Cross-slip on the first order pyramidal plane (10\bar 11) of a-type dislocations [1\bar 210] in the plastic deformation of α-titanium single crystals

The nature of the cross-slip plane was determined by electron microscopy observations of α-titanium single crystal specimens, oriented for single prismatic slip (10 \(\bar 1\) 0) [1 \(\bar 2\) 10]. The occurrence of cross slip on the first order pyramidal plane (10 \(\bar 1\) 1) was proved for a-type dislocations [1 \(\bar 2\) 10]. Furthermore, two types of dislocation configuration due to the double cross-slip were observed: edge dislocation dipoles and loops elongated along the Burger's vector.     

Effect of a magnetic field on the specific heat jump of a superconducting alloy containing paramagnetic impurities with local states within the gap

The effect of a uniform magnetic field on the specific heat jump \({\Delta C}\) of a superconductor containing paramagnetic impurities has been investigated. The impurities are described by the Shiba-Rusinov model. Taking the normalized position of the bound state within the BCS gap ε₀=0.8 and 0.0 and the parameter α(=〈S _z ² 〉/S²)=1.0 and 1/3 as typical values, we find the detailed dependence of \({\Delta C}\) on the impurity concentration \(\bar c\) and the transition temperature T_c. In some cases \({\Delta C}\) diverges at certain values of \(\bar c\) or T_c, signaling a change of the normal-superconductor phase transition from second order to first order.     

Dielectric function for the Anderson model

In recent years the study of alloys and compounds containing rare-earth and actinide elements is receiving increasing attention. The Anderson model is most popularly used for studying the theory of these systems. As it displays a large number of anomalous characters in magnetic and electrical properties, it was felt worthwhile to study the dielectric properties of this model. Using the linear response theory of Kubo, the energy and wave vector-dependent dielectric function \(\varepsilon \left( {\bar q,E} \right)\) is related to the retarded Green’s function of Fourier components of electron density fluctuations \(\left\langle {\left\langle {\rho _{\bar q} ;\rho _{ - \bar q} } \right\rangle } \right\rangle \) . Thus a many-body calculation of \(\varepsilon \left( {\bar q,E} \right)\) requires the calculation of \(\left\langle {\left\langle {\rho _{\bar q} ;\rho _{ - \bar q} } \right\rangle } \right\rangle \) . The Greens function is calculated using the equation-of-motion method with RPA decoupling. Further, since certain ensemble averages are required as inputs to the calculation, the relevant single-particle Green’s functions are also evaluated.     

Transient and steady state creep behaviour of polycrystalline MgO

Stress change experiments during compressive creep tests at high stresses on polycrystalline MgO at 1596 K have shown that the creep rate at any instant during transient and steady state creep is predicted by the ratio,r/h, wherer is the rate of recovery (=??σ/t6t) andh is the coefficient of strain hardening (=?σ/?ε). Over most of transient and steady state creep, whenh is constant and the decrease in creep rate, \(\dot \in\) , is a direct result of a decrease inr, the variation of the creep strain,ε, with time,t, is accurately described as $$ \in = \in _0 + \in _T (1 - e^{ - mt} ) + \dot \in _s t$$ whereε ₀ is the instantaneous strain on loading,ε _T the transient creep strain,m relates to the rate of exhaustion of transient creep and \(\dot \in _s\) is the steady creep rate. Deviations from this equation occur during the initial 10 to 15% of the transient creep life, whenh increases rapidly. The variations in \(\dot \in\) ,r andh during transient and steady state creep are explained in terms of a model for creep in which the rate-determining process is the diffusion controlled growth of the three-dimensional dislocation network within subgrains to form dislocation sources allowing slip to occur.     

Evaluation of microstructural instability during the differential strain rate test of a superplastic alloy

Stress (σ)-strain rate ( \(\dot \varepsilon \) ) data of banded and elongated grain microstructures of the Pb-Sn eutectic alloy were analysed over 298 to 443 K to evaluate microstructural instability during differential strain rate tests in the superplastic region. With reference to a stable equiaxed microstructure exhibiting uniqueσ- \(\dot \varepsilon \) relation, banded structure is more susceptible to strain hardening while the elongated grain microstructure exhibits either strain softening or strain hardening depending on the test temperature. This flow behaviour is considered in terms of a change in grain size, represented by the cube root of the grain volume. Activation energy for grain growth calculated from the differential strain rate test data indicates that the activation energy depends on strain rate and type of microstructure.     

Computer simulation of vortex pinning in type II superconductors. II. Random point pins

Pinning of vortices in a type II superconductor by randomly positioned identical point pins is simulated using the two-dimensional method described in a previous paper (Part I). The system is characterized by the vortex and pin numbers (N _v ,N _p ), the vortex and pin interaction ranges (R _v ,R _p ), and the amplitude of the pin potentialA _p . The computation is performed for many cases: dilute or dense, sharp or soft, attractive or repulsive, weak or strong pins, and ideal or amorphous vortex lattice. The total pinning forceF as a function of the mean vortex displacementX increases first linearly (over a distance usually much smaller than the vortex spacing and thanR _p ) and then saturates, fluctuating about its average \(\bar F\) . We interpret \(\bar F\) as the maximum pinning forcej _c B of a large specimen. For weak pins the prediction of Larkin and Ovchinnikov for two-dimensional collective pinning is confirmed: \(\bar F\) =const· \(\bar W\) /R _p c ₆₆, where \(\bar W\) is the mean square pinning force andc ₆₆ is the shear modulus of the vortex lattice. If the initial vortex lattice is chosen highly defective (“amorphous”) the constant is 1.3–3 times larger than for the ideal triangular lattice. This finding may explain the often observed “history effect”. The function \(\bar F\) (A _p ) exhibits a jump, which for dilute, sharp, attractive pins occurs close to the “threshold value” predicted for isolated pins by Labusch. This jump reflects the onset of plastic deformation of the vortex lattice, and in some cases of vortex trapping, but isnot a genuine threshold. For strong pins \(\bar F\) ～(N _p \(\bar W\) )^1/2 approaches the direct summation limit. For both weak and strong pinningj _c B is related to the mean squareactual (not maximum) force of each pin. This mean square in general is not proportional toA _p ² but, due to relaxation of the vortex lattice, may be smaller or larger than its rigid-lattice limit. Therefore, simple power lawsj _c ～n _p A _p ² orj _c ～n _p A _p in general donot hold except for very weak or unphysically strong pinning.     

Microstructural development during the liquid-phase sintering of two-phase alloys,with special reference to the NbC/Co system

An investigation was made of the grain growth and other microstructural changes occurring during the liquid-phase sintering of NbC alloys with ～20 wt % cobalt. The effects of sintering time, sintering temperature, and small alloying additions were studied. It was found that the grain growth of NbC in liquid cobalt, at 1420° C, can be described by the equation: $$\bar d^3 - \bar d_0 ^3 = {\text{K}}t$$ where \(\bar d\) is the mean linear intercept of the grains after time t, and \(\bar d_0\) the initial mean intercept, K being a temperature-dependent constant with an “activation energy” of 95±15 kcal/mole. This equation suggests that grain growth occurs by a solution/ precipitation process controlled by diffusion in the liquid phase. Small alloying additions of WC, TiC or NbB₂ inhibit the growth and/or alter the growth process, as well as affecting such properties as the shape and contiguity of the carbide grains. The relative significance of grain coalescence to grain growth in a liquid phase is discussed. By examining theoretically the effect of anisotropy of interface energy on the cube ? sphere grain-shape change, it has been possible to explain the observed sensitivity of grain shape towards sintering conditions.     

Comparing Transition-Edge Sensor Response Times in a Modified Contact Scheme with Different Support Beams

We present measurements of the thermal conductance, G, and effective time constants, \(\tau \) , of three transition-edge sensors (TESs) populated in arrays operated from 80–87 mK with T \(_\mathrm{C}\)   \(\sim \)  120 mK. Our TES arrays include several variations of thermal architecture enabling determination of the architecture that demonstrates the minimum noise equivalent power, the lowest \(\tau \) , and the trade-offs among designs. The three TESs we report here have identical Mo/Cu bilayer thermistors and wiring structures, while the thermal architectures are: (1) a TES with straight support beams of 1 mm length, (2) a TES with meander support beams of total length 2 mm and with two phonon-filter blocks per beam, and (3) a TES with meander support beams of total length 2 mm and with six phonon-filter blocks per beam. Our wiring scheme aims to lower the thermistor normal state resistance R \(_{N}\) and increase the sharpness of the transition \(\alpha =\)  dlogR/dlogT at the transition temperature T \(_\mathrm{C}\) . We find an upper limit of \(\alpha \) given by ( \(25\pm 10\) ), and G values of 200 fW/K for (1), 15 fW/K for (2), and 10 fW/K for (3). The value of \(\alpha \) can be improved by slightly increasing the length of our thermistors.     

Study of an operating characteristic function of the sampling inspection plan of concrete lots

This paper makes an overall analysis of the Sampling Inspection Plan of Concrete Lots based on the estimation \(f_k = \bar f_n - \lambda S_n \) of the mechanical svrength of this building material. With the help of the non-central t variable, two valuesλ _S andλ _E of the acceptance factor λ are determined for each value of n in the set {5, 6,..., 29, 30)}. These λ values have the important propriety of making it possible that inspection plans be formulated for the concrete which does not comply either with the economy or the safety prescribed by the Joint Committee RILEM/CEB on the statistical control of the quality of concrete. Finally, an extremely simple process which permits to obtain the OCC corresponding to \(\hat f_k \) estimator without using the tables of the non-central variable t is presented.     

Numerical simulation of burning front propagation

In the context of a numerical experiment, it is shown that the switching wave described by the reaction-diffusion equation can be delayed at a medium inhomogeneity with a thickness Δ and amplitude Δβ for a finite time τ = τ(Δβ, Δ) up to a complete stop at it (τ = ∞). Critical values Δβ _c and Δ _c corresponding to the autowave stop are found. The similarity laws \(\tau \sim (\Delta _c - \Delta )^{ - \gamma _\Delta } \) and \(\tau \sim (\Delta \beta _c - \Delta \beta )^{ - \gamma _\beta } \) are established, and the critical indices and are found. The similarity law is established for critical values of amplitude and width of the inhomogeneity corresponding to the autowave stop Δβ _c ～ Δ _c ^-δ where δ ≈ 1.     

Generalized fracture mechanics of ductile steels

The generalized fracture mechanics approach is applied to two ductile steels, namely mild steel and 18/8 stainless steel in plane stress. The theory defines a fracture parameter \(\mathcal{T}\) , which is a truly plastic analogue of theJ contour integral and, for an edge crack specimen, is given by $$\mathcal{T} = k_1 ( \in _0 )cW_{0_c } $$ wherek ₁ is an explicit function,c is the crack length andε ₀, W_0c are respectively the strain and input energy density at fracture, remote from the crack. The functionk ₁(ε _o) is derived experimentally and the constancy of \(\mathcal{T}\) with respect to crack length and applied load is demonstrated. The variation of \(\mathcal{T}\) with crack extension during slow growth is investigated, as is the rate dependence of \(\mathcal{T}\) in mild steel.     

Containerless Measurements of Density and Viscosity for a Cu_{48}Zr_{52} Liquid

The densities of solid and liquid Cu \(_{48}\) Zr \(_{52}\) and the viscosity of the liquid were measured in a containerless electrostatic levitation system using optical techniques. The measured density of the liquid at the liquidus temperature (1223 K) is (7.02 \(\pm \) 0.01) g \(\cdot \) cm \(^{-3}\) and the density of the solid extrapolated to that temperature is (7.15 \(\pm \) 0.01) g \(\cdot \) cm \(^{-3}\) . The thermal expansion coefficients measured at 1223 K are (6.4 \(\pm \) 0.1) \(\,\times \,10^{-5}\) K \(^{-1}\) in the liquid phase and (3.5 \(\pm \) 0.3) \(\,\times \,10^{-5}\) K \(^{-1}\) in the solid phase. The viscosity of the liquid, measured with the oscillating drop technique, is of the form \(A\exp \left[ \left( {{E}_{0}}+{{E}_{1}}\left( 1/T-1/{{T}_{0}} \right) \right) \times \left( 1/T-1/{{T}_{0}} \right) \right] \) , where \({{T}_{0}}=1223\) K, \(A= (0.0254 \pm 0.0004)\) Pa \(\cdot \) s, \({{E}_{0}}\) =  (8.43 \(\pm \) 0.26) \(\,\times \,10^3\) K and \({{E}_{1}}\) =  (1.7 \(\pm \) 0.2) \(\,\times 10^7\) K \(^{2}\) .     

Work hardening and recovery during compressive creep of polycrystalline MgO

High precision equipment has been used to study the effects of small stress changes during steady state creep of magnesia at 1596 K. When the stress,σ ₁, is reduced by a small amount,Δσ, the creep rate decreased to zero for a period,Δt, before accelerating to a new steady value. Calculating the rate of recovery,r(=?δσ/δt) asΔσ/Δt and the coefficient of strain hardeningh(=δσ/δε) asΔσ/Δε (whereΔε is the instantaneous strain recorded on increasing the stress byΔσ) gave the ratio,r/h, which predicts accurately the observed steady creep rate, \(\dot \in _s \) . It is proposed that when \(\dot \in _s \) ∝ σ ³, creep is recovery controlled. The results are explained in terms of a model for creep in which the rate controlling process is the growth of the 3-D dislocation network within subgrains, to form dislocation sources allowing slip to occur.     

Decomposition of the Heusler alloy Cu2MnAl at 360°C

During thermomagnetic studies, the as-quenched Heusler alloy Cu_2.00 Mn_1.00 Al_1.01 exhibits two Curie temperatures \(\theta _{C_I } \) and \(\theta _{C_{II} } \) . After 98 h at 360° C, above the Curie point, X-ray diffraction patterns indicate two ferromagnetic phases: Cu₂MnAl (I) witha _I=5.8707 Å and \(\theta _{C_I } \) = 151 ± 10° C; Cu₂MnAl (II) witha _II=5.9656 Å and \(\theta _{C_{II} } \) = 332 ± 4° C, whereas the 850° C as-quenched alloy exhibitsa=5.9612 Å andθ _c=341±5° C. The results are discussed in terms of the early stages of the decomposition of the Heusler phase. A mechanism, involving mainly the atomic migration of manganese, is suggested in order to reach the equilibrium phases of the ternary Cu-Mn-Al diagram. The kinetics of the decomposition should be ruled by the nucleation and the growth of the Cu₃Mn₂Al intermetallic compound.     

Superconducting transition temperature of aluminum,indium, and lead fine particles

Aluminum, indium, and lead fine particles with free surfaces were made by evaporation in helium gas to study the size dependence of the superconducting transition temperatureT _c in very small particles. The transition temperature was determined from the change of diamagnetic susceptibility with temperature. The present experiment shows thatT _c rises with decrease of the average diameter \(\bar d\) for aluminum and indium, while it remains nearly constant for lead. The enhancement factorsT _c /T _c ^b (T _c ^b isT _c for the bulk material) in the case of \(\bar d = 100 {\AA}\) are determined as 1.45, 1.15, and 1.0 for aluminum, indium, and lead, respectively. The effect of the soft phonon mode arising from the increasing fraction of surface satisfactorily explains the experiment with respect to both the size dependence and the difference among elements by a rather simple model.     

Molecular beam epitaxy of semipolar AlN(11\bar{2}2) and GaN(11\bar{2}2) on m-sapphire

We report on the plasma-assisted molecular-beam epitaxy of semipolar $\hbox{AlN}(11\bar{2}2)$ and GaN( $11\bar{2}2$ ) films on $(1\bar{1}00)$ m-plane sapphire. AlN deposited on m-sapphire settles into two main crystalline orientation domains, $\hbox{AlN}(11\bar{2}2)$ and $\hbox{AlN}(10\bar{1}0),$ whose ratio depends on the III/V ratio. Growth under moderate nitrogen-rich conditions enables to isolate the $(11\bar{2}2)$ orientation. The in-plane epitaxial relationships of $\hbox{AlN}(11\bar{2}2)$ on m-plane sapphire are $[11\bar{2}\bar{3}]_{\rm AlN} \vert \vert [0001]_{\rm sapphire}$ and $[1\bar{1}00]_{\rm AlN} \vert \vert [11\bar{2}0]_{\rm sapphire}.$ GaN deposited directly on m-sapphire results in ( $11\bar{2}2$ )-oriented layers with ( $10\bar{1}\bar{3}$ )-oriented inclusions. A ～100 nm-thick AlN( $11\bar{2}2$ ) buffer imposes the ( $11\bar{2}2$ )-orientation for the GaN layer grown on top. By studying the Ga-desorption on GaN( $11\bar{2}2$ ), we conclude that these optimal growth conditions corresponds to a Ga excess of one monolayer on the GaN( $11\bar{2}2$ ) surface.     

High-Frequency Shear Viscosity of Low-Viscosity Liquids

A thickness shear quartz resonator technique is described to measure the shear viscosity of low-viscosity liquids in the frequency range from 6 MHz to 130 MHz. Examples of shear-viscosity spectra in that frequency range are presented to show that various molecular processes are accompanied by shear-viscosity relaxation. Among these processes are conformational variations of alkyl chains, with relaxation times \(\tau _{\eta }\) of about 0.3 ns for \(n\) -pentadecane and \(n\) -hexadecane at 25  \(^{\circ }\) C. These variations can be well represented in terms of a torsional oscillator model. Also featured briefly are shear-viscosity relaxations associated with fluctuations of hydrogen-bonded clusters in alcohols, for which \(\tau _{\eta }\) values between 0.3 ns ( \(n\) -hexanol) and 1.5 ns ( \(n\) -dodecanol) have been found at 25  \(^{\circ }\) C. In addition, the special suitability of high-frequency shear-viscosity spectroscopy to the study of critically demixing mixtures is demonstrated by some illustrative examples. Due to slowing, critical fluctuations do not contribute to the shear viscosity at sufficiently high frequencies of measurements so that the non-critical background viscosity \(\eta _\mathrm{bg}\) of critical systems can be directly determined from high-frequency shear-viscosity spectroscopy. Relaxations in \(\eta _\mathrm{bg}\) appear also in the shear-viscosity spectra with, for example, \(\tau _{\eta }\,\approx \) 2 ns for the critical triethylamine–water binary mixture at temperatures between 10  \(^{\circ }\) C and 18  \(^{\circ }\) C. Such relaxations noticeably influence the relaxation rate of order parameter fluctuations. They may be also the reason for the need of a special mesoscopic viscosity when mutual diffusion coefficients of critical polymer solutions are discussed in terms of mode-coupling theory.