Specific Heat Of Graphite Research Articles

Evidence of power law decay of superexchange coupling in a disordered two-dimensionalπ-electron system

We report the specific heat of graphite, highly oriented pyrolytic graphite (HOPG), graphene oxide (GO), and reduced graphene oxide (RGO) from 300 K to 50 mK. Graphite and HOPG exhibits transition from three dimensions $({C}_{v}\ensuremath{\propto}{T}^{3})$ to two dimensions $({C}_{v}\ensuremath{\propto}{T}^{2})$ as the temperature increases above 4 K and approaching linearity in temperature for both around room temperature is observed. We observe a Schottky-like peak in specific heat of graphene oxide and reduced graphene oxide near 0.1 K, whose intensity and peak position varies with external magnetic field. We find that the random Heisenberg superexchange interaction between the Anderson (disorder) localized $\ensuremath{\pi}$ electrons of GO/RGO is responsible for the specific-heat peak. The exchange interaction strength between the localized spins falls off with distance as a weak power law $(\ensuremath{\propto}\frac{1}{{r}^{2.5}})$, rather than the usual exponential fall in insulating magnets.

Research on temperature measurement technology for graphite-cone-absorption-cavity absolute calorimeter.

The nonlinear effect of materials and sensors in high-energy laser calorimeters is especially obvious-due to the steep temperature gradients of their absorbers. Significant measurement errors occur when traditional integral temperature sensors and methods are utilized. In an effort to remedy this, a method is proposed in this paper in which an absorption cavity is divided into many parts and multiple discrete thermocouple sensors are used to measure the temperature rise of the absorbers. The temperature distribution in the absorbers is theoretically analyzed, numerically simulated, and verified through experimentation. Energy measurement results are compared according to the temperature distribution for different layouts of thermocouples. A high-accuracy calorimeter is developed by setting and optimizing thermocouple layout, as well as correcting various elements such as the specific heat of graphite and responsivity of thermocouples. The calorimeter employing this measurement method is calibrated against a standard energy meter, resulting in correction coefficient of 1.027 and relative standard deviation of the correction coefficient of only 0.8%. Theoretical analysis, numerical simulation, and experimental verification all prove that the proposed method successfully improves measurement accuracy.

The specific heat of graphite: An evaluation of measurements

This paper reviews the measurements and evaluations of the specific heat at constant pressure for graphites in the temperature range 200 K to 3500 K. A polynomial fit to the data is made for use with nuclear graphite, valid over the range 250 K–3000 K. Some consideration is given to the difference between the specific heat at constant volume and at constant pressure. A measurement of the graphite phonon frequency spectrum at 1800 K is used to calculate the specific heat at constant volume, and then to modify slightly the polynomial fit to the constant pressure data.

Specific Heat of Mercury and Thallium between 0.35 and 4.2°K

The specific heat of mercury and thallium were measured between 0.35 and 4.2\ifmmode^\circ\else\textdegree\fi{}K. In the normal state below 0.7\ifmmode^\circ\else\textdegree\fi{}K the mercury results are given by: ${C}_{n}=1.79T+5.23{T}^{3}$ mJ/mole deg. The coefficient $\ensuremath{\alpha}$ of the ${T}^{3}$ term corresponds to a value of the Debye parameter ${\ensuremath{\Theta}}_{0}$ of 71.9\ifmmode^\circ\else\textdegree\fi{}K. For temperatures higher than 0.7\ifmmode^\circ\else\textdegree\fi{}K, the lattice specific heat deviates above the ${T}^{3}$ law. A plot of $\ensuremath{\Theta}(T)$ is given. Below 0.6\ifmmode^\circ\else\textdegree\fi{}K, the specific heat of thallium in the normal state is given by: ${C}_{n}=1.47T+4.03{T}^{3}$ mJ/mole deg. The corresponding value of ${\ensuremath{\Theta}}_{0}$ is 78.5\ifmmode^\circ\else\textdegree\fi{}K. Above 0.6\ifmmode^\circ\else\textdegree\fi{}K, the lattice specific heat of thallium shows a deviation below the pure ${T}^{3}$ law, a result contrary to that found for most solids. This would imply a deviation in the dispersion curve above the linear portion. A similar effect was observed in the specific heat of graphite which was explained on the basis of bond-bending modes of vibration. It is suggested that similar modes may explain this behavior for thallium. In the superconducting state the specific heat of both materials can be represented by a sum of the normal lattice term and a superconducting electronic term ${C}_{\mathrm{es}}$ of the form a$\ensuremath{\gamma}{T}_{c}\mathrm{exp}(\ensuremath{-}\frac{b{T}_{c}}{T})$. For mercury, values are obtained for a=15 and $b=1.64$ with ${T}_{c}=4.16\ifmmode^\circ\else\textdegree\fi{}$K; for thallium a=9 and $b=1.52$ with ${T}_{c}=2.38\ifmmode^\circ\else\textdegree\fi{}$K. In the case of thallium the critical field as a function of temperature ${H}_{c}(T)$ is determined, with ${H}_{c}(0)=176.5$ G.

LXXXI. Lattice vibrations and specific heat of graphite

Abstract The vibrations of the graphite lattice can be treated approximately by ignoring the interaction between displacements parallel and perpendicular to the layer planes. The normal modes then separate into two types, which may be called planar and transverse. The complete frequency distribution of the transverse modes is calculated, and, with the aid of an approximate calculation of the distribution of the planar modes, the specific heat is deduced and compared with experimental results from 1·5° to 1000°K. Above 200° the atomic model gives results close to those obtained by superimposing two Debye two-dimensional continuum models, but below 100° the interaction between layers becomes important. Below 20°, the transverse modes are dominant, and the result is very sensitive to the coefficient of interaction between second neighbours in the layer This coefficient is close to a critical value which it would attain if the transverse restoring forces on the atoms of a single layer could be considered as acting only against out-of-plane bending of the bonds. It is shown that for any two-dimensional crystal the spectrum of the transverse vibrations is anomalous at low frequencies whenever the potential energy function satisfies certain conditions, and that these conditions are satisfied if the function is independent of any uniform small rotation of the crystal.

Theory of the Lattice Vibration of Graphite

A theory of the lattice vibration and specific heat of graphite, which has a typical lamellar structure, is worked out using the Born-von Karman method. Four types of restoring forces are assumed; the first and second ones are associated with changes in the bond lengths and bond angles of the honey-comb net planes, respectively, the third with change in distance between neighoring atoms on adjacent net planes, and the fourth with the bending of the net planes. We have obtained modes whose polarizations are parallel and perpendicular to the planes. The former are essentially two-dimensional, but the latter are of more complex characters and play a particular role in the temperature range 45° to 100°K. As our main interest is in this and higher temperature ranges, we neglect the shearing forces between neighboring net planes which are effective at much lower temperatures. For small wave numbers, our theory naturally reduces to the semi-continuum theory developed by Komatsu and Nagamiya (1951) and Komatsu (1...

Specific Heat of Graphite at Very Low Temperatures

Specific Heat of Graphite at Very Low Temperatures

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

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.

XCIV. The specific heat of graphite below90°k

Abstract Values are given of the specific heat of graphite between 1·5°k and 90°k. Below about 12° the specific heat varies with temperature as T 2·4; this is inconsistent with the work of several authors who, on theoretical grounds, have predicted a T 2 temperature dependence.

The Specific Heat of Graphite from 13° to 300°K

The specific heat of high-purity Acheson graphite prepared by the National Carbon Company has been measured from 13° to 300°K. In the region 13° to 54°K the Cp data follows a T2 dependence quite accurately in agreement with previous experimental work and recent theoretical investigations of specific heat in strongly anisotropic solids. On the basis of some recent studies for other highly anisotropic solids, it is suggested that the specific heat of graphite will eventually follow a T3 dependence at still lower temperatures. The derived thermodynamic functions, entropy, enthalpy, and free energy, have been determined by graphical integration and tabulated at integral values of temperature up to 300°K. The entropy of graphite at 298.16°K is 1.372±0.005 cal/g-atom deg, of which 0.004 is extrapolated from 13° to 0°K assuming the third law and the T2 dependence.

The Specific Heat and Thermal Conductivity of Graphite

The specific heat of graphite is discussed in terms of a modified Debye treatment. It is shown that the contribution from the longitudinal waves varies as T3 below 45 �K, and as T2 at higher temperatures, whereas the usual two-dimensional treatment leads to a T2 variation at all low temperatures. Similarly the transverse contribution varies as T3 at lowest temperatures, But above 10 �K it varies as T2.