Anelastic Mechanisms Research Articles

Shear attenuation and anelastic mechanisms in the central Pacific upper mantle

We determine the mantle attenuation (1/Qμ) structure beneath 70 Myr seafloors in the central Pacific. We use long-period (33-100 sec) Rayleigh waves recorded by the NoMelt array of broadband ocean-bottom seismometers. After the removal of tilt and compliance noise, we are able to measure Rayleigh wave phase and amplitude for 125 earthquakes. The compliance correction for ocean wave pressure on the seafloor is particularly important for improving signal-to-noise at periods longer than 55 sec. Attenuation and azimuthally anisotropic phase velocity in the study area are determined by approximating the wavefield as the interference of two plane waves. We find that the amplitude decay of Rayleigh waves across the NoMelt array can be adequately explained using a two-layer model: Qμ=1400 in the shallow layer, Qμ=110 in the deeper layer, and a transition depth at 70 km, although the sharpness of the transition is not well resolved by the Rayleigh wave data. Notably, Qμ observed in the NoMelt lithosphere is significantly higher than values in this area from global attenuation models. When compared with lithospheric Qμ measured at higher frequency (∼3 Hz), the frequency dependence of attenuation is very slight, revising previous interpretations. The effect of anelasticity on shear velocity (VS) is estimated from the ratio of observed velocity to the predicted anharmonic value. We use laboratory-based parameters to predict attenuation and velocity-dispersion spectra that result from the superposition of a weakly frequency dependent high-temperature background and an absorption peak. We test a large range of frequencies for the position of the absorption peak (fe) and determine, at each depth, which values of fe predict Qμ and VS that can fit the NoMelt Qμ and VS values simultaneously. We show that between depths of 60 and 80 km the seismic models require an increase in fe by at least 3-4 orders of magnitude. Under the assumption that the absorption peak is caused by elastically accommodated grain-boundary sliding, this increase in fe reflects a decrease in grain-boundary viscosity of 3-4 orders of magnitude. A likely explanation is an increase in the water content of the mantle, with the base of the dehydrated lid located at ∼70-km depth.

On the Relation between Bulk and Shear Seismic Dissipation

Abstract In global Earth models such as the preliminary reference Earth model (PREM), seismic attenuation is dominated by shear friction, which is expressed by the relation Q K ≫ Q μ between the bulk and shear Q factors. Weak bulk attenuation appears to be one of the most general observations for Earth materials, which is often used as an assumption for building attenuation models. Nevertheless, we consider three observations suggesting that Q K may generally be comparable to or below Q μ . First, shear-dominated dissipation is a stringent limit requiring “auxetic” behavior of materials in respect to internal friction, that is, analogous to elastic materials with extreme negative Poisson’s ratios. Although possible, auxetic behavior is extremely rare in elasticity, and it is unlikely that it is common for internal friction. To avoid pervasive auxetic effects, the quality factors should generally satisfy Q K Q μ . Second, the relation between Q K and Q μ may depend on the wave modes in which these quantities are measured. Knopoff (1964) observed that in mantle surface waves, Q K may be lower than Q S despite Q K ≫ Q μ in free oscillations. Third, many observations and micromechanics-based models of Q K exist, particularly for rock containing grains, fractures, pores, and fluids. Almost all of these models show Q K values comparable to or below Q μ within the seismic frequency band. Thus, seismic attenuation is broadly variable and likely not shear dominated. The relation Q K ≫ Q μ inverted for the whole Earth could be caused by the use of a constant- Q parameterization, whereas the Q S can be strongly frequency dependent for free oscillations. In addition, key mechanisms of anelasticity (nonlinear viscosity, grain-boundary sliding, effects of partial melts) are not of viscoelastic type and cannot be accurately described by Q factors.

Contributions of phase and structural transformations in multicomponent Al-Mg alloys to the linear and nonlinear mechanisms of anelasticity

The effects of the processes of severe plastic deformation (SPD), recrystallization, and precipitation of the β phase in multicomponent alloys of the Al-5Mg-Mn-Cr and Al-(4–5%)Mg-Mn-Zn-Sc systems on the mechanisms of grain-boundary relaxation and dislocation-induced microplasticity have been studied in some detail. To stabilize the ultrafine-grained structure and prevent grain growth, dispersed Al-transition-metal particles, such as Al3Zr, Al6Mn, Al7Cr, Al6(Mn,Cr), Al18Cr2Mg3 have been used. We have special interest in alloys with additions of scandium, which forms compounds of the Al3Sc type and favors the precipitation of finer particles compared to the aluminides of other transition metals. After SPD, Al-(4–5%)Mg-Mn-Zr-Sc alloys exhibit an enhanced recrystallization temperature. The general features of the dislocation and grain-boundary anelasticity that have been established for the binary Al-Mg alloys are retained; i.e., (1) the decrease in the dislocation density in the process of recrystallization of cold-worked alloys leads to the formation of a pseudo-peak in the curves of the temperature dependences of internal friction (TDIF) and to a decrease in the critical amplitude of deformation corresponding to the onset of dislocation motion in a stress field; (2) the precipitation of the β phase suppresses the grain-boundary relaxation; (3) the dissolution of the β phase, the passage of the magnesium atoms into the solid solution, and the precipitation of the β’ phase upon heating hinder the motion of dislocations; (4) the coarsening of the highly dispersed particles containing Zr and Sc increases the dislocation mobility. The grain-boundary relaxation and dislocation-impurity interaction and their temperature dependences, as well as processes of the additional alloying of the binary alloys by Mn, Cr, Zr, and Sc, have been estimated quantitatively.

Contribution of phase and structural transformations to linear and nonlinear mechanisms of anelasticity in binary Al-Mg alloys

Effects of the processes of the recrystallization and precipitation of the β phase in Al-(0.3–12%)% Mg alloys on the mechanisms of grain-boundary relaxation and dislocation-induced microplasticity have been studied in some detail. The decrease in the dislocation density due to the process of recrystallization of cold-worked alloys leads to the formation of a pseudopeak in the curves of the temperature dependence of internal friction and to a decrease in the critical amplitude of deformation necessary to initiate dislocation motion in a stress field. The precipitation of the β phase in the structure suppresses the mechanism of grain-boundary relaxation; the dissolution of the β phase, which leads to the formation of impurity atmospheres, then to the passage of magnesium atoms into the solid solution, impedes dislocation motion. Depending on the total content of Mg in the alloy, the dislocation mobility upon the measurements of amplitude dependences of internal friction can be described in terms of either breakaway or friction models. The characteristics of grain-boundary relaxation and dislocation-impurity interaction and of their temperature dependences have been estimated quantitatively.

Structural mechanisms of anelasticity in Fe–Ga-based alloys

Abstract Thermally activated frequency and temperature dependent anelastic effects in Fe–Ga and Fe–Ga–Al alloys with 13, 17%Ga and 5%Al are analyzed. Activation parameters for thermally activated relaxation peaks are evaluated. Frequency independent effects caused by structural transformations (ordering and disordering) are studied. Physical mechanisms are proposed for most of these effects. Origin of high damping capacity of Fe–Ga alloy is checked by applying magnetic field and different heat treatment regimes.

Study of order–disorder transitions in Fe–Ge alloys and related anelastic phenomena

Several methods were used to study the phase transitions and related anelastic mechanisms in some alloys of the Fe–Ge system. Obtained results show the appearance of the DTA and dilatometric effects at temperature 200–350°C due to ordering process corresponding to the peak on internal friction curves (denoted as the P3 peak in this paper). The formation of ordered structure in Fe–Ge system at low Ge concentration is sensitive to the thermal history of the specimen. The formation of the ordered structure (with activation energy of ordering H≈1.14eV for a concentration of 12at.% Ge) leads to the increase in the microhardness of studied alloys.

A Microcantilever Platform for Measuring Internal Friction in Thin Films Using Thermoelastic Damping for Calibration

Measuring structural damping due to internal friction (IF) in deposited thin films can generate valuable insights into the effects of size and confinement on the mechanisms of anelasticity and provide useful guidelines for the design of high- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> micro/nanomechanical resonators used in microelectromechanical systems for sensing, communications, and vibration energy harvesting. However, accurate measurement of IF has been a long-standing challenge because of the difficulty associated with calibrating the background damping. In this paper, we present an approach based on a silicon microcantilever platform that resolves these difficulties. This approach is built upon the ability to operate silicon microcantilevers at the fundamental limits of dissipation established by thermoelastic damping (TED) and the ability to compute TED in metal-coated silicon beams without using any free parameters. Using this method, we present the first accurate measurements of IF at room temperature in films of aluminum, silver, and gold with thickness ranging from 50 to 500 nm. Gold films dissipate less energy than either aluminum or silver at the frequencies measured in this paper. In all cases, IF is dominated by defect-induced processes occurring within the bulk of these films and not at the silicon/film interface or at the free surface of the metals.

Internal friction, dilatometric and calorimetric study of anelasticity in Fe–13 at.% Ga and Fe–8 at.% Al–3 at.% Ga alloys

This paper investigates the structural transitions associated with different cooling rates from a high temperature disordered state and the effect of substitution of Ga atoms by Al atoms in Fe–Ga binary alloys on the ordering processes. Two iron-based low carbon (about 0.04 at.% C) alloys Fe–13 at.% Ga and Fe–8 at.% Al–3 at.% Ga are studied. Internal friction, dilatometric and calorimetric tests are carried out to check ordering in these alloys and contribution of structural defects to relaxation spectrum. Several thermally activated internal friction peaks have been observed and their activation parameters evaluated by means of temperature and frequency dependent internal friction tests using forced vibration. For most of these peaks physical mechanisms are proposed. Apart from these thermally activated relaxation peaks, a structural, frequency independent relaxation takes place at 250–300 °C. Dilatometric and DSC curves show the appearance of a contraction effect in the same temperature range. This effect was studied in alloys cooled down with different cooling rates. We believe that the frequency independent internal friction peak (denoted as the P3 peak in this paper) and peaks at dilatometric and DSC curves are controlled by the same structural mechanism and therefore the activation energy for this anelastic mechanism is derived from DSC data.

Mechanisms of anelasticity in Fe–13Ga alloy

Thermally activated frequency and temperature dependent anelastic effects in Fe–Ga alloys are practically not studied as yet in spite of the capacity of these alloys to dissipate energy of mechanical vibrations due to magneto-mechanical damping. In this paper we have studied iron-based composition with 13 at.% Ga. Several thermally activated peaks have been discovered and their activation parameters are evaluated by means of temperature and frequency dependent internal friction tests using free-decay and forced vibrations. Physical mechanisms are proposed for most of these peaks. In addition to thermally activated relaxation peaks, an irreversible internal friction peak is recorded due to structural transformation around 200 °C. This peak is frequency independent and is accompanied by inverted modulus behaviour. High damping capacity of Fe–13Ga alloy is confirmed.

Structure and anelasticity of ordered and disordered Fe–Ge alloys

Internal friction effects in a series of Fe–Ge–C alloys with 3–27 at% Ge and about 0.01–0.04 at% C have been investigated and related to possible mechanisms of anelasticity according to the different alloy structures, which were examined by X-ray diffraction, calorimetry, vibrating sample magnetometry, optical and electron microsopy. While the alloys with 3, 8, 12 and 19 at% Ge have bcc structure (for 3 and 8 at% without ordering and for 12 and 19 at% with ordering of Ge atoms) and show distinct Snoek-type relaxations (with peaks for Fe–C–Fe and for Fe–C–Ge neighbours), in alloys with 22 and 27 at%Ge, where hexagonal phases dominate, no Snoek relaxation is observed as expected. A pronounced Zener relaxation at elevated temperatures occurs in Fe–12–27 at%Ge, with an activation enthalpy of H = 1.78 eV (preexponential time τ 0 = 2 × 10 −17 s −1) for Fe–27at%Ge and near 2 eV for Fe–12at%Ge, which is consistent with diffusion data. The mixed order/disorder structures of Fe–12–19 at% Ge give rise to a further peak, even found also in nominally disordered Fe–8%Ge, which is due to ordering involving quenched-in vacancies. In the temperature range below room temperature two neighbouring peaks are detected which are supposed to be related to dislocation motion.

Anelasticity of polycrystalline indium

Mechanisms of anelasticity of polycrystalline indium have been studied over wide ranges of temperature (7–320 K) and strain amplitude (2 × 10 −7–3.5 × 10 −4). Measurements of the internal friction and Young's modulus have been performed by means of the piezoelectric resonant composite oscillator technique using longitudinal oscillations at frequencies of about 100 kHz. The stages of the strain amplitude dependence of the internal friction and Young's modulus defect, which can be attributed to dislocation – point defect and dislocation – dislocation interactions, have been revealed. It has been shown that thermal cycling gives rise to microplastic straining of polycrystalline indium due to the anisotropy of thermal expansion and to appearance of a “recrystallization” internal friction maximum in the temperature spectra of amplitude-dependent anelasticity. The temperature range characterized by formation of Cottrell's atmospheres of point defects around dislocations has been determined from the acoustic data.

Mechanisms of anelasticity in Fe–Ge-based alloys

Internal friction (IF) effects in a series of Fe–Ge–C alloys with 3–27 at.%Ge and about 0.01–0.04 at.%C have been examined and are related to possible mechanisms of anelasticity according to the different alloy structures. While Fe–3 at.%Ge and Fe–12 at.%Ge are bcc and show distinct Snoek-type relaxation, this relaxation is absent in Fe–27 at.%Ge with hexagonal structure. Here a pronounced Zener relaxation at elevated temperatures is observed. The mixed structures (bcc + hexagonal) of Fe–19–21 at.%Ge give rise to a non-thermally activated peak which already appears in Fe–12 at%Ge and may be due to ordering and/or vacancy complexes. In the temperature range below room temperature two neighbouring peaks are detected in the bcc structures which are supposed to be related to dislocations.

Anelastic Behavior of Plasma‐Sprayed Zirconia Coatings

Low‐temperature thermal cycling of plasma‐sprayed zirconia coatings reveals unique mechanical responses in their curvature measurements, namely nonlinear and cyclic hysteresis, collectively termed as anelastic. These features arise from the inherent layered, porous, and cracked morphology of thermal‐sprayed ceramic materials. In this paper, the mechanisms of anelasticity are characterized by crack closure and frictional sliding models, and stress–strain relations of various thermal‐sprayed zirconia coatings were determined via an inverse analysis procedure. These results demonstrate process conditions such as powder morphology and spray parameters significantly influence the mechanical behaviors of coatings. The unique anelastic responses can be used as valuable parameters in identifying coating quality as well as process reliability in manufacturing.

Effective Modulus and Stress Relaxation of Freestanding Aluminum Microtensile Beams

ABSTRACTFreestanding Al thin film microtensile beams 600 μm long, 100 μm wide, and with thicknesses of 0.25 μm, 0.50 μm, 0.75 μm, and 1.00 μm were tested under uniaxial tension with a custom-built microtensile system. Displacement controlled experiments employing five strain rates between 8.3 × 10−4 s−1 and 8.3 × 10−1 s−1 were performed. Three crosshead displacements of 1.00 μm (0.17% strain), 2.60 μm (0.43%), and 3.60 μm (0.60% strain) were exercised in order to investigate behavior in the elastic, anelastic, and the inelastic sections of the stress/strain curve.At a 0.17% strain amplitude, the 0.50 μm thick microtensile beams exhibit an effective modulus that increases with increasing strain rate. The 1.00 μm, 0.75 μm, and 0.25 μm microtensile beams do not show a similar trend. The 0.25 μm and the 0.75 μm thick microtensile beams have similar grain sizes and similar moduli; the 0.50 μm and the 1.00 μm microtensile beams have similar but smaller grain sizes and higher effective moduli. This suggests that grain size is more significant than film thickness in determining the effective modulus of freestanding Al thin films. Furthermore, no stress relaxation behavior was identified for any of the films during the hold at the 0.17% strain amplitude.At a strain amplitude of 0.43%, the effective moduli are very similar to the values measured at a 0.17% strain amplitude; however, the 0.50 μm and 1.00 μm thick microtensile beams show measurable stress relaxation while the 0.25 μm and 0.75 μm microtensile beams do not. This result combined with a lower observed modulus suggests that the particular anelastic mechanisms operating in these films at these time scales activate sooner and provide a faster stress relaxation process in the larger grained films.

Short-period PKP phases and the anelastic mechanism of the inner core

Short-period seismograms are synthesized for PKP phases in anelastic Earth models. The synthetics were constructed using a synthetic technique valid at grazing incidence, a source-time function appropriate for deep-focus earthquakes, and an instrument response for either a short-period WWSSN or SRO seismograph. The agreement between predicted and observed amplitudes and spectral ratios requires neither a low- Q α zone at 0.2–2 Hz nor a low or negative P-velocity gradient at the bottom of the outer core. Thin low- Q α zones beneath the inner core boundary fit spectral ratio data that sample the upper 200 km of the inner core but fail to fit data that sample the lower inner core. Only a model having Q α −1 ϵ[0.003, 0.004] at 0.2–2 Hz, nearly constant with depth in the inner core, satisfies all of the spectral ratio and amplitude data. The assumption of a bulk viscosity of 10-10 3 Pa s for the liquid phase of a partially molten inner core combined with the observation of low shear attenuation in the inner core at frequencies less than 0.005 Hz limit the physical parameters associated with two possible attenuation mechanisms: (1) fluid flow and viscous relaxation due to ellipsoidally shaped inclusions of melt, and (2) the solid-liquid phase transformation induced by the stress change during the passage of a seismic wave. Both mechanisms require an order of 0.1% partial melt to reproduce the observed Q α −1. In the outer core, the time constant of the mechanism of phase transformation is predicted to be 10 4–10 6 s. Confirmation of small shear attenuation in the inner core in the frequency band of seismic body waves would favor the mechanism of phase transformation.

Internal friction near the néel temperature of chromium

Abstract The characteristics of the internal friction near the Néel temperature of chromium are consistent with a magnetic rather than an anelastic mechanism. The transition at the Néel temperature, as revealed by internal friction measurements, is sensitive to thermal history and the disposition of nitrogen in chromium.