The low temperature contributions to β-uranium hydride specific heat

Recent observation of Proton Magnetic Resonance in ferromagnetic β-uranium hydride by Barash et al. led us to perform a new analysis of the specific heat data of Flotow and Obsborne for this compound. In the temperature region 1.469K?T?3.927K, the specific heat C was found to be given by the expression C=29.504T+0.099T³mJK^?1mol^?1 while, for $\text{4.332K?T?15.184K, C=28.464T+0.157T}{}^3\text{+55.906 [T}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{+}\text{4}\text{5}\text{T}{}_0\text{T}\text{1}\text{2}\text{+}\text{4}\text{15}\text{T}{}^2{}_0\text{T}{}^{\mathrm{<mtext>sol?1</mtext><mtext>2</mtext>}}$. exp (?T₀/T) in the same units, with T₀=79.3K. This result indicates that the dispersion relation for magnons in this compound has the form E=k_BT₀+Dk². The large energy gap (k_BT₀) is attributed to the high magneto-crystalline anisotropy arising from the unquenched orbital moment of the uranium ions. To our knowledge this is the first energy gap reported for magnons in an actinide compound.     

Satellite electron-diffraction in NbSe3 below T = 59 K

At temperatures below 59 K, coexistence of two types of satellite was observed in reciprocal lattice plane of b¹?c¹ as expressed by $\text{q}{}_1\text{= 0.24}\text{b}{}^1$ and $\text{q}{}_2\text{= 0.26}\text{b}{}^1\text{+0.50}\text{c}{}^1$. On the basis of nesting conditions by these q₁ and q₂, a feature of the Fermi surface for NbSe₃ is discussed.     

Hopping conductivity in amorphous carbon films

The electrical resistivity of amorphous carbon films getter-sputtered at 95°K is well fitted between 300 and 20°K by the relation $\text{? = ?}{}_0\text{exp}\text{[(T}{}_0\text{/T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{]}$ with T₀ ? 7 × 10⁷K. This behavior suggests a hopping conductivity very similar to that found in other amorphous semiconductors.     

Temperature dependent scattering from Cr impurities in Pd

The incremental resistivity Δ?(T) associated with small amounts (between 0.05 and 0.3 at% Cr) of Cr in Pd has been measured between 1.4 and 300 K and has been assumed to contain two principle contributions. The first decreases monotonically with increasing temperature, while the second consists of a rapid increase in Δ?(T) with increasing temperature between 15 and 60 K and has been attributed to conventional deviations from Matthiessen's rule (DMR). With the latter assumed to temperature independent above 70 K, Δ?(T > 70 K) has been fitted to

$\text{Δ?(T) = Ac + Bc 1n(T}{}^2\text{+ T}{}^2{}_{\mathrm{s}}\text{)}{}^{\mathrm{1/2}}$

yielding a concentration independent estimate of T_s ? 44 K. By comparing the experimental data with the extention of the above equation at temperatures below 70 K it is possible to estimate both the conventional DMR and the coefficient of the T² term predicted at low temperatures. While the former are in reasonable agreement with DMR observed in dilute non-magnetic Pd alloys, the T² coefficients measured in Δ?(T ? T_s) differ from their predicted values. Sources for this discrepency are discussed.     

A Mössbauer study of amorphous Fe40Ni40B20

Amorphous Fe₄₀Ni₄₀B₂₀ (VITROVAC 0040) alloy has been investigated using ⁵⁷Fe Mössbauer Spectroscopy. The Curie temperature T_c is found to be well defined and is 695 ± 1 K. The quadrupole splitting just above T_c is 0.64 mm sec^?1. The crystallization temperature is 698 ± 2 K, close to but definitely above T_c. The average hyperfine field H_eff(T) of the glassy state shows a temperature dependence of $\text{H}{}_{\mathrm{<mtext>eff</mtext>}}\text{(0)[1 ? B}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{(T/T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{? C}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{(T/T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{? …]}$ indicative of the existence of spin wave excitations. The values of $\text{B}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{C}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ are found to be 0.40 and 0.06, respectively, for T/T_c ? 0.72. At temperatures close to T_c, H_eff(T) varies as (1 ? T/T_c)^β where β is one of the critical exponents and its value is found to be 0.29 ± 0.02.     

Electron spin relaxation of irradiated ferroelectric KDP: K2SeO4

Electron spin resonance relaxation times were measured for the radiation induced radical ion SeO₄^3? in selenium doped KDP single crystals. The spin-lattice relaxation time was found to obey the relation $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>R</mtext>}}{}^{\mathrm{?1}}\text{= AT + BT}{}^5\text{∫}{}_0{}^{\mathrm{<mtext>\theta </mtext><mtext>2T</mtext>}}\text{x}{}^4\text{csch}{}^2\text{x}\text{d}\text{x}$ from 7 K to 200 K except in the neighborhood of the transition temperature where the data fit the expression T₁^?1 = T_1R^?1b_±T ? T_c^m± where θ is the Debye temperature and the plus and minus signs refer to data at temperatures above and below T_c respectively.     

Spontaneous birefringence and order parameter of KMnF3 below the 186°K transition point

The birefringence of KMnF₃ was measured in a temperature range between 130 and 186°K. It is shown that the birefringence is proportional to the square of displacement of F^- ion and fits closely to $\text{(T}{}_{\mathrm{a}}\text{?T)}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$ near the transition point, where T_a lies at about 1.5°K above the transition temperature. Values of the order parameter are determined at each temperature.     

Two-electron,one-photon transitions in nickel

The two emission lines, Kα₁α₃^h and Kα₂α₃^h resulting from the two-electron transitions $\text{1s}{}^{\mathrm{?2}}\text{→ 2s}{}^{\mathrm{?1}}\text{2p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ and $\text{1s}{}^{\mathrm{?2}}\text{→ 2s}{}^{\mathrm{?1}}\text{2p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ were resolved for elemental nickel. Their measured energies agree well with calculations. Their relative intensity $\text{I(Kα}{}_1\text{α}{}_3{}^{\mathrm{h}}\text{)/I(Kα}{}_2\text{α}{}_3{}^{\mathrm{h}}\text{) ≈}\text{3}\text{4}$ and their intensity relative to that of the Kα diagram lines is about 10^?4. This is some 10⁴ times larger than both theoretical results and the results of ion-atom collision experiments.     

Electron temperatures in Si-MOSFETs: Determination from broadband far infrared emission

Electron temperatures in n-inversion layers of (1 0 0)-Si-MOSFETs are measured as a function of the electric field by analysing the absolute intensities of the broadband thermal far infrared emission from the two-dimensional electron gas. The electron heating δT is proportional to the square root of the input power in the experimentally accessible range of 2 K ? ΔT ? 30 K at 4.2 K lattice temperature. Data in the whole electron concentration range (1 to 5 x 10¹² cm^?2) are presented resulting in a concentration-independent heating of $\text{ΔT/(eμE}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= (}\text{0.7 ± 0.2}\text{) x}\text{10}{}^{\mathrm{?2}}\text{Ks}\text{1}\text{2}\text{(}\text{eV}\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$. An increase of the electron heating (especially at high electron concentrations) is observed when a negative substrate bias is applied.     

Electrical transport and magnetic properties of Nd2(WO4)3

Measurements of the molar magnetic susceptibility (X_m) of a powdered sample of Nd₂(WO₄)₃ in the temperature range 300–900 K, and the electrical conductivity (σ) and dielectric constant (?$\text{)}\text{?}$ of pressed pellets of the compound in the temperature range 4.2–1180 K are reported. X_m obeys the Curie-Weiss law with a Curie constant C= 3.13 K/mole, a paramagnetic Curie temperature θ= ?60 K and a moment of Bohr magnetons, p= 3.49 for the Nd³⁺ ion. The electrical conductivity data can be explained in terms of the usual band model and impurity levels. Both the σ and ?$\text{\$}\text{?}$data indicate some sort of phase transition round 1025 K. The conductivity follows Mott's law $\text{σ = A exp (?B/T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{)}$ in the temperature range $\text{200 < T < 3000}\text{K with}\text{B = 45.00 (}\text{K}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{and}\text{A = 1.38 × 10}{}^{\mathrm{?5}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}$. The dielectric constant increases slowly up to 600 K, as is usual for ionic solids. The increase becomes much faster above 600 K, which is attributed to space-charge polarization of thermally generated charge carriers.     

Charge density wave commensurability in 2H-TaS2 and AgxTaS2

The charge density wave transition in 2H-TaS₂near 75 K has been observed to be incommensurate, using electron diffraction, with $\text{q}{}^1\text{= (}\text{0.338}\text{±}\text{0.002}\text{)a}{}^1{}_0$ along the 〈10.0〉 directions which, within the experimental uncertainty, remains temperature independent to about 14 K. Incommensurate charge density formation is also observed in Ag_xTaS₂ samples for $\text{x?}\text{0.26}$ with an increase in q¹ to $\text{(}\text{0.347}\text{±}\text{0.002}\text{)a}{}^1{}_0$ when x?0.26. Within the experimental error q¹ appears to be temperature independent to 25 K.     

Gravitational collapse in quantum mechanics with relativistic kinetic energy

It is proved that the quantum mechanical Hamiltonian $\text{H = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{N}}\text{(p}{}^2\text{+ m}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? κ Σ}{}_{\mathrm{i>j}}\text{|x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{|}{}^{\mathrm{?1}}$ for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^?1 (resp. $\text{N ≤ c}{}_{\mathrm{f}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). H is unbounded from below if N ≥ c_b^lκ^?1 (resp. $\text{N ≥ c}{}_{\mathrm{f}}{}^{\mathrm{l}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).     

Electron exchange between Fe2+ and Fe3+ ions on octahedral sites in spinels studied by means of paramagnetic Mössbauer spectra and susceptibility measurements

Mössbauer spectra were obtained of the paramagnetic spinels $\text{Zn}{}^{\mathrm{2+}}\text{|}\text{Zn}{}^{\mathrm{2+}}{}_{\mathrm{<mtext>(1?x)</mtext><mtext>2</mtext>}}\text{Ti}{}^{\mathrm{4+}}{}_{\mathrm{<mtext>(1+x)</mtext><mtext>2</mtext>}}\text{Fe}{}^{\mathrm{3+}}{}_{\mathrm{<mtext>(1?</mtext><mtext>x)</mtext>}}\text{Fe}{}^{\mathrm{2+}}{}_{\mathrm{x}}\text{|}\text{O}{}_4$ and susceptibilities were measured. The strong difference between the paramagnetic Fe²⁺ and Fe³⁺ spectrum, due to the different quadrupole splitting, is used for the distinction between the two species. At 300 K a superposition of the Fe³⁺ and the Fe²⁺ spectra is found for most of the iron and, in addition, some continuous absorption. The latter is strongest for equal Fe³⁺ and Fe²⁺ concentration $\text{(x =}\text{1}\text{2}\text{)}$ while it disappears towards the end members (Fe³⁺ only or Fe²⁺ only) as well as with decreasing temperature (between 78 and 200 K). From this it is concluded that it arises from thermally activated electron exchange, the frequency of which passes a “critical” value of ～10⁸ sec^?1 for increasing temperature. Paramagnetic susceptibilities are found to obey a Curie-Weiss law down to low temperatures. From the dependence of the asymptotic Curie temperature on the composition the magnetic interaction parameters J₁₁ = ?1.4 K, J₂₂ = ?3.3 K and J₁₂ = + 1.6 K for the Fe³⁺Fe³⁺, Fe²⁺Fe²⁺ and Fe³⁺Fe²⁺ interactions are derived. The experimental results are discussed in terms of a hopping model with an activation energy q ～- 0.12eV and a non-equivalence of the octahedral sites expressed by a varying potential energy difference U₀ between neighbouring sites. The continuous absorption at 300 K for $\text{x =}\text{1}\text{2}$ is attributed to about 17% of the iron on sites with U₀ running from 0 to ??0.06 eV. The ferromagnetic Fe³⁺, Fe²⁺ interaction (J₁₂) is attributed to electron transfer from localized Fe²⁺ ions to Fe³⁺ neighbours via a transfer integral b of the order of 0.05 eV. The magnitudes of J₁₂ and b are tentatively explained.     

Magnetization of amorphous alloys — Deviations from spin wave theory at low temperatures

Spin resonance measurements have been used to obtain the temperature dependence of the magnetization in (Fe_xNi_1?x)₇₅P₁₆B₆A?₃ alloys for 4 ? T ? 300K. With x = 0.5, spin wave theory is adequate to account for the observations. For x = 0.4 and 0.3 marked deviations from $\text{T}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ behavior are noted below ～ 70K and we propose a simple model to account for these deviations.     

Heat capacity and thermodynamic properties of α-Fe2O3 in the region 300–1050 K. antiferromagnetic transition

The heat capacity of synthetic α-Fe₂O₃ has been measured in the range 300–1050K by adiabatic shield calorimetry with intermittent energy inputs and temperature equilibration in between. A λ-type transition, related to the change from antiferro- to paramagnetism in the compound, is delineated and a maximum heat capacity of about 195 JK^?1 mole^?1 is observed over a 3 K interval around 955 K. Values of thermodynamic functions have been derived and C_P (1000K), [H⁰(1000K)-H⁰(0)], and [S⁰(1000K)-S⁰(0)] are 149.0JK^?1 mole^?1, 115.72 kJ mole^?1, and 252.27 JK^?1 mole^?1, respectively, after inclusion of earlier low-temperature results [X⁰ (298.15K)-X⁰(0)]. The non-magnetic heat capacity is estimated and the thermodynamic properties of the magnetic transition evaluated. The results are compared with spin-wave calculations in the random phase approximation below the Néel temperature and the Oguchi pair model above. An upper estimate of the total magnetic entropy gives 32.4JK^?1 mole^?1, which compares favorably with that calculated for randomization of five unpaired electron spins on each iron, ΔS = 2R ln 6 = 29.79 JK^?1 mole^?1 for α-Fe₂O₃. The critical exponent α in the equation $\text{C}{}_{\mathrm{m}}\text{= (}\text{A}\text{α}\text{) [(|T}{}_{\mathrm{<mtext>n</mtext>}}\text{?T|/T}{}_{\mathrm{<mtext>n</mtext>}}\text{)?1]}{}^{\mathrm{?\alpha }}\text{+ B}$ is ?(0.50±0.10) below the maximum and 0.15±0.10 above, for T_n = 955.0K. The high temperature tail is discussed in terms of short range order.     

Temperature dependence of the static dielectric constant of Rb2ZnBr4: Solitons in a modulated structure?

The static dielectric constant of Rb₂ZnBr₄ was measured as a function of temperature for a number of different single crystals. In a part of the samples a Curie-Weiss behaviour was observed at the lock-in transition from the incommensurate to the commensurate phase. Besides, in a few samples, a deviation of this behaviour was observed which can be ascribed to the appearance of solitons yielding a soliton density n_s proportional to $\text{(T?T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. At temperatures below T_c two new peaks are observed in the direction of the $\text{a}\text{-}\text{axis}$.     

A least upper bound on the superconducting transition temperature

It is rigorously shown that the superconducting transition temperature of any material for which the Eliashberg theory is valid must satisfy k_BT_c ? 0.2309 A, where A is the area under its electron-phonon spectral function α²F(ω). This relation is a least upper bound, not just an upper bound, in the sense that there is an optimal situation in which the equality holds. This occurs when the Coulomb pseudopotential parameter $\text{μ}{}^1$ is zero and the spectral function is the Einstein spectrum Aδ(ω ? 1.750 A). These results are generalized in an approximate, but sufficiently accurate, way to the case $\text{μ}{}^1\text{≠ 0}$ to obtain the more useful least upper bound $\text{k}{}_{\mathrm{<mtext>B</mtext>}}\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{? c(μ}{}^1\text{) A}$ and the corresponding optimal spectrum $\text{Aδ[ω ? d(μ}{}^1\text{)A]}$. Numerical results for the functions $\text{c(μ}{}^1\text{)}$ and d(μ¹) are presented for $\text{0 ? μ}{}^1\text{? 0.20}$. It is shown that the T_c's of many materials (including Nb₃Sn), for which experimental values of A and $\text{μ}{}^1$ are available, do not lie very far below the upper bound.     

Magnetic field dependence of red emission intensity of ruby at various temperatures

Application of a magnetic field perpendicular to the c-axis of a thin slice of pink ruby at low temperatures reduces the intensity of R-line and vibronic emission. At field intensity H = 6 kG the loss of vibronic emission exceeds 10%. The decay time decreases by a similar fraction. The method used for studying intensity involves on-off modulation of the field, and digital integration. A function which describes the observed fractional reduction of intensity is $\text{F(H) =}\text{AH}{}^2\text{(1 + BH}{}^2\text{)}$ where A and B are nearly constant below 77 K, but decrease rapidly between 100 K and 200 K. The function can be derived by assuming that radiationless transitions to the ground state occur with probability proportional to H² from low-lying vibronic states of ²E. Thermal excitation from these states to states in the neighborhood of ²T₁ is proposed as the mechanism for quenching the magnetic field effects.     

Parity violation in atoms in SO(3) gauge models

We have evaluated the parity-violation contribution in atoms in the framework of SO(3) gauge theory. Various hadronic models have been used: first, for simplicity, the unrealistic five-quark one, next, others involving three ordinary SU(3) triplets for which all unwanted strangeness-changing processes are suppressed, up to order $\text{Gα}\text{or}\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$. In the free quark approximation, we obtain quite similar parity-violation effects which are proportional to $\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$ (ΔM² is the difference of squared masses of leptons (M_X0² ? M_ν² = M_X0²), or of quarks (ΔM_q²)). Namely, in large atoms (Z ? 1) the electronic contribution which is proportional to

gives the largest effect ($\text{σ}{}_{\mathrm{?}}\text{,}\text{p}{}_{\mathrm{?}}\text{and}\text{m}{}_{\mathrm{?}}$are the spin, momentum operators and mass of the lepton). Parity-violating effects in SO(3) gauge models are ?10^?4 smaller than those evaluated in the Weinberg theory with a neutral parity-violating current and will remain undetectable in the near future.     

Nuclear matrix elements from L/K electron capture ratios in 59Ni decay

Using a recent theoretical method, the ratio of nuclear matrix elements $\text{R = (}{}^{\mathrm{v}}\text{F}{}^0{}_{220}\text{?√}\text{3}\text{2}{}^{\mathrm{A}}\text{F}{}^0{}_{221}\text{/}{}^{\mathrm{v}}\text{F}{}^0{}_{211}\text{)}$ was determined to be either 20.50^+0.35_?0.55 or 25.22^+0.28_?0.17 in the second-forbidden nonunique decay of 8 × 10⁴ y ⁵⁹Ni. These values of R were obtained from a value of L₃/K = 0.008 ± 0.002 found by subtracting the theoretical ratio $\text{(L}{}_1\text{+ L}{}_2\text{)}\text{K}$ = 0.113 (based on Q_PEC = 1070 ± 8 keV) from the total ratio L/K = 0.121 ± 0.002, which was measured with a reactor-produced, doubly-mass-separated ⁵⁹Ni source introduced as gaseous nickel-ocene, (C₅H₅)₂, into a wall-less, anticoincidence, multiwire proportional counter. The 854–1008 eV L and the 8.33 keV K peaks were measured simultaneously.