Discontinuity In Specific Heat Research Articles

Evolution Characters of Thermodynamic Quantities in Thin Disk-Accretion of Black Holes

Evolution characters of thermodynamic quantities of the central black hole (BH) of an accretion disk. such as temperature, entropy and specific heat, are investigated in prograde accretion and retrograde accretion, respectively. Compared with prograde accretion, a BH has some unusual characters in retrograde accretion: (i) There exists a maximum BH temperature; (ii) There exists an infinite discontinuity of BH specific heat; (iii) The rates of change of BH temperature and entropy are much bigger for fast-spinning BH than those for slowly-spinning BH.

A Relation Between Fragility, Specific Heat, and Shear Modulus Temperature Dependence for Simple Supercooled Liquids

AbstractIt is often said that the fragility and specific heat discontinuity at the glass transition are related characteristic features of glasses. We give a relation between these quantities for simple liquids, and also find that the temperature dependence of the shear modulus should be closely related to these quantities. According to the Interstitialcy Theory, the liquid state shear modulus G = Go, exp (-βc) = Go exp {-γ[(T/To)-l ]}, where Gois the shear modulus at a reference temperature To, which can be taken to be the glass temperature. In these relations, βis the diaelastic shear susceptibility, c is the interstitialcy concentration, T is the temperature, and dc/dT = γ/βTo. It has been proposed by Dyre, Olsen and Christensen that U in the viscosity η = ηo exp (U/kT) be given as the work done in shoving aside particles during a diffusion step, and therefore be proportional to the (liquid state) shear modulus. If so, then combining the above relations, the fragility F = [d log η/d (Tg/T]T=Tg becomes F=(1+γ) log [η (Tg)/ηo], where γ = - (Tg/G)(dG/dT). Then, since δCv, = UF(dc/dT), where UF is the interstitialcy formation energy, one obtains further with reasonable simplifying approximations δCv/Cv∼γG(T)/Goo, where Goo is the zero temperature crystalline shear modulus. For a typical fragile glass γ ∼ 2 (F ∼ 50) with G(Tg)/Goo ∼ 1/2, then δCv/Cv, ⊼ 1, ut close to zero for strong glasses, in fair agreement with available experimental results. The perspective given by the Interstititialcy Theory is then that the fragility is given phenomenologically by the temperature dependence of the shear modulus, or microscopically by the rate of increase of the equilibrium interstitialcy concentration with temperature.

Ferroelectric specific heat of telluric acid ammonium phosphate single crystal near T c

Precise specific heat data on good quality Telluric Acid Ammonium Phosphate (TAAP) have been obtained in the vicinity of the ferroelectric-paraelectric phase transition ( T c ≈ 44.8 °C). The experimental specific heat discontinuity at T c, ΔC P exp( T c) = 0.085J/gK, is somewhat lower than the expected value, Δ C P cal( T c) = 3/2 Nk B(1 − 3 g) −1 ϱ −1 = 0.129J/gK, with g = 0.28 determined from spontaneous polarization Ps( T). Using a linear background interpolation for the non-ferroelectric contributions to the specific heat, we get Δ S exp( T c) = 5.25 × 10 −3J/gK<Nk Bϱ −1 Ln2 = 9.65 × 10 −3J/gK (transition entropy), and Δ Q exp( T c) = 1.608J/g<1/2 Nk B T cϱ −1 = 2.214J/g (transition heat).

Comparison of magnetocaloric properties from magnetic and thermal measurements

The isothermal change of the magnetic entropy of a magnetically ordered material upon application of external magnetic field can be calculated from the temperature and field dependence of the magnetization or of the specific heat. The adiabatic temperature change, i.e., the magnetocaloric effect (MCE) can be measured directly or can be calculated via different methods using the field-dependent specific heat values, or a combination of data obtained via magnetization and thermal measurements. In the present study, magnetic and thermal measurements were carried out on Gd75Y25(TC=232 K) and Gd48Y52(TC=161 K) samples, for applied fields ranging between 0 and 7 T. From both datasets, the magnetic entropy change and MCE values were calculated and compared, in order to assess the mutual reliability of the methods applied. The magnetically or thermally deduced specific heat discontinuities show a reasonable agreement within experimental error. Similar comparison of the calculated magnetic entropy changes reveals that the measured transition temperature and the shape of the curve do not depend on the method selected. It is demonstrated that the choice of an integration constant during entropy calculation has a significant impact on the adiabatic temperature change deduced from the field and temperature dependence of the entropies. For the MCE, a better approximation can be obtained using the magnetically acquired magnetic entropy change and the field-dependent specific heat. The results prove that magnetic measurements carried out in high enough magnetic fields provide reliable information on the isothermal magnetic entropy change and, when combined with field-dependent specific heat measurements, on the magnetocaloric effect as well.

Anisotropic Latent Heat of Vortex-Lattice Melting in UntwinnedYBa2Cu3O7−δ

We report a distinct thermal signature of the first-order vortex-lattice melting for the external magnetic field $H$ both parallel and perpendicular to the $c$ axis of an untwinned ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ single crystal. Latent heats and discontinuities in specific heat were observed for each configuration. The entropies of melting and the melting lines ${H}_{\mathrm{m}}(T)$ both scale with an anisotropy parameter $\ensuremath{\gamma}\ensuremath{\approx}8$. The specific heat of the vortex fluid is considerably larger than that of the vortex solid (by up to $2\mathrm{mJ}/\mathrm{mole}{\mathrm{K}}^{2}$), which is not explained by simple arguments based on counting the numbers of thermodynamic degrees of freedom.

εexpansion analysis of very weak first-order transitions in the cubic anisotropy model. II

A companion article analyzed very weakly first-order phase transitions in the cubic anisotropy model using $\eps$ expansion techniques. We extend that analysis to a calculation of the relative discontinuity of specific heat across the transition.

Specific heat of superconducting indium in porous Vycor glass

Thermal measurements were made on indium-impregnated 5.6 nm Vycor glass at low temperatures in applied magnetic fields up to 1 Tesla. The indium lattice specific heat is enhanced relative to the bulk value, while the electronic contribution was unchanged. A slightly broadened superconducting transition with a bulk-like specific heat discontinuity indicate that the indium nanoparticles are strongly coupled. The phase diagram and size of the specific heat jump at T c ( H) yield κ ≈ 15. A field-periodic magnetocaloric effect has also been observed which may be related to flux depinning in the superconducting network.

Frequency-dependent thermal response of indium nanoparticles in porous glass

AC thermal measurements were made on indium nanoparticles in the dielectric porous host Vycor in the temperature range of 1.4 K to 10 K. The width of the superconducting transition and the size of the specific heat discontinuity at the transition were the same as for bulk indium, indicating that thermal fluctuations are negligible and that the indium particles are moderately coupled. The heat transfer process was studied via the frequency dependence of the thermal response. The response changes dramatically when the indium nanoparticles can no longer follow the driving heater. The temperature dependence of the indium system thermal response time can be estimated from the data. Using a model which considers only electronic thermal conduction, we find a temperature-independent (for T>Tc) electronic mean free path of 1 nm, consistent with resistivity and critical field data.

High-accuracy differential thermal analysis: A tool for calorimetric investigations on small high-temperature-superconductor specimens.

We describe a technique for measuring small heat capacities below room temperature, which represents a simple but significant improvement of the conventional differential thermal-analysis (DTA) method by means of high-precision electronic components. It is thereby possible to measure the heat capacity {ital C}({ital T}) of milligram samples with a relative accuracy {delta}{ital C}/{ital C}{lt}0.02%. This simple and fast DTA method is suitable not only to detect the specific-heat discontinuity at {ital T}{sub {ital c}} of high-temperature superconductors, but also to study the thermodynamics at the irreversibility boundary {ital H}{sub irr}({ital T}) in the magnetic phase diagram of cuprate superconductors. From respective measurements on a YBa{sub 2}Cu{sub 3}O{sub 7} single crystal, we deduce an upper limit for a latent heat {ital L} associated with a hypothetical first-order transition at {ital H}{sub irr}({ital T}), namely {ital L}{lt}0.05{ital k}{sub {ital B}}{ital T} per vortex per layer for an external field {mu}{sub 0}{ital H}=7 T parallel to the {ital c} axis of the investigated specimen.

Landau theory of the nematic-smectic a tricritical phase transition in a binary mixture of liquid crystals

Abstract We have developed in this study a thermodynamic model for the nematic-smectic A (NA) tricritical phase transition of a binary mixture of liquid crystals in analogy with the model for quasi fluid mixtures due to Griffiths. Using the Landau theory with a symmetrical TCP, we have predicted the critical behaviours of the nematic susceptibility, order parameter and the specific heat discontinuity in the vicinity of the TCP. Our predictions for the tricritical exponents for the order parameter and the specific heat discontinuity are those predicted by the mean field theory (β=1/4 and α=1/2) with a symmetrical TCP. Our exponent value of γ=1/2 for the nematic susceptibility does not agree with the mean field value of γ=1. Our predicted values agree with those obtained experimentally for some binary mixtures of liquid crystals. This means that the mean field model with a symmetrical TCP is capable of describing the nematic-smectic A tricritical phase transition for a symmetrical binary mixture of liquid crystals.

Effects of boron substitution on the superconducting state of UBe13.

Specific heat, magnetic susceptibility, and resistivity were measured on polycrystalline samples of U(Be[sub 1[minus][ital x]]B[sub [ital x]])[sub 13] with 0[le][ital x][le]5.2[times]10[sup [minus]3]. Small amounts of B greatly affect the specific-heat discontinuity at the superconducting phase transition in UBe[sub 13], while only weakly decreasing the superconducting transition temperature. The presence of B impurities also influences the resistivity. These observations are discussed in terms of possible impurity-induced changes in the symmetry and/or pairing interaction of the superconducting state in UBe[sub 13].

Interlayer tunneling mechanism of high- Tc superconductivity: Nonuniversal discontinuity in specific heat

Interlayer tunneling mechanism of high- T c superconductivity is considered with emphasis on the thermodynamics close to T = T c . For a k-independent interlayer Josephson coupling T J , we find that, for | T − T c |/ T c ⪡ 1, the gap on the Fermi surface is Δ( T) = T c η( T c ; T J )(1 − T/ T c ) α , with mean-field exponent α = 1 2 . The nonun iversal prefactor η( T c ; T J ) drops rapidly from the BCS-value π( 8 7 ς(3)) 1 2 ≈ 3.06 , as a function of T J . The nor malized. specific heat discontinuity at T = T c , ΔC v / N n (0) T c = η 2( T c ; T J )/[1 − T J /4 T c ] 2, increases initiall y rapidly as a function of T J , while lim T J → 0 ΔC v / N n (0) T c = 8 π 2/7 ς(3) ≈ 9.4.

Superconductivity in Y-Ni-B base compounds

Carbon introduced in Y-Ni-B ternary alloy material was shown to stabilise aquaternary compound YNi 2B 2C which is also responsible for the appearance of superconductivity in Y-Ni-B alloys YNi 4− x B 1+ x . Rietveld refinement of a nearly single-phase material of YNi 2B 2C confirmed isotypism with the filled ThCr 2Si 2-type ( z B =0.353(1)). Magnetic and specific heat measurements indicate type-II superconductivity in YNi 2B 2C with a T c-onset of 15.2 K and a normalised specific heat discontinuity ΔC/ γT c =1.57. We present a first estimate of the upper critical field μ 0 H c2 (0)=3.7 T, the coherence length ξ GL =9.4 nm and the Ginzburg-Landau parameter κ=10.5 of this new compound.

Specific heat of Zn- and Co-substituted Bi1.8Pb0.2Sr2Ca(Cu1-xMx)2Oy.

The specific heat of several Zn- and Co-doped ${\mathrm{Bi}}_{1.8}$${\mathrm{Pb}}_{0.2}$${\mathrm{Sr}}_{2}$Ca(${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${)}_{2}$${\mathrm{O}}_{\mathit{y}}$ superconductors was investigated. Co substitution is paramagnetic, and introduces a linear term in ${\mathit{C}}_{\mathit{p}}$ at low temperatures, without reduction in the specific-heat discontinuity \ensuremath{\Delta}${\mathit{C}}_{\mathit{p}}$/${\mathit{T}}_{\mathit{c}}$ at ${\mathit{T}}_{\mathit{c}}$. The results can be understood as gapless superconductivity in a highly anisotropic s-wave or d-wave superconductor. Zn substitution is nonmagnetic and does not lead to these phenomena.

Quantitative analysis of the complex magnetic phase diagram of HoAlGa.

A recent self-consistent periodic-field model, set up for long-period magnetic systems, is shown to give a satisfactory quantitative description of the main features of a complex magnetic phase diagram below T N of an antiferromagnet, namely the hexagonal HoAlGa compound. From the crystal-field and exchange parameters it has been possible to account for (i) the multistep magnetization processes with the correct values of the transition field and the intermediate structures along the easy axis, (ii) magnetization curves along the hard axes, (iii) the amplitude and direction of each moment during all these processes, (iv) the reduced value of the specific-heat discontinuity of the λ anomaly at T N

Exact treatment of some phenomenological models of layered high-T c superconductors

Existing treatments of phenomenological models of Bi and Tl based superconductors consisting of n layers of copper oxide are unsatisfactory because they ignore the important φ 4 terms in the free energy. An exact treatment of these models is presented, and it is shown that the condition of minimum free energy automatically excludes ( n − 1) of the n critical temperatures. The critical exponent β of the order parameter is found to be independent of n and equal to 1 2 as usual in the Landau theory. The specific heat discontinuity Δ c at the critical temperature is calculated as a function of n. A meaningful comparison with experimental measurements of Δ c at the moment is hindered by the limited availability of experimental results. Reliable determinations of Δ c of a given series of layered superconductors will enable a check of the validity of theoretical results.

Specific heat of the high T c organic superconductor κ-(ET) 2Cu[N(CN) 2]Br

An anomally in the specific heat of κ-(ET) 2Cu[N(CN) 2]Br, where ET is the radical-cation donor molecule bis(ethylenedithio)tetrathiafulvalene, has been observed around T c ∼ 11.5K, indicating bulk superconductivity in this organic charge-transfer salt. The normal-state electronic specific heat coefficient, γ = 22 ± 3 mJK -2 mol was obtained by the suppression of superconductivity with a sufficiently strong magnetic field applied parallel to the crystallographic b direction. The ratio of the specific heat discontinuity Δ C to γ T indicates strong coupling. Comparisons with other ET-based organic superconductors are made.

Specific heat in some gadolinium compounds. I. Experimental.

Specific-heat measurements have been performed on the gadolinium compounds ${\mathrm{GdCu}}_{2}$${\mathrm{Si}}_{2}$, ${\mathrm{GdNi}}_{2}$${\mathrm{Si}}_{2}$, ${\mathrm{GdGa}}_{2}$, and ${\mathrm{GdCu}}_{5}$ in order to investigate the phase transitions between paramagnetic and commensurate or incommensurate antiferromagnetic states. Various shapes of specific-heat curves are observed at and below the ordering temperature ${\mathit{T}}_{\mathit{N}}$. In particular, the specific-heat discontinuity at ${\mathit{T}}_{\mathit{N}}$ is strongly reduced in the incommensurate systems. This behavior is related to the exact type of magnetic arrangement involved.

Specific heat in some gadolinium compounds. II. Theoretical model.

A detailed thermodynamical analysis of commensurate and incommensurate magnetic phases in localized magnetic systems within a mean-field theory is presented. Interesting results are obtained concerning the specific heat of amplitude-modulated magnetic structures: In particular, the specific-heat discontinuity at the ordering temperature ${\mathit{T}}_{\mathit{N}}$ is reduced by a factor of 2/3 relative to that expected in ferromagnetic or helimagnetic structures. In addition, the exact shape of the specific-heat curves strongly depends on the relative magnitude of the successive exchange couplings J(nQ). Under certain conditions, the maximum of specific heat at ${\mathit{T}}_{\mathit{N}}$ is shifted to a temperature lower than ${\mathit{T}}_{\mathit{N}}$. Recent experimental data on ${\mathrm{GdCu}}_{2}$${\mathrm{Si}}_{2}$, ${\mathrm{GdNi}}_{2}$${\mathrm{Si}}_{2}$, ${\mathrm{GdGa}}_{2}$, and ${\mathrm{GdCu}}_{5}$ compounds support very well these peculiarities.

Effect of Cu 2+ magnetic moments on the superconductivity of YBa 2Cu 3O 7: the origin of the “linear term” in the specific heat; the volume fraction of superconductivity

The concentration ( n 2 ) of Cu 2+ magnetic moments located on the YBa 2 Cu 3 O 7 lattice is determined by the specific heat in a 7 T magnetic field. The discontinuity in specific heat at T c [Δ C ( T c )] and also the coefficient of the linear term [γ(0)] are correlated with n 2 in a way that suggests the operation of a pair-breaking mechanism that limits the transition to the superconducting state and provides a criterion for the volume fraction of superconductivity. γ(0) can be represented by the sum of two contributions, both associated with Cu 2+ moments, implying that there is no contribution that is an intrinsic property of the superconducting state. The interpretation of the data provides estimates of parameters relevant to the recognition of strong-coupling effects.