Thermal expansion,heat capacity,and entropy of MgO at mantle pressures

The pressure dependence of the Raman spectrum of forsterite was measured over its entire frequency range to over 200 kbar. The shifts of the Raman modes were used to calculate the pressure dependence of the heat capacity, C _v, and entropy, S, by using statistical thermodynamics of the lattice vibrations. Using the pressure dependence of C _v and other previously measured thermodynamic parameters, the thermal expansion coefficient, , at room temperature was calculated from = K _S (T/P) _S C _V/TVK _T, which yields a constant value of ( ln / ln V)_T= 6.1(5) for forsterite to 10% compression. This value is in agreement with ( ln / ln V)_T for a large variety of materials.At 91 kbar, the compression mechanism of the forsterite lattice abruptly changes causing a strong decrease of the pressure derivative of 6 Raman modes accompanied by large reductions in the intensities of all of the modes. This observation is in agreement with single crystal x-ray diffraction studies to 150 kbar and is interpreted as a second order phase transition.     

Mechanisms of the transformations between the α, β and γ polymorphs of Mg2SiO4 at 15 GPa

Data on the mechanisms of mantle phase transformations have come primarily from studies of analogue systems reacted experimentally at low pressures. In order to study transformation mechanisms in Mg₂SiO₄ at mantle pressures, forsterite () has been reacted in the stability field of -phase, at 15 GPa and temperatures up to 900° C, using a multianvil split-sphere apparatus. Transmission electron microscope studies of samples reacted for times ranging from 0.25–5.0 h show that forsterite transforms to -phase by an incoherent nucleation and growth mechanism involving nucleation on olivine grain boundaries. This mechanism and the resultant microstructures are very similar to those observed at much lower pressures in analogue systems (Mg₂GeO₄ and Ni₂SiO₄) as the result of the olivine to spinel () transformation. Metastable spinel () also forms from Mg₂SiO₄ olivine at 15 GPa, in addition to -phase, by the incoherent nucleation and growth mechanism. With time, the spinel progressively transforms to the stable -phase. After 1 h, spinels exhibit a highly striated microstructure along {110} and electron diffraction patterns show streaking parallel to [110] which indicates a high degree of structural disorder. High resolution imaging shows that the streaking results from thin lamellae of -phase intergrown with the spinel. The two phases have the orientation relationship [001]//[001] and [010]//[110] so that the quasi cubic-close-packed oxygen sublattices are continuous between both phases. These microstructures are similar to those observed in shocked meteorites and show that spinel transforms to -phase by a martensitic (shear) mechanism. There is also evidence that the mechanism changes to one involving diffusion-controlled growth at conditions close to equilibrium.     

Field-induced oscillation and rotation of diamagnetic oxide crystals

The harmonic oscillations of large diamagnetic mineral samples induced by a magnetic field is reported, for single crystals of quartz, corundum, and calcite. It was seen for the first time that the period of oscillation, , was proportional to the reciprocal of the magnetic field, H, where the restoring force of the string suspending the crystal became negligible in the high magnetic field. Accordingly, the value of diamagnetic anisotropy, , could be measured from the — H curve with a sensitivity of 5 × 10^–10 emu/cc. The values were 5.50 × 10^–9 emu/cc for quartz, 4.20 × 10^–9 emu/cc for corundum, 9.9 × 10^–8 emu/cc for calcite, and 8.8 × 10^–8 emu/cc for polycrystalline talc piled with the (001) planes aligned parallel. Significant field-induced rotations were observed for the suspended crystals. When the field was applied along the direction of the diamagnetic hard axis of the stationary crystal, the crystal gradually rotated with increasing field, so that the direction of the hard-axis was perpendicular to the applied field. The field-induced energy has a the maximum value when the field is applied along the diamagnetic hard axis. This reorientation of the crystal occurs because the torque due to the field-induced anisotropic energy exceeds that of the restoring force in high magnetic fields.     

Structural relaxation in silicate melts and non-Newtonian melt rheology in geologic processes

The timescale of structural relaxation in a silicate melt defines the transition from liquid (relaxed) to glassy (unrelaxed) behavior. Structural relaxation in silicate melts can be described by a relaxation time, , consistent with the observation that the timescales of both volume and shear relaxation are of the same order of magnitude. The onset of significantly unrelaxed behavior occurs 2 log₁₀ units of time above . In the case of shear relaxation, the relaxation time can be quantified using the Maxwell relationship for a viscoelastic material; _S = _S/G (where _S is the shear relaxation time, G is the shear modulus at infinite frequency and _S is the zero frequency shear viscosity). The value of G known for SiO₂ and several other silicate glasses. The shear modulus, G , and the bulk modulus, K , are similar in magnitude for every glass, with both moduli being relatively insensitive to changes in temperature and composition. In contrast, the shear viscosity of silicate melts ranges over at least ten orders of magnitude, with composition at fixed temperature, and with temperature at fixed composition. Therefore, relative to _S, G may be considered a constant (independent of composition and temperature) and the value of _S, the relaxation time, may be estimated directly for the large number of silicate melts for which the shear viscosity is known.For silicate melts, the relaxation times calculated from the Maxwell relationship agree well with available data for the onset of the frequency-dependence (dispersion) of acoustic velocities, the onset of non-Newtonian viscosities, the scan-rate dependence of the calorimetric glass transition, with the timescale of an oxygen diffusive jump and with the Si-O bond exchange frequency obtained from ²⁹Si NMR studies.     

Dynamics of the α-β phase transitions in quartz and cristobalite as observed by in-situ high temperature 29Si and 17O NMR

Relaxation times (T₁) and lineshapes were examined as a function of temperature through the - transition for ²⁹Si in a single crystal of amethyst, and for ²⁹Si and ¹⁷O in cristobalite powders. For single crystal quartz, the three ²⁹Si peaks observed at room temperature, representing each of the three differently oriented SiO₄ tetrahedra in the unit cell, coalesce with increasing temperature such that at the - transition only one peak is observed. ²⁹Si T₁'s decrease with increasing temperature up to the transition, above which they remain constant. Although these results are not uniquely interpretable, hopping between the Dauphiné twin related configurations, ₁ and ₂, may be the fluctuations responsible for both effects. This exchange becomes observable up to 150° C below the transition, and persists above the transition, resulting in -quartz being a time and space average of ₁ and ₂. ²⁹Si T₁'s for isotopically enriched powdered cristobalite show much the same behavior as observed for quartz. In addition, ¹⁷O T₁'s decrease slowly up to the - transition at which point there is an abrupt 1.5 order of magnitude drop. Fitting of static powder ¹⁷O spectra for cristobalite gives an asymmetry parameter () of 0.125 at room T, which decreases to <0.040 at=" the=" transition=" temperature.=" the=" electric=" field=" gradient=" (efg)=" and=" chemical=" shift=" anisotropy=" (csa),=" however,=" remain=" the=" same,=" suggesting=" that=" the=" decrease=" in="> is caused by a dynamical rotation of the tetrahedra below the transition. Thus, the mechanisms of the - phase transitions in quartz and cristobalite are similar: there appears to be some fluctuation of the tetrahedra between twin-related orientations below the transition temperature, and the -phase is characterized by a dynamical average of the twin domains on a unit cell scale.     

Mössbauer study of the thermal decomposition of lepidocrocite and characterization of the decomposition products

The lepidocrocite (-FeOOH) to maghemite (-Fe₂O₃), and the maghemite to hematite (-Fe₂O₃) transition temperatures have been monitored by TGA and DSC measurements for four initial -FeOOH samples with different particle sizes. The transition temperature of -FeOOH to -Fe₂O₃ and the size of the resulting particles were not affected by the particle size of the parent lepidocrocite. In contrast, the -Fe₂O₃ to -Fe₂O₃ transition temperature seems to depend on the amount of excess water molecules present in the parent lepidocrocite. Thirteen products obtained by heating for one hour at selected temperatures, were considered. Powder X-ray diffraction was used to qualify their composition and to determine their mean crystallite diameters. Transmission electron micrographs revealed the particle morphology. The Mössbauer spectra at 80 K and room temperature of the mixed and pure decomposition products generally had to be analyzed with a distribution of hyperfine fields and, where appropriate, with an additional quadrupole-splitting distribution. The Mössbauer spectra at variable temperature between 4.2 and 400 K of two single-phase -Fe₂O₃ samples with extremely small particles show the effect of superparamagnetism over a very broad temperature range. Only at the lowest temperatures (T55 K), two distributed components were resolved from the magnetically split spectra. In the external-field spectra the m_I=0 transitions have not vanished. This effect is an intrinsic property of the maghemite particles, indicating a strong spin canting with respect to the applied-field direction. The spectra are successfully reproduced using a bidimensional-distribution approach in which both the canting angle and the magnetic hyperfine field vary within certain intervals. The observed distributions are ascribed to the defect structure of the maghemites (unordered vacancy distribution on B-sites, large surface-to-bulk ratio, presence of OH^- groups). An important new finding is the correlation between the magnitude of the hyperfine field and the average canting angle for A-site ferric ions, whereas the B-site spins show a more uniform canting. The Mössbauer parameters of the two hematite samples with MCD₁₀₄ values of respectively 61.0 and 26.5 nm display a temperature variation which is very similar to that of small-particle hematites obtained from thermal decomposition of goethite. However, for a given MCD the Morin transition temperature for the latter samples is about 30 K lower. This has tentatively been ascribed to the different mechanisms of formation, presumably resulting in slightly larger lattice parameters for the hematite particles formed from goethite, thus shifting the Morin transition to lower temperatures.Senior Research Associate, National Fund for Scientific Research (Belgium)     

β(Mg0.9, Fe0.1)2SiO4: Single crystal structure,cation distribution,and properties of coordination polyhedra

The synthesis boundaries of the phase transformation; ++ in (Mg_0.9, Fe_0.1)SiO₄, have been clarified at temperatures to 2000° C and pressures up to 20 GPa in order to synthesize single crystals of high quality. A single crystal of (Mg_0.9, Fe_0.1)₂SiO₄ was grown successfully to a size of 500 m. The crystal structure has been refined from single-crystal X-ray intensities. The ferrous ions prefer M1 and M3 sites to over the larger M2 site. The volume change of all the occupied polyhedra does not contribute to the decrease of total volume in the transformation; rather it tends to increase the bulk volume through the expansion of occupied tetrahedra. The volume reduction in the phase transformations is accounted for by unoccupied polyhedra, with the octahedra contributory 60% and the tetrahedra 40% to the V of the transition. The volume change in the transformation is caused also partly by the volume decrease of MO ₆ (25%), partly the unoccupied tetrahedra (45%) and octahedra (30%).     

Al-Si ordering in Sr-feldspar SrAl2Si2O8: IR,TEM and single-crystal XRD evidences

Al-Si ordering in Sr-feldspar has been followed by isothermal annealing, starting from a disordered metastable configuration. Ordering could not be followed by changes in the spontaneous strain as cell parameters did not show significant changes with thermal treatment from 0.016 h to 452 h at T=1350° C, while, on the contrary, significant changes in IR spectra are observed. A single crystal obtained from melt (Q _od 0) has been progressively heated up to 678 h at T=1350° C and the relevant structural refinements enabled to monitor changes in degree of Al-Si order up to Q_od = 0.86. In isothermal treatment for Sr-feldspar it is observed a significantly lower Q _od than in anorthite after the same annealing time. TEM observation has shown in Sr-feldspar, also for shortest annealing, b type reflections, while in anorthite, in the same conditions, e type reflections have been observed (Carpenter 1991a). In the first stages of ordering b APDs sized 100 Å (at T=1350° C, 0.33 h) have been observed in Sr-feldspar; APD coarsening occurs with an activation energy of 120±7 kcal mol^-1, not significantly different from anorthite. The ordering process seems to be a slower process in Sr-feldspar than in anorthite, even though data from longer annealing suggest that the Q _od close to the equilibrium is the same in Sr and Ca-feldspar (Q _od = 0.86 at T=1350° C).     

The elasticity of the upper mantle orthosilicates olivine and garnet to 3 GPa

The elastic moduli of single crystals of pyrope-rich garnet and San Carlos olivine have been measured over a 3 GPa pressure range at room temperature. The combination of improved ultrasonic techniques and this large pressure range provide for more reliable characterization of the pressure dependence of acoustic wave velocities than has previously been possible. First and second pressure derivatives of the velocities have been determined within 1 percent and 10 percent respectively. The Hashin-Shtrikman bounds for the pressure dependences of the bulk and shear moduli of the garnet used in this study are; K = 173.6 GPa, K = 4.93, K = –0.28 GPa^–1, G= 94.9 GPa, G = 1.56, G = –0.08 GPa^–1 and the Hashin-Shtrikman least-upper bounds and greatestlower bounds for the pressure dependences of the bulk and shear moduli of the San Carlos olivine are K=129.8 GPa, K = 4.66, K= –0.15 GPa^–1, G = 77.8 GPa, G = 1.93, G = –0.11 GPa^–1 and K = 129.2 GPa, K = 4.63, K= –0.15 GPa^–1 G = 77.3 GPa, G=1.96, G = –0.11 GPa^–1 respectively. The determination of the room-pressure elastic moduli of this pyrope-almandine garnet removes the previously observed anomaly in the predictions of systematic treatments of variations of the elastic moduli of garnets with composition. The determination of the second pressure derivatives of the moduli of garnet and olivine illustrates the importance of these terms in extrapolations to higher pressures — with K/P for these crystals being reduced by 17 percent and 9 percent respectively over the 3 GPa pressure range.     

Diamagnetic anisotropies of oxide minerals

The diamagnetic anisotropy of oxide minerals is analyzed in terms of a new model, in which the anisotropy is assigned to the individual chemical bond in the [MO₆] octahedral unit of the crystal. The diamagnetic principal axis of the individual M-O bond is assumed to be parallel to the direction of the bond. The calculated anisotropy based on this model shows a good correlation with the measured diamagnetic anisotropy, , for various minerals such as talc, sericite, kaolinite of the sheetsilicate group, forsterite of the orthosilicate group, and corundum of the hematite group. The values of many diamagnetic minerals are still unknown since the measurement is difficult to perform by means of conventional methods. The magnetic grain orientation recently observed in the mineral suspensions is effective for estimating the value, when the single crystal of the mineral cannot be obtained. The observation of fieldinduced crystal oscillation in the high magnetic fields can be applied for measuring the minerals with small values of less than 5 × 10^–10 emu/cc. The chemical bond model on the diamagnetic anisotropy can be confirmed, when the compiling of data on various mineral is made by means of the above two methods.     

Topological properties of random crack networks

The junctions of cracks in mudcrack, patterned ground, and columnar joint patterns can be categorized into Y, T,and Xtypes. The mean number of sides, ,to the polygonal areas in such nets is = 2(2J_T + 3J_Y + 4J_X)/(J_T + J_Y + 2J_X)where J_T, J_Y,and J_X are the proportions of T, Y,and Xjunctions, respectively.     

Mössbauer study of a California desert celadonite and its pedogenically-related smectite

Celadonite from the northwestern Mojave Desert area of California was examined by detailed Mössbauer spectroscopy at temperatures from 10 K to 400 K. In addition to the predominant Fe³⁺ doublet with isomer shift 0.4 mm s^–1 and quadrupole splitting 0.4 mm s^–1, another Fe³⁺ doublet with 0.4, 1.2 mm/s and two Fe²⁺ doublets with 1.1, 1.7, 2.7 mm s^–1 at 300 K were distinguished. The minor Fe³⁺ component is ascribed to dehydroxylated surface sites. Most of the remaining Fe(90%) is M2 cis-OH octahedral in an ordered M⁺–M²⁺ array. However, about 10% is M1 trans-OH Fe²⁺. Isomer shift vs. T gives Debye temperatures of 570 K for Fe³⁺ in M2 and 380 K for both Fe²⁺ sites, indicating greater vibrational freedom for Fe²⁺. Quadrupole splitting vs. T for Fe²⁺ gives a valence electronic energy splitting of 760 cm^–1 between the ground and first excited state for M2. The M1 sites have a more drastic variation in vs. T which indicates not only a lower first excited state but a rhombic distortion at these sites. A proposed explanation is a neighboring M2 site vacancy. The soil clay formed from this celadonite, which is mostly Fe-rich smectite, was also studied by Mössbauer spectroscopy. About half the Fe²⁺ has been oxidized in the clay, but the isomer shifts and quadrupole splittings are essentially the same as in the original celadonite. A texture orientation in the clay absorber was detected by measuring the absorber at 55° to the source radiation. This texture effect produces asymmetric doublets in the usual 90° measurement.     

Pressure and temperature dependence of the elastic properties of synthetic MnO

The adiabatic elastic stiffness constants of synthetic single-crystal MnO were measured in this study using pulse superposition interferometry. Data were obtained up to 1.0 GPa in pressure and over the temperature range 273 to 473 K. As a result, we were able to determine the complete set of second-order stiffness moduli (C _ij ^s ) and their pressure and temperature derivatives, as well as higher-order properties for selected modes. Relevant results for the adiabatic bulk modulus are: K ^s=155.1±0.8 GPa; (K^s/P)_T=4.70±0.13; and, (K ^s/T)_P= -0.0203±0.0009 GPa/K. Our results for the second-order moduli are generally consistent with the data from previous studies. However, relative to the estimated uncertainties, small and systematic discrepancies appear to characterize the data set. The available evidence indicates that the differences result from microstructural variations (in particular, microcracks and Mn₃O₄ inclusions) between the synthetic MnO specimens used in different investigations. The pure shear mode C ₄₄ exhibits anomalous soft-mode behavior with both temperature (the ambient derivative is positive) and pressure (the ambient derivative is negative). In both cases the C ₄₄ data trends appear to primarily reflect the influence of Mn-Mn magnetoelastic interactions associated with the onset of a paramagnetic-antiferromagnetic (PM AFM) phase transition.     

High-temperature creep and kinetic decomposition of Ni2SiO4

To investigate high-temperature creep and kinetic decomposition of nickel orthosilicate (Ni₂SiO₄), aggregates containing 3 vol% amorphous SiO₂ have been deformed in uniaxial compression at a total pressure of one atomsphere. Twenty-three samples with grain sizes (d) from 9 to 30 m were deformed at temperatures (T) from 1573 to 1813 K, differential stresses () from 3 to 20 MPa, and oxygen fugacities (f o ₂) from 10^-1 to 10⁵ Pa. At temperatures up to 1773 K, the steady-state creep rate () can be described by the flow law

Spontaneous strain at the structural phase transition in NaNO3

The temperature dependence of the hexagonal c unit cell parameter of high-purity NaNO₃ shows an anomaly at 553 K corresponding to the orientational ordering transition. The a unit cell parameter is barely influenced by the transition. The single component spontaneous strain for this zone boundary instability is large (55×10^–3 at 295 K), and couples quadratically with the order parameter. The critical exponent is found to have the value 0.22 ± 0.01, which differs from that expected in the classical case. Below ca 450 K, crossover to tricritical behaviour is observed (=1/4). The temperature evolution of the macroscopic order parameter as revealed by the temperature dependence of the spontaneous strain follows a tricritical behaviour between 70 K and 450 K. At temperatures below 70 K order parameter saturation is observed. Combined with recent data from specific heat measurements, the critical exponents suggest that the three-dimensional, three-states Potts model may describe the transition.Precursor spontaneous strain above T _c is consistent with local ordering and may result from fluctuations associated with an antiordered NO₃ group pair configuration.     

Jankovićite,Tl5Sb9(As,Sb)4S22, a new TI-sulfosalt from Allchar,Macedonia

Summary A hitherto unknown TI-sulfosalt, containing antimony and arsenic, was discovered by ore microscopy (including quantitative reflectance measurements) and electron microprobe analysis in samples from the Allchar TI-Sb-As sulfide ore deposit (Macedonia). The chemical formula is TI₅Sb₉(As,Sb)₄S₂₂, X-ray single crystal and powder diffration data gave the lattice parameters _o = 7.393(4) Å, b₀ = 8.707(2) Å, c_o = 17.584(3) Å, = 103.81(1)°, = 91.79(1)°, = 109.50(1)°; space group , Z = 1. The new mineral and the new mineral naine jankoviéite have been approved by the IMA/CNMMN.

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Jankoviit, Tl₅Sb₉(As,Sb)₄S₂₂, ein neues TI-Sulfosalz aus Allehar, Macedonien

Zusammenfassung Ein bislang unbekanntes Thallium-Antimon-Arsen-Sulfosalz wurde mittels Erzmikroskopie (inklusive quantitativer Reflexionsmessungen) und Elektronenstrahl-Mikrosonde in Proben aus der TI-Sb-As-Sulfid-Lagerstätte Allchar in Macedonien entdeckt. Die chemische Formel lautet Tl₅Sb₉(As,Sb)₄S₂₂, aus Röntgen-Einkristallaufnahmen und Pulverdiffraktogrammen konnten folgende Gitterkonstanten bestimmt werden: a_o = 7.393(4) Å, b_o = 8.707(2) _Å, c_o = 17.584(3) Å, a = 103.81(1)°, = 91.79(1)°, = 109.50(1)°; Raumgruppe , Z = 1. Das neue Mineral, sowie der neue Mineralname Jankoviit wurden durch die IMA/CNMMN anerkannt.

     

Electrical conductivity,thermopower and <Superscript>57</Superscript>Fe Mössbauer spectroscopy of aegirine (NaFeSi<Subscript>2</Subscript>O<Subscript>6</Subscript>)

DC and AC electrical conductivities were measured on samples of two different crystals of the mineral aegirine (NaFeSi₂O₆) parallel () and perpendicular () to the [001] direction of the clinopyroxene structure between 200 and 600 K. Impedance spectroscopy was applied (20 Hz–1 MHz) and the bulk DC conductivity _DC was determined by extrapolating AC data to zero frequency. In both directions, the log _DC – 1/T curves bend slightly. In the high- and low-temperature limits, differential activation energies were derived for measurements [001] of E_A 0.45 and 0.35 eV, respectively, and the numbers [001] are very similar. The value of _DC [001] with _DC(300 K) 2.0 × 10^{–6 –1}cm^–1 is by a factor of 2–10 above that measured [001], depending on temperature, which means anisotropic charge transport. Below 350 K, the AC conductivity () (/2=frequency) is enhanced relative to _DC for both directions with an increasing difference for rising frequencies on lowering the temperature. An approximate power law for () is noted at higher frequencies and low temperatures with () ^s, which is frequently observed on amorphous and disordered semiconductors. Scaling of () data is possible with reference to _DC, which results in a quasi-universal curve for different temperatures. An attempt was made to discuss DC and AC results in the light of theoretical models of hopping charge transport and of a possible Fe²⁺ Fe³⁺ electron hopping mechanism. The thermopower (Seebeck effect) in the temperature range 360 K < T <770 K is negative in both directions. There is a linear – 1/T relationship above 400 K with activation energy E 0.030 eV [001] and 0.070 eV [001]. ⁵⁷Fe Mössbauer spectroscopy was applied to detect Fe²⁺ in addition to the dominating concentration of Fe³⁺.     

Editorial

Other papers presented at the meeting will be published in 1989 and 1990 in two special issues of Tourism Recreation Research devoted to North American perspectives on international tourism and International tourism in developing countries.     

Natural boehmite single crystals from Ceylon

Single crystals of boehmite, up to 0.1 mm in size, were found in open cavities inside a corundum crystal from the Ratnapura area gem gravels in Ceylon. The unit cell parameters are (X-ray powder pattern): a ₀=3.695 Å b ₀=12.212 Å, c ₀=2.867 Å. The crystallographic orientation is based on X-ray single-crystal precession photographs. The crystals show the faces (it010), (001), (101), and (221). Systematic extinctions agree with the space group Amam. Optical orientation: a, b, c. Refractive indices are given. The mineral is optically positive with a large optic axial angle.     

Heterogeneous deformation resulting from stress gradients in calcite single crystals

The stress gradient calculated from an isotropic elastic approximation does not directly reflect the distribution of permanent deformation in a crystal of the same shape under the same conditions. However, with additional crystallographic constraints, it serves to predict locations where twinning and slip are first activated in a stressed crystal. In this study, thick-walled hollow cylinders were cored from single calcite crystals parallel to 0001 and . One cylinder of each orientation was loaded at room temperature under one of two conditions: internal pressure (P _p )=60 MPa, external pressure (P _c )=100 MPa, or P _p = 20 MPa, P _c = 50 MPa. These conditions would produce a radial stress gradient in an isotropic elastic cylinder. Mechanical twins in the deformed calcite samples had a hexagonal distribution in the 0001 oriented cylinder and an orthorhombic distribution in the oriented cylinder.Zones of dense r-slip dislocations were observed in the cylinder. Calculated resolved shear stresses for r-slip in either cylinder remained far below the published critical resolved shear stress (c.r.s.s.) value. Calculated contributions from twinning back stress and anisotropy do not account for the difference between the resolved shear stress and the c.r.s.s. These results underscore the necessity of considering dislocation activiation stresses rather than c.r.s.s. in quantitative analyses of heterogeneous of deformation in single crystals.