J. Phys. Earth, 27, 209-238, 1979 THE ELASTIC CONSTANTS OF Mn2SiO4, Fe2SiO4 AND Co2SiO4, AND THE ELASTIC PROPERTIES OF OLIVINE GROUP MINERALS AT HIGH TEMPERATURE Yoshio SUMINO Departmentof Earth Sciences,Nagoya University,Nagoya, Japan (ReceivedOctober 14,1978) Elastic constants of single-crystal Mn2SiO4, Fe2SiO4 and Co2SiO4 olivine are measured by the rectangular parallelepiped resonance (RPR) method at temperatures between 20° and 400℃. Elastic constants Cij (Mbar) and their temperature derivatives ∂Cij/∂T (kbar/deg) are: The isotropic properties, density ρ, adiabatic bulkmodulus K3, rigidity μ, the Poisson's ratio σ, and their temperature derivatives calculated by the Voigt-Reuss-Hill scheme are: By combining the present results with the previous data on a magnesium rich olivine, the effect of cation substitution on the elastic properties of oli- vine group minerals is discussed and the elastic constants of olivine at high temperature in the earth's mantle are clarified. 209 210 Y. SUMINO 1. Introduction The olivineis one of the major constituentsin the upper mantle of the earth,and an accuratedetermination of itselastic constants is of basicim- portancein the interpretationof structureof the upper mantle. In nature olivineoccurs mostly as the solidsolution of forsteriteMg2SiO4 and fayalite Fe2SiO4. The six-coordinatedcations (Mg and Fe) are substitutedby small amounts of Ca, Mn, Co, and Ni. The known end members of olivinesolid solutionare tephroiteMn2SiO4, Co-olivineCo2SiO4, and Ni-olivineNi2SiO4 in additionto forsteriteand fayalite. The elasticconstants of forsteriteMg2SiO4 have been determined with fairlygood accuracy by KUMAZAWA and ANDERSON (1969),GRAHAM and BARSCH (1969),and SUMINO et al.(1977) by usingsingle crystalline samples. The olivinespecimens for which a setof nine elasticconstants has been re- ported so far are naturalperidot (Fe/(Mg+Fe)=0.072-0.083) (VERMA, 1960; KUMAZAWA and ANDERSON, 1969;OHNO, 1976). On the other hand, a set of elasticconstants of singlecrystal fayalite Fe2SiO4has not yet been reported.The reportedelastic properties of fayalite are limitedto threedilatational wave velocitiesalong the a, b and c axes of imperfect fayalitecrystal (Furuhashi, see SUWA, 1964; MIZUTANI et al., 1970), the ultrasonicvelocities in polycrystallinesample (MIZUTANI et al., 1970; CHUNG, 1970, 1971;AKIMOTO, 1972;revised data of MIZUTANI et al., 1970),and thecompressibilities determined by a volumetrictechnique (ADAMS, 1931),and an X-ray diffractiontechnique (TAKAHASHI, 1970; YAGI et al., 1975). The elasticproperties of otherolivine type silicateminerals have never been reported. In thispaper, the elasticconstants of fayalite,tephroite Mn2SiO4, and Co-olivine Co2SiO4, Which are analogue of forsterite and fayalite, are deter- mined at temperatures between 20° and 400℃ by means of the RPR method (rectangular parallelepiped resonance method). By combining the present results with previous results of forsterite, the elastic parameters of olivine group minerals are summarized and the elasticity systematics relating to cation substitution is discussed. The temperature variation of seismic wave velocities of olivine at high temperature in the earth's mantle is investigated . 2. Specimens The singlecrystal specimens of Mn2SiO4,Fe2SiO4, and Co2SiO4olivine were provided as a loan from Prof. H. Takei of Tohoku University, who grew them for his own work (TAKEI, 1976, 1978). Severalpieces of single crystallineCo2SiO4 olivine were providedby Prof.S .Naka, Dr. H. Furuhashi, and Prof.T. Noda of Nagoya University(NAKA et al.,1968). The Elastic Constants of Mn2SiO4, Fe2SiO4 and Co2SiO4 Olivine 211 Mn2SiO4olivine Singlecrystal of Mn2SiO4was grown by the Czoch- ralski pulling technique, and the specimen for the present purpose was the same one as sample T-6 of TAKEI (1976) . The as-grown boule of this crystal was brownish dark under a room light. The polished thin section was clearly transparent to visible light and looked bluish gray. It does not contain any inclusion or any flaw (see the photograph of T-6 specimen in TAKEI, 1976). The boule was cut along {100} plane to yield a rectangular parallelepiped specimen (designated sample Mn2SiO4 (T)). The prescribed orientation were determined within 0.5° using a Laue back-reflection X-ray camera. The surface of the specimen was polished by abrasive powder #3,000. Fe2SiO4 olivine Single crystal of Fe2SiO4 was grown by the floating- zone method, and the specimen for the present purpose was sample number Fa-15 (TAKEI, 1978). Although the as-grown boule of this crystal was opaque under a room light, the polished thin section was clearly transparent (brown in transmitted light) to visible light. From an original boule, two rectangular parallelepiped specimens were prepared in the same way as Mn2SiO4 (des- ignated sample Fe2SiO4 (TA) and Fe2SiO4 (TB)). The sample Fe2SiO4 (TA) was perfect, but in the case of sample Fe2SiO4 (TB), a few minutes cracks (〓10-2mm) had developed at edge of specimen along (010) plane during the preparation. Co2SiO4 olivine Singlecrystal of Co2SiO4 obtainedfrom Takei (un- published)was grown by the floating-zonemethod. The as-grown boule of thiscrystal was opaque under a room light,and the polishedthin section was transparentto visiblelight. The colorof the thin sectionwas pale purple in transmittedlight. From the originalboule, a specimen was cut out and designatedCo2SiO4 (T). Singlecrystals of Co2SiO4 obtainedfrom NAKA et al.(1968) were grown by the Bridgman technique,and the specimen used for the presentpurpose was the sample E-I-3 describedin NAKA et al.(1968). From the original boule,a specimen was cut and designatedCo2SiO4 (F). The colorof the thin section,lattice constants, and refractiveindex of thiscrystal Co2SiO4 (F) are the same as those of Co2SiO4(T) as listedin Table 1. However, the bulk densityof Co2SiO4(F) was largerthan thatof Co2SiO4(T) and the X-ray den- sityof Co2SiO4 (F) by 0.9%, probably as a resultof deviationfrom Co2SiO4 stoichiometry.The singlecrystal Co2SiO4 (F) was directlygrown from the compositionwith an excessCoO (1.4mol%) to stoichiometricCo2SiO4 (NAKA et al.,1968). The presenceof a small amount of CoO phase in the single crystalCo2SiO4 (F) was recognizedby X-ray diffraction,and alsoit could be detectedby E.P.M.A. analysisas an inclusion(less than a few microns in length).When theCo2SiO4 (F) is regarded as themixture of CoO and Co2SiO4, the amount of CoO includedin Co2SiO4(F) iscalculated to be 2.3mol% from 212 Y. SUMINO Table 1. Basic descriptions of olivine Mn2SiO4, Fe2SiO4 and Co2SiO4. comparison of bulk densities. Table1 showsthe basic descriptions of the specimens; the three edge lengthsof the specimen,density, lattice constants ,mean atomicweight, molar volume, refractiveindex, and chemical composition. The bulk densityof each specimen is in good agreement with the X-ray densitywith the excep- tion of Co2SiO4(F). The measurements forelastic constants were carriedout on the fivespecimens described above . 3. Measurement and Results 3.1 Thermal expansion Thermalexpansivity data of the specimen are necessary forreducing the The Elastic Constants of Mn2SiO4, Fe2SiO4 and Co2SiO4 Olivine 213 temperature derivatives of elastic constants from measured temperature vari- ation of resonance frequencies. The coefficients of linear thermal expansion of Mn2SiO4 have been reported by OKAJIMA et al. (1978), and those of Fe2SiO4 by SUWA (1964), SUZUKI et al. (1977), and TAKEI (1978) by using a diatometric method. All the expansivity data of Fe2SiO4 are consistent within 17%. In the present data analysis of Mn2SiO4 and Fe2SiO4, the values reported by OKAJIMA et al. (1978) for Mn2SiO4 and those of SUZUKI et al. (1977) for Fe2SiO4 were employed, since the specimens measured by Okajima et al. and Suzuki et al. were the same ones as used in the present work. Although the linear thermal expansivity of Co2SiO4 has been determined by SATO (1970) at temperatures between 20° and 400℃ by using the X-ray diffractometer, the data are presumed to be not reliable. Since the volume expansivities of olivine group minerals are almost the same within 10% (SUZUKI, 1975; SUZUKI et al., 1977; OKAJIMA et al., 1978), the size correc- tions for temperature for the determination of the elastic constants of Co2SiO4 were made by using the thermal expansivity data of Mn2SiO4. It is noted that this procedure is justified because the thermal expansion affects the tem- perature derivatives of elastic constants only several percent (SUMINO et al., 1977). 3.2 Elastic constants The elastic constants were determined by an RPR method. The theory and the technical details of this method have been reported by OHNO (1976), SUMINO et al. (1976), and the details of measuring the temperature variation of elastic constants have been described in SUMINO et al. (1977). Measurement of resonance frequencies was made at temperatures between room temperature and 410℃ on the lower ca. 30 vibrational modes for each specimen as listed in Table 2 ((a), (b), and (c)). In this table, type nomen- clature of the modes follows those of OHNO (1976), and the observed values (Fobs)of resonance frequencies, the calculated most probable values (Fcal), and the normalized residuals [ΔF=(Fobs-Fcal)/Fobs] are presented. At high temperatures up to 410℃, the resonance frequencies were measured at ir- regular temperature intervals. Several examples of temperature variation of the resonance frequency are shown in Fig. 1 (A, B, C, and D) for each speci- men. As seen in Fig. 1, the resonance frequency data at high temperatures