Stacking and twin faults in close-packed crystal structures: exact description of random faulting statistics for the full range of faulting probabilities

The classical model of independent random single deformation faults and twin faulting in face-centered-cubic and hexagonal close packing is revisited. The model is extended to account for the whole range of faulting probabilities. The faulting process resulting in the final stacking sequences is described by several equivalent computational models. The probability sequence tree is established. Random faulting is described as a finite-state automaton machine. An expression giving the percent of hexagonality from the faulting probabilities is derived. The average sizes of the cubic and hexagonal domains are given as a function of single deformation and twinning fault probabilities. An expression for the probability of finding a given sequence within the complete stacking arrangement is also derived. The probability P(0)(Delta) of finding two layers of the same type Delta layers apart is derived. It is shown that previous generalizations did not account for all terms in the final probability expressions. The different behaviors of the P(0)(Delta) functions are discussed.