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[MIS14-07] Kinetics and surface dynamics of evaporation of a crystal
Keywords:evaporation, chemical kinetics, transition state theory, chemical evolution
Introduction: Evaporation is an important process to produce elemental and isotopic fractionation in early chemical evolution of planetary systems, and thus, evaporation rates of major minerals and melts of the early Solar System have been experimentally investigated. Conventionally, the experimental results have been described by the Hertz-Knudsen (HK) equation [e.g., 1-3], which is formulated as a general expression of evaporation rate using the equilibrium vapor pressure, temperature, the mass of evaporating molecule, and the evaporation coefficient defined as a ratio of a measured rate to the ideal rate. The HK equation is based on the detailed balance in equilibrium, and thus, it can be erroneous in non-equilibrium [4, 5]. In fact, evaporation behaviors of crystals cannot be explained simply by the HK equation. For example, the evaporation coefficients vary by orders of magnitudes among different substances and show dependence on temperature and crystal orientation [3, 6], and reaction orders do not necessarily accord with that arise from the equilibrium vapor pressure [7]. In this study, we propose a novel derivation of the absolute evaporation rate based on the transition state theory (TST) and apply it to a specific experimental system by combining with a model of crystal surface dynamics.
Methods and Results: We applied the TST to evaporation of crystals by regarding it as a chemical reaction, which is the same strategy adopted in [8] but for condensation. In the TST, the energy distribution of the reactant (the solid phase) and the transition state is assumed to be in accordance with the Maxwell-Boltzmann distribution even when the whole system is not in equilibrium. The evaporation rate was derived from this premise and compared to the HK equation, which yielded the explicit formulation of the evaporation coefficient consistent with previously derived condensation coefficient [8, 9]. We also derived the rate of congruent evaporation and found out that consistency of reaction orders with the HK equation depends on the ratio of the speciation of the transition state to the gas phase .
In order to apply the theory to a real case, we carried out experiments on evaporation of forsterite in the presence of gaseous H2 and H2O(Mg2SiO4→2Mg+SiO+3H2O), focusing on reaction orders of the coexisting gas. While the HK equation predicts that the rate is proportional to PH2/PH2O [10], our experiments suggested smaller dependence on PH2/PH2O, although it should be confirmed by further experiments.
Discussion: To evaluate the reaction orders of H2 and H2O, we constructed models of reaction mechanisms, in which the overall evaporation is expressed by a combination of elementary steps including dissociative adsorption, surface redox reactions [11], and elemental evaporation. When the TST-based elemental evaporation controls the overall rate, the reaction orders of H2 and H2O were expressed using the ratio of the speciation of the transition state to the gas phase in some of the models. In this case, the overall rate can be consistent with the HK equation when the ratio is unity. Previous and present experiments on forsterite evaporation may be explained in this framework, while further experimental and theoretical investigation of surface dynamics is necessary.
References: [1] Tsuchiyama A. et al. (1998) Min. J. 20, 113. [2] Tachibana S. and Tsuchiyama A. (1998) GCA 62, 2005. [3] Richter F. M. et al. (2007) GCA 71, 5544. [4] Marek and Strauß (2001) Int. J. Heat. Mass Trans. 44, 39. [5] Persad A. H. and Ward C. A. (2016) Chem. Rev. 116, 7727. [6] Takigawa A. et al. (2009) ApJ 707, L97. [7] Lew S. et al. (1992) Chem. Eng. Sci. 47, 1421. [8] Nagayama G. and Tsuruta T. (2003) J. Chem. Phys. 118, 1392. [9] Mortensen E. M. and Eyring H. (1960) J. Phys. Chem. 64, 846. [10] Tsuchiyama A. et al. (1999) GCA 63, 2451. [11] Souvi S. M. et al. (2013) Surf. Sci. 610, 7.
Methods and Results: We applied the TST to evaporation of crystals by regarding it as a chemical reaction, which is the same strategy adopted in [8] but for condensation. In the TST, the energy distribution of the reactant (the solid phase) and the transition state is assumed to be in accordance with the Maxwell-Boltzmann distribution even when the whole system is not in equilibrium. The evaporation rate was derived from this premise and compared to the HK equation, which yielded the explicit formulation of the evaporation coefficient consistent with previously derived condensation coefficient [8, 9]. We also derived the rate of congruent evaporation and found out that consistency of reaction orders with the HK equation depends on the ratio of the speciation of the transition state to the gas phase .
In order to apply the theory to a real case, we carried out experiments on evaporation of forsterite in the presence of gaseous H2 and H2O(Mg2SiO4→2Mg+SiO+3H2O), focusing on reaction orders of the coexisting gas. While the HK equation predicts that the rate is proportional to PH2/PH2O [10], our experiments suggested smaller dependence on PH2/PH2O, although it should be confirmed by further experiments.
Discussion: To evaluate the reaction orders of H2 and H2O, we constructed models of reaction mechanisms, in which the overall evaporation is expressed by a combination of elementary steps including dissociative adsorption, surface redox reactions [11], and elemental evaporation. When the TST-based elemental evaporation controls the overall rate, the reaction orders of H2 and H2O were expressed using the ratio of the speciation of the transition state to the gas phase in some of the models. In this case, the overall rate can be consistent with the HK equation when the ratio is unity. Previous and present experiments on forsterite evaporation may be explained in this framework, while further experimental and theoretical investigation of surface dynamics is necessary.
References: [1] Tsuchiyama A. et al. (1998) Min. J. 20, 113. [2] Tachibana S. and Tsuchiyama A. (1998) GCA 62, 2005. [3] Richter F. M. et al. (2007) GCA 71, 5544. [4] Marek and Strauß (2001) Int. J. Heat. Mass Trans. 44, 39. [5] Persad A. H. and Ward C. A. (2016) Chem. Rev. 116, 7727. [6] Takigawa A. et al. (2009) ApJ 707, L97. [7] Lew S. et al. (1992) Chem. Eng. Sci. 47, 1421. [8] Nagayama G. and Tsuruta T. (2003) J. Chem. Phys. 118, 1392. [9] Mortensen E. M. and Eyring H. (1960) J. Phys. Chem. 64, 846. [10] Tsuchiyama A. et al. (1999) GCA 63, 2451. [11] Souvi S. M. et al. (2013) Surf. Sci. 610, 7.