Non-analyticity of the entropy and Nernst's law in random spin systems

It is shown explicitly for a soluble model that a random spin system can have an entropy which is non-analytic at (H = 0, T = 0), with $\text{(}\text{?S}\text{?H}\text{)}{}_{\mathrm{H=0}}$ and/or $\text{(}\text{?}{}^2\text{S}\text{?H}{}^2\text{)}{}_{\mathrm{H=0}}$non-vanishing in the T → 0 limit, while nevertheless Nernst's law is satisfied.     

Reflection of long waves by interfaces

We derive comparison identities for waves satisfying the equation d²Ψ/dz²+q²(z)Ψ=0. One of these identities is used to show that to second order in the product (wavenumber component normal to interface) × (interface thickness), the reflection amplitude is given by $\text{r=(1?2q}{}_1\text{q}{}_2\text{l}{}^2\text{)}\text{(q}{}_1\text{?q}{}_2\text{)}\text{(q}{}_1\text{+q}{}_2\text{)}$, where l is a legnth determined by the deviation of the interface profile from a step, and q₁, q₂ are the normal components of the wave numbers in media 1 and 2 on either side of the interface. For the continuous interfaces discussed, l is about two-fifths of the 10–90 interface thickness. The corresponding formula for the transmission amplitude is $\text{t=(1+}\text{1}\text{2}\text{(q}{}_1\text{?q}{}_2\text{)}{}^2\text{l}{}^2\text{)}\text{2q}{}_1\text{(q}{}_1\text{+q}{}_2\text{)}$.     

Relativistic correction to the deuteron magnetic moment and angular condition

The relativistic correction (RC) to the deuteron magnetic moment is calculated using the light-cone dynamics. The restrictions imposed by the angular condition on the electromagnetic current operator of the deuteron are discussed in detail. It is shown that the additive model for the current operator of interacting constituents is consistent with the angular condition only for the two first terms of the expansion of the “good” current component $\text{j}{}_{\mathrm{+}}\text{=}\text{1}\text{2}\text{(j}{}_0\text{+ j}{}_{\mathrm{<mtext>z</mtext>}}\text{)}$ in powers of the momentum transfer q. The RC to μ_d is expressed through the matrix element of the “good” component j₊ and is found to be equal to $\text{(0.6–0.8) × 10}{}^{\mathrm{?2}}\text{e}\text{h}\text{?}\text{/2m}{}_{\mathrm{<mtext>p</mtext>}}\text{c}$ for realistic NN potentials. Taking account of RC decreases essentially the discrepancy between the theoretical and experimental values of μ_d. Possible solutions of the angular condition for squared q-terms of the j₊ current component are also discussed.     

Non-equilibrium structure factor for the disordering of adsorbed monolayers

We consider the non-equilibrium, time-dependent elastic-scattering structure factor S(q,t), for the disordering of an ordered overlayer, initially in equilibrium at temperature T_I and characterized by the structure factor S(q,0)=x(q,T_I, upon a sudden increase in temperature T_I→T_F at constant coverage, such that the adsorbates equilibrate at T_F in a disordered phase. The initial decay of a peak in x(q,T_I) proceeds exponentially in time, $\text{exp}\text{(−}\text{t}\text{τ}{}_{\mathrm{q}}\text{)}$, where τ_q is a wavevector-dependent lifetime, before it crosses over to a power-law, t⁻¹ decay. When x(q,T_I) is peaked at the boundaries of the Brillouin zone (BZ), the peak approximately maintains its shape in q-space as it decays exponentially. Except near the center of the BZ, after the peak has decayed sufficiently, the dependence of S(q,t) on q is as though the spins quasi-equilibrate to the equilibrium structure factor associated with T_F, x(q,T_F), in that the ratio $\text{S(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ is independent of q, is dependent on time, approaching unity as t⁻¹ for large t. For systems exhibiting an initial peak for q ≈ 0, the peak decays exponentially but does not preserve its shape, since τ_q strongly depends on q, diverging as q⁻² for q→0. For these systems too, away from the center of the BZ, $\text{S}\text{(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ rapidly evolves to a slowly decaying function of $\text{t}\text{t}{}_{\mathrm{w}}$, independent of q. In this case, however, the characteristic time scale, t_w, is anomalously long, proportional to ξ², where ξ is the correlation length associated with the initial state. This behavior of t_w can be related to the random walk of domain boundaries.     

Can the optical excitations of surface plasmons be used to study (liquid) metal surfaces?

The surface plasmon dispersion relation is obtained for a metal with a free electron density given by N(z) = N_b + (N_s ? N_b) exp $\text{(}\text{?z}\text{a}\text{)}$ for z ? 0 and N = 0 for z < 0. We have used a local theory which includes the effects of retarded fields and found the dispersion relation to be sensitive to the parameters $\text{(N}{}_{\mathrm{s}}\text{? N}{}_{\mathrm{b}}\text{)}\text{N}{}_{\mathrm{b}}$ and a, which characterize our density profile.     

Free energies of the spherical model of a spin glass

Free energies g(m, m_s) and f(m, q) of the spherical spin glass (SG) model due to Kosterlitz et al. are calculated explicitly as functions of the uniform magnetization m, and SG order parameter m_s and the Edwards-Anderson order parameter q. It is shown that g(0, m_s) and f(0, q) below the transition temperature T_g are constant in the ranges 0 ≦ m_s ≦ m_s⁰ and 0 ≦ q ≦ q₀ respectively, where $\text{q}{}_0\text{= (1 -?}\text{T}\text{T}{}_{\mathrm{g}}\text{) = m}{}^2{}_{\mathrm{s}}{}^0$. The proper equilibrium values of m_s( = m_s⁰) and q( d=q₀) are then fixed from the inspection of their behaviors under infinitesimal uniform field proproportional to N^-a($\text{a ≧ 0}$).     

Long-lived non-equilibrium population of Fe3+ electronic states after the K-capture of 57Co

Mössbauer emission spectra of a frozen aqueous solution of ⁵⁷CoCl₂ show contributions from the $\text{S}{}_{\mathrm{z}}\text{= +}\text{5}\text{2}$ and the $\text{S}{}_{\mathrm{z}}\text{= +}\text{3}\text{2}$ Zeeman levels of Fe³⁺ ions at T = 4.2 K in H ? 30 kG. The K-capture results in a non-equilibrium state of relaxation time comparable to the lifetime of the nuclear excited state (～ 10^?7 s).     

Inclusive π electroproduction in the deep inelastic region

Using 20.5 GeV electrons on protons, we measured inclusive π⁰'s (of transverse momentum, p_T, from 0 to 1.4 GeV/c) produced by virtual photons of energy, ν, from 4 to 16.5 GeV and four-momentum squared, q², from ?1.8 to ?8.5 (GeV/c)². Comparing with charged pion data, we find , supporting the quark model. Photon knockout of a quark is favored as the interpretation of these data because of scaling in z = E_π/ν and similarity in z-dependence of other pion production data. Consistent with this interpretation are the dependence of 〈p_T〉 on q², the azimuthal dependence, and fits to the constituent interchange model. We also observe a possible p_T^?4 dependence at large |q²| over a limited p_T range.     

Investigation of the central component of SrTiO3 by neutron scattering with eV resolution

We studied the energy width and the width in reciprocal space Δq of the central mode of SrTiO₃ above T_c. At T_c+4° we observed an energy width of about 6×10^?7 eV. If the measured Δq is interpreted by a correlation length $\text{Δq}{}^{\mathrm{?1}}\text{= ξ = ξ}{}_0\text{?}{}^{\mathrm{<mtext>?</mtext><mtext>2</mtext><mtext>3</mtext>}}$ we obtain $\text{ξ}{}_0\text{= 75}\text{A}\text{?}$.     

Temperature dependence of dispersive hopping transport and diffusion in disordered solids

The time- and temperature-dependent drift mobility μ_d for dispersive transients in disordered solids is $\text{μ}{}_{\mathrm{d}}\text{(T,t) =}\text{L}\text{Et}{}_{\mathrm{T}}$ in terms of distance L, field E and transit time t_T. Since current I ∝ tsu?(1?α) for t <_Tand 0<α<1 by Scher-Montroll theory for hopping among localized states, it follows that $\text{μ}{}_{\mathrm{d}}\text{(T) = α[μ}{}_{\mathrm{d}}\text{(T,t)]}{}^{\mathrm{\alpha }}\text{(}\text{L}\text{Eτ}\text{)}{}^{\mathrm{1?\alpha }}$ where τ≈ 10^?13s is estimated. Further $\text{μ}{}_{\mathrm{d}}\text{(T) ∝ exp (}\text{?Δ}{}_0\text{KT}\text{)}$ and the activation energy Δ₀ is time independent. On this basis Δ for the carbazole polymers is ca. zero, that for a-Se is ca. 0.05 eV, and that for a-As₂Se₃ is 0.35 eV rather than 0.5, 0.3 and 0.6 eV respectively on a phenomenological basis for μ_d(T,t). Trap-controlled hopping transport may be excluded. Time-resolved optical studies of excess carrier recombination supplement mobility measurements in a-Si:H and a-As₂Se₃ as well as other systems. Combined results suggest a dielectric response mechanism in which the time-dependent hopping frequency of localized carriers ν ∝ t^α?1 arises from distortion of the medium at localization sites. This is satisfied by Δ(T,t) = Δ₀+(1?α)KTT ln(t/τ) where τ is the mean initial localization time of the carrier, 10^?13?10^?12s, Δio is the height of the barrier at T, and 0<α<l. Consequently ν = ν₀(t/τ)^α?1 exp(frsol|?Δ₀/KT) which applies also to bimolecular recombination.     

Variational principle for t-dependent classical Hamiltonian systems

For a non-conservative, classical system described by Lagrangian L(q?, q_i, t), the functional $\text{Z = ?}{}^{\mathrm{T}}{}_0\text{L}\text{d}\text{t + KT}$, where K is constant, is stationary with respect to variations in q_i(t) and T, given suitable boundary conditions. In the conservative case, for systems with a single periodic coordinate, this variational procedure reduces to that given by Luttinger and Thomas.     

The law of corresponding states for metals

Using the similarity of the effective potentials seen by ions in metals a reduced phonon equation of state is derived. It is shown that the melting point T_m(0) and the atomic volume Ω₀ at T = 0 K and at p = 0 are suitable macroscopic parameters for scaling ? and σ characterizing the interatomic potentials of metals having similar structures. The temperature and pressure dependence of thermodynamical quantities reduced with the above parameters are discussed and the results are compared with the experiment. It is shown that the pressure dependence of the reduced thermodynamic quantities can be described by the pressure dependence of the scaling parameters T_m(p) and Ω₀(p).The general form of the reduced equation of state (containing the electronic contributions as well) obtained gives that the reduced pressure is a universal function of the following reduced variables: the volume, temperature, de Broglie wavelength, Gibbs free energy of electrons $\text{3}\text{5}\text{zE}{}_{\mathrm{fo}}\text{?}$ (E_fo is the Fermi energy at T = 0 K) and depe of the valence z as well. It is shown that $\text{E}{}_{\mathrm{fo}}\text{?}$ is a function of $\text{Ω}{}_{\mathrm{o}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ and $\text{(}\text{E}{}_{\mathrm{fo}}\text{/?}\text{)Ω}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is approximately constant within the same sub-group of the periodic table.     

Subject index for volume 88

The emission and excitation spectra of the aromatic thioketone xanthione have been measured in Shpolskii matrices at 15 K. Under these conditions a sharp and rich vibrational structure is observed in the lowest triplet and the first and second excited singlet states. The phosphorescence excitation spectrum places the origin of the T₁ ← S₀ transition at 15 143 cm^?1, while that of the $\text{S}{}_1\text{(n, π}{}^1\text{) ← S}{}_0$ absorption is tentatively assigned to the band at 16 093 cm^?1. The phosphorescence spectrum, which shows only a weak CS stretch vibrational band, is dominated by ring vibrations. In accordance with the previous analysis of ODMR measurements, it is suggested that T₁ and T₂ states are energetically very close, thereby resulting in a lowest triplet state of heavily mixed n, $\text{π}{}^1\text{-π}$, $\text{π}{}^1$ character. No mirror-image relationship is found between the relatively strong S₂ → S₀ fluorescence and the excitation spectrum of the $\text{S}{}_2\text{(π, π}{}^1\text{) ← S}{}_0$ transition. The latter is dominated by a long, pronounced 336-cm^?1 progression.     

Molecular structure of phosgene as studied by gas electron diffraction and microwave spectroscopy: The rz structure and isotope effect

The r_z structure of phosgene has been determined by a joint analysis of the electron diffraction intensity and the rotational constants as follows: $\text{r}{}_{\mathrm{z}}\text{(}\text{CO}\text{) = 1.1785 ± 0.0026}\text{A}\text{?}$, $\text{r}{}_{\mathrm{z}}\text{(}\text{CCl}\text{) = 1.7424 ± 0.0013}\text{A}\text{?}$, ∠_z;ClCCl = 111.83 ± 0.11°, where uncertainties represent estimated limits of experimental error. The effective constants representing bond-stretching anharmonicity have been obtained from an analysis of the isotopic differences in the r_z structure: $\text{a}{}_3\text{(}\text{CO}\text{) = 2.9 ± 0.9}\text{A}\text{?}{}^{\mathrm{?1}}$, $\text{a}{}_3\text{(}\text{CCl}\text{) = 1.6 ± 0.4}\text{A}\text{?}{}^{\mathrm{?1}}$. The equilibrium bond distances have been estimated from the r_z structure for the normal species and from the anharmonic constants to be $\text{r}{}_{\mathrm{e}}\text{(}\text{CO}\text{) = 1.1756 ± 0.0032}\text{A}\text{?}$, $\text{r}{}_{\mathrm{e}}\text{(}\text{CCl}\text{) = 1.7381 ± 0.0019}\text{A}\text{?}$.     

Study by brillouin scattering of the C33 constant of thiourea submitted to an electric field

The C₃₃ constant is discontinuous for the lock-in transition at T₁ = 169 K. The variation ΔT₁ of the temperature of transition is a linear function of the applied electric field E and we find $\text{d}\text{T}{}_1\text{d}\text{E}\text{=0.82 deg.cm kV}{}^{\mathrm{?1}}$.Above a mean field E = 10 kV cm^?1 the transition observed for a first heating spreads on several degrees because damages appear in the incommensurate phase and the electric field becomes inhomogeneous.The results obtained at low fields are in very good accordance with the value of $\text{d}\text{T}{}_1\text{d}\text{E}$ calculated from the Clapeyron formula.Taking into account of the incommensurability of the phase above T₁, it can be shown that

$\text{dT}{}_1\text{dE}\text{=}\text{C}\text{2πP}{}_{\mathrm{o}}\text{3}\text{3}\text{?}\text{2}$

The knowledge of the spontaneous polarisation P₀ gives for the Curie constant C = 2.1 × 10³ K in qualitative agreement with the value deduced from measurements of the dielectric constant in the ferroelectric direction.     

“Forbidden” rotational spectra of symmetric-top molecules: PH3 and PD3

A millimeter-wave spectrometer having a sensitivity of 4 × 10^?10 cm^?1 in the 2-mm region has been constructed for observation of extremely weak millimeter-wave spectra of gases. It has been used to measure J → J, K = 0 ← 3 transitions in PH₃ and J → J, K = 0 ← 3 as well as K = ±1 ← ±4 transitions in PD₃. The B₀ and C₀ spectral constants (in MHz) are: for PH₃, B₀ = 133 480.15 ± 0.12 and C₀ = 117 488.85 ± 0.16; for PD₃, B₀ = 69 471.10 ± 0.03 and C₀ = 58 974.37 ± 0.05. The effective ground-state values obtained for the bond angle and bond length are: for PH₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.420}{}_0$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.34}{}_5$; for PD₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.417}{}_6$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.35}{}_9$. The corresponding zero-point-average values were calculated to be: for PH₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4269}{}_9\text{± 0.0002}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.228}{}_7$; for PD₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4226}{}_5\text{± 0.0001}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.256}{}_7\text{± 0.004}$. For both species, the equilibrium values are $\text{r}{}_{\mathrm{e}}\text{(}\text{A}\text{?}\text{) = 1.4115}{}_9\text{± 0.0006}$ and $\text{α}{}_{\mathrm{e}}\text{(}{}^{\mathrm{o}}\text{) = 93.32}{}_8\text{± 0.02}$.     

A model for phase transitions in Tetrathiafulvalene-Tetracyanoquinodimethane (TTF-TCNQ)

The observed phase transitions in Tetrathiafulvalene-Tetracyanoquinodimethane (TTF-TCNQ) are discussed using a simple model for the interchain coupling of charge density waves. Estimates based on Coulomb energies show that for 38 K < T < 49 K the components $\text{q}{}_{\mathrm{x}}\text{=}\text{π}\text{a}\text{+ q′}{}_{\mathrm{x}}$ and q_z of the wave vector associated with the charge density wave satisfy $\text{q}{}_{\mathrm{z}}\text{c}\text{q′}{}_{\mathrm{x}}\text{a?0.1}$, with $\text{q′}{}_{\mathrm{x}}\text{a～(T}{}_2\text{? T)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and T₂ = 49 K. A possible mechanism for the first order transition at 38 K is proposed. The results are compared with neutron and X-ray scattering and with isotope shifts of the transition temperatures.     

Microwave spectra of deuterated ethylenes: Dipole moment and rz structure

The pure rotational spectra of three deuterated ethylenes, CH₂CD₂, CH₂CHD, and cis-CHDCHD, were observed by microwave spectroscopy, and the rotational and centrifugal distortion constants were determined precisely. The dipole moment of CH₂CD₂ was calculated from the Stark effects to be 0.0091 ± 0.0004 D. From the observed rotational constants the average structure was calculated to be $\text{r}{}_{\mathrm{z}}\text{(CC)}\text{= 1.3391 ± 0.0013}\text{A}\text{?}$, $\text{r}{}_{\mathrm{z}}\text{(CH)}\text{= 1.0869 ± 0.0013}\text{A}\text{?}$, θ_z(CCH) = 121.28 ± 0.10°, and $\text{r}{}_{\mathrm{z}}\text{(CH)}\text{- r}{}_{\mathrm{z}}\text{(CD)}\text{= 0.00137 ± 0.00037}\text{A}\text{?}$, where the errors include one standard deviation in the fitting and errors due to an uncertainty (±0.03°) in θ_z(CCH) - θ_z(CCD).     

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.