以石墨烯为例分析二维六角晶格结构及振动模式
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摘要
石墨烯因其独特的六角晶格结构,使其具有优异的力、热、光、电等特性,成为目前应用研究最广泛的新型材料之一.本文从固体物理学的教学角度出发,以单层石墨烯的晶格结构为例,采用图像的形式描述了二维六角晶格的正格子原胞和基矢、倒格子原胞和基矢、q空间和第一布里渊区,并推导了二维六角晶格的振动模式.
Graphene has become one of the most widely used new materials because of its unique hexagonal lattice structure,which has excellent mechanical,thermal,optical and electrical properties.From the point of view of solid state physics teaching,taking the lattice structure of single-layer graphene as an example,this paper describes the normal lattice primitive cell and base vector,inverted lattice primitive cell and base vector,wave vector space and first Brillouin region of two-dimensional hexagonal lattice in the form of images,and derives the vibration mode of two-dimensional hexagonal lattice.
Graphene has become one of the most widely used new materials because of its unique hexagonal lattice structure,which has excellent mechanical,thermal,optical and electrical properties.From the point of view of solid state physics teaching,taking the lattice structure of single-layer graphene as an example,this paper describes the normal lattice primitive cell and base vector,inverted lattice primitive cell and base vector,wave vector space and first Brillouin region of two-dimensional hexagonal lattice in the form of images,and derives the vibration mode of two-dimensional hexagonal lattice.
引文
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[2] 黄昆固体物理学[M].韩汝琦,改.北京:高等教育出版社,1988.
[3] 梁先庆.石墨烯能带结构的紧束缚近似计算[J].广西物理,2011(1):7-10.
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[5] 施仲诚,房鸿.紧束缚近似方法在计算石墨烯能带中的应用[J].西安工业大学学报,2011,31(6):528-532.
[6] 王晴晴,宫昊,程荣龙,等.晶格振动模式密度研究[J],大学物理,2018,37 (8):4-7.
[7] 任亚杰,黄文登.石墨烯的晶格振动与导热机理的研究[J].陕西理工大学学报(自然科学版),2014(5):68-72.
[8] 任吉昌.石墨烯及相关结构物理性质的调控之第一性原理计算设计[D].中国科学技术大学,2015.
[9] Borysenko K M,Mullen J T,Barry E A,et al.First-principles analysis of electron-phonon interactions in graphene[J].2009,81(12):121412.
[10] Plachinda P,Evans D,Solanki R.Thermal Conductivity of Graphene Nanoribbons:Effect of the Edges and Ribbon Width[J].Journal of Heat Transfer,2012,134(134):122401.
[2] 黄昆固体物理学[M].韩汝琦,改.北京:高等教育出版社,1988.
[3] 梁先庆.石墨烯能带结构的紧束缚近似计算[J].广西物理,2011(1):7-10.
[4] 黄铁铁.石墨烯电子能带结构的计算[J].湖南理工学院学报(自然科学版),2010,23(2):42-44.
[5] 施仲诚,房鸿.紧束缚近似方法在计算石墨烯能带中的应用[J].西安工业大学学报,2011,31(6):528-532.
[6] 王晴晴,宫昊,程荣龙,等.晶格振动模式密度研究[J],大学物理,2018,37 (8):4-7.
[7] 任亚杰,黄文登.石墨烯的晶格振动与导热机理的研究[J].陕西理工大学学报(自然科学版),2014(5):68-72.
[8] 任吉昌.石墨烯及相关结构物理性质的调控之第一性原理计算设计[D].中国科学技术大学,2015.
[9] Borysenko K M,Mullen J T,Barry E A,et al.First-principles analysis of electron-phonon interactions in graphene[J].2009,81(12):121412.
[10] Plachinda P,Evans D,Solanki R.Thermal Conductivity of Graphene Nanoribbons:Effect of the Edges and Ribbon Width[J].Journal of Heat Transfer,2012,134(134):122401.