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应用双模PFC模型,计算二维PFC相图,模拟二维六角晶格向正方晶格的结构转变过程, 观察新相(二维正方相)的形核、长大特点,以及相结构转变的动力学特征. 结果表明:六角结构相向正方结构相的转变,正方相最易在六角相晶界处, 尤其是在三晶粒的交汇处首先生成正方相的晶核,之后是正方相逐渐通过吞噬六角相的边缘, 向六角相内部推进,并不断长大.对于结构转变生成的正方相晶粒,其晶粒取向几乎是随机的, 与原先六角相晶粒取向角没有明显的关系.正方相转变的面积分数随时间变化的动力学曲线 呈现典型的S形.由Avrami曲线可将相变曲线看成由两阶段组成. 计算模拟得到的Avrami曲线的第二阶段直线斜率K的范围在2.0和3.0之间, 与JMAK理论的指数n相符合.The two-mode phase-field-crystal (PFC) method is used to calculate the phase diagram and to simulate the transformation of hexagonal to square structure in two dimensions. The nucleation, grain growth and dynamic feature of the phase structure transformation show that square phase prefers to be present at the juncture place of the three hexagonal grains, and swallows the hexagonal phase at grain boundary. The square grains grow and push the boundary of hexagonal grain toward the inside of hexagonal grain and then the square grains grow up and extend the area of square phase. The orientations of new square grains due to the structure transformation are nearly randomly distributed, and have no relation to those of hexagonal grains. The dynamic curve of area fraction of square phase shows the typical S shape with time increasing. The Avrami index curve shows that there are two stages in the transformation. The Avrami index n of second satge in simulation is in a range from 2.0 to 3.0, which is in good agreement with the value from the JMAK theory.
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Keywords:
- structure transformation /
- phase-field-crystal /
- phase diagram /
- grain orientation
[1] Wang Y Z, Li J 2010 Acta Mater. 58 1212
[2] Chen L Q 2002 Annu. Rev. Mater. Res. 32 113
[3] Steinbach I 2009 Modell. Simul. Mater. Sci. Eng. 17 73001
[4] Gao Y J, Luo Z R,Hu X Y,Huang C G 2010 Acta Metall. Sin. 46 1161 (in Chinese) [高英俊, 罗志荣, 胡项英, 黄创高 2010 金属学报 46 1161]
[5] Zhang X G, Zong Y P, Wu Y 2012 Acta Phys.Sin. 61 088104 (in Chinese) [张宪刚, 宗亚平, 吴艳 2012 物理学报 61 088104]
[6] Wei C Y, Li S Y 2011 Acta Phys.Sin. 60 100701 (in Chinese) [魏承炀, 李赛毅 2011 物理学报 60 100701]
[7] Rountree C L, Kalia R K, Lidorikis E, Nakano A, Brutzel L V, Vashishta P 2002 Annu. Rev. Mater. Res. 32 377
[8] Millet P C, Selvam R D, Saxeua A 2006 Acta Mater. 54 297
[9] Stefanovic P, Haataja M, Provatas N 2009 Phys. Rev. E 80 046107
[10] Elder K R, Grant M 2004 Phys. Rev. E 70 51605
[11] Elder K R, Katakowski M, Haataja M, Grant M 2002 Phys Rev Lett. 88 245701
[12] Ren X, Wang J C, Yang Y J, Yang G C 2010 Acta Phys. Sin. 59 3595 (in Chinese) [任秀, 王锦程, 杨玉娟, 杨根仓 2010 物理学报 59 3595]
[13] Yang T, Chen Z, Dong W P 2011 Acta Metall. Sin. 47 1301 (in Chinese) [杨涛, 陈铮, 董卫平 2011 金属学报 47 1301]
[14] Zhang Q, Wang J C, Zhang Y C, Yang G C 2011 Acta Phys. Sin. 60 088104 (in Chinese) [张琪, 王锦程, 张亚丛, 杨根仓 2011 物理学报 60 088104]
[15] Yang T, Chen Z, Zhang J, Dong W P, Wu L 2012 Chin. Phys. Lett. 29 078103
[16] Yu Y M, Backofen R, Voigt A 2011 J. Cryst. Growth 318 18
[17] Greenwood M, Provatas N, Rottler J 2010 Phys. Rev. Lett. 105 045708
[18] Wu K A, Aaland A, Karma A 2010 Phys. Rev. E 81 061601
[19] Gao Y J, Luo Z R, Zhang S Y, Huang C G 2010 Acta Metall. Sin. 46 1473 (in Chinese) [高英俊, 罗志荣, 张少义, 黄创高 2010 金属学报 46 1473]
[20] Cheng M, Warren J A 2008 J. Comput. Phys. 227 6241
[21] Lupis C L 1983 Chemical thermodynamics of materials (New Youk: Elsevier Science Press) p195-230
[22] Shao J L, He A M, Duan S Q, Wang P, Qin C S 2010 Acta Phys. Sin. 59 4888 (in Chinese) [邵建立, 何安民, 段素青, 王裵, 秦承森 2012 物理学报 59 4888]
[23] Xu Z, Zhao L C 2004 Solis state transformation of metal (Beijing: Science Press) p25-30 (in Chinese) [徐洲, 赵连城 2004 金属固体相变原理 (北京: 科学出版社) 第25–30页]
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[1] Wang Y Z, Li J 2010 Acta Mater. 58 1212
[2] Chen L Q 2002 Annu. Rev. Mater. Res. 32 113
[3] Steinbach I 2009 Modell. Simul. Mater. Sci. Eng. 17 73001
[4] Gao Y J, Luo Z R,Hu X Y,Huang C G 2010 Acta Metall. Sin. 46 1161 (in Chinese) [高英俊, 罗志荣, 胡项英, 黄创高 2010 金属学报 46 1161]
[5] Zhang X G, Zong Y P, Wu Y 2012 Acta Phys.Sin. 61 088104 (in Chinese) [张宪刚, 宗亚平, 吴艳 2012 物理学报 61 088104]
[6] Wei C Y, Li S Y 2011 Acta Phys.Sin. 60 100701 (in Chinese) [魏承炀, 李赛毅 2011 物理学报 60 100701]
[7] Rountree C L, Kalia R K, Lidorikis E, Nakano A, Brutzel L V, Vashishta P 2002 Annu. Rev. Mater. Res. 32 377
[8] Millet P C, Selvam R D, Saxeua A 2006 Acta Mater. 54 297
[9] Stefanovic P, Haataja M, Provatas N 2009 Phys. Rev. E 80 046107
[10] Elder K R, Grant M 2004 Phys. Rev. E 70 51605
[11] Elder K R, Katakowski M, Haataja M, Grant M 2002 Phys Rev Lett. 88 245701
[12] Ren X, Wang J C, Yang Y J, Yang G C 2010 Acta Phys. Sin. 59 3595 (in Chinese) [任秀, 王锦程, 杨玉娟, 杨根仓 2010 物理学报 59 3595]
[13] Yang T, Chen Z, Dong W P 2011 Acta Metall. Sin. 47 1301 (in Chinese) [杨涛, 陈铮, 董卫平 2011 金属学报 47 1301]
[14] Zhang Q, Wang J C, Zhang Y C, Yang G C 2011 Acta Phys. Sin. 60 088104 (in Chinese) [张琪, 王锦程, 张亚丛, 杨根仓 2011 物理学报 60 088104]
[15] Yang T, Chen Z, Zhang J, Dong W P, Wu L 2012 Chin. Phys. Lett. 29 078103
[16] Yu Y M, Backofen R, Voigt A 2011 J. Cryst. Growth 318 18
[17] Greenwood M, Provatas N, Rottler J 2010 Phys. Rev. Lett. 105 045708
[18] Wu K A, Aaland A, Karma A 2010 Phys. Rev. E 81 061601
[19] Gao Y J, Luo Z R, Zhang S Y, Huang C G 2010 Acta Metall. Sin. 46 1473 (in Chinese) [高英俊, 罗志荣, 张少义, 黄创高 2010 金属学报 46 1473]
[20] Cheng M, Warren J A 2008 J. Comput. Phys. 227 6241
[21] Lupis C L 1983 Chemical thermodynamics of materials (New Youk: Elsevier Science Press) p195-230
[22] Shao J L, He A M, Duan S Q, Wang P, Qin C S 2010 Acta Phys. Sin. 59 4888 (in Chinese) [邵建立, 何安民, 段素青, 王裵, 秦承森 2012 物理学报 59 4888]
[23] Xu Z, Zhao L C 2004 Solis state transformation of metal (Beijing: Science Press) p25-30 (in Chinese) [徐洲, 赵连城 2004 金属固体相变原理 (北京: 科学出版社) 第25–30页]
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