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.     

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.     

Titania precipitation in sapphire containing iron and titanium

Titania, TiO₂, precipitation in natural blue sapphire (Fe, Ti: -Al₂O₃) has been investigated using high resolution and analytical transmission electron microscopy. The structure and habit of the TiO₂ precipitate depends on both the Ti⁴⁺ concentration and the temperature at which the precipitate formed. Tetragonal TiO₂ (Rutile) grows at 1350° C but at 1150° C an orthorhombic non-equilibrium TiO₂ polymorph precipitates. Both TiO₂ polymorphs nucleate in the (0001)s plane as lens shaped discs twinned along their diameter. The crystallographic alignment of each type of TiO₂ precipitate with respect to the -Al₂O₃ host matrix provides a high degree of structural coherency with minimal lattice mismatch. Electron diffraction analysis established the following precipitate/host orientation relationships: tetragonal TiO₂: {011}r {11 07B;100}r(0001)s and 01 r10 0s twinned along the (011)r planeand orthorhombic TiO₂: {021}{11 0}s, {100}(0001)s and 0 2 10 0s twinned along the (021) plane.     

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%).     

Formulation of the thermodynamic functions for mantle minerals: MgO as an example

The formulas for thermodynamic functions for minerals are presented, couched in terms of the important thermodynamic variable K_T= (P/T)_v, where is the volume thermal expansivity and K_T is the isothermal bulk modulus. Presenting the formulas in this way leads to simplification since K_T as a product varies only slightly with volume, and is close to being independent of temperature at high temperature. Using our equations, we present as examples some computed data in the form of graphs on the entropy, internal energy, Helmholtz free energy, and Gibbs free energy in the high temperature regime (up to 2000 K) and for high compression (up to 0.7), for MgO. For entropy, knowledge of the V, T dependence of K_T is sufficient. For enthalpy and internal energy, the equation of state is needed in addition.     

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.     

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.     

Phase transitions in leucite: X-ray diffraction studies

Lattice parameters, and intensities of selected X-ray reflexions, have been measured as a function of temperature for natural leucite, to characterise the phase transformation behaviour. At low temperatures leucite has a large ferroelastic distortion, but the temperature evolution of lattice parameters cannot be explained in terms of a purely ferroelastic phase transition; in particular, the considerable change in volume with temperature implies an additional transition mechanism, which we correlate with off-centring of K-ions in the low-temperature phase, and a collapse of the 111 structural channels. The transition behavior can therefore be rationalised in terms of two competing mechanisms: (I) Ferroelastic (consistent with the change m3m 4/mmm); (II) Volume-changing (consistent with m3m 4/m). Coupling of the two order parameters Q_I, and Q_II gives rise to the intermediate 4/mmm tetragonal phase.Our results confirm the existence of an I4 ₁/aI4 ₁/acd transition, but the non-disappearance of the 200 reflexion at high temperatures implies that the expected transition from I4₁/acd to Ia3d (cubic) symmetry does not occur. We attribute this to a residual strain field conjugated to the order parameter, due to defects (with possible Al/Si order). Nevertheless, within our experimental resolution, the lattice becomes metrically cubic at 665° C.     

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.     

Partition of magnesium and iron between Olivine and spinel,and between pyroxene and spinel

Partition of Fe²⁺ and Mg between coexisting (Mg, Fe)₂SiO₄ spinel and (Mg, Fe)SiO₃ pyroxene was investigated at pressures 80 and 90 kbar and at temperatures 840 and 1050° C, using tetrahedral-anvil type of high pressure apparatus. Olivine-spinel solid solution equilibria in the system Mg₂SiO₄-Fe₂SiO₄ were discussed in the light of the partition reaction. Partition of Fe²⁺ and Mg in both olivine-spinel and pyroxene-spinel systems can not be regarded as that between ideal solid solutions. By applying the simple solution model for the partition of Fe²⁺ and Mg, sign of the heat of mixing was estimated to be positive for all olivine, spinel and pyroxene. Relative concentration of Fe²⁺ in spinel in the pyroxene-spinel system is likely to cause some change in the chemical composition of modified spinel () or spinel () in the transition zone of the mantle. A considerable change is also expected in the transition pressure of to ( + ) and ( + ) to .Presented at the symposium Recent Advances in the Studies of Rocks and Minerals at High Pressures and Temperatures held in Montreal, 1972. Jointly sponsored by the International Mineralogical Association and the Commission on Experimental Petrology.     

Chemistry of some Pb-(Cu,Fe)-(Sb,Bi sulfosalts from France and Portugal. Implications for the crystal chemistry of lead sulfosalts in the Cu-poor part of the Pb2S2-Cu2S-Sb2S3-Bi2-Bi2S3 system

Electron microprobe analysis of Pb-Cu(Fe)-Sb-Bi sulfosalts from Bazoges and Les Chalanches (France), and Pedra Luz (Portugal), give new data about (Bi, Sb) solid-solution and incorporation of the minor elements Cu, Fe or Ag in jaskolskiite, and in izoklakeite-giessenite and kobellite-tintinaite series. Jaskolskiite from Pedra Luz has high Sb contents (from 17.9 to 20.7 wt.%), leading to the extended general formula: Cu _x Pb_2+x (Sb_1–y Bi _y )_2–x S₅, with 0.10 x 0.22 and 0.19 y 0.41. Fe-free, Bi-rich izoklakeite from Bazoges has high Ag contents (up to 2.2 wt. %), leading to the simplified formula Cu₂Pb₂₂Ag₂(Bi, Sb)₂₂S₅₇; in Les Chalanches it contains less Ag content (1.2 wt.%), but has an excess of Cu that gives the formula: Cu_2.00 (Cu_0.49Ag_1.18)_=1.67Pb_22.70(Bi_12.63Sb_8.99)_=21.62S_57.27.In tintinaite from Pedra Luz, the variation of the Fe/Cu ratio can be explained by the substitution: Cu + (Bi, Sb) Fe + Pb; Fe-free kobellite from Les Chalanches has a Cu-excess, corresponding to the formula Cu_2.81Ag_0.54Pb_9.88(Bi_10.37Sb_5.21)_=15.38S_35.09. Eclarite from the type locality, structurally related to kobellite, shows a Cu excess too. In natural samples of the kobellite homologous series, Fe is positively correlated with Pb, and its contents never exceed that of Cu. Ag substitutes for Pb, together with (Bi, Sb). Taking into account the possibility of Cu excess, but excluding formal Cu²⁺ and Fe³⁺, general formulae can be written:     

The α-β phase transition in cristobalite,SiO2

Cristobalite, a high temperature phase of silica, SiO₂, undergoes a (metastable) first-order phase transition from a cubic, , to a tetragonal, P4₃2₁2 (or P4₁2₁2), structure at around 220° C. The cubic C9-type structure for -cristobalite (Wyckoff 1925) is improbable because of two stereochemically unfavorable features: a 180° Si-O-Si angle and an Si-O bond length of 1.54 Å, whereas the corresponding values in tetragonal -cristobalite are 146° and 1.609 Å respectively. The structure of the -phase is still controversial. To resolve this problem, a symmetry analysis of the (or P4₁2₁2) transition in cristobalite has been carried out based on the Landau formalism and projection operator methods. The starting point is the ideal cubic ( ) C9-type structure with the unit cell dimension a (7.432 Å) slightly larger than the known a dimension (7.195 Å at 205° C) of -cristobalite, such that the Si-O-Si angle is still 180°, but the Si-O bond length is 1.609 Å. The six-component order parameter driving the phase transition transforms according to the X₄ representation. The transition mechanism essentially involves a simultaneous translation and rotation of the silicate tetrahedra coupled along 110. A Landau free-energy expression is given as well as a listing of the three types of domains expected in -cristobalite from the transition. These domains are: (i) transformation twins from a loss of 3-fold axes, (ii) enantiomorphous twins from a loss of the inversion center, and (iii) antiphase domains from a loss of translation vectors 1/2 110 (FP). These domains are macroscopic and static in -cristobalite, and microscopic and dynamic in -cristobalite. The order parameter , couples with the strain components as ², which initiates the structural fluctuations, thereby causing the domain configurations to dynamically interchange in the -phase. Hence, the - cristobalite transition is a fluctuation-induced first-order transition and the -phase is a dynamic average of -type domains.     

Johillerit,Na(Mg,Zn)3 Cu(AsO4)3, ein neues Mineral aus Tsumeb,Namibia

Zusammenfassung Die chemische Analyse des neuen Minerals Johillerit mit der Elektronenmikrosonde ergab: Na₂O 5,4, MgO 18,3, ZnO 5,4, CuO 15,8 und As₂O₅ 55,8, Summe 100.7%. Aus diesem Ergebnis wurde die idealisierte Formel Na(Mg, Zn)₃ Cu(AsO₄)₃ abgeleitet. Johillerit ist monoklin mit der RaumgruppeC2/c. Die Gitterkonstanten sind:a=11,870 (3),b=12,755 (3),c=6,770 (2) , =113,42 (2)°,Z=4. Die stärksten Linien des Pulverdiagramms sind: 4,06 (5) (22 ), 3,50 (4) (310), 3,25 (8) (11 ), 2,75 (10) (330, 240), 2,64 (5) (311, 13 , 40 ), 1,952 (4) (13 , 35 ), 1,682 (4) (20 , 460), 1,660 (5) (40 , 71 , 550, 64 ), 1,522 (4) (442, 153, 13 ). Es bestehen enge strukturelle Beziehungen zwischen Johillerit und O'Danielit, Na(Zn, Mg)₃H₂(AsO₄)₃, sowie einigen synthetischen. Verbindungen.Johillerit ist violett durchscheinend. Die Spaltbarkeit nach {010} ist ausgezeichnet und nach {100} und {001} gut.H (Mohs)3.D=4,15 undD _X =4,21 g·cm^–3. Das Mineral ist optisch zweiachsig positiv, 2V80 (5)°. Die Werte der Lichtbrechung sindn =1,715 (4),n =1,743 (4) undn =1,783 (4). Die Auslöschung istn b und auf (010)n c16°. Johillerit ist stark pleochroitisch mit den AchsenfarbenX=violett-rot,Y = blauviolett undZ = grünblau. Das neue Mineral kommt in radialstrahligen Massen gemeinsam mit kupferhaltigem Adamin und Konichalcit in zersetzem Kupfererz von Tsumeb, Namibia, vor. Die Benennung erfolgte nach Prof. Dr.J.-E. Hiller (1911–1972).

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Johillerite, Na(Mg, Zn) ₃ Cu(AsO ₄ ) ₃ , a new mineral from Tsumeb, Namibia

Summary Electron microprobe analysis of the new mineral johillerite gave Na₂O 5.4, MgO 18.3, ZnO 5.4, CuO 15.8, and As₂O₅ 55.8, total 100.7%. From this result, the ideal formula is given as Na(Mg, Zn)₃ Cu(AsO₄)₃. Johillerite crystallizes monoclinic,C2/c. The unit cell dimensions are:a=11.870(3),b=12.755 (3),c=6.770 (2) , =113.42 (2)°,Z=4. The strongest lines on the X-ray powder diffraction pattern are: 4,06 (5) (22 ), 3,50 (4) (310), 3,25 (8) (11 ), 2,75 (10) (330, 240), 2,64 (5) (311, 13 , 40 ), 1,952 (4) (13 , 35 ), 1,682 (4) (20 , 460), 1,660 (5) (40 , 71 , 550, 64 ), 1,522 (4) (442, 153, 13 ). There is a close relationship between johillerite, o'danielite, Na(Zn, Mg)₃H₂(AsO₄)₃, and some synthetic compounds. Johillerite is violet in colour, transparent. Cleavage is {010} perfect, {100} and {001} good.H (Mohs)3.D=4.15 andD _X =4.21 g·cm^–3. The mineral is optically biaxial positive, 2V80 (5)°. The refractive indices are:n =1.715 (4),n =1.743 (4),n =1.783 (4). The extinction isn b and on (010)n c16°. Strongly pleochroic with axial coloursX=violet-red,Y=bluish violet andZ=greenish blue. The new mineral was found in radiated masses together with cuprian adamite and conichalcite in an oxidized copper ore from Tsumeb, Namibia. It is named in honour of Prof. Dr.J.-E. Hiller (1911–1972).

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Mit 1 Abbildung     

An ion microprobe study of anhydrous oxygen diffusion in anorthite: a comparison with hydrothermal data and some geological implications

The diffusion rate of ¹⁸O tracer atoms in anorthite (An₉₇Ab₀₃) under anhydrous conditions has been measured using SIMS techniques. The tracer source was ¹⁸O₂ 98.4% gas at 1 bar, in the temperature range 1300° C–850° C. The measured diffusion constants are D ₀=1 _–0.6 ⁺¹ ×10^–9 m²s^–1 Q=236±8 kJ mol^–1 Comparison of these values with published data for ¹⁸O diffusion in anorthite under hydrothermal conditions shows that dry oxygen diffusivities are orders of magnitude lower than equivalent wet values at similar temperatures. The effect of these differences on oxygen isotope equilibration during cooling is discussed.     

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.     

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.     

A case of ore deposition associated with paleogeothermal activity: The polymetallic ore veins of Aïn Barbar (NE Constantinois,Algeria)

The Aïn Barbar area was at Langhian times the site of a terrestrleial high energy geothermal field related to acid Langhian magmatic activity. A granite body probably occurs at depth, as evidenced by microgranite and rhyolite dikes. The reservoir is made up of Upper Cretaceous Massylian flyschs, overlain by an impermeable cover of Oligo-Miocene Numidian flysch. Due to erosional unroofing, its thickness, initially on the order of one kilometer, was probably halved towards the termination of activity of the liquid-dominated geothermal field.Geothermal activity, which lasted about 1 Ma, developed in two stages: