Hall to drift mobility ratio in Ga1−xAlxAs alloys

Hall concentration measurements as a function of temperature ($\text{750 ? T ? 77}\text{K}$) on n-type epitaxial layers of Ga_1?xAl_xAs in the composition range $\text{0 ? x ? 0.78}$, have been used to evaluate the composite dependence of the Hall to drift mobility ratio in this alloy at 300 K. This ratio is found to be close to unity for alloy compositions $\text{0 ? x ? 0.25}$ and $\text{0.6 ? x ? 0.78}$, but attains a maximum value of 3.8 at x = 0.42 due to the multiconduction Hall effect.     

Evolution of the density for a chaotic map

For the discrete-time map x_t+11 = 4x_t(1?x_t) an exact, explicit expression is given for the time-dependent density r_t (x) evolving from a uniform initial density on (0,1). As t → ∞, r_t(x) approaches the known invariant density $\text{r(x) = 1/[π}\text{x(1?x)}\text{]}$.     

Lattice dynamics study of the solid solution (Bi1−xLax) FeO3 by i.r. spectroscopy

By i.r. absorption spectral measurements, (Bi_1?xLa_x) FeO₃ solid solution is shown to have phase transitions near x = 0.20; 0.40; 0.75, the range $\text{0.20?x?0.40}$ being of an intermediate nature.     

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.     

Electrical conductivity of (Bi,Pb)2MO4 (M = Pd,Pt) linear chain compounds

Partial oxidation of Pd in Bi₂PdO₄ is achieved by substitution of Pb²⁺ for Bi³⁺ up to Bi₁₉₁Pb₀₀₉PdO₄, partial oxidation is necessary to stabilize the isostructural Pt compound, Bi_1?xPb_xPtO₄ within the range 0.33 ? x ? 0.52. In both cases, the tetragonal cell c parameter, therefore metal-metal distance $\text{(d}{}_{\mathrm{<mtext>M?M</mtext>}}\text{=}\text{c}\text{2}\text{)}$, decreases linearly with increasing mean oxidation degree (MOD) of transition metal atom For the insulator B1₂CuO₄, no substitution occurs Powder electrical conductivity measurements of the partially oxidized compounds show that these materials are semiconductors Platinum compounds exhibit relatively high conductivities $\text{(σ?10 (Ω}\text{cm}\text{)}{}^{\mathrm{?1}}\text{)}$ and low activation energies (?0 02 eV) with small variations with x Palladium compounds exhibit lower conductivities which linearly increases with MOD These electronic properties are comparable with those of the most one-dimensional Pt or Pd chain conductors.     

Positive cones in enveloping algebras

The concept of strong ordering on enveloping algebras of finite-dimensional Lie algebras is introduced and studied as a generalization of the corresponding notion for the commutative polynomial algebra. A linear functional f on an enveloping algebra $\text{E}$ (G) is called strongly positive if f(x) ? 0 for all x ? $\text{E}$(G) which are mapped on positive operators for all G-integrable irreducible representations of $\text{E}$(G). We prove that for each real connected Lie group G ≠ R₁ there are positive, not strongly positive, linear functionals on $\text{E}$(G). A non-commutative problem of moments is defined. It has a solution iff the corresponding linear functional is strongly positive.     

Angular distributions and structure functions from two-jet events at the CERN SPS pp collider

The two-jet cross section measured in the UA1 apparatus at the CERN $\text{p}\text{p}$ Collider has been analysed in terms of the centre-of-mass scattering angle θ and the scaled longitudinal parton momenta x₁ and x₂. The angular distribution dσ/d cos σ rises rapidly as cos → 1, independent of x₂ and x₂, as expected in vector gluon theories (QCD). The differential cross section in x₁ and x₂ is consistent with factorization and provides a measurement of the proton structure function $\text{F(x) = G(x) +}\text{4}\text{9}\text{[Q(x) +}\text{Q}\text{(x)]}$ at values of the four-momentum transfer squared, -t? ≈ 2000 GeV². Over the range x = 0.10?0.80 the structure function shows an exponential x dependence and may be parametrized by the form F(x) = 6.2 exp (?9.5x).     

Step algebras of semi-simple subalgebras of Lie algebras

For each pair (G,K) where G is a complex finite-dimensional Lie algebra and K a semi-simple subalgebra of G, we construct an associative algebra (step algebra) $\text{Y}$ (G,K) and a homomorphism i_*: $\text{Y}$ (G,K)→E(G) is the enveloping algebra of G. $\text{Y}$ (G,K) has the following properties: (1) If V is any G-module and x ? V a K-maximal vector, then sx = i_* (s)x is K-maximal for any s ? $\text{Y}$ (G,K); (2) If V is irreducible and a certain simple criteria is fulfilled, then any K-maximal vector can be written in the form sx_m, s ? $\text{Y}$ (G,K), where x_m is some fixed K-maximal vector. Because of these properties $\text{Y}$ (G,K) has great practical value when constructing irreducible representations of Lie algebras in a form which makes the reduction with respect to a semi-simple subalgebra explicit.     

Perturbation theory for the effective interaction in nuclei

Starting from a decomposition of the Hamiltonian H(x) of the nuclear many-body problem in the form H(x) = H₀ + xV, where H₀ is a shell-model Hamiltonian, V the residual interaction, and x a strength parameter, we introduce a general effective interaction W(x) describing the interaction of nucleons within a shell, and the associated effective operators $\text{A}\text{?}\text{(x)}$. We display some properties of these operators. From a particular choice of W(x) we obtain the expressions introduced earlier by several authors. The convergence of the expansions for W(x) and $\text{A}\text{?}\text{(x)}$ in powers of x is investigated. It is shown that W(x) and $\text{A}\text{?}\text{(x)}$ are holomorphic in a domain of the complex x-plane including the point x = 0. With the help of a generalization of the von Neumann-Wigner noncrossing rule, we exhibit the nature of the common singularity of W(x) and $\text{A}\text{?}\text{(x)}$ which is closest to the origin and thus defines the radius r₀ of convergence of the expansions of W and $\text{A}\text{?}$. It is shown that r₀ is unaffected by the cancellation of unlinked diagrams. A criterion of consistency is established, which shows that most of the practical calculations of W lead to results which are inconsistent with the definition of W.     

Role of p-d hybridization in the Tc-variation of Y(Rh1−xRux)4B4 superconductors

Auger and photoemission studies for Y(Rh_1?xRu_x)₄B₄ superconductors elucidate the mechanism for the abrupt drop in T_c near x=0.5. The B $\text{p}$-states admix more strongly with Ru than Rh $\text{d}$-states, thereby yielding low-T_c values for Ru-rich compounds due to broadening of the $\text{d}$-band feutures. These effects underlie a previous suggestion that the preservation of Rh₄ tetrahedral units is essential for high-T_c values in ternary boride compounds.     

Hydrogen absorption in Zr(AlxB1−x)2 (BFe,Co) laves phase compounds

The hydrogen absorption capacity of the systems Zr(Al_xFe_1?x)₂ and Zr(Al_xCo_1?x)₂ (0? x ?1) was measured at hydrogen pressure of 70 atm and room temperature and at 40 atm and liquid nitrogen temperature. The two systems present very interesting and unexpected results.A dramatic rise in the hydrogen capacity occurs for small x values similar to previous results for the systems Zr(A_xB_1?x)₂ (A  V, Cr, Mn; B  Fe, Co; 0?x?1). The maximum hydrogen content in both systems is achieved for x ≈ $\text{2}\text{12}$ at 40 atm and 80 K. Further increase of the Al content leads, however, to a steep decrease in the hydrogen capacity. This general behaviour is well described by a phenomenological model, recently proposed by us, and thus supporting the importance of short-range neighbouring effects for the hydrogen absorption capacity. The influence of Al on the hydrogen sorption properties in different intermetallic compounds is discussed.     

Local moment spin resonance in a Kondo system

The ESR of the system $\text{Yb:}\text{Au}{}_{\mathrm{x}}\text{Ag}{}_{\mathrm{1?x}}$ has been investigated for 0.7 ? x ? 1. The g-shift (Δg) and the temperature derivative of the linewidth $\text{(}\text{ΔH}\text{ΔT}\text{)}$ increase with decreasing Au concentration. For T ? 2°K effects in $\text{(}\text{ΔH}\text{ΔT}\text{)}$ are observed, which are attributed to the Kondo effect.     

Lithium mobility in the layered oxide Li1−xCoO2

The Li⁺-ion chemical diffusion coefficient in the layered oxide Li_0.65CoO₂ has been measured to be $\text{D}\text{?}\text{= 5 × 10}{}^{\mathrm{?12}}$ m² s^?1 by three independent techniques: (1) from the Warburg prefactor, (2) from the transition frequency for semi-infinite to finite diffusion lengths in steady-state ac-impedence measurements and (3) from a modified Tubandt method that uses ac-impedance data to distinguish interfacial and surface-layer resistances from the bulk resistance of the sample. This value and a small increase in D? with (1 ? x) in Li_1?xCoO₂, 0.45 < (1 ? x) < 0.80, compare favorably with the $\text{D}\text{?}\text{= 5}\text{to}\text{7 × 10}{}^{-12}\text{m}{}^2\text{s}{}^{-1}$ obtained by Honders for this system with pulse techniques. A qualitative discussion is presented as to why this composition dependence and why D? for this system is a factor of five larger than that for Li⁺-ion diffusion in Li_xTiS₂.     

Monopoles,duality, triality

The existence of magnetic charges could be a raison d'être not only for the quantization of electricity in units $\text{1}\text{3}\text{e}$ but also for the confinement of the quarks at the end of “observable”, “electric” Dirac strings (quarks have no magnetic charge in this scheme). We first review the Dirac quantization condition, using a “sum over histories” approach, and get a more general result: A string attached to the dyon (e₁, g₂) is observable by a dyon (e₂, g₂) unless (1?x) e₂g₁ ? xe₁g₂ = nh, where x is an arbitrary parameter which reflects an ambiguity in the action principle. The Dirac and Schwinger-Zwanziger quantization rules are special cases, with $\text{x = 0}\text{and}\text{1}\text{2}$, respectively. Then, we look for the values of x and of the magnetic charges to “explain” that (i) the electric charge is quantized in units $\text{1}\text{3}\text{e}$, (ii) the string attached to an electron is unobservable, (iii) the string attached to a quark is observable. We find a denumerable set of solutions. In most cases, the magnetic charges also are connected with observable strings.     

Properties of quark matter governed by quantum chromodynamics (II). Renormalization schemes in quark matter

Renormalization schemes are examined (in the Coulomb gauge) for quantum chromodynamics in the presence of quark matter. We demand that the effective coupling constant for all schemes become congruent with the vacuum QCD running coupling constant as the matter chemical potential, μ, goes to zero. Also, to enable us to standardize with the vacuum QCD running coupling constant at some asymptotic momentum transfer, $\text{|}\text{p}{}_0\text{|,}\text{we keep}\text{μ ? ¦}\text{p}{}_0\text{¦}$, to ensure that the matter contribution is negligible at this point. This means all schemes merge with vacuum QCD at $\text{|}\text{p}{}_0\text{|}$ and beyond. Two renormalization group invariants are shown to emerge: (i) the effective or invariant charge, g_inv², which is, however, scheme dependent and (ii) g²(M)/S(M), where S(M)^?1 is the Coulomb propagator, which is scheme independent. The only scheme in which g_inv² is scheme independent and identical to g²(M)/S(M) is the screened charged scheme (previous paper) characterised by the normalization of the entire Green function, S^?1, to unity. We conclude that this is the scheme to be used if one wants to identify with the experimental effective coupling in perturbation theory. However, if we do not restrict to perturbation theory all schemes should be allowed. Although we discuss matter QCD in the Coulomb gauge, the above considerations are quite general to gauge theories in the presence of matter.     

Self-consistent Hartree-Fock calculation of exchange effects in a weakly inhomogeneous electron gas

An exact calculation is given for the function B_x(n) which enters the Hohenberg-Kohn-Sham expansion, in powers of $\text{?n(}\text{r}\text{)}$, of the echange energy of an inhomogeneous eletron gas. The calculation is made for arbitrary inter-particle interaction. It is shown that the gradient expansion does not exist, in the case of Coulomb interaction, unless correlations are taken into account.     

The effect of hydrogen on the superconducting and structural properties of b.c.c. Nb-Ru alloys

The superconducting transition temperature (T_c) has been measured before and after the introduction of hydrogen into Nb_(1?x)Ru_x$\text{(0.20?x?0.33)}$. In all cases, the presence of appreciable amounts of this interstitial component led to a sharp increase in the T_c. All the evidence suggests that conversion of the host metal lattice to f.c.c. is necessary for the appearance of the elevated T_c.     

Effects of composition on the upper critical field of V-Ga

Measurements of the temperature dependence of the upper critical field, H_c2(T), for a series of V_100?xGa_x materials are presented for 20.5 ≤ × ≤ 29.6. Fits of the data to conventional theory for a paramagnetically limited, dirty, type II superconductor show: 1) a maximum in T_c and H_c2(0) for x ? 25; 2) a constant ( for x ≤ 25; 3) a slowly increasing value of λ_so with increasing x up to x ～ 25; and 4) good agreement with stoichiometric ordered and thermally disordered V₃Ga. Above $\text{x ? 25}$ broader transitions are observed. For x = 25, T_c = 15.3 K, (, λ_so = 0.3 and H_c2(0) = 23.4 tesla. The effects of inclusion of strong-coupling in the theory are discussed briefly.     

A thermodynamic study of nonstoichiometric cerium dioxide

Thermogravimetric measurements were performed on nonstoichiometric CeO_2?x in the temperature range 750–1500°C and from oxygen pressures of 10^?2 to 10^?26 atm. From this data the deviation from stoichiometry x = x(T, P_o2) was determined. The thermodynamic quantities Δ$\text{H}$_o2 and Δ$\text{S}$_o2 were calculated in the region 0.001? x ? 0.3 and found to be independent of temperature.In the composition region 0.001< x < 0.006, the variation of Δ$\text{S}$_o2 with x is consistent with a defect model involving randomly distributed doubly ionized oxygen vacancies. The experimental dependence of x and σ (electrical conductivity) is shown to be consistent with this model as Δ$\text{H}$_o2 (≈ -10 eV) exhibits a slight dependence on x. It is postulated that the variation in Δ$\text{H}$_o2 may result from lattice parameter increases with x, while the defects remain essentially randomly distributed.In the composition region 0.006 < x < 0.1, x ∝ with 1 < n < 5, and in the region 0.1 < x < 0.3, x ∝ with n increasing rapidly with x to n? 30. This behavior is believed to result from increasing defect interaction with increasing departures from stoichiometry. It is interesting to note that the ordered phase observed by Bevan and Kordis between CeO_1·72 and CeO_1·70 was not observed in this study at temperatures between 1300° and 1500°C.     

Spectroscopic investigation of [(NH4)xK1−x]2SnCl6 mixed crystals

Polycrystalline samples of the solid solution [(NH₄)_xK_1?x]₂SnCl₆(0?x? 1) have been investigated by DSC, X-ray diffraction and Raman scattering experiments. Substitution of K⁺ by NH⁺₄ depresses the phase transition temperature T₁. For 0? x ?0.05 a linear temperature coefficient $\text{d}\text{T}{}_1\text{dx=?5.16}\text{K/mol}$ % is obtained. The cubic lattice constant roughly obeys Vegard's law, whereas the linewidth of the SnCl₆^2?F_2g internal vibration displays a nonlinear dependence on composition.