The elastic behaviour of the ternary zincblende structure semiconductor CuGe2P3

A single crystal has been grown of CuGe₂P₃, a ternary semiconductor with a zincblende structure in which the copper and germanium atoms are randomly distributed on the cation sites. The second order elastic constants measured by the ultrasonic pulse echo overlap technique (C₁₁ = 13.66, C₁₂ = 6.17, C₄₄ = 6.66 and bulk modulus B = 8.67 in units of 10¹⁰Nm^?2 at 291 K) are closely similar to those of GaP and conform well to Keyes' correlation for zincblende structure crystals. The hydrostatic pressure derivatives of the second order elastic constants ($\text{?C}{}_{11}\text{?P}\text{= 4.40}$, $\text{?C}{}_{12}\text{?P}\text{= 3.9}$, $\text{?C}{}_{44}\text{?P}\text{= 0.93}$ and $\text{?B}\text{?P}\text{= 4.07}$) and the third order elastic constants (C₁₁₁ = ? 8.45, C₁₁₂ = ? 3.49, C₁₂₃ = ? 1.13, C₁₄₄ = ? 2.82, C₁₅₅ = ? 1.44 and C₄₅₆ = ? 0.69 in units of 10¹¹Nm^?2) also resemble those of GaP: even the anharmonicity of the long wavelength acoustic modes of this ternary semiconductor resembles that of its binary “parent” compound. The positive signs of the hydrostatic pressure derivatives and the negative signs of the third order elastic constants show that the acoustic modes at the long wavelength limit stiffen under pressure, an effect which is quantified here by computation of the mode Grüneisen parameters, which are all positive. The harmonic and anharmonic force constants, obtained in the valence force field model, fit well into the pattern shown by related zincblende structure compounds: the ratio ($\text{β}\text{α}$) for bond bending (β) to stretching (α) force constants is greater than 4:1; the dominating anharmonic force constant is γ: most of the anharmonicity is associated with nearest neighbour atoms. Analysis of the temperature dependence of the elastic constants on the basis of a simple anharmonic model again emphasises the similarity between the elastic behaviour of CuGe₂P₃ and GaP. The thermal expansion of CuGe₂P₃ varies almost linearly with temperature between 291 K and 1000 K, the linear coefficient of thermal expansion α being 8.21 ± 0.02 × 10^?6 °C^?1. The similar lattice parameters and elastic behaviour of CuGe₂P₃ and GaP indicate that semiconducting devices made of epitaxial deposits of CuGe₂P₃ on a GaP substrate should prove to be almost strain-free.     

Structure of cyclobutanone

The microwave spectra of the ¹⁸O and the α,α,α′,α′-tetradeuterated isotopic species of cyclobutanone have been investigated. Structural parameters determined are $\text{r}{}_{\mathrm{<mtext>CO</mtext>}}\text{= 1.204 ± 0.006}\text{A}\text{?}$, , ∠ H_αCH_α = 109.2 ± 1° with the methylene group tilted toward the carbonyl group by 4.6 ± 0.8°.     

Specific heat and resistivity of GdSb and HoSb above the néel temperature

The specific heat C_P is found to vary as $\text{dR}\text{dT}$ in the critical region above T_N for the antiferromagnets GdSb and HoSb. This correspondence holds despite a dramatic difference between the two systems in the strength of the divergence C_P = A?^?α, $\text{? =}\text{(T ? T}{}_{\mathrm{N}}\text{)}\text{T}{}_{\mathrm{N}}$, where for HoSb we find α = 0.83 ± 0.10 while for GdSb α = 0.20 ± 0.10.     

On the difference between pp and pp topological cross sections up to 100 GeV/c

New 100 GeV/c$\text{p}$p data are used to find moments of the difference between the $\text{p}$p and pp topological cross sections. The mean multiplicity for annihilations at 100 GeV/c is estimated to be 9.06 ± 0.56, and the value of the quantity 〈n〉/D to be 2.75 ± 0.33. It is shown that $\text{R}{}_{\mathrm{n}}\text{= {σ}{}_{\mathrm{n}}\text{(}\text{p}\text{p) ? σ}{}_{\mathrm{n}}\text{(pp)}/σ}{}_{\mathrm{n}}\text{(pp)}$ appears at 100 GeV/c to have acquired an asymptotic form, R_n = s^?αβⁿ, with α and β constant.     

Determination of the α decay parameter of ω-

A determination of the decay α parameter of the omega^? → K^? λ decay mode on the basis of fifteen omega-events from K^?p interactions at 10 GeV/c yields the value $\text{αomega = -0.66}{}^{\mathrm{+36}}{}_{\mathrm{?0.30}}$.     

Nuclear size dependence of inclusive particle production

The inclusive production of π⁺, π^?, K⁺, K^?, p and $\text{p}$ for protons incident on carbon and tungsten targets was studied at the Internal Target Area of the Fermilab. We assume an A^α dependence for the inclusive cross sections and report here on the variation of α with incident momentum, transverse momentum and particle species.     

Inelastic scattering and satellite fine structure in the high-resolution uv photoelectron spectrum of CS2

The outer valence region in CS₂ has been studied by high-resolution UV photpelectron Spectroscopy. The spectra reveal detailed vibrational structure in the X$\text{\$}\text{?}$²Π_g, A$\text{\$}\text{?}$²Π_u, B$\text{\$}\text{?}$²Σ⁺_u and C$\text{\$}\text{?}$²Σ⁺_g bands. Some of the fine-structure peaks in the X$\text{,}\text{?}$B$\text{\$}\text{?}$and C$\text{\$}\text{?}$bands are shown to be pressure-dependent. The reason for the pressure dependence is assumed to be inelastic scattering of electrons emitted in the adiabatic transitions. It is established that the two CI satellite bands present in the He(I)-excited spectrum contain vibrational structure.     

Second order QCD contributions to thrust and spherocity

In e⁺e^? annihilation there are regions of high spherocity S and low thrust $\text{T(S >}\text{16}\text{3π}{}^2\text{and}\text{T <}\text{2}\text{3}$ in which these distributions are given in QCD perturbation theory by the subprocesses e⁺e^? → qq?GG and e⁺e^? → qq?qq? neglecting only cubic and higher order terms in α_S. We give the corresponding QCD predictions which suggest that the calculable corrections to these variables may be slowly convergent.     

A spectrum of rhenium oxide

The arc emission spectrum of the ReO molecule has been photographed in the region 590–860 nm and three bands of a single electronic transition have been rotationally analyzed. The separation of lines of the isotopic molecules ¹⁸⁵ReO and ¹⁸⁷ReO leads to the conclusion that the vibrational assignments for these bands are 1-0, 0-0, and 0–1. It is conceivable that an electronic isotope shift of ～0.08 cm^?1 exists. The following vibrational and rotational data (cm^?1) have been determined: ν₀(0-0) = 14 038.42, $\text{Δ}\text{G′(}\text{1}\text{2}\text{) = 867.85}$, $\text{Δ}\text{G″(}\text{1}\text{2}\text{) = 979.14}$; B′_e = 0.3889, α′_e = 0.0019, B″_e = 0.4257, α″_e = 0.0043. It is concluded that Λ′ ? Λ″ = +1 with Λ″ ≥ 2.     

Ω− produced in K−p reactions at 4.2 GeV/c

Forty $\text{Ω}{}^{\mathrm{?}}$ events have been observed in a large (133 events/βb) experiment at 4.2 GeV/c incident K^? momentum. Thirty nine of the events come from the three-body reaction $\text{K}{}^{\mathrm{?}}\text{p}\text{→Ω}{}^{\mathrm{?}}\text{K}{}^{\mathrm{+}}\text{K}{}^0$. The $\text{Ω}{}^{\mathrm{?}}$ is mainly produced in the forward hemisphere (direction of the incident K^?). The lifetime is measured to be τ = (0.75 _+0.14?0.11 × 10^?10 sec substantially less than the Particle Data Group value of (1.3 _?0.3^+0.2) × 10^?10 sec. The mass is determined to be 1671.7 ± 0.6 MeV, in good agreement with other determinations. The decay asymmetry parameter α (for the decay mode $\text{Ω}{}^{\mathrm{?}}\text{→ Λ}\text{K}{}^{\mathrm{?}}$) is found to be ?0.2 ± 0.4.     

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.     

Attenuation and dispersion of first sound in a 19.4% 3He-4He mixture near the λ-transition

Attenuation α and dispersion D=u(ω) ? u(0) of first sound have been measured in a 19.4% ³He-⁴He mixture for frequencies $\text{2.25}\text{kHz}\text{?}\text{ω}\text{2π}\text{?594}\text{kKz}$, and at temperatures 1 μK?|T ? T_λ|?10 mK. They are interpreted as arising from a relaxation and a fluctuation process.     

The irreducible Raman scattering tensor operator for the 32 crystallographic point groups and its application to the resonance and electronic Raman effect

The irreducible components of the Raman scattering tensor operator $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ under the symmetry of a general point group are calculated. The unitary transformations U(Γ_γΓ_ksΓ_k′s′, ρσ) from the Cartesian $\text{α}\text{?}{}_{\mathrm{\rho \sigma }}$ and spherical $\text{α}\text{?}{}_{\mathrm{Q}}{}^{\mathrm{K}}$ components, respectively, to the irreducible components $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ for the 32 crystallographic point groups are collected in tables. As an example the unitary transformation U(Γ_γΓ_ksΓ_k′s′, ρσ) is used to discuss the behavior of the scattering tensor in a resonance Raman experiment. With the help of the general formalism the scattering tensor for electronic Raman transitions of transition metal ions is calculated. As an example the scattering tensors of electronic Raman transitions within the ⁵T₂ state of the high-spin trigonal distorted octahedral Fe²⁺ are calculated and the refinement of the selection rules is discussed.     

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.     

Effect of hexadecapole deformations on i132 orbits and pickup cross sections in the tungsten nuclei

Previous (d,t) and (τ,α) cross sections to $\text{13}\text{2}{}^{\mathrm{+}}$ states in odd-mass tungsten nuclei have been interpreted in terms of moderate hexadecapole deformations (?₄≈0.06) while a recent Coulomb excitation measurement has suggested a much larger value for ¹⁸²W. We have calculated the pickup spectra and show that in fact the data can be successfully interpreted with a wide range of ?₄ values from ≈0.06 to ≈0.16.     

NMR investigation of the structure of NiZrF6·.6H2O at low temperatures

Previous studies have shown that NiZrF₆.6H₂O can be described by an axial spin Hamiltonian with parameters g = 2.33 and $\text{D}\text{k}\text{= ?3.14}\text{K}$, and exhibits ferromagnetic ordering at T_c = 164mK. Our room temperature X-ray measurements confirm that NiZrF₆·.6H₂O is isomorphous with NiSnCl₆·.6H₂O and give lattice parameters of $\text{a = 6.55}\text{A}\text{?}$ and α = 96°09′. Proton NMR measurements show that there exist important molecular motions at room temperature and that the space group remains $\text{R}\text{3}$ down to liquid helium temperatures. The positions of all twelve protons have been determined and are found to lie on a sphere of radius 2.9 Å centered on the nickel ion.     

Elastic scattering of α particles on light nuclei at Pα=7 GeV/c

Elastic scattering differential cross sections of α particles have been measured at P_α=7.0 GeV/c ($\text{T}\text{N}\text{=1.05}\text{GeV}$) on ¹H, ²H, ³He and ⁴He target up to a momentum transfer of ～4 (GeV/c)². A preliminary interpretation of the data is given in the framework of the Glauber theory.     

Turbulent diffusion for the radial twist map

An analytical tool is given to study the statistical properties of the radial twist map, X_n+1 = X_n + α(Y_n+1) and Y_n+1 = Y_n + Af (X_n), with arbitrary rotation number α(Y) and arbitrary periodic force f(X). The case for which f(X) = sin 2 πX and with arbitrary α is treated in the region of large A. The turbulent diffusion coefficient D for the chaotic orbit relaxes as $\text{t}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ to $\text{A}{}^2\text{4}$, except for the case of the standard map, where the eventual value of D is different from $\text{A}{}^2\text{4}$.     

On (πμ) atoms produced in K0L decay

The branching ratio for producing (πμ) atoms in K⁰_L decay is calculated. Using the approximate solution of the Bethe-Salpeter equation for the (πμ) atom, the S-matrix element of this process is written in a more precise form than that obtained intuitively. Furthermore, all corrections of $\text{O}\text{(α) (α =}\text{e}{}^2\text{4π}\text{)}$ are considered. As a result, the branching ratio may be used to determine the form factor ζ = f_?(0)/f₊(0) of K⁰_L.