Dislocations and faults in some alloys containing copper and aluminum

By using the method of variance of the respective X-ray diffraction line profile, the effective particle size (p) and r.m.s.. strain (S ^21/2) of four alloys containing copper and aluminium (Al-0.08, 4 and 10 wt% Cu and Cu-5.87 wt% Al) at different annealing stages (starting from the cold filed stages) have been determined. From the peak shift of these samples, their average stacking fault probability = – where is the intrinsic stacking fault probability and the corresponding extrinsic stacking fault probability, respectively, were determined. Similarly, from the angular distance between the peak and the centroid of the diffraction profiles, the magnitude of + 4.5, where is the twinning fault probability, was measured. From these, the true particle sizeT, the stacking and twinning fault probabilities , and and the minimum stacking fault widthD _min have been determined. The hardness of alloys at different annealing stages was found to be dependent on the dislocation density and the stored energy in the alloys. The relationT S ^21/2 = constant was found to be valid for the alloys and from this a mechanism of grain growth with annealing has been suggested. With annealing the dislocation density and stored energy per unit volume were found to decrease until finally, in the fully annealed stages, they disappeared. The same was found to be valid for stacking and twinning fault probabilities as well as the minimum stacking fault width. A mechanism for the creation and annihilation of the intrinsic and extrinsic stacking faults has been suggested.     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

Electrical resistivity of single-crystal lithium ammonium sulphate between 300 and 500 K

The d.c.,electrical resistivity, , of pure LiNH₄SO₄ single crystals has been measured between 300 and 500 K in three successive runs. Anomalous behaviour before and at the transition point was observed and thermal annealing was necessary for reproducible results. The temperature dependence of along the polar axis yielded the values E=0.54 and 1.48 eV and E=1.95 eV for the energy activating the charge transport mechanisms in the ferroelectric and the paraelectric phases, respectively. A pre-transition phenomenon was observed while measuring along the a- and b-axes. The J-E characteristics indicated possible space-charge effects at low measuring fields. The mechanism of electrical conduction in the measuring range has been discussed.     

The piezoresistance coefficients of copper and copper-nickel alloys

This paper attempts to further a better understanding of the piezoresistance coefficients by studying the piezoresistive effects in copper and copper-nickel alloys. The experimental evidence of isotropic piezoresistance coefficients (₁₁=₁₂) has been obtained for the annealed copper and copper-nickel alloys. The piezoresistance coefficients of the cold-worked copper and Cu₆₀Ni₄₀ alloy are of the tensor character (₁₁₁₂). A physical explanation has been given to the change of the ( _ij ) tensor.     

Crystallization kinetics in glassy Ge20Se80−x In x alloys

Crystallization kinetics is studied in glassy Ge₂₀Se_80–xIn_x (0 x 20) using isothermal annealing at temperatures between the glass transition and melting. D.c. conductivity is taken as a parameter to estimate the extent of crystallization (). The activation energy of crystallization (E) and the order parameter (n) are calculated by fitting the values of in the Avrami equations of isothermal crystallization. The results indicate that E is highly composition-dependent, which is explained in terms of the stable phases in the Ge-Se-In system.     

Thermal diffusivity of inhomogeneous systems

The possibility of analyzing the nonsteady temperature fields of inhomogeneous systems using the quasi-homogeneous-body model is investigated.Notation t, t_I, t_i temperature of quasi-homogeneous body inhomogeneous system, and i-th component of system - a, , c thermal diffusivity and conductivity and volume specific heat of quasi-homogeneous body - a_{i i}, c_i same quantities for the i-th component - q heat flux - S, V system surface and volume - x, y coordinates - macrodimension of system - dimensionless temperature Fo=a/² - Bi=/ Fourier and Biot numbers - N number of plates - =h/ ratio of micro- and macrodimensions - _V, volumeaveraged and mean-square error of dimensionless-temperature determination - time - m_i i-th component concentration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 126–133, July, 1980.     

The athermal α → ω transformation in Zr-2 at% Nb alloy

The athermal transformation in Zr-2 at.% Nb alloy has been investigated by transmission electron microscopy. Analysis of the selected-area diffraction pattern has shown that the orientation relationships between the omega and the parent-phase in quenched Zr-2 at.% Nb alloy are the same as have been previously observed for the reaction in pure zirconium. Thus it was deduced that the direct transition has taken place in the alloy during cooling. The-originated -particles were visualized using the dark-field technique. The formation of the athermal omega in the-region of-stabilized Zr-Nb alloy is discussed in terms of the relative positions of the free energy equilibrium curvesT ₀ ,T ₀ ,T ₀ and the correspondingM _s ,M _s andT _s start curves. It is concluded that the omega phase can occur over a much wider range of alloy compositions than is usually recognized on the basis of transformation data.     

The Ni3Al-Ni3Cr-Ni3Ru section of the Ni-Cr-Al-Ru system

An investigation is reported of the 75 at% nickel section of the Ni-Cr-Al-Ru system at 1523 and 1273 K. Constitutional data obtained by electron probe microanalysis, X-ray diffraction and microscopical examination are presented as partial isothermal sections. At 1523 K, the major part of the section consists of phase, while the aluminium-rich region contains a and+ region; the extent of the solid solution of chromium and ruthenium in totals ~ 4 at%. The ruthenium-rich corner of the section shows a two-phase region consisting of + ruthenium-rich solid solution. At 1273 K the,+ and + ruthenium regions increase in extent. The/ mismatch values in the equilibrated alloys studied lie in the range ~ –0.08 to –0.39%. Constitutional features of as-cast alloys are also reported.     

Numerical method for solving heat-conduction problems for two-dimensional bodies of complex shape

A finite-difference scheme is described for a curvilinear orthogonal net which permits the use of a single algorithm for calculating bodies of various shapes.Notation x, y independent variables - u, v orthogonal coordinates - F(w)=F(u + iv) function of a complex variable - g(u,v)= F(w)/w Jacobian of transformation from (u,v) to (x,y) - thermal conductivity - c volumetric heat capacity - Q heat release per unit volume - T temperature - f value of temperature on boundary of region - time - L, L₁, L₂ differential operators - (u,v) solution of differential problem in canonical region - ^j, ₁ ^j , ₂ ^j , t^J, t ₁ ^j , t ₂ ^j network functions in canonical region - ^j, t^*j solutions of difference problems using rectangular and orthogonal nets respectively - {u_i, v_k} rectangular net in canonical region G - {x_i,k, y_i, k} orthogonal net in given region G^* - u_i, v_k dimensions of cell of rectangular net - u_i,v _i,k dimensions of cell of orthogonal net - h, maximum dimension of cell for rectangular and orthogonal nets respectively - ₁, ₂, difference operators for rectangular and orthogonal nets - A, B, C, D, A^*, B^*, C^*, D^* coefficients of difference scheme for rectangular net - D, Ã, B coefficients of difference scheme for orthogonal net Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 503–509, March, 1981.     

Effect of Gd3+ substitution on dielectric behaviour of copper-cadmium ferrites

The dielectric constant, , loss tangent (tan ) and a.c. resistivity (_a.c.) are measured in the frequency range of 100 Hz to 5 MHz for the series of samples Cd _x Cu_1–x Fe_2–y Gd _y O₄ prepared by the ceramic technique. The dispersion in for all the values of x and y=0 and 0.1 shows a normal behaviour except for y=0.1 and x=0.4. The lowering of dielectric intensity in substituted ferrites (y=0.1) and fast dispersion of (_a.c.) with frequency, are explained as due to the reduced number of Fe³⁺ participating in the polarization process and the hindrances caused by Gd³⁺ to the polarization process by localizing Fe²⁺ ions thereby increasing the resistivity and activation energy. The dispersion in tan for unsubstituted samples (y=0.0) shows a normal trend while substituted samples (y=0.1) show relaxation behaviour, which is explained by existing theories.     

Temperature dependence of the experimental penetration depth of superconducting thin films

Experimental magnetic field penetration depths (t, d, H) of the stable and superheated Meissner state were calculated as a function of temperature for various applied magnetic fields and various film thicknesses for two cases: (1) (t)/d and (2) 2(t)/d ( is the Ginzburg-Landau penetration depth,d is the film thickness, is the GL parameter). The results of the first case should be a useful tool for obtaining (0) of amorphous superconducting thin films.¹ This work was supported in part by NSF Grant No. INT 8006927.     

Specific heat near the lambda point in 4He and 3He-4He mixtures: Test of universality of the critical exponent and the amplitude ratio,and observation of the critical-tricritical crossover effect

The specific heat under saturated vapor pressure of pure ⁴He and of six ³He-⁴He mixtures up to X = 0.545 was measured in the temperature range 3 × 10^–6 <¦T-T ¦ <10^–2 K. The critical exponents and along the path = are independent of X up to X = 0.545, where (= ₃ – ₄) is the difference between chemical potentials. If we take account of higher order terms, the exponent (= ) and the amplitude ratio A /A are independent of X up to X = 0.545. The values of and A /A are –0.023 and 1.090, respectively. The critical-tricritical crossover effect was observed for X = 0.545 and the boundary of crossover region closest to the critical region was at /T = (1–2) × 10^–4, where is the distance ¦T – T ¦ along the path = . This value is in good agreement with the estimated value by Riedel et al. But, remarkably, in the case of X = 0.439 this effect was not observed.     

Mixed convection flow of micropolar fluid over an isothermal plate with variable spin gradient viscosity

Summary A steady two-dimensional mixed convection flow of viscous incompressible micropolar fluid past an isothermal horizotal heated plate with uniform free stream and variable spin-gradient viscosity is considered. With appropriate transformations the boundary layer equations are transformed into nonsimilar equations appropriate for three distinct regimes, namely, the forced convection regime, the free convection regime and the mixed convection regime. Solutions of the governing equations for these regimes are obtained by an implicit finite difference scheme developed for the present problem. Results are obtained for the pertinent parameters, such as the buoyancy parameter, in the range of 0 to 10 and the vortex viscosity parameters, =0.0, 1.0, 3.0, 5.0 and 10.0 for fluid with Prandtl number Pr=0.7 and are presented in terms of local shear-stress and the local rate of heat transfer. Effects of these parameters are also shown graphically on the velocity, temperature and the couple stress distributions. From the present analysis, it is observed that both the momentum boundary layer and the thermal boundary layer increase due to an increase in the vortex viscosity of the fluid.List of symbols f, F, dimensionless stream function for forced convection free convection and mixed convection, respectively - g acceleration due to gravity - Gr_x local Grashof number - j micro-inertia density - m ₂₃ distribution of couple stress - N microrotation component normal to (x, y)-plane - p pressure of the fluid - q dimensionless rate of heat transfer - Re_x local Reynolds number - T temperature of the fluid in the boundary layer - T temperature of the ambient fluid - T temperature at the surface - u, v thex andy-components of the velocity field - U free stream velocity - x, y axis in direction along and normal to the plate Greek thermal diffusivity - coefficient of volume expansion - vortex viscosity parameter - stream function - , , nondimensional similarity variables - buoyancy parameter (=Gr _x Re _x ^/5/2 ) - vortex viscosity - density of the fluid - v kinematic coefficient of viscosity - spin-gradient viscosity - stream function - dimensionless skin-friction - fluid viscosity     

Elevated temperature deformation behaviour of multi-phase Ni-20 at % Al-30 at % Fe and its constituent phases

The mechanical behaviour of the multi-phase ( + /) alloy Ni-20 at % Al-30 at % Fe and alloys similar to its constituent and / phases, Ni-30 at % Al-20 at % Fe and Ni-12 at % Al-40 at % Fe, respectively, were investigated. When tested in tension at 300 K, the alloys exhibited 20%, 2% and 28% elongation, respectively. At elevated test temperatures (700, 900 and 1100 K), the multi-phase alloy exhibited increased ductility, reaching an elongation in excess of 70% at 1100 K without necking or fracture. Similarly, the alloy demonstrated increased ductility with increasing test temperatures. In contrast, the / alloy showed greatly reduced ductility with increasing temperature and was quite brittle both at 900 and 1100 K. Thus, whilst at room temperature the / phase improved the ductility of the + / aggregate, at elevated temperatures the phase alleviated the brittleness of the / phase, thereby preventing any embrittlement of the multi-phase alloy over the temperature range 300–1100 K. Also, whilst the phase improved the room-temperature strength of the multi-phase alloy, at elevated temperatures where the phase is known to be weak, the / phase improved the strength of the multi-phase alloy up to 900 K, beyond which the strength deteriorated due to disordering and lack of anomalous strengthening in the / component.     

Solution hardening of lead single crystals at liquid air temperature

Single crystals of lead with either thallium, indium, bismuth, cadmium, mercury or antimony were tested in tension in liquid air. The critical resolved shear stress ₀ increases linearly with increasing solute content c in a limited concentration range. The increase ₀/C is lowest for lead-thallium and highest for lead-antimony. When log ₀/C is plotted against log (sf + elf) where sf*[(d ₁)_Pb – (d ₁)_sol/(d ₁)_Pb]10^Pb, d ₁ being the closest distance of approach, and elf = En, En being the sum of the electronegativities of solvent and solute, a straight line of slope 2 results. A similar result is obtained with data from the literature for single crystals of copper alloys and of magnesium alloys. However in these cases a different size factor has to be used.     

A superconducting vibrating reed applied to flux-line pinning. I. Theory

A theoretical treatment is given of a superconducting reed clamped at one end and performing flexural vibrations in a homogeneous longitudinal magnetic fieldB _a. When the flux lines are rigidly pinned the reed behaves like an ideal diamagnet whose bending distorts the external field. This generates a magnetic restoring force (line tension) B _a ² which is independent of the reed thicknessd, whereas the mechanical restoring force (stiffness) is d ³. Therefore, the resonance frequency /2 of a thin superconducting reed increases drastically when a fieldB _a is applied, or for a givenB _a, when the reed is cooled below its critical temperatureT _c. With decreasing pinning strength (characterized by Labusch's parameter ) the resonance frequency decreases, ²²– _pin ² where _pin ^{2 –1}, and an attenuation _v ^–2 occurs due to the viscous motion of flux lines. For larger vibration amplitudes an additional, amplitude-dependent damping _h ^–3 occurs due to the hysteretic losses caused by elastic instabilities during flux motion.On leave from Centro Atómico, Bariloche, Argentina.     

Ordered state of one-dimensional antiferromagnetic superconductors in the presence of a homogeneous magnetic field

Assuming a one-dimensional electron band and examining the free energy difference F (=F _S–F _N) for an antiferromagnetic superconductor in the presence of a homogeneous magnetic field H₀, it is shown that (i) for temperatureT=0, the spatially varying order parameter _Q (having the same period as the antiferromagnetic fieldH _Q) and the BCS order parameter coexist when |–H _QH ₀<+H _Q (here, the pairing coupling constant for _Q is assumed small), and (ii) forT near the second-order phase transition temperature the coexistence of _Q and is always realized whenH ₀0.Work supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.On leave of absence from Physics Department, Tohoku University, Sendai, Japan.     

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.     

Theory of RF SQUIDs Operating in the Presence of Large Thermal Fluctuations

A comprehensive analytical theory is presented for non-hysteretic RF SQUIDs operating in the adiabatic mode in the presence of large thermal fluctuations. When 1 ( = 2LI_c/₀ is the hysteresis parameter, L is the SQUID inductance, I_c is the critical current of the Josephson junction, and ₀ is the flux quantum) the theory is applicable also for RF SQUIDs operating in the non-adiabatic mode. In contrast to previous theories in which the noise is treated perturbatively and which therefore are applicable only if the product 1 ( = 2k_BT/ ₀ I_c is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature)—the case of small thermal fluctuations—the present theory is valid for around unity or higher. In the limit 0 the theory reproduces the results of small thermal fluctuations theories. It has been found that in the presence of large thermal fluctuations the screening current in the SQUID inductance is suppressed by a factor that increases with increasing . Taking into account this new basic fact, all SQUID characteristics (output signal, transfer function, noise spectral density and energy sensitivity) have been recalculated and a good agreement with experimental data has been obtained. It has been also found that RF SQUIDs can be operated with substantially higher values of the inductance and of the noise parameter than DC SQUIDs. These two aspects, which are of particular importance at liquid nitrogen temperature, make high T_c RF SQUIDs very attractive.     

Negatively isotone optimal policies for random walk type Markov decision processes

Summary This paper considers a random walk type Markov decision process in which the state spaceI is an integer subset of IR ^m , and the action spaceK is independent ofi I. The natural order, overI, and a quasi order,, overK, is assumed, together with aconditional convexity assumption on the returns {r _i ^k }, and certain other assumptions about these rewards and the transition probabilities in relationship to the orders and.A negatively isotone policy is one for whichi i(i))(i) (i.e.(i) (i) or(i) i)). It is shown that, under specified conditions, a negatively isotone optimal policy exists. Some consideration is given to computational implications in particular relationship to Howard's policy space method.

---

Zusammenfassung Wir betrachten einen Markovschen Entscheidungsprozeß vom random walk Typ. Der ZustandsraumI sei eine Teilmenge des IR^m, wobeii I ganzzahlige Komponenten habe. Die MengeK der zulässigen Aktionen ini I sei unabhängig voni I. Sei die natürliche Ordnung aufI und sei eine Quasiordnung aufK. Die Erträge {r _i ^k }seienbedingt konvex, darüberhinaus seien weitere Voraussetzungen über diese Erträge und die Übergangswahrscheinlichkeiten in Bezug auf die Ordnungen und erfüllt. Eine Politik heißt negativ isoton, falls ausi i folgti(i) (d. h.(i) (i) oder(i)(i)). Wir zeigen, daß unter gewissen Voraussetzungen einenegativ isotone optimale Politik existiert: Auch diskutieren wir einige Folgerungen für die Numerik, insbesondere hinsichtlich Howards Politikiteration.