Electronic Specific Heat Constant Research Articles

Correction to: On the Role of Fermi Energy in Determining Properties of Superconductors: a Detailed Comparative Study of Two Elemental Superconductors (Sn and Pb), a Non-cuprate (MgB2) and Three Cuprates (YBCO, Bi-2212 and Tl-2212)

Fermi energies (E Fs) of high- T c superconductors (SCs) have of late been evincing considerable interest because they are believed to be the cause of their high T cs and gap structures. Since Bardeen-Cooper-Schrieffer (BCS) equations for elemental and generalized-BCS equations for non-elemental SCs are derived under the blanket of the assumption E F/ k θ > > 1 (k = Boltzmann constant, θ = Debye temperature), they cannot shed light on the E Fs of these SCs. This fact leads us to address the gaps (Δ0s) and T cs of both types of SCs via recently derived equations which incorporate E F as a variable. For the specification of the E F of any SC, we now need another of its properties. Choosing j 0, the critical current density of the SC at T = 0, and following an idea due to Pines, we present for both types of SCs new equations for j 0 that depend solely on the following properties of the SC: E F, θ, gram-atomic volume, electronic specific heat constant and a dimensionless construct $y=k\theta \sqrt {2m\ast } \text {/}P_{\text {0}} \sqrt {E_{\mathrm {F}} } \text {,}$ where m* is the effective mass of superconducting electrons and P 0 their critical momentum. Appeal to the experimental values of Δ0, T c and j 0 of any SC then not only leads to values of E F, m* and P 0 but also provides plausible clues about how its j 0—and therefore T c—may be increased.

Linear response results for phonons and electron–phonon coupling in hexagonal closepacked Sc-spin fluctuations, and implications for superconductivity

We present a FP-LMTO (full-potential linear muffin-tin orbital) study of the variation inthe electronic structure, phonon frequencies and electron–phonon coupling in hexagonalclose packed (hcp) Sc under pressure. The electron–phonon coupling constantλ is found to increase steadily with pressure in the hcp phase, until the pressure reaches a valuewhere the hcp phase becomes unstable. Linear response calculations for the normal pressurec/a ratio predict a phase change somewhere between calculated pressures of 22 and 30 GPa.The calculated frequencies for the equilibrium hcp lattice parameters are in goodagreement with the inelastic neutron scattering results. There is a small upward shift in theΓ-pointE2g mode frequency under pressure, in qualitative agreement with the Raman spectroscopystudy of Olijnyk et al (2006 J. Phys.: Condens. Matter 18 10971). From the measured valueof the electronic specific heat constant and the calculated values of the Fermi leveldensity of states and electron–phonon coupling constant, we conclude that theelectron–paramagnon coupling constant in hcp Sc should be comparable to theelectron–phonon coupling constant. This indicates that the spin fluctuation effects arestrong enough to suppress superconductivity completely in hcp Sc. We argue that spinfluctuations should be reduced by a factor of two or more in the high pressure Sc-II phase.On the basis of estimates of the electron–paramagnon coupling constants and thecalculated or estimated electron–phonon coupling constants, we argue that thehcp phase may become superconducting with a very low transition temperatureimmediately prior to the transition to the Sc-II phase and that the Sc-II phaseshould indeed be superconducting. The electronic, electron–phonon and spinfluctuation properties of hcp Sc under pressure are compared with those of the highpressure hcp phase of Fe, which was reported to be superconducting a few yearsback.

The taming of palladium: the influence of cerium additions on the magnetic and transport properties of palladium in the composition range of 5 to 16.7 at.% Ce

Low-temperature studies (resistivity, magnetic susceptibility and heat capacity) of the Pd-rich CePd alloys (5, 8 and 12.5 (CePd 7) at.% Ce) reveal that, when Ce is added to Pd, the unusual magnetic behavior of Pd is destroyed and the CePd alloys behave more or less as common metals. That is, the 4f electron of Ce is transferred to the 4d band of Pd and tends to fill it, leading to an unusually low, nearly temperature-independent paramagnetic susceptibility, x = 12.5 × 10 −6 e.m.u. (g at.) −1, and electronic specific heat constant, γ = 0.467 mJ (g at.) −1 K −2 for CePd 7. L-CePd 5 (16.7 at.% Ce), on the other hand, appears to behave as an intermediate-valence compound which appears to be ordering below 2 K. It has a γ value of 41.6 mJ (mole Ce) −1 K −2, which is about 10% larger than that of CePd 3.

Electronic Structure and Fermi Surface of UB12

Based on the itinerant-electron model for the 5f electrons, the energy band structure and the Fermi surface are calculated for the cubic uranium dodecaboride UB 12 , known to be a paramagnet having the electronic specific heat constant of 20 mJ/K 2 mole, by a self-consistent relativistic APW method with the exchange and correlation potential in the local-density approximation. The energy band structure is that of a compensated metal having 0.32 holes/cell and the compensating number of electrons. Both the hole and the electron sheets of the Fermi surface are multiply-connected with open orbits, the direction of which is consistent with the high-field magnetoresistance. By these Fermi surfaces, both the magnitude and the angular dependence of the frequency branches of the de Haas-van Alphen effect observed recently by Ōnuki et al . can be explained reasonably well.

Influence of high magnetic fields (10 T) on paramagnons in rare-earth intermetallic compounds

Low temperature (0.5–20 K) high field (0–10T) heat capacity and low field (0–2T) magnetic susceptibility (60 μK−300K) measurements were used to study and characterize the quenching of spin fluctuations (paramagnons) in the highly exchange enhanced RCo 2 phases, where R = Sc, Y and Lu. These RCo 2 compounds are characterized by large many-body mass enhancements (2.54 to 5.38) and large Stoner factors (15.5 to 25.3). The application of magnetic fields lowers their electronic specific heat constants by 7 to 10% at 10 T. For YCo 2 the coefficient of the T 3 term (β) in the normal heat capacity equation is found to increase with increasing field, but for ScCo 2 and LuCo 2 β remains constant.

Effect of high magnetic fields on the heat capacity of single-crystal terbium.

The low-temperature (1.3 to 20.0 K) heat capacity of an electrotransport-purified terbium single crystal was measured in magnetic fields up to 10 T applied along the magnetically hard basal-plane direction, i.e., 〈112\ifmmode\bar\else\textasciimacron\fi{}0〉 or a axis. The electronic specific-heat constant, \ensuremath{\gamma}=3.71\ifmmode\pm\else\textpm\fi{}0.09 mJ/g-at. ${\mathrm{K}}^{2}$, and the Debye temperature at 0 K, ${\ensuremath{\Theta}}_{D}$=169.6\ifmmode\pm\else\textpm\fi{}0.8 K, were obtained from an analysis of the zero-field data. The heat capacity is almost independent of the magnetic field below 12 K, but above 12 K systematically increases as a function of increasing field up to \ensuremath{\sim}3 T and then it remains almost unchanged. This indicates that the spin-wave energy gap due to the magnetic anisotropy in terbium increases with increasing fields at the rate of about 4 and 0.3 K/T below and above \ensuremath{\sim}3 T, respectively.

Influence of composition on some physical properties of the narrow band material CeSn3

Abstract The results of low temperature (1.5 to 20 K) high magnetic field (0 to 10 T) heat capacity, magnetic susceptibility (1.5 to 300 K), electrical resistivity ratio and optical metallographic analysis of a series of alloys near the CeSn3.00 composition are reported here. We have found that CeSn3±y exists over a solid solution region from CeSn2.99 to CeSn3.05. The electronic specific heat constant, the resistance ratio, the magnetic susceptibility at T = 0 K, and the quenching of spin fluctuations vary from large values for the Ce-rich alloys to small values for Sn-rich alloys.

Low-temperature heat capacity of electrotransport-purified scandium, yttrium, gadolinium, and lutetium.

The low-temperature heat capacity of electrotransport-purified scandium, yttrium, gadolinium, and lutetium have been measured from 1 to 20 K. The electronic specific-heat constant \ensuremath{\gamma} and the Debye temperature ${\mathrm{CTHETA}}_{D}$ are determined to be 10.334\ifmmode\pm\else\textpm\fi{}0.011 mJ/g-at. ${\mathrm{K}}^{2}$ and 354.3\ifmmode\pm\else\textpm\fi{}1.0 K, respectively, for scandium, 7.878\ifmmode\pm\else\textpm\fi{}0.004 mJ/g-at. ${\mathrm{K}}^{2}$ and 244.4\ifmmode\pm\else\textpm\fi{}0.5 K, respectively, for yttrium, 6.380\ifmmode\pm\else\textpm\fi{}0.026 mJ/g-at. ${\mathrm{K}}^{2}$ and 163.4\ifmmode\pm\else\textpm\fi{}0.1 K, respectively, for gadolinium, and 8.194\ifmmode\pm\else\textpm\fi{}0.016 mJ/g-at. ${\mathrm{K}}^{2}$ and 183.2\ifmmode\pm\else\textpm\fi{}0.3 K, respectively, for lutetium. We believe that the above electronic specific-heat constants and Debye temperatures represent the intrinsic values for these four rare-earth metals. The use of the low-temperature heat-capacity results for these metals to evaluate the various contributions to the heat capacities of the magnetic lanthanide metals is examined. The total many-body enhancement factor and its components (the electron-phonon, electron-paramagnon, and spin-wave) are calculated.

The magnetic susceptibility of lutetium-hydrogen solid solution alloys from 2 to 300 K and a re-evaluation of the low temperature heat capacity results

The magnetic susceptibility, χ, of several lutetium-hydrogen solid solution alloys was measured between 2–300 K. Compositions varied from an electrotransport purified Lu (0.018 at% H) sample to 6.4 at% H alloy. Several samples exhibited large magnetic anisotropies, which complicated the analysis. The measured susceptibilities were compared to low temperature heat capacity results measured earlier on the same samples. It appears that pure Lu is a spin fluctuation material and the fluctuations are quickly degraded by impurities. While the variation of χ vs. composition is similar to that of γ (the electronic specific heat constant) vs. composition, the low temperature χ peaks near 3.0 at% H compared to 1.4 at% H for γ. This difference is thought to be due to hydrogen tunneling, which gives rise, in part, to a linear contribution to the heat capacity. Correcting for this brings the concentration dependence of γ in good agreement with the χ dependence of the hydrogen content.

Effect of high magnetic fields on the heat capacity of strongly Pauli-paramagnetic Pd-Ni alloys

The low-temperature [(1.3-20.0)-K] heat capacity of strongly Pauli-paramagnetic Pd-Ni alloys containing 0.47 and 0.97 at.% Ni was measured in magnetic fields up to 10 T. The electronic specific-heat constant becomes smaller with increasing fields (12% or 13% at 9.98 T). This is probably due to the depression of the spin-fluctuation enhancement of heat capacity by the high magnetic fields and is in accord with the recent theoretical predictions. The coefficient $\ensuremath{\beta}$ of the ${T}^{3}$ term in the heat capacity becomes larger with increasing fields and at $H\ensuremath{\ge}5.39$ T it reaches almost the same value as that for alloys containing more than \ensuremath{\sim}5 at.% Ni. Two possible mechanisms have been proposed to account for the increase in $\ensuremath{\beta}$: (1) The increase is due to the magnetic quenching of localized spin fluctuations in the vicinity of the nickel atoms, or (2) the increase is due to a magnetic contribution to the heat capacity which results from an induced magnetic moment on the nickel atoms by the applied magnetic field. Additional experiments are needed to determine which mechanism is the correct one.

The specific heats of LaAg, GdAg and Gd2O3from 0.5 to 22K

Specific heat measurements on monoclinic Gd2O3 show a cooperative peak at 3.8K. The entropy associated with this peak is the full 2R ln 8 expected for the Gd3+ ions. Measurements on GdAg are affected by the presence of small inclusions of Gd2O3, but it proves possible to allow for these and to deduce values for the electronic specific heat constant gamma which is 11.4+or-1.7 mJ mol.-1 K-2. For LaAg, gamma =9.9+or-0.2 mJ mol.-1 K-2. The lattice heat capacities are analysed in terms of a Debye temperature which is found to vary strongly with temperature; the low-temperature limiting values are 208K and 150K for GdAg and LaAg respectively.

Quenching of spin fluctuations in scandium

The low temperature (1.3 to 20 K) heat capacity of electrotransport purified scandium metal was measured in magnetic fields up to ∼10 T. The electronic specific heat constant, γ, decreases with increasing magnetic fields (11% at 10 T), while the coefficient to the T 3 term of the heat capacity, β, rises rapidly with increasing field and becomes almost constant at T > 5 T. The decrease in γ is thought to be due to the depression of spin fluctuation enhancement by the magnetic field. The increase in β is believed to be due to an induced magnetic moment on the scandium atoms caused by the applied magnetic field.

Influence of electron concentration on the hydrogen absorption by RM5Haucke compounds

Analysis of the electronic specific heat constant for some Y(Ni,Al)5, La(Ni,Al)5, La(Ni,Cu)5 and Th(Ni,Al)5 alloys suggests that the amount of hydrogen absorbed in excess of 3 H atoms per RM5 formula unit (0.5 H atom per metal atom) by the RM5 phases depends upon the number of unpaired 3d nickel electrons. The so-called 'aluminium anomaly' is also explained on the basis of these results.

Heat capacity and thermodynamic functions of the RFe 2 compounds ( R =Gd, Tb, Dy, Ho, Er, Tm, Lu) over the temperature region 8 to 300 K

Experimental heat capacity data for the Laves phase RFe 2 intermetallic compounds ( R =Gd, Tb, Dy, Ho, Er, Tm, and Lu) have been determined over the temperature range 8 to 300 K. The error in these data is thought to be less than 1%. Smoothed heat capacity values and the thermodynamic functions, ( H° T − H° 0) and S° T, are reported throughout the temperature range for the RFe 2 series. In addition, ( G° 298 − H° 0) at 298 K is reported for all the RFe 2 compounds. These data were analyzed and it was shown that the maxima in the thermodynamic functions near HoFe 2 are due to the magnetic contribution of the lanthanide element. The lattice contribution to the entropy at 300 K was estimated, and from this quantity the Debye temperature was calculated to be about 300 K, which is in good agreement with the low-temperature heat capacity. Furthermore, this analysis indicates that the apparent electronic specific heat constants, γ′, for TbFe 2, DyFe 2, and HoFe 2, reported earlier, are in error.

Influence of lattice instability on the superconducting properties of “La 3S 4”

The normal state properties (the electronic specific heat constant, Debye temperature and electrical resistivity) and superconducting state properties [the superconducting transition temperature, T c, and the upper critical field at 0 K, H c 2 (0)] have been studied in the La 3S 4-La 2S 3 system. The superconducting properties and the electronic specific heat constant exhibit the maximum values in the alloy with the lowest sulfur content that does not undergo a low temperature crystallographic transformation. At lower sulfur contents the alloys exhibit a cubic to tetragonal transformation at ∼80 K with a serious degradation in their superconducting properties, especially H c 2 (0). These alloys clearly illustrate that materials which are almost but not quite unstable are good superconductors, relative to the more stable compositions.

Influence of the lattice and electronic factors on the hydrogenation properties of the RNi 5-base (R is a rare earth) haucke compounds: Results of low temperature heat capacity measurements

The low temperature heat capacities (1 – 20 K) and the hydrogen absorption properties of some ternary Haucke compounds — LaNi 5− x Al x (0 ⩽ x ⩽ 1.5), LaNi 5−xPt x (0 ⩽ x ⩽ 5) and La 1−xTh x Ni 5 (0 ⩽ x ⩽ 1)—were investigated to examine any correlation between the ability of these compounds to absorb hydrogen and their physical properties, e.g. their electronic structure and elastic properties. The density of states at the Fermi level has a minimum near x = 1 in LaNi 5− x Al x . The electronic specific heat constants of LaNi 5−xPt x decrease in a smooth fashion as the concentration of nickel decreases. La 1−xTh xNi 5 alloys, however, only exhibit a slight change in their electronic specific heat constants. The low temperature heat capacities were also measured for the hydrides of these compounds. The electronic specific heat constant γ and the Debye temperature θ D of the LaNi 5− x Al x H y phase do not change as drastically, relative to the corresponding LaNi 5− x Al x phase, as those for the RH 2 compounds change relative to the corresponding pure metal R. This is probably caused by filling of the new bonding states formed in these compound hydrides with the added electrons of hydrogen.

Low-temperature heat-capacity study of Haucke compounds CaNi5, YNi5, LaNi5, and ThNi5

Low-temperature heat capacities of some Haucke compounds (Ca${\mathrm{Ni}}_{5}$, Y${\mathrm{Ni}}_{5}$, La${\mathrm{Ni}}_{5}$, and Th${\mathrm{Ni}}_{5}$) were studied. The electronic specific-heat constants of these compounds are nearly the same and slightly smaller than that of pure nickel. The Deybe temperatures of these compounds show a wider variation than the electronic specific-heat constants. It is found that the lattice rigidity of these four compounds varies considerably, with that of La${\mathrm{Ni}}_{5}$ being the softest, followed by Ca${\mathrm{Ni}}_{5}$, Th${\mathrm{Ni}}_{5}$, and Y${\mathrm{Ni}}_{5}$ in order of increasing rigidity. This appears to influence their hydrogen absorption capacity. The relative softness is correlated with the Ni-Ni distances in the midplane [$3(g)$ sites], and it is suggested that the Ni atoms in this plane play a critical role in governing the hydrogenation behavior of these materials.

Low-temperature heat capacity of Sc-Zr and Sc-Mg alloys

The low-temperature heat capacity of nineteen Sc-Zr alloys with compositions ranging from pure Sc to 34-at.% Zr in Sc and five Sc-Mg alloys with magnesium concentrations less than 8 at.% were measured from 1 to 20 K. Zirconium additions up to 0.5 at.% raises the electronic specific-heat constant ($\ensuremath{\gamma}$); then it decreases monotonically with further zirconium additions up to 34-at.% Zr. The effect of magnesium is to decrease the electronic specific-heat constant slowly. The heat-capacity results were used to calculate an experimental density of states (DOS) curve for scandium. The theoretical DOS curves are significantly different from the experimental DOS curve. The various enhancement factors have been calculated using these DOS curves. A change in slope in $\ensuremath{\gamma}$ at \ensuremath{\sim} 2-at.% Mg and the peak in $\ensuremath{\gamma}$ at 0.5-at.% Zr are probably associated with the second energy band crossing the Fermi energy at the points $H$ and $L$ in the Brillouin zone as the electron concentration is lower or raised, respectively. The effect of dilute amounts of zirconium and magnesium on the Debye temperature (${\ensuremath{\Theta}}_{D}$) of scandium is unusual, initially rising for zirconium additions and falling for magnesium additions. At high solute concentrations ${\ensuremath{\Theta}}_{D}$ rises and falls more or less in a "saw-tooth"-like fashion. It is suggested that this variation in ${\ensuremath{\Theta}}_{D}$ is due to the formation of short-range-order configurations of Sc impurity atoms in the solid solution alloys.

Influence of hydrogen on the low temperature heat capacity of lutetium-rich lutetium-hydrogen alloys

The low temperature (1–20K) heat capacity results of lutetium containing up to 15.5 at.%H in solid solution were measured. In alloys containing between 0.1 and <3.0 at.%H a low temperature anomaly was observed in the C/T vs. T 2 plots below 2.5K, but alloys containing 3.0 or more at.% H were linear down to the lowest temperature measured. The electronic specific heat constant, γ, initially increased by ∼35% when 1.5 at.% H was added, and then γ decreased at higher hydrogen concentrations. The Debye temperature, θ D, may also show a similar variation. These anomalous behaviors are thought to be due to hydrogen tunneling.