Theoretical Simulation Of Helium Diffusion In Crystals Of SiO₂ And CaCO₃

The study of material transport and energy transfer in minerals is the basis of understanding the evolution of geodynamics.Therefore,the quantitative study of material transport properties in minerals has become one of the important research fields in solid earth science.Helium is an important trace element involved in Earth evolution,the migration characteristics of He in deep Earth are significant for studying the thermal and chemical properties of the Earth.However,the transport behaviors of helium in the deep crust and mantle are still unclear due to the scarcity of measured diffusion parameters of helium gas in minerals under mantle conditions.Traditional experimental methods face many difficulties in the study of the diffusion properties of inert gases in minerals.The main difficulty is that the present experimental conditions are difficult to reach the high temperature and high pressure conditions in the deep crust and mantle environments.In addition,the collection and preparation of mineral samples are also restricted by many experimental conditions.For example,the sample inevitably contains a certain amount of impurity elements,crystal defects,fractures,fluid inclusions,etc.,all of which have some influence on the diffusion rate of gas in minerals,thus limiting the applicability of the measured diffusion parameters.With the rapid development of theoretical simulation technology and computing power greatly improved,atomic simulation and computational chemistry based on quantum mechanics plays an important role in earth science.Especially in the field of high temperature and high pressure technology,atomic theory simulation has gradually become an indispensable means of mutual promotion and verification with experimental research due to its unique advantages.In this paper,we report helium diffusion mechanism in crystals of quartz,coesite,calcite and aragonite based on the first-principles study.The diffusion paths,activation barriers(Ea),and frequency factors(v)of helium under ambient and high pressure conditions were calculated based on Density Functional Theory(DFT)and climbing image nudged elastic band(CI-NEB)method.The main research results include the following two aspects:(1)Calculated diffusive coefficients of quartz in different orientations are:D[100] = 1.24 × 10-6 exp(-26.83 k J / mol / RT)m2 /sD[010] = 1.11 × 10-6 exp(-31.60 k J / mol / RT)m2 /s and of coesite:D[100] = 3.00 × 10-7 exp(-33.79 k J / mol / RT)m2 /sD[001] = 2.21 × 10-6 exp(-18.33 k J / mol / RT)m2 /sThe calculated results indicate that diffusivity of helium is anisotropic in both quartz and coesite.The calculations of helium diffusion in coesite under high pressures up to 12 GPa indicated that activation energies increased with pressure but the diffusion coefficients decreased with the pressure.Our calculations show that helium will not be largely retained in silica under typical Earth surface conditions,consistent with previous studies.The closure temperature of 10-6 to 10-2 m coesite crystal varies from 88 K to 142 K in the direction [100] and 46 K to 74 K in the direction [001].The closure temperature is lower in the directions [100] in quartz and in the direction [001] in coesite.(2)Calculated diffusive coefficients of calcite of different orientations are:D[010]([100])= 5.46×10-7 exp(-67.64 k J/m/ RT)m2 /sD[001] = 4.65×10-7 exp(-97.36 k J/mol/ RT)m2 /s and of aragonite:D[100] = 9.64×10-7 exp(-82.40 k J/mol/ RT)m2/sD[001] = 1.06×10-6 exp(-96.00 k J/mol/ RT)m2/sCalculations show marked anisotropy of helium diffusion in calcite,with more energetically favorable directions along a(b)axis,but slowest along c axis.The calculations of helium diffusion in aragonite under high pressures up to 14 GPa indicated that activation energies increased with pressure but the diffusion coefficients decreased with the pressure.The closure temperature of 0.2 mm to 2 mm grain size of calcite crystal varies from-54 ℃ to-25 ℃ in the direction [010] and 40 ℃ to 82 ℃ in the direction [001],and for aragonite varies from-12 ℃ to 23 ℃ in the direction[100] and 30 ℃ to 69 ℃ in the direction [001].