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Using the pseudopotential plane wave (PPPW) method, we performed first principles calculation for the multilayer relaxations and the electron properties of the high-Miller-index stepped Cu(311), (511), (331) and (221) surfaces, which are expressed by 2(100)×(111), 3(100)×(111), 3(111)×(111) and 4(111)×(111), respectively, in the terrace-step notation, i.e. n(hkl)×(uvw). The interlayer relaxations of them are -+-…, --+-…, --+-… and ---+-…, respectively, which follow the atom-row trend: for stepped Cu surface which has n atom rows in the (100) or (111) terrace, the outermost n－1 interlayer spaces contract, then the n interlayer space expands, and the following n+1 interlayer space contracts again. For the stepped surfaces with the same (hkl)×(uvw), the larger the number of atom rows n in the terrace, the greater the contraction magnitude for Δd1,n. We did not find any indication of anomalous relaxation behavior for Cu(511) and (331) as mentioned in some references. Below Fermi energy level, the density of states of the first layer atom at stepped edge has the largest peak value in higher energy regions and has no peak in lower energy regions, so the first layer atom is most unstable and can be dislodged and peeled off more easily than other surface atoms. For the stepped surfaces with the same (hkl)×(uvw), the curves of the density of states have similar shapes for the atoms at the step edge, at the corner, at the terrace and near the corner, and the atoms under the step edge and near the corner.
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Keywords:
- stepped surface /
- first principles /
- multilayer relaxation /
- density of states
[1] Desjonquères M C, Spanjaard D 1995 Concepts in Surface Science (New York: Springer Press) p1
[2] Zangwill A 1988 Physics at Surfaces (Cambridge: Cambridge University Press) p1
[3] Widdra W, Trischberger P, Frieβ W, Menzel D, Payne S H, Kreuzer H J 1998 Phys. Rev. B 57 4111
[4] Cai J Q, Tao X M, Chen W B, Zhao X X, Tan M Q 2005 Acta Phys. Sin. 54 5350 (in Chinese) [蔡建秋、陶向明、陈文斌、赵新新、谭明秋 2005 物理学报 54 5350]
[5] Zhao X X, Tao X M, Chen W B, Chen X, Shang X F, Tan M Q 2006 Acta Phys. Sin. 55 6001 (in Chinese) [赵新新、陶向明、陈文斌、陈 鑫、尚学府、谭明秋 2006 物理学报 55 6001]
[6] Zhao W, Wang J D, Liu F B, Chen D R 2009 Acta Phys. Sin. 58 3352 (in Chinese) [赵 巍、汪家道、陈峰斌、陈大荣 2009物理学报 58 3352]
[7] Zhao X X, Tao X M, Chen W B, Chen X, Shang X F, Tan M Q 2006 Acta Phys. Sin. 55 3629 (in Chinese) [赵新新、陶向明、陈文斌、陈 鑫、尚学府、谭明秋 2006 物理学报 55 3629]
[8] Silva D J L F, Schroeder K, Blügel S 2004 Phys. Rev. B 69 245411
[9] Sinnott S B, Stave M S, Raeker T J, DePristo A E 1991 Phys. Rev. B 44 8927
[10] Silva D J L F, Schroeder K, Blügel S 2005 Phys. Rev. B 72 33405
[11] Spiak D 2001 Surf. Sci. 489 151
[12] Watson P R, Mitchell K A R 1988 Surf. Sci. 203 323
[13] Parkin S R, Watson P R, McFarlane R A, Mitchell K A R 1991 Solid State Commun. 78 841
[14] Yamaguchi M, Kaburaki H, Freeman A J 2004 Phys. Rev. B 69 45408
[15] Heid R, Bohnen K P, Kara A, Rahman T S 2002 Phys. Rev. B 65 115405
[16] Walko D A, Robinson I K 2001 Phys.Rev. B 64 045412
[17] Walko D A, Robinson I K 1999 Phys. Rev. B 59 15446
[18] Geng W T, Freeman A J 2001 Phys. Rev. B 64 115401
[19] Durukanoglu S, Kara A, Rahman T S 1997 Phys. Rev. B 55 13894
[20] Sklyadneva I Y, Rusina G G, Chulkov E V 1998 Surf. Sci. 416 17
[21] Loisel B, Gorse D, Pontikis V, Lapujoulade J 1989 Surf. Sci. 221 365
[22] Tian Y, Lin K W, Jona F 2000 Phys. Rev. B 62 12844
[23] Silva D J L F, Schroeder K, Blügel S 2004 Phys. Rev. B 70 245432
[24] Jona F 1999 Surf. Sci. Lett. 6 621
[25] Vanderbilt D 1990 Phys. Rev. B 41 7892
[26] Kresse G, Hafner J 1993 Phys. Rev. B 47 558
[27] Kresse G, Hafner J 1994 Phys. Rev. B 49 14251
[28] Kresse G, Furthmuller J 1996 Comput. Mater. Sci. 6 15
[29] Kresse G, Furthmuller J 1996 Comput. Mater. Sci. 54 11169
[30] Finnis M W, Heine V 1974 J. Phys. F: Met. Phys. 4 L37
[31] Smoluchowski R 1941 Phys. Rev. 60 661
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[1] Desjonquères M C, Spanjaard D 1995 Concepts in Surface Science (New York: Springer Press) p1
[2] Zangwill A 1988 Physics at Surfaces (Cambridge: Cambridge University Press) p1
[3] Widdra W, Trischberger P, Frieβ W, Menzel D, Payne S H, Kreuzer H J 1998 Phys. Rev. B 57 4111
[4] Cai J Q, Tao X M, Chen W B, Zhao X X, Tan M Q 2005 Acta Phys. Sin. 54 5350 (in Chinese) [蔡建秋、陶向明、陈文斌、赵新新、谭明秋 2005 物理学报 54 5350]
[5] Zhao X X, Tao X M, Chen W B, Chen X, Shang X F, Tan M Q 2006 Acta Phys. Sin. 55 6001 (in Chinese) [赵新新、陶向明、陈文斌、陈 鑫、尚学府、谭明秋 2006 物理学报 55 6001]
[6] Zhao W, Wang J D, Liu F B, Chen D R 2009 Acta Phys. Sin. 58 3352 (in Chinese) [赵 巍、汪家道、陈峰斌、陈大荣 2009物理学报 58 3352]
[7] Zhao X X, Tao X M, Chen W B, Chen X, Shang X F, Tan M Q 2006 Acta Phys. Sin. 55 3629 (in Chinese) [赵新新、陶向明、陈文斌、陈 鑫、尚学府、谭明秋 2006 物理学报 55 3629]
[8] Silva D J L F, Schroeder K, Blügel S 2004 Phys. Rev. B 69 245411
[9] Sinnott S B, Stave M S, Raeker T J, DePristo A E 1991 Phys. Rev. B 44 8927
[10] Silva D J L F, Schroeder K, Blügel S 2005 Phys. Rev. B 72 33405
[11] Spiak D 2001 Surf. Sci. 489 151
[12] Watson P R, Mitchell K A R 1988 Surf. Sci. 203 323
[13] Parkin S R, Watson P R, McFarlane R A, Mitchell K A R 1991 Solid State Commun. 78 841
[14] Yamaguchi M, Kaburaki H, Freeman A J 2004 Phys. Rev. B 69 45408
[15] Heid R, Bohnen K P, Kara A, Rahman T S 2002 Phys. Rev. B 65 115405
[16] Walko D A, Robinson I K 2001 Phys.Rev. B 64 045412
[17] Walko D A, Robinson I K 1999 Phys. Rev. B 59 15446
[18] Geng W T, Freeman A J 2001 Phys. Rev. B 64 115401
[19] Durukanoglu S, Kara A, Rahman T S 1997 Phys. Rev. B 55 13894
[20] Sklyadneva I Y, Rusina G G, Chulkov E V 1998 Surf. Sci. 416 17
[21] Loisel B, Gorse D, Pontikis V, Lapujoulade J 1989 Surf. Sci. 221 365
[22] Tian Y, Lin K W, Jona F 2000 Phys. Rev. B 62 12844
[23] Silva D J L F, Schroeder K, Blügel S 2004 Phys. Rev. B 70 245432
[24] Jona F 1999 Surf. Sci. Lett. 6 621
[25] Vanderbilt D 1990 Phys. Rev. B 41 7892
[26] Kresse G, Hafner J 1993 Phys. Rev. B 47 558
[27] Kresse G, Hafner J 1994 Phys. Rev. B 49 14251
[28] Kresse G, Furthmuller J 1996 Comput. Mater. Sci. 6 15
[29] Kresse G, Furthmuller J 1996 Comput. Mater. Sci. 54 11169
[30] Finnis M W, Heine V 1974 J. Phys. F: Met. Phys. 4 L37
[31] Smoluchowski R 1941 Phys. Rev. 60 661
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