The importance of defining chemical potentials, substitution mechanisms and solubility in trace element diffusion studies: the case of Zr and Hf in olivine

Abstract

The diffusion, substitution mechanism and solubility limits of Zr and Hf in synthetic forsterite (Mg2SiO4) and San Carlos olivine (Mg0.9Fe0.1)2SiO4 have been investigated between 1,200 and 1,500 °C as a function of the chemical potentials of the components in the system MgO(FeO)–SiO2–ZrO2(HfO2). The effect of oxygen fugacity and crystallographic orientation were also investigated. The solubilities of Zr in forsterite are highest and diffusion fastest when the coexisting three-phase source assemblage includes ZrSiO4 (zircon) or HfSiO4 (hafnon), and lower and slower, respectively, when the source assemblage includes MgO (periclase). This indicates that Zr and Hf substitute on the octahedral sites in olivine, charge balanced by magnesium vacancies. Diffusion is anisotropic, with rates along the crystal axes increasing in the order a < b < c. The generalized diffusion relationship as a function of chemical activity (as \(a_{{{\text{SiO}}_{2} }}\)), orientation and temperature is: \(logD_{\text{Zr}} = \frac{1}{4}loga_{{{\text{SiO}}_{2} }} + logD_{0} - \left( {\frac{{368 \pm 17\;{\text{kJ}}\;{\text{mol}}^{ - 1} }}{{2.303\;{\text{RT}}}}} \right)\) where the values of log D 0 are −3.8(±0.5), −3.4(±0.5) and −3.1(±0.5) along the a, b and c axes, respectively. Most experiments were conducted in air (fO2 = 10−0.68 bars), but one at fO2 = 10−11.2 bars at 1,400 °C shows no resolvable effect of oxygen fugacity on Zr diffusion. Hf is slightly more soluble in olivine than Zr, but diffuses slightly slower. Diffusivities of Zr in experiments in San Carlos olivine at 1,400 °C, fO2 = 10−6.6 bars are similar to those in forsterite at the same conditions, showing that the controls on diffusivities are adequately captured by the simple system (nominally iron-free) experiments. Diffusivities are in good agreement with those measured by Spandler and O’Neill (Contrib Miner Petrol 159:791–818, 2010) in San Carlos olivine using silicate melt as the source at 1,300 °C, and fall within the range of most measurements of Fe–Mg inter-diffusion in olivine at this temperature. Forsterite–melt partitioning experiments in the CaO–MgO–Al2O3–SiO2–ZrO2/HfO2 show that the interface concentrations from the diffusion experiments represent true equilibrium solubilities. Another test of internal consistency is that the ratios of the interface concentrations between experiments buffered by Mg2SiO4 + Mg2Si2O6 + ZrSiO4 or Mg2SiO4 + ZrSiO4 + ZrO2 (high silica activity) to those buffered by Mg2SiO4 + MgO + ZrO2 (low silica activity) agree well with the ratios calculated from thermodynamic data. This study highlights the importance of buffering chemical potentials in diffusion experiments to provide constraints on the interface diffusant concentrations and hence validate the assumption of interface equilibrium.