Contrib Mineral Petrol (2010) 159:175–186 DOI 10.1007/s00410-009-0422-5 ORIGINAL PAPER Ca–Mg diffusion in diopside: tracer and chemical inter-diffusion coefficients Xiaoyu Zhang Æ Jibamitra Ganguly Æ Motoo Ito Received: 20 March 2009 / Accepted: 8 July 2009 / Published online: 2 August 2009 Ó Springer-Verlag 2009 Abstract We have experimentally determined the tracer chemical diffusion coefficient of Ca and Mg must take into diffusion coefficients (D*) of 44Ca and 26Mg in a natural account the effect of thermodynamic factor (TF) on dif- diopside (*Di96) as function of crystallographic direction fusion coefficient. We calculate the dependence of the TF and temperature in the range of 950–1,150 °C at 1 bar and and the chemical interdiffusion coefficient, D(Ca–Mg), on f(O2) corresponding to those of the WI buffer. The exper- composition in the diopside–clinoenstatite mixture, using imental data parallel to the a*, b, and c crystallographic the available data on mixing property in this binary system. directions show significant diffusion anisotropy in the a–c Our D*(Ca) values parallel to the c axis are about 1–1.5 log and b–c planes, with the fastest diffusion being parallel units larger than those Dimanov et al. (1996). Incorporating to the c axis. With the exception of logD*(26Mg) parallel the effect of TF, the D(Ca–Mg) values calculated from our to the a* axis, the experimental data conform to the data at 1,100–1,200 °Cis*0.6–0.7 log unit greater than empirical diffusion ‘‘compensation relation’’, converging the experimental quasibinary D((Ca–Mg ? Fe)) data of to logD * -19.3 m2/s and T * 1,155 °C. Our data do not Fujino et al. (1990) at 1 bar, and *0.6 log unit smaller show any change of diffusion mechanism within the tem- than that of Brady and McCallister (1983) at 25 kb, 1,150 perature range of the experiments. Assuming that D* varies °C, if our data are normalized to 25 kb using activation roughly linearly as a function of angle with respect to the c volume (*4 and *6cm3/mol for Mg and Ca diffusion, axis in the a–c plane, at least within a limited domain of respectively) calculated from theoretical considerations. *20° from the c-axis, our data do not suggest any sig- nificant difference between D*(//c) and D*(\(001)), the Keywords Diffusion Á Thermodynamic factor Á latter being the diffusion data required to model composi- Diopside Á Eucrites Á Cooling rates tional zoning in the (001) augite exsolution lamellae in natural clinopyroxenes. Since the thermodynamic mixing property of Ca and Mg is highly nonideal, calculation of Introduction Clinopyroxenes in both slowly cooled terrestrial and Communicated by T.L. Grove. planetary samples often show compositional zoning of X. Zhang Á J. Ganguly (&) major divalent cations and exsolution lamellae (e.g. Department of Geosciences, University of Arizona, McCallum and O’Brien 1996; Schwartz and McCallum Tucson, AZ 95721, USA 2005). These features can be modeled to constrain the e-mail: [email protected] cooling histories of the host rocks, if the appropriate dif- M. Ito fusion kinetic parameters of the divalent cations are known. ARES, NASA Johnson Space Center, The relatively coarse exsolution lamellae, in which com- Houston, TX 77058, USA positional zoning could be measured, are typically parallel to (001) so that the diffusion direction during the growth of M. Ito Lunar and Planetary Institute, 3600 Bay Area Boulevard, the lamellae is normal to the (001) direction, or at an angle Houston, TX 77058, USA of 16–18° to the c-axis. In addition, the coarsening of the 123 176 Contrib Mineral Petrol (2010) 159:175–186 exsolution lamellae can also be modeled using the theory effect on the diffusion process. However, so far no data of Brady (1987) and the available data on lamellar coars- have been available for D*(Mg) in clinopyroxene. The ening kinetics (McCallister 1978; Nord and McCallister primary purpose of this work is the determination of 1979; Nord and Gordon 1980) to provide complementary D*(Ca) and D*(Mg) in natural diopside crystals as func- constraints on the cooling rates of the host rocks. Several tions of crystallographic orientation and temperature, and workers, thus, have carried out experimental studies over to use these data and thermodynamic mixing properties of approximately the past three decades to determine the Ca and Mg to calculate the binary chemical interdiffusion diffusion parameters of the divalent cations in diopside. coefficient. Brady and McCallister (1983) determined the quasibi- nary chemical interdiffusion coefficient of Ca and (Mg ? Fe) at 25 kb, 1,150–1,250 °C from kinetic experi- Experimental and analytical methods ments involving homogenization of fine scale (001) coherent pigeonite exsolution lamellae in a sub-calcic Sample preparation diopside megacryst from Mabuki kimberlite, Tanzania. (As discussed later, a chemical interdiffusion coefficient rep- Chips of a gem quality natural diopside crystal, *Di96, were resents a product of a weighted average of tracer diffusion oriented in a 4-circle X-ray diffractometer and cut normal to coefficients and a thermodynamic factor.) They presented a*, b and c axial directions. Complete microprobe analysis their data as ‘‘average’’ (chemical) inter-diffusion coeffi- of the crystal yields a formula Ca0.96Na0.02Mg0.96Fe0.05 cient, DðÞCaÀMg (which, in fact is DCaðÞðMg þ Fe) ; at Mn0.01Al0.04Si1.97O6, and shows the crystal to be effectively the annealing temperatures since the inter-diffusion coef- homogeneous. The cut surfaces were ground and were ficient must have varied as a function of composition polished down to 0.25 lm diamond powder and finally during homogenization as a result of the strong deviation finished to a mirror polish by a combination of mechanical from thermodynamic ideality of mixing of the Ca and Mg and chemical polishing using silica suspension on OP-chem components (e.g. Lindsley et al. 1981), as discussed later. cloth from Struers. The last step was intended to remove a Fujino et al. (1990) determined DCaðÞðMg þ Fe) ; from very thin disturbed layer that usually develops very close to modeling the compositional profiles, as determined by a crystal surface by the abrasive action of mechanical pol- analytical transmission electron microscopy (ATEM) in ishing. The polished wafers were pre-annealed for 1–2 days (001) pigeonite exsolution lamellae and augite host in a at or close to the conditions of the diffusion experiments in natural crystal that was annealed to promote coarsening of order to equilibrate the point defects to a condition that is the the lamellae at several temperatures between 1,000 and same as or close to the experimental condition, and also to 1,200 °C at 1 bar pressure and controlled f(O2) conditions. anneal the surface defects that might have been generated by Dimanov et al. (1996) determined tracer diffusion coeffi- the polishing process. cient of Ca, using natural crystal, whereas Azough and The source materials for Ca and Mg tracer diffusion Freer (2000) determined that of Fe2? using both natural experiments were 44Ca enriched CaO and 26Mg rich MgO, ´ and synthetic (Fe-free) crystals. Preliminary experimental respectively. A thin layer (*200–250 A˚ ) of a source data for Ca and Mg tracer diffusion coefficients in natural material was deposited on the polished surface of a diopside were also presented from our group (Stimpfl et al. pre-annealed crystal by thermal evaporation under high- 2003) and were used by Schwartz and McCallum (2005)to vacuum condition. Initially, we tried to use 44Ca enriched 44 model the compositional zoning in (001) exsolution finely powdered CaCO3 as a source material for Ca, but lamellae of augite in pigeonite host in unequilibrated eu- the powder kept on flying off the tungsten filament upon crites. Miyamoto and Takeda (1994) and Miyamoto (1997) which it was deposited for thermal evaporation by resistive used the quasi-binary Ca–(Mg ? Fe) inter-diffusion data heating. The problem was solved by decarbonation and of Fujino et al. (1990) to estimate the cooling rate (and grain coarsening in a furnace prior to deposition on the from that the burial depth) of an eucrite on the basis of the tungsten filament. compositional zoning in (001) exsolved lamellae in clinopyroxene. Tracer diffusion experiments Availability of the tracer diffusion coefficients of the diffusing species, D*(i), as function of crystallographic All experiments were carried out in a computer controlled orientation, along with their thermodynamic mixing prop- vertical gas-mixing furnace. The oxygen fugacity was erties, permits flexibility in the modeling of compositional controlled by a flowing mixture of CO and CO2 and cross zoning as function of diffusion direction and composition. checked by a zirconia sensor. The furnace was pre-condi- There are now adequate data (e.g. Lindsley et al. 1981; tioned to the desired temperature and f(O2) condition of an Ganguly and Saxena 1987) to evaluate thermodynamic experiment keeping the ends of the vertical ceramic tube 123 Contrib Mineral Petrol (2010) 159:175–186 177 closed. The sample with a thin layer of diffusing material 0 500 1000 1500 2000 2500 was quickly inserted from the top to the hot spot of the 1500 furnace, and the ends of the ceramic tube were completely Mg diffusion in Diopside o sealed immediately thereafter. In order to minimize gas (1100 C, 48 hours, fO2 =WI) consumption, the gas mixture was forced to recirculate into 1000 the furnace and was vented out periodically through a 30 Si pressure release valve. After the end of an experiment, the sample was quenched quickly by pulling it out of the fur- 500 42 nace and cooling in air.