Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-26T10:27:11.265Z Has data issue: false hasContentIssue false

Formation Energy, Stress, and Relaxations of Low-Index Rhodium Surfaces

Published online by Cambridge University Press:  10 February 2011

Alessio Filippetti
Affiliation:
INFM – Dipartimento di Scienze Fisiche, Universita di Cagliari, I-09124 Cagliari, Italy
Vincenzo Fiorentini
Affiliation:
INFM – Dipartimento di Scienze Fisiche, Universita di Cagliari, I-09124 Cagliari, Italy
Kurt Stokbro
Affiliation:
(also at Mikroelektronik Centret, Danmarks Tekniske Universitet, Lyngby, Denmark)
Riccardo Valente
Affiliation:
INFM and Scuola Internazionale Superiore di Studi Avanzati, I-34014 Trieste, Italy
Stefano Baroni
Affiliation:
INFM and Scuola Internazionale Superiore di Studi Avanzati, I-34014 Trieste, Italy
Get access

Abstract

Ab initio local-density- functional- theory calculations of formation energies, surface stress, and multilayer relaxations are reported for the (111), (100), and (110) surfaces of Rh. The study is performed using ultrasoft pseudopotentials and plane waves in a parallel implementation.

Type
Research Article
Copyright
Copyright © Materials Research Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Feibelman, P. J., Phys. Rev. B 51, 17867 (1995).Google Scholar
2. Zangwill, A., Physics at surfaces (Cambridge University Press, 1988).Google Scholar
3. Several accurate ab initio LDA calculations of diffusion barriers and paths on Al surfaces exist: see Feibelman, P. J., Phys. Rev. Lett. 65 729 (1990), and R. Stumpf and M. Scheffier, 72, 254 (1994).Google Scholar
4. Stokbro, K. and Baroni, S., to be published.Google Scholar
5. Kellog, G., Phys. Rev. Lett. 72, 1662 (1994).Google Scholar
6. Dreizler, R. and Gross, E. K. U., Density functional theory (Springer, Berlin, 1990). The exchange-correlation energy by D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980) is used in the parametrization of J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).Google Scholar
7. Vanderbilt, D., Phys. Rev. 41, 7892 (1990).Google Scholar
8. Valente, R. and Baroni, S., to be published.Google Scholar
9. Stokbro, K., to appear in Phys. Rev. B.Google Scholar
10. Methfessel, M. and Paxton, A. P., Phys. Rev. B 40, 3616 (1989).Google Scholar
11. de Gironcoli, S., Phys. Rev. B 51, 6773 (1995).Google Scholar
12. Recent unpublished work (Stumpf, R., private communication) indicates however that surface relaxation may follow the opposite trend on hcp transition metals (Ti, Zr), similarly to “simple” hcp metals such as Be.Google Scholar
13. Methfessel, M., Hennig, D., and Scheffler, M., Phys. Rev. B 46, 4816 (1992).Google Scholar
14. Fu, C. L., Ohnishi, S., Wimmer, E. and Freeman, A. J., Phys. Rev. Lett. 53, 675 (1984).Google Scholar
15. Pettifor, D. G., J. Phys. F 8, 219 (1978). A simpler model, proposed by M. W. Finnis and V. Heine, J. Phys. F 4, L37 (1974), applies the Smoluchowski [16] smoothening argument to sp metals: cleavage of the cristal causes the charge density to spill-out into vacuum, which reduces the electronic kinetic energy. As a consequence, a dipole moment arises at the surface, causing an inward electrostatic force acting on top-layer atoms.Google Scholar
16. Smoluchowski, R., Phys. Rev. 60, 661 (1941).Google Scholar
17. Boettger, J. C., Phys. Rev. B 49, 16798 (1994).Google Scholar
18. Fiorentini, V. and Methfessel, M., to be published.Google Scholar
19. Fiorentini, V., Methfessel, M., and Scheffler, M., Phys. Rev. Lett. 71, 1051 (1993).Google Scholar
20. Müller, S., Kinne, A., Kottcke, M., Metzler, R., Bayer, P., Hammer, L., and Heinz, K., Phys. Rev. Lett. 75 2859 (1995).Google Scholar
21. Needs, R. J., Phys. Rev. Lett. 58 53 (1986); D. H. Vanderbilt, 59, 1456 (1987).Google Scholar
22. Nielsen, O. H. and Martin, R. M., Phys. Rev. B 32, 3792 (1985).Google Scholar
23. Fiorentini, V., to be published.Google Scholar