Calculation of surface stress in a linear combination of atomic orbitals representation

Peter J. Feibelman

doi:10.1103/PhysRevB.50.1908

Access by Xinjiang University

Calculation of surface stress in a linear combination of atomic orbitals representation

Peter J. Feibelman

Solid State Theory Division, Sandia National Laboratories, Albuquerque, New Mexico 87185

PDF

Phys. Rev. B 50, 1908 – Published 15 July, 1994

DOI: https://doi.org/10.1103/PhysRevB.50.1908

Abstract

A method is presented for separating ‘‘bulk’’ and ‘‘surface’’ contributions to the strain derivative of the total energy of a two-dimensionally periodic, several-layer slab. The method, involving a layerwise decomposition of the sums and integrals required to calculate the derivative, makes it possible to compute a surface stress via a single, linear combination of atomic orbitals slab calculation. Application to Al(111) yields a predicted tensile surface stress of magnitude 0.090 eV/A $̊^{2}$ .

References (18)

P. J. Feibelman, Phys. Rev. B 44, 3916 (1991).
P. Pulay, in Modern Theoretical Chemistry, edited by H. F. Schaefer (Plenum, New York, 1977), Vol. 4, pp. 153–185; Mol. Phys. 17, 197 (1969).
R. J. Needs and M. J. Godfrey, Phys. Rev. B 42, 10933 (1990).
s need not be the length of the bulk lattice translation vector in the z direction. For example, in the case of a hcp(0001) surface, since there are two physically equivalent layers in the bulk hcp unit cell, s can be chosen as the interlayer spacing, or 1/2 the bulk-lattice's repeat distance c along the surface normal.
M. C. Payne, N. Roberts, R. J. Needs, M. Needels, and J. D. Joannopoulos, Surf. Sci. 211/212, 1 (1989).
R. J. Needs and M. J. Godfrey, Phys. Scr. T19, 391 (1987).
R. J. Needs, Phys. Rev. Lett. 58, 53 (1986).
For a review of the local-density approximation, see The Theory of the Inhomogeneous Electron Gas, edited by S. Lundqvist and N. H. March (Plenum, New York, 1983).
D. R. Hamann, Phys. Rev. B 40, 2980 (1989).
G. P. Kerker, J. Phys. C 13, 1189 (1980).
D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. J. Perdew and A. Zunger45, 566 (1980), as parametrized by , Phys. Rev. B 23, 5048 (1981).
P. J. Feibelman, Phys. Rev. B 46, 15 416 (1992), Table I. When using the Kerker potential, I replace the pseudo-s-function in this table by a sum of Gaussians with attenuation constants α =0.18, 0.25, 0.4, 0.7, and 1.3 and corresponding coefficients $c_{α}$ =2.281 360 1, -3.077 563 0, 2.275 832 7, -1.582 774 0, and 0.322 821 44. Otherwise the basis set remains the same.
For the l=2 pseudopotential, which I also use as the local potential, I retain that which is generated by Hamann's prescrition (Ref. 9). I obtain the l=0 and 1 Kerker potentials from a computer code distributed by N. Troullier and J. L. Martins.
P. J. Feibelman, Phys. Rev. B 46, 15416 (1992).
F. Jona, D. Sondericker and P. Marcus, J. Phys. C 13, L155 (1980); H. B. Nielsen and D. L. Adams, ibid. 15, 615 (1982); J. R. Noonan and H. L. Davis, J. Vac. Sci. Technol. A 8, 2671 (1990).
J. S. Nelson and P. J. Feibelman, Phys. Rev. Lett. 68, 2188 (1992).
This estimate is based on comparing two calculations in which I hold the lattice parameter at its experimental value and assume an ``ideal'' surface. In the first I use a Kerker pseudopotential and obtain a surface stress of 0.079 eV/ A ang "" sup 2_. In the other I use a GNCPP and obtain 0.082 eV/ A ang "" sup 2_. This small difference, 4%, indicates the accuracy level in a stress calculation where one needs to begin worrying about pseudopotential transferability.
R. J. Needs and M. Mansfield, J. Phys. Condens. Matter 1, 7555 (1989).

[c1] P. J. Feibelman, Phys. Rev. B 44, 3916 (1991).

[c2] P. Pulay, in Modern Theoretical Chemistry, edited by H. F. Schaefer (Plenum, New York, 1977), Vol. 4, pp. 153–185; Mol. Phys. 17, 197 (1969).

[c3] R. J. Needs and M. J. Godfrey, Phys. Rev. B 42, 10933 (1990).

[c4] s need not be the length of the bulk lattice translation vector in the z direction. For example, in the case of a hcp(0001) surface, since there are two physically equivalent layers in the bulk hcp unit cell, s can be chosen as the interlayer spacing, or 1/2 the bulk-lattice's repeat distance c along the surface normal.

[c5] M. C. Payne, N. Roberts, R. J. Needs, M. Needels, and J. D. Joannopoulos, Surf. Sci. 211/212, 1 (1989).

[c6] R. J. Needs and M. J. Godfrey, Phys. Scr. T19, 391 (1987).

[c7] R. J. Needs, Phys. Rev. Lett. 58, 53 (1986).

[c8] For a review of the local-density approximation, see The Theory of the Inhomogeneous Electron Gas, edited by S. Lundqvist and N. H. March (Plenum, New York, 1983).

[c9] D. R. Hamann, Phys. Rev. B 40, 2980 (1989).

[c10] G. P. Kerker, J. Phys. C 13, 1189 (1980).

[c11] D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. J. Perdew and A. Zunger45, 566 (1980), as parametrized by , Phys. Rev. B 23, 5048 (1981).

[c12] P. J. Feibelman, Phys. Rev. B 46, 15 416 (1992), Table I. When using the Kerker potential, I replace the pseudo-s-function in this table by a sum of Gaussians with attenuation constants α =0.18, 0.25, 0.4, 0.7, and 1.3 and corresponding coefficients $c_{α}$ =2.281 360 1, -3.077 563 0, 2.275 832 7, -1.582 774 0, and 0.322 821 44. Otherwise the basis set remains the same.

[c13] For the l=2 pseudopotential, which I also use as the local potential, I retain that which is generated by Hamann's prescrition (Ref. 9). I obtain the l=0 and 1 Kerker potentials from a computer code distributed by N. Troullier and J. L. Martins.

[c14] P. J. Feibelman, Phys. Rev. B 46, 15416 (1992).

[c15] F. Jona, D. Sondericker and P. Marcus, J. Phys. C 13, L155 (1980); H. B. Nielsen and D. L. Adams, ibid. 15, 615 (1982); J. R. Noonan and H. L. Davis, J. Vac. Sci. Technol. A 8, 2671 (1990).

[c16] J. S. Nelson and P. J. Feibelman, Phys. Rev. Lett. 68, 2188 (1992).

[c17] This estimate is based on comparing two calculations in which I hold the lattice parameter at its experimental value and assume an ``ideal'' surface. In the first I use a Kerker pseudopotential and obtain a surface stress of 0.079 eV/ A ang "" sup 2_. In the other I use a GNCPP and obtain 0.082 eV/ A ang "" sup 2_. This small difference, 4%, indicates the accuracy level in a stress calculation where one needs to begin worrying about pseudopotential transferability.

[c18] R. J. Needs and M. Mansfield, J. Phys. Condens. Matter 1, 7555 (1989).

Physical Review B

Export citation

Export citation

Calculation of surface stress in a linear combination of atomic orbitals representation

Abstract

References (18)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation