Surface mass diffusion and step stiffness on an anisotropic surface; Mo(0 1 1) M. Ondrejcek * , W. Swiech, C.P. Flynn Department of Physics and Materials Research Laboratory, University of Illinois at Urbana-Champaign, 1110 W. Green Street, Urbana, IL 61801, USA Received 10 January 2006; accepted for publication 26 July 2006 Available online 17 August 2006 Abstract Results of step fluctuation experiments for Mo(0 1 1), using low-energy electron microscopy, are re-examined using recently developed procedures that offer accurate coefficients of surface mass diffusion. By these means, surface diffusion D s is documented at T/T m  0.5, while the crossover to relaxation driven by bulk vacancy diffusion is inferred for T/T m  0.6. Here, T m is the melting temperature T m = 2896 K. We obtain D s =4 · 10 4 exp(1.13 eV/k B T) cm 2 /s for the temperature interval 1080–1680 K. Possible indications of dif- fusion along step edges appear for T/T m  0.4. The same measurements of step fluctuation amplitudes determine also the step stiffness, which by symmetry is anisotropic on Mo(0 1 1). It is shown that three independent procedures yield mutually consistent step stiffness anisotropies. These are (1) step fluctuation amplitudes; (2) step relaxation rate anisotropies; and (3) the observed anisotropies of islands in equilibrium on the Mo(0 1 1) surface. The magnitude of the step stiffness obtained from step edge relaxation is consistent with earlier measurements that determine diffusion from grain boundary grooving. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Low-energy electron microscopy (LEEM); Molybdenum; Surface diffusion 1. Introduction Recent papers report a study of Mo using step fluctua- tion spectroscopy to determine the stiffness and free energy of step edges on the (0 1 1) surface [1,2]. They follow theo- retical and experimental description developed over the years and summarized in review publications [3–6]. New procedures have since been developed that make it possible to determine surface diffusion coefficients accurately from step fluctuation measurements [7,8]. It is therefore worth- while to revisit the Mo data in order to derive results for the surface mass diffusion coefficient D s in the range of tem- peratures examined. The present paper reports values of D s and updates stiffnesses ~ b for Mo(0 1 1) obtained by these means. A study of Mo(0 1 1) holds special interest because the samples were single crystal grown as epitaxial films by MBE on sapphire [9], and because the anisotropic surface of a bcc metal was investigated. Few earlier results for Mo have proved reliable. For surface diffusion, Allen [10] measured grain boundary grooving in polycrystals, and his results have been reinterpreted by Srinivasan [11] in an effort to derive both surface and bulk diffusion coeffi- cients (see below). Relaxation of sinusoidal grooves on atomically clean Mo (0 1 1) above 0.75T m (T m = 2896 K) yields unreasonably large values [12] for both the activation energy (2.99 eV) and the prefactor (400 cm 2 /s) for surface mass diffusion. Drechsler et al. [13] mention a change of diffusion mechanism at 0.65T m . No measurement of the hopping diffusion of Mo on Mo has been reported, but Rh on Mo(0 1 1) has activation energy 0.62 eV and D 0 = 10 3 cm 2 /s [14]. For bulk diffusion measured using radio tracers, the activation energies Q and prefactors D 0 determined from a narrow range of T are reported as 4.0 eV and 0.1 cm 2 /s, and for a wide range of T, 5.06 eV 0039-6028/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2006.07.035 * Corresponding author. Tel.: +1 217 333 9316; fax: +1 217 244 2278. E-mail address: ondrejce@uiuc.edu (M. Ondrejcek). www.elsevier.com/locate/susc Surface Science 600 (2006) 4673–4678