Statistical Thermodynamics as a Tool for Evaluating Atom Clustering around Interstitial Atom

Hydrogen absorption in epitaxial bcc V (001) thin films analysed by statistical thermodynamics

“…(2), values of Q and R ln f H , were evaluated [6][7][8][9][10][13][14][15][16]. However, for the epitaxial bcc VH x (001) thin films constrained over non-H absorbing MgO substrate, such simplifying statistical model developed for bulk specimen was demonstrated to be not straightforwardly applicable.…”

“…The determination of θ was made with an a priori assumption that the interaction energy E(H-H) between the nearest neighbour H atoms would hold constant within the same phase at a given T and the subsequent statistical thermodynamic analyses for a variety of non-stoichiometric interstitial MX x systems (X = H, C, N, P or S but not O) were undertaken with this simplifying a priori assumption and the derived values for the interaction parameters E(i − j) between neighbouring constituents i and j in the MX x lattice appeared to be rational [6][7][8][9][10][13][14][15][16]. Thus, the employed a priori assumption for the series of statistical thermodynamic analyses was judged to be valid on the basis of the self-consistency of the evaluation results acquired by this simplifying postulate although there was no first-principle-based justification to validate this a priori assumption.…”

“…However, as consistently practiced in the earlier statistical thermodynamic analyses for extensive range of non-stoichiometric interstitial solutions [6][7][8][9][10][13][14][15][16], change of E(X-X) within a given crystalline phase under consideration is appreciated as representing inadequate modelling and linear A vs. x isotherm must be derived when realistic choice of θ is made. Accepting this criterion, H absorptions in the range x b 0.75 and that in the range x N 0.75 were decided to be analysed separately considering that the mode of H distribution in the epitaxial bcc V (001) thin film changed at around x = 0.75.…”

“…Derived K vs. T data are plotted in Fig. 5 which yield the least-mean-squares relationships with considerable extent of deviation from linearity unlike in the case with the epitaxial bcc VH x (001) film in the range of x b 0.75 as reviewed above in the text or for other general cases of analysis for interstitial elements in bulk specimens [6][7][8][9][10][13][14][15][16] …”

“…In another H distribution model, H atoms up to composition x = 0.75 are assumed to Table 1 in Ref. [15] as a function of T with 100 K interval. The validity range of this expression is for T between 300 K and 1500 K. b Expression for K(VH x ) for the bulk VH x was presented earlier [7,9] as KðVHxÞ = 223:604−0:0647TðkJ mol −1 Þ but it was with a trivial calculation mistake (correct value of T = 562.9 K was erroneously input as T = 569.9 K in the earlier least-mean-squares calculation over T range between 827 K and 518.6 K using the P-T-C data reported by Veleckis and Edwards [5]).…”