Crucial role of surface in stability and mobility of vacancy clusters in metals

Ab initio electronic structure calculations are employed to study the stability and mobility of vacancy clusters at or below the Cu(111) surface. The monovacancy formation energy decreases on going from bulk to surface. The strong binding of a nearest-neighbor (NN) surface divacancy and the negligible binding of a NN divacancy, consisting of a surface and subsurface vacancy, demonstrate the strong (weak) intraplane (interplane) attractive interaction between vacancies. Similarly, NN surface trivacancies exhibit a wide range of layer-dependent binding behavior. The underlying mechanism is the different elastic contribution (atomic relaxation) of each layer, giving rise to a preferential two-dimensional clustering of vacancies on the surface. The results reveal a migration mechanism for a NN surface divacancy involving a two-step counterclockwise and clockwise rotation of the center of mass. The migration paths of the NN surface trivacancy include purely translation, rotation, and mixed translation-rotation mechanisms with different energy barriers.