Thermoelastic properties of magnesiowüstite, (Mg1−xFex)O: determination of the Anderson–Grüneisen parameter by time-of-flight neutron powder diffraction at simultaneous high pressures and temperatures

The ability to perform neutron diffraction studies at simultaneous high pressures and high temperatures is a relatively recent development. The suitability of this technique for determiningP–V–Tequations of state has been investigated by measuring the lattice parameters of Mg1−xFexO (x= 0.2, 0.3, 0.4), in the rangeP < 10.3 GPa and 300 <T< 986 K, by time-of-flight neutron powder diffraction. Pressures were determined using metallic Fe as a marker and temperatures were measured by neutron absorption resonance radiography. Within the resolution of the experiment, no evidence was found for any change in the temperature derivative of the isothermal incompressibility, ∂KT/∂T, with composition. By assuming that the equation-of-state parameters either varied linearly or were invariant with composition, the 60 measured state points were fitted simultaneously to aP–V–T–xequation of state, leading to values of ∂KT/∂T= −0.024 (9) GPa K−1and of the isothermal Anderson–Grüneisen parameter δT= 4.0 (16) at 300 K. Two designs of simultaneous high-P/Tcell were employed during this study. It appears that, by virtue of its extended pressure range, a design using toroidal gaskets is more suitable for equation-of-state studies than is the system described by Le Godec, Dove, Francis, Kohn, Marshall, Pawley, Price, Redfern, Rhodes, Ross, Schofield, Schooneveld, Syfosse, Tucker & Welch [Mineral. Mag.(2001),65, 737–748].

Download Full-text

Determination of the Cation Distribution in NiFe2(PO4)2 using Resonant X-ray and Neutron Powder Diffraction

Journal of Applied Crystallography ◽

10.1107/s0021889894012628 ◽

1995 ◽

Vol 28 (5) ◽

pp. 494-502 ◽

Cited By ~ 5

Author(s):

J. K. Warner ◽

A. K. Cheetham ◽

D. E. Cox

Keyword(s):

Powder Diffraction ◽

National Laboratory ◽

Time Of Flight ◽

Brookhaven National Laboratory ◽

Neutron Powder Diffraction ◽

Anomalous Scattering ◽

Edge Structure ◽

X Ray ◽

Scattering Correction

The distribution of divalent iron and nickel over two metal sites of differing coordination geometry in NiFe2(PO4)2, sarcopside, has been investigated by resonant X-ray and time-of-flight neutron powder diffraction. To assess the reproducibility of the X-ray technique, data have been collected from instruments X7A at Brookhaven National Laboratory and 8.3 at the Synchrotron Radiation Source, Daresbury Laboratory, England, using wavelengths λ X1 = 1.7437 (3) Å and λ X2 = 1.7434 (1) Å, respectively, close to the Fe2+ K edge determined by X-ray absorption near-edge structure. The real part of the anomalous-scattering correction for iron at each energy, f′(Fe) X1 = −7.81 (9) and f′(Fe) X2 = −10.16 (6), was determined experimentally by diffraction from Fe3(PO4)2 under identical conditions. Occupancies obtained for iron at the M(1) site were found to be M(1) X1 = 0.366 (6) and M(1) X2 = 0.376 (3), compared with M(1) N = 0.26 (15) from time-of-flight neutron powder diffraction.

Download Full-text

Pressure dependence of the Grüneisen parameter and melting temperature of some metals

International Journal of Modern Physics B ◽

10.1142/s0217979221502556 ◽

2021 ◽

pp. 2150255

Author(s):

K. Sunil ◽

D. Ashwini ◽

Vijay S. Sharma

Keyword(s):

Experimental Data ◽

Molecular Dynamics ◽

Equation Of State ◽

Pressure Dependence ◽

High Pressures ◽

Grüneisen Parameter ◽

Thermal Equation ◽

Gruneisen Parameter ◽

Melting Temperatures ◽

Volume Dependence

We have used a method for determining volume dependence of the Grüneisen parameter in the Lindemann law to study the pressure dependence of melting temperatures in case of 10 metals viz. Cu, Mg, Pb, Al, In, Cd, Zn, Au, Ag and Mn. The reciprocal gamma relationship has been used to estimate the values of Grüneisen parameters at different volumes. The results for melting temperatures of metals at high pressures obtained in this study using the Lindemann law of melting are compared with the available experimental data and also with the values calculated from the instability model based on a thermal equation of state. The analytical model used in this study is much simpler than the accurate DFT calculations and molecular dynamics.

Download Full-text

Constraints on the Equations of State of stiff anisotropic minerals: rutile, and the implications for rutile elastic barometry

Mineralogical Magazine ◽

10.1180/mgm.2019.24 ◽

2019 ◽

Vol 83 (03) ◽

pp. 339-347 ◽

Cited By ~ 5

Author(s):

Gabriele Zaffiro ◽

Ross J. Angel ◽

Matteo Alvaro

Keyword(s):

Equation Of State ◽

Equations Of State ◽

Harmonic Approximation ◽

Unit Cell ◽

Elastic Behaviour ◽

Published Data ◽

Grüneisen Parameter ◽

Unit Cell Parameters ◽

Gruneisen Parameter ◽

Cell Parameters

AbstractWe present an assessment of the thermo-elastic behaviour of rutile based on X-ray diffraction data and direct elastic measurements available in the literature. The data confirms that the quasi-harmonic approximation is not valid for rutile because rutile exhibits substantial anisotropic thermal pressure, meaning that the unit-cell parameters change significantly along isochors. Simultaneous fitting of both the diffraction and elasticity data yields parameters of KTR0= 205.14(15) GPa, KSR0= 207.30(14) GPa, $K_{TR0}^{\prime} $= 6.9(4) in a 3rd-order Birch-Murnaghan Equation of State for compression, αV0= 2.526(16) × 10–5 K–1, Einstein temperature θE = 328(12) K, Anderson-Grüneisen parameter δT = 7.6(6), with a fixed thermal Grüneisen parameter γ = 1.4 to describe the thermal expansion and variation of bulk modulus with temperature at room pressure. This Equation of State fits all of the available data up to 7.3 GPa at room temperature, and up to 1100 K at room pressure within its uncertainties. We also present a series of formulations and a simple protocol to obtain thermodynamically consistent Equations of State for the volume and the unit-cell parameters for stiff materials, such as rutile. In combination with published data for garnets, the Equation of State for rutile indicates that rutile inclusions trapped inside garnets in metamorphic rocks should exhibit negative residual pressures when measured at room conditions.

Download Full-text

Comments on the paper entitled “Pressure variation of melting temperatures of alkali halides”

International Journal of Modern Physics B ◽

10.1142/s0217979219750018 ◽

2019 ◽

Vol 33 (17) ◽

pp. 1975001 ◽

Cited By ~ 1

Author(s):

A. Vijay

Keyword(s):

Bulk Modulus ◽

High Pressures ◽

Equations Of State ◽

Alkali Halides ◽

Pressure Variation ◽

Grüneisen Parameter ◽

Gruneisen Parameter ◽

Melting Temperatures ◽

Melting Curves

The expressions for the pressure dependences of bulk modulus and the Grüneisen parameter used by Arafin and Singh [Int. J. Mod. Phys. B 30, 1750031 (2016)] in the Lindemann law for determining melting curves of 14 alkali halides have been found to yield no results which are consistent with the recent studies on equations of state. It is demonstrated here that Arafin–Singh’s expressions are physically not acceptable as they are shown here to give unrealistic values of bulk modulus and Grüneisen parameter for the materials at high pressures.

Download Full-text

TheP–V–Tequation of state of D2O ice VI determined by neutron powder diffraction in the range 0

Journal of Applied Crystallography ◽

10.1107/s0021889812014847 ◽

2012 ◽

Vol 45 (3) ◽

pp. 523-534 ◽

Cited By ~ 25

Author(s):

A. D. Fortes ◽

I. G. Wood ◽

M. G. Tucker ◽

W. G. Marshall

Keyword(s):

Equation Of State ◽

Bulk Modulus ◽

Powder Diffraction ◽

Equations Of State ◽

Brillouin Scattering ◽

Personal Communication ◽

Neutron Powder Diffraction ◽

Unit Cell ◽

Cell Parameters ◽

Neutron Powder Diffraction Data

Neutron powder diffraction data have been collected from deuterated ice VI (space groupP42/nmc,Z= 10) at 76 state points in its field of thermodynamic stability above 150 K (approximately 0.6 <P< 2.1 GPa) and in a region of metastable persistence below 150 K (0 <P< 2.6 GPa). The refined unit-cell parameters and unit-cell volume have been fitted with six-parameter functions based upon a Murnaghan equation of state (EoS), with simple polynomial expressions to describe the temperature dependence of the volume (or axis length) and the bulk modulus (or axial incompressibility). ThisP–V–TEoS is compared with earlier empirically derived and computationally obtained equations of state, and with the elastic properties determined by ultrasonic or Brillouin scattering methods. It is found that D2O ice VI is ∼5% stiffer (i.e.it has a larger bulk modulus,K, at a givenPandT) than H2O ice VI, in agreement with unpublishedcij/ρ data for D2O ice VI provided by the Shimizu Laboratory, Gifu University, Japan (S. Sasaki, personal communication). This difference is due entirely to a greater incompressibility parallel to theaaxis than for the protonated isotopologue; the incompressibilities of thecaxis for both H2O and D2O ice VI are very similar. TheP–V–TEoS is used to estimate the volume change and enthalpy of melting. Additional data on the isothermal compression of ices II and V at 240 K (0.2–0.4 and 0.4–0.7 GPa, respectively), and of ice VII at 295–300 K (2–7 GPa), are also reported and compared with earlier literature data.

Download Full-text

Thermoelastic properties and crystal structure of CaPtO3post-perovskite from 0 to 9 GPa and from 2 to 973 K

Journal of Applied Crystallography ◽

10.1107/s0021889811023582 ◽

2011 ◽

Vol 44 (5) ◽

pp. 999-1016 ◽

Cited By ~ 7

Author(s):

Alex Lindsay-Scott ◽

Ian G. Wood ◽

David P. Dobson ◽

Lidunka Vočadlo ◽

John P. Brodholt ◽

...

Keyword(s):

Crystal Structure ◽

High Pressure ◽

Equation Of State ◽

Powder Diffraction ◽

Ambient Pressure ◽

Full Range ◽

Unit Cell ◽

Similar Amount ◽

Grüneisen Parameter ◽

Gruneisen Parameter

ABX3post-perovskite (PPV) phases that are stable (or strongly metastable) at ambient pressure are important as analogues of PPV-MgSiO3, a deep-Earth phase stable only at very high pressure. The thermoelastic and structural properties of orthorhombic PPV-structured CaPtO3have been determined to 9.27 GPa at ambient temperature and from 2 to 973 K at ambient pressure by time-of-flight neutron powder diffraction. The equation-of-state from this high-pressure study is consistent with that found by Lindsay-Scott, Wood, Dobson, Vočadlo, Brodholt, Crichton, Hanfland & Taniguchi [(2010).Phys. Earth Planet. Inter.182, 113–118] using X-ray powder diffraction to 40 GPa. However, the neutron data have also enabled the determination of the crystal structure. Thebaxis is the most compressible and thecaxis the least, with theaandcaxes shortening under pressure by a similar amount. Above 300 K, the volumetric coefficient of thermal expansion, α(T), of CaPtO3can be represented by α(T) =a0+a1(T), witha0= 2.37 (3) × 10−5 K−1anda1= 5.1 (5) × 10−9 K−2. Over the full range of temperature investigated, the unit-cell volume of CaPtO3can be described by a second-order Grüneisen approximation to the zero-pressure equation of state, with the internal energy calculatedviaa Debye model and parameters θD(Debye temperature) = 615 (8) K,V0(unit-cell colume at 0 K) = 227.186 (3) Å3,K′0(first derivative with respect to pressure of the isothermal incompressibilityK0) = 7.9 (8) and (V0K0/γ′) = 3.16 (3) × 10−17 J, where γ′ is a Grüneisen parameter. Combining the present measurements with heat-capacity data gives a thermodynamic Grüneisen parameter γ = 1.16 (1) at 291 K. PPV-CaPtO3, PPV-MgSiO3and PPV-CaIrO3have the same axial incompressibility sequence, κc > κa > κb. However, when heated, CaPtO3shows axial expansion in the form αc > αb > αa, a sequence which is not simply the inverse of the axial incompressibilities. In this respect, CaPtO3differs from both MgSiO3(where the sequence αb > αa > αcis the same as 1/κi) and CaIrO3(where αb > αc > αa). Thus, PPV-CaPtO3and PPV-CaIrO3are better analogues for PPV-MgSiO3in compression than on heating. The behaviour of the unit-cell axes of all three compounds was analysed using a model based on nearest-neighbourB—XandA—Xdistances and angles specifying the geometry and orientation of theBX6octahedra. Under pressure, all contract mainly by reduction in theB—XandA—Xdistances. On heating, MgSiO3expands (at high pressure) mainly by lengthening of the Si—O and Mg—O bonds. In contrast, the expansion of CaPtO3(and possibly also CaIrO3), at atmospheric pressure, arises more from changes in angles than from increased bond distances.

Download Full-text

ChemInform Abstract: Determination of the Cationic Arrangement in Sn2F6 from Neutron Powder Diffraction.

ChemInform ◽

10.1002/chin.199121008 ◽

2010 ◽

Vol 22 (21) ◽

pp. no-no

Author(s):

N. RUCHAUD ◽

C. MIRAMBET ◽

L. FOURNES ◽

J. GRANNEC ◽

J. L. SOUBEYROUX

Keyword(s):

Powder Diffraction ◽

Neutron Powder Diffraction

Download Full-text

Isothermal equation of state and high-pressure phase transitions of synthetic meridianiite (MgSO4·11D2O) determined by neutron powder diffraction and quasielastic neutron spectroscopy

Acta Crystallographica Section B Structural Science Crystal Engineering and Materials ◽

10.1107/s2052520616018254 ◽

2017 ◽

Vol 73 (1) ◽

pp. 33-46 ◽

Cited By ~ 8

Author(s):

A. Dominic Fortes ◽

Felix Fernandez-Alonso ◽

Matthew Tucker ◽

Ian G. Wood

Keyword(s):

High Pressure ◽

Phase Transitions ◽

Equation Of State ◽

Powder Diffraction ◽

Diffraction Data ◽

Neutron Powder Diffraction ◽

Bulk Liquid ◽

Icy Satellites ◽

Neutron Spallation Source ◽

Quasielastic Neutron

We have collected neutron powder diffraction data from MgSO4·11D2O (the deuterated analogue of meridianiite), a highly hydrated sulfate salt that is thought to be a candidate rock-forming mineral in some icy satellites of the outer solar system. Our measurements, made using the PEARL/HiPr and OSIRIS instruments at the ISIS neutron spallation source, covered the range 0.1 < P < 800 MPa and 150 < T < 280 K. The refined unit-cell volumes as a function of P and T are parameterized in the form of a Murnaghan integrated linear equation of state having a zero-pressure volume V 0 = 706.23 (8) Å3, zero-pressure bulk modulus K 0 = 19.9 (4) GPa and its first pressure derivative, K′ = 9 (1). The structure's compressibility is highly anisotropic, as expected, with the three principal directions of the unit-strain tensor having compressibilities of 9.6 × 10−3, 3.4 × 10−2 and 3.4 × 10−3 GPa−1, the most compressible direction being perpendicular to the long axis of a discrete hexadecameric water cluster, (D2O)16. At high pressure we observed two different phase transitions. First, warming of MgSO4·11D2O at 545 MPa resulted in a change in the diffraction pattern at 275 K consistent with partial (peritectic) melting; quasielastic neutron spectra collected simultaneously evince the onset of the reorientational motion of D2O molecules with characteristic time-scales of 20–30 ps, longer than those found in bulk liquid water at the same temperature and commensurate with the lifetime of solvent-separated ion pairs in aqueous MgSO4. Second, at ∼ 0.9 GPa, 240 K, MgSO4·11D2O decomposed into high-pressure water ice phase VI and MgSO4·9D2O, a recently discovered phase that has hitherto only been formed at ambient pressure by quenching small droplets of MgSO4(aq) in liquid nitrogen. The fate of the high-pressure enneahydrate on further compression and warming is not clear from the neutron diffraction data, but its occurrence indicates that it may also be a rock-forming mineral in the deep mantles of large icy satellites.

Download Full-text