Specific heat of diamond

The specific heats of diamond and graphite are reduced to 19 and Tx() respectively between the ordinary temperature and the boiling-point of liquid hydrogen the specific heats of the substances between the temperatures of liquid air and liquid hydrogen are in fact less than those of any other substances, even less than that of a gas at constant volume. 

A much greater heat quantity is involved in cooling the diamond from 550° C. to 90° K. The specific heat of diamond at 500° is about 0.4 cal./g. °C. and this decreases to only 0.0025 cal./g. °C. at 90° K. The average specific heat over this temperature range is about 0.23 cal./g. °C. and the sensible heat is, therefore, 160 cal. per gram. This is about 105 times greater than the heat of adsorption. 

The specific heat varies most rapidly with the temperature in the case of non-metals of low atomic weight. Particularly is this true of carbon, above all in the non-conducting crystalline form of diamond. The specific heat of diamond increases from 01128 to 046, that is to say, about four-fold in the interval between 0° and 1000°. 

The specific heat of diamond is generally comparable to that of graphite and is higherthan most metals (see Ch. 3, Sec. 4.3 and Table 3.5). The specific heat of diamond, like that of all elements, increases with temperature (see Table 11.3). 

Houston, W. V. Lattice vibrations and specific heat of diamond. Z. Natur-forsch. 3a, 607 (1948). 

The specific heat of both diamond and graphite decreases sharply on cooling to 90° K. Using diamond as an example, values are listed in Table II at several... 

It was naturally of extreme interest to test the above result experimentally on suitable examples, for according to it the specific heats of all solids, whether amorphous or crystalline, elementary or compound, become small to the third degree of infinity at very low temperatures. My measurements on diamond gave some indication, but a more detailed test was made on a series of substances by Eucken and Schwers (84), and then a still more exhaustive one by Nemst and Schwers (95). Quite recently (cf. p. 52), Kamerlingh-Onnes and Keesom were able to verify the law accurately for copper. To-day the TMaw may be regarded as having been proved to be true as a limiting law valid for all solids. 

Fig. 13. Magnetic moments and specific heats of nickel clusters as a fimction of the temperature, (a) Magnetic moment per atom. Solid squares, n = 40-50 solid circles, n = 140-160 solid diamonds, n = 200-240 open circles, n = 550-600. (b) Sptecific heat obtmned by averaging over n = 200-240. Open circles, experimental data thick line, the mean field theory dashed line, the classicrd Dulong-Petit prediction. (Adapted from Ref. 25.)...

In 1819, DULONG and PETIT [1.1] published the results of their specific heat measurements of thirteen solid elements at room temperature. From these measurements, they deduced that the product of the specific heat and the atomic weight was approximately a constant C = 3R = 5.96 cal mole K . BOLTZMANN in 1871 demonstrated that the law of Dulong and Petit follows from his equi-partition principle. However, in 1875, WEBER [1.2] found that the atomic specific heat of silicon, boron and carbon are considerably lower than the Dulong-Petit value. For example, the atomic specific heat of silicon, boron and diamond were found to be 4.8, 2.7, and 1.8 cal mole K", respectively, at room temperature. Subsequent specific heat measurements at T < 300 K revealed that the specific heat of solids decreased rapidly with decreasing temperature. Classical theory does not explain this behaviour. 

Fig.3.10. Einstein and Debye specific heat as a function of reduced temperature. 0 is either the Einstein or the Debye temperature, depending on which curve is being examined. The Debye specific heat is compared with the observed specific heats of Ag( ), 0n = 215 K A1(A), 0p = 394 K C(diamond)( ),...

There is, however, a fatal objection to the theory of Boltzmann. At very low temperatures the oscillations will be small, and should conform to the theory. But the atomic heats, instead of approaching the limit 5 955 at low temperatures, diminish very rapidly, and in the case of diamond the specific heat is already inappreciable at the temperature of liquid air. A new point of view is therefore called for, and it is a priori very probable that this will consist of a replacement of the hypothesis of Equipartition of Energy adopted by Boltzmann. This supposition has been verified, and the new law of partition of energy derived... 

By means of the experimental methods briefly referred to in 9 a large number of specific-heat measurements have been made at very low temperatures. In Fig. 91 we haye the atomic heats of some metals, and of the diamond, represented as functions of the temperature. The peculiar shape of the curves will. be at once apparent. At a more or less low temperature, the atomic heat decreases with extraordinary rapidity, then apparently approaches tangentially the value zero in the vicinity of T = 0. The thin curves represent the atomic heats calculated from the equation ... 

Evolution did not use this element, only in certain plants is it important as a trace element. The element became well-known because of heat-resistant borosilicate glasses. Boranes are chemically interesting as B-H bonds react very specifically. Perborates are used in laundry detergents (Persil). The hardness of cubic boron nitride approaches that of diamond. Amorphous (brown) boron burns very quickly and gives off much heat and is therefore used in solid-propellant rockets and in igniters in airbags. 

While we have not yet carried out detailed kinetic measurements on the rate of photocorrosion, our impression is that the process is relatively insensitive to the specific composition of the strontium titanate. Trace element compositions, obtained by spark-source mass spectrometry, are presented in Table I for the four boules of n-SrTi03 from which electrodes have been cut. Photocorrosion has been observed in samples from all four boules. In all cases, the electrodes were cut to a thickness of 1-2 mm using a diamond saw, reduced under H2 at 800-1000 C for up to 16 hours, polished with a diamond paste cloth, and etched with either hot concentrated nitric acid or hot aqua regia. Ohmic contacts were then made with gallium-indium eutectic alloy, and a wire was attached using electrically conductive silver epoxy prior to mounting the electrode on a Pyrex support tube with either epoxy cement or heat-shrinkable Teflon tubing. 

Figure 3 compares the exchange current densities on the initial nanodispersed diamond (4), modified nanodispersed diamond (after heat - treated treatment)(5), acetylene black AD-100 (1) and on the known catalysts tungsten (2) and vanadium (3) carbides. The specific surfaces of all samples of the powders were about 140 rrr/g. The exchange current density on modified diamond nanopowders is higher than that on tungsten or vanadium carbides by a factor of 1.6. 

When determined from the physical constants, the values of the time constant are found to vary because of the appreciable change of the specific heat with temperature. The precision is limited by the uncertainties in the values of the thermal conductivity of powders. Large single diamond crystals have a high thermal conductivity (see Table I), being of the same order of magnitude as for silver... 

The opposite of adiabatic is either diabatic or diathermal. The best way to provide diathermal walls is connect the system (inner vessel) to the surroundings (outer vessel) with metal (an excellent heat conductor) or water (a good thermal conductor with very large specific heat capacity) or diamond (the best heat conductor and, simultaneously, the best electrical insulator). 

One of the major markets for wide band-gap materials is in electronics. Specifically, they are suitable for and have been used for heat sinks (diamond), short wavelength optoelectronic devices (GaP, GaN, SiC), high-temperature electronics (SiC, GaN), radiation resistant devices, and high-power/high-frequency electronic devices (diamond, GaN, SiC). " Recent research showed that Mn-doped GaN can be used for spintro-nic applications.f" Atomically flat technology developed by NASA for SiC and GaN WBG material can introduce a new dimension of application for WBG materials. 

Actually Ch. Lindemann (55) and (58), and Rdntgen have been able to prove that there is an approximate proportionality between specific heats and thermal expansion. Since in the former case the attainment of a zero value at low temperatures may be regarded as proved, we may assume the same for thermal expansion in any case, the papers cited, particularly Rdntgen s measurements on diamond, show directly that the coefficient of thermal expansion falls off very considerably at low temperatures, as it should on our Theorem. 

Furthermore, diamond exhibits the largest thermal conductivity among all naturally occurring materials. With 20 Wcm K , it is about five times higher than that of copper. At the same time it expands only to small extents, which reflects in a coefficient of thermal expansion of 1.06 x 10 K (mK ). The specific heat capacity at 25 °C is 6.12 J mol- K-. ... 

We may compare the three substances whose specific heats are represented in Fig. 13. Diamond is excessively hard, infusible, and involatile, lead soft and fusible, while aluminium is intermediate in character. Thus the frequencies, in so far as they depend upon the strength of the forces holding the atoms in the crystal, will tend to be in the order... 

Let us consider the effect of the degree of elastic anisotropy of the lattice of, for example, a diamond-t3 e crystal on the form of the frequency spectrum and on the temperature dependence of the specific heat and pther thermodynamic functions. In order to see the effect of such an anisotropy, we will vary the anisotropy coefficient A - 2c44/(cu - C42) 2y when the ratios of the bulk moduli to the shear moduli are constant ... 

Figure 11.15 Specific heat (heat capacity per gram) versus temperature T for solids diamond ( ), graphite (o), and fuiierenes ( ). This iog-iog plot emphasizes the behavior at iow temperatures. The Einstein modei of independent oscillators ( ) characterizes fuiierenes from about T = 5 K - 100 K, but the more...

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