Geometrical factors for parts of an infinite cylindrical surface

A method is described for calculating geometrical factors, allowing for attenuation of radiation by the medium, and computing radiative heat transfer between coaxial strips forming part of a cylinder.Notation mean generalized geometrical factor - local generalized geometrical factor for a closed infinite cylindrical surface - F surface area - l length of ray between elements dF_m - D and H diameter and length of cylinder - k ray attenuation coefficient - equivalent solid angle [1] determined from the condition _mm=1 at =0 for a closed surface - f () indicatrix of the specific radiation intensity (a quantity analogous to the specific luminous intensity [1]) - angle between the normal to an element of surface and the ray linking the surface elements - and angles in a section of the surface - angle between the radius and the chord subtending the projections of dF_mon the section - angle between the radius and the chord subtending the projection of element dF_mon the section and the edge of the surface - acute angle between rayl and the generator of the cylinder - ₀ half subtended angle for the arc of a section of the surface - S₂ and M generalized local geometrical factors in the notation of [2] (s₂ and is shown in Table 2 - M local factor for an infinite cylinder with a semicircular cross section for a point in the middle of the plane part of the surface; a table of values of M is given in [2]) - n number of strips     

Deformation behaviour of retained β phase inβ-eutectoid Ti-Cr alloys

Plastic deformation mode and its relation to tensile properties were investigated in retained phase of-eutectoid type Ti-Cr alloys. A plate-like single variant phase is induced during deformation of the most unstable phase having a minimum chromium content required to suppress martensitic transformation. A selected area electron diffraction pattern taken from a boundary region of the stress-induced phase plate can be explained by the idea that a single variant of phase is induced in a {3 3 2} 1 1 3 twin produced during deformation. Anisotropy in population of four phase variants decreases with increasing chromium content. On further increasing chromium content, deformation occurs by slip. Enhanced ductility is obtained in as-quenched Ti-Cr alloys accompanied by phase transformation or {332} 1 1 3 twinning during deformation, phase of as-quenched Ti-Cr alloys changes continuously from commensurate structure with sharp reflections to incommensurate structure with diffuse reflections with increasing chromium content. The obtained results in-eutectoid type Ti-Cr alloys are quite similar to those in-isomorphous type Ti-V alloys.     

Morphological evolution of α/γ interface in Fe-Mn-Al alloy

Series of multiphase diffusion couples were assembled with various terminal and alloys in a Fe-Mn-Al system. These couple series were employed to investigate the development of diffusion structures with planar and non-planar interfaces. Morphology in the diffusion interface was observed by scanning electron microscopy (SEM) and the concentration profile for the constituent element was obtained by electron probe X-ray microanalysis (EPMA) with the aid of quantitative analysis. Transitions from planar interfaces in the / two-phase diffusion couples were indexed by varying the compositions of the terminal alloys. Couples with planar / interfaces exhibited path crossings of the (/) two-phase region parallel to tie-lines. However, the two-phase path crossings for couples developing non-planar interfaces were inclined to tie-lines. The / phase boundary can be determined by the interfacial compositions of the diffusion couple in which the interface is planar.     

Tensile properties and plastic deformation modes ofβ Zr-Nb alloys

Tensile properties and plastic deformation modes of zirconium-niobium alloys were investigated at 290 and 77 K in the wide composition range from metastable to stable phase. Three types of plastic deformation modes, {332}113 twinning, {112}111 twinning and slip, were observed depending on alloy composition and temperature. {332}113 twinning, which occurs in metastable zirconium alloys, is related to the stability of phase to decomposition and leads to low yield stress and large elongation. On the other hand, {112}111 twinning, which appears in stable zirconium alloys, results from high critical stress for slip due to solution hardening and high Peierls stress and does not affect tensile properties significantly. The results obtained for zirconium-alloys are similar to those for titanium alloys, strongly suggesting that {332}113 twinning is an important plastic deformation mode which is common to phase alloys containing athermal phase.     

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.     

Method of Summation‐Integral Equations for Solving the Mixed Problem of Nonstationary Heat Conduction

The solution of a mixed axisymmetric nonstationary problem of heat conduction is obtained in the region of Laplace transforms. In solution of this problem, there occur summation–integral equations with the parameter of the integral Laplace transform (Lparameter) and the additional parameter of the finite integral Hankel transform (Hparameter). The laws governing the development of spatial nonstationary temperature fields in a bounded cylinder and a halfspace when one end surface of the cylinder is in contact with the surface of the halfspace in a circular region are determined.     

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.     

Structure and decomposition behaviour of rapidly solidified AI-Cu-Li-Mg-Zr alloys

The microstructural characteristics of AI-Cu-Li-Mg-Zr alloys have been studied after rapid solidification by melt spinning and after subsequent annealing at temperatures in the range 160 to 500°C, by using a combination of optical microscopy, scanning and transmission electron microscopy, X-ray diffraction, differential scanning calorimetry and microhardness measurements. The as-melt-spun alloys consist of a cellular microstructure with fine scale precipitates and icosahedral particles distributed within the cells and at cell boundaries. The icosahedral structure is equivalent to the T₂ phase reported by Hardy and Silcock. Annealing the melt-spun alloys leads to a complex precipitation sequence: + I + + I + S + + I + + T₁ + T₂ (bcc) + two other phases. The icosahedral particles coarsen progressively during annealing, especially at higher annealing temperatures. Fine-scale precipitates grow during annealing at low temperature, dissolve at higher annealing temperatures below 500°C, and then reprecipitate during cooling after annealing at 500°C. During annealing at low temperature, plates of and S precipitate and then dissolve, providing solute atoms for icosahedral particle growth. Stable T₁, T₂ (bcc) and two other phases precipitate after decomposition of the icosahedral particles during annealing at 500°C.     

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.     

Microstructural changes during ageing of Cu-2.5 wt% Ti

Microstructural changes in Cu-2.5wt % Ti during ageing at 573 and 773 K have been studied by transmission electron microscopy. Ageing times ranged from 60 sec to 200 h. Ordering of the precipitates was observed after very short ageing treatments at 773 K, and coarsening according tot ^1/3 was also observed from very early times. The particles were observed to become increasingly aligned into rod-like groups along 10 0 as ageing progressed. These results permit a new interpretation of the strengthening mechanisms in this alloy.     

Effect of magnetic pickups on the input transformers of measuring devices

Summary The asymmetry coefficient for all types of transformers depends on the core permeability, which in turn depends on the ratio ofl _av/s or D_av/s. In order to reduce core permeability, it is necessary to select toroidal cores with a small diameter and a large cross section, and provide laminas of O-shaped and shell-type cores with a shape to make these cores short and large in cross section.Under actual operating conditions, transformers with toroidal cores provide a higher immunity from noise. For the same designs, sizes, and relative parameter dispersions, the transformers with toroidal and O-shaped cores have a ratio of _max equal to 1.6. In shell-type transformers it is imperative to take into account the polarity of their windings on which the transformer's noise stability depends to a great extent.     

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.     

Investigation of the excitonic insulator phase in bismuth-antimony alloys

Pressure-induced metal-semiconductor transitions in bismuth-antimony alloys in a strong magnetic field (up to 70 kOe) at helium temperatures have been investigated. It is found that for values of the overlap-gap |G|1 meV the alloy forms an excitonic insulator (EI) in magnetic fields above a certain threshold (30–40 kOe). It is inferred that the EI energy gap increases with the magnetic field. The maximum gap observed in fields of 70 kOe turns out to be ₀₀7.5 K. An analysis of the results shows that transitions to the EI phase are observed from both the semimetal and the semiconducting states. The critical transition temperatureT _c is related to the EI gap by the expressionT _c0.7. Arguments are advanced in support of the fact that the formation of the EI phase involves the pairing of electrons at theL point with holes at theT point.     

Study of the paramagnetic-antiferromagnetic transition and the γ → ε martensitic transformation in Fe-Mn alloys

The paramagnetic-antiferromagnetic transition and the martensitic transformation of Fe-Mn (Mn 15–32 wt%) alloys have been investigated by resistivity, dilatometry and X-ray diffraction (XRD). The results show that paramagnetic-antiferromagnetic transition increases the resistivity and the volume of alloys, whereas the martensitic transformation reduces the resistivity and volume of alloys. The A _f that was determined by the dilatometric method is not the temperature that martensites in the Fe-Mn alloys have reverse transformed to austenites completely. Mn additions reduce M _s, increase T _N and the lattice parameter of austenite in the Fe-Mn alloys. Both the antiferromagnetic transition and the martensitic transformation lead to an increase in the lattice parameter of austenite. The lattice parameters both above T _N and below T _N decrease linearly with temperature. The lattice parameter below M _s increases first and then decreases. Moreover, the (110) and (002) atomic planes in the Fe-15Mn-0.15C alloy are separated into two peaks: 2 for (002) is 44.16°, 2 for (110) is 44.47°.     

Quantum statistical foundation to the fermi liquid model and Ginzburg-Landau wave function

An energy eigenvalue equation for a quasi-particle is derived, starting with the Heisenberg equation of motion for an annihilation operator. An elementary derivation of the Fermi liquid model having a sharply defined Fermi surface in thek-space is given, starting with a realistic model of a metal including the Coulomb interaction amongand between electrons and lattice-ions. The Ginzburg-Landau wave function (r), where represents the superconducting pairon (Cooper-pair) state, is shown to be connected with the one-pairon density operatorn by (r) = r¦_n ^1/2¦. A close analogy between supercurrent and laser is indicated.On sabbatical leave from Department of Physics and Astronomy, State University of New York at Buffalo, Buffalo, New York.     

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.     

The stress dependence of superconducting parameters in pure In and Sn and in α-phase In-Sn alloys

We have measured the length change due to the transition from the super-conducting to the normal state in pure In and Sn and in In-Sn alloys. The measurements were made on single-crystal specimens. The alloys had Sn content ranging from zero to 12 at %. Crystals parallel and perpendicular to the tetragonal axis were grown at each alloy content. We find that the relative length changes l/l are very sensitive to alloy content. From l/l we have calculated the stress derivatives H _c/ and T _c / and we find that T _c / changes from +59 to –92 mK/bar for stress along the tetragonal axis, and from –9 to 46 mK/kbar for stress perpendicular to the tetragonal axis. We suggest that these large changes are due to Fermi surface topology changes upon increasing the Sn content in In.     

Molar momentum and heat transfer

Universal relations governing the molar transfer of momentum and heat are derived on the basis of a hypothesis about the dependence of the boundaries of the molar transfer region on the flow structure and with the use of a special mathematical transformation.Notation u average longitudinal velocity, m/sec - T average temperature, °K - T_w wall temperature, °K - kinematic viscosity coefficient, m²/sec - density, kg/m³ - c_p specific heat, J/kg·K - tangential stress, N/m² - t_w tangential stress at wall, N/m² - q_w specific heat flux at wall, W/m² - u_*=_w/ dynamic velocity, m/sec - *=q_w/c_pu_* characteristic temperature, °K - thickness of boundary layer, m - ₀ thickness of laminar sublayer, m - l = /u transverse space scale of average mole at wall, m - y⁺ = y/l _22C6; dimensionless coordinate - u⁺=u/u* dimensionless velocity - ⁺=(T_w – T)/* dimensionless temperature - ⁺=/_w dimensionless tangential stress - R=In (y⁺/ _o ⁺ )/In (⁺/ _o ⁺ ) generalized dimensionless co-ordinate - U = (u⁺ - u _o ⁺ )/(u _o ⁺ - u _o ⁺ ) generalized dimensionless velocity - Pr Prandtl number Indices * flow parameters evaluated at y⁺=1 - parameters at y⁺=⁺ - 0 parameters at y⁺= _o ⁺ - w parameters at wall Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 441–448, September, 1981.     

Morphology, crystallography and defects of the intermetallic χ-phase precipitated in a duplex (δ + γ) stainless steel

The ferritic matrix in the Fe-22Cr-5Ni-3Mo-0.03C ferritic-austenic duplex stainless steel undergoes a variety of decomposition processes when aged in the temperature range 650–750°C. These processes involve the precipitation of the austenite and of the and Frank-Kasper phases. The intermetallic -phase is found at both the grains boundaries (homo and heterophase interfaces) and inside the ferritic grains where it adopts an unexpected hexagonal shape. At the early stage of its precipitation, it nucleates at the / and /heterophase interfaces and then grows by expanding exclusively in the ferritic matrix. This study is basically focused on this intermetallic -phase. The crystal structure and the chemical composition are respectively studied by electron diffraction and energy dispersive X-ray spectroscopy. The -phase exhibits rational orientation relationships with the austenite and the -phase with which it is in contact and an invariably cube-on-cube orientation relationship with the ferritic matrix into which it grows. Based on the orientation relationship, the morphology and the number of variants of this -phase are understood in terms of the group theory. The planar defects present in a large density in the -phase, are roughly parallel to {0 1 1}//{0 1 1}. The fault vectors are determined as: 110 and 111, the latter corresponding for a bcc structure to a phase shift, the defects can be simply described as boundaries. Based on the obtained results, a structural proximity between the -phase and a super-cell derived from the ferritic matrix has been brought to light. This super-cell is described as a stacking of corrugated and planar layers obeying the following parallelism {0 1 1}//{0 1 1}. Indeed this super-cell approach provides an interpretation for several microstructural features such as the / interface plane, the planar defects in the -phase and their related fault vectors.It has been also stated that Mo is an efficient -phase forming element. Upon these considerations a detailed characterization provided valuable insights into the precipitation mechanism associated with the -phase formation.     

Morphology of nitrated layers in titanium alloys of different structural classes

This paper generalizes the results of investigations of the effect of nitrogen on titanium alloys at temperatures of isothermal exposure of 800 – 1100°C and gas pressures of 10⁵ – 10^–1 Pa. As a result of nitration, a gas-saturated area appears on the surfaces of the alloys (in addition to the nitride area). Its qualitative and quantitative characteristics depend on the phase composition of the alloys. The gas-saturated area consists of two layers. For all the investigated alloys, the first layer (adjacent to the nitride area) can be described as the -titanium structure stabilized with nitrogen. If the saturation temperature is lower than the temperature of the polymorphic transformation, then the structure of the second layer is identical to the alloy matrix. As a result of nitration in the (+)--region, this structure undergoes the transformation and, for - and pseudo--alloys, turns into an -grain of smaller size but with higher etchability compared to the -structure of the first layer. For (+)-alloys, this is mainly the -phase (-plates) in the -transformed structure. For -alloys, the morphology of the gas-saturated area does not depend on the saturation temperature and is identical to other structural types nitrated in the -region.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 29, No. 5, pp. 35–41, September–October, 1993.