Dependence of the contact heat conductivity of granular systems on the external load

An examination has been made of the dependence of the contact heat conductivity of granular systems on the external load. The calculation formulas proposed for contact heat conduction are applicable over a wide range of materials.Notation s_a area of actual contact of two particles in a granular material - _c conductivity of the contact between two particles - h_r height of a micro-roughness - _s thermal conductivity of the material of the particles - d=2r particle diameter - _c contact thermal conductivity of the granular material - p porosity of the system - S_a1, S_a2 area of contact of two particles in the freely poured state and under the action of a load - f thermal conductivity of the granular system in the freely poured state - () portion of the thermal conductivity of a granular material that depends on the external load - relative area of contact - s_n nominal area of contact of the two particles - external specific load - E modulus of elasticity of the particle material - E₀ effective modulus of elasticity of the granular material - k₁, k₂, k₃, k_m, k_b empirical coefficients     

Equations of generalized thermoelasticity of a Cosserat medium in stresses

Thermoelasticity equations in stresses are derived in this paper for a Cosserat medium taking into account the finiteness of the heat propagation velocity. A theorem is proved on the uniqueness of the solution for one of the obtained systems of such equations.Notation u displacement vector - small rotation vector - absolute temperature - ₀ initial temperature of the medium - relative deviation of the temperature from the initial value - , , , , , ,, m constants characterizing the mechanical or thermophysical properties of the medium - density - I dynamic characteristic of the medium reaction during rotation - k heat conduction coefficient - ₀ a constant characterizing the velocity of heat propagation - X external volume force vector - Y external volume moment vector - w density of the heat liberation sources distributed in the medium - E unit tensor - T force stress tensor - M moment stress tensor - nonsymmetric strain tensor - bending-torsion tensor - s entropy referred to unit volume - V volume occupied by the body - surface bounding the body - (T)_ki, (M)_ki components of the tensorsT andM - q thermal flux vector Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 482–488, March, 1981.     

Melting of the flux line lattice observed by specific heat experiments in YBa2Cu3O7−δ

High resolution adiabatic specific heat experiments on YBa₂Cu₃O₇– (00.05) are performed in magnetic fields from 0 to 14 T (Bc and Bc). In a 0.3 gram, twinned crystal with strong pinning, a step is consistently observed at the melting temperature T_m of the vortex solid up to a critical point that depends on . The field B_m and step temperature T_m obey the relation B_m=B_mo()(1–T_m/Tc)^4/3. The anisotropy of B_m and that of the upper critical field B_c2 are found to be equal. Alternatively, in a 18 mg, twinned crystal of high purity with low pinning, first-order-like specific heat peaks are observed on the melting line from 8 to 14 T. The entropy under these peaks is 0.5 kB /vortex/bilayer. These characteristic features are attributed to the melting of a vortex glass in the former case and that of a vortex lattice in the latter case.     

Vortex Dynamics in a Thin Film of Tl2Ba2CuO6

The vortex dynamics in a Tl ₂ Ba ₂ CuO ₆ (Tl-2201) thin film with a critical temperature T _c = 80.8 K has been studied by electrical resistivity measurements for magnetic fields 0B12 T. The vortex glass line, as determined from the disappearance of linear resistivity, was found to be well described by B _g (T) = B ₀ [(1–T/T _c )/(T/T _c )], with B ₀ 0.65 T and 1.9. The glass line of Tl-2201 is observed to be located below the one of Tl ₂ Ba ₂ CaCu ₂ O ₈₊ (Tl-2212) in a magnetic phase diagram based on a reduced temperature scale T/T _c , thus suggesting a higher anisotropy for Tl-2201.     

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.     

Thermodynamics of the quasiequilibrial growth of crazes

By comparing the morphology and physical properties (averaged over the scale of 1 to 10m) of a crazed and uncrazed polymer, it can be concluded that crazing is a new phase development in the initially homogeneous material. The present study is based on recent work on the general thermodynamic explanation of the development of a damaged layer of material. The treatment generalizes the model of a crack-cut in mechanics. The complete system of equations for the quasiequilibrial craze growth follows from the conditions of local and global phase equilibrium, mechanical equilibrium and a kinematic condition. Constitutive equations of craze growth-equations are proposed that are between the geometric characteristics of a craze and generalized forces. It is shown that these forces, conjugated with the geometric characteristics of a craze, can be expressed through the known path independent integrals (J, L, M,). The criterion of craze growth is developed from the condition of global phase equilibrium. F Helmholtz's free energy - G Gibb's free energy (thermodynamic potential) - f density ofF - g density ofG - T absolute temperature - S density of entropy - strain tensor - components of - stress tensor - components of - _y stress along the boundary of an active zone (yield stress) - _b stress along the boundary of an inert zone - applied stress - value of at the moment of craze initiation - K stress intensity factor - C tensor of elastic moduli - C ^–1 tensor of compliance - internal tensorial product - V volume occupied by sample - V ₁ volume occupied by original material - V ₂ volume occupied by crazed material - V boundary ofV - (V) vector-function localized on V - (x) characteristic function of an area - (x) variation of(x) - (x) a finite function - tensor of alternation - components of the boundary displacement vector - l components of the vector of translation - n components of the normal to a boundary - _k components of the vector of rotation - e symmetric tensor of deviatoric deformation of an active zone - expansion of an active zone - J ⁽ⁱ⁾ ,L _k ⁽ⁱ⁾ ,M ⁽ⁱ⁾,N ⁽ⁱ⁾ partial derivatives ofG ⁽ⁱ⁾ with respect tol , _k, ande , respectively - [ ] jump of the parameter inside the brackets - thickness of a craze - 2l length of a craze - 2b length of an active zone - l _c distance between the geometrical centres of the active zone and the craze - ^* craze thickness on the boundary of an active and the inert zone - l ^* craze parameter (length dimension) - A craze parameter (dimensionless) - ^* extension of craze material     

Asymptotic behavior of the vector potential and the order parameter for an isolated vortex

Eilenberger's formulation of the theory of inhomogeneous superconductors is used to study an isolated vortex in a type-II superconductor. Exact integral expressions for the vector potential and the order parameter are obtained and used to determine the asymptotic behavior of these quantities. Far from the axis of the vortex, the vector potential approaches its BCS value in an approximately exponential fashion, the decay constant being equal to the quantity obtained by Eilenberger and Büttner in the local case, and equal to {2[(k _BT)²+ _BCS ² ]^1/2/v_F+(1/v _F)}^–1 in the case where nonlocal effects dominate. The order parameter also approaches its BCS value approximately exponentially, the decay constant being equal to the quantity of Eilenberger and Büttner when <2, and equal to 1/2 when >2.Supported in part by the National Research Council of Canada.Sole affiliation is now the University of Toronto.     

Interface shapes in a torsionally oscillating,layered medium of viscoelastic liquids

Summary The free surface motion of a layered medium of liquids in a gravitationally stable configuration, resting on top of a layer of mercury, driven by a torsionally oscillating, cylindrical outer wall is investigated. The non-linear problem in the unknown physical domain is expressed as a series of linear problems in the rest state by means of a domain perturbation method. The flow variables and the stress are expanded into series in terms of the amplitude of the oscillation of the cylinder. The shapes in the mean of the interfaces between layers and the flow field are determined up to second order in the perturbation parameter, the amplitude of the oscillation.Nomenclature Density - Modified pressure field - Amplitude of the oscillation - Frequency of the oscillation - Interfacial value of the surface tension - Dynamic viscosity - , , Material functions - Complex viscosity - Stream function - Position vector at timet= - ₁, ₂ The first two Rivlin-Ericksen constants - Quadratic shear relaxation modulus - ,t Time - u Velocity vector - u,v,w Velocity components - S Extra stress tensor - h Interface elevation - D Stretching tensor - G Strain history tensor - A ₁ The first Rivlin-Ericksen tensor - J Mean curvature - p Pressure - t Unit tangent vector - n Unit normal vector - G Shear relaxation modulus - X Position vector in the rest stateD ₀ - r, ,z Rest state coordinates - x Position vector in the physical spaceD - R, ,Z Physical space coordinates - r ₀ Radius of the oscillating cylinder - e _r ,e ,e _z Physical basis vectors inD ₀ - e _R ,e ,e _Z Physical basis vectors inD - Indicates the jump in the enclosed quantity across an interface With 1 FigurePresented at the Xth Canadian Congress of Applied Mechanics, The University of Western Ontario, London, Ontario, Canada, June 2–7, 1985.     

The Interplay of Electronic and Nuclear Magnetism in PtFe x at Milli-, Micro-, and Nanokelvin Temperatures

We have measured ac susceptibility, nuclear magnetic resonance, and nuclear heat capacity of two PtFe _x samples with concentrations of magnetic impurities x = 11 ppm and 41 ppm at magnetic fields (0 ± 0.05) mTB248 mT. The susceptibility data have been measured at temperatures of 0.3 KT100 mK, no hint for nuclear magnetic ordering could be detected to a temperature of 0.3 K. The nuclear heat capacity data taken at 1.4 KT10 mK show enhanced values which scale with x at low polarization. This effect is described by a model assuming an internal magnetic field caused by the impurities. No indication for nuclear magnetic ordering could be detected to 1.4 K. The nuclear magnetic resonance experiments have been performed on these samples at 0.8 KT0.5 mK and 2.5 mTB22.8 mT as well as on three other samples with x = 5, 10, 31 ppm in a different setup at 40 KT0.5 mK and at 5.4 mTB200 mT. Spin-lattice and effective spin-spin relaxation times ₁and ₂ ^* of ¹⁹⁵ Pt strongly depend on x and on the external magnetic field. No temperature dependence of ₁and ₂ ^* could be detected and the NMR data, too, give no hint for nuclear magnetic ordering to 0.8 K.     

Vortex motion in high-T c superconductors near the upper critical fieldH c2

The vortex dynamics in layered superconductors such as YBaCuO and BiSrCaCuO near the upper critical field H_c2 is considered. The magnetic field is parallel to the layers and a transport current flows along the layers perpendicular toH. There exists a finite pinning force for the vortex motion across the layers in a macroscopically homogeneous superconductor. The critical current vanishes exponentially in the limit of weakly layered structure, _c (T)s. The current-voltage characteristic is calculated in case _c (T)s. The initial part of the characteristic may have a negative slope depending on the magnetic fieldH.     

Self-diffusion of Ti,Zr, and Hf in their hcp phases,and diffusion of Nb95 in hcp Zr

Preliminary values for the self-diffusion constants of -(hexagonal cp) Hf and new values for the self-diffusion constants of -(hcp) Zr are given. A new determination of the latter was considered necessary since existing values disagree widely and the experimental methods employed in their determination are not considered to be sound. Values obtained by the authors for the self-diffusion constants of -Ti are reviewed.The activation energies obtained are much smaller than those predicted by relationships based on physical properties of the elements and, within the experimental error, they have similar values to those corresponding to the -(body-centred cubic) phases. Frequency factors are too small to satisfy Zener's theory; when interpreted according to a vacancy model they give negative activation entropies, and the relationship D ₀()/D ₀() is approximately the same for the three elements.It is suggested that the same diffusion mechanism operates in both the - and -phases. If two mechanisms operate in the -phase, the low temperature one is the same as operates in the -phase.     

Nearly isochoric finite torsion of a compressible isotropic elastic circular cylinder

Summary Finite torsion of a circular bar of isotropic compressible hyperelastic material is considered. A procedure suggested by Truesdell is used to obtain solutions for a particular strain energy function although the method used is not restricted to this particular form. The procedure is applicable if the volume strain is small. Results for finite twist with the length prevented from changing and with the length allowed to change so that the resultant longitudinal force is zero are presented.

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Fast-isochore endliche Torsion eines kompressiblen, isotropen, elastischen Kreiszylinders

Zusammenfassung Betrachtet wird die endliche Verdrehung eines Stabes mit Kreisquerschnitt aus einem isotropen, kompressiblen, hyperelastischen Werkstoff. Eine von Truesdell vorgeschlagene Vorgangsweise wird zur Bestimmung der Lösungen, für eine spezielle Verzerrungsenergiefunktion, verwendet, obwohl die verwendete Methode nicht auf diese spezielle Form beschränkt ist. Diese Vorgangsweise ist anwendbar, sofern die Volumsverzerrung klein ist. Ergebnisse für die endliche Verdrehung werden angegeben, wobei entweder die Längenänderung unterbunden ist oder die Länge sich ändern kann, so daß die resultierende Längskraft verschwindet.

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Notation F deformation gradient tensor - B=FF ^T left Cauchy-Green tensor - I identity matrix - I ₁=trB first invariant ofB - I ₂=1/2[(trB)²–trB ²] second invariant ofB - I ₃=detB third invariant ofB - W strain energy per unit volume of unstrained stateB ₀ - gradient operator for stateB - u small displacement from stateB - H=u small displacement gradient based on stateB - T true stress tensor based on stateB - f body force vector - T additional stress - =T+T true stress for final configuration - elastic constant equivalent to shear modulus for small deformation - elastic constant equivalent to Poisson's ratio for small deformation - r, ,z cylindrical polar coordinates - _r , , _z , _z physical components of stress tensor for cylindrical polar coordinates With 3 Figures     

Natural convection in a rectangular enclosure in the presence of a magnetic field with uniform heat flux from the side walls

Summary A numerical study is presented for magnetohydrodynamic free convection of an electrically conducting fluid in a two-dimensional rectangular enclosure in which two side walls are maintained at uniform heat flux condition. The horizontal top and bottom walls are thermally insulated. A finite difference scheme comprising of modified ADI (Alternating Direction Implicit) method and SOR (Successive-Over-Relaxation) method is used to solve the governing equations. Computations are carried out over a wide range of Grashof number, Gr and Hartmann number, Ha for an enclosure of aspect ratio 1 and 2. The influences of these parameters on the flow pattern and the associated heat transfer characteristics are discussed. Numerical results show that with the application of an external magnetic field, the temperature and velocity fields are significantly modified. When the Grashof number is low and Hartmann number is high, the central streamlines are elongated and the isotherms are almost parallel representing a conduction state. For sufficiently large magnetic field strength the convection is suppressed for all values of Gr. The average Nusselt number decreases with an increase of Hartmann number and hence a magnetic field can be used as an effective mechanism to control the convection in an enclosure.List of symbols Ar aspect ratio,H/L - B ₀ induction magnetic field - H ₀ magnetic field,H ₀=B ₀/ _m - g gravitational acceleration - Gr Grashof number,gq(L/k)L ³/v ² - H height of the enclosure - Ha Hartmann number, - k thermal conductivity - Nu local Nusselt number - average Nusselt number - p pressure - Pr Prandtl number, / - q heat flux - t time - T dimensionless temperature, (–₀)/q(L/k) - u vertical velocity - U dimensionless vertical velocity,uL/ - v horizontal velocity - V dimensionless horizontal velocity,vL/ - x vertical coordinate - X dimensionless vertical coordinate,x/L - y horizontal coordinate - Y dimensionless horizontal coordinate,y/L - thermal diffusivity - thermal expansion coefficient - temperature - ₀ reference temperature - density - kinematic viscosity - viscosity - _m magnetic permeability - electrical conductivity - stream function - dimensionless stream function, / - dimensionless time,t/L ² - vorticity - dimensionless vorticity, L ²/ - X grid spacing inX-direction - Y grid spacing inY-direction - time increment - ² Laplacian operator     

Non-Newtonian properties of emulsions in solutions of surface-active agents

The adsorption of surface-active agents (surfactants) on channels changes the effective viscosity of an emulsion and gives it non-Newtonian properties.Notation a drop radius - C and C° concentration of surfactant near a drop and averaged over the medium - D diffusion coefficient of the surfactant - I second-rank unit tensor - n_i components of the unit normal vector to the drop surface - r radius vector directed from the center of the drop - s surface area of the drop occupied by one molecule of surfactant - t_j and T characteristic times - and sorption and desorption constants - gG and ° true and equilibrium surface concentrations of surfactant - , , and gh₁ effective viscosity and the viscosities of the disperse phase and dispersion medium - volume concentration of the disperse phase - surface tension of the drop - T_j, and characteristic times Indices + and * quantities near and inside the drop - t tangential components of vectors and tensors. The operators div_s and grad_s have the same meaning as the ordinary divergence and gradient operators, but with fixed values of the radius vector ra Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 787–793, May, 1989.     

Bounding-surface plasticity: Stress space versus strain space

Summary A bounding-surface plasticity model is formulated in stress space in a general enough manner to accommodate a considerable range of hardening mechanisms. Conditions are then established under which this formulation can be made equivalent to its strain-space analogue. Special cases of the hardening law are discussed next, followed by a new criterion to ensure nesting. Finally, correlations with experimental data are investigated.Notation (a) centre of the stress-space (strain-space) loading surface; i.e., backstress (backstrain) - ^* (a ^*) centre of the stress-space (strain-space) bounding surface - (a ) target toward which the centre of the stress-space (strain-space) loading surface moves under purely image-point hardening - (b) parameter to describe how close the loading surface is to nesting with the bounding surface in stress (strain) space; see (H10) - (c) elastic compliance (stiffness) tensor - (d) parameter to describe how close the stress (strain) lies to its image point on the bounding surface; see (H10) - (D) generalised plastic modulus (plastic compliance); see (1) - function expressing the dependence of the generalised plastic modulus on (plastic complianceD ond) - ^* (D ^*) analogue to (D) for the bounding surface - function expressing the dependence of ^* on (D ^* ond) - () strain (stress) - ' (') deviatoric strain (stress) - ^P ( ^R ) plastic strain (stress relaxation); see Fig. 1 - () image point on the bounding surface corresponding to the current strain (stress) - _iso (f _iso) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change of radius; i.e., fraction of isotropic hardening in the stress-space theory - _kin (f _kin) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change in the backstress (backstrain); i.e., fraction of kinematic hardening in the stress-space theory - _nor (f _nor) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - _ima (f _ima) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - function relating _iso to , , and (f _iso tob,d, andl) - function relating _kin to , , and (f _kin onb,d, andl) - function relating _nor to , , and (f _nor onb,d, andl) - function relating _ima to , , and (f _ima onb,d, andl) - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change of radius - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change in the centre - function relating _iso ^* to (f _iso ^* tod) - function relating _kin ^* to (f _kin ^* tod) - (l) parameter to describe the full extent of plastic loading up to the present, giving the arc length of plastic strain (stress relaxation) trajectory; see (H10) - function relating the direction for image-point translation of the loading surface to various other tensorial directions associated with the current state; see (H5). With 6 Figures     

Finite element analysis of cracked elastic bodies under unsteady translation and rotation

Summary The broad objective of the investigations described in this report is the accurate finite element computation of stress intensity factors in cracked elastic bodies under steady or unsteady translational and rotational loads. Applications of interest include fatigue under adverse environments, such as stall in turbomachinery and critical speeds in elastic mechanisms. The enriched element formulation of Gifford and Hilton [1] has been extended to include inertial, centrifugal, Coriolis and angular acceleration effects, and to include Mode III (tearing), which is coupled to Modes I and II under unsteady rotation. The extension is based on the fact, which does not appear to be widely appreciated, that inertial effects near the crack tip are completely accounted for by the time dependence of the stress intensity factors. For Mode III, the Mindlin formulation for a plate in bending has been adopted in order to extend the enriched element formulation to torsion and bending effects. The centrifugal and angular acceleration effects are fully coupled to the displacements. A finite element code by Gifford and Hilton [2] for static problems in Modes I and II has been thoroughly rewritten and expanded to implement the dynamic features and Mode III. The code incorporates matrices and vectors representing translational, Coriolis, centrifugal and angular acceleration effects. It implements the Newmark method for time integration, and a non-symmetric wave front solver. The elements are validated by comparison with several benchmark problems.List of symbols A element area - A ^*,B ^*,C ^*,D ^*,E ^* shape functions of singular displacements - B elastic body - B undeformed elastic body - B strain-displacement matrix - D equivalent viscous damping matrix - D material stiffness matrix - E elastic modulus - f _b balancing force - f _c consistent force - f force due to centrifugal acceleration - f force due to angular acceleration - H centrifugal matrix - h thickness of element - J torsion constant - K stiffness matrix - K _I,K _II,K _III stress intensity factor in Mode I, II and III - M consistent mass matrix - N composite shape function - N _i shape function - r, polar coordinates - S surface - t, time - t surface traction vector - u _i ,v _i ,w _i x _i ,y _i andz _i displacement in element - u _n nonsingular part of displacement field - u _s singular part of displacement field - u, v, w cartesian displacement components - V volume - x, y, z Cartesian coordinates - x _i ,y _i ,z _i X, Y, Z coordinate fori ^th node in each element - , natural coordinates - angular acceleration - crack angle - time derivative ofu - r variation ofr - strain tensor - Coriolis matrix - vector of nodal + nodeless unknowns - angular acceleration matrix - shear modulus - Poisson's ratio - angular velocity - density of material - stress tensor     

Mixing displacement of viscoplastic fluids feom a channel with a rectangular cavity

Different mixing displacement regimes for viscoplastic fluids are investigated theoretically and experimentally.Notation x and y Cartesian coordinates - h half-width of the gap - H, L dimensionless depth and length of the cavity - v_x, v_y velocity components - density - _ik components of the viscous stress tensor - e_ik components of the deformation rate tensor - dynamic viscosity - dynamic viscosity for infinitely high displacement velocity - ₀ analog of the limiting shear stress in Bingham's fluid - W parameter in Williamson's model - =/gh dimensionless viscosity - stream function - vorticity - ₀, ₀ distributions of and at the inlet - r,a, b, and c auxiliary constants - C concentration of the displacing fluid - D diffusion coefficient - Pe Peclet's number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 432–439, March, 1981.     

Ultrasonic study of the temperature and pressure dependences of the elastic properties of β-silicon nitride ceramic

Ultrasonic wave velocity measurements have been used to determine the elastic stiffness moduli and related elastic properties of high-purity, dense -Si₃N₄ ceramic samples as functions of temperature in the range 150–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. Due to its covalently bonded, rigid structural framework -Si₃N₄ is an elastically stiff material; the elastic stiffness moduli of the ceramic at 295 K are: C _L = 396 GPa, = 119 GPa, B ^S = 238 GPa, E = 306 GPa, Poisson's ratio = 0.285. The longitudinal elastic stiffness C _L increases with decreasing temperature and shows a knee at about 235 K; the decrease in slope below the knee indicates mode softening. The shear elastic stiffness shows mode softening which results in a plateau centred at about 235 K and an anomalous decrease with further reduction in temperature. The hydrostatic-pressure derivatives of elastic stiffnesses at 295 K are (C _L/P) _P=0 = 4.5 ± 0.1, (B ^S/P) _P=0 = 4.3 ± 0.1 and (/P) _P=0 = 0.17 ± 0.02 (pressure < 0.12 GPa). An interesting feature of the nonlinear acoustic behaviour of this ceramic is that, in the pressure range above 0.12 GPa, the values obtained for (/P) _P=0 and the shear mode Grüneisen parameter (_S) are small and negative, indicating acoustic-mode softening under these higher pressures. Both the anomalous temperature and pressure dependences of the shear elastic stiffness indicate incipient lattice shear instability. The shear _S(=0.005) is much smaller than the longitudinal _L(=1.18) accounting for the thermal Grüneisen parameter ^th(=1.09): since the acoustic Debye temperature _D(=923 ± 5 K) is so high, the shear modes play an important role in acoustic phonon population at room temperature. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic -Si₃N₄.     

Influence of proton irradiation on the critical current densityj c(B,T) of NbTi

The critical current densityj _c of a copper-coated single-core wire of Nb-50 wt.% Ti has been measured as a function of the magnetic flux density (1B8T) and the temperature (2.5 KTT _c). Irradiation with 3.1-MeV protons at 25 K up to a flux of1·10 ¹⁷ cm ^–2 led to aT _c drop of 0.17 K and an almost uniform degradation of 19% over the completej _c(B, T) surface. After annealing for 1 h at 285 K only 40% of thej _c degradation remained. Thej _c(B, T) surface can be described, independent of the irradiation dose, approximately byj _c(B, T) B _c2(T) – B, giving a pinning force density ofF _p=j _cB4F _p,max b(1–b), whereb=B/B _c2 andF _p,max B _c2 ² . The defect structure responsible for the vortex pinning is not affected by irradiation. Thej _c decrease on irradiation results from approximately 70% from a decrease ofF _p,max and 30% from theT _c decrease.This work has been supported by the technological program of the Federal Department of Research and Technology of the FRG. The author alone is responsible for the contents.