boiling Points ◽  
Royal Institution ◽  
Series Of Experiments ◽  
The Mean

A method of determining the specific heat of substances at low temperatures was described in a paper on “Studies with the Liquid Hydrogen and Air Calorimeter,” also in the abstract of a lecture delivered at the Royal Institution entitled“ Liquid Hydrogen Calorimetry,” where the apparatus then used is illustrated. Continuing the use of the same method, but with some modification of the apparatus, the investigation has been extended to a large number of inorganic and organic bodies. In this later series of experiments, the measurements of the specific heats of materials by the liquid hydrogen calorimeter were made over a range of temperature from boiling nitrogen to boiling hydrogen, a fall of temperature of some 57° Abs.

ON THE SPECIFIC HEAT OF SOLIDS AT LOW TEMPERATURES

1957 ◽  
Vol 35 (7) ◽  
pp. 799-810 ◽  
Author(s):  
T. H. K. Barron ◽  
J. A. Morrison
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Noble Metals ◽  
Theoretical Models ◽  
Experimental Results ◽  
Continuum Approximation ◽  
Low Frequencies ◽  
Specific Heats ◽  
Additional Information ◽  
The Continuum

The temperature dependence of the specific heat of solids at very low temperatures is examined, using theoretical models and certain recent experimental results. The temperature region over which the continuum approximation (Cν = aT3) is strictly reliable is shorter than has often been supposed, and the series expansion Cν = aT3 + bT5 + cT7 + … is needed for the analysis of accurate experimental results. For insulators θ0 can best be estimated from measured specific heats by plotting Cν/T3 versus T2; the result is a curve whose intercept at T2 = 0 gives the coefficient of T3 (and hence θ0), and whose slopeand curvature give additional information about the vibrational spectrum at low frequencies. For metals the usual plot of Cν/T versus T2 can be used, but here again neglect of curvature may lead to errors in the estimates of γ and θ0. A brief discussion is given of the low temperature specific heats of a number of solids for which suitable data are available: potassium chloride, lithium fluoride, white tin, tungsten, the noble metals, and elements of diamond structure.

The measurement of lattice specific heats at low temperatures using a heat switch

1955 ◽  
Vol 230 (1183) ◽  
pp. 549-559 ◽  
Keyword(s):  
Specific Heat ◽  
Potassium Chloride ◽  
Thermal Insulation ◽  
Low Temperatures ◽  
Lattice Structure ◽  
Specific Heats ◽  
Simple Lattice ◽  
Order Of Magnitude

The accuracy of the measurement of small specific heats at low temperatures is often limited by the difficulty of achieving adequate thermal insulation of the specimen, especially when exchange gas has been used to cool it down. The paper describes a make-and-break contact which makes possible a degree of thermal insulation an order of magnitude higher than is usually obtained. This ‘heat switch’ has been used to measure the specific heats of three substances with a simple lattice structure. It has been verified that the temperature varia­tion of the specific heats of potassium chloride and grey tin is very close to a T 3 relation at temperatures below about θ D /60. The specific heat of graphite is more complex because of the anisotrophy of the lattice.

scholarly journals On the measurement of the ratio of the specific heats using small volumes of gas.—The ratios of the specific heat of air and of hydrogen at atmospheric pressure and a temperatures between 20°C. and —183°C

1925 ◽  
Vol 107 (743) ◽  
pp. 510-543 ◽  
Keyword(s):  
Systematic Error ◽  
Low Temperatures ◽  
Room Temperature ◽  
Expansion Chamber ◽  
Small Vessels ◽  
Specific Heats ◽  
Large Expansion ◽  
Before And After ◽  
The One ◽  
Chamber Capacity

Introduction .—In nearly all the previous determinations of the ratio of the specific heats of gases, from measurements of the pressures and temperature before and after an adiabatic expansion, large expansion chambers of fror 50 to 130 litres capacity have been used. Professor Callendar first suggests the use of smaller vessels, and in 1914, Mercer (‘Proc. Phys. Soc.,’ vol. 26 p. 155) made some measurements with several gases, but at room temperature only, using volumes of about 300 and 2000 c. c. respectively. He obtained values which indicated that small vessels could be used, and that, with proper corrections, a considerable degree of accuracy might be obtained. The one other experimenter who has used a small expansion chamber, capacity about 1 litre, is M. C. Shields (‘Phys. Rev.,’ 1917), who measured this ratio for air and for hydrogen at room temperature, about 18° C., and its value for hydroger at — 190° C. The chief advantage gained by the use of large expansion chambers is that no correction, or at the most, a very small one, has to be made for any systematic error due to the size of the containing vessels, but it is clear that, in the determinations of the ratio of the specific heats of gases at low temperatures, the use of small vessels becomes a practical necessity in order that uniform and steady temperature conditions may be obtained. Owing, however, to the presence of a systematic error depending upon the dimensions of the expansion chamber, the magnitude of which had not been definitely settled by experiment, the following work was undertaken with the object of investigating the method more fully, especially with regard to it? applicability to the determination of this ratio at low temperatures.

Specific heat of ordered and isotopically disordered lattices

1978 ◽  
Vol 56 (10) ◽  
pp. 1390-1394
Author(s):  
K. P. Srivastava
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Numerical Study ◽  
Three Dimensional ◽  
Constant Volume ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Appreciable Difference ◽  
Substantial Change ◽  
Neighbour Interaction

An extensive numerical study on specific heat at constant volume (Cv) for ordered and isotopically disordered lattices has been made. Cv at various temperatures for ordered and disordered linear and two-dimensional lattices have been compared and no appreciable difference in Cv between these two structures has been observed. Effect of concentration of light atoms on Cv for three-dimensional isotopically disordered lattices has also been shown.In spite of taking next-nearest-neighbour interaction into account, no substantial change in Cv between the ordered and isotopically disordered linear lattices has been found. It is shown that the low lying modes contribute substantially at low temperatures.

The specific heats of three paramagnetic salts at very low temperatures

1956 ◽  
Vol 237 (1210) ◽  
pp. 395-403 ◽  
Keyword(s):  
Specific Heat ◽  
Absolute Temperature ◽  
Magnesium Nitrate ◽  
Paramagnetic Resonance ◽  
Specific Heats ◽  
Ammonium Alum ◽  
Relaxation Measurements ◽  
Ferric Ammonium ◽  
The Absolute ◽  
Measured Specific Heat

The specific heats of three paramagnetic salts, neodymium magnesium nitrate, manganous ammonium sulphate and ferric ammonium alum, have been measured at temperatures below 1°K using the method of γ -ray heating. The temperature measurements were made in the first instance in terms of the magnetic susceptibilities of the salts, the relation of the susceptibility to the absolute temperature having been determined for each salt in earlier experiments. The γ -ray heatings gave the specific heat in arbitrary units. The absolute values of the specific heats were found by extrapolating the results of paramagnetic relaxation measurements at higher temperatures. The measured specific heat of neodymium magnesium nitrate is compared with the value calculated from paramagnetic resonance data, and good agreement is found.

scholarly journals III. Investigations of the specific heat of solid bodies

1865 ◽  
Vol 155 ◽  
pp. 71-202 ◽  
Keyword(s):  
Specific Heat ◽  
Thermal Action ◽  
General View ◽  
Specific Heats ◽  
General Law ◽  
Different Temperatures ◽  
The Times ◽  
The Individual ◽  
Solid Bodies

I. About the year 1780 it was distinctly proved that the same weights of different bodies require unequal quantities of heat to raise them through the same temperature, or on cooling through the same number of thermometric degrees, give out unequal quantities of heat. It was recognized that for different bodies the unequal quantities of heat, by which the same weights of different bodies are heated through the same range, must be determined as special constants, and considered as characteristic of the individual bodies. This newly discovered property of bodies Wilke designated as their specific heat , while Crawford described it as the comparative heat, or as the capacity of bodies for heat . I will not enter upon the earliest investigations of Black, Irvine, Crawford, and Wilke, with reference to which it may merely be mentioned that they depend essentially on the thermal action produced when bodies of different temperatures are mixed, and that Irvine appears to have been the first to state definitely and correctly in what manner this thermal action (that is, the temperature resulting from the mixture) depends on the original temperature, the weights, and the specific heats of the bodies used for the mixture. Lavoisier and Laplace soon introduced the use of the ice-calorimeter as a method for determining the specific heat of bodies; and J. T. Mayer showed subsequently that this determination can be based on the observation of the times in which different bodies placed under comparable conditions cool to the same extent by radiation. The knowledge of the specific heats of solid and liquid bodies gained during the last century, and in the first sixteen years of the present one, by these various methods, may be left unmentioned. The individual determinations then made were not so accurate that they could be compared with the present ones, nor was any general conclusion drawn in reference to the specific heats of the various bodies. 2. Dulong and Petit’s investigations, the publication of which commenced in 1818, brought into the field more accurate determinations, and a general law. The investigations of the relations between the specific heats of the elements and their atomic weights date from this time, and were afterwards followed by similar investigations into the relations of the specific heats of compound bodies to their composition. In order to give a general view of the results of these investigations, it is desirable to present, for the elements mentioned in the sequel, a synopsis of the atomic weights assumed at different times, and of certain numbers which stand in the closest connexion with these atomic weights.

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