Hexiong Yang

Thermal history of mesosiderites: Quantitative constraints from compositional zoning and Fe-Mg ordering in orthopyroxenes

Abstract We have derived mathematical relations to calculate cooling rates from the extent of compositional zoning developed during cooling across the interface of a natural diffusion couple. These relations were used to calculate the high temperature cooling rates of the mesosiderites Lowicz and Clover Springs from the available data on compositional zoning across core-overgrowth interface of orthopyroxene grains. We have also determined the cation ordering in four selected orthopyroxene crystals from Bondoc and Estherville mesosiderites with very high precision, and used these data to calculate their low temperature cooling rates. The compositional zoning of orthopyroxene crystals reflects extremely rapid cooling rates, at least ~1°C/100 years in the temperature range 850–1150°C. However, simultaneous consideration of both metallographic and cation ordering data for Estherville, within the framework of either an asymptotic or an exponential cooling model, requires a cooling rate of ~l°C/Ma near 250°C. The cation ordering data for Bondoc, for which no metallographic data are yet available, are suggestive of even slower cooling rate, which implies excavation from a somewhat greater depth in the parent body. However, within the limits of their uncertainties, the measured site occupancies of the orthopyroxene crystals from Bondoc can be reconciled with a cooling rate similar to that of Estherville. The calculated cooling rates at both high- and low-temperatures have been used to develop a thermal evolution model of mesosiderites. The suggested model is not incompatible with an asteroidal parent body for these meteorites. Further, it is shown that the closure temperature of Ar-Ar age must be tied to the slow cooling rate below 500°C.

Effects of cation substitution and order-disorder on P-V-T equations of state of cubic spinels

Abstract The geometric simplicity of the cubic spinel structure allows prediction of equation-of-state parameters from cation-anion bond distances, bond compressibilities, and bond thermal expansivities, which can be estimated from crystal chemical systematics. We calculate effects of cation substitution and order-disorder reactions for phases of geological interest: MgAl2O4 (spinel), MgFe2O4 (magnesioferrite), Fe3O4 (magnetite), and Mg2SiO4 (ringwoodite). Compressibilities for normal vs. inverse variants of A2+B23+O4 and A4+B22+O4 spinels are predicted to differ by as much as 17%, and thermal expansivities by as much as 15%, as a result of the differential compressibilities or thermal expansivities of divalent, trivalent, and tetravalent cations in tetrahedral vs. octahedral coordination. These effects are unexpectedly large, and they suggest that care must be taken to document the state of cation order before and after any pressure-volume-temperature equation-of-state measurements on phases subject to a range of ordered states.

On the crystal structure of pseudowollastonite (CaSiO 3 )

Abstract Nine tourmaline crystals for which major and minor element composition data are available have been examined by single-crystal X-ray structure refinement. The single crystals were then analyzed for major elements (by electron microprobe methods), Fe3/Fe2+ (by synchrotron micro- X-ray absorption near-edge spectroscopy). B and Li (by secondary ion mass spectrometry), and bulk H content (by uranium extraction). Despite recent claims based on chemical analyses, structure analysis suggests that no B exists in tetrahedral coordination in these samples. Analysis of cation ordering between the Y and Z octahedral sites suggests that the occurrence of an Fe2+ atom on a Y octahedral site may be locally associated with the absence of Mg at both of the neighboring Z sites, as substitutions of Fe2+ on Y and Mg on Z require antithetic shifts of the O6 anion.

Compressibility and crystal structure of kyanite, Al2SiO5, at high pressure

Abstract The unit-cell dimensions and crystal structure of kyanite at various pressures up to 4.56 GPa were refined from single-crystal X-ray diffraction data. The bulk modulus is 193(1) GPa. assuming K′ = 4.0. Calculated unit-strain tensors show that kyanite exhibits more isotropic compressibility than andalusite or sillimanite. The most and least compressible directions in the kyanite structure correspond approximately to the most and the least thermally expandable directions. The analysis of the distortion of the closest packing in kyanite indicates that the most compressible direction of the structure (along [012]) corresponds to the direction along which the closest-packed O monolayers are stacked. The bulk moduli for the Al1, Al2, Al3, and Al4 octahedra are 274(43). 207(14). 224(26). and 281(24) GPa. respectively, and those for the Si1 and Si2 tetra-hedra are 322(80) and 400(95) GPa. respectively. Four AlO6 octahedra that all become less distorted at higher pressures do not display clearly dominant compression directions. The average unshared O-O distance for each octahedron is considerably more compressible than the shared O-O distance. The high-pressure behaviors of the Al1 and Al4 octahedra are very similar but different from those of the Al2 and Al3 octahedra. Bulk moduli for the three Al2SiO5 polymorphs (kyanite. sillimanite. and andalusite). as well as those for the AlO6 octahedra in their structures, appear to decrease linearly as their volumes increase. The significantly larger bulk modulus and more isotropic compressibility for kyanite than for andalusite or sillimanite are a consequence of the nearly cubic close-packed arrangement of O atoms and the complex edge-sharing among four distinct AlO6 octahedra in the kyanite structure.

High temperature single crystal X-ray diffraction studies of the ortho-proto phase transition in enstatite, Mg2Si2O6 at 1360 K

A high temperature single-crystal X-ray diffraction study of enstatite, Mg2Si2O6 was undertaken at 296, 900, 1200, 1360 and 1400 K. During the X-ray data collection at 1360 K (T0), orthoenstatite (Pbca) transformed to protoenstatite (Pbcn). The unit cell parameters measured at T0 are a=18.456(4), b=8.960(2) and c=5.270(1) Å for ortho and a=9.306(1), b=8.886(1) and c=5.360(1) Å for proto. The discontinuous increase in c and decrease in b due to the ortho to proto transformation are associated with the drastic unkinking of the silicate chains, whereas the abrupt increase in a results from the large expansion of the M2 — O distances along a coupled with the increase in the out-of-plane tilting of the silicate tetrahedra. Stacking faults form in ortho prior to the phase transition, as well as in proto between 1360 and 1400 K. With increasing temperature, the silicate B chain in ortho straightens faster than the A chain as the configurations of the SiA and SiB tetrahedra tend to become similar. At T0, the A and B chains with the O3-O3-O3 angles (O3 being the bridging oxygen atom) of 163.0° and 149.5° in ortho, respectively, attain an identical angle of 168.4° in proto. The configuration of the silicate chain in proto resembles that of the A chain in ortho. Rigid-body thermal vibration analysis suggests that between 1200 and 1400 K the largest, the second largest and the smallest thermal librational motions of the [SiO4] tetrahedra in both ortho and proto are approximately around a, c and b, respectively. Below 1200 K, the largest thermal librational amplitudes of the SiA and SiB tetrahedra in ortho are quite different, but become nearly equivalent at T0. In contrast to the results reported for all iron-bearing orthopyroxenes at high temperature, switching of the O3B atoms coordinated with the M2 cation occurs during the ortho to proto transformation, but not in ortho below T0. The ortho-proto transition does not affect the configuration of the M1 octahedron significantly, but results in a decrease of the mean M2 — O bond distance by 0.043 Å and a highly distorted M2 octahedron in proto.

Comparative high-pressure crystal chemistry of wadsleyite, β-(Mg1-xFex)2SiO4, with x = 0 and 0.25

Abstract High-pressure crystal structures are reported for two synthetic wadsleyite crystals, β-Mg2SiO4 (Fe00) and P-(Mg0.75Fe0.25)2SiO4 (Fe25), at six pressures to 10.12 GPa. In both compositions, bulk compressibilities are equal to the average compressibility of divalent cation octahedra. Individual silicate tetrahedra, by contrast, are relatively rigid, though the Si-O-Si angle between tetrahedra in Si2O7 dimers decreases systematically with pressure. Wadsleyites display anisotropic compression, with the c axis approximately 40% more compressible than a or b. This behavior results from differential compression of (Mg, Fe)-O bonds; in each of the structure’s three symmetrically independent octahedra, the longest and most compressible bonds are roughly parallel to the b axis. Although the linear compressibilities of FeOO and Fe25 are similar, details of structural changes with pressure differ. Iron-enriched M1 and M3 octahedral sites in Fe25 are significantly less compressible than analogous Mg sites in Fe00.

Ferroelastic phase transition in cryolite, Na3AlF6, a mixed fluoride perovskite: High temperature single crystal X-ray diffraction study and symmetry analysis of the transition mechanism

Cryolite, Na3AlF6[ = 2Na+(Na0.5+Al0.53+)F3] is a mixed fluoride perovskite, in which the corner-sharing octahedral framework is formed by alternating [NaF6] and [AlF6] octahedra and the cavities are occupied by Na+ ions. At 295 K, it is monoclinic (α phase), space group P21/n with a = 5.4139 (7), b = 5.6012 (5) and c = 7.7769 (8) Å and β = 90.183 (3)∘, Z = 2. A high temperature single crystal X-ray diffraction study in the range 295–900 K indicates a fluctuation-induced first-order phase transition from monoclinic to orthorhombic symmetry at T0 ∼ 885 K, in contrast to a previous report that it becomes cubic at ∼823 K. The space group of the high temperature β phase is Immm with a = 5.632 (4), b = 5.627 (3) and c = 7.958 (4) Å, Z = 2 at 890 K. Above T0, the coordination number of the Na+ ion in the cavity increases from eight to twelve and the zigzag Na1 — Al octahedral chains parallel to c become straight with the Na1-F-Al angle = 180 °. The phase transition is driven by two coupled primary order parameters. The first corresponds to the rotation of the nearly rigid [AlF6] group and transforms according to the Γ4+ irreducible representation of Immm. Coupled to the [AlF6] rotation is a second primary order parameter corresponding to the displacement of the Na2+ ion in the cavity from its equilibrium position. This order parameter transforms according to the X3+ irreducible representation of Immm. Following Immm → P21/n phase transition, four equivalent domains of P21/n are determined relative to Immm, which are in an antiphase and/or twin relationship. The abrupt shortening of the octahedral Al-F and Na-F bonds and a sudden change in orientations of the atomic thermal vibration ellipsoids above T0 indicate a crossover from displacive to an order-disorder mechanism near the transition temperature. The β phase is interpreted as a dynamic average of four micro-twin and -antiphase domains of the a phase. This view is consistent with the entropy of phase transition, ΔStrans (11.43 JK−1 mol−1) calculated from heat capacity measurements (Anovitz et al. 1987), which corresponds closely to R ln4 (11.53 JK−1 mol−1), where 4 is the number of domains formed during the phase transition. The dynamic nature of the β phase is independently confirmed from a considerable narrowing of the 27Al nuclear magnetic resonance (NMR) line-shape above T0 (Stebbins et al. 1992).

A new pyroxene structure at high pressure; single-crystal X-ray and Raman study of the Pbcn-P2 1 cn phase transition in protopyroxene

Abstract The crystal structure of (Mg1.54Li0.23Sc0.23)Si2O6 protopyroxene has been studied with single- crystal X-ray diffraction at pressures to 9.98 GPa and Raman spectroscopy to 10.4 GPa. A first-order displacive phase transformation from the Pbcn space group to P21cn was observed between 2.03 and 2.50 GPa, which is characterized by a discontinuous decrease in a, c, and V by 1.1, 2.4, and 2.6%, respectively, and an increase in b by 0.9%, along with appearance of intensities of some 0kl reflections with k ≠ 2n. This is the first substantiated example of protopyroxene having the symmetry predicted by Thompson (1970). Evidence for the phase transition from Raman spectroscopy is also presented. The prominent structural changes associated with the Pbcn-to-P21cn transformation involve the abrupt splitting of one type of O-rotated silicate chain in low-pressure protopyroxene into S-rotated A and O-rotated B chains in high-pressure protopyroxene, coupled with a marked decrease in the O3-O3-O3 angles and a re-configuration of O atoms around the M2 site. The kinking angle of the silicate chain in the low-pressure phase at 2.03 GPa is 165.9°, whereas the angles are 147.9° and 153.9° for the A and B chains, respectively, in highpressure phase at 2.50 GPa. Strikingly, the two types of silicate chains in the P21cn structure alternate along the b axis in a tetrahedral layer parallel to (100). Such a mixed arrangement of two differently rotated silicate chains in a tetrahedral layer has not been observed in any other pyroxene structure. Compression anisotropy of the protopyroxene structure is affected by the phase transition. The relative linear compressibilities (βa:βb:βc) are 1.00:1.72:0.99 for low-pressure protopyroxene, but are 1.00:1.28:1.65 for high-pressure protopyroxene. The bulk moduli of low- and high-pressure phases are 130(3) and 111(1) GPa, respectively. This study concludes that the Pbcn-to-P21cn phase transition results from the differential compression between SiO4 tetrahedra and MO6 octahedra.

Thermal expansion, Debye temperature and Grneisen parameter of synthetic (Fe, Mg)SiO3 orthopyroxenes

Thermal expansion properties of synthetic orthopyroxenes (Fe0.20Mg0.80)SiO3, (Fe0.40Mg0.60)SiO3, (Fe0.50Mg0.50)SiO3, (Fe0.75Mg0.25)SiO3 and (Fe0.83Mg0.17)SiO3 were systematically studied by means of single-crystal x-ray diffraction in the temperature range from 296 to 1300 K. The measurements of unit cell dimensions as a function of temperature reveal that the a and c dimensions and the unit cell volume V increase nonlinearly with a positive curvature with rising temperature, whereas the b dimension behaves differently, depending on the total Fe content. For Mg-rich orthopyroxenes (Fe/(Fe+Mg)<30%), the b dimension expands similarly as the a and c dimensions, but it exhibits a nonlinear increase with a negative curvature for orthopyroxenes with Fe/(Fe+Mg)>30%. Together with the high temperature neutron diffraction data on enstatite (MgSiO3) (McMullan, Haga and Ghose, unpublished) and x-ray diffraction data on ferrosilite (FeSiO3) (Sueno et al. 1976), the measured unit cell dimensions were analyzed in terms of the Grüneisen theory of thermal expansion. The linear thermal expansion coefficients αa and αc both increase as temperature is elevated, with αc increasing faster, while αb changes gradually from increasing for Mg-rich orthopyroxenes to decreasing for Fe-rich orthopyroxenes. The relative magnitudes of linear thermal expansion coefficients are always in the order αb>αc>αa between 300 and 500 K, but at higher temperatures, the order changes to αc>αb>αa for Mg-rich orthopyroxenes and αc>αa>αb for Fe-rich ones. The linear thermal expansion behavior is interpreted on the basis of the structural mechanical model of Weidner and Vaughan (1982). The anomalous behavior of αb is mainly attributed to the changes in the Fe2+ population at the M2 site and the relative stiffness of the M2(Fe2+)-O bonds compared to the M2(Mg2+)-O bonds. The volume thermal expansion coefficients are nonlinear functions of temperature and lie between 23 and 49×10−6/K. The previously reported results of mean volume thermal expansion coefficients appear to represent the αV values characteristic of higher temperatures compared to our results. The thermal Debye temperatures are composition-dependent, decreasing linearly from 812 (MgSiO3) to 561 K (FeSiO3), and are systematically higher than the corresponding acoustic Debye temperatures. The Grüneisen parameters range from 0.85 to 0.89 and do not seem to vary with composition. The linear compressibilities derived from thermal expansion and elastic moduli data agree very well. The pressure derivatives of the isothermal bulk modulus (dK0/dP) are also composition-dependent and decrease from 11.2 (MgSiO3) to 8.77 (FeSiO3). Such large values indicate possible anomalous elastic behavior of orthopyroxenes at high pressures in the Earths upper mantle.

Thermodynamics of the amphiboles; Fe-Mg cummingtonite solid solution

Pyroelectric coefficients were measured from a series of natural tourmaline crystals between -170 and 500 K to quantify the variation of the pyroelectric effect with chemical composition. The amount of Fe in tourmaline has a prominent influence on the pyroelectricity. Fe content linearly decreases the pyroelectric coefficient in the composition range between 0.01(1) and 14.6(2) wt% FeO. Thus, to a first approximation, tourmaline pyroelectric coefficients may be predicted directly from the chemical composition derived by routine electron probe microanalysis. The relationships between pyroelectricity and chemistry indicate that the pyroelectric coefficient is influenced to different extents by the occupancies of the X, Y, and Z cation sites in the tourmaline structure. The octahedral Y site occupancy strongly influences the pyroelectric coefficient due to the preference of Fe for this site. This work further suggests that the addition of Fe and Mg cations to the smaller Z octahedral site causes the pyroelectric coefficient to increase. However, because an extended suite of samples is not available in which the Z site contains ions other than AI, this proposed trend has not been experimentally determined. The chemistry of the ninefold coordinated X site and the population of this site do not influence the pyroelectric coefficients of tourmaline.