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Naocrystalline (nc) material shows lower thermal conductivity than its coarse grain counterpart, which restricts its engineering applications. In order to study the effects of grain size and grain boundary on the thermal conductivity of nc material, nc copper is prepared by the high pressure sintering method. The pure nc Cu powder is used as the starting material, and the high pressure sintering experiment is carried out under a DS614 MN cubic press. Prior to the high pressure sintering experiment, the Cu powders are first pre-compressed into cylinders, then they are compressed under 5 GPa at temperatures ranging from 700 to 900 ℃ for 30 min. The grain size and micro-structural characteristics are investigated by the scanning electron microscope (SEM) and X-ray diffraction (XRD). The results show that the sintered Cu bulk material can achieve nearly full densification with a relative density of 99.98% and the grain growth of the Cu particles is effectively inhibited. The thermal conductivity measurement is performed by NETZSCH LFA-427 at 300 K and 45% RH. The test results show that the thermal conductivity of nc copper is lower than that of its coarse grain counterpart, and the thermal conductivity increases with grain size increasing. For example, as the grain size increases from 390 to 715 nm, the corresponding thermal conductivity increases from 200.63 to 233.37 Wm-1K-1, which are 53.4% and 60.6% of the thermal conductivity of the coarse grain copper, respectively. For a better understanding of the effects of grain boundary and size on the thermal conductivity of nc material, a simple modified model, with special emphasis on the contributions of electron and phonon conduction, is presented by incorporating the concept of the Kapitza resistance into an effective medium approach. The theoretical calculations are in good agreement with our experimental results. The combination of experimental results and theoretical calculations concludes that the thermal conductivity of nc material is weakened mainly by two factors: the grain boundary-electron (phonon) scattering on the grain boundary and the electron (phonon)-electron (phonon) scattering in the grain interior. That is to say, the thermal resistance of nc material can be divided into two parts: one is the intragranular thermal resistance from the grain, the other is the intergranular thermal resistance from the grain boundaries. As is well known, when the grain size decreases to a nano-range, the volume fraction of the grain boundary presents a sharp increase, and the intergranular thermal resistance from the grain boundaries becomes more important.
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Keywords:
- nanocrystalline Cu /
- thermal conductivity /
- grain size /
- Kapitza resistance
[1] Bai X M, Zhang Y F, Tonks M R 2015 Acta Mater. 85 95
[2] Wang S, Brooks I, McCrea J L, Palumbo G, Cingara G, Erb U 2011 Adv. Mater. Res. 409 561
[3] Li Q H, Chen S S, Zeng J H 2013 Chin. Phys. B 22 120204
[4] Benkassem S, Capolungo L, Cherkaoui M 2007 Acta Mater. 55 3563
[5] Angadi M A, Watanabe T, Bodapati A, Xiao X C, Auciello O, Carlisle J A, Eastman J A, Keblinski P, Schelling P K, Phillpot S R 2006 J. Appl. Phys. 99 114301
[6] Tritt T M, Subramanian M A 2006 Mater. Res. Soc. Bull. 31 188
[7] Maldovan M 2011 J. Appl. Phys. 110 114310
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[9] Biswas K, He J, Zhang Q, Wang G, Uher C, Dravid V, Kanatzidis M 2011 Nat. Chem. 3 160
[10] Khader M M, Kumar S, Abbasbandy S 2013 Chin. Phys. B 22 110201
[11] Chen G (translated by Zhou H C, Li B S, Huang Z F, Liu H B) 2014 Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons (Beijing: Tsinghua University Press) pp14-15 (in Chinese) [陈刚 著 (周怀春, 李冰水, 黄志峰, 刘华波 译) 2014 纳米尺度能量输运和转换: 对电子、分子、声子和光子的统一处理 (北京: 清华大学出版社)第14-15页]
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[13] Yang H S, Bai G R, Thompson L J, Eastman J A 2002 Acta Mater. 50 2309
[14] Hao Q 2012 J. Appl. Phys. 111 014309
[15] Soyez G, Eastman J A, Thompson L J, Bai G R, Baldo P M, McCormick A W 2000 Appl. Phys. Lett. 77 1155
[16] Hua C Y, Minnich A J 2014 Semicond. Sci. Tech. 29 1
[17] Bux S K, Blair R G, Gognal P K, Lee H, Chen G, Dresselhaus M S, Kaner R B, Fleurial J P 2009 Adv. Funct. Mater. 19 2445
[18] Joshi G, Lee H, Lan Y C, Wang X W, Zhu G H, Wang D Z, Gould R W, Cuff D C, Tang M Y, Dresselhaus M S, Chen G, Ren Z F 2008 Nano Lett. 8 4670
[19] Nan C W, Birringer R 1998 Phys. Rev. B 57 8264
[20] Yao W J, Cao B Y, Yun H M, Chen B M 2014 Nanoscale Res. Lett. 9 408
[21] Dong H, Wen B, Melnik R 2014 Sci. Rep.-UK 4 7037
[22] Chen X F, He D W, Wang F L, Zhang J, Li Y J, Fang L M, Lei L, Kou Z L 2009 Chin. J. High Pressure Phys. 23 98 (in Chinese) [陈晓芳, 贺端威, 王福龙, 张剑, 李拥军, 房雷鸣, 雷力, 寇自力 2009 高压物理学报 23 98]
[23] Wang S, Brooks I, McCrea J L, Palumbo G, Cingara G, Erb U 2011 Adv. Mater. Res. 409 561
[24] Jeng M S, Yang R G, David S, Chen G 2008 J. Heat Transfer 130 042410
[25] Wang Z, Alaniz J E, Jang W, Garay J E, Dames C 2011 Nano Lett. 11 2206
[26] Hua Y C, Dong Y, Cao B Y 2013 Acta Phys. Sin. 62 244401 (in Chinese) [华钰超, 董源, 曹炳阳 2013 物理学报 62 244401]
[27] Joshi A A, Majumdar A 1993 J. Appl. Phys. 74 31
[28] Heino P, Ristolainen E 2003 Microelectron. J. 34 773
[29] Han G Z, Guo Z Y 2007 Proc. Chin. Soc. Electrical Eng. 17 98 (in Chinese) [韩光泽, 过增元 2007 中国电机工程学报 17 98]
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[1] Bai X M, Zhang Y F, Tonks M R 2015 Acta Mater. 85 95
[2] Wang S, Brooks I, McCrea J L, Palumbo G, Cingara G, Erb U 2011 Adv. Mater. Res. 409 561
[3] Li Q H, Chen S S, Zeng J H 2013 Chin. Phys. B 22 120204
[4] Benkassem S, Capolungo L, Cherkaoui M 2007 Acta Mater. 55 3563
[5] Angadi M A, Watanabe T, Bodapati A, Xiao X C, Auciello O, Carlisle J A, Eastman J A, Keblinski P, Schelling P K, Phillpot S R 2006 J. Appl. Phys. 99 114301
[6] Tritt T M, Subramanian M A 2006 Mater. Res. Soc. Bull. 31 188
[7] Maldovan M 2011 J. Appl. Phys. 110 114310
[8] Seo D, Ogawa K, Sakaguchi K, Miyamoto N, Tsuzuki Y 2012 Surf. Coat. Tech. 207 233
[9] Biswas K, He J, Zhang Q, Wang G, Uher C, Dravid V, Kanatzidis M 2011 Nat. Chem. 3 160
[10] Khader M M, Kumar S, Abbasbandy S 2013 Chin. Phys. B 22 110201
[11] Chen G (translated by Zhou H C, Li B S, Huang Z F, Liu H B) 2014 Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons (Beijing: Tsinghua University Press) pp14-15 (in Chinese) [陈刚 著 (周怀春, 李冰水, 黄志峰, 刘华波 译) 2014 纳米尺度能量输运和转换: 对电子、分子、声子和光子的统一处理 (北京: 清华大学出版社)第14-15页]
[12] Guo Z Y, Gao B Y, Zhu H Y, Zhang Q G 2007 Acta Phys. Sin. 56 3306 (in Chinese) [过曾元, 曹炳阳, 朱宏晔, 张清光 2007 物理学报 56 3306]
[13] Yang H S, Bai G R, Thompson L J, Eastman J A 2002 Acta Mater. 50 2309
[14] Hao Q 2012 J. Appl. Phys. 111 014309
[15] Soyez G, Eastman J A, Thompson L J, Bai G R, Baldo P M, McCormick A W 2000 Appl. Phys. Lett. 77 1155
[16] Hua C Y, Minnich A J 2014 Semicond. Sci. Tech. 29 1
[17] Bux S K, Blair R G, Gognal P K, Lee H, Chen G, Dresselhaus M S, Kaner R B, Fleurial J P 2009 Adv. Funct. Mater. 19 2445
[18] Joshi G, Lee H, Lan Y C, Wang X W, Zhu G H, Wang D Z, Gould R W, Cuff D C, Tang M Y, Dresselhaus M S, Chen G, Ren Z F 2008 Nano Lett. 8 4670
[19] Nan C W, Birringer R 1998 Phys. Rev. B 57 8264
[20] Yao W J, Cao B Y, Yun H M, Chen B M 2014 Nanoscale Res. Lett. 9 408
[21] Dong H, Wen B, Melnik R 2014 Sci. Rep.-UK 4 7037
[22] Chen X F, He D W, Wang F L, Zhang J, Li Y J, Fang L M, Lei L, Kou Z L 2009 Chin. J. High Pressure Phys. 23 98 (in Chinese) [陈晓芳, 贺端威, 王福龙, 张剑, 李拥军, 房雷鸣, 雷力, 寇自力 2009 高压物理学报 23 98]
[23] Wang S, Brooks I, McCrea J L, Palumbo G, Cingara G, Erb U 2011 Adv. Mater. Res. 409 561
[24] Jeng M S, Yang R G, David S, Chen G 2008 J. Heat Transfer 130 042410
[25] Wang Z, Alaniz J E, Jang W, Garay J E, Dames C 2011 Nano Lett. 11 2206
[26] Hua Y C, Dong Y, Cao B Y 2013 Acta Phys. Sin. 62 244401 (in Chinese) [华钰超, 董源, 曹炳阳 2013 物理学报 62 244401]
[27] Joshi A A, Majumdar A 1993 J. Appl. Phys. 74 31
[28] Heino P, Ristolainen E 2003 Microelectron. J. 34 773
[29] Han G Z, Guo Z Y 2007 Proc. Chin. Soc. Electrical Eng. 17 98 (in Chinese) [韩光泽, 过增元 2007 中国电机工程学报 17 98]
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