Nuclear specific heat

Lounasmaa, O.V., 1967, Nuclear specific heats in metals and alloys, in Freeman, A.J. and R.B. Frankel, eds., Hyperfine interactions (Academic Press, New York) pp. 467-496. 

Strong depression of C is found at lower temperatures, with a crossing-over towards higher T where C is increased in a magnetic field. The up-turn of C below 0.2 K towards low T is due to the nuclear specific heat contribution arising... 

Cl = lattice specific heat Cm = magnetic specific heat Cn = nuclear specific heat C, = specific heat in garnet D = crystal field tensor of the ion... 

In EuIG, the nuclear specific heat, Cn, must be included. The linear residual part had a temperature coefficient of (0.23 0.03) x 10" R, and it is 15% of Cy above 2K, but becomes negligible below 1.2 K (Henderson et al., 1969). The Cy data of TmlG behave approximately the same as for EuIG and YIG. Their analysis is hampered by the uncertainty on the value of D for TmIG. No evidence of a Tm optical level becoming populated at temperatures below 4.5 K was found in the Cy data. 

Nuclear magnetic resonance spectroscopy of the solutes in clathrates and low temperature specific heat measurements are thought to be particularly promising methods for providing more detailed information on the rotational freedom of the solute molecules and their interaction with the host lattice. The absence of electron paramagnetic resonance of the oxygen molecule in a hydroquinone clathrate has already been explained on the basis of weak orientational effects by Meyer, O Brien, and van Vleck.18... 

The properties of the hydrogen molecule and molecule-ion which are the most accurately determined and which have also been the subject of theoretical investigation are ionization potentials, heats of dissociation, frequencies of nuclear oscillation, and moments of inertia. The experimental values of all of these quantities are usually obtained from spectroscopic data substantiation is in some cases provided by other experiments, such as thermochemical measurements, specific heats, etc. A review of the experimental values and comparison with some theoretical... 

A special attention is to be devoted to copper, which is very often used in a cryogenic apparatus. The low-temperature specific heat of copper is usually considered as given by c = 10-5 T [J/g K], However, an excess of specific heat has been measured, as reported in the literature [59-69], For 0.03 K < T< 2K, this increase is due to hydrogen or oxygen impurities, magnetic impurities (usually Fe and Mn) and lattice defects [59-66], The increase of copper specific heat observed in the millikelvin temperature range is usually attributed to a Schottky contribution due to the nuclear quadrupole moment of copper [67,68],... 

In the literature [55], typical energies involved in the nuclear quadrupole moments -crystalline electric field gradient interactions range up to A E 2x 10-25 J. The measured AE seems to confirm the hypothesis that the excess specific heat of the metallized wafer is due to boron doping of the Ge lattice. 

Because the melting point of sodium metal is about 98° C (a bit lower than the boihng point of water), it is heated into a liquid phase and then transported in rail tank cars, where it cools and solidifies. When it arrives at its destination, heating coils in the tanks warm it back to the liquid stage, and it is then stored for use. Because sodium has a high specific heat rating, a major use is as a liquid coolant for nuclear reactors. Even though sodium (both solid and liquid) is extremely reactive with water, it has proven safe as a coolant for nuclear reactors in submarines. 

Thanks to the extensive literature on Aujj and the related smaller gold cluster compounds, plus some new results and reanalysis of older results to be presented here, it is now possible to paint a fairly consistent physical picture of the AU55 cluster system. To this end, the results of several microscopic techniques, such as Extended X-ray Absorption Fine Structure (EXAFS) [39,40,41], Mossbauer Effect Spectroscopy (MES) [24, 25, 42,43,44,45,46], Secondary Ion Mass Spectrometry (SIMS) [35, 36], Photoemission Spectroscopy (XPS and UPS) [47,48,49], nuclear magnetic resonance (NMR) [29, 50, 51], and electron spin resonance (ESR) [17, 52, 53, 54] will be combined with the results of several macroscopic techniques, such as Specific Heat (Cv) [25, 54, 55, 56,49], Differential Scanning Calorimetry (DSC) [57], Thermo-gravimetric Analysis (TGA) [58], UV-visible absorption spectroscopy [40, 57,17, 59, 60], AC and DC Electrical Conductivity [29,61,62, 63,30] and Magnetic Susceptibility [64, 53]. This is the first metal cluster system that has been subjected to such a comprehensive examination. 

The speeific heat of AU55 has been recently measured between 60 mK and 3 K, as a funetion of external magnetic field [54]. The increase in the specific heat at the lowest temperatures was attributed to a possible Schottky tail from Au nuclear quadrupole splitting. 

The measured Q.S. values for the surface sites of AU55 give nuclear splittings of 21 mK, 13 mK, and 4 mK for the PPhj coordinated sites, the Cl coordinated sites, arid the bare surface sites respectively. From these values, and the known site occupations, the nuclear quadrupole contribution to the zero field specific heat by these three two-level systems [143] has been calculated directly [144], This value is 5 times as large as that experimentally observed [54]. The maximum value of a linear term in the specific heat of AU55 has been estimate to be no more than one fifth of the bulk value [144]. 

The coordination numbers based on this structure work extremely well for describing the microscopic physical properties of this material, including the Mossbauer I.S.s of the surface sites and of the specific heat of the clusters below about 65 K. No linear electronic term in the specific heat is seen down to 60 mK, due to the still significant T contribution from the center-of-mass motion still present at this temperature. The Schottky tail which develops below 300 mK in magnetic fields above 0.4 T has been quantitatively explained by nuclear quadrupole contributions. 

Evidence of molecular rotation may be given by non-crystallographic evidence the transition from a rotating to a non-rotating state is accompanied by sudden changes in specific heat, in dielectric constant, and in width of nuclear magnetic resonance bands (see Chapter VIII). 

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