In order to understand more clearly the behaviour at depth within the Earth's upper mantle of the (Mg,Fe)Si03 ortho- and clinopyroxenes, it is important to determine both the responses of the structures of these pyroxenes to non-ambient conditions, as well as their equations of state (ie. the volume variation with pressure and/or temperature). Although these Ca“'*'-poor pyroxenes transform to higher density garnet structures at depths in excess of 400 km (Casparik, 1989), there are several polymorphic phase transitions which occur at the lower pressures and temperatures characteristic of the pyroxene stability field (see Chapters 5 and 7), which may be responsible, at least in part, for other seismic discontinuities present at shallower depths. Such transitions include the orthopyroxene to high-pressure ciinopyroxene phase transition (which is described for the FeSiOg system in Chapter 5), which may contribute to the Lehmann discontinuity at depths of —200km in sub-continental mantle. The high-pressure ciinopyroxene phase produced as a result of this transformation is non-quenchable, reverting to the lower symmetry (P2/c ) ciinopyroxene phase upon pressure release. Thus all experiments on the high-pressure ciinopyroxene phase (and other such non-quenchable phases), and also experiments to determine the effect of pressure on the pyroxene structure, must be performed in situ. The diamond-anvil cell (DAC; see Chapter 2 for details) is an ideal tool for investigating such non-quenchable high-pressure phases, since it may be designed to be suitable for X-ray diffraction experiments at pressures of up to ~ 12 GPa, thus enabling the measurement to a high degree of precision of the structural and volume variations with pressure.
Other experimental techniques regularly used for determining the compressibilities and EOS's of pyroxenes and other minerals include Ultrasonics and Brillouin spectroscopy. The ultrasonic technique involves the measurement of transit times of ultrasonic waves between parallel faces of the crystal (held at a constant temperature and pressure) using a pulse superimposition method. Although ultrasonic measurements have been performed for more than 25 years, Webb and Jackson (1993) have recently determined a reliable method for measuring the travel times of ultrasonic waves through crystals, and their experimental details will be outlined briefly below.
Transducers of a given size are bonded to the single crystals and travel-time measurements are made for waves of the fundamental frequency propagating through the crystals. In order to measure the actual travel-time through the crystal alone, the relative contributions from the propagation and reflection phase shifts may be determined by comparative one- and two-transducer experiments (see Jackson et al.,
1981). The elastic moduli of the crystal were then calculated from the twelve modes of propagation using Cook's algorithm for crystals of orthorhombic symmetry (see Webb, 1989).
Brillouin spectroscopy involves the interaction between electromagnetic waves and vibration modes of the crystal due to acoustic phonons. The sample is generally (eg, Bass and Weidner, 1984; Kandelin and Weidner, 1988a, 1988b; etc.) immersed in a fluid of similar refractive index to the sample, in order to reduce both refraction and the intensity of elastically scattered light at the crystal surface. Light from an Ar- ion laser is focused onto the sample, and analysed at 90° to the incident direction, the crystal orientation within the Brillouin spectrometer having been determined to within ~ 0.5° by back-scattering of the laser light from the crystal faces. A small portion of this scattered light is Doppler-shifted due to the interaction with thermally generated phonons in the sample - this is the Brillouin-scattered component of the spectrum. The magnitude of the frequency shift gives the acoustic velocity for each orientation of the crystal. Compressional and shear modes are separated by controlling the polarisation of the incident and scattered light; elastic constants (Cy ) may then be calculated from the wave velocities in particular crystallographic directions.
Finally, it is important to note that while X-ray diffraction experiments measure the isothermal bulk modulus (K^), both ultrasonics and Brillouin spectroscopy measure the adiabatic bulk modulus (Kg) of the material. This isothermal bulk modulus is determined at constant temperature, whereas the adiabatic bulk modulus is measured at a constant heat content (ie., with no heat exchange with the surroundings), and therefore generally results in an increase in temperature.
The conversion factor between these two bulk moduli is given below:
Ks = ( l + a y T ) Kj. (1.1)
where a represents the volume thermal expansion coefficient of the material, and y is its Grüneisen parameter, defined as:
Y = (1.2)
P C,, pCp
Thus the magnitude of K j is always somewhat less than that of Kg. Due to inconsistencies in the published data for both OL and y for Ca^^-poor pyroxenes, the difference in magnitude of Kg and K j is assumed to be of the order of — 1 % throughout this work. Table 1.3 illustrates this problem, giving a range of published values of OL and y for Mg^^-rich orthopyroxenes.
Author(s) a (K ') Y CCyT (298K)
Frisillo, A.L. and Barsch, G.R. (1972) 47.0 X 10^ 1.56 0.02
Dietrich, P. and Arndt, J. (1982) 20 .8 X 10^ 0.84 0.005
Skinner, B.J. (1966) 24 X 10
Saxena, S.K. and Eriksson, (1983) 24.1 X 10-"
Saxena, S.K. (1988) 12.7 X 10-"
Yang, H. and Ghose, S. (1993) 23 X 10-" 0 .8 8 0.006
Table 1«5: Comparison of some of the published values of the volume thermal expansion coefficient, OL, and the Grüneisen parameter, y, at 298K for Mg^^-rich orthopyroxenes.
1.4 ORGANISATION OF THE THESIS
This thesis reports the results of a series of compression experiments on poor and Ca-^-free ortho- and clino-pyroxenes along or near the enstatite - ferrosilite join, using high-pressure single-crystal X-ray diffraction techniques. In Chapter 2, details of the methods of synthesis of the pyroxene samples, the design and operation of the diamond anvil cells used to generate pressure on the samples, details of the X- ray diffraction experiments and data reduction are described. Chapter 2 also presents the results of characterisation of all the pyroxene crystals used in this study using Transmission Electron Microscopy. Structural data collected from three synthetic (Mg,Fe)Si03 orthopyroxene samples and a natural orthopyroxene of approximate mantle composition allow identification of the compression mechanisms operating in these structures at pressure; they are described in detail in Chapter 3. Unit cell data collected from all the orthopyroxene samples at pressure intervals of — 0.4 GPa were used to determine their EOS’s which are presented in Chapter 4; the observed values of both the isothermal bulk modulus (K^t) and its pressure derivative. Kg’, are also compared with the available published data for orthopyroxenes of similar compositions using different experimental techniques.
Since phase transitions between pyroxene phases of different symmetries are probably responsible, at least in part, for some of the seismic discontinuities within the Earth’s upper mantle, experiments demonstrating that both the low-clinoferrosilite (space group P2/c) and orthoferrosilite phases of FeSiO^ transform to a previously unidentified C2/c phase at high-pressures are presented in Chapter 5. The crystal chemistry of this newly characterised high-pressure C2/c clinoferrosilite is discussed in Chapter 6, and, with the assistance of other data from the available literature, this crystal chemistry is then extended to include all clinopyroxenes along the (Mg,Fe)SiOg join. The structures of the high-pressure C2/c (Mg,Fe)Si03 clinopyroxenes are demonstrated to be distinct from those of either high-temperature or Ca“‘^-containing clinopyroxenes. Chapter 6 finally describes the compressional behaviour of the high- pressure C2/c clinoferrosilite structure and its EOS.
The history of the determination of the pyroxene phase diagrams across the MgSiOg - FeSiOg join since 1906 is reviewed in Chapter 7, in which all the compressibility data of these Ca-^-poor pyroxenes is also consolidated into phase diagrams. From these data, and from the slopes of the equilibrium phase boundaries, estimates of AH, and AV of the transformations between the low-clino, ortho- and high-pressure ciinopyroxene polymorphs of end-member compositions are calculated. A short summary of the conclusions reached during these experiments is given in Chapter 8 with a few suggestions for future work in the field.