Eur. J. Mineral. 2006, 18, 449-462 The thermoelasticproperties of MgSOa.TD1O(epsomite) from powder neutron diffraction and ub initio calculation ANonEw D. FORTESI*,IeN G. WOODT, Mnnrn ALFREDSSONT, Lrorrnra VOeRnLOt and KBvrN S. KNIGHT2,3 lResearchSchool of Geological and GeophysicalSciences, University College London, Gower Street, London, WCIE 68l United Kingdom zISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OXl l OQX, United Kingdom 3Natural Historv Museum. Cromwell Road London. SW7 5BD. United Kinsdom Abstract: time-of-flight powder neutron diffraction has beenused to measurethe molar volume of MgSOa.TD2O(i) from L8 - 300 K at ambientpressure, (ii) from 50 -290Kat1.4,3.0, and 4.5 kbar,(iii) from 0 - 5.5 kbar at 290K, and (iv) from 0 - 4.5 kbar at 50 K. The data have allowed us to determinethe temperaturedependence of the incompressibility,(aK/aDr, (thermody- namically equivalentto the pressuredependence of the thermal expansion,(Dc/DP)1) of epsomitethroughout its stabilify field. We observedthat the a-axis exhibits negativethermal expansion,cto, from 30 - 250 K at room pressure,turning positive above250 K and being zero below 30 K. However,each of the crystallographicaxes exhibits a sharpchange in (dcr/DT)at -125 K, and this appearsto correspondto significant changesin the axial incompressibilitieswith the a- and c-axessoftening, and the b-axis stiff- eningconsiderably below -125 K. Our thermoelasticresults are in agreementwith ab initio calculationsat zero Kelvin; howeverthe calculationsoffer no obvious insight into the mechanismresponsible for the changein behaviourat low temperature. Key-words: epsomite,neutron diffraction, high-pressure,incompressibility, thermal expansion. l.Introduction icy moons, Europa, Ganymede,and Callisto and these spectra have been interpreted as showing deposits of Epsomite, MgSOa.7H2O, is a widespread evaporite hydratedalkali salts(McCord et a1.,2001;Dalton et al., mineral on Earth (seeHardie, 1984),being the stablephase 2005;Orlando et a\.,2005). in contact with a saturated solution at temperatures from If we are to incorporateepsomite as a major rock- 275 - 320 K (Fig. l); it may also be abundant in the forming mineral in geophysicalmodels of icy-moon inte- Martian regolith (e.g.,Feldman et a1.,2004: Zolotov et al., riors we must know its bulk physical properties under 2004). In addition, epsomite is known to occur as an conditionsfar removedfrom room pressureand tempera- aqueous alteration product in chondritic meteorites ture; the icy Galileanmoons have surface temperatures of (Frederiksson& Kerridge, 1988) and is therefore thought - 90 K andcore-mantle pressures may be - 1.5GPa. likely to be presentin many rocky asteroids.The presence We thereforereview briefly the literature relating to of saltssuch as MgSOa,Na2SOa, and Na2CO3in chondritic epsomiteat high pressureand low temperature;an exten- meteorites led to the suggestion that the water-rich icy sive review of earlier literature is presentedelsewhere moons of the Gas Giant planets would have ice mantles (Fortes,2005). dominated by multiply-hydrated salts, including epsomite, The structureof epsomitewas solvedby Baur (1964) resulting from leaching by aqueous fluids during accretion and subsequentlystudied by Ferrariset al. (1973), using and differentiation (Kargel, 1991), with implications for neutrons,and Calleri et al. (1984)using X-rays.The space the geophysics and astrobiology of these objects groupis P2221 with Z : 4 andcell parameters q : | 1.866 (Hogenboom et al., 1995;,Kargel et al., 2000; Spaun & A, b : 11.998 A, c :6.855 A at 295K. The structure(Fig. Head, 2001; McKinnon, 2002; McKinnon & Zolensky, 2) consistsof SOoz-tetrahedra and Mg(H2O)e2*octahedra 2003). This suggestion has been supported by observa- linked togetherby orderedhydrogen bonds. The seventh tional evidence from the Near Infrared Mapping water moleculeis not coordinatedto the magnesium,but Spectrometer(NIMS) instrument aboard the Galileo space- occupiesa 'void'in the structure. craft, which orbited Jupiter from 1995 to 2003. NIMS The earliest high-pressurework was carried out by collected multispectral images of the surfacesof Jupiter's Bridgman (1948a,b)upon polycrystallineand single *E-mail'[email protected] 093s -r22r I 06t0018-0449 s 6.30 DOI: I 0. I 127I 0935 -1221120061 0018-0449 O 2006 E. Schweizerbart'scheVerlagsbuchhandlung. D-701 76 Stuttgart 450 A. D. Fortes,I. G. Wood, M. Alfrcdsson,L. Vodadlo,K. S. Knight E .'""roo L a rvcight7u MgSOl Fig. l. Temperature compositionphase diagram for the binary systemH2O MgSOa at atmosphericpressure showing the solid phases in equilibrium with aqueoussolutions of magnesiumsulfate ('MS solution').The markedphases are, H2O ice lh, MS l2 - MgSOa.l2H2O (Fritzsche'ssalt); MS7 - MgSOa.TH2O(epsomite); MS6 - MgSO4.6H2O(hexahydrite); MSI - MgSOa.H2O(kieserite). crystal epsomite at pressuresup to 4 GPa in a piston- sition may correspondto Bridgmans' first phase change, cylinder apparatus.Bridgman observed a sluggish phase and the IV *> V transition to one of Bridgmans' 2.5 GPa transitionbetween 1.0 1.5GPa, and suggestedtwo further phase changes.Livshits et al. (1963) also reported weak sluggish transitionsat - 2.5 GPa. evidence for breaks in their pressure volume curves at - The piston compression method was subsequently 0.2 GPaand at 0.7 - 0.8 GPa. employed by Livshits et al. (1963) in work on crystalline More recently,a number of groups have studiedmelting hydrates of magnesium sulfate. These authors claimed to relations in the H2O - MgSOa system (Hogenboom er a/., have observed the following series of phase transitions; 1995,to 0.4 GPa; Grassetet al.,200l4b, to -2 GP1' I ++ II (- 0.45 GPa);II t- III (- 1.2GPa); III *+ IV (- 1.6 Nakamura,2003, to - 5 GPa) and in more complex ternary GPa); and IV ++ V (- 2.5 GPa). Of these,the II ++ III tran- systems considered applicable to Europa's subsurface ocean and icy crust; e.g., H2O - MgSOa - H2SO4 (Hogenboom et a1.,2007). Of these studies, Grassetet al. (2001a,b) noted by visual observation,a probable phase soo transition in epsomiteat 0.6 GPa. tetrahedron The only measurementsat low temperaturerelate to the heat capacity.The isobaric heat capacity, Cp, of epsomite was measuredfrom 15 - 300 K (Cox et al., 1955) in order to correct the measured heat capacity of hexahydrite (MgSOa.6H2O).However, the Cp values for the heptahy- drate were not published an4 to our knowledge, are lost. Hence,there only remainsthe measuredvalue of Cp for the heptahydratein the range31 I 321 K (Kopp, 1865,pl56) and four values, determined by Differential Scanning Calorimetry,at 223, 263, 273, and 298 K (Prieto & Kargel, 2001). Clearly, there is not complete agreementbetween the preceding high-pressure experiments, and considerable doubt remains as to the polymorphic phase behaviour of epsomite under pressure. Essentially nothing is known about the structure and behaviour of epsomite at low t*"temperarures. Our goals in this work are thereforeas follows; To establishthe structure of epsomite at low tempera- Fig. 2. Polyhedralrepresentation of the epsomitecrystal structure ture (i.e.. close to absolutezero). viewed along the c-axis. Thcrmoelastic properties of epsomite 451 To determinethe coeflicientof volume thermalexpan- Section 3, and discussour interpretation of the results in sion, cry,throughout the stabilityfield of the low-pressure Section4. phase. To measurethe incompressibility,Ke, and its tempera- ture dependence,dK/dT, fbr epsomite. 2. Method To constrainthe pressurestability field of the ambient- pressurephase of epsomite. 2.1 Computational method The principal method of choice for achievingmost of these goals is neutron drftiaction. Neutrons are necessary The plane-wave pseudopotential method based on to determine the location of hydrogen atoms in the crystal density functional theory (Hohenberg& Kohn, 1964; Kohn structure, although in practicc deuteratedanalogues must & Sham, 1965),was usedfor calculatingthe total energyof be used to avoid the large incoherent scattering of the crystal lattice.The Perdew-Wanggeneralised gradient hydrogen, which contributes to the background of the corrected functional (PW9l, Perdeq 199l; Perdew & diffraction pattern (e.g., Finney, 1995). It is worth Wang, 1992) was applied to representthe exchange-corre- observing that the only neutron diffraction experiment to lation potential, this form of the generalised gradient date (Ferraris et al., 1973) was done with hydrogenous approximation (GGA) having been demonstratedto yield epsomite.This is the first time that a neutron scattering the most accurate results in hydrogen-bonded systems experimenthas been carried out using a deuteratedsample. (Tsuzuki & Liithi, 2001; Langlet et al.,2004) despitenot We have therefore carried out three experimentalruns correctly representingdispersion forces. Core electronsare on the High Resolution Powder Diflractometer (HRPD) replacedby ultrasoft non-normconservingpseudopoten- (lbberson et al., 1992) at the ISIS facility, Rutherford tials (Vanderbilt,1990), themselves fbrmulated within the Appleton Laboratory,U.K. HRPD is ideally suited to rapid GGA. Total energy calculationswere perfbrmed using the and accuratedetermination of cell parametersby virtue of VASP (ViennaAb initio Simulation Package)code (Kresse its essentiallyconstant resolution (Ldld - 10-+ in the & Furthmiiller,1996). Convergence tests were carriedout backscatteringdetectors) across all d-spacings.Moreover, to optimise the fi-point sampling of the Brillouin zone the instrument