The effect of quenching on the martensitic transformation in ß1 phase of Au-Cd alloys

The effect of quenching on the martensitic transformation mechanism in ₁ Au-Cd alloys has been investigated by measurements of the electrical resistivity and X-ray diffraction. In the case of the Au-47.5 at%Cd alloy, the ₂-martensite is the characteristic product under quenching conditions, but it always exists with the equilibrium ₂-martensite phase. Consequently, the _{1 2} and ₂transformations occur simultaneously during the heating and cooling cycles. The corresponding resistivity behaviour is very complicated and extremely sensitive to thermal treatments such as quenching temperature and thermal cycling. On the other hand, in the case of the Au-49.0 at%Cd alloy, only the _{1 2} transformation occurs even when quenched, and the transformation is unaffected structurally by quenching. A distinct resistivity anomaly, which is considered to be due to the disappearance of quenched-in vacancies, is observed in quenched alloys. Some important characteristics of this anomaly are determined. In particular, the quenching effect disappears when the specimen is heated above the temperature at which the resisitivity anomaly begins. This result suggests that the quenched-in vacancies play an essential role in the martensitic transformation process under quenching conditions.     

The critical curve in an antiferromagnetic superconductor with nonmagnetic impurities

The critical curve of a transition of the second kind in an antiferromagnetic superconductor (AFS) with nonmagnetic impurities has been studied. The AFS is described by using the mean-field model given by Nass, Levin, and Grest and assuming a one-dimensional electron band. We find that the points on the critical curve satisfy the thermodynamic stability condition for 0₁/₀5.04 and 0.49H_Q/₀1.64.Here ₁ is the inverse lifetime of a conduction electron for nonmagnetic impurity scattering,H _Q is the antiferromagnetic molecular field, ₀ is the zero-temperature order parameter of a superconductor in the absence ofH _Q and impurities. Further, ₁ and H_Q denote the values of these quantities for points on the critical curve. For ₁/₀>5.04 and H_Q/₀>1.64, the phase transition from the superconducting to the normal state is always of the second kind. Some thermal properties of the system near the critical curve have also been investigated and we find that these depends dramatically on the impurity concentration.     

Synthesis, crystal structure and X-ray powder diffraction data of the phosphor matrix 4SrO·7Al2O3

The white phosphor matrix 4SrO·7Al₂O₃ has been synthesized by firing the appropriate mixture of SrCO₃, Al(OH)₃ and H₃BO₃ in the molar ratios 1:3.5:0.135 at 1300°C for 4–7 h. The crystal structure of 4SrO·7Al₂O₃ has been determined as a orthorhombic Pmma space group with a=24.7451(2)Å, b=8.4735(6)Å, c=4.8808(1)Å, V=1023.41(3)ų, Z=2, and D=3.66 g cm^–3 by the Rietveld analysis. The refinement figures of merit are R_p=8.26, R_wp=11.60, R_bragg=4.44 and s=2.61 for 844 reflections with 2<119.94°. And the corresponding X-ray powder diffraction data are presented for search/match analysis.     

Functional derivative ofT c with α2(ω)F(ω) for weak coupling anisotropic superconductors

Approximate analytic calculations of the functional derivative ofT _c with respect to ²()F() for anisotropic superconductors are presented, with the primary purpose of identifying the determining material parameters. The square-well model for the phonon-mediated electron-electron interaction, the weak coupling limit ( _c /2T _c 1), and separable anisotropy are used. The general behavior of T _c /²()F() is the same as that found in numerical calculations for the case of small anisotropy, a ²/(–*)1; the regime of * is also discussed.     

Paramagnetic resonance in a “dirty” spin-glass

For a spin-glass with nonmagnetic defects (n _m ^1/3l 1, where n _m is the magnetic impurity concentration and l is the mean free path) an absorption function () is derived. Three ranges of temperature and external magnetic field are considered. In the vicinity of the transition the value of () d is estimated as a function of temperature and field.     

A finite volume technique to simulate the flow of a viscoelastic fluid

Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.List of symbols D rate of strain tensor - L slit halfheight - P pressure, indeterminate part of the Cauchy stress tensor - R the Reynolds number - t time - U average velocity in the slit - u velocity vector - u,v velocity components - W the Weissenberg number based on the difference between stress relaxation time and retardation time - W ₁ the Weissenberg number based on stress relaxation time - x,y rectangular Cartesian coordinates - ratio of retardation time to stress relaxation time - zero-shear-rate viscosity, ₁ + ₂ - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to - ₁ stress relaxation time - ₂ retardation time - density - (, , ) xx, yy and xy components of ₁, respectively - determinate part of the Cauchy stress tensor - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to      

Regularizing algorithm for inverting the Abel equation

The article presents a regularizing algorithm for solving the Abel equation using information on the statistics of the error of measurement of the right-hand side of the equation.Notation (r), f(x) solution and right-hand side of the Abel equation, respectively - f_i value of the right-hand side measured at point x_i - _i uncertainty of the i-th measurement - n number of measurements of the right-hand side - V correlation matrix of the uncertainty of measurement - smoothing parameter - S_n(x) interpolating spline - S_n,(x) smoothing spline - a_i, b_i, c_i, d_i coefficients of the smoothing spline - (r) regularized solution of the Abel equation - e() discrepancy vector - Sp[V] trace of the matrix V Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 270–274, August, 1980.     

Equation of state of3He near its liquid-vapor critical point

We report high-resolution measurements of the pressure coefficient (P/T) for³He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals–0.1t+0.1 and–0.2+0.2, wheret=(T–T _c )/T _c and =(– _c )/ _c . We have determined the discontinuity (P/T) of (P/T) between the one-phase and the two-phase regions along the coexistence curve as a function of . The asymptotic behavior of (1/) (P/T) versus near the critical point gives a power law with an exponent (+–1)^–1=1.39±0.02 for0.010.2 or–1×10 ^–2t–10 ^–6 , from which we deduce =1.14±0.01, using =0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity (P/T) with a correction-to-scaling term gives =1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (/T) _c as a function oft. In the two-phase region the slope (²/T ²)_c is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores 0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of – ( _c ,t) as a function of on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the ranget0.1. A fit of our data to the linear model approximation is obtained for0.10 andt0.02, giving a value of =1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (P/T) data analysis for ⁴ He by Kierstead. A power law plot of (1/) P/T) versus belowT _c leads to =1.13±0.10. An analysis with a correction-to-scaling term gives =1.06±0.02. In contrast to ³ He, the slopes (²/T ²)_c above and belowT _c are only marginally different.Work supported by a grant from the National Science Foundation.     

Ordinary size effects and deviations from Matthiessen's rule in the resistance of fine wires

Contrary to previous statements in the literature, large deviations from Matthiessen's rule in fine wiresare to be expected on the basis of a straight-forward solution of the ordinary transport equation, assuming the relaxation-time approximation and imposing the idealized condition of diffuse scattering of electrons at the boundaries. Using Chambers' path-integral method to evaluate the current density in a wire of arbitrary cross-sectional shape, the effects of boundary scattering on the resistivity in the regimed 0.1 have been calculated for two model Fermi surface geometries. For the temperature-dependent part of the resistivity, _d (T) _d (T)– _d (0), two distinct types of behavior are found in the alternative cases: (1) for a spherical Fermi surface, _d(T) increases logarithmically with _d(0); (2) for a cylindrical Fermi surface, _d (T) increases essentially linearly with _d (0). [In each case the qualitative dependence of _d(0) on /d is, for practical purposes, linear. However, the correct value of the product in the cylindrical case is not simply given in the ordinary way by the slope of an empirical plot of _d (0) vs.d ^–1.] A comparison of theoretical results for the two simple models with the published data for indium and gallium shows that the actual temperature-dependent size effects are consistent, both qualitatively and, by a rough estimation, quantitatively, with the expected behavior.     

Structural features of certain Ni-Al-Ta and Ni-Al-Hf alloys containing the γ′- and β -phases

An investigation has been made of the structure of certain alloys of the Ni-Al-Ta and Ni-Al-Hf systems. The compositions chosen for investigation were: Ni-28.75 at% Al-2.5 at% Ta; Ni-26.75 at% Al-2.5 at% Ta; Ni-20.0 at% Al-7.5 at% Ta; Ni-20.0 at% Al-7.5 at% Hf; Ni-22.5 at% Al-5.0 at% Hf. The Ni-Al-Ta alloys consisted of +-phases (or-phase transformed during rapid cooling to a martensitic product). Two types of morphology were observed in the transformed-phase, one consisting of parallel sided plates and the other of acicular shaped plates; the plates contained fine twins on {1 0 1} b c t planes. The as-cast Ni-Al-Nf alloys consisted of the -phase, together with eutectic regions of-phase and (Ni, Al)₇Hf₂; both lamellar and discontinuous eutectic morphologies were observed. Extensive solid solution of tantalum and hafnium in the -phase occurred.     

Thermodynamic Functions of Fermi Gas with Quadruple BCS-Type Binding Potential with dx2 - y2 d_{x^2 - y^2 } -Wave-Pairing Symmetry

A gas of spin 1/2 fermions with an interaction V+W = -||^-1 _k,k g _k,k(k)(k) b _k b _-k - 2 _k(k)n _k+ n _k-, where n _k± = a _k±, b _k = a _k+ a _k- and a _k, satisfy Fermi anticommutation relations, is investigated in the -pairing case. W+V₄ is nonzero only within a thin layer of one-fermion energies around the chemical potential , and (k) denotes the characteristic function of the corresponding range of momenta. Two cases are studied: 1⁰ = 0, 2⁰ = 0.10025 eV. In the first case the system exhibits a first order transition, in the second, the transition is second order. Temperature dependence of the system's thermodynamic functions is examined and compared with that of the s-pairing case.     

Structure and Diamagnetic Properties of (Pb0.6SnyCu0.4 ? y)Sr2(Y1 ? xCax)Cu2Oz

The effect of Sn doping in (Pb_0.6Sn _y Cu_{0.4 – y} )Sr₂(Y_{1 – x} Ca _x )Cu₂O _z with 0 y 0.3 and 0 x 0.7 was investigated. It was established that a nearly pure 1212 phase can be obtained at 0 y 0.1 and 0 x 0.3. The obtained XRD patterns as well as the results of the EDX and ICP-AES analyses showed that Sn substitution is possible in the (Pb,Cu)-1212 phase. Superconductivity was observed at 0.4 x 0.7. The onset of the diamagnetic transitions varied from 10 to 30 K. The influence of the strong Pb deficiency on the superconducting properties of the samples was discussed.     

Breakup of an anomolously viscous liquid film in a centrifugal force field

An equation is obtained for the breakup radius with consideration of tipping moments and Laplacian pressure forces acting on the liquid ridge at the critical point.Notation K, n rhenological constants - density - surface tension - r current cup radius - R maximum cup radius - r_c critical radius for film breakup - ¯r=¯r=r/R dimensionless current radius - ¯r_c=r_c/R dimensionless critical radius - ₀, _c actual and critical film thicknesses - current thickness - R_r ridge radius - h₀ ridge height - h current ridge height - ₀ limiting wetting angle - current angle of tangent to ridge surface - angle between axis of rotation and tangent to cup surface - angular velocity of rotation - q volume liquid flow rate - v₁ and v meridional and tangential velocities - =4vv _lm/r,=4v_m/r dimensionless velocities - M moments of surface and centrifugal forces - M_v moment from velocity head - p_r pressure within ridge - P_vm pressure from velocity head - p_m, p_pm pressures from centrifugal force components tangent and normal to cup surface - deviation range of breakup radius from calculated value - ¯r_max, ¯r_min limiting deviations of breakup radius - _c angle of tangent to curve _c/°₀=f(¯r) at critical point - t random oscillation of ratio _c/_c Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 51–56, July, 1980.     

An isothermal theory of anisotropic rods

Summary To provide an isothermal, deterministic theory of anisotropic rods is the primary objective of this paper. Our starting point is the 3-D linear theory of micropolar elastodynamics. First, the governing equations of the theory are established by the use of a suitable averaging procedure together with a separation of variables solution for kinematic variables. Next, without making the usual definiteness assumption for the strain energy density, a dynamic uniqueness theorem is constructed for the solutions of the governing equations. Logarithmic convexity arguments are then used to enumerate a set of conditions sufficient for uniqueness. The theory includes the effects of warping and shearing deformations, and in fact, it incorporates as many higher order effects as deemed necessary in any special case. Also, the application of the theory is illustrated in a sample example.Nomenclature Euclidean 3-space - X_k, X₁z, X a system of right-handed Cartesian coordinates in, rod axis, lateral coordinates; k=1, (=2, 3) - , , a regular region of space in , its closure and boundary surface - L _d,L complementary subsets of, on which deformations and stresses are prescribed, respectively;L _d L =L,L _d L = 0 - L length of rod - A area of cross-section of rod - C a Jordan curve which boundsA - V, L entire volume of rod and its boundary surface - L ₁,L _t lateral surface of rod, surface portion ofL ₁ on which stresses are prescribed - A _r,L ₁ right and left faces of rod - dv, dA, ds element of volume and area onA, and line element alongC - n_i,v _i unit exterior normal vectors toL andC - t time - t_kl, m_kl components of stress and couple stress tensors - f_i, l_i body force and body couple vectors per unit volume - , J_kl mass density, components of microinertia tensor - u_i, _i displacement and microrotation vectors - prescribed steady temperature increment - _kl, _klm components of Kronecker's delta and alternating tensor - t_i, m_i stress and couple stress vectors - _kl, e_kl components of strain and infinitesimal strain tensors - C_klmn, D_klmn components of isothermal elastic stiffnesses - B_kl thermal coefficients of material - , Lamé's elasticity constants - , , , elastic moduli of microisotropic continuum - B coefficient of linear thermal expansion - d_i, d_kl u_i or _i, _kl or e_kl and/or _kl - T _kl ^(m,n) , M _kl ^(m,n) components of stress and couple stress resultants of order (m, n) - T _k ^(m,n) M _k ^(m,n) components of stress and couple stress vector resultants of order (m, n) - d _k ^(m,n) , d _kl ^(m,n) components of deformation (u _k ^(m,n) , _k ^(m,n) ) and strain ( _kl ^(m,n) , e _kl ^(m,n) , _kl ^(m,n) ) of order (m, n) - F _i ^(m,n) , L _i ^(m,n) body force and body couple resultants of order (m, n) - U _i ^(m,n) , _i ^(m,n) displacement and microrotation resultants of order (m, n) - P _i ^(m,n) , Q _i ^(m,n) effective loads of order (m, n) - N , M, , P, Q, w, T ₁₁ ^(0,0) ,M ₁₁ ^(0,0) , P ₁ ^(0,0) , Q ₁ ^(0,0) , U ₁ ^(0,0) , ₁ ^(0,0) - v₀ rod velocity, (E/)^1/2 - K, W kinetic and potential energy densities - V, U kinetic and potential energies per unit length of rod - total energy of rod - C^(m,n) functions with derivatives of order up to and including (m) and (n) with respect to space coordinates and time, respectively - G (t) logarithmic convexity function - ()^. time differentiation, /t () - () partial differentiation with respect to the axial coordinate, /z () - E,v Young's modulus, Poisson's ratio     

An extension of the theory of oscillating cup viscometers

The theory of the fluid motion in the interior of an oscillating or rotating cup is reexamined. The quantity of interest in viscometry is the torque exerted by the fluis on the sides and rims of the cup. In this paper expressions for the torque are obtained for geometries for which the cup height approaches a fluid boundary layer thickness. Interest in such geometries is due to viscosity measurements made in mixtures in the critical region where cups of small height are used in order to minimize gravity effects.Nomenclature D() Torque on the cup, Eq. (5) - E() Truncation error term, Eq. (24) - h Internal half-height of a filled cup or the height of the liquid in a partially filled cup - I Moment of inertia of cup and suspension system - I Moment of inertia of fluid inside cup - I _n Modified Bessel function of order n - J _{i, n} Defined in Eq. (13) - R Radius of the cup - S _n Defined in Eq. (7) - S _n Defined in Eq. (10) - x Variable 2 ₀/ - z Variable 2 ₀^1/2 - () Angular displacement of the cup - Boundary layer thickness - Logrithmic decrement - Laplace transform variable - ₀ Dimensionless height h/ - Frequency ratio / ₀ - Kinematic viscosity - ₀ Dimensionless radius R/ - Density of liquid - Dimensionless time ₀ t - Phase angle of oscillation - Angular frequency of oscillation with liquid present in cup - ₀ Angular frequency of oscillation in a vacuum     

Cross-Correlated Dynamic Resistance of a Direct Current Superconducting Quantum Interference Device

This paper presents experimental data on a comparative study of a dc SQUID with voltage and current bias. We introduce a cross-correlated dynamic resistance of the device defined as a ratio R _dCV = _VC/_IV, where _VC = (V/) _A is the slope of the voltage-to-flux characteristics measured in the current bias mode and _IV = (I/) _A is the slope of the current-to-flux characteristics measured with voltage bias. It has been found that R _dCV may deviate strongly from the dynamic resistance observed in the current bias mode of operation. The intrinsic energy resolution of the SQUID remains unchanged for both modes of operation, but the current noise of the voltage biased device scales with the cross-correlated dynamic resistance. In our SQUID with the loop inductance L = 105 pH, is equal to 37 h in the white noise region at a temperature of 4.2 K.     

On a simple wave approximation of a set of linear dispersive wave equations

Summary The validity of an approximation ₀ of one of the solutions of a set of two linear coupled dispersive wave equations has been discussed. ₀ is the solution of a linear Korteweg-de Vries equation and satisfies the same initial condition as . It is shown that for square integrable solutions having a spectral range not exceeding [–, ] the approximation is useful if ^{5 2}t«1 in the sense that –₀(t)« (t)(L ₂ -norm). is a measure for the dispersion. The approximation fails in that sense ast . Some remarks to a similar nonlinear problem are made.     

Flux motion in anisotropic type-II superconductors nearH c 2 with arbitrary vortex orientation

Flux motion in anisotropic type-II superconductors near H_{c 2} is studied in the framework of the time-dependent Ginzburg-Landau (TDGL) theory for the case that the average flux densityB is oriented in an arbitrary direction relative to the principal axes of the sample. The linearized TDGL equation for a uniformly translating order parameter is solved and expressions for all elements of the flux-flow resistivity tensor _ij (including the off-diagonal Hall elements) are obtained. The diagonal elements _ii show the angular scaling property that _ii(B) = _ii(B/H_{c 2}(, ø)), whereas the Hall elements _ij (i j) have additional angular dependences that are not contained in H_c2. For the case that the normal state Hall elements _ij ⁽ⁿ⁾ B _k with i j k, the ratios _ij/ _ij ⁽ⁿ⁾ are functions of B/H_c2 (, ) only.     

Superconductivity in irradiated A-15 compounds at low fluences II. Alpha-particle-irradiated Nb3Sn and Nb3Ge

The T _c behavior of vapor-deposited Nb₃Ge and Nb₃Sn is examined as a function of low-fluence alpha-particle irradiation. It is found that for Nb₃Sn with 15 -cm the T _c is insensitive to low doses of radiation, whereas Nb₃Ge with ₀ 50 -cm has its T _c depressed immediately with irradiation. It is suggested that the T _c behavior of A-15 superconductors in the regime of small dose is strongly influenced by the initial state of the sample. Furthermore, it is argued that the behavior of the T _c with dose can be qualitatively explained by considering a sharp structure in the density of states N(E), the smearing of which by defects leads to a depression in T _c .Work performed under the auspices of the U.S. Energy Research and Development Administration.Also at Materials Science Department, SUNY at Stony Brook.Also at Physics Department, SUNY at Stony Brook.     

Densities,Viscosities, and Refractive Indices of Binary Mixtures of Benzene with Isomeric Butanols at 30°C

The densities, , viscosities, , and refractive indices, n, of binary mixtures of benzene with 1-butanol, 2-methyl-1-propanol, 2-butanol, and 2-methyl-2-propanol, including those of the pure liquids, were measured over the complete composition range at 30°C. The dependence of , , and n on composition was checked by using an empirical relation. The experimental data were used to calculate excess molar volumes, V^E, deviations in viscosity, , excess free energies of activation of viscous flow, G^*E, deviations in refractive index, n, apparent molar volumes, V_,1 and V_{, 2}, and partial molar volumes, , of benzene in alcohols and alcohols in benzene, respectively, at infinite dilution. The variations of these parameters with composition and the effect of branching in alcohols were discussed from the point of view of intermolecular interactions in these mixtures.