van Veenendaal E, de Theije FK, van Suchtelen J, van Enckevort WJP

Abstract:
Almost all {111} surfaces of natural diamond crystals show trigons: triangular etch pits centred on dislocations. The step
patterns that arise when two trigons meet allow us to propose an analytical expression for the velocity of steps during
etching as a function of their orientation. This step velocity function has a deep global minimum for <110> steps on a
surface inclined towards {110} and a local minimum for <110> steps on a surface inclined towards {100}. Continuum
simulations, based on the kinematic wave theory, of the evolution of step patterns using the step velocity function are
able to reproduce quite satisfactorily intricate step patterns formed by multiple interacting trigons. This means that the
assumption, implicit in the simulation, that bulk and surface diffusion are not rate limiting during etching is valid.
Occasionally, growth hillocks are observed on a {111} surface of a natural diamond. The step patterns on these
surfaces show that the step velocity function governing growth does not have the local minimum for <110> steps on a
surface inclined towards {100}. This confirms that the occasionally observed growth patterns and the usually observed
etching patterns are formed under fundamentally different conditions.