Peak In Specific Heat Research Articles

A neutron scattering study of the structures and phase transitions of 36Ar submonolayers on grafoil

The phases of 36Ar submonolayers adsorbed on Grafoil were investigated by neutron diffraction. It was observed that the adsorbed film forms a triangular lattice, incommensurate with the graphite substrate. For coverages from x=0.25 to x=0.93 monolayers there is no evidence for a sharp melting transition (triple point). This is confirmed by inelastic neutron scattering and by a very broad specific heat peak. Thus the melting of 36Ar on Grafoil does not show a first order transition as expected for a 2D Van der Waals system.

Helicity modulus and specific heat of classicalXYmodel in two dimensions

A Monte Carlo simulation of the helicity modulus and the specific heat of the classical $\mathrm{XY}$ model in two dimensions is presented. In particular, we have investigated the dependence of these quantities with the size of the Monte Carlo sample. The height of the specific-heat peak is found to saturate as the infinite-volume limit is approached. The peak height of the derivative of the helicity modulus is found to grow rapidly with the increase in the size of the system and is located only 7% below the temperature at which the specific heat has the maximum.

Dynamical Plane Rotator Model. I. Derivation of Hamiltonian and Molecular Dynamics

It is shown that the motion of the plane rotator model should be described by a set of equations \(\ddot{\varphi}_{i}{=}I^{-1}\sum_{j}J_{ij}\sin(\varphi_{j}-\varphi_{i}),\quad i{=}1,2,\cdots,N\), and that the Hamiltonian should be H =∑ i p j 2 /2 I +∑ i < j J i j (1-cos (ϕ i -ϕ j )). To this Hamiltonian one can apply the method of molecular dynamics. For the case of the nearest neighbor interaction, energy-temperature curve is calculated for one, two and three dimensions. In one dimension our result agrees well with the exact solution. In two dimension a sharp peak of specific heat is found at T ∼1.1 J / k . In three dimension a singularity is observed at T ∼2.2 J / k .

Monte Carlo study of the planar spin model

We have simulated the two-dimensional classical planar spin model using the Metropolis Monte Carlo technique. The loss of long-range order as a function of the size of the lattice was confirmed. The energy and specific heat were calculated for a square lattice of 900, 3 600, and 10 000 spins. A sharp specific-heat peak was found at $\frac{{k}_{B}T}{J}=1.02$ $J$ is the nearest-neighbor coupling), 15% above the transition temperature $\frac{{k}_{B}{T}_{c}}{J}=0.89$. ${T}_{c}$ was determined by fitting the spin-spin correlation function and the susceptibility to the forms of the Kosterlitz-Thouless theory. The density of vortex pairs was computed and found to increase exponentially with inverse temperature. At ${T}_{c}$ vortex pairs begin to unbind and also larger clusters of vortices appear and unbind as the temperature is increased. These larger clusters may be responsible for the specific-heat peak being sharper and closer to ${T}_{c}$ than simple theories predict.

Kinetics of order–disorder transformations in alloys. III

Calculations of specific heat vs temperature curves corresponding to measurements with finite heating rates have been carried out for alloys under various initial conditions utilizing the pair approximation of the Path Probability method of time dependent cooperative phenomena and are compared with experiments on Mg3Cd, FeCo, and Cu3Au. New experiments on Mg3Cd suitable for comparison are also presented here. The main emphases of the comparisons are (1) the appearance of a specific heat subpeak below the main specific heat peak at Tc for well annealed alloys, (2) the shift of the subpeak by a change of the heating rate, (3) the appearance of a specific heat dip for alloys quenched from higher temperatures, and (4) the appearance of two specific heat dips for highly disordered alloys quenched from above the critical point of order–disorder. Good qualitative agreement of theory and experiment is obtained in each of these four categories.

Heat capacity of Ar monolayer adsorbed on basal plane graphite

The specific heat of Ar monolayer film adsorbed on basal planes of graphite has been measured for film coverage ranging from 0.31 to 0.97 monolayers for 4.2 < T < 68 K. It is found that a broad specific heat peak centered around 50 K exists over most of the submonolayer coverages until reaching monolayer completion. A comparison with recent neutron scattering and LEED studies relates the anomaly to a possible higher order phase transition between 2D solid and 2D fluid.

Specific heat anomalies and spin-spin interactions in carbons: A review

In the introductory part of the paper the classification of carbons according to mode of preparation and structure into soft and hard, carbon blacks, pyrocarbons, evaporated films, and whiskers, and their response to heat treatment, including the kinetics of carbonization and graphitization, are briefly described. The changes occurring in electronic properties as the hopping conductivity of raw carbons transforms into band conductivity upon departure of organics and the further evolution of bands toward graphitic structure, as well as various doping techniques, are then briefly discussed. In the second part, after a brief review of the early research on low-temperature specific heat of carbon materials heat treated to graphitizing temperatures and corresponding efforts at interpretation, information gathered through the last ten years on specific heat anomalies in variously heat-treated and neutron-irradiated soft and hard carbons is reviewed. In soft carbons two specific heat peaks at about 0.3 and 0.65 K, and a large, linear term of nonconduction origin, are observed at all stages of carbonization up to quite high degrees of graphitization or when disorder is introduced by neutron irradiation. In this latter case a spectacular disappearance of the anomalies by subsequent thermal anneal to 300°C has been observed. The peaks and the linear term are shown to have a magnetic origin, the specific heat varying greatly with applied magnetic field. In hard carbons no clear specific heat peaks were found—only a small, broad hump at around 0.3–0.7K and continuously increasing values of C/T down to lowest temperature (0.1 K), and again a large linear term. As in soft carbons the anomalies are greatly diminished by heat treatment to 2700°C or above, but are brought back by neutron irradiation. Since all the facts point toward a localized free electronic spin origin of the anomalies, in the third part a condensed discussion of the electron spin effects in carbons is presented. After a short description of the ESR of conduction carriers in well-graphitized materials, the technique of separation of the localized spin from conduction carrier contribution and the mixing of g- values and of the widths by exchange in carbons are discussed. Information on the heat treatment dependence, neutron irradiation, and thermal anneal and on doping effects for various types of carbons heat treated above 1500°C follows. Next, the formation of localized spins in carbonization and condensation processes of organic materials, and their subsequent gradual decay after appearance of conductivity, with an exchange narrowing of the ESR line somewhat after the concentration crosses its peak, as well as production of artificial spin centers by gas reactions, all in temperature range below 1000°C, are described. Finally the difficulties and uncertainties in obtaining data, caused by broadening effects in the heat treatment range 1000–1500°C, are pointed out. In the last part of this review the spin concentration data supplied by ESR studies are compared with specific heat data. It turns out that only about a quarter of all localized spins are condensing in the two peaks, the rest of them (or a part) being involved in the linear term anomaly. Whereas a general picture of the specific heat anomalies can be outlined, none of the known exchange interactions can explain the values at which the fractions condense into presumably an antiferromagnetic phase, nor the high values necessary for the conflict areas to be responsible for the linear term. Thus the most basic questions remain unanswered and further experimental studies, coupled with some theoretical attempts, are badly needed.

Nouvelles donnes experimentales sur les proprietes magnetiques de Cr3 Se4 et des solutions solides Cr3 Set S4−t

Abstract Magnetic susceptibility and specific heat measurements and neutron diffraction experiments allow to locate Neel temperatures T N and also two types of transitions below T N . At T t of order T N/2 the susceptibility is maximum, and the magnetic structure is modified (for Se-rich compounds). The second transition takes place around 15 K and is characterized by a specific heat peak and a susceptibility anomaly but no modification of the magnetic structure, according to our powder diffraction data.

Magnetic anomaly in superconducting TmRh4B4

We have investigated the magnetic and superconducting properties of TmRh4B4 (which becomes superconducting at 9.6 K) by means of ac and dc magnetic susceptibility and specific heat measurements. At 10.7 K, an ac susceptibility peak similar to those found in spin glasses has been observed. In addition, a pronounced specific heat peak has been observed at 11.4 K. The susceptibility peak is essentially unaffected by substitution of 1% Lu or Er for the Tm, but it diminishes when much larger amounts of Er are substituted. The physical origin of this anomalous peak will be discussed.

Tricritical behavior in two dimensions. I. Model-dependent behavior from finite size effects

The onset of two-dimensional tricritical behavior in $N\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ strips of spins in an Ising-like model is investigated. This is done through numerical computation of the largest eigenvalue of the single-spin advance transfer matrix. Primary attention is paid to the specific heat at constant nonordering field. The usual phase diagram, in zero ordering field, locates the tricritical point at the intersection of a first-order line and a $\ensuremath{\lambda}$ line; it is found here that a curve of large-field, rounded and bounded specific-heat peaks also seems to intersect this point. This curve, when it exists, may be helpful in experimentally locating tricritical points in any dimension. Evidence is also presented, at zero nonordering field, for the validity of the Onsager specific-heat temperature shift ${N}^{\ensuremath{-}2}\mathrm{ln}N$ in the model.

Low temperature specific heat anomalies and spin-spin interactions in soft carbons and in neutron irradiated polycrystalline graphite

In continuation of previous studies of the specific heat of carbons and graphite in the He 4 and He 3 temperature range (0.4–4.5°K) work was extended down to 0.07°K using a dilution refrigerator at the NASA Lewis Center in Cleveland. The presence of a second specific heat peak at around 0.3°K was ascertained and its relation to the first one at around 0.65°K was studied in dependence on heat treatment, neutron irradiation and post irradiation anneal. Both peaks, as well as the linear component, seem to be due to the presence of localized spin centers, interacting in an antiferromagnetic manner. A general explanation of the relationships observed is suggested.

Kinetics of order-disorder transformations in alloys

Relaxation of order (both long-range and short-range) in b.c.c. binary alloys is theoretically worked out based on the vacancy mechanism of atomic migration, using the path-probability method of time-dependent cooperative phenomena and choosing the pair approximation. With this approximation, the system reduces to the equilibrium state specified by the Bethe approximation as the time dependence ceases. The relaxation times τ k for order parameters are calculated as functions of temperature. Necessity of more than one τ k is demonstrated. One of the τ's shows the critical slowing down, and all of the τ's increase sharply at low temperatures. Using τ k , temperature dependence of thermodynamic properties are calculated as the system is first cooled down to the freezing region, and is then heated with a constant rate of temperature change in both ways. Theoretical results show hysteresis. It is noteworthy that a second peak of specific heat appears in addition to the peak at the order-disorder transition point. The second peak is the consequence of “melting” of the “frozen in” state. The results are compared with experiments for FeCo alloys. The limitation of the “corresponding state” concept, often used in the discussion of phase transitions as well as in glass transitions, is shown by calculating the isothermal annealing behavior of the “frozen in” state at the corresponding (fictive) temperature. Since the glass transition is a “frozen in” phenomenon, the theory presented in the paper is also to be used in interpreting some experimental vitrification processes.

Analysis of experimental specific heat data near the critical temperature. II. Analysis of DAG, MnCl2.4H2O, GdVO4and GdAlO3

For pt.I see ibid., vol.8, p.4037 (1975). The method of data analysis developed previously is applied to the analysis of real specific heat data for three rare earth salts, DAG, GdVO4 and GdAlO3, and MnCl2.4H2O. All these compounds order antiferromagnetically at liquid helium temperature. The data are fitted to C/R=B+A(T/TN-1)- alpha for T>TN, and it is found that alpha =0.13+or-0.04 for all four compounds, A approximately=-B=1.2+or-0.5 for the three rare earth salts and A approximately=-B=2.0+or-0.7 for MnCl2.4H2O. This is in surprisingly good agreement with theoretical Ising model predictions of alpha =1/8, A approximately=1.1 and B approximately=-1.24, despite the fact that only DAG and MnCl2.4H2O have Ising-like anisotropy. For all four compounds the Neel temperature was found to lie between 1/2 and 11/2 mK above the specific heat peak.

Revised thermodynamic relations for lambda transitions in adsorbed layers

Thermodynamic relations of the Pippard type have been obtained for lambda transitions in adsorbed films on both liquid and solid surfaces. For gases adsorbed on solids, estimates based on these relations indicate that no marked change in the adsorption isotherm need necessarily accompany the lambda peak in specific heat.

Magnetic field dependence of the specific heat peak at 0.6–0.7°k in soft carbons

The magnetic field dependence of the specific heat peak was investigated for a polycrystalline graphite of nuclear purity neutron irradiated for 50 hr and for a soft carbon heattreated to HTT 1250°C. It was found that the relatively broader peak for irradiated graphite is located at 0.72°K and the sharper one for the soft carbon at 0.635°K. In both cases the dependence on the magnetic field is similar, —the specific heat increases with the magnetic field from 0 to 20 kG in the whole range of temperature investigated (0.4–4.5°K), the increase on the high temperature side of the peak being greater than on the low temperature side. The peak's maximum shifts slightly to higher temperature with increase of the field (by 10% at 20 kG). The increase in the total specific heat at the peak's maximum is at 20 kG around 80% for the irradiated graphite and only 50% for the 1250°C carbon. It is shown that the peak is due to a cooperative antiferromagnetic interaction between localized electronic spins distributed at random throughout the material. The reasons for various complications in the overall effect are discussed.

Magnetic field dependence of the specific heat peak at 0.6–0.7°K in soft carbons

Magnetic field dependence of the specific heat peak at 0.6–0.7°K in soft carbons

Specific heat of glassy carbon between 0.4° and 4.5°K—I

The specific heat of Glassy Carbon was investigated in the temperature range from 0.4°–4.5°K. Samples of Glassy Carbon heat-treated to 1000°C (GC10) were prepared in form of tubes by the Tokai Electrode Manufacturing Company of Japan. They were heat-treated to various temperatures up to 3200°C in our graphite tube furnace. It was found that above 2°K, all samples follow the relation C = γT + αT 3, with γ going through a strong maximum and α varying only slightly with increase in heat-treatment temperature. On the average the cubic term α is about the same as for soft carbons heat-treated to 1000–1250°C. In the lower temperature range evidence of a specific heat peak located below 0·4°K is obtained. The observed high temperature tail of the peak increases and then decreases in parallel with changes of the linear term γ. The room temperature specific heat of Glassy Carbon changes very little with heat-treatment giving evidence of the nongraphitizability of this material.

Cooperative Phenomena in Solid Electrolytes

A theory of cooperative effects in ionic solids is presented, which points to the ionic carrier density as the main source of the anomalous behavior found in solid electrolytes. Depending on the parameter values, it predicts either an exponential increase of the conductivity with temperature, or a discontinuous change of the conductivity with an associated peak in the excess specific heat. The predicted behavior corresponds to that found in most solid electrolytes, particularly Rb${\mathrm{Ag}}_{4}$${\mathrm{I}}_{5}$.

Specific heat anomaly of nonstoichiometric U 4O 9−y

A λ-type specific heat anomaly of U 4O 9−y, which occurs slightly above room temperature, was measured for the samples with different O/U ratios. The transition temperatures obtained from the peak of λ-type specific heat anomaly are in fairly good agreement with the data by X-ray diffraction and electrical conductivity measurements. The entropy increment for the transition was obtained to be 0.46 e.u. for UO 2.250, 0.56 e.u. for UO 2.240 and 0.70 e.u. for UO 2.228, depending on O/U ratio. On the basis of the entropy change with O/U ratio, the mechanism of the phase transition is discussed. The entropy change due to the phase transition is mainly divided into two terms: one is due to the order-disorder rearrangement of U(IV) and U(V) ions,the other is associated with the displacement of oxygens ions. The former term is estimated to be rather smaller than the entropy change calculated by the Bragg-Williams approximation, and the latter is calculated using the X-ray diffraction data with the assumption of the Willis model.

Low-temperature properties of CeAl 2 and comparison to LaAl 2

The total dilatation of CeAl 2 from 2.5 to 300 K was found to be similar to that of LaAl 2, thus making the assumption of a Ce 4+→Ce 3+ transition unlikely. A negative peak in the dilatation curve of CeAl 2 coincides with the specific-heat peak at 3.36 K. A second transition occurs at 4.5–4.8 K. Magnetization measurements confirm the antiferromagnetism of CeAl 2.