High-pressure recovery of olivine: implications for creep mechanisms and creep activation volume

High-temperature and high-pressure recovery experiments were made on experimentally deformed olivines at temperatures of 1613–1788 K and pressures of 0.1 MPa to 2.0 GPa. In the high-pressure experiments, a piston cylinder apparatus was used with BN and NaCl powder as the pressure medium, and the hydrostatic condition of the pressure was checked by test runs with low dislocation density samples. No dislocation multiplication was observed. The kinetics of the dislocation annihilation process were examined by different initial dislocation density runs and shown to be of second order, i.e.

$\text{d}\text{ρ}\text{d}\text{t}\text{= ?p}{}^2\text{K}{}_0\text{exp}\text{[?(}\text{E}{}^1\text{+PV}{}^1\text{RT}\text{]}$

where ρ is the dislocation density, k₀ is a constant, $\text{E}{}^1\text{and}\text{V}{}^1$ are the activation energy and volume respectively, and P, R and T are pressure, gas constant and temperature, respectively. Activation energy and volume were estimated from the temperature and pressure dependence of the dislocation annihilation rate as $\text{E}{}^1\text{=389±59}\text{kJ mol}{}^{\mathrm{?1}}$ and $\text{V}{}^1\text{=14±2}\text{cm}{}^3\text{mol}{}^{\mathrm{?1}}$, respectively.The diffusion constants relevant to the dislocation annihilation process were estimated from a theoretical relation k=αD where $\text{k=k}{}_0\text{exp}\text{[?(E}{}^1\text{+ PV}{}^1\text{)/RT], D}$ is the diffusion constant and α is a non-dimensional constant of ca. 300. The results agree well with the self-diffusion constant of oxygen in olivine. This suggests that the dislocation annihilation is rate-controlled by the (oxygen) diffusion-controlled dislocation climb.The mechanisms of creep in olivine and dry dunite are examined by using the experimental data of static recovery. It is suggested that the creep of dry dunite is rate-controlled by recovery at cell walls or at grain boundaries which is rate-controlled by oxygen diffusion. Creep activation volume is estimated to be 16±3 cm³ mol^?1.     

High-temperature anelasticity and elasticity of mantle peridotite

An apparatus has been devised which allows precise creep and relaxation measurements to be made on minerals and rocks at temperatures up to 1600°C and at very low deviatoric stresses (1 < σ < 300 bar). This paper is concerned with measurements on mantle peridotite (lherzolite) from Balmuccia (Zone of Ivrea, Italy).The reaction of the sample to a step-like increase in stress is called its “creep function”. It is shown that the creep function contains all the necessary information to derive the spectra of the quality factor Q(ω) and of Young's modulus E(ω), within the seismic range of frequencies, provided the material behaves as a linear system. This has been proven up to a strain of 5 × 10^?5.The Q^?1-spectra at 1200 and 1300°C, obtained by Fourier inversion from the creep function, show no pronounced peak in the frequency band 0.01 < tf < 1 Hz and exhibit a general tendency to decrease slightly with frequency. The creep function: ?(t) = ?_u · [1 + 3.7 · q · {(1 + 50t)^0.27 ? }], where q is related to Q, satisfactorily describes the data at high temperatures and leads to $\text{Q}{}^{\mathrm{?1}}\text{(ω, T) = 3 × 10}{}^3\text{· ω}{}^{\mathrm{<mtext>?0.27\; ·\; </mtext><mtext>exp</mtext>}}\text{(}\text{?30}\text{RT}\text{)}$E(ω) is related to Q(ω) by the material dispersion equation. Above 1100°C the unrelaxed Young's modulus decreases rapidly with temperature according to an activation energy of about 20 kcal/mole. A lowering of short period S-wave velocity by 40% and P-wave velocity by 10% occurs below the solidus. Therefore, no partial melting is required in the asthenosphere.Steady-state creep at low axial stresses (20 < σ < 100 bar), obtained from the same rock, follows the relation $\text{?}\text{?}\text{= 3 × 10}{}^7\text{· δ}{}^{1.4}\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ indicative of grain boundary diffusion or superplasticity. At higher stresses a power law $\text{?}\text{?}\text{= 45 · δ}{}^4\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ typical of dislocation creep, is found.The frequency dependence of Q and the ratio of the activation energies of Q and are indicative of so called “high-temperature background absorption”, as the dominant mechanism, and of a diffusion-controlled dislocation mobility common to both absorption and creep. From a, b, and c, relations between the effective viscosity η_f and Q of the form: $\text{log}\text{η}{}_{\mathrm{e??}}\text{=}\text{1}\text{α}\text{·}\text{log}\text{Q ? (n ? 1) ·}\text{log}\text{ω +}\text{log}\text{D}$ are derived, where α ～ 0.25, n is the power of σ, and D is a constant.     

Mineralogy and stable isotope geochemistry of hydrothermally altered oceanic rocks

Data for the diffusion of cations in pyroxenes are relevant to a variety of sub-solidus processes including order-disorder and exsolution. Similar data must also be available if the reliability of geobarometers and geothermometers involving pyroxenes is to be assessed. Two types of diffusion experiment have been performed to determine cation diffusion rates in pyroxenes: (1) interdiffusion between single crystals of diopside and polycrystalline sinters enriched in Al and Fe, and (2) interdiffusion between single crystals of diopside and a glass of the same composition which was isotopically enriched in²⁶Mg and⁴³Ca. Following high-temperature annealing for periods up to several hundred hours, analysis of the diffusion couples, using an electron microprobe and an ion microprobe respectively, failed to show any measurable diffusion profiles. From these “null result” experiments the diffusion coefficients (D) for Al and Fe in diopside are estimated to be less than4×10^?14cm²s^?1 at 1200°C, and values ofD for Ca and Mg in diopside are estimated to be less than7 × 10^?14cm²s^?1 at 1250°C. These rates are significantly slower than published tracer-type diffusion data for Ca and Al.A review of studies of order-disorder, microstructural coarsening, and diffusion in pyroxenes suggest that activation energies for cation exchange are typically in excess of 60 kcal mol^?1. Transport rates will be assisted, and activation energies lowered by sample non-stoichiometry, inhomogeneities, high dislocation densities and the presence of water.The collective data for Al, Mg and Ca diffusion in diopside indicate diffusion coefficients? 10^?15cm²s^?1 at 1200°C. A comparison with data for diffusion in garnet, olivine and spinel suggests that pyroxenes may have the highest blocking temperatures.     

Lateral variation of differential stress in the uppermost mantle across the island arc of southwest Japan

The dislocation density and the subgrain size of olivine in peridotite xenoliths in southwest Japan were investigated in order to draw out the lateral variation of the differential stress in the upper mantle of the island arc. Alkali basaltic and andesitic dykes including peridotite xenoliths of Dogo, Kikuma, and Shingu are situated about 200 km behind the Nankai Trough, and those of Oki-Dogo and Takashima located at the portions 400–500 km apart from the trough. The mean dislocation densities of olivine are 2 × 10⁶ cm^?2 for Oki-Dogo, 8 × 10⁶ cm^?2 for Takashima, 1 × 10⁷ cm^?2 for Hamada, 5 × 10⁷ cm^?2 for Aratoyama, 4 × 10⁷ cm^?2 for Kikuma, 3 × 10⁷ cm^?2 for Dogo, and 5 × 10⁶ cm^?2 for Shingu peridotites.It is concluded that the differential stress is high in the uppermost mantle beneath the island arc and low in the back-arc and the mantle wedge behind the plate boundary. The lateral variation of stress may be due to the diapiric upwelling of upper mantle materials under the island arc. The size of the diapir is suggested to be 200 km in width and 60–150 km in depth.     

Upper mantle plasticity from laboratory experiments

On the basis of two assumptions i.e. (1) plastic and anelastic behaviour of the upper mantle can be approximated by the behaviour of the dominant mineral olivine, and (2) the behaviour of natural olivine and synthetic forsterite are similar, we have investigated the flow laws and the flow microstructures of forsterite single crystals. The results obtained between 1400–1650°C and 10–100 MPa suggest a model of climb controlled creep in which the a edge dislocations are dominant. The activation energy measured in that regime is 4.7 eV, close to that of Si self-diffusion and the flow law is $\text{?}\text{?}\text{=10}{}^6\text{σ}{}^{2.6}\text{exp}\text{(?4.7}\text{eV/k}\text{T)}$, where σ is in MPa. Extrapolation of these results to the upper mantle would imply very low stresses (i.e. ?10 MPa) in the asthenosphere. However the effect of pressure and grain size are unknown and extrapolation to very low stresses is not straightforward.     

Effect of oxygen partial pressure on the dislocation recovery in olivine: a new constraint on creep mechanisms

The dislocation annihilation rate in experimentally deformed olivine single crystals was measured as a function of oxygen partial pressure (P_O2). It was shown that the dislocation annihilation rate decreased with increasing P_O2. This result is inconsistent with the reported P_O2 dependence of creep rate () in single olivine crystals, thus indicating that the creep in single olivine crystals is not rate-controlled by recovery, under the experimentally investigated conditions.     

Spectral analysis of body waves for earthquakes and their source parameters in the Himalaya and nearby regions

The source characteristics of 33 earthquakes with magnitude m_b between 4.4 and 6.0, which occurred in the Himalayan and nearby regions, are investigated using the records of the Hyderabad seismograph station. The P- and S-wave spectra of these events are interpreted in terms of Brune's seismic source model for estimating the source parameters, i.e., seismic moment, source dimension, stress drop, average dislocation, apparent stress and the radiated energy. Seismic moments, M₀, vary between 0.3 × 10²⁴ and 9.0 × 10²⁶ dyne cm; source dimensions, r, between 4.3 and 18.6 km; stress-drops, Δσ between 0.3 and 151.6 bar; average dislocations, $\text{u}$ between 0.6 and 381 cm; apparent stresses, $\text{η}\text{σ}$ between 0.1 and 73.2 bar. The radiated energy, E_R is estimated by the spectrum integration method and is found to vary between 0.2 × 10¹⁸ and 9.3 × 10²² erg. In general, the stress drop and apparent stress are found to be high, indicating high stresses in these regions.     

Shear modulus and Q of forsterite and dunite near partial melting from forced-oscillation experiments

An apparatus designed to determine the complex shear modulus of rock samples by forced torsion oscillations at high temperature and in the seismic frequency band 0.003–30 Hz is briefly described. Measurements were performed on natural dunite from Åheim (Norway) up to 1400°C and on polycrystalline forsterite up to 1500°C at 1 atm pressure. The two materials were chosen to study, by comparison, the effect of melt on the elasticity and anelasticity of mantle rocks.Between 1000 and 1200°C the absolute values of the shear modulus G are almost equal for both materials. Above 1200°C G for natural dunite decreases progressively with temperature and at 1400°C and 1 Hz reaches $\text{～}\text{1}\text{3}$ of its value at 1100°C. In contrast, G of pure forsterite depends little on temperature. For petrological reasons, supported by simultaneous measurements of the electric resistivity, there is strong evidence that the decrease of G in dunite above 1200°C is due to melt from the lower melting components of the dunite. Based on different models estimates of the melt fraction are made.At high temperature, in both materials Q^?1 is characterized by a monotonic decrease with frequency according to ω^?α, with α ≈ 0.25. An apparent activation energy of 38±5 kcal mol^?1 for forsterite and 48±8 kcal mol^?1 for dunite was found with no significant change in the regime of partial melting. From this it is concluded that Q^?1, even at partial melting, is dominated by solid state high temperature background absorption. There is no indication from these experiments for a constant-Q-band at low seismic frequencies or an increase of Q proportional to frequency as suggested by some seismologists. The present results are in good qualitative agreement with those for Young's modulus obtained previously by strain retardation experiments.     

Magnetic properties of synthetic titanomagnetites

Magnetic properties and crystal structure parameters of synthetic solid solutions Fe₃O₄Fe₃TiO₄, Fe₂O₄MgFe₂O₄ and Fe₃O₄Mg₂TiO₄ have been studied. Basic regularities in the behaviour of saturation magnetisation (I_s), Curie temperature (T_C) and cubic lattice parameter a during the substitution of Ti and Mg ions for Fe ions have been found. As the concentration of Ti ions increases, I_s reduces from 70 Gs·cm³ g^?1 to 0, T_C changes from 580 to 130°C and a from 8.391 to 8.520 Å. Growth of the Mg concentration leads to changes in I_s to 19.8 Gs·cm³, g^?1, T_C, to 440°C and a, to 8.360 Å. The full Fe ions substitution gives $\text{“a”=8.440}\text{A}\text{?}$.Chemical compositions of the samples, in which the valency variation of Fe ions at oxidation leads to an increase in susceptibility and T_C, have been determined.     

Solidus and liquidus temperatures and mineralogies for anhydrous garnet-lherzolite to 15 GPa

A review of experimental data for systems, pertaining to anhydrous fertile garnet-lherzolite shows strong convergence in the liquidus and solidus temperatures for the range 6.5–15 GPa. These can converge either to a common temperature or to temperatures which differ by only ～ 100°C. The major-element composition of magmas generated by even minor degrees of partial melting may be similar to the primordial bulk silicate Earth composition in an upper-mantle stratigraphic column extending over 160 km in depth.The convergence of the solidus and liquidus temperatures is a consequence of the highly variable $\text{d}\text{T}\text{d}\text{P}$ of the fusion curves for minerals which crystallize in peridotite systems. In particular, $\text{d}\text{T}\text{d}\text{P}$ for the forsterite fusion curve is much less than that for diopside and garnet. Whether or not the solidus and liquidus intersect, the liquidus mineralogy for undepleted garnet-lherzolite compositions changes from olivine at low pressures to pyroxene, garnet, or a complex pyroxene-garnet solid solution at pressures in excess of 10–15 GPa. Geochemical data for the earliest Archean komatiites are consistent with an upper-mantle phase diagram having garnet as a liquidus phase for garnet-lherzolite compositions at high pressures. All estimates of the anhydrous solidus and liquidus for the range 10–15 GPa are consistent with silicate liquid compressibility data, which indicate that olivine may be neutrally buoyant in ultramafic magmas at these pressures.     

The cooling Earth: A reappraisal

By treating the lithosphere as a diffusive boundary layer to mantle convection, the convective speed or mantle creep rate, $\text{?}\text{?}$, can be related to the mantle-derived heat flux, $\text{Q}\text{?}$. If cell size is independent of $\text{Q}\text{?}{}^2$ then $\text{?}\text{?}\text{∝}\text{Q}\text{?}$. (If cell size varies with $\text{Q}\text{?}$, then a different power law prevails, but the essential conclusions are unaffected.) Then the factthat for constant thermodynamic efficiency of mantle convection, the mechanical power dissipation is proportionalto $\text{Q}\text{?}$, gives convective stress $\text{σ ∝}\text{Q}\text{?}{}^{\mathrm{?1}}$, i.e. the stress increases as the convection slows. This means an increasing viscosityor stiffness of the mantle which can be identified with a cooling rate in terms of a temperature-dependent creep law. If we suppose that the mantle was at or close to its melting point within 1 or 2 × 10⁸ years of accretionof the Earth, the whole scale of cooling is fixed. The present rate of cooling is estimated to be about 4.6 × 10^?8 deg y^?1 for the average mantle temperature, assumed to be 2500 K, but this very slow cooling rate represents a loss ofresidual mantle heat of 7 × 10¹² W, about 30% of the total mantle-derived heat flux. This conclusion requires theEarth to be deficient in radioactive heat, relative to carbonaceous chondrites. A consideration of mantle outgassing and atmospheric argon leads to the conclusion that the deficiency is due to depletion of potassium, and that the K/U ratio of the mantle is only about 2500, much less than either the crustal or carbonaceous chondritic values. Thetotal terrestrial potassium is estimated to be about 6 × 10²⁰ kg. Acceptance of the cooling of the Earth removes the necessity for potassium in the core.     

The thermal boundary-layer interpretation of D″ and its role as a plume source

The “anomalous” layer in the lowermost mantle, identified as D″ in the notation of K.E. Bullen, appears in the PREM Earth model as a 150 km-thick zone in which the gradient of incompressibility with pressure, $\text{d}\text{K}\text{d}\text{P}$, is almost 1.6, instead of 3.2 as in the overlying mantle. Since PREM shows no accompanying change in density or density gradient, we identify D″ as a thermal boundary layer and not as a chemically distinct zone. The anomaly in $\text{d}\text{K}\text{d}\text{P}$ is related to the temperature gradient by the temperature dependence of K_s, for which we present a thermodynamic identity in terms of accessible quantities. This gives the numerical result (?K_s/?T)_P=?1.6×10⁷ Pa K^?1 for D″ material. The corresponding temperature increment over the D″ range is 840 K. Such a layer cannot be a static feature, but must be maintained by a downward motion of the lower mantle toward the core-mantle boundary with a strong horizontal flow near the base of D″. Assuming a core heat flux of 1.6 × 10¹² W, the downward speed is 0.07 mm y^?1 and the temperature profile in D″, scaled to match PREM data, is approximately exponential with a scale height of 73 km. The inferred thermal conductivity is 1.2 W m^?1 K^?1. Using these values we develop a new analytical model of D″ which is dynamically and thermally consistent. In this model, the lower-mantle material is heated and softened as it moves down into D″ where the strong temperature dependence of viscosity concentrates the horizontal flow in a layer ～ 12 km thick and similarly ensures its removal via narrow plumes.     

An experimental study of magnetite-titanomagnetite interdiffusion

Interdiffusion experiments were performed between Fe₃O₄ (single crystal) and Fe_2.8Ti_0.2O₄ (powder), under self-buffering conditions (temperature range 600–1034°C), and for various oxygen potentials at 1400°C. Profiles of Fe and Ti were obtained by electronprobe microanalysis, and the interdiffusion coefficient $\text{D}$ was calculated by the Boltzmann-Matano method. Low-temperature data at 3 mole% Ti could be described by $\text{D}\text{= (3.85}{}_{\mathrm{?1.11}}{}^{\mathrm{+1.68}}\text{) × 10}{}^{\mathrm{?3}}\text{exp}\text{(2.23 ± 0.04}\text{eV}\text{/kT)}\text{cm}{}^2\text{/}\text{s}$. An estimate is given for the time to interdiffuse 2μm at various temperatures, and the results compared with recent experiments.     

Olivine flow mechanisms at 8 GPa

The mechanisms responsible for high-temperature olivine deformation are investigated at a pressure of 8 GPa and temperatures up to 1780 K. San Carlos olivine specimens of different average grain sizes (0.5 and 5 μm) were deformed simultaneously between hard-alumina pistons during relaxation experiments. These experiments are carried out in a multi-anvil high-pressure apparatus coupled with synchrotron X-ray radiation. The different grain-size specimens experienced identical P-T-stress condition at any given time. A new method for measuring strains and strain rates (≥10⁻⁶ s⁻¹) of specimens at high pressure is documented. This method uses time-resolved in situ X-ray imaging and an image-analysis computation. The microstructures of run products, recovered after being quenched at different temperatures were characterized by transmission electron microscopy (TEM). We find that high-temperature olivine flow is grain-size insensitive at 8 GPa, which suggests that dislocation creep dominates olivine deformation at high pressure. This result is confirmed by the TEM investigation of our deformed specimens in which we find evidences of the activation of olivine dislocation slip systems. Specimen microstructures are consistent with dynamic recrystallization as an assisting process in olivine deformation during the high-pressure experiments. Extrapolation of our results to the low stress level and large grain size expected in the mantle suggests that dislocation creep assisted by dynamic recrystallization may also dominate natural olivine deformation in the upper mantle.     

Volume relaxation of compacted SiO2 glass: a model for the conservation of natural diaplectic glasses

Relaxation experiments on vitreous SiO₂, densified at 900°C, 20 kbar to a permanent density of 2.36 g cm^?3 yield an activation energy of69 ± 5kcal mol^?1 in the temperature range 700–800°C. The data can be used to estimate minimum cooling rates, maximum depositional temperatures or maximum thicknesses of shock-metamorphosed rocks containing diaplectic glasses, if relaxation of a glass densified under dynamic conditions is assumed to be similar to that of statically densified glass.     

Rupture process of the Miyagi-Oki,Japan, earthquake of June 12, 1978

The faulting mechanism and multiple rupture process of the M = 7.4 Miyagi-Oki earthquake are studied using surface and body wave data from local and worldwide stations. The main results are as follows. (1) P-wave first motion data and radiation patterns of long-period surface waves indicate a predominantly thrust mechanism with strike N10° E, dip 20°W, and slip angle 76°. The seismic moment is 3.1 × 10²⁷ dyne-cm. (2) Farfield SH waveforms and local seismograms suggest that the rupture occurred in two stages, being concordant with the two zones of aftershock activity revealed by the microearthquake network of Tohoku University. The upper and lower zones, located along the westward-dipping plate interface, are separated by a gap at a depth of 35 km and have dimensions of 37 × 34 and 24 × 34 km², respectively. Rupture initiated at the southern end of the upper aftershock zone and propagated at N20°W subparallel to the trench axis. About 11 s later, the second shock, which was located 30 km landward (westward) of the first, initiated at the upper corner of the lower aftershock zone and propagated down-dip N80°W. Using Haskell modelling for this rupture process, synthetic seismograms were computed for teleseismic SH waves and nearfield body waves. Other parameters determined are: seismic moment $\text{M}{}_0\text{= 1.7 × 10}{}^{27}\text{dyne-cm, slip dislocation}\text{u}\text{= 1.9}\text{m}\text{, Δσ = 95}\text{bar, rupture velocity}\text{ν = 3.2}\text{km s}{}^{\mathrm{?1}}\text{,}\text{rise time}\text{τ = 2}\text{s}$, for the first event; $\text{M}{}_0\text{= 1.4 × 10}{}^{27}\text{dyne-cm}\text{,}\text{u}\text{= 2.4}\text{m}\text{, Δσ = 145}\text{bar}$, for the second event; and time separation between the two shocks ΔT = 11 s. The above two-segment model does not explain well the sharp onsets of the body waves at near-source stations. An initial break of a small subsegment on the upper zone, which propagated down-dip, was hypothesized to explain the observed near-source seismograms. (3) The multiple rupture of the event and the absence of aftershocks between the two fault zones suggests that the frictional and/or sliding characteristics along the plate interface are not uniform. The rupture of the first event was arrested, presumably by a region of high fracture strength between the two zones. The fracture energy of the barrier was estimated to be 10¹⁰ erg cm^?2. (4) The possible occurrence of a large earthquake has been noted for the region adjacent to and seaward of the area that ruptured during the 1978 event. The 1978 event does not appear to reduce the likelihood of occurrence of this expected earthquake.     

Global electromagnetic induction in the Moon and planets

A summary of experiments and analyses concerning electromagnetic induction in the Moon and other extraterrestrial bodies is presented. Magnetic step-transient measurements made on the lunar dark side show the eddy current response to be the dominant induction mode of the Moon. Analysis of the poloidal field decay of the eddy currents has yielded a range of monotonic conductivity profiles for the lunar interior: the conductivity rises from 3·10^?4 mho/m at a depth of 170 km to 10^?2 mho/m at 1000 km depth. The static magnetization field induction has been measured and the whole-Moon relative magnetic permeability has been calculated to be $\text{μ}\text{μ}{}_0\text{= 1.01 ± 0.06}$. The remanent magnetic fields, measured at Apollo landing sites, range from 3 to 327 γ. Simultaneous magnetometer and solar wind spectrometer measurements show that the 38-γ remanent field at the Apollo 12 site is compressed to 54 γ by a solar wind pressure increase of 7·10^?8 dyn/cm². The solar wind confines the induced lunar poloidal field; the field is compressed to the surface on the lunar subsolar side and extends out into a cylindrical cavity on the lunar antisolar side. This solar wind confinement is modeled in the laboratory by a magnetic dipole enclosed in a superconducting lead cylinder; results show that the induced poloidal field geometry is modified in a manner similar to that measured on the Moon. Induction concepts developed for the Moon are extended to estimate the electromagnetic response of other bodies in the solar system.     

Velocity-density systematics,mean atomic weight,and the interior of the moon

Mean atomic weight profiles for the lunar mantle have been calculated from velocity-density systematic relations using lunar density and seismic velocity models. Despite large variability among the models, the calculation including Poisson's ratio yields a range of mean atomic weight values between 22 and 23 g mol^?1 below 150 km. A similar calculation for the Earth's mantle produces a mean atomic weight of 21.1 ±0.4 g mol^?1. This suggests that the Moon cannot be derived directly from the Earth's mantle, or that it has had a differentiation history different from the Earth's. The lunar $\text{m}\text{'}\text{s}$ require an Fe mole fraction between 0.25 and 0.33 for a pure olivine mantle, or between 0.33 and 0.45 for pure pyroxene.The present profiles are 0.5–3.0 g mol^?1 higher than those calculated from lunar compositional models based on lunar rock compositions and petrology and assumed lunar histories, indicating inadequacies in either the seismic or compositional models, or in both. The mean atomic weight approach provides a method of comparing the consistency of seismic and compositional models of planetary interiors.     

Fracture toughness and subcritical crack growth during high-temperature tensile deformation of Westerly granite and Black gabbro

The double torsion testing method has been used to determine catastrophic and subcritical crack propagation parameters for pre-cracked specimens of Westerly granite and Black gabbro under a number of environmental conditions.The critical stress intensity factor for catastrophic crack propagation (fracture toughness) of granite and gabbro has been measured at temperatures from 20 to 400°C, in a vacuum. At 20°C, the fracture toughness of Westerly granite was $\text{1.79 ± 0.02}\text{MPa}\text{·}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, and for two blocks of Black gabbro it was $\text{3.03 ± 0.08}\text{MPa}\text{·}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{2.71 ± 0.15}\text{MPa}\text{·}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, respectively. These values are very close to those reported by other investigators for tests conducted in air of ambient humidity at room temperature. For both rocks, fracture toughness at first increased slightly, and then decreased steadily on raising the temperature above ambient conditions. This behaviour is explained in terms of the density and distribution of thermally induced microcracks, as determined by quantitative optical microscopy.Subcritical crack growth behaviour has been studied at temperatures up to 300°C, and under water vapour at pressures of 0.6 to 15 kPa. Both the load relaxation and incremental constant displacement rate forms of the double torsion testing method were utilised to generate stress intensity factor/crack velocity diagrams. Crack growth was measured over the velocity range 5 × 10^?3 to 10^?7 m · s^?1. Increasing both temperature and water vapour pressure resulted in substantially higher crack growth rates. The overall effect of raising the temperature over the range studied here (20–300°C) was to increase the crack growth rate in granite and gabbro by ～5 and 7 orders of magnitude, respectively, at constant stress intensity factor and vapour pressure of water. For both rocks, the slopes of stress intensity factor/crack velocity curves were sensitive to changes in both temperature and water vapour pressure at low values of the latter parameter. Slopes fell substantially on raising the water vapour pressure, but were relatively insensitive to changes in temperature at these higher pressures. No subcritical crack growth limit was encountered.Estimates of the uncertainty in our experimental data are given. From the results of multiple load relaxation experiments on Westerly granite specimens, we estimate the uncertainty in position of stress intensity factor/crack velocity curves along the stress intensity axis to be c. 10% of the fracture toughness, and the uncertainty in slope of such curves to be c. 12%.Problems associated with the extrapolation of our experimental data to regions of higher effective confining pressure in the Earth's crust are discussed.