Anelastic Measurements Research Articles

Anelastic and Dielectric Relaxation of Excess Vibrational Modes in Silica

Anelastic and dielectric measurements of fused-silica and soda-silica glasses have been made at low temperatures. The results indicate the presence of distinct relaxation processes at \ensuremath{\sim}11 and \ensuremath{\sim}35\ifmmode^\circ\else\textdegree\fi{}K. It is suggested that these relaxations are due to vibrational modes in excess of the usual Debye spectrum. The existence of these additional modes, or "Einstein modes," has already been deduced from low-temperature specific-heat measurements. A simple theoretical treatment of a charged harmonic oscillator coupled to the strain through a Gr\"uneisen constant shows that anelastic and dielectric relaxations are expected from an excess mode of this kind. Very general considerations of the interactions between the "Einstein oscillator" and the bulk phonons suggest that the relaxation time $\ensuremath{\tau}$ describing the approach to equilibrium of the perturbed oscillator is of the form $\ensuremath{\tau}={\ensuremath{\tau}}_{0}{e}^{\frac{Q}{\mathrm{kT}}}$. This expression is found to be in good agreement with the experimental observations. For the 11\ifmmode^\circ\else\textdegree\fi{}K relaxation $Q=0.0140\ifmmode\pm\else\textpm\fi{}0.0008$ eV, while for the 35\ifmmode^\circ\else\textdegree\fi{}K relaxation $Q=0.053\ifmmode\pm\else\textpm\fi{}0.007$eV.

Interstitial Conduction in BaF2 Crystals

The behavior of the F− interstitial in BaF2 crystals has been examined using ionic-conductivity measurements on BaF2 crystals doped with various amounts of GdF3. The interstitial mobility was found to be μ = (4 × 103 / T) exp(−0.79 ± 0.03 / kT), and the association energy between the Gd3+ ion and the interstitial was 0.44 ± 0.04 eV. Very similar results were obtained for BaF2 doped with monovalents halides. A detailed comparison between the present work, dielectric and anelastic loss measurements, and NMR studies has been made.

Anelasticity measurements in the Mg-Cd alloy system

Internal friction measurements of a Zener relaxation phenomenon were made with Cd—Mg alloys over the composition range 15–90 at.% Mg. The values of damping maxima are reported as a function of composition and the symmetry of the results about 50 at.% are correlated with the current phase diagram. Minimum damping was observed at 25, 50 and 75 at.% Mg. Damping maxima were found at 33 and 66 at. % Mg. Slight maxima were observed at 15 and 85 % Mg. A previously reported anomalous minimum at 33 at.% Mg is explained in terms of atmospheric contamination. Although it is thought that only one type of substitutional diffusion mechanism is responsible for the phenomenon, activation energy measurements were not conclusive.

The clustering of oxygen in solid solution in niobium—II. Interpretation

Anelastic measurements on niobium-oxygen alloys containing 0.1–1.5 at. % oxygen in solid solution are quantitatively interpreted as showing that oxygen is present partly as single, unassoeiated atoms and partly, in more than random numbers, as clusters of two atoms (pairs), three atoms (triplets), and possibly four atoms (quadruplets). The interpretation is based on (1) the constancy of the relaxation times of the relaxation processes at a fixed temperature and over a wide range of oxygen concentrations and (2) the behavior of the component relaxation strengths according to the law of mass action when the strengths are used as measures of the concentrations of the clusters. From the variation of the component relaxation strengths with temperature, binding enthalpies (enthalpies required to dissociate the clusters) are determined. These quantities are 0.07 ± 0.03 eV for pairs, 0.18 ± 0.04 eV for triplets, and 0.27 ± 0.05 eV for quadruplets. From the variation of the component relaxation strengths with total oxygen concentration, the specific relaxation strength of each cluster (relaxation strength of oxygen atoms per unit concentration of cluster) is determined. These quantities are used to estimate values of the standard free energies and entropies of dissociation of the clusters.

The Effect of Atomic Order and Ferromagnetism on the Elastic and Anelastic Properties of Fe ‐ 25 atom % Al

AbstractMeasurements of the temperature dependence of the dynamic elastic modulus E and internal friction Q−1 are reported from 25‐900 °C at frequencies near 1 kHz for an alloy of Fe ‐ 24.8 atom% Al. The influence of ferromagnetism on E and Q−1 is investigated using a variable direct current magnetic field of 0‐1500 Oe. Ambient temperature measurements as a function of field strength exhibit an influence from macro‐eddy current damping and magneto‐elastic hysteresis in agreement with theory. A DL E effect, of maximum magnitude 0.06, is reported for measurements of E (for H = 0 and H = 1500 Oe) as a function of temperature. This modulus defect disappears at approximately 500 °C in agreement with reported measurements of the longitudinal magnetostriction. A small modulus maximum at 540 °C is reported with even the highest applied fields. Two possible explanations are presented. Anelastic measurements show three damping maxima: a Snoek peak due to interstitial carbon at ∼ 250° C, a Zener peak and a grain boundary peak near 700 °C. The values of Q for the first two are 23 kcal/mol and 61 kcal/mol respectively, and corresponding τ0 ‐values are 3.1 × 10−13 s and 3.9 × 10−18 s.

Dislocation Relaxation Phenomena in Oxide Crystals

The dislocation relaxation of MgO and Al2O3 crystals was studied by means of anelastic measurements. The experimental data are analyzed according to the theory of Seeger, Donth, and Pfaff. It is shown that the ratio of Peierls force to shear modulus is about 2×10−5 for MgO and possibly also for Al2O3. Comparison of the dislocation relaxation phenomena of oxides and metals indicates, rather surprisingly, that the ratio of Peierls force to shear modulus in oxides is about an order of magnitude smaller than that in fcc metals.

Interactions of interstitials with dislocations in iron

The interaction between interstitial N and C with dislocations in b.c.c. iron has been examined by use of anelastic measurements. Use has been made of both the Snoek damping peak and the cold-work damping peak. If is suggested that methods which depend on use of either effect alone are insufficient for calculation of the strength of the interaction because such methods involve assumptions about the Cottrell atmosphere which apparently are unwarranted. A method is suggested whereby some of these assumptions can be avoided. By its use the binding energy between interstitial C and dislocations is estimated to be 0.5 eV per atom.

Study of Order in Annealed and Irradiated Alpha Brass by Lattice Parameter Measurements

The increase in short-range order in alpha brass (25% and 30% Zn) produced by thermal treatment or neutron irradiation is accompanied by a measurable decrease in lattice parameter (up to 0.02%). The equilibrium values of the lattice parameter decrease markedly with annealing temperature in the lower range of the measurements, i.e., in the vicinity of 125°C. The activation energies calculated from the kinetics of the lattice parameter changes are 40.7 kcal/mole for the 25% Zn alloy, and 39.5 kcal/mole for the 30% Zn alloy, in agreement with results of anelastic measurements and electrical resistivity studies. From thermodynamic data it is estimated that a decrease in lattice parameter of 0.01% corresponds to an increase of about 0.05 in the Bethe short range order parameter.

Al-Cu系合金の析出および加工恢復の非弾性的研究

Al-Cu系合金の析出および加工恢復の非弾性的研究

Anelastic Measurements of Atomic Mobility in Substitutional Solid Solutions

A recently developed method for obtaining atomic mobility in solid solutions from the rate of anelastic relaxation makes possible the measurement of mobilities at temperatures far below those at which conventional diffusion experiments can be carried out. It is shown that the anelastic effects obtained in substitutional solid solutions are due to a phenomenon of stress-induced ordering and that the relaxation rate is determined primarily by the rate of movement of the slower atomic species. This method is applied to a series of silver-zinc solid solutions (silver rich) and the relaxation time measured as a function of temperature and concentration. The results show a slight deviation from an Arrhenius law, but a mean heat of activation may be obtained for each alloy concentration. Values for the heat of activation as a function of zinc concentration range from 36.1 kcal/mole at 15.8 atom percent zinc to 32.5 kcal/mole at 30.2 atom percent zinc. The entropy of activation, in each case, is positive and in reasonable agreement with Zener's "strain theory." A correlation of the magnitude of the anelastic effects for various specimens of the same composition with the rigidity modulus of these specimens, shows that the contribution to the torsional anelasticity from grains with $〈111〉$ direction close to the specimen axis is much larger than from grains aligned in the $〈100〉$ direction.

LXX. Anelastic measurements of diffusion coefficients in F.C.C. substitutional solid solutions

Summary It is shown in this paper how in face-centred cubic substitutional solid solutions of metals, measurements upon that form of anelasticity which is associated with the preferential reorientation of pairs of solute atoms in the presence of a tensile stress, may be used to obtain the diffusion coefficient of the solute atoms. The method is closely analogous to the one employed recently by Zener and by Wert to measure diffusion coefficients in inter-stitial solid solutions.

Viscous Slip Along Grain Boundaries and Diffusion of Zinc in Alpha-Brass

The viscous behavior of the grain boundaries in 70–30 alpha-brass was demonstrated by anelastic measurements. It was shown that the grain boundaries cannot sustain permanently a shear stress and have a coefficient of viscosity decreasing with an increase of temperature. Using the same alpha-brass specimen, the activation energy associated with the stress-induced preferential orientation of pairs of zinc atoms in alpha-brass (which is a diffusion process) was determined. This activation energy was found to be identical, within experimental error, to the activation energy associated with the grain boundary slip in alpha-brass. This finding indicates that the grain boundary slip in alpha-brass is a diffusion process and the diffusion mechanism is similar to the volume diffusion in alpha-brass.

Experimental Evidence of the Viscous Behavior of Grain Boundaries in Metals

The mechanical behavior of grain boundaries in metals has been a subject of constant controversy. The present research is designed to examine thoroughly the mechanical behavior of grain boundaries in metals in a quantitative manner. A simple torsional apparatus has been devised for measuring four types of anelastic effects at very low stress levels, namely: internal friction at low frequencies; variation of dynamic rigidity with temperature; creep under constant stress; and stress relaxation at constant strain. All four types of anelastic effects have been studied in 99.991 percent polycrystalline aluminum as well as in single crystal aluminum; these effects are practically absent in single crystal aluminum. The four types of anelastic effects observed in polycrystalline aluminum are completely recoverable and are linear with respect to the applied stress and prior strain. They satisfy the interrelations derived by Zener from Boltzmann's superposition principle within experimental error. These are consistent with the viewpoint that the grain boundaries behave in a viscous manner. The maximum amount of shear stress relaxation in polycrystalline aluminum determined by the four types of anelastic measurements is about 33 percent. This is in good agreement with the theoretical value of 36 percent calculated by assuming the grain boundary to be viscous. The heat of activation associated with the viscous slip along the grain boundaries has been found to be 34,500 calories per mole. The coefficient of viscosity of the grain boundaries in aluminum estimated using this heat of activation, is consistent with that of molten aluminum at the same temperature. Similar anelastic effects have been also observed in polycrystalline magnesium, indicating that the viscous behavior is common to all metals.