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The phase-field crystal (PFC) model is used to simulate crystal growth from undercooled liquid by the finite difference method. The effects of phase region and undercooling on crystal growth process are analyzed. The simulation results show that crystal growth is inhibited in the region of liquid-crystal coexistence where liquid-crystal boundary becomes thicker gradually. In the single crystal phase region, crystallization is enhanced with undercooling increasing,while liquid-crystal boundary becomes thinner. It is found that there is a linear relationship between crystal growth velocity and undercooling.
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Keywords:
- phase-field crystal /
- free energy function /
- undercooled liquid /
- crystal growth
[1] Boettinger W J, Warren J A, Beckermann C, Karma A 2002 Annual Review of Materials Research 32 163
[2] Yu Y M, Yang G C, Zhao D W, Karma A, Beckermann C 2001 Acta Phys. Sin. 50 2423 (in Chinese) [于艳梅、杨根仓、赵达 文、Karma A、Beckermann C 2001 物理学报 50 2423] 〖3] Zhu C S, Wang Z P, Jing T, Xiao R Z 2006 Acta Phys. Sin. 55 1502 (in Chinese) [朱昌盛、王智平、荆 涛、肖荣振 2006 物理学报 55 1502]
[3] Long W Y, Cai Q Z , Wei B K 2005 Acta Phys. Sin. 54 256(in Chinese)[龙文元、蔡启舟、陈立亮、魏伯康 2005 物理学报 54 256]
[4] Zhu Y C, Wang J C, Yang G C, Yang Y J 2007 Acta Phys. Sin. 56 5542 (in Chinese) [朱耀产、王锦程、杨根仓、杨玉娟 2007 物理学报 56 5542]
[5] Wang Y U, Jin Y M, Cuitino A M, Khachaturyan A G 2001 Appl. Phys. Lett. 78 2324
[6] Chen L Q, Khachaturyan A G 1991 Scr. Metall. Mater. 25 61
[7] Warren J A, Kobayashi R, Carter W C 2000 J. Cryst. Growth 18 211
[8] Elder K R, Grant M 2004 Phys. Rev. E 70 051605
[9] Elder K R, Katakowski M, Haataja M, Grant M 2002 Phys. Rev. Lett. 88 245701
[10] Goldenfeld N, Athreya B P, Dantzig J A 2005 Phys. Rev. E 72 020601
[11] Athreya B P, Goldenfeld N, Dantzig J A Greenwood M, Provatas N 2007 Phys. Rev. E 76 056706
[12] Wu K A, Karma A, Hoyt J J, Asta M 2006 Phys. Rev. B 73 094101
[13] Elder K R, Provatas N, Berry J, Stefanovic P Grant M, 2007 Phys. Rev. B 75 064107
[14] Cahn J W, Hilliard J E 1957 J. Chem. Phys. 28 258
[15] Cahn J W 1961 Acta. Metall. 9 795
[16] Ramalingam H, Asta M, Walle A, Hoyt J J 2002 Inter.Sci. 10 149
[17] Flemings M C 1974 Solidification Processing (New York: McGRAW-HILL) p290
[18] Ohsaka K, Trinh E H, 1998 J. Cryst. Growth 194 128
[19] Steinbach I, Berckermann C, Kauerauf B, Li Q, Guo J 1999 Acta Mater. 47 971
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[1] Boettinger W J, Warren J A, Beckermann C, Karma A 2002 Annual Review of Materials Research 32 163
[2] Yu Y M, Yang G C, Zhao D W, Karma A, Beckermann C 2001 Acta Phys. Sin. 50 2423 (in Chinese) [于艳梅、杨根仓、赵达 文、Karma A、Beckermann C 2001 物理学报 50 2423] 〖3] Zhu C S, Wang Z P, Jing T, Xiao R Z 2006 Acta Phys. Sin. 55 1502 (in Chinese) [朱昌盛、王智平、荆 涛、肖荣振 2006 物理学报 55 1502]
[3] Long W Y, Cai Q Z , Wei B K 2005 Acta Phys. Sin. 54 256(in Chinese)[龙文元、蔡启舟、陈立亮、魏伯康 2005 物理学报 54 256]
[4] Zhu Y C, Wang J C, Yang G C, Yang Y J 2007 Acta Phys. Sin. 56 5542 (in Chinese) [朱耀产、王锦程、杨根仓、杨玉娟 2007 物理学报 56 5542]
[5] Wang Y U, Jin Y M, Cuitino A M, Khachaturyan A G 2001 Appl. Phys. Lett. 78 2324
[6] Chen L Q, Khachaturyan A G 1991 Scr. Metall. Mater. 25 61
[7] Warren J A, Kobayashi R, Carter W C 2000 J. Cryst. Growth 18 211
[8] Elder K R, Grant M 2004 Phys. Rev. E 70 051605
[9] Elder K R, Katakowski M, Haataja M, Grant M 2002 Phys. Rev. Lett. 88 245701
[10] Goldenfeld N, Athreya B P, Dantzig J A 2005 Phys. Rev. E 72 020601
[11] Athreya B P, Goldenfeld N, Dantzig J A Greenwood M, Provatas N 2007 Phys. Rev. E 76 056706
[12] Wu K A, Karma A, Hoyt J J, Asta M 2006 Phys. Rev. B 73 094101
[13] Elder K R, Provatas N, Berry J, Stefanovic P Grant M, 2007 Phys. Rev. B 75 064107
[14] Cahn J W, Hilliard J E 1957 J. Chem. Phys. 28 258
[15] Cahn J W 1961 Acta. Metall. 9 795
[16] Ramalingam H, Asta M, Walle A, Hoyt J J 2002 Inter.Sci. 10 149
[17] Flemings M C 1974 Solidification Processing (New York: McGRAW-HILL) p290
[18] Ohsaka K, Trinh E H, 1998 J. Cryst. Growth 194 128
[19] Steinbach I, Berckermann C, Kauerauf B, Li Q, Guo J 1999 Acta Mater. 47 971
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