Simulation of the Process of Water Freezing in a Round Pipe

The problem of freezing of pure water in a round pipe is treated with due regard for convection under asymmetric thermal boundary conditions in the absence of motion along the pipe. The problem is solved numerically using the control volume approach, SIMPLER algorithm, and the enthalpy method. Results are obtained for three Grashof (Gr) and six Biot (Bi) numbers: Gr = 1.55 × 10⁶, Bi = 0.305 (0 < ), Bi = 0.044 ( < 2); Gr = 1.24 × 10⁷, Bi = 0.610 (0 < ), Bi = 0.087 ( < 2); Gr = 9.89 × 10⁷, Bi = 1.220 (0 < ), Bi = 0.174 ( < 2). The correctness of calculation of the problem disregarding free-convection flows is analyzed.     

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.     

High-frequency dielectric properties of Mg-Al-Si,Ca-Al-Si and Y-Al-Si oxynitride glasses

Recently developed coaxial line techniques [1] have been used to determine, at room temperature, the values of the real () and imaginary (') parts of the dielectric constants for some Mg-Al-Si, Ca-Al-Si and Y-Al-Si oxynitride glasses over the frequency range 500 MHz to 5 GHz. The frequency dependencies of and ' are consistent with the universal law of dielectric response in that (-_t8)^(n–1) and '^(n–1) for all glass compositions; the high experimental value of the exponent (n=1.0±0.1) suggests the limiting form of lattice loss [2] situation. In this frequency range, as previously reported [3] at longer wavelengths, the addition of nitrogen increases the dielectric constant, (); in both the oxide and oxynitride glasses is also influenced by the cation, being increased with cation type in the order magnesium, yttrium, calcium as at lower frequencies.     

Mössbauer studies of α″-Fe16N2 and α′-Fe8N films

Conversion-electron Mössbauer spectra of epitaxial -Fe₁₆N₂ and -Fe₈N films have been studied and their differences are discussed in detail. The Mössbauer spectrum of -Fe₁₆N₂ can be decomposed into three subspectra, which correspond to the 4d, 8h and 4c sites. The Mössbauer spectrum of -Fe₈N can be fitted using four spectra based on a nitrogen-atom-random-distribution model. The average hyperfine field is larger (3%) for -Fe₁₆N₂ than for -Fe₈N, which is approximately consistent with a 4.1% enhancement of the magnetic moments for -Fe₁₆N₂. The iron moments tend to locate in the film plane for -Fe₁₆N₂ and to arrange perpendicularly to the film plane for -Fe₈N.     

Variation of the Kondo temperature with the nature and concentration of the solute metal

From the available data on the physical properties of dilute magnetic alloys, Daybell and Steyert obtain V-shaped semilog plots ofT _K vs. N (whereT _K is the Kondo temperature andN is the serial number of the magnetic solute in the 3d series). This requires a large variation in the rather small exchange interaction parameterJ, while the Kondos–d exchange model is based on a smallJE _F (whereE _F is the Fermi energy). Taking the ordinary scattering into account,T _K =T _F exp((1– cos ²)/(JD cos²)), whereJ<0, 1, is the phase shift for ordinary scattering, andD is the density of states of one spin direction per atom. It has been shown by us recently, from the concentration dependences of the Kondo slopes and the extremum values of the thermoelectric power of dilute magnetic alloys, that 0<d shells, and 3/4<< for those having less-than-half filled 3d shells. We show, on this basis, that the range of variation ofJ is now reduced to more acceptable values, as the solute metal traverses the 3d series. Again, based on our inference that increases with the increase of the solute concentrationc, we show that an increase of the more-than-half filled solute concentration decreasesT _K , while the increase of the less-than-half filled solute concentration increasesT _K . The fact that the increase of cobalt content in copper or gold favors magnetism while the increase of vanadium content in gold favors nonmagnetism is understandable on this basis.     

Conventional Electronic Structure of MgB2 and ZrB2: LDA vs. de Haas-v. Alphen & ARPES Data

We compare full potential LDA band calculations of the Fermi surfaces areas and band masses of MgB₂ and ZrB₂ previously reported and new dHvA data. Discrepancies in areas in MgB₂ can be removed by a small shift of bands relative to bands. Comparison of effective masses lead to orbit averaged el-ph coupling constants =1.3 and =0.5, whereas for ZrB₂ only weak el-ph coupling with <0.3 is found. The ARPES data can be also well described by the LDA showing the presence of surface states.     

The electrical conductivity of some azine compounds

Correlation of the molecular structure and thermal study of the electrical conductivity of benzaldazine (BA) and its NO₂-derivatives were carried out. The values of the activation energies, obtained from the electrical conductivity measurements, as well as the energy gaps calculated from ultra violet (u.v.) and visible spectra obtained either in liquid or in solid forms indicate that all compounds behave like a semiconducting material. Both n*s and *s were found to be the main sources participatiog in the cooduction processes.     

Determination of the total coefficient of internal gamma-radiation conversion of 57 139 La

Conclusions The resultant value of =0.254±0.006 agrees well with the result in [3], but is somewhat less than the theoretical value of for an M1-transition.Translated from Izmeritel'naya Tekhnika, No. 12, pp. 61–62, December, 1971.     

Thermal Landau jet

The author considers the steady-state temperature distribution in a jet of incompressible fluid emitted in pulsed bursts from a point source, with and without account taken of viscous dissipation. When viscous dissipation is not taken into account, an exact solution is obtained for the energy equation, bounded in the entire closed interval 0 . When viscous dissipation is considered, the energy equation is obtained using the introduced separation of variables.     

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.     

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 ).     

Torsional load transfer from a rigid shaft to an elastic plane with a slit

A plane elastostatic problem for an elastic wedge loaded by a concentrated moment at its apex provides an example of violation of the Saint-Venant principle for apex angles 2 larger than . Considering the problem for a truncated wedge, Neuber demonstrated the method of construction of an applicable solution for any apex angles in the range 22, despite the failure of the Saint-Venant principle. In the present paper the particularly important case of the truncated-wedge problem is examined. The truncated wedge degenerates into a slitted elastic plane, while a rigid circular shaft, acted upon by a torsional moment, is inserted into the plane. The analytical solution of the mixed boundary-value problem is obtained. Numerical results turn out to be in complete agreement with Neuber's results for the slitted elastic plane.     

Phase transformations in permanent-mould-cast aluminium bronze

The phases obtained in aluminium bronze (Cu-10Al-4Fe) cast into a permanent mould were investigated. The parameters examined were the pre-heating temperature of the mould and the graphite coating thickness. The phases and ₂ were detected as well as the metastable phases and . The intermetallics of the system Fe-Al were obtained in various stoichiometric compositions. The different cooling rates of the casting resulted in two mechanisms of transformation to grains out of the unstable phase, one being nucleation and growth producing needle-shaped grains, the other exhibiting a massive transformation to spherical grains. These two mechanisms determine the changes in the size of the a grains as result of changes in the cooling rate in its various ranges.     

Effect of elastic interaction energy on coarsening of γ′ precipitates in a mechanically alloyed ODS Ni-base superalloy

The coarsening behavior of precipitates with a uniform size distribution and with a bimodal size distribution in a mechanically alloyed ODS Ni-base superalloy were investigated to clarify the effect of elastic interaction energy on the coarsening behavior of precipitates. The coarsening rate decreased with increasing size of precipitates with a uniform size distribution, contrary to the classical LSW theory, and the coarsening behavior of precipitates with a bimodal size distribution exhibited Ostwald ripening in which the larger precipitates grow at the expense of smaller precipitates. The driving force for coarsening of precipitates was analyzed based on the two-particle model, considering the effect of elastic interaction energy in addition to the effect of interfacial energy. The contribution of elastic interaction energy on the total energy was found to increase with increasing size of precipitates, and the decelerated coarsening of precipitates was attributed to the decrease in the driving force for coarsening with increasing size of precipitates.     

Nonlinear Response of a Continuous Wave NMR Spectrometer for Samples with a Large Magnetization

We present a new insight in the response of a CW NMR spectrometer for highly magnetized samples above 100 MHz. The spectrometer is a bridge made of a magic T. The output of the bridge is proportional to the reflection coefficient, , of a resonant circuit, which is built with a coil containing the sample. The sensitivity of the reflection coefficient to the complex susceptibility of the sample, () = () – j(), depends on the quality factor, Q, of the circuit and filling factor, . When the condition Q 1 is not fulfilled, we show indeed that the use of a simple crystal detector, which is only sensitive to || gives rise to a strong nonlinear response of the spectrometer. Measurements of the complex value of by means of phase sensitive detection allow to recover a linear behavior. We discuss and illustrate those issues with a few circuits we designed for our measurements on liquid ³ He with spin polarizations up to 15 %. A method is described to build in a reproducible and predictable way resonant circuits matched to 50 in the frequency range 100 – 400 MHz with a quality factor as high as 1000 at 4 K.     

Scattering Rate Anisotropy in the Pseudogap State of BSCCO

We study quasi-particle lifetime anisotropy in BSCCO as a function of temperature and doping by relaxational analysis of symmetrized Raman response functions. For moderately underdoped BSCCO the pseudogap behavior manifests itself in anisotropic suppression of the low-frequency scattering rates, sharper in the vicinity of (, 0) and equivalent points of the Brillouin zone, or the hot spots, and milder in the vicinity of (/2, /2) points, or the cold spots. With stronger underdoping the scattering rate suppression becomes more pronounced and isotropic.     

Anisotropic spin diffusion and multiple spin echoes in3He-4He solutions

We propose a ₁-t₁-₂ pulse-NMR experiment to detect the spin-diffusion anisotropy, =D-D, in degenerate spin-polarized³He-⁴He mixtures, where D and dare the transverse and longitudinal spin diffusion coefficients. In such an experiment the nonlinearity of the dynamics produces multiple spin echoes (MSE). At the ³He concentration x₃ 4% the spinrotation parameter vanishes (M 0), so that the nonlinearity of the equations of motion is entirely due to the anisotropy. In this situation, detection of MSE amounts to observation of D. For slight anisotropy, i.e. D/D 0.25, we use a perturbation scheme similiar to that developed by Einzel et al. (in that case, for small M and small demagnetizing field) to calculate the second and third echo heights. For larger anisotropy we numerically calculate the echo heights. We find that for D/D = 0.5 the heights are 2 % of the first echo, and should be detectable. The (₁, ₂) tip-angle dependence of the D echoes is different from that of the M and demagnetization echoes, and furthermore, they occur at right angles to these echoes (in spin space). Thus, even when small spin-rotation and demagnetization effects are present, the ₁-t₁-₂ experiment provides a sensitive means of detecting the anisotropy.     

A dilatometric method to measure the thermal diffusivity of nonmetallic liquids

A new method to measure the thermal diffusivity of liquids is presented. It requires determination of the time dependence of the thermal expansion of the liquid when it is subjected to a heat source at the top of the cell containing the liquid. The high accuracy of the method (about 3%) is due to an essential reduction of convective currents and also to the absence of temperature detectors, which generally introduce unwanted perturbations on the thermal Field.Nomenclature Thermal conductivity - c Specific heat - Density - c = specific heat x density - h Newton coefficient - Thermal diffusivity - T, 0 Temperature - tV Electric signal - Calibration coefficient - _exp, _th Volume change of the liquid     

Ageing characteristics of Al-2.5% Li rapidly solidified alloy

The present work was performed on an Al–2.5 wt% Li alloy produced by melt spinning. The ribbons were aged in the temperature range 180 to 310° C for times between 1 min and 120h. The kinetics of coarsening of (Al₃Li) and (AlLi) phase particles were investigated using transmission electron microscopy and hardness measurements. The results show that coarsening of (Al₃Li) follows a simple linear relation with the cube root of Me, whereas coarsening of (AlLi) does not follow the same trend. We believe that the (AlLi) phase nucleates at the (Al₃Li)/matrix interface and grows by the dissolution of the nearby (Al₃Li) particles. The mechanical properties of the powder metallurgy alloy show that a large volume fraction of PFZ contributes to the alloy ductility, 11 %, in the aged condition. Also, the yield strength is greatly improved due to refinement effects enhanced by rapid solidification.     

Some observations on the deformation characteristics of bulk polycrystalline zirconium hydrides

The deformation behaviour of bulk polycrystalline zirconium hydrides in the composition range ZrH_1.27 to ZrH_1.66 has been investigated by compressive loading at temperatures between room temperature and 500° C. Single-phase -zirconium hydride is brittle below 100° C. Analyses of slip traces on specimens deformed at temperatures between 100 and 250° C have shown that the glide planes are {111} types. The deformation characteristics of and ( + ) alloys at temperatures between 100 and 500° C are consistent with the hydrogen vacancies in the -phase providing significant lattice friction to the movement of dislocations in the zirconium lattice of the hydride structure. The room temperature fracture stress of ( + ) alloys increases with the volume fraction of the -phase and this can be related to the resistance offered by platelets to the propagation of cleavage cracks in the matrix. In a ( + + ) alloy the resistance to crack propagation at room temperature is further increased by the soft -zirconium phase.