PSI - Issue 5

Jesús Toribio et al. / Procedia Structural Integrity 5 (2017) 1291–1298 Toribio and Kharin / Structural Integrity Procedia 00 (2017) 000 – 000

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which have been argued relevant to the kinetics of HEAF (Hirth (1980), Lu et al. (1981), Pasco and Ficalora (1983)). The surface physics (see, e.g., Morris et al. (1984), Christmann (1988), Pisarev and Ogorodnikova (1997), Shanabarger (1985)) provides the rates of the involved individual moves in terms of forward and reversed atom number fluxes of the species between involved releaser sites Y and receptor sites Z ) { , , } ( ,        Y Z G per unit metal surface area, respectively q YZ and q ZY , as follows: ( i ) for physisorption from the gas and molecular desorption back into the gas H 2 ( G )  H 2 (  )         1 2 ( ) s p q G and     C q G G 2  , (5)

( ii ) for dissociative chemisorption and associative desorption, H 2 (  )  2H(  )   2 1 2         C q and           1 2 C q ,

(6)

( iii ) for the transitions from the chemisorption sites  to the subsurface interstitial sites A   and in reverse, H(  )  H( solute )   A A A q C        1 and          1 A A A q C (  A   ), (7) where   , C and C C l A A  are the atom number concentrations of hydrogen residing in indicated type sites per unit surface area (referring the last one to the surface layer, which representative thickness is associated with the diffuser jump length l in crystal),  Y = C Y / N Y ) (   Y are corresponding site occupancies, s is the sticking probability, and  YZ =  Y exp( –  E YZ ) are the frequencies of particle transitions, which try to leave the states Y with the intrinsic (vibration) frequency  Y and are able to attain the neighbour sites Z overcoming the potential barriers  E YZ = E YZ – G Y on the way from Y to Z along the potential relief for hydrogen in a system (Fig. 1), where the species free energies E YZ and G Y correspond, respectively, to the saddle point between the sites Y and Z and to the Y -site well. Having arrived to the subsurface interstitial positions in metal, hydrogen continues the journey to fracture sites by diffusion. The connections between concerned transport steps should be established basing on the partial conditions of mass conservation for the species staying in the sites of each type involved there. Generalised model of interstitial diffusion and trapping in solids in the presence of multiple trap types and an imposed force field has recently been built up by Toribio and Kharin (2015) as continuum implementation of the notions of the theory of thermally activated discrete random walking. Its key element is derivation of partial diffusion fluxes carried out by particle jumps A  B between specified types of interstitial diffuser releaser sites A and receptor sites B ( A , B   ), taking into account ( i ) the jump attempt frequencies of particles from A to B sites  AB =  A exp( –  E AB ), where  A specify the frequencies of particle vibrations in the A -type sites contributing to the jumps in definite direction, ( ii ) the particle jump success probabilities Y B =  B (1 –  B ), which combine the probabilities that a particle from A site hits a B -type one, which is defined by the fraction  B = N B / N of the B -type sites among the sites totality N =  B   N B , and that this site B is empty, 1 –  B , ( iii ) an imposed potential field U ( x ), e.g., due to stresses, which changes the energy barriers  E AB to overcome saddle points half a way d x from A to B additively by the value d U  x 2 1 . The net partial flux J AB of the species trough a control material surface by identical type jumps A  B departing from A -type and hitting B -type sites in forward and backward senses of the same cross-surface direction reads:   d Y C C Y Y C U B A AB B A A B AB         J , (8) 2.3. Diffusion