Showing papers by "Donald J. Weidner published in 1984"

Single‐crystal elastic properties of the spinel phase of Mg2SiO4

Abstract: The single-crystal elastic moduli of the spinel (gamma) phase of Mg2SiO4 have been experimentally determined from Brillouin spectroscopy at ambient conditions. They are C11 = 327, C44 = 126, and C12 = 112 (GPa) yielding a bulk modulus of 184. and a shear modulus of 119 GPa. This value of bulk modulus is lower than expected from previous measurements. The elastic properties of the spinel and modified spinel (beta) phases of Mg2SiO4 are quite similar with the greatest differences related to the c axis of the beta which is relatively soft under compression. The polycrystal 1ine acoustic velocities differ by only 1% for these two phases. Thus there should be no seismic discontinuity associated with the beta to gamma phase transition in the mantle. The similarity of elastic properties of these two phases suggests that effects of pressure, temperature, and iron content on the elastic properties should be similar for both phases. Estimates of the effect of iron content are made from the extant data on fayalite spinel in conjunction with the data presented here. The derivatives of elastic moduli with respect to iron content are very similar to those observed for the olivine phase. Based on comparisons with aluminate analogue compositions in the spinel structure, there is no justification to predict the pressure or temperature derivatives of the elastic moduli of these high pressure phases at this time.

Single-Crystal Elastic Properties of the Modified Spinel (Beta) Phase of Magnesium Orthosilicate

Abstract: The single-crystal elastic moduli of the modified spinel structure (beta phase) of magnesium orthosilicate (Mg(2)SiO(4)) have been measured by Brillouin spectroscopy under ambient conditions. Single crystals with dimensions up to 500 micrometers were grown at 22 gigapascals and 2000 degrees C over a period of 1 hour. Growth of crystals larger than 100 micrometers was achieved only when the pressure was within 5 percent of the pressure of the phase boundary separating the beta- and gamma-phase stability fields. A comparison of the elastic properties of the modified spinel phase with those of the olivine phase suggests that the 400-kilometer seismic discontinuity in the earth's mantle can be described by a mantle with 40 percent olivine. These results confirm that the 400-kilometer discontinuity can be due to the transition from olivine to modified spinel. The amount of olivine that must be present is less than that in a pyrolite model, although the results do not exclude pyrolite as a possible mantle model.

Elasticity of single‐crystal orthoferrosilite

Abstract: The elastic moduli of a synthetic single crystal of pure FeSiO3, orthoferrosilite, have been measured at 1 bar and 20°C by Brillouin spectroscopy. The moduli are (in megabars) c11 = 1.98, c22 = 1.36, c33 = 1.75, c44 = 0.59, c55 = 0.58, c66 = 0.49, c12 = 0.84, c13 = 0.72, c23 = 0.55. A comparison of the pyroxene crystal structure with elasticity data shows that distortion of the tetrahedral chains parallel to c is related to c33 Straight or extended chains increase c33, and highly kinked chains weaken the structure. However, the ferrosilite data show that beyond a certain degree of distortion the tetrahedral chains are essentially passive. Previous models of pyroxene elasticity have indicated that c11 should be most sensitive to composition. This is supported by the current study and is reflected in the elasticity data via a positive linear correlation of c11 with the size of the M1 octahedron, as measured by the average M1-0 distance. The average longitudinal modulus c¯11 ((c11 + c22 + c33)/3) varies linearly with composition in the system orthoenstatite-orthoferrosilite, whereas the average shear moduli c¯¯44 and c¯¯12 are constant for Fe contents of at least 20%. By comparison, data for the solid solution forsterite-fayalite are consistent with a linear variation of modulus versus composition between the end-members for all three average moduli. We suggest that this difference between orthopyroxene and olivine is due to a strong preference of Fe2+ for the M2 octahedral site in pyroxene. The isotropic shear modulus μ is 30% lower for ferrosilite than enstatite. Despite a similar contrast in end-member values of μ, the olivine data are consistent with a linear variation of μ between Fo100 and Fa100. At high temperatures, Fe and Mg in orthopyroxene will be randomly distributed, and a linear variation of μ with molar content of Fe is expected. A comparison of laboratory elasticity data with observed mantle properties shows that Vp, Vs, and ρ of the upper mantle are satisfied by pure olivine. However, the data strongly suggest that without the coexistence of a garnet phase, no more than 10% orthopyroxene may be present in a model mantle assemblage. Ca-clinopyroxene increases the upper limit on mantle garnet content but does not greatly affect constraints on the quantity of orthopyroxene in the upper mantle.

Elasticity of the olivine and spinel polymorphs of Ni2SiO4

Abstract: The single-crystal elastic moduli, cij x, of the olivine (α) and spinel (γ) polymorphs of nickel orthosilicate have been measured at atmospheric pressure and 20° C by Brillouin spectroscopy. The results are (Mbar), Ni2SiO4 olivine: c11=3.40(2), c22=2.38(2), c33=2.53(2), c44=0.71(1), c55=0.87(1), c66=0.78(1), c12=1.09(2), c13=1.10(4), c23=1.13(3), Ni2SiO4 spinel: c11=3.66(3), c44=1.06(1), c12=1.55(3). In comparing these results with extant elasticity data for olivine- and spinel-type compounds we find distinctive elastic characteristics related to crystal structure, and systematic trends due only to compositional variation. For silicate olivines, the longitudinal moduli decrease in the order c11>c33>c22, regardless of composition. The moduli c55 and c66 are approximately equal, and greater than c44. The former relationship is related to differences in polyhedral linkages along the crystallographic axes, whereas the latter may result from rotational freedom of SiO4 tetrahedra in response to different directions of shear. Composition affects elasticity most directly through the relative magnitudes of \(\bar c_{12} > \; = (c_{12} + c_{13} + c_{23} )/3\) and \(\bar c_{44} = (c_{44} + c_{55} + c_{66} )/3\). When transition-metal cations are six-coordinated by oxygen \(\bar c_{12} > \bar c_{44}\), and when alkaline-earth cations are six-coordinated \(\bar c_{44} > \bar c_{12}\).

Method for measuring the refractive index of transparent solids

Abstract: A method for determining the refractive indices of transparent isotropic or anisotropic solids is presented. The method utilizes null position measurements of light deflected by a sample immersed in a liquid of known index. Measurements of absolute deflection angles are not involved. Natural crystal growth faces, even at right angles, can serve as prism faces, thus eliminating the need for extensive surface preparation. Consequently, this method is particularly well suited for measuring the refractive index of small samples with high indices. Using a simple refractometer, results were obtained for two biaxial and one isotropic material with high refractive indices: Ni2SiO4 with the spinel structure (maximum dimension of 0.12 mm), Ni2SiO4 (olivine structure), and GdAlO3 (perovskite structure). Uncertainties of less than 0.1% are obtained from visual observations of the refracted light. Increased accuracy is possible by improving the calibration of the immersion liquid refractive index and the detection system.