Nadia Curetti

Equation of state and compressibility of phlogopite by in-situ high-pressure X-ray powder diffraction

The elastic properties of a natural phlogopite have been studied by in-situ high-pressure X-ray powder diffraction experiments on the ID9 beamline at the ESRF, at room temperature. Several EoS models (Birch-Murnaghan, Vinet, Poirier-Tarantola) have been fitted to the experimental P-V data and the results obtained are presented and discussed. The third-order Birch-Murnaghan EoS, assuming V 0 fixed at its experimental value, yields K 0 = 49.7(±0.5) GPa, K’ 0 =8.59(±0.19), K’ 0 =-0.5953 GPa −1 (implied value). The axial compressibilities at room conditions, determined by the third-order Birch-Murnaghan EoS, result in β EoS a0 =3.48(5), β EoS b0 =3.2(1), β EoS c0 =13.2(1) 10 −3 GPa −1 . Equilibrium thermodynamic calculations have been carried out to show how the new elastic parameters here reported affect the stability field of phlogopite.

Coexisting 3T and 2M1 polytypes of phengite from Cima Pal (Val Savenca, western Alps): Chemical and polytypic zoning and structural characterisation.

Randomly oriented phengite flakes, up to 15 cm across and 5 cm thick, occur in a metamorphic dyke at Cima Pal (upper Val Savenca, western Alps). The phengite formed in the Sesia zone at quartz-eclogite-facies conditions ( T ∼ 550°C, P ∼ 16–18 kbar) in the presence of hydrous fluid. A greenschist-facies retrogression (∼ 4–5 kbar and 500°C) locally altered the eclogite-facies assemblage. The mica flakes show yellowish and greenish zoning. This zoning is superposed by a structural zoning of 3 T and 2 M 1 (more abundant) polytypes. Single-crystal X-ray diffraction data were collected and the structures refined from the following samples. [mathrm{(K_{0.90}Na_{0.05}) (Al_{1.51}Mg_{0.32}Fe_{0.18}Ti_{0.03}) [Si_{3.40}Al_{0.60}O_{10}](OH)_{2} [yellowish 3mathit{T}; mathit{a} 5.220(1), mathit{c} 29.762(9) {AA}]}] , [mathrm{(K_{0.95}Na_{0.01}) (Al_{1.40}Mg_{0.34}Fe_{0.27}Ti_{0.03}) [Si_{3.50}Al_{0.50}O_{10}](OH)_{2} [greenish 3mathit{T}; mathit{a} 5.228(1), mathit{c} 29.73(1) {AA}]}] , [mathrm{(K_{0.98}Na_{0.02}) (Al_{1.55}Mg_{0.24}Fe_{0.21}Ti_{0.02}) [Si_{3.38}Al_{0.62}O_{10}](OH)_{2} [yellowish 2mathit{M}_{1}; mathit{a} 5.2132(8), mathit{b} 9.051(2), mathit{c} 19.937(5) {AA}, {beta} 95.76(2){^circ}]}] , and [mathrm{(K_{0.99}Na_{0.02}) (Al_{1.42}Mg_{0.33}Fe_{0.24}Ti_{0.04}) [Si_{3.45}Al_{0.55}O_{10}](OH)_{2} [greenish 2mathit{M}_{1}; mathit{a} 5.225(1), mathit{b} 9.057(2), mathit{c} 19.956(6) {AA}, {beta} 95.73(2){^circ}]}] . Tetrahedral cation order is absent in both polytypes, although partial octahedral order is present in the 3 T polytype. Colour and limited chemical zoning is attributed to a fluctuation in the fluid-phase composition. The 2 M 1 polytype with disordered pattern of octahedral cations was probably crystallised from the pre-existing 3 T polytype by a solid state reaction. The transformation occurred during the sharp decompression stage leading to the greenschist facies, which triggered nucleation and growth of the 2 M 1 polytype.

Structural evolution of a 3T phengite mica up to 10 GPa : an in-situ single-crystal X-ray diffraction study

Abstract The high-pressure structural evolution of a natural 3T-phengite [(K0.90Na0.05)S = 0.95(Al1.51Mg0.32Fe0.18Ti0.03)S = 2.04(Si3.40Al0.60)O10(OH)2, a = b = 5.2279(11) and c = 29.752(7) Å, space group: P3112] from Cima Pal (Sesia Zone, Western Alps, Italy) was studied by single-crystal X-ray diffraction with a diamond anvil cell under hydrostatic conditions up to about 10 GPa. Nine structural refinements were performed at selected pressures within the P-range investigated. The compressional behavior of the same phengite sample was previously studied up to about 27 GPa by synchrotron X-ray powder diffraction, and the corresponding P–V curve was modeled by a third-order Birch–Murnaghan Equation of State (BM-EoS). The significant elastic anisotropy of the 3T-phengite (i.e. β(c) > β(a)) is mainly controlled by the compression of the K-polyhedra. The evolution of the volume of the inter-layer K-polyhedron as a function of P is monotonic, without any evidence of discontinuity. Fitting the P–V data with a truncated second-order BM-EoS, we obtain a bulk modulus value of K0(K-polyhedron) = 35(3) GPa. The tetrahedra and octahedra in the 3T-phengite structure are significantly less compressible than the K-polyhedron, and behave similarly to rigid units within the P-range investigated. The main P-induced effect on the tetrahedral sheet consists in a cooperative rotation of the tetrahedra, describable by the evolution of the “tetrahedral rotation angle” (or “ditrigonal rotation angle”, α) as a function of P. The value of the ditrigonal rotation angle increases significantly with P: α (°) = αP0 + 0.57(2)P (GPa) [R about 99%]. The volume of the K-polyhedron and the value of ditrigonal rotation parameter (α) are not independent of one another, showing a correlation of about 99%.

Deprotonation and order-disorder reactions as a function of temperature in a phengite 3T (Cima Pal, western Alps) by neutron diffraction and Mössbauer spectroscopy.

The results on deprotonation and cation partitioning as a function of temperature in the tetrahedral and octahedral sites of a phengite 3 T , (K 0.94 Na 0.02 ) ∑0.96 (Al 1.43 Mg 0.33 Fe 0.25 ) ∑2.01 (Si 3.47 Al 0.53 ) ∑4 O 10 (OH) 2 , from Cima Pal (western Alps) are presented and discussed. They have been obtained by a synergic approach based on neutron powder diffraction from 293 K to 873 K, and on Mossbauer spectroscopy at ambient conditions, of the sample before and after heating. Order is observed at room temperature in both tetrahedral (Si fully occupies T 1) and octahedral (Al almost fills M 2) sites. Upon heating, deprotonation [mainly according to the reaction 2[(OH) - + Fe 2+ ] → 2O 2- + 2Fe 3+ + H 2 ↑], Fe oxidation and inter-site cation re-ordering reactions take place. Al moves by ~ 0.1 atoms from M 2 to M 3, and is replaced by Mg and Fe; Fe 2+ and Fe 3+ occupy different M -sites, after cooling, whereas Fe 2+ was partitioned on two sites, one site shared with Fe 3+ , before heating.

P-V and T-V equations of State of natural biotite : An in-situ high-pressure and high-temperature powder diffraction study, combined with Mossbauer spectroscopy

Abstract The P-V and T-V equations of state of a natural biotite sample (Mg/Fe ratio ≈ 1) have been studied using in-situ high-pressure (0.0001.11 GPa) synchrotron radiation powder diffraction at the European Synchrotron Radiation Facilities (ESRF) in Grenoble, France, and in-situ high-temperature (298.610 K) laboratory X-ray powder diffraction. A third-order Birch-Murnaghan model [V0 = 498.7(1) Å3, measured value] provides the following elastic parameters: K0 = 49(1) GPa, K’ = 8.1(5). The volume thermal expansion is satisfactorily described by a constant value resulting in 37(2) 10.6 K-1. Mössbauer spectroscopy proves that REDOX reactions have occurred upon heating, presumably 2(OH- + Fe2+) → 2O2- + 2Fe3+ + H2 ↑ and/or 4Fe2+ + 2OH- + O2 → 4Fe3+ + 3O2- + H2O. On the basis of the elastic and thermal parameters measured we have modeled the deformation contribution (Gdeform) to the Gibbs energy. The third-order Birch-Murnaghan model with V0 fixed at its experimental value and the model with refined V0 do not significantly differ from one another in terms of Gdeform. A comparison based on Gdeform between biotite and phlogopite shows a better compliance to P of the former, though balanced in mineral reactions by a difference of molar volume, i.e., V0(biotite) > V0(phlogopite).

High-pressure structural evolution and equation of state of analbite

Abstract The volume and unit-cell parameters of analbite (i.e., NaAlSi3O8 with complete Al,Si disorder) have been determined by single-crystal X-ray diffraction to a maximum pressure of ~8.71 GPa. The volume variation with pressure is described by a fourth-order Birch-Murnaghan equation of state with K0T = 50.3(5) GPa, K0′ = 8.9(5), and K0″ = -2.4(3) GPa-1. The value of the room-pressure bulk modulus is ~4% lower than that of low albite, and the onset of volume softening in analbite is at ~6.7 GPa, some 1.7 GPa higher than the onset in albite. The anisotropy of compression of analbite is less than that in albite. Single-crystal structure determinations of analbite to ~9.4 GPa show that there is no significant detectable compression of the T-O bonds within the structure, and the compression of the framework of tetrahedra is therefore accommodated by changes in the T-O-T angles, which result in significant compression of the “crankshaft chains” within the framework. No significant shear of the tetrahedral rings of analbite was detected, in contrast to the structural compression of albite. Overall, the structural changes that occur in analbite from 0.0001 to 9.4 GPa resemble those seen in ordered albite over the pressure range 0.0001-4 GPa. Therefore analbite shows a significantly greater structural rigidity than low albite up to pressures of 9.4 GPa

Correlation between crystallization pressure and structural parameters of phengites

Abstract Linear correlations of lnP vs. the thickness, t, of the TOT mica module and vs. the ditrigonal distortion, α, have been established by analyzing a population of 43 natural phengites for which estimates of the crystallization pressure P independent of the Si content are available. Synthetic phengites are not included because they behave as a separate population. The equations for the resultant regression lines are lnP = -0.35(3)α + 5.0(3) (R = 0.90, 26 observations) and lnP = -29(2)t + 293(22) (R = 0.90, 43 observations). These linear correlations are evidence of the links involving P, chemical composition, structural parameter c (i.e., t), and α. In turn, there is a linear correlation between t and α: t = 0.0110(9)α + 9.859(7) (R = 0.92, 26 observations). The linear correlations of lnP, t, and α vs. Si content have equations: lnP = 4.2(4)Si - 12(1) (R = 0.86, 43 observations), t = -0.13(1)Si + 10.37(4) (R = 0.87, 43 observations), and α = -12.7(9)Si + 50(3) (R = 0.94, 26 observations). The observed dispersion of the data are mainly due to the uncertainty in the pressures estimated from mineral assemblages. The possibility of calculating P from only a measurement of c neither overcomes this type of uncertainty nor pretends to be competitive with petrologic geobarometers, but is does open the possibility of estimating the crystallization pressure of nanoscale phengite relics (e.g., by transmission electron diffraction).

High-pressure equation of state and phase transition in PbAl2Si2O8 feldspar

Abstract In situ high-pressure X‑ray diffraction study was performed on synthetic lead feldspar with composition PbAl2Si2O8 (PbFsp). The crystals were synthesized from the melt and thermally treated at T = 1150 °C for 12 h and at T = 1000 °C for 70 h. At room condition the unit-cell parameters are a = 8.3936(4), b = 13.0498(7), c = 14.3258(8) Å, β = 115.281(6)°, V = 1418.9(1) Å3; space group: I2/c; Qod = 0.7. A single-crystal of lead feldspar was loaded in an ETH-type diamond-anvil cell and unit-cell parameters were measured at 26 different pressures up to 8.4 GPa at room T. The evolution with P of the unit-cell parameters and volume shows a strong discontinuity between 7.7 and 8.2 GPa indicating a first-order phase transition. The discontinuous character of the transition is especially noticeable in the behavior of the β angle, which decreases from 114.83° to 114.03°, and in the b parameter, which reduces from 12.746 to 12.567 Å. In the P range 0.0001-7.72 GPa, the trend shown by the axial compressibility (βa > βc > βb) is similar to that observed in the previous HP powder diffraction study, performed on lead feldspar using high-brilliance synchrotron radiation up to 7.1 GPa. In the P range 0.0001-4.27 GPa at room T, the P-V data of the I2/c lead feldspar were fitted with a second-order Birch-Murnaghan EoS. The parameters obtained are: V0 = 1422.2(1) Å3 and KT0 = 76.4(9) GPa. At P > 4.27 GPa, the volume values deflect from the BM2 curve and show a volume softening, precursor of the reported HP phase transition. A volume softening was recently observed in strontium feldspar (SrFsp) above 4.2 GPa. A second crystal of PbFsp was loaded in the DAC cell and in situ high-pressure X‑ray diffraction intensities were measured at P = 0.0001, 2.4, 3.1, 5.4, 6.0, 7.2, 8.4, and 9.7 GPa. The appearance of c and d-type reflections at 8.4 GPa, the analysis of the systematic absence and the structural refinements indicate the HP first-order transformation as an I2/c-P21/c phase transition. Structural results show that the main variations with compression in lead feldspar are in Pb-O bond lengths and in T-O-T bond angles, while T-O distances and O-T-O angles do not change meaningfully, indicating that the Si,Al tetrahedra behave with pressure as a rigid body. Changes observed in the compressional behavior of the structure between 3 and 5 GPa could explain the softening observed at P > 4 GPa in the volume compressibility. The results obtained in the present work allow comparing the pressures of the HP I2/c-P21/c phase transition occurring in lead feldspar with those observed in alkaline-earth feldspars.

The effect of type-B carbonate content on the elasticity of fluorapatite

The mechanical behavior of carbonate-bearing fluorapatite (CFAP) (with up to 5.5xa0wt% CO3) was investigated at high pressure up to 7 GPa. The incorporation of carbonate in CFAP samples was investigated by FTIR spectroscopy. The chemical formulae and cell parameters are Ca4.90Fe0.04 (PO4)2.87 (CO3)0.13 F1.23 and au2009=u20099.3527(1), cu2009=u20096.8752(1) Å, Vu2009=u2009520.83(1) Å3 for the FOW CFAP (Fowey Consols area, UK), and Ca4.97Sr0.03 (PO4)2.55 (CO3)0.45 F1.42 and au2009=u20099.3330(1), cu2009=u20096.8984(1) Å, Vu2009=u2009520.38(1) Å3 for the FRA CFAP (Framont region, France). Preliminary characterization at ambient conditions was done by single-crystal X-ray diffraction study. The structure refinements, in space group P63/m, confirm a type-B substitution of the phosphate (PO4)3− group by the carbonate ion (CO3)2−. The site occupancies for the C atom are 0.04 for FOW and 0.11 for FRA CFAP, in quite good agreement with the 1.6 and 5.5xa0wt% CO3 amount obtained by analytical methods. Single-crystal high-pressure XRD study on the two type-B CFAP samples was performed. The FOW and FRA crystals were mounted concurrently in a ETH-type DAC and cell parameters were determined at 26 different pressures up to 6.86 GPa at room T. The variation with pressure of the unit-cell parameters and volume shows no discontinuity that could be related to any possible phase transition in the P range investigated. The linear compressibility coefficients are βau2009=u20093.63u2009×u200910−3 GPa−1 and βcu2009=u20092.47u2009×u200910−3 GPa−1 for FOW, and βau2009=u20093.67u2009×u200910−3 GPa−1 and βcu2009=u20092.65u2009×u200910−3 GPa−1 for FRA, giving an axial anisotropy of βa:βcu2009=u20091.47:1 and 1.38:1, respectively. The P-V data were fitted by a second-order Birch–Murnaghan EoS and the resulting BM2-EoS coefficients are V0u2009=u2009519.81(7) Å3, KT0 = 92.1(3) GPa for FOW, and V0u2009=u2009518.95(9) Å3, KT0 = 89.1(4) GPa for FRA CFAP. The results obtained indicate that a 5.5xa0wt% CO3 content (type-B) reduces the isothermal bulk modulus by about 9%.

High-pressure structural configuration and phase transition in celsian, BaAl2Si2O8

In situ high-pressure X-ray diffraction study was performed on celsian (Cls97Or3) from Jakobsberg, Sweden. A single crystal of celsian was loaded in an ETH-type diamond anvil cell, and unit-cell parameters were measured at 20 different pressures up to 6.0xa0GPa at room T. The evolution of the unit-cell parameters and volume as a function of pressure shows a discontinuity at Pxa0~xa05.7xa0GPa indicating a displacive first-order phase transition. The P–V data were fitted by a second-order Birch–Murnaghan EoS only up to 2.55xa0GPa, because at higher pressures a slight change in the compressional behavior of the unit-cell volume is observed, indicating a pre-transition volume softening. The resulting EoS coefficients are V0xa0=xa01461.4(1)xa0Å3 and KT0xa0=xa088.1(6)xa0GPa. A second crystal of celsian was loaded in the DAC cell, and single-crystal in situ HP X-ray diffraction was performed at Pxa0=xa00.0001, 2.1, 4.2, 5.5, 5.9, 6.5 and 7.8xa0GPa. The data collections between 0 and 5.5xa0GPa show only a- and b-type reflections confirming the I2/c space group. The appearance of c and d-type reflections at 5.9, 6.5 and 7.8xa0GPa, the analysis of the systematic absence and the structural refinements define the HP phase transition as an I2/c–P21/c transition. The most significant changes with compression in celsian are the deformation in the Ba polyhedra and the variation in the T–O–T angles.