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In this paper the theoretical calculation methods for CP(T) (molar heat capacity at constant pressure) values of nanoparticle and nanocrystalline are investigated. Theoretical formulas for calculating CP(T), Debye temperature and volume expansion coefficient of nanoparticle using melting point of nanoparticle are set up and the calculated values of CP(T) for copper nanoparticle are fairly consistent with the experimental ones. A relationship between Debye temperature and density of nanocrystalline is proposed, and Debye temperature can decrease with the reduction of nanocrystalline density. The calculated values of CP(T) of copper nanocrystalline are also quite consistent with the experimental ones. The bulk modulus of elasticity of nanocrystalline will drop off with the decrease of grain size of nanocrystalline, which should be taken into account when the CP(T) of nanocrystalline is calculated. The calculation methods proposed in this paper are feasible.
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Keywords:
- nanoparticle /
- nanocrystalline /
- molar heat capacity at constant pressure /
- Debye temperature
[1] Dong L N 2005 M.S. Dissertation(Dalian: Dalian Maritime University) (in Chinese) [董丽娜 2005硕士学位论文(大连:大连海事大学)]
[2] Rupp J,Birringer R 1987 Phys. Rev. B 36 7888
[3] Nishiguchi N,Sakuma T 1981 Solid State Commun. 38 1073
[4] Zhang H Z,Banfield J F 1998 Nanostruct. Mater. 10 185
[5] Wang B X, Zhou L P, Peng X F 2004 J. Therm. Sci. Technol. 31 (in Chinese) [王补宣、周乐平、彭晓峰 2004 热科学与技术 31]
[6] Liu Y 2008 M.S. Dissertation(Changchun: Jilin University) (in Chinese)[刘 洋 2008 硕士学位论文(吉林:吉林大学)]
[7] Li L M,Song X Y, Zhang J X, Yang K Y 2007 Progress in Natural Science 17 1316 (in Chinese) [李凌梅、宋晓艳、张久兴、杨克勇 2007 自然科学进展 17 1316 ]
[8] Li X M 2003 M.S. Dissertation (Changsha: Central South University (in Chinese) [李新梅2003 硕士学位论文(长沙:中南大学)]
[9] Joseph K A 1978 Course In Thermodynamics(Ⅱ)(New York: Hemisphere Publishing Corporation) p185
[10] Chinese Society for Metals, Nonferrous Metals Society of China 1987 Handbook of Physics Performance of Metals Materials (vol.1)(Beijing: Metallurgical Industry Press) (in Chinese) [中国金属学会,中国有色金属学会编 1987 金属材料物理性能手册(第一册)(北京:冶金工业出版社)]
[11] Pan R, Nair M V, Wunderlich B 1989 J. Therm. Anal. 35 955
[12] Fantian X Y,Daye H L,Shen Q X, Xionggu K F, Zetian Z S (Translated by Qu C Z)Common Data in Physics (2nd Ed.) (Beijing: Science Press ) p121(in Chinese) [饭田修一、大野和朗、神前熙、熊谷宽夫、泽田正三编,曲长芝译 1987 物理学常用数表(第二版)(北京:科学出版社) 第121页]
[13] Comsa G H, Heitkamp D, Rade H S 1977 Solid State Commun. 24 547
[14] Yang C C, Xiao M X, Li W, Jiang Q 2006 Solid State Commun. 139 148
[15] Cheng B P, Kong J, Luo J,Dong Y D 1993 Mater. Res. Prog. 7 240 (in Chinese) [程本培、孔 捷、罗 菊、董远达 1993 材料科学进展 7 240]
[16] Zhang W, Chen L, Zhang L D 1997 Acta Metal. Sin. 33 987 (in Chinese) [张 伟、陈 莉、张立德 1997 金属学报 33 987]
[17] Rao W H 2006 M. S. Dissertation (Shanghai: Shanghai University) (in Chinese) [饶卫红 2006 硕士学位论文 (上海:上海大学)]
[18] Lu K, Sheng H W, Jin Z H 1997 Chin. J. Mater. Res. 11 658 (in Chinese) [卢 柯、生红卫、金朝晖 1997 材料研究学报 11 658 ]
[19] Jin Y M, Cheng J L, Varma-Nair M, Liang G H, Fu Y G, Bernhard Wunderlich 1992 J. Phys. Chem. 96 5151
[20] Thammarat A,Hans-Beat B 2006 J. Phys. Chem. B 110 26129
[21] Di Y X, Ji X H, Li L A, Qin Y W,Chen J L 2007 J. Mech. Strength 29 16 (in Chinese) [邸玉贤、计欣华、李林安、秦玉文、陈金龙 2007 机械强度 29 16]
[22] Li D B, Wei Q S, Liu H, Chen X B, Li Y F 2008 Mater. Rev.(Net Edition) 3 29 (in Chinese) [李东波、魏钦帅、刘 环、陈晓斌、李依帆 2008 材料导报网刊 3 29]
[23] Hu Z F, Yan B, He G Q 2009 Materials Physics Introduction(Beijing: Chemical Industry Press ) p272 (in Chinese) [胡正 飞、严 彪、何国求 2009 材料物理概论 (北京:化学工业出版社)第272页] 〖24] Zhang H L, Lei H L, Tang Y J,Luo J S,Li K,Deng X C 2010 Acta Phys. Sin. 59 471 (in Chinese) [张洪亮、雷海乐、唐永健、罗江山、李 恺、邓晓臣 2010 59 471]
[24] Chen D 1994 Acta Metal. Sin. 30 A 348 (in Chinese) [陈 达 1994 金属学报 30 A 348]
[25] Liu C, Zhou T, Zheng R L 2006 J. Southwest China Norm. Univ.(NSE) 31 83 (in Chinese) [刘 超、周 铁、郑瑞伦 2006 西南师范大学学报(自然科学版) 31 83]
[26] Chang M, Sun W, Guo C H, Yang B H 1997 Acta Phys. Sin. 46 1326 (in Chinese) [常 明、孙 伟、郭长海、杨保和 1997 46 1326]
[27] Zhang H B, Wang L Y 2004 J. Southwest China Norm. Univ. (Nat. Sci. Ed.) 29 67 (in Chinese) [张浩波、王莉艳 2004 西南师范大学学报(自然科学版) 29 67]
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[1] Dong L N 2005 M.S. Dissertation(Dalian: Dalian Maritime University) (in Chinese) [董丽娜 2005硕士学位论文(大连:大连海事大学)]
[2] Rupp J,Birringer R 1987 Phys. Rev. B 36 7888
[3] Nishiguchi N,Sakuma T 1981 Solid State Commun. 38 1073
[4] Zhang H Z,Banfield J F 1998 Nanostruct. Mater. 10 185
[5] Wang B X, Zhou L P, Peng X F 2004 J. Therm. Sci. Technol. 31 (in Chinese) [王补宣、周乐平、彭晓峰 2004 热科学与技术 31]
[6] Liu Y 2008 M.S. Dissertation(Changchun: Jilin University) (in Chinese)[刘 洋 2008 硕士学位论文(吉林:吉林大学)]
[7] Li L M,Song X Y, Zhang J X, Yang K Y 2007 Progress in Natural Science 17 1316 (in Chinese) [李凌梅、宋晓艳、张久兴、杨克勇 2007 自然科学进展 17 1316 ]
[8] Li X M 2003 M.S. Dissertation (Changsha: Central South University (in Chinese) [李新梅2003 硕士学位论文(长沙:中南大学)]
[9] Joseph K A 1978 Course In Thermodynamics(Ⅱ)(New York: Hemisphere Publishing Corporation) p185
[10] Chinese Society for Metals, Nonferrous Metals Society of China 1987 Handbook of Physics Performance of Metals Materials (vol.1)(Beijing: Metallurgical Industry Press) (in Chinese) [中国金属学会,中国有色金属学会编 1987 金属材料物理性能手册(第一册)(北京:冶金工业出版社)]
[11] Pan R, Nair M V, Wunderlich B 1989 J. Therm. Anal. 35 955
[12] Fantian X Y,Daye H L,Shen Q X, Xionggu K F, Zetian Z S (Translated by Qu C Z)Common Data in Physics (2nd Ed.) (Beijing: Science Press ) p121(in Chinese) [饭田修一、大野和朗、神前熙、熊谷宽夫、泽田正三编,曲长芝译 1987 物理学常用数表(第二版)(北京:科学出版社) 第121页]
[13] Comsa G H, Heitkamp D, Rade H S 1977 Solid State Commun. 24 547
[14] Yang C C, Xiao M X, Li W, Jiang Q 2006 Solid State Commun. 139 148
[15] Cheng B P, Kong J, Luo J,Dong Y D 1993 Mater. Res. Prog. 7 240 (in Chinese) [程本培、孔 捷、罗 菊、董远达 1993 材料科学进展 7 240]
[16] Zhang W, Chen L, Zhang L D 1997 Acta Metal. Sin. 33 987 (in Chinese) [张 伟、陈 莉、张立德 1997 金属学报 33 987]
[17] Rao W H 2006 M. S. Dissertation (Shanghai: Shanghai University) (in Chinese) [饶卫红 2006 硕士学位论文 (上海:上海大学)]
[18] Lu K, Sheng H W, Jin Z H 1997 Chin. J. Mater. Res. 11 658 (in Chinese) [卢 柯、生红卫、金朝晖 1997 材料研究学报 11 658 ]
[19] Jin Y M, Cheng J L, Varma-Nair M, Liang G H, Fu Y G, Bernhard Wunderlich 1992 J. Phys. Chem. 96 5151
[20] Thammarat A,Hans-Beat B 2006 J. Phys. Chem. B 110 26129
[21] Di Y X, Ji X H, Li L A, Qin Y W,Chen J L 2007 J. Mech. Strength 29 16 (in Chinese) [邸玉贤、计欣华、李林安、秦玉文、陈金龙 2007 机械强度 29 16]
[22] Li D B, Wei Q S, Liu H, Chen X B, Li Y F 2008 Mater. Rev.(Net Edition) 3 29 (in Chinese) [李东波、魏钦帅、刘 环、陈晓斌、李依帆 2008 材料导报网刊 3 29]
[23] Hu Z F, Yan B, He G Q 2009 Materials Physics Introduction(Beijing: Chemical Industry Press ) p272 (in Chinese) [胡正 飞、严 彪、何国求 2009 材料物理概论 (北京:化学工业出版社)第272页] 〖24] Zhang H L, Lei H L, Tang Y J,Luo J S,Li K,Deng X C 2010 Acta Phys. Sin. 59 471 (in Chinese) [张洪亮、雷海乐、唐永健、罗江山、李 恺、邓晓臣 2010 59 471]
[24] Chen D 1994 Acta Metal. Sin. 30 A 348 (in Chinese) [陈 达 1994 金属学报 30 A 348]
[25] Liu C, Zhou T, Zheng R L 2006 J. Southwest China Norm. Univ.(NSE) 31 83 (in Chinese) [刘 超、周 铁、郑瑞伦 2006 西南师范大学学报(自然科学版) 31 83]
[26] Chang M, Sun W, Guo C H, Yang B H 1997 Acta Phys. Sin. 46 1326 (in Chinese) [常 明、孙 伟、郭长海、杨保和 1997 46 1326]
[27] Zhang H B, Wang L Y 2004 J. Southwest China Norm. Univ. (Nat. Sci. Ed.) 29 67 (in Chinese) [张浩波、王莉艳 2004 西南师范大学学报(自然科学版) 29 67]
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