Thermodynamics and Modeling

Diffusion of aluminum in MgO: A thermodynamic approach study

“…[26]) is used to calculate the corresponding expansivity and elastic data (a, B, and Ω ) based on the equation of state (EOS) of MgO. [8,9,55] The frequency ν is estimated from Eq. ( 5) in terms of the experimental Debye temperature.…”

“…a [8] / Å B [55] /GPa Ω [9] / Å3 D exp [26] /m 2 Once c act is known, we can proceed to calculate the diffusion coefficient D calc from Eq. ( 3) using the approximate elastic and expansivity data listed in Table 1 for each temperature.…”

“…( 1), where β is the thermal (volume) expansion coefficient. For example, at T = 2273 K and P = 1 atm, by inserting c act = 0.3281, Ω = 10.026 × 10 −24 cm 3 , [9] β = 3.16 × 10 −5 K −1 , [55] B = 101.641 GPa, [55] and (dB/dT ) P = −0.023 GPa/K [14] into Eq. ( 5), we find h act = 2.91 eV.…”

“…[36] As a consequence, such anharmonic properties would introduce additional uncertainties into the present calculations, as our calculated results of T and P dependences of D calc , h act , and υ act in the framework of the cBΩ model do not consider anharmonicities which may be present. P/GPa a [8] / Å B [55] /GPa Ω [9] / Å3 D exp [21] /m 2 •s −1 D calc /m 2 •s −1 D theor [27] /m 1577-1768 K [26] 1873 K [26] 2273 K at 15 GPa [21] 2273 K at 25 GPa [21] theoretical results: Monte Carlo simulations [27] five frequency model [27] Lidiard's expression [56] 1 6 7 3 K…”