Temperature and orientation dependences of the grain-boundary diffusion coefficient of antimony in copper bicrystals

An investigation is made of the diffusion of antimony through the bulk and along grain boundaries in copper bicrystals containing a symmetric 〈100〉 misorientation boundary with misorientation angles from 20 to 37.2°. The bicrystals are grown by the method of horizontal zone recrystallization. The temperature range for these studies is 480–580 °C, where the solubility of Sb in Cu is about 6 atomic % and practically temperature-independent. The concentration profiles are obtained by x-ray spectral microanalysis, and the grain-boundary diffusion parameters are computed by the method of Whipple and Suzuoka. The orientation dependence of the triple product P=sδD _b (where s is the segregation coefficient, δ the width of the grain boundary, and D _b the grain-boundary diffusion coefficient) is nonmonotonic, with a maximum for the special ∑5 misorientation boundary (36.9°). The effective activation energy for grain-boundary diffusion ranges from ∼70 kJ/mol for ∑5 to140 kJ/mol for general boundaries. Fiz. Tverd. Tela (St. Petersburg) 39, 1153–1157 (July 1997)     

Study of cation tracer diffusion in NaF

Cation tracer diffusion coefficients were measured in pure NaF crystals in the intrinsic ionic conductivity range (876–970 °C). The results can be rationalized satisfactorily in terms of contributions to the observed Na tracer diffusivities arising from both free vacancies and neutral vacancy pairs, the latter contribution amounting to about 53 per cent of the total Na diffusion at the highest measuring temperature. The best-fit defect parameters derived in an earlier conductivity study [21] from this laboratory on similar NaF crystals give for the free vacancy contribution D_v^*(Na) = 4·25 exp (?2·21 eV/kT) cm²s^?1. A combination of these D_v^*(Na) values with the present diffusion data yields for the vacancy-pair contribution D_p^*(Na) = 1·15 × 10⁸exp (?4·04 eV/kT) cm²s^?1. Comparison of the present findings with published values of the anion tracer diffusion coefficient in NaF showed that D_p^* (F) is 2·3 to 4·4 times larger than D_p^*(Na) over the temperature range of our observations, the difference between the two contributions increasing with decreasing temperature. When approximate account is taken of the temperature-dependence of the two pair correlation factors, this last result indicates that the anion jumps into the vacancy pair occur with a higher frequency, and increasingly so at lower temperatures, than do those involving the cations.     

Pressure-volume-temperature relations of a poly-ε-caprolactam and its nanocomposite

The equation of state of a poly-ε-caprolactam melt, PA-6, of molar mass M _n = 22 kg/mol was investigated in a Gnomix apparatus (Gnomix Inc., Boulder, Colorado) between 300 and 560 K, and pressures up to 150 MPa. Corresponding measurements were performed with addition of 1.6 wt% of montmorillonite exfoliated particles. Reductions in specific volume of about 1.0 and 1.4%, respectively, at 10 and 150 MPa, are observed. For the melt, excellent agreement between experiment and the results from lattice-hole theory is found for both systems. Addition of the nanoparticles reduced the hole (free volume) fraction by 14%. Evidently, the hole fraction is a sensitive indicator of structural changes. It is noteworthy that such a small quantity of added nanoparticles increases the tensile strength by about 14% and modulus by 26%, at a cost of reduction in the elongation at break by about 25%. For a treatment of the PNC, and as an approximation, our earlier model of a particulate composite was adopted. To calculate the binary interaction parameters it was assumed that: (1) the clay particles are in form of flat disks, 100 nm diameter and 1 nm thick; (2) the hard core segments of polymer and of solid occupy the same lattice volume, i.e. v ^* ₁₁ = v ^* ₂₂; (3) the energetic interactions of polymer with solid are given by the geometric average between the two self-interactions. These assumptions lead to the following results ('11' represents polymer-polymer, '22' represents clay-clay and '12' represents polymer-clay interactions): ε ^* ₁₁= 32.09; ε ^* ₁₂ = 313.54 and ε ^* ₂₂ = 3063 (kJ/mol) v ^* ₁₁ = 24.89; v ^* ₁₂ = 33.53 andv ^* ₂₂ = 24.89 (ml/mol)     

Relaxed energy and structure of edge dislocation in iron

With modified analytical embedded-atom method and molecular dynamics simulation, this paper simulates the strain energy and the equilibrium core structure of a<100> edge dislocation in BCC metal iron on atomistic scale. In addition, the trapping effect of dislocation on vacancy is investigated as well. The results show that the equilibrium dislocation core is quite narrow and has a C_2v symmetry structure. Calculated strain energy E_s of the dislocation is a linear function of ln (R/2b) while R≥5.16 Å (1 Å=0.1 nm), in excellent agreement with the elasticity theory prediction. Determined core radius and energy are 5.16 Å and 0.62 eV/Å, respectively. The closer the vacancy to the dislocation line is, the lower the vacancy formation energy is, this fact implies that the dislocation has a trend to trap the vacancy, especially for a separation distance of the vacancy from dislocation line being less than two lattice constants.     

Magnetoelastic waves in an in-plane magnetized ferromagnetic plate

The spectrum of magnetoelastic waves propagating along the magnetic field in an in-plane magnetized ferromagnetic plate is numerically investigated in the exchangeless approximation. No restrictions are imposed either on the field pattern of backward volume magnetostatic waves (BVMSWs) or elastic waves supported by a plate of a given geometry across the plate or on the relationship between the sound velocity v _S and the phase velocity of the magnetoelastic waves v=ω/q (ω is the frequency, q is the wave number). The resonance interaction of the BVMSWs and elastic waves is accompanied, as a rule, by the formation of “stop” bands δω that are proportional to the magnetoelastic coupling constant b. When the BVMSWs are in resonance with Lamb and shear elastic modes the values of the magnetoelastic gaps δω at v≈v _S turn out to be of the same order. For v≫v _S , the efficiency of the interaction between the BVMSWs and transverse Lamb modes is almost one order of magnitude higher. If the frequency spacing Δω between the elastic modes is smaller than the mag-netoelastic gap in the spectrum (Δω≤δω), which takes place, particularly, in the region of crowding the elastic mode spectrum (v≈v _S), the resonant interaction results in mixing the dispersion laws for the elastic modes. Namely, a surface mode may transform into a volume one and a shear mode, into the Lamb mode or into a shear mode with another number. The resonance interaction of the shear and Lamb elastic modes not only forms the magnetoelastic gaps δω∼b ² but also changes the efficiency of elastic wave coupling with the magnetic subsystem. This may show up as the coexistence of the effects of “repulsing” both the dispersion laws and the damping decrements of the elastic waves at the resonance frequency. It is shown that magnetostriction splits the cutoff frequencies of both transverse Lamb modes and shear modes, as well as the long-wave (q → 0) frequency limits f ₀ of the BVMSW modes. This may cause the resonance interaction between BVMSW modes of equal evenness in a narrow frequency band Δ∼b near f ₀.     

Analysis of the ΛQ baryons in the nuclear matter with the QCD sum rules

In this article, we study the Λ c and Λ b baryons in the nuclear matter using the QCD sum rules, and obtain the in-medium masses M\varLambda c*=2.335 GeVM_{\varLambda _{c}}^{*}=2.335~\mathrm{GeV}, M\varLambda b*=5.678 GeVM_{\varLambda _{b}}^{*}=5.678~\mathrm{GeV}, the in-medium vector self-energies \varSigma \varLambda cv=34 MeV\varSigma ^{\varLambda _{c}}_{v}=34~\mathrm{MeV}, \varSigma \varLambda bv=32 MeV\varSigma ^{\varLambda _{b}}_{v}=32~\mathrm {MeV}, and the in-medium pole residues l\varLambda c*=0.021 GeV3\lambda_{\varLambda _{c}}^{*}=0.021~\mathrm{GeV}^{3}, l\varLambda b*=0.026 GeV3\lambda_{\varLambda _{b}}^{*}=0.026~\mathrm{GeV}^{3}. The mass-shifts are M\varLambda c*-M\varLambda c=51 MeVM_{\varLambda _{c}}^{*}-M_{\varLambda _{c}}=51~\mathrm{MeV} and M\varLambda b*-M\varLambda b=60 MeVM_{\varLambda _{b}}^{*}-M_{\varLambda _{b}}=60~\mathrm{MeV}, respectively.     

Positron trapping and self-diffusion activation energies in chromium

The activation energy for self-diffusion in chromium is found to be 3.51±0.13 eV from positron trapping measurements. The 4.51 eV activation energy seen in tracer diffusion work is therefore ascribed to divacancies, theQ ₂/Q ₁ ratio being typical of the bcc refractory group. The positron data give 0.55 for the ratioH _1v ^M /H _1v ^F of vacancy migration and formation energies, in agreement with quenching data for tungsten.     

Double structure of molten metals

Experiments show that two structures occur in solid amorphous and in molten Bi, i.e. the spherical close packing and the layer lattice structure. Here the layer lattices are neither a fragment nor a part of the Bi lattice, but they are produced from the lattice by a reduction of the interlayer distance.

This double structure is also found in the monoatomic metal melts. In the atomic distribution curves of molten In and Sn the double structure shows up as a straight atomic chain with the respective distances within the chain r_v =v×r ₁ and rv/' =v×r 1/', where r ₁ and r 1/' mean the shortest atomic distance in the spherical close packing and in the layer lattice structure. In the melts of Au, Ag, Pb and T1 as of Na and Cs, however, the spherical close packing shows up as a zig-zag chain. The straight atomic chain and the zig-zag chain are in fact imaginary, being parts of layer lattices with limited order.

In conclusion the real zig-zag chain of solid amorphous Se is considered. Even here layer lattices, composed of plane atomic chains, are found, but never single isolated atomic chains.     

Ferroelectricity associated with the metastable phase “III” of AgNO3

The dielectric constant, dc resistance, D-E ferroelectric hysteresis loop and dilatometric analysis of the three phases I, II, and III of AgNO₃ single crystals has been studied over the temperature range 100–200° C. A ferroelectric behaviour of the metastable phase III was detected here for the first time similar to what happened in KNO₃. The ferroelectric is attributed here to Ag⁺-ion vacancy formation in the unit cell of AgNO₃. The energy activating the process of vacancy formation was found to beE _v=2.6 eV. It was found that an ionic shift from one lattice point to another requires an amount of energy to overcome a potential barrierE _m=0.1 eV. A model is suggested to explain such behaviour. Dilatometric analysis indicated that this metastable phase transition III is accompanied by an expansion of the unit cell.     

Diffusion of sodium in rubidium chloride

The diffusion of Na²²Cl in RbCl was measured in the temperature range 377–707°C by the tracer-sectioning technique. The activation energy is 2.06± 0.02 and 0.59 ± 0.01 eV in the intrinsic and extrinsic regions, respectively. The temperature dependence of the correlation factor, as deduced from isotope-effect measurements, is 0.19 eV in the intrinsic region and -0.05 eV in the extrinsic region. When a theoretical value for the Na^+- vacancy binding energy is used, values of ½h_f =1.22, eV and h_m= 0.55 eV are obtained where h_f is the energy of formation, and h_m the energy of motion, of a cation vacancy. These values are not in agreement with the calculation by Tosi and Doyama.     

Evolution of the structure of Rb2ZnCl4 over the temperature range 4.2–310 K

X-ray diffraction is used to study the temperature dependence of the lattice parameters and the sequence of structural realignments in crystalline Rb₂ZnCl₄ over temperatures of 4.2–310 K. The appearance of and changes in the system of satellite reflexes indicative of structural ordering are studied. Below 74 K, on going into the monoclinic phase (space group A11a), anomalies are observed in the behavior of the lattice parameters, and superstructural reflexes develop with wave vectors q=a ^*/3+b ^*/2+c ^*/2 corresponding to an increase by a large factor in initial parameters a, b, and c of the Pnma-phase. Fiz. Tverd. Tela (St. Petersburg) 41, 1084–1090 (June 1999)     

Magnetic aftereffects in nickel ferrites

We have studied the magnetic aftereffects in the Ni _x Fe_3−x−ΔO₄ system, for 0≦x≦1 and 10⁻⁵≦Δ≦2×10⁻¹, between 80 and 500 K. The samples were obtained by sintering at 1400°C in an appropriate gas atmosphere. The measurements are based on the deviation from equilibrium that is produced in a Maxwell-Wien bridge when the self-induction of a coil with ferrite core varies because of the phenomenon of magnetic aftereffects. The numerical analysis of the results shows the presence of relaxation processes at 300 K (III), 330 K (IIa), and above 500 K (I). The Processes III and IIa are related to the concentration of nickel,x, and of vacancy, Δ. It is seen that the IIa peak can be attributed to a process of diffusion of Ni ions in the spinel lattice by means of vacancies on octahedral sites.     

Experimental determination of U diffusion in α-Ti

α-spectrometry was used in order to measure the diffusion of U in bulk α-Ti in the temperature range 863–1123?K (540–850?°C). A straight Arrhenius plot was found, giving diffusion parameters Q?=?297?kJ/mol and D ₀?=?5?×?10^?3?m²/s, which are similar to the α-Ti self-diffusion ones, when measured in Ti samples with a similar impurity content than presently. This behaviour is compatible with the hypothesis of U diffusing via a vacancy-assisted mechanism in the α-Ti lattice and contrasts with older results in which the activation energy is almost a third the self-diffusion one, even lower than the vacancy formation energy.     

Grain-boundary diffusion and solubility of helium in submicrocrystalline palladium

The diffusion and solubility of helium in palladium with a submicrocrystalline structure are investigated by thermal desorption of helium from He-saturated specimens at temperatures T = 293–508 K and saturation pressures P = 0.1–35 MPa. As the saturation pressure rises, the effective diffusion coefficient increases, exhibits a plateau, and then decreases to its initial value. Along with the four plateaus discovered earlier, the solubility versus saturation pressure dependence in the range 25.5–35.0 MPa demonstrates a fifth plateau, where the solubility is as high as (3.0 ± 0.4) × 10¹⁷ cm⁻³. It is shown that the helium diffuses along grain boundaries, at which clusters (traps) consisting of eight to ten vacancies are localized, and dissolves in these clusters. The high value of C _eff in the fifth plateau is explained by pairwise merging of adjacent vacancy clusters. From the D _eff(P) dependences, the vacancy clusters concentration is estimated as C* = 2.32 × 10¹⁶ cm⁻³. Within the experimental error, this value coincides with that obtained from the solubility data. Calculations of the energy of helium-defect interaction in submicrocrystalline Pd that are made using the molecular dynamics method support the experimental results.     

Rapid nickel diffusion in cold-worked carbon steel at 320–450 °C

The diffusion coefficient of nickel in cold-worked carbon steel was determined with the diffusion couple method in the temperature range between 320 and 450 °C. Diffusion couple was prepared by electro-less nickel plating on the surface of a 20% cold-worked carbon steel. The growth in width of the interdiffusion zone was proportional to the square root of diffusion time to 12,000 h. The diffusion coefficient (D_Ni) of nickel in cold-worked carbon steel was determined by extrapolating the concentration-dependent interdiffusion coefficient to 0% of nickel. The temperature dependence of D_Ni is expressed by D_Ni = (4.5 + 5.7/?2.5) × 10^?11 exp (?146 ± 4 kJ mol^?1/RT) m²s^?1. The value of D_Ni at 320 °C is four orders of magnitude higher than the lattice diffusion coefficient of nickel in iron. The activation energy 146 kJ mol^?1 is 54% of the activation energy 270.4 kJ mol^?1 for lattice diffusion of nickel in the ferromagnetic state iron.     

Critical exponents,hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2 ₄ – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2 ₄ –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R _g ² >/<R _e ² >=0.14026±0.00007, <R _m ² >/<R _e ² >=0.43961±0.00034, and ^*=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent ₁=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for ₁. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R _g ² >/<R _e ² >=0.1599±0.0002 and ^*=0.2471±0.0003; since ^*>0, hyperscaling holds. The approach to ^* is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2 ₄ – for two-dimensional SAWs.     

Optical characteristics of the plasma of a transverse volume discharge in Cl2 and He/Cl2 mixtures

Results are presented from a study of UV and VUV emission from the plasma of a transverse volume discharge in chlorine and a He/Cl₂ mixture. In the wavelength range Δλ=140–300 nm, the Cl₂(D′-A′) band with an edge at 258 nm and the Cl ₂ ^* band with edge at λ=195 nm are found to be dominant. It is shown that, in the pressure range [Cl₂]=0.1–2.0 kPa, the intensity of emission with λ≤195 nm is higher than the intensity of the Cl₂(D′-A′) band. At [Cl₂]≥2 kPa, emission in the 258-nm band is dominant.     

Influence of pressure on ionic transport in amorphous electrolytes: Comparison between glasses and salt polymer complexes

Accurate conductivity measurements as a function of hydrostatic pressure (1 – 5000 bars) and temperature (20 – 150 °C) have been performed on a cationic inorganic glass and a cationic conducting polymer. In both cases, the conductivity decreases with increasing pressure and the variation of Inσ at constant temperature as a function of pressure gives straight lines with slopes which allow an “activation volume”, ΔV*, to be obtained by the relationship (∂lnσ/∂P)_T=− (ΔV*/RT). In the case of silver metaphosphate glass, studied below its glass transition temperature, the activation volume (5 cm³⋅mol⁻¹) is temperature independent and equal to the molar volume of the silver cation. Since the transport mechanism implies a free energy barrier, this volume is a real activation volume, corresponding to the difference in volume between a mole of the moving species in its activated transition state and its volume at normal equilibrium. In the case of the sodium conductive polymer, studied above its glass transition temperature, the previous thermodynamic definition does not hold any more because the ionic transport follows a V.T.F. behaviour rather than an Arrhenius law. Consequently, ΔV* is an “apparent activation volume” without a simple physical meaning. Experimental values are higher (20 to 30 cm³⋅mol⁻¹) and decrease with temperature. In this polymer, the mobility of the charge carriers is interpreted in terms of free volume mechanism. From the variations of the apparent activation volume with temperature, the critical free volume V_f* for an elementary displacement is estimated. For the Na⁺ conductive ionomer V_f* is estimated to be equal to 13 cm³⋅mol⁻¹. This large value would indicate the participation of macromolecular chain segments in the ionic transport. Paper presented at the 5th Euroconference on Solid State Ionics, Benalmádena, Spain, Sept. 13–20, 1998.     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

Theoretical investigation of the EPR parameters and the crystal lattice defects of the trigonal symmetry in RbCdF3:Cr3+

In this paper, the electron paramagnetic resonance (EPR) parameters in RbCdF₃:Cr³⁺ have been studied by means of energy matrices and the Newman superposition model, the theoretical results are in excellent agreement with the experimental ones. The existence of Rb⁺ vacancy and the lattice distortion have been verified. The EPR parameters arising from the Rb⁺ vacancy itself and the crystal lattice distortion are analyzed and calculated. We obtain that the six ligand F⁻ ions move to the central Cr³⁺ ion by Δ = 0.0013 nm, and the front three F⁻ ions rotate 2.98° away from the [111] axis while the back three F⁻ ions rotate 1.016° toward it.