1 Diffusion

^[1]The fundamental kinetic equation for surface diffusion is given in eq 2. D={\nu}a^2(\frac{-E_{diff}}{k_BT}) where D = diffusion coefficient, \nu = jump frequency = k_BT/h = \sim6\times10^{12} s⁻¹ at 300 K, a = jump distance (\sim2\times10^{−8} cm for the activation step), and E_{diff} = diffusion activation energy.

^[2]The kinetic equation for surface diffusion is given by Ref.^[1], D=D_0exp(\frac{-E_m}{k_BT})={\nu}d^2exp(\frac{-E_m}{k_BT}) where D is the diffusion coefficient, D_0 is the diffusion prefactor, n is the attempt frequency, d is the jump distance, and E_m is diffusion barrier. Assume that the motion of Ca atom around its equilibrium position is harmonic, the attempt frequency n can be estimated by a parabolic fit the curve of total energy as a function of Ca near the equilibrium position along the diffusion path using Eq. (2). with k is the force constant and m the mass of Ca. E=\frac{1}{2}kr^2 \nu=\frac{1}{2\pi}\sqrt{k/m} The calculated attempt frequency and the diffusion prefactor are 1.64 THz and 1.37\times10 ^{-3} cm²/s, respectively. The estimated diffusioncoefficient for Ca on the novel boron sheet at 300 K is 1.2\times10^{-10} cm²/s.

2 Stability

^[2]The stability of the hydrogen adsorbed structures is judged by the relative energy, which are defined by formula (5) and (6) for CaB₈(H₂)_n and Ca₂B₈(H₂)₁₂, respectively, of the adsorbed system with respected to the separated species: E_r=E_{CaB_8(H_2)_n}-E_{CaB_8}-n(E_{H_2}+\mu_{H_2}(T,P)) Where E_{CaB_8(H_2)_n}, E_{CaB_8} and (E_{H_2} are still the DFT energy for CaB_8(H_2)_n , CaB_8 and H_2 molecule, respectively. \mu_{H_2}(T,P) is chemical potential of hydrogen molecule at given pressure and temperature. The \mu_{H_2}(T,P) can be calculated by the formula \mu_{H_2}(T,P)=\Delta{H}-T\Delta{S}+k_BTln(\frac{P}{P^0}) where P^0 = 1 bar=0.1 mPa, k_B is Boltzmann constant, (\Delta{H}-T\Delta{S}) is the changing of chemical potential due to changing the temper- ature from T=0 K to target temperature T at constant pres- sure P^0 . \Delta{H }is the changing in the enthalpy and T\Delta{S} is entropy factor. For calculation values of (\Delta{H}-T\Delta{S}) the thermochemical tables[50] were used.