用Weiss分子场理论对有外电场时铁电体系相变特征的研究

张晋鲁; 李玉强; 赵兴宇; 黄以能

doi:10.7498/aps.61.140501

摘要

Weiss分子场理论(WMFT)对晶体中顺磁-铁磁和顺电-铁电相变特征的定量描述是相当成功的. 由于是平均场理论,又可作为初步分析结构无序体系和复杂组分体系相变行为的理论依据. 但是迄今为止,并没有对有外场时WMFT的相变特征进行详细研究. 而对铁电体系,仅仅对分子取向为两个状态时WMFT的相变特征进行了研究. 另外,虽然铁磁与铁电体系的WMFT描述极为相似,但是由于两种体系中微观磁化和极化的单元不同,导致相应的数学描述与结果也有所不同. 本文首先对外电场中分子取向包含任意状态的铁电体系的WMFT相变特征, 包括自发极化、内能和比热以及静态极化率随温度变化进行严格推导, 然后对相变特征随外电场的演变进行了研究.结果表明: 1)无外场时,体系发生二级顺电-铁电相变,且随状态数的增加,相变温度减小, 这是与铁磁体系不同的地方,同时单分子的平均极化强度减小,而内能、比热和极化率增大; 2)外场的存在,使得体系原有的二级相变转化为弥散相变,且外场越强,弥散温区越大. 上述结果对深入研究铁电体系的相变,特别是弥散相变无疑是有益的.

关键词:

Abstract

The descriptions of the paramagnetic-ferromagnetic and paraelectric-ferroelectric phase transitions (PTs) by Weiss's molecular field theory (WMFT) are quite successful, and the WMFT is also a theoretical basis of initial analysis of the PTs of structural disorder and complex compositional systems because of its mean-field characteristic. However, there is not any study on the PT behaviors of the WMFT with external field, and only the case of two orientational states of molecules for ferroelectric systems has been investigated by the WMFT. Although the descriptions of the above two kinds of PTs by the WMFT are quite similar, the exact ones and the corresponding results are different more or less due to the difference in microscopic unit between the magnetization and polarization In this work, the exact descriptions of the ferroelectric systems with arbitrary orientational states of molecules by the WMFT are provided, including the temperature dependences of the spontaneous polarization, the internal energy, the specific heat and the static polarizability, and then the evolutions of the PTs with an external field are studied. The obtained results are as follows. 1) Without the external field, the PTs of the systems are of the second order, and the transition temperatures and spontaneous polarizations decrease, which are different from those of the ferromagnetic systems, but the internal energy, the specific heat and the polarizability increase with the increase of the orientational states. 2) The external field drives the second order PT to a diffusive one, and diffusive temperature range becomes wider as the field is increases. The results mentioned above would benefit the deep studies of ferroelectric PT, especially the diffusive one.

Keywords:

作者及机构信息

1.
新疆教育学院科研处, 乌鲁木齐 830043;

2.
伊犁师范学院物理科学与技术学院, 新疆凝聚态相变与微结构实验室, 伊宁 835000;

3.
南京大学物理学院, 国家固体微结构实验室, 南京 210093

基金项目: 国家自然科学基金(批准号: 30860076)、国家重点基础研究发展计划(批准号: 2012CB821500)、新疆自治区高技术发展项目(批准号: 200916126) 和新疆自治区科技厅自然基金(批准号: 200821104, 200821184)资助的课题.

Authors and contacts

1.
Scientific Research Department, Xinjiang Education Institute, Urumqi 830043, China;

2.
Xinjiang Laboratory of Phase Transitions and Microstructures in Condensed Matter Physics, Physical College of Science and Technology, Yili Normal University, Yining 835000, China;

3.
National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 30860076), the National Basic Research Program of China (Grant No. 2012CB821500), the Science and Technology Program of Xinjiang Uygur Autonomous Region, China (Grant No. 200916126), and the Natural Science Foundations of Xinjiang Uygur Autonomous Region, China (Grant Nos. 200821104, 200821184).

参考文献

[1]	Weiss P 1907 J. de Phys. 6 661
[2]	Weiss P 1908 Physikalische Zeitschrift 9 358
[3]	Gans R 1920 Ann. de Phys. 63 382
[4]	Gans R 1922 Ann. de Phys. 66 396
[5]	Heisenberg W 1928 Z. Phys. A: Hadrons Nucl. 9 619
[6]	McKeehan L W 1930 Nature 126 952
[7]	Neel L 1932 Ann. de Phys. 17 5
[8]	Selwood P W 1933 J. Am. Chem. Soc. 55 3161
[9]	Neel L 1936 Ann. de Phys. 17 232
[10]	Bitter F 1938 Phys. Rev. 54 79
[11]	Neel L 1947 C. R. Acad. Sc. 224 1488
[12]	Neel L 1948 Ann. de Phys. 3 137
[13]	Anderson P W 1950 Phys. Rev. 79 705
[14]	Smart J S 1953 Rev. Modern Phys. 25 327
[15]	Rado G T, Folen V J 1960 J. Appl. Phys. 31 62
[16]	Haar D T, Lines M E 1962 Philosophical Transactions of the Royal Society of London Series A: Mathematical and Physical Sciences 254 521
[17]	Tsang T 1964 J. Chem. Phys. 40 729
[18]	Gianino P D, Grossbar N 1967 J. Appl. Phys. 38 129
[19]	Dionne G F 1970 J. Appl. Phys. 41 4874
[20]	Kaneyoshi T 1973 J. Phys. C: Solid State Phys. 6 3130
[21]	Southern B 1975 J. Phys. C: Solid State Phys. 8 L213
[22]	Idogaki T, Kimura I 1976 J. Phys. Soc. Jpn. 40 968
[23]	Ghatak S K, Moorjani K 1976 J. Phys. C: Solid State Phys. 9 L293
[24]	Dai D S, Qian K M 1987 Ferromagnetics (Vol. 1) (Beijing: Science Press) p102 (in Chinese) [戴道生, 钱昆明 1987 铁磁学(上册) (北京:科学出版社) 第102页]
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[26]	Lu J M, Yu T Y, Yang Y L 1993 Science in China A 36 624
[27]	Fähnle M 2000 J. Magn. Magn. Mater. 210 L1
[28]	Ai S T, Zhong W L, Wang C L, Wang J F, Zhang P L 2000 Acta Phys. Sin. 51 1739 (in Chinese) [艾树涛, 钟维烈, 王春雷, 王矜奉, 张沛霖 2000 51 1739]
[29]	Shen B G, Zhao J G, Zhan W S, Chen J C 1986 Acta Phys. Sin. 35 124 (in Chinese) [沈保根, 赵见高, 詹文山, 陈金昌 1986 35 124]
[30]	Liu P Q 1987 Acta Phys. Sin. 36 540 (in Chinese) [刘品清 1987 36 540]
[31]	Zhang C Z, Zhang G Y, Yu P 1992 Acta Phys. Sin. 41 1087 (in Chinese) [张存洲, 张光寅, 俞平 1992 41 1087]
[32]	Tang Q W, Shen G R, Fang L 2006 Acta Phys. Sin. 55 1346 (in Chinese) [唐秋文, 沈明荣, 方亮 2006 55 1346]
[33]	Yu H F, Zhang L S, Wu X H, Guo Y Q 2011 Acta Phys. Sin. 60 107306 (in Chinese) [于洪飞, 张鲁山, 吴小会, 郭永权 2011 60 107306]
[34]	Zhou C C, Liu F M, Ding P, Cai L G, Zhong W W, Zhang H 2010 Chin. Phys. B 19 067503
[35]	Ai S T 2005 Chin. Phys. 14 1246
[36]	Zhou X Y, Ge S H, Han X F, Zuo Y L, Xiao Y H, Wen Z C, Zhang L, Li M J 2009 Chin. Phys. B 18 4025
[37]	Zou J D, Li W, Shen B G 2009 Chin. Phys. B 18 4366
[38]	Huang Y N, Wang C J, Riande E 2005 J. Chem. Phys. 122 144502
[39]	Huang Y N, Zhang J L, Ying X N 2006 Prog. Phys. 26 359 (in Chinese) [黄以能, 张晋鲁, 应学农 2006 物理学进展 26 359]
[40]	Huang Y N 2006 J. Yili Normal Univ. 3 39 (in Chinese) [黄以能 2006 伊犁师范学院学报 3 39]
[41]	Zhang J L, Wang L N, Zhou H W, Zhang L L, Zhao X Y, Huang Y N 2010 Chin. Phys. B 19 056403
[42]	Zhang J L, Wang L N, Zhao X Y, Zhang L L, Zhou H W, Wei L, Huang Y N 2010 Chin. Phys. B 20 026401
[43]	Zhao X Y, Wang L N, Fan X H, Zhang L L, Wei L, Zhang J L, Huang Y N 2011 Acta Phys. Sin. 60 036403 (in Chinese) [赵兴宇, 王丽娜, 樊小辉, 张丽丽, 卫来, 张晋鲁, 黄以能 2011 60 036403]
[44]	Wang Q, Zhang X W, Gu B L 1989 Acta Phys. Sin. 38 1748 (in Chinese) [王强, 张孝文, 顾秉林 1989 38 1748]
[45]	Song X P, Zhang Y G, Luo X Q, Xu L F, Chao W X, Yang C P 2009 Acta Phys. Sin. 58 4980 (in Chinese) [宋学平, 张永光, 罗晓婧, 徐玲芳, 曹万强, 杨昌平 2009 58 4980]
[46]	Zhu C, Liu J M 2010 Chin. Phys. B 19 097702
[47]	Yue Z X, Wang X L, Zhang L Y, Yao X 1997 Chin. Phys. B 6 913

施引文献

[1]	Weiss P 1907 J. de Phys. 6 661
[2]	Weiss P 1908 Physikalische Zeitschrift 9 358
[3]	Gans R 1920 Ann. de Phys. 63 382
[4]	Gans R 1922 Ann. de Phys. 66 396
[5]	Heisenberg W 1928 Z. Phys. A: Hadrons Nucl. 9 619
[6]	McKeehan L W 1930 Nature 126 952
[7]	Neel L 1932 Ann. de Phys. 17 5
[8]	Selwood P W 1933 J. Am. Chem. Soc. 55 3161
[9]	Neel L 1936 Ann. de Phys. 17 232
[10]	Bitter F 1938 Phys. Rev. 54 79
[11]	Neel L 1947 C. R. Acad. Sc. 224 1488
[12]	Neel L 1948 Ann. de Phys. 3 137
[13]	Anderson P W 1950 Phys. Rev. 79 705
[14]	Smart J S 1953 Rev. Modern Phys. 25 327
[15]	Rado G T, Folen V J 1960 J. Appl. Phys. 31 62
[16]	Haar D T, Lines M E 1962 Philosophical Transactions of the Royal Society of London Series A: Mathematical and Physical Sciences 254 521
[17]	Tsang T 1964 J. Chem. Phys. 40 729
[18]	Gianino P D, Grossbar N 1967 J. Appl. Phys. 38 129
[19]	Dionne G F 1970 J. Appl. Phys. 41 4874
[20]	Kaneyoshi T 1973 J. Phys. C: Solid State Phys. 6 3130
[21]	Southern B 1975 J. Phys. C: Solid State Phys. 8 L213
[22]	Idogaki T, Kimura I 1976 J. Phys. Soc. Jpn. 40 968
[23]	Ghatak S K, Moorjani K 1976 J. Phys. C: Solid State Phys. 9 L293
[24]	Dai D S, Qian K M 1987 Ferromagnetics (Vol. 1) (Beijing: Science Press) p102 (in Chinese) [戴道生, 钱昆明 1987 铁磁学(上册) (北京:科学出版社) 第102页]
[25]	Mitsui T, Tatsuzaki I, Nakamura E (Translated by Ni G J, Wang Y L, Lin S W, Yin Q R) 1983 An Introduction to the Physics of Ferroelectrics (Beijing: Science Press) p208 (in Chinese) [三井利夫, 达崎达, 中村英二著 (倪冠军, 王勇令, 林盛卫, 殷庆瑞译) 1983 铁电物理学导论(北京:科学出版社) 第208页]
[26]	Lu J M, Yu T Y, Yang Y L 1993 Science in China A 36 624
[27]	Fähnle M 2000 J. Magn. Magn. Mater. 210 L1
[28]	Ai S T, Zhong W L, Wang C L, Wang J F, Zhang P L 2000 Acta Phys. Sin. 51 1739 (in Chinese) [艾树涛, 钟维烈, 王春雷, 王矜奉, 张沛霖 2000 51 1739]
[29]	Shen B G, Zhao J G, Zhan W S, Chen J C 1986 Acta Phys. Sin. 35 124 (in Chinese) [沈保根, 赵见高, 詹文山, 陈金昌 1986 35 124]
[30]	Liu P Q 1987 Acta Phys. Sin. 36 540 (in Chinese) [刘品清 1987 36 540]
[31]	Zhang C Z, Zhang G Y, Yu P 1992 Acta Phys. Sin. 41 1087 (in Chinese) [张存洲, 张光寅, 俞平 1992 41 1087]
[32]	Tang Q W, Shen G R, Fang L 2006 Acta Phys. Sin. 55 1346 (in Chinese) [唐秋文, 沈明荣, 方亮 2006 55 1346]
[33]	Yu H F, Zhang L S, Wu X H, Guo Y Q 2011 Acta Phys. Sin. 60 107306 (in Chinese) [于洪飞, 张鲁山, 吴小会, 郭永权 2011 60 107306]
[34]	Zhou C C, Liu F M, Ding P, Cai L G, Zhong W W, Zhang H 2010 Chin. Phys. B 19 067503
[35]	Ai S T 2005 Chin. Phys. 14 1246
[36]	Zhou X Y, Ge S H, Han X F, Zuo Y L, Xiao Y H, Wen Z C, Zhang L, Li M J 2009 Chin. Phys. B 18 4025
[37]	Zou J D, Li W, Shen B G 2009 Chin. Phys. B 18 4366
[38]	Huang Y N, Wang C J, Riande E 2005 J. Chem. Phys. 122 144502
[39]	Huang Y N, Zhang J L, Ying X N 2006 Prog. Phys. 26 359 (in Chinese) [黄以能, 张晋鲁, 应学农 2006 物理学进展 26 359]
[40]	Huang Y N 2006 J. Yili Normal Univ. 3 39 (in Chinese) [黄以能 2006 伊犁师范学院学报 3 39]
[41]	Zhang J L, Wang L N, Zhou H W, Zhang L L, Zhao X Y, Huang Y N 2010 Chin. Phys. B 19 056403
[42]	Zhang J L, Wang L N, Zhao X Y, Zhang L L, Zhou H W, Wei L, Huang Y N 2010 Chin. Phys. B 20 026401
[43]	Zhao X Y, Wang L N, Fan X H, Zhang L L, Wei L, Zhang J L, Huang Y N 2011 Acta Phys. Sin. 60 036403 (in Chinese) [赵兴宇, 王丽娜, 樊小辉, 张丽丽, 卫来, 张晋鲁, 黄以能 2011 60 036403]
[44]	Wang Q, Zhang X W, Gu B L 1989 Acta Phys. Sin. 38 1748 (in Chinese) [王强, 张孝文, 顾秉林 1989 38 1748]
[45]	Song X P, Zhang Y G, Luo X Q, Xu L F, Chao W X, Yang C P 2009 Acta Phys. Sin. 58 4980 (in Chinese) [宋学平, 张永光, 罗晓婧, 徐玲芳, 曹万强, 杨昌平 2009 58 4980]
[46]	Zhu C, Liu J M 2010 Chin. Phys. B 19 097702
[47]	Yue Z X, Wang X L, Zhang L Y, Yao X 1997 Chin. Phys. B 6 913

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