Maximum In Specific Heat Research Articles

The Magnetic Susceptibility and Specific Heat of Constantan at Low Temperatures

The magnetic susceptibility of constantan has been measured in the temperature region between 1 and 0.033 K, and its specific heat between 1 and 0.76 K. Both measurements give evidence of a phase transition near 0.76 K. In addition we find a susceptibility anomaly near 0.08 K which is associated with a previously reported specific heat maximum.

Electrocaloric properties of OH- molecules in KCl

The electrocaloric effect in the KCl: OH − system is used to cool the system down to 0·36°K starting from 1·3°K by a method of adiabatic depolarization. The limit to the temperature attainable by this means is set by the zero field splitting of the OH − energy levels in the lattice which is 0·3°K. The specific heat of KCl: OH −, measured as a function of applied E field at constant temperature, has a maximum at a value of E which depends on the direction of the applied field with respect to the crystal axes. The data is fitted by a non-interacting dipole theory that assumes the dipoles are oriented along [100] directions in the lattice. The position of the maximum gives a value of the uncorrected dipole moment of the OH −, p u , and the value of the maximum gives a measure of the concentration of OH −, N. The value of the dipole moment varies with concentration and for the low concentration of 10 17/cm 3 is 4·4 ± 0·l deb. The reorientation time of the dipoles between [100] directions, t 1, is estimated to be less than 5·10 −8 sec. The specific heat of KCl: OH −, measured as a function of temperature, shows a deviation from the Debye theory at low temperature. Below 1°K this is consistent with a contribution from the zero field splitting. In the region 1°K < T < 4°K the increased specific heat may be due to interactions between the dipoles or to a modification of the phonon spectrum of the lattice. The concentration of OH − measured optically yields a higher value than the concentration measured from the specific heat maximum except at the lowest concentration where the two are equal. A qualitative explanation assumes regions of local order where the dipoles are frozen in and do not contribute to the caloric properties.

Interfacial, Boundary, and Size Effects at Critical Points

Exact results for the interfacial and boundary free energies (for free and for ferromagnetic boundaries) are presented for the square, triangular, and honeycomb Ising lattices. The boundary energies and specific heats diverge as $\mathrm{ln}|T\ensuremath{-}{T}_{c}|$ and ${({T}_{c}\ensuremath{-}T)}^{\ensuremath{-}1}$, respectively. This behavior is interpreted generally in terms of the rounding and displacement of the specific-heat maximum in a finite system.

Calorimetric Study of Several Rare-Earth Gallium Garnets

Specific-heat measurements on the gallium garnets (GaG) of Nd, Sm, Gd, Er, Dy, Ho, and Yb between 0.35 and 4.2\ifmmode^\circ\else\textdegree\fi{}K are presented. The transition to the ordered state for the garnets of Nd, Sm, and Er is studied in detail, the transition temperature ${T}_{N}$ being, respectively, 0.516, 0.967, and 0.789\ifmmode^\circ\else\textdegree\fi{}K. Another Sm sample had a transition at ${T}_{N}=0.921$\ifmmode^\circ\else\textdegree\fi{}K. From this study, the exchange coupling parameter ${J}_{\mathrm{cc}}$ between the rare-earth ions situated on the $c$ sites is derived in different ways, namely, from ${T}_{N}$, the magnetic energy, and the high-temperature specific-heat "tail." These determinations are found to be reasonably consistent. The entropy and magnetic energy are found to be approximately those of a Heisenberg system with spin \textonehalf{}. For GdGaG, the rounded specific-heat maximum is interpreted in terms of a Schottky anomaly. The specific-heat anomaly can be well fitted by a calculated curve assuming a cubic crystalline field. Unexpectedly, the splitting is much larger than that obtained for the diluted garnet from ESR data. For HoGaG, the specific heat shows the population of the first excited singlet at $\frac{E}{k}=7.4$\ifmmode^\circ\else\textdegree\fi{}K and a second-order hyperfine splitting at temperatures below 1\ifmmode^\circ\else\textdegree\fi{}K. For YbGaG, the specific heat increases as the temperature decreases, and from the temperature region where the magnetic contribution is proportional to ${T}^{\ensuremath{-}2}$, the transition to an ordered state is expected at about 0.3\ifmmode^\circ\else\textdegree\fi{}K. The DyGaG shows a maximum specific heat at about 0.36\ifmmode^\circ\else\textdegree\fi{}K, but no satisfactory analysis could be carried out on this compound.

LIQUID HELIUM AND THE PROPERTIES OF FINITE BOSE–EINSTEIN ASSEMBLIES

In order to explain certain properties of thin helium films, Ziman has proposed an ideal gas model in which the bulk liquid is treated as a collection of independent, Bose–Einstein assemblies each a few hundred angstroms in extent. In this paper, an extensive numerical study is made of the thermodynamic properties of such finite assemblies. In particular, the specific heats of thin films have been calculated on the basis of the model and the results compared with the experimental data of Frederikse. It is found that the model predicts a shift of the specific-heat maxima to higher temperatures as the film thickness is decreased, rather than to lower temperatures as required by the observations on actual helium films. The nature of the Bose–Einstein condensation in finite assemblies is discussed in some detail and some general conclusions are drawn concerning Ziman's model.

Magnetic and Thermal Properties of Nickel-and Copper Fluosilicates below 1°K

The adiabatic magnetization curves have been measured on single crystals of NiSiF 6 ·6H 2 O and CuSiF 6 ·6H 2 O using a Cioffi-type recording flux-meter. The specific heats have also been determined. Nickel fluosilicate was found to be ferromagnetic with the easy axis parallel to the c -axis. The magnetic Curie temperature is about 0.15°K while the specific heat maximum is at 0.13 5 °K. The magnetic behaviour of copper fluosilicate is ferromagnetic and nearly isotropic. The magnetic Curie temperature is about 0.07°K. The entropy versus temperature curve has a kink at 0.10°K (at an entropy value of 0.46 R) showing the ordering in two steps. Weiss constants were determined at helium temperatures; θ // =+0.15°K, θ ⊥ =+0.08°K for nickel salt; and θ(powder)=+0.07°±0.02°K, θ // c =+0.08°±0.02°K, θ ⊥ c =0.05°±0.02°K, and g (powder)=2.2 5 , g // c =2.2 5 , g ⊥ c =2.2 6 (mean values) for copper salt.

Antiferromagnetic Structures of Manganese and Cobalt Fluosilicates below 1°K

Using a recording Flux-meter, adiabatic magnetization curves from initial fields of isothermal magnetization (maximum: 24K gauss) to zero have been measured on the hybrid column crystals of low temperature modification, parallel (//) and perpendicular (⊥) to the hexagonal axis of the room temperature form. Both salts have been found to be antiferromagnetic with the preferred axis nearly along the (//)-direction accompanying weak ferromagnetism with the tilt angle of about 1°. T N is 0.17°K for MnSiF 6 6H 2 O, and 0.20°K for CoSiF 6 6H 2 O, and the corresponding temperature of the specific heat maximum is 0.15°K for (Mn–) and 0.19°K for (Co–). The antiferromagnetic molecular field ( H E ) was observed to be 400 gauss for (Mn–), and 700 gauss for (Co–). From susceptibility measurements above 1°K, θ // =+0.11°K, θ ⊥ =-0.12°K (Mn–); θ // =-0.19°K, θ ⊥ =-0.15°K; g // c =6.8, g ⊥ c =2.5 5 (mean values, not refered to the trigonal crystalline field) (Co–). The specific heat tail can be expressed as C M T 2 / R =...

The Thermodynamics of Spins Coupled to Lattices

The usual assumption that the specific heat of a paramagnetic crystal can be written as the sum of a lattice specific heat and a spin specific heat needs modification when there is strong spin-lattice coupling. The necessary theory is developed for two simple examples, and it is shown to lead to an increase in the maximum of the Schottky specific heat. It is suggested that the previously unexplained magnitudes of the specific heat maxima in cerium and praseodymium ethyl sulphates arise from strong spin-lattice couplings.

Giant Thermal Expansion Coefficients in Rare Earth Metals at Low Temperatures

The thermal expansion of lanthanum, cerium, neodymium, gadolinium, and ytterbium from 1.5 to 14 nif- K were measured. Large negative values of the linear thermal expansion coefficient, alpha , were observed for polycrystalline samples of Ce and Nd below the temperatures of their first specific-heat maxima at 12.5 and 7 nif- K, respectively. For La alpha shows a normal temperature dependence above its critical temperature of 5.9 nif- K. Yb has a normal behavior apart from a small anomaly around 2.3 nif- K. Gd shows an anomalous behavior in its polycrystalline form, in that alpha changes sign twice below 12 nif- K. The particular anomalies are discussed. (C.E.S.)

Specific Heat of Single-Crystal MnCl2in Applied Magnetic Fields

The specific heat of a single-crystal sample of Mn${\mathrm{Cl}}_{2}$ has been measured, in the liquid-helium temperature region, in applied magnetic fields extending up to 7.26 kOe. In all cases the magnetic field was applied parallel to an $a$ axis of the hexagonal cell. The two specific heat maxima, which have been previously reported at 1.81 and 1.96\ifmmode^\circ\else\textdegree\fi{}K in zero field, are associated with antiferromagnetic transitions. Both transition temperatures are found to be field dependent. The upper transition temperature increases with applied field while the lower transition temperature decreases. These results are correlated with neutron diffraction studies of the magnetic structure transitions.