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基于密度泛函微扰理论（DFPT）结合模守恒赝势方法进行晶格动力学模拟.得到了钇铝石榴石（YAG）的声子态密度、分波声子态密度和声子的色散谱.利用第一Brillouin区的特殊点取样方法，计算了YAG的比热容和布局数平均的声子群速度.在非谐相互作用下，利用Fermi黄金公式结合第一Brillouin区的特殊点取样方法，得出了YAG非谐声子平均自由程.综合考虑了两种声子散射机制，得到了YAG陶瓷的热导率.结果表明，对于YAG陶瓷，在低温时，晶界散射将对热阻起主要作用；在高于一定温度时，三声子相互作用对热阻的贡献将占主导地位.同时也从理论上证明了Sato等提出的在室温以上，YAG陶瓷与单晶的热导率的差异可以忽略的观点.所得到的热导率、比热容随温度的变化与实验结果很好地符合.
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关键词:
- 声子平均自由程 /
- 密度泛函微扰理论 /
- Y3Al5O12声子结构 /
- 热导率
Based on density functional perturbation theory (DFPT) combined with the norm-conserving pseudopotential method，the lattice dynamic simulation is presented. The total phonon density of states，partial phonon density of states and phonon dispersion spectrum of YAG are obtained. By using the special point sampling method within the first Brillouin zone，the special heat capacity and the population averaged group speed of phonon of YAG are calculated. The anharmonic phonon mean free path is calculated theoretically within anharmonic interaction and by using the Fermis golden rule scheme combined with the special point sampling method within the first Brillouin zone. We comprehensively considered two types of the phonon scattering mechanisms，the thermal conductivity of YAG ceramic is obtained. The result indicates that the grain boundary scattering plays a major role in the thermal resistance at low temperature in YAG ceramic，while the three-phonon interaction contribution to the thermal resistance will prevail above a certain temperature. Meanwhile，the viewpoint held by Y. Sato et al. that the difference of the thermal conductivity of between YAG ceramic and single crystal can be ignored above room temperature is theoretically proved. The temperature variations of the calculated thermal conductivity and special heat capacity agree well with the experimental results.-
Keywords:
- anharmonic phonon mean free path /
- density functional perturbation theory /
- Y3Al5O12 phonon structure /
- thermal conductivity
[1] ［1］Fields R C，Birnhaum M，Fincher L 1987 Appl. Phys. Lett. 51 1885
[2] ［2］Li S M，Huang W L 2005 Theory and Design of Laser Devices (2th) (Beijing: National Defense Industry Press) p179 (in Chinese) ［李适民、黄维玲 2005 激光器件原理与设计（第二版）（北京：国防工业出版社）第179页］
[3] ［3］Koechner W 2006 Solid State Laser Engineering (6th Ed.) (Berlin: Springer) p55
[4] ［4］Liu C，Ge J H，Xiang Z，Chen J 2008 Acta Phys. Sin. 57 1704 (in Chinese) ［刘崇、 葛剑虹、项震、陈军 2008 57 1704］
[5] ［5］Song X L，Guo Z，Li B B，Wang S Y，Cai D F，Wen J G 2009 Acta Phys. Sin. 58 1700 (in Chinese) ［宋小鹿、过振、李兵斌、王石语、蔡德芳、文建国 2009 58 1700］
[6] ［6］Tang B，Shu X J，Chen F L 2005 High Power Laser Part. Beams 17 71 (in Chinese) ［唐兵、束小建、陈发良 2005 强激光与粒子束 17 71］
[7] ［7］Zhang Y P，Zhang H Y，Zhong K，Wang P，Li X F，Yao J Q 2009 Acta Phys. Sin. 58 3193 (in Chinese) ［张玉萍、张会云、钟凯、王鹏、李喜福、姚建铨 2009 58 3193］
[8] ［8］Wang N，Lu Y T，Li X L，Jiao Z Y 2008 Acta Phys. Sin. 57 5632(in Chinese) ［王宁、陆雨田、李晓莉、焦志勇 2008 57 5632］
[9] ［9］Hurrell J P，Porto S P S，Chan I F，Mirta S S，Bauman P 1968 Phys. Rev. 173 851
[10] ］Stoddart P R，Ngoepe P E，Mjwara P M，Comis J D，Saunders G A 1993 J. Appl. Phys. 73 7298
[11] ］Srivastava G P 1990 The Physics of Phonons (Bristol: Adam Hilger)
[12] ］Baroni S，Gironcoli S，Corso A D，Giannozzi P 2001 Rev. Mod. Phys. 73 515
[13] ］Kohn W，Sham L J 1965 Phys. Rev. 140 A1133
[14] ］Perdew J P，Chevary J A，Vosko S H，Jackson K A，Pederson M R，Singh D J 1992 Phys. Rev. B 46 6671
[15] ］Monkhorst H J，Park J D 1976 Phys. Rev. B 13 5188
[16] ］AlShaikhi A，Srivastava G P 2007 Phys. Rev. B 76 195205
[17] ］Yogurtcu Y K，Miller A J，Saunders G A 1980 J. Phys. C 13 6585
[18] ］Euler F，Bruce J A 1965 Acta Crystallogr. 19 971
[19] ］Sato Y，Akiyama J，Taira T 2009 Opt. Mater. 31 720
[20] ］Ziman J M 1960 Electrons and Phonons (Oxford: Clarendon)
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[1] ［1］Fields R C，Birnhaum M，Fincher L 1987 Appl. Phys. Lett. 51 1885
[2] ［2］Li S M，Huang W L 2005 Theory and Design of Laser Devices (2th) (Beijing: National Defense Industry Press) p179 (in Chinese) ［李适民、黄维玲 2005 激光器件原理与设计（第二版）（北京：国防工业出版社）第179页］
[3] ［3］Koechner W 2006 Solid State Laser Engineering (6th Ed.) (Berlin: Springer) p55
[4] ［4］Liu C，Ge J H，Xiang Z，Chen J 2008 Acta Phys. Sin. 57 1704 (in Chinese) ［刘崇、 葛剑虹、项震、陈军 2008 57 1704］
[5] ［5］Song X L，Guo Z，Li B B，Wang S Y，Cai D F，Wen J G 2009 Acta Phys. Sin. 58 1700 (in Chinese) ［宋小鹿、过振、李兵斌、王石语、蔡德芳、文建国 2009 58 1700］
[6] ［6］Tang B，Shu X J，Chen F L 2005 High Power Laser Part. Beams 17 71 (in Chinese) ［唐兵、束小建、陈发良 2005 强激光与粒子束 17 71］
[7] ［7］Zhang Y P，Zhang H Y，Zhong K，Wang P，Li X F，Yao J Q 2009 Acta Phys. Sin. 58 3193 (in Chinese) ［张玉萍、张会云、钟凯、王鹏、李喜福、姚建铨 2009 58 3193］
[8] ［8］Wang N，Lu Y T，Li X L，Jiao Z Y 2008 Acta Phys. Sin. 57 5632(in Chinese) ［王宁、陆雨田、李晓莉、焦志勇 2008 57 5632］
[9] ［9］Hurrell J P，Porto S P S，Chan I F，Mirta S S，Bauman P 1968 Phys. Rev. 173 851
[10] ］Stoddart P R，Ngoepe P E，Mjwara P M，Comis J D，Saunders G A 1993 J. Appl. Phys. 73 7298
[11] ］Srivastava G P 1990 The Physics of Phonons (Bristol: Adam Hilger)
[12] ］Baroni S，Gironcoli S，Corso A D，Giannozzi P 2001 Rev. Mod. Phys. 73 515
[13] ］Kohn W，Sham L J 1965 Phys. Rev. 140 A1133
[14] ］Perdew J P，Chevary J A，Vosko S H，Jackson K A，Pederson M R，Singh D J 1992 Phys. Rev. B 46 6671
[15] ］Monkhorst H J，Park J D 1976 Phys. Rev. B 13 5188
[16] ］AlShaikhi A，Srivastava G P 2007 Phys. Rev. B 76 195205
[17] ］Yogurtcu Y K，Miller A J，Saunders G A 1980 J. Phys. C 13 6585
[18] ］Euler F，Bruce J A 1965 Acta Crystallogr. 19 971
[19] ］Sato Y，Akiyama J，Taira T 2009 Opt. Mater. 31 720
[20] ］Ziman J M 1960 Electrons and Phonons (Oxford: Clarendon)
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