Dislocation dissociation in CaGeO3 perovskite

Dissociated dislocations have been observed for the first time by transmission electron microscopy in the perovskite-structure compound CaGeO₃. Dislocations with Burgers vectors \(\left[ {1\bar 10} \right]\) and [001] (in pseudo-cubic index) are dissociated into collinear partials on the (110) plane: $$\left[ {1\bar 10} \right] = {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\left[ {1\bar 10} \right] + {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\left[ {1\bar 10} \right]$$ and [001] = 1/2[001] + 1/2[001]. The partials react to form octagonal extended nodes. The stacking fault ribbons with displacement vector \(\left[ {1\bar 10} \right]\) have a width of 350 A, which corresponds to a stacking fault energy of 35 erg/cm² (or mJ/m²).     

Cation stacking faults in magnesium germanate spinel

Widely extended, cation stacking faults in experimentally deformed Mg₂GeO₄ spinel have been studied using transmission electron microscopy (TEM). The faults lie on {110} planes. The displacement vector is of the form \(\frac{1}{4}\left\langle {1\bar 10} \right\rangle \) and is normal to the fault plane. The partial dislocations which bound the stacking fault have colinear Burgers vectors of the form \(\frac{1}{4}\left\langle {1\bar 10} \right\rangle \) which are normal to the fault plane.     

Cordierite microstructure and texture in a moldanubian gneiss

The microstructure and texture in cordierites of a moldanubian gneiss from the Bohemian Massif has been analysed by transmission electron microscopy (TEM) and universal stage in order to get information on the deformation mechanisms and textural development of this rock-forming mineral. Deformation may have taken place at temperatures between about 500° C and 630° C and pressures smaller than about 3 kb. The elongated cordierite xenoblasts show a typical dislocation creep microstructure consisting of subgrain boundaries and free dislocations. The dislocations have [001], [010] and 1/2<110> Burgers vectors. [001] dislocations often have pure screw and edge character the latter type being climb-dissociated on (001). Among the dislocations reactions are common. The main subgrain boundaries observed are (010)[001], {110}[001] and (001)[010] tilt boundaries. Burgers vectors and dislocation line directions reveal (100)[001], (010)[001], (100)[010], {110} 1/2<110> and (001)1/2<110> as activated slip systems. The crystallographic preferred orientation (here referred to as texture) consists of a [001] maximum in the foliation parallel to the mineral lineation. [100] and [010] maxima are perpendicular to it within and normal to the foliation, respectively, with a girdle tendency normal to the lineation. The texture may be explained by simple shear deformation on the {hkO}[001] slip systems with preference of (010)[001].     

Quantitative characterization of plastic deformation of zircon and geological implications

The deformation-related microstructure of an Indian Ocean zircon hosted in a gabbro deformed at amphibolite grade has been quantified by electron backscatter diffraction. Orientation mapping reveals progressive variations in intragrain crystallographic orientations that accommodate 20° of misorientation in the zircon crystal. These variations are manifested by discrete low-angle (<4°) boundaries that separate domains recording no resolvable orientation variation. The progressive nature of orientation change is documented by crystallographic pole figures which show systematic small circle distributions, and disorientation axes associated with 0.5–4° disorientation angles, which lie parallel to rational low index crystallographic axes. In the most distorted part of the grain (area A), this is the [100] crystal direction. A quaternion analysis of orientation correlations confirms the [100] rotation axis inferred by stereographic inspection, and reveals subtle orientation variations related to the local boundary structure. Microstructural characteristics and orientation data are consistent with the low-angle boundaries having a tilt boundary geometry with dislocation line [100]. This tilt boundary is most likely to have formed by accumulation of edge dislocations associated with a 〈001〉{100} slip system. Analysis of the energy associated with these dislocations suggest they are energetically more favorable than TEM verified 〈010〉{100} slip. Analysis of minor boundaries in area A indicates deformation by either (001) edge, or [100](100) and [001](100) screw dislocations. In other parts of the grain, cross slip on (111), and (112) planes seems likely. These data provide the first detailed microstructural analysis of naturally deformed zircon and indicate ductile crystal-plastic deformation of zircon by the formation and migration of dislocations into low-angle boundaries. Minimum estimates of dislocation density in the low-angle boundaries are of the order of ∼3.10¹⁰ cm⁻². This value is sufficiently high to have a marked effect on the geochemical behavior of zircon, via enhanced bulk diffusion and increased dissolution rates. Therefore, crystal plasticity in zircon may have significant implications for the interpretation of radiometric ages, isotopic discordance and trace element mobility during high-grade metamorphism and melting of the crust.     

Transmission electron microscope study of experimentally deformed K-Feldspar single crystals

Single crystals of sanidine which were experimentally deformed so as to introduce the (010)[100] slip system were examined by transmission electron microscopy (tem). Dislocation glide is mainly manifested in the samples deformed at 700° C, with a strain rate \(\dot \varepsilon = 1 - 2 \times 10^{ - 6} s^{ - 1} \) . In addition to the expected slip system another more important one, (12 \(\bar 1\) )[101], was found. The dislocations lying in (010) present a glissile dissociation. These observations have been discussed in term of the feldspar structure. Models for glissile dissociation in (010) are proposed: [100]=1/2[100]+1/2[100] or 1/2[101]+1/2[10 \(\bar 1\) ] and [101]=1/2[101]+1/2[101].     

Dislocations in CaTiO3 perovskite deformed at high-temperature: a transmission electron microscopy study

Dislocation configurations in natural single crystals of CaTiO₃ perovskite deformed in high-temperature creep were examined and characterized by transmission electron microscopy. Screw dislocations with Burgers vector [100]_pc and [011]_pc, dissociated on the $(01\bar 1)_{{\text{pc}}} $ plane, form rectangular networks with extended four-fold nodes in the shape of octagons, a configuration never observed in any of the previously investigated perovskites, except CaGeO₃. Screw dislocations with Burgers vector [101]_pc and $(\bar 101)_{{\text{pc}}} $ , on the (010)_pc plane, react to form a twist wall; the dislocations with Burgers vector [002] produced by the reaction decompose into two perfect dislocations [001]_pc. This results in a new configuration, never observed before, with three-fold nodes at the corners of rectangles. Both the octagonal extended nodes and the junctions decomposed into perfect dislocations are seen in samples deformed indifferently by slip on {100}_pc or {110}_pc planes, but they seem to appear only above 1520 K, in the cubic phase.     

Room temperature microplasticity of a spodumene LiAlSi2O6

As uniaxial compression tests of α spodumene LiAlSi₂O₆ at various temperatures and strain rates systematically led to brittle fracture, room-temperature microindentations have been performed with a view to characterizing the glide systems. Transmission electron microscopy (TEM) investigations show that only the [010] (100) glide system is activated. The resulting dislocations are widely dissociated (up to 3,000 Å) following the reaction [010]→[0 1/2 1/6]+[0 1/2 \(\bar 1\) /6]. In contrast, in naturally deformed spodumene the activated glide systems found in TEM studies are [001] {110} and 1/2〈110〉{1 \(\bar 1\) 0} and the corresponding dislocations are not dissociated. Such a difference in mechanical behaviour is interpreted in considering the necessary impingement of the oxygen atoms during dislocation glide. It is shown that only the dissociated b dislocations can glide with a moderate lattice friction at room temperature. The proposed model is supported by the first exploratory deformation runs performed under confining pressure.     

Basal slip and texture development in calcite: new results from torsion experiments

The deformation behavior of calcite has been of longstanding interest. Through experiments on single crystals, deformation mechanisms were established such as mechanical twinning on in the positive sense and slip on and both in the negative sense. More recently it was observed that at higher temperatures slip in both senses becomes active and, based on slip line analysis, it was suggested that slip may occur. So far there had been no direct evidence for basal slip, which is the dominant system in dolomite. With new torsion experiments on calcite single crystals at 900 K and transmission electron microscopy, this study identifies slip unambiguously by direct imaging of dislocations and diffraction contrast analysis. Including this slip system in polycrystal plasticity simulations, enigmatic texture patterns observed in compression and torsion of calcite rocks at high temperature can now be explained, resolving a long-standing puzzle.     

TEM characterization of dislocations and slip systems in stishovite deformed at 14 GPa, 1,300°C in the multianvil apparatus

Transmission electron microscopy (TEM) has been used to investigate deformation microstructures of synthetic stishovite specimens deformed at 14 GPa, 1,300°C. Geometrical characteristics of numerous dislocations have been characterized by dislocation contrast and stereographic analyses in order to identify the easy slip systems of stishovite. TEM data allowed us to characterize the following slip systems: 〈100〉{001}, 〈100〉{010}, 〈100〉{021}, [001]{100}, [001]{110}, [001]{210} and Observation of sub-grain boundaries and scalloped edge dislocations suggest that climb has been activated in the specimens.     

Experimental study of subsolidus phase relations and mixing properties of pyroxene and plagioclase in the system Na2O-CaO-Al2O3-SiO2

In the system Na₂O-CaO-Al₂O₃-SiO₂ (NCAS), the equilibrium compositions of pyroxene coexisting with grossular and corundum were experimentally determined at 40 different P-T conditions (1,100–1,400° C and 20.5–38 kbar). Mixing properties of the Ca-Tschermak — Jadeite pyroxene inferred from the data are (J, K): $$\begin{gathered} G_{Px}^{xs} = X_{{\text{CaTs}}} X_{{\text{Jd}}} [14,810 - 7.15T - 5,070(X_{{\text{CaTs}}} - X_{{\text{Jd}}} ) \hfill \\ {\text{ }} - 3,350(X_{{\text{CaTs}}} - X_{{\text{Jd}}} )^2 ] \hfill \\ \end{gathered} $$ The excess entropy is consistent with a complete disorder of cations in the M2 and the T site. Compositions of coexisting pyroxene and plagioclase were obtained in 11 experiments at 1,190–1,300° C/25 kbar. The data were used to infer an entropy difference between low and high anorthite at 1,200° C, corresponding to the enthalpy difference of 9.6 kJ/mol associated with the C \(\bar 1\) =I \(\bar 1\) transition in anorthite as given by Carpenter and McConnell (1984). The resulting entropy difference of 5.0 J/ mol · K places the transition at 1,647° C. Plagioclase is modeled as ideal solutions, C \(\bar 1\) and I \(\bar 1\) , with a non-first order transition between them approximated by an empirical expression (J, bar, K): $$\Delta G_T = \Delta G_{1,473} \left[ {1 - 3X_{Ab} \tfrac{{T^4 - 1,473^4 }}{{\left( {1,920 - 0.004P} \right)^4 - 1,473^4 }}} \right],$$ where $$\Delta G_{1,473} = 9,600 - 5.0T - 0.02P$$ The derived mixing properties of the pyroxene and plagioclase solutions, combined with the thermodynamic properties of other phases, were used to calculate phase relations in the NCAS system. Equilibria involving pyroxene+plagioclase +grossular+corundum and pyroxene+plagioclase +grossular+kyani te are suitable for thermobarometry. Albite is the most stable plagioclase.     

Transmission electron microscopy of experimentally deformed chalcopyrite single crystals

Two crystals of natural chalcopyrite, CuFeS₂, experimentally deformed at 200° C have been studied by means of transmission electron microscopy (TEM). The activated glide planes are (001) and {112}. The dislocations in (001) have the Burgers vector [110] and a predominating edge character. They are split into two colinear partials b=1/2[110] and can cross split into {112}. The dislocations in {112} consist of straight segments along low index lattice lines. They are often arranged in dipoles generating trails of loops. Few dislocations with b=1/2[ \(\overline {11} \) 1] and [1 \(\bar 1\) 0] are present and dislocations with b=[0 \(\bar 2\) 1] occur in low angle subgrain boundaries. From weak beam contrasts it is presumed that most of the dislocations gliding in {112} have b=1/2〈3 \(\overline {11} \) 〉. They are dissociated into up to four partials. Microtwins and different types of stacking faults in {112} also occur. Models of the dissociation of dislocations are discussed.     

Peierls dislocation modelling in perovskite (CaTiO<Subscript>3</Subscript>): comparison with tausonite (SrTiO<Subscript>3</Subscript>) and MgSiO<Subscript>3</Subscript> perovskite

We present here a numerical modelling study of dislocations in perovskite CaTiO₃. The dislocation core structures and properties are calculated through the Peierls–Nabarro model using the generalized stacking fault (GSF) results as a starting model. The GSF are determined from first-principles calculations using the VASP code. The dislocation properties such as collinear, planar core spreading and Peierls stresses are determined for the following slip systems: [100](010), [100](001), [010](100), [010](001), [001](100), [001](010), and All dislocations exhibit lattice friction, but glide appears to be easier for [100](010) and [010](100). [001](010) and [001](100) exhibit collinear dissociation. Comparing Peierls stresses among tausonite (SrTiO₃), perovskite (CaTiO₃) and MgSiO₃ perovskite demonstrates the strong influence of orthorhombic distortions on lattice friction. However, and despite some quantitative differences, CaTiO₃ appears to be a satisfactory analogue material for MgSiO₃ perovskite as far as dislocation glide is concerned.     

Characterization of the glide planes of the [001] screw dislocations in olivine using electron tomography

A San Carlos olivine polycrystal has been deformed under uppermost mantle conditions, by compression at 900 °C, at a strain rate of 1.1 × 10^?5 s^?1, under a confining pressure of 300 MPa, using the Paterson press. Transmission electron tomography of dislocations has been performed by scanning transmission electron microscopy, by conventional transmission electron microscopy using the weak-beam dark-field technique, associated with precession or not, in order to determine the glide planes of [001] screw dislocations. This recent technique is the most suitable one since most [001] dislocations exhibit straight screw segments due to the high lattice friction on this character at low temperature. We find that [001] dislocations glide in (100), (010) and {110} as already reported, but also more unexpectedly in {120} and {130}. We show that at 900 °C, [001] {110} glide is dominant in polycrystals. We have, however, noted and characterized numerous cross-slip events in the specimen.     

Equilibrium thermodynamics of Al/Si ordering in anorthite

Variations in the equilibrium degree of Al/Si order in anorthite have been investigated experimentally over the temperature range 800-1535° C. Spontaneous strain measurements give the temperature dependence of the macroscopic order parameter, Q, defined with respect to the \(C\bar 1 \rightleftharpoons I\bar 1\) phase transition, while high temperature solution calorimetric data allow the relationship between Q and excess enthalpy, H, to be determined. The thermodynamic behaviour can be described by a Landau expansion in one order parameter if the transition is first order in character, with an equilibrium transition temperature, T _tr, of ～2595 K and a jump in Q from 0 to ～0.65 at T_tr. The coefficients in this Landau expansion have been allowed to vary with composition, using Q=1 at 0 K for pure anorthite as a reference point for the order parameter. Published data for H and Q at different compositions allow the calibration of the additional parameters such that the free energy due to the \(C\bar 1 \rightleftharpoons I\bar 1\) transition in anorthite-rich plagioclase feldspars may be expressed (in cal. mole^-1) as: \(\begin{gathered}G = \tfrac{1}{2} \cdot 9(T - 2283 + 2525X_{Ab} )Q^2 \\ {\text{ + }}\tfrac{1}{4}( - 26642 + 121100X_{Ab} )Q^4 \\ {\text{ + }}\tfrac{1}{6}(47395 - 98663X_{Ab} )Q^6 \\ \end{gathered}\) where X _Ab is the mole fraction of albite component. The nature of the transition changes from first order in pure anorthite through tricritical at ～An₇₈ to second order, with increasing albite content. The magnitude of the free energy of \()\) ordering reduces markedly as X _Ab increases. At ～700° C incommensurate ordering in crystals with compositions ～An₅₀–An₇₀ needs to have an associated free energy reduction of only a few hundred calories to provide a more stable structure. These results, together with a simple mixing model for the disordered ( \()\) ) solid solution, an assumed tricritical model for the incommensurate ordering and published data for ordering in albite have been used to calculate a set of possible free energy relations for the plagioclase system. The incommensurate structure should appear on the equilibrium phase diagram, but its apparent stability with respect to the assemblage albite plus anorthite at low temperatures depends on the values assigned to the mixing parameters of the $$$$ solid solution.     

Thermodynamic modelling of non-convergent ordering in orthopyroxenes: a comparison of classical and Landau approaches

The excess Gibbs free energy due to non-convergent ordering is described by a Landau expansion in which configurational and non-configurational entropy contributions are separated:

Deformation and recrystallisation mechanisms in naturally deformed cordierite

Cordierite — (Mg,Fe)₂Al₄Si₅O₁₈ — occurs as porphyroclasts within metapelitic and metavolcanic rocks from the Kemiö-Orijärvi belt, SW Finland. After crystallisation the cordierites have been deformed at temperatures between 550–825° C and pressures of 3–5 kbar. Optical microscopy reveals the following deformation-induced microstructures: a bimodal size distribution between host, 0.3 to 4.0 mm, and recrystallised (new) grains, 0.1 to 0.5 mm; the intracrystalline defect-structures of host grains yield undulatory extinction, subgrains and some twinning. Recrystallised grains are optically strain free. Grain and subgrain boundaries are generally straight and parallel to crystallographic low-index planes. Orientation distribution diagrams for host and recrystallised grains yield similar fabric diagrams, i.e. [010] perpendicular to foliation -S-, [001] and [100] parallel to S and [001] parallel to lineation -L-. The fabric diagrams indicate that [001] (010) is the dominant slip system. Transmission electron microscopy reveals straight free dislocations, glide and climb loops, minor {130} and {110} microtwins, isolated nodal points and dislocation walls. Contrast analyses yield Burgers vector b = [001] being dominant and b = [100] subordinate. Climb loops consist of 〈c〉-dislocations that are dissociated in (001) planes, glide loops are defined by [100] [010] and [001] (100). The cordierite microstructures have been interpreted to be generated by dislocation creep. The dominant recrystallisation mechanism is thought to be subgrain rotation subsequently followed by minor grain or twin-band boundary migration.     

Dislocation substructure of mantle-derived olivine as revealed by selective chemical etching and transmission electron microscopy

Cleaved and mechanically polished surfaces of olivine from peridotite xenoliths from San Carlos, Arizona, were chemically etched using the techniques of Wegner and Christie (1974). Dislocation etch pits are produced on all surface orientations and they tend to be preferentially aligned along the traces of subgrain boundaries, which are approximately parallel to (100), (010), and (001). Shallow channels were also produced on (010) surfaces and represent dislocations near the surface that are etched out along their lengths. The dislocation etch channel loops are often concentric, and emanate from (100) subgrain boundaries, which suggests that dislocation sources are in the boundaries. Data on subgrain misorientation and dislocation line orientation and arguments based on subgrain boundary energy minimization are used to characterize the dislocation structures of the subgrain boundaries. (010) subgrain boundaries are of the twist type, composed of networks of [100] and [001] screw dislocations. Both (100) and (001) subgrain boundaries are tilt walls composed of arrays of edge dislocation with Burgers vectors b=[100] and [001], respectively. The inferred slip systems are {001} 〈100〉, {100} 〈001〉, and {010} 〈100〉 in order of diminishing importance. Exploratory transmission electron microscopy is in accord with these identifications. The flow stresses associated with the development of the subgrain structure are estimated from the densities of free dislocations and from the subgrain dimensions. Inferred stresses range from 35 to 75 bars using the free dislocation densities and 20 to 100 bars using the subgrain sizes.     

(Ca,Mg)2Si2O6 clinopyroxenes: A solution model based on nonconvergent site-disorder

Experiments at high pressure and temperature indicate that excess Ca may be dissolved in diopside. If the (Ca, Mg)₂Si₂O₆ clinopyroxene solution extends to more Ca-rich compositions than CaMgSi₂O₆, macroscopic regular solution models cannot strictly be applied to this system. A nonconvergent site-disorder model, such as that proposed by Thompson (1969, 1970), may be more appropriate. We have modified Thompson's model to include asymmetric excess parameters and have used a linear least-squares technique to fit the available experimental data for Ca-Mg orthopyroxene-clinopyroxene equilibria and Fe-free pigeonite stability to this model. The model expressions for equilibrium conditions \(\mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction A) and \(\mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction B) are given by: 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Mg}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ W_{21} [2(X_{{\text{Ca}}}^{{\text{M2}}} )^3 - (X_{{\text{Ca}}}^{{\text{M2}}} ] \hfill \\ {\text{ + 2W}}_{{\text{22}}} [X_{{\text{Ca}}}^{{\text{M2}}} )^2 - (X_{{\text{Ca}}}^{{\text{M2}}} )^3 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{Wo}}}^{{\text{opx}}} )^2 \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Ca}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ 2W_{21} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^2 - (X_{{\text{Mg}}}^{{\text{M2}}} )^3 ] \hfill \\ {\text{ + W}}_{{\text{22}}} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^3 - (X_{{\text{Mg}}}^{{\text{M2}}} )^2 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{En}}}^{{\text{opx}}} )^2 \hfill \\ \hfill \\ \end{gathered} $$ where 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = 2.953 + 0.0602{\text{P}} - 0.00179{\text{T}} \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = 24.64 + 0.958{\text{P}} - (0.0286){\text{T}} \hfill \\ {\text{W}}_{{\text{21}}} = 47.12 + 0.273{\text{P}} \hfill \\ {\text{W}}_{{\text{22}}} = 66.11 + ( - 0.249){\text{P}} \hfill \\ {\text{W}}^{{\text{opx}}} = 40 \hfill \\ \Delta {\text{G}}_*^0 = 155{\text{ (all values are in kJ/gfw)}}{\text{.}} \hfill \\ \end{gathered} $$ . Site occupancies in clinopyroxene were determined from the internal equilibrium condition 1 $$\begin{gathered} \Delta G_{\text{E}}^{\text{O}} = - {\text{RT 1n}}\left[ {\frac{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}{{X_{{\text{Ca}}}^{{\text{M2}}} \cdot X_{{\text{Mg}}}^{{\text{M1}}} }}} \right] + \tfrac{1}{2}[(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} )(2{\text{X}}_{{\text{Ca}}}^{{\text{M2}}} - 1) \hfill \\ {\text{ + }}\Delta G_*^0 (X_{{\text{Ca}}}^{{\text{M1}}} - X_{{\text{Ca}}}^{{\text{M2}}} ) + \tfrac{3}{2}(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} ) \hfill \\ {\text{ (1}} - 2X_{{\text{Ca}}}^{{\text{M1}}} )(X_{{\text{Ca}}}^{{\text{M1}}} + \tfrac{1}{2})] \hfill \\ \end{gathered} $$ where δG _E ⁰ =153+0.023T+1.2P. The predicted concentrations of Ca on the clinopyroxene Ml site are low enough to be compatible with crystallographic studies. Temperatures calculated from the model for coexisting ortho- and clinopyroxene pairs fit the experimental data to within 10° in most cases; the worst discrepancy is 30°. Phase relations for clinopyroxene, orthopyroxene and pigeonite are successfully described by this model at temperatures up to 1,600° C and pressures from 0.001 to 40 kbar. Predicted enthalpies of solution agree well with the calorimetric measurements of Newton et al. (1979). The nonconvergent site disorder model affords good approximations to both the free energy and enthalpy of clinopyroxenes, and, therefore, the configurational entropy as well. This approach may provide an example for Febearing pyroxenes in which cation site exchange has an even more profound effect on the thermodynamic properties.     

Intergrowth of pyroxene and pyroxenoid; chain periodicity faults in pyroxene

Intergrowth of clinopyroxenes (augite, A) and pyroxenoids (Fe-rhodonite and pyroxferroite, Pxo) was observed by transmission electron microscopy. The following orientation relationship was found: (001)_Pxo is parallel to \((1\mathop {\bar 1}\limits^ + \bar 1)_{\text{A}}\) and \([1\bar 10]_{Pxo}\) is parallel to [011]_A. This relationship can be explained by similarities of the structures of clinopyroxenes and pyroxenoids. It contradicts a suggestion based on structural arguments of Koto et al. (1976). Chain periodicity faults parallel to \((1\mathop {\bar 1}\limits^ + \bar 1)\) are also observed in pure clinopyroxenes.     

The effect of aluminum and water on the development of deformation fabrics of orthopyroxene

The effect of alumina and water solubility on the development of fabric in orthopyroxene in response to simple shear deformation has been investigated at a pressure of 1.5 GPa and a temperature of 1,100 °C using the D-DIA apparatus. The microstructure observations at these conditions indicate that dislocation glide is the dominant deformation mechanism. In MgSiO₃ enstatite and hydrous aluminous enstatite, partial dislocations bounding the stacking faults in [001] glide parallel to the (100) (or) the (100) [001] slip system. Electron backscattered diffraction analysis of anhydrous aluminous enstatite, however, indicates operation of the (010) [001] slip system, and microstructure analysis indicates dislocation movement involving [001] on both (100) and {210} planes. The strong covalent bonding induced by the occupation of M1 and T2 sites by Al could have restricted the glide on (100), activating slip on {210}. The resulting seismic anisotropies (~2 %) in orthopyroxene are weaker compared to olivine (~9.5 %), and reduced anisotropy can be expected if orthopyroxene coexists with olivine. Weak anisotropy observed in stable cratonic regions can be explained by the relatively high abundance of orthopyroxene in these rocks.