The age hardening effect in Ti-6 Al-4 V due to ω and α precipitation in the β grains

The structure at room temperature of a quenched TA6V titanium alloy has been investigated. This structure is + or + according to the treatment temperature; it is always metastable. During ageing the grains decomposed by the reaction + + +; this decomposition was accompanied by a large increase of the 0.2% yield stress. No structural modification was observed in. The and phase of TA6V were separately investigated in the form of single-phase alloys. The hardness of was insensitive to ageing, while was considerably hardened by and; we deduced that the strengthening of the minor phase during ageing is mainly responsible for the hardening of TA6V.     

The influence of ageing on the stability of β-γ/γ′ derived microstructures in Ni-Al-Cr-(Co) alloys

Multiphase Ni-Al-(Fe)-(Cr)-(Co)-based intermetallics with (B2)- (A1)/(L1₂), - or - microstructures can exhibit significant room-temperature tensile ductility. In the case of Ni-Al-Cr-based alloys, microstructural development is complicated by the precipitation of -Cr, which can supplant the -phase during ageing of three-phase -/ microstructures. An investigation of the stability, during ageing, of cast Ni-Al-Cr-(Co) alloys with microstructures derived from -/ is reported. In the as-cast condition, the materials investigated consisted of a dendritic matrix containing L1₀ type martensite and interdendritic /. Extensive intra- and interdendritic -Cr precipitation was also observed. The stability during ageing of the interdendritic / microstructure is also considered and transformation of the L1₀ martensite is examined.     

Superfluid density near the lambda point of4He under pressure

The superfluid density in ⁴ He was determined near T from the second-sound velocity as a function of T–T and pressure. The critical exponent of the superfluid density was found to depend, even slightly, on the pressure. Furthermore, the fundamental length ₀ in the coherence length = ₀ [1–(T/T)]^–' seemed to be proportional to the mean interatomic distance. The implications of the results are also discussed.This work was partly supported by The Ito Science Foundation and by The Nishina Memorial Foundation.     

Equivariant estimation functions and normal distribution assumption for the model of linear regression

Summary When estimating a linear functional g() in a linear modelM=(Y, X, ² I), it is well known that, for convex loss, the OLS estimator minimizes the risk uniformly in the class (M, g) of all unbiased estimators providedY is normally distributed. For squared error loss andX a (n×2)-matrix we identify allX andg for which, in some sense, the converse holds:Y is necessarily normally distributed if the OLS estimator minimizes the risk uniformly in the class of equivariant estimators in (M, g).

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Zusammenfassung Bekanntlich minimiert bei der Schätzung einer linearen Parameterfunktion() im linearen ModellM=(Y, X, ² I) und bei konvexer Schadensfunktion die OLS-Schätzfunktion das Risiko gleichmäßig in der Klasse (M, g) aller erwartungstreuen Schätzfunktionen, wenn nurY normal verteilt ist. Für eine quadratische Schadensfunktion und einenx2-DesignmatrixX werden alleX undg bestimmt, für die in einem gewissen Sinn die Umkehrung gilt:Y ist notwendignormalverteilt, falls die OLS-Schätzfunktionen das Risiko in der Klasse der äquivarianten Schätzfunktionen von (M, g) gleichmäßig minimiert.

     

Supercarrier Effective Mass Isotope Effect by Interband Scattering

Supercarrier effective mass isotope effect (exponent ) is investigated using a two-band model with interband pair scattering. The corresponding repulsive interaction incorporates besides the dominating electronic (Coulomb) part an electron-phonon contribution inversely proportional to the ionic mass factor. Calculations illustrating the behaviour of T _c , its isotope exponent , and with doping in La _2–x Sr _x CuO ₄ type underdoped system reflect the observed tendencies. ² Both and diminish with doping, the sign of is opposite to . A typical estimation gives || 0.2.     

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.     

Size-strength effects in sapphire and silicon nitride whiskers at 20° C

Tensile tests at 20° C have been carried out on seventy-three sapphire whiskers and on seventeen silicon nitride whiskers. The sapphire whiskers were of 0001, 1¯120, 10¯10, and 10¯11 orientations, while the silicon nitride whiskers were 0001, 11¯20, and 10¯13. Tensile strengths were in the range 45 to 1500 kg/mm², and deformation was found to be purely elastic. The tensile strength data have been analysed and fitted to empirical equations describing the effect of size on strength for different orientations. These empirical equations have been used to deduce possible fracture nucleation mechanisms. It is concluded that, in the case of 0001 sapphire whiskers, fracture nucleation may be due to dislocation pile-ups or interactions, while in the other cases a Griffith flaw mechanism is probably applicable.     

Growth of Gray Tin Crystals

A method is proposed for growing large -Sn single crystals without their disintegration as a result of the phase transition. -Sn crystals are prepared by freezing the closed system water–Sn–seed in such a way that the pressure exerted by the expanding ice minimizes the amount of -Sn nuclei and reduces the growth rate.     

Eutectoid decomposition mechanisms in hypoeutectoid Ti-X alloys

A TEM study has been made of the bainite reaction in five hypoeutectoid Ti-X alloys, where X was successively cobalt, chromium, copper, iron and nickel. Rational orientation relationships were demonstrated amongst eutectoid , eutectoid intermetallic compound and the matrix in Ti-Ni, Ti-Co and Ti-Cr. Formation of Ti₂Co at : boundaries was observed. Eutectoid in bainite was found to be slightly misoriented with respect to proeutectoid , indicating that it is separately nucleated, perhaps sympathetically, rather than the result of the continued growth of proeutectoid . Eutectoid Ti₂Co and Ti₂Cu crystals in bainite were approximately equiaxed whereas Ti-Cr₂ crystals were elongated, a result ascribed to a ledge height-to-spacing ratio / at intermetallic compound crystal: boundaries approaching that of eutectoid (: boundaries in Ti-Cr but not in the other two systems. In the Ti-Fe alloy, eutectoid and eutectoid TiFe were directly observed to have ledged interphase boundaries with their matrix, but with different inter-ledge spacings and growth directions. Observation of pearlite lamellae growing normal to the broad faces of proeutectoid plates in the Ti-Ni alloy indicates that this mode of eutectoid decomposition, like that of bainite, can develop from partially coherent interphase boundaries. The suggestion was offered that pearlite forms when approachesh at the nucleating proeutectoid : interface and that bainite develops when h at this interface.     

Flow-stress recovery of nickel-aluminium alloys

Flow-stress recovery measurements along with structural observations using electron microscopy have been carried out on room-temperature prestrained alloys of Ni-11.9, 13.1 and 13.5 at.% Al aged at 735° C. These alloys contained respectively 0, 5, and 8 vol% Ni₃Al) in a fine dispersion. Samples were recovered at and below the ageing temperature for times ranging from 0.1 to 100 h. The influence of volume fraction of , distribution, amount of prestrain and recovery temperature on recovery kinetics was investigated.Results for samples recovered at 735° C showed a large fractional recovery (about 30%) following the first 0.1 h anneal for all samples. About 50 to 70% of the flow stress is recovered at the end of 100 h recovery anneals. The changes in dislocation structure agreed quantitatively with the changes in flow stress.Interpretation of the data in terms of a network growth model of recovery show the solid solution alloy to agree with theory for long recovery times (t>10 h) whereas the -strengthened alloys deviate considerably from the simple model.     

Analytical Theory of DC SQUIDS Operating in the Presence of Thermal Fluctuations

A comprehensive analytical theory of symmetric DC SQUIDs is presented taking into account the effects of thermal fluctuations. The SQUID has a reduced inductance < 1/ where = 2LI_c/₀, L is the loop inductance, ₀ is the flux quantum, and I_c is the critical current of the identical Josephson junctions which are assumed to be overdamped. The analysis, based on the two dimensional Fokker–Planck equation, has been successfully performed in first order approximation with considered a small parameter. All important SQUID characteristics (circulating current, current-voltage curves, transfer function, and energy sensitivity) are obtained. In the limit 1( = 2k_BT/I_c0 is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature) the theory reproduces the results of numerical simulations performed for the case of small thermal fluctuations. It was found that for < 1 the SQUID energy sensitivity is optimum when is higher than 1/, i.e., outside the range for which the present analysis is valid. However, for 1 the energy sensitivity has a minimum at L = L_F , where L_F = ( ₀ /2) ²/k_B , and therefore, in this case, the optimal reduced DC SQUID inductance is _opt = 1/, i.e., within the range for which the present analysis is valid. In contrast to the case of an RF SQUID, for a DC SQUID the transfer function decreases not only with increasing L/L_F but also with increasing (as 1/). As a consequence, the energy sensitivity of a DC SQUID with < 1/ degrades more rapidly (as ⁴ ) with the increase of than that of an RF SQUID does (as ² ).     

Isotone policies for the value iteration method for Markov decision processes

Summary This paper considers the value iteration process for countable state discounted Markov decision processes and shows that under certain conditions there will exist anN-isotone sequence of optimal decision rules and value functions, whereN-isotonicity of a sequence of decision rules { _n }, n {1,2,...}=N requires that, for a specified partial order overK=UK(i) (K(i) being the feasible action space fori) then _n–1(i) _n (i), n2 and alli I, with a similar definition ofN-isotonic for the value functions {v _n },n1.

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Zusammenfassung Wir betrachten die Wertiteration bei diskontierten Markovschen Entscheidungsprozessen mit abzählbarem Zustandsraum. Wir zeigen, daß unter gewissen Bedingungen eineN-isotone Folge von optimalen Entscheidungsregeln und Wertfunktionen existiert.N-isoton heißt eine Folge von Entscheidungsregeln { _n },n {1,2,...}=N, dann, wenn für eine Halbordnung überK=UK(i) gilt _n–1 (i) _n–1(i) _n (i) für allen2 undi I. (K(i is die Menge der zulässigen Aktionen im Zustandi). Eine analoge Definition derN-Isotonie gilt für die Wertfunktionen {v_n},n1.

     

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.     

Room temperature age-hardening in a β titanium alloy

A metastable titanium alloy containing 10 wt % Zr and 12 wt % V has been found to undergo a substantial age-hardening reaction at temperatures as low as 20° C. The reaction involves continued growth of athermal-phase particles produced during water quenching from the-phase field. The morphology of the as-quenched is retained, implying the absence of long-range diffusion during ageing: this is consistent with the low value of the activation energy measured (93 kJ kg mol^–1). It is suggested that the growth is caused by unpinning of/ interfaces as a result of the short-range motion of interstitials present in the alloy. The age-hardening produces a severe loss in tensile ductility and inhibition of stress-induced martensite formation.     

Thermodynamic investigations of liquid Bi-Na and Sn-Na alloys by coulometric titration using β″-alumina

The following double galvanic cell was assembled and the thermodynamic properties of liquid Bi-Na and Sn-Na alloys, and the ion selectivity of -alumina during coulometric titration, were investigated. Mo, Na(I)¦-alumina¦M-Na(I), Mo [I] M-Na(I)¦-alumina¦Au + Au₂Na, Mo [II] (M = Bi or Sn) where M-Na(1) and Au + Au₂Na were used as the common electrode and reference electrode, respectively. Sodium was coulometrically titrated through the -alumina electrolyte of cell I both ways, and the EMFs were measured. It was found that no ion-exchange reaction occurs between the liquid alloys and the -alumina, and only Na was transferred in the -alumina during coulometric titrations. The thermodynamic properties of liquid Sn-Na and Bi-Na alloys were found to be in agreement with the literature.     

Numerical calculation of turbulent flow in symmetric two-dimensional diffusers

Summary This study presents numerical predictions on the fluid flow characteristics for turbulent flow in symmetric two-dimensional diffusers. The grids are established by employing the nonorthogonal bodyfitted coordinate system and associating them with the multi-block to handle the complex geometry. The turbulent governing equations are solved by the control-volume-based finite-difference method. The parameters studied include the entrance Reynolds numbers of the diffusers (Re=6000, 9000 and 12000), the diffusion angle (=22.5°, 30°, 60° and 90°), and the diffusers expansion ratioER=3. The numerical results show that the influence on the size of the recirculation region for turbulent flow was ambiguous with Reynolds numbers effect, but evident with the change of diffusion angles. From the streamline contours, it can be seen that there is a large recirculation region on the top wall, and a small recirculation region is formed at the corner of the bottom wall, but the recirculation region of the bottom wall is ambiguous at =22.5°. In addition, with increasing Reynolds numbers of diffusion angle the pressure recovery coefficientC _PR decreases.Nomenclature C ₁,C ₂,C turbulent constant - C _P pressure coefficient - C _PR pressure recovery coefficient - ER expansion ratio - f ₁,f ₂,f empirical constants for low Reynolds number turbulence model - G generation rate of turbulent kinetic energy - H height of the diffuser - k turbulent kinetic energy - Re Reynolds number (U _S W ₁)/ - S source term - U _S maximum velocity upstream of the diffuser - W ₁ height of the upstream channel - W ₂ height of the downstream channel - Reynolds stress Greek symbols , axes of nonorthogonal curvilinear coordinate system - transported scalar - density - _l , _t laminar and turbulent viscosity - kinematic viscosity - diffusion angle - turbulent energy dissipation rate - _k , empirical constants in turbulence model equations - diffusion coefficient     

Theory of periodically driven,current-carrying,superconducting filaments. I. Spatially homogeneous states

Starting from the nonequilibrium theory of dirty superconductors in the Ginzburg-Landau regime, spatially homogeneous states with an applied currentI=I ₀+I ₁ cos (t) are considered. Expressions for the linear response (I₁ small) valid up to high frequencies (k _BT_c) are derived and evaluated analytically for the experimentally important case of smallI ₀ and ₀(T). Then the nonlinear response is treated for frequencies with _E1. Interesting new behavior is found for frequencies ₀ 1, where ₀ is essentially the GL relaxation time.     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

γ ? α2 Phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%)

The ₂ phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%) alloy has been studied by analytical electron microscopy. ₂ and phases were found at grain boundaries. ₂ layers that suspended in layers and interfacial ledge higher than 2d ₍₁₁₁₎ at /₂ interfaces were observed in the lamellar grains. These facts indicated that ₂ phase transformation and dynamic recrystallization have occurred during high temperature stress rupture deformation. It can be concluded that deformation induced ₂ phase transformation and dynamic recrystallization resulted in the presence of particles at grain boundaries. A structural and compositional transition area between deformation-induced ₂(or ) and its adjacently original (or ₂) phases was found by HREM and EDS and is suggested as a way to transform between and ₂ phase during high temperature stress rupture deformation. The transition area was formed by slide of partial dislocations on close-packed planes and diffusion of atoms.     

Mechanical properties and microstructure of β-SiAION-β-SiC composites by pressureless sintering

-SiAION--SiC composites containing up to 12 wt% -SiC were prepared by pressureless sintering. The strength of composites at room temperature remained relatively unchanged, whereas strength at 1200 °C increased for composites. The fracture toughness (K _IC) for composites was higher than that for -SiAION ceramics. The maximum value was 5.4 MPa m^1/2 for 6 wt% -SiC, and this was an improvement of 15% in comparison with -SiAION ceramics. From SEM observations, an improvement inK _IC values was attributed to crack deflections and branching-off of cracks. Intra-granular fractures were frequently observed in -SiAION. From TEM observations, -SiAION crystals were nanocomposites, within which existed the fine crystals in -SiAION crystal. For composite, -SiAION and -SiC crystals were directly in contact. The mismatching zone was observed in -SiC.