Refutation of “further rebuttal” by Aaronson and coworkers

Abstract

We are challenged in (1) to state what we consider to be the assumptions of the ACO model and why we think they are mutually incompatible and we now respond to this invitation. The original model, presented in a valuable paper [(18) of (1)], assumed plate morphology to be a growth phenomenon resulting from the formation of virtually immobile, partly coherent, planar interfaces. Growth parallel to the plane of the plate was considered to be rapid because the interfaces are disordered, and thickening was attributed to the migration of ledges, with disordered riser interfaces. The immobility of the terrace (habit plane) interface was attributed to its dislocation structure and the necessity for climb. Strain energy was considered not to influence the morphology. In a second important review paper [(13) of (1)] the rate of normal growth was stated to be restricted by structural considerations in the regions of forced coherence. Sessile dislocations were still postulated in the interface structure, but it was implied that the ledge model obviated in some way the necessity for them to climb as the plate thickened. The inconsistencies to which we have drawn attention are: 1. 1) Disordered riser interfaces cannot co-exist with partly coherent habit plane interfaces, and could not produce a shape change with an appreciable shear component. [The riser interfaces were later considered to be partly coherent, but as shown above and in more detail in (7) this would carry the implication that the average shape deformation is zero.] 2. 2) Immobility of the M atoms is not reconciable with an interface which includes large linear misfits in particular directions in its plane, or indeed with any interface containing sessile misfit dislocations. [Several attempts have been made by ACO to escape this dilemma. In AR1, it was dismissed under paragraph 9CE as making no sense. The problem was admitted in AR2 but glossed over by invoking mechanism (i) of HEA. When confronted with the implications of mechanism (i), they now write in (1) about “fully conservative mechanisms such as (ii) which permit transfer of misfit dislocations from terraces…” Mechanism (ii) in fact requires climb, as shown in Fig. 1. It is obvious that there is no way of avoiding this problem.] 3. 3) If there is a shape deformation, steps on a planar interface must be fully coherent. Superledges of this type would have impossibly high energies. 4. 4) It is implicit in our discussion that the role of strain energy cannot be ignored in any particle in which the stress free strains of a shape change are constrained by a surrounding matrix. Unless the particle is plate-shaped with a habit parallel to the invariant plane of the macroscopic shape deformation, its energy will be very large.