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采用密度泛函理论的第一性原理平面波赝势方法，基于虚拟晶体势函数近似，通过计算Ir-xRh（x=0，5，10，20，30，40，50，60，70，80，90，100）合金的弹性常数、体积模量、剪切模量、杨氏模量、泊松比等力学常数、电荷密度和能态密度，研究Rh含量对Ir-Rh合金力学性能的影响. 通过实验对计算结果加以验证，证明将虚晶近似法运用在Ir-Rh合金力学性能的计算中是合理的. 研究结果表明，Ir-Rh合金的强度和硬度随Rh含量的升高迅速增大，在Ir-10 Rh 处达到最大值后快速下降到Ir-40 Rh处后先缓慢上升再缓慢下降. Rh的添加会引起材料脆化，其脆性大小随着Rh含量的升高先增大后减小，在Ir-50 Rh处达到最大值. 另外，计算了纯Ir，Ir-10 Rh，Ir-50 Rh、纯Rh的电荷密度、Ir和Rh的差分电荷密度以及能态密度，结果表明在铱铑合金中存在一种伪共价键，从而导致其力学性质的异常.Platinum metal Ir-Rh alloy presents a promising candidate as future ultra-high-temperature gas turbine material due to its excellent high-temperature properties. In this paper, the mechanical properties of Ir-xRh (x=0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100) alloys with different rhodium content are investigated. Self-consistent, periodic, density functional theory calculations, Perdew-Burke-Ernzerhof functional, virtual crystal approximation are employed to calculate the elastic constants C11, C12, C44, Cauchy pressure (C12-C44), Young modulus E, shear modulus G, bulk modulus B and the ratio G/B, anisotropic factor A, and strain energy of dislocation per unit length. These parameters are adopted to characterize and assess the effect of Rh content on the mechanical property of Ir-Rh alloy. The results indicate that it is reasonable to use the virtual crystal approximation to calculate the mechanical properties of Ir-Rh alloys. The Young modulus E, shear modulus G and bulk modulus B increase rapidly with the increase of rhodium content, and the maximum value is reached at rhodium content 10%. Then it fast dereases down to a minimum value at 40% after the slowly rises and then slowly drops down. It is found to be in remarkable agreement with the strain energy of dislocation per unit length. This indirectly explains its changing trend. The Cauchy pressure (C12-C44), G/B value and the Poisson's ratio reflect the change of the brittleness of the alloy. Therefore, we can come to a conclusion: the addition of Rh can cause the brittleness of the Ir-Rh alloys. The value of the brittleness first increases and then decreases with the increase of Rh content, and its maximum value is reached at 50%. The charge densities and the densities of states of pure Ir, Ir-10Rh, Ir-50Rh and pure Rh are calculated and compared. At the same time, we also establish a 2 2 1 solid solution supercell structure of Ir-Rh alloy and calculate its differential charge density. The results show that in the Ir-Rh alloys exists a pseudo covalent bond, which leads to the abnormal mechanical properties. The pseudo covalent bond is not a metal bond nor a covalent bond but a kind of transition bond or a mixed type. Finally, the experimental results show that the calculation method is reasonable and it can play an important role in understanding the microscopic mechanism of the abnormal mechanical properties of Ir-Rh alloys.
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Keywords:
- virtual crystal approximation /
- mechanical property /
- charge density
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[2] Ohriner E K 2008 Platinum Met. Rev. 52 186
[3] Xiang C S, Ge Y, Zhang H L, Li Z F, Huang Y P, Tang H P {2009 Mater. Rev. 23 7 (in Chinese) [向长淑, 葛渊, 张晗亮, 李增峰, 黄愿平, 汤慧萍 2009 材料导报 23 7]
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[5] Sekido N, Hoshino A, Fukuzaki M, Maruko T, Yamabe-Mitarai Y 2011 J. Phase Equilib. Diff. 32 219
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[7] Wang Y, Lu T C, Wang Y Z, Yue S L, Qi J Q, Pan L 2012 Acta Phys. Sin. 61 167101 (in Chinese) [王颖, 卢铁城, 王跃忠, 岳顺利, 齐建起, 潘磊 2012 61 167101]
[8] Chen S, Lu J S, Xie M, Xia L, Pan Y, Hu J Q {2015 Rare Metals 39 276 (in Chinese) [陈松, 陆建生, 谢明, 夏璐, 潘勇, 胡洁琼 2015 稀有金属 39 276]
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[10] Wang L X, Yao S, Wen B {2014 J. At. Mol. Phys. 31 305 (in Chinese) [王兰馨, 姚山, 温斌 2014 原子与分子 31 305]
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[14] Wang Y L, Cui H L, Yu B R, Chen X R 2008 Commun. Theor. Phys. 49 489
[15] Hartnett T M, Maguire E A, Gentilman R L, Corbin N D, Mccauley J M 1982 Cera. Eng. Sci. Proc. 3 67
[16] L L H 2013 M. S. Dissertation (Kunming: Kunming University of Science and Technology) (in Chinese) [吕连灏 2013 硕士学位论文 (昆明: 昆明理工大学)]
[17] Wang P 2014 M. S. Dissertation (Kunming: Kunming University of Science and Technology) (in Chinese) [王鹏 2014 硕士学位论文 (昆明: 昆明理工大学)]
[18] Hu J Q 2012 M. S. Thesis (Kunming: Kunming Institute of Precious Metals) (in Chinese) [胡洁琼 2012 硕士学位论文 (昆明:昆明贵金属研究所)]
[19] Liu Y, Chen D Q, Chen J L, Dai H, Li Z L, Luo X M, Li W, Xu K 2014 Precious Metal. 35 40 (in Chinese) [刘毅, 陈登权, 陈家林, 戴华, 李泽丽, 罗锡明, 李伟, 许昆 2014 贵金属 35 40]
[20] Wen X Z 1996 Crystal Defects and Metal Strength (Changsha: Central South University Press) p55 (in Chinese) [文先哲 1996 晶体缺陷与金属强度 (长沙: 中南大学出版社)第55页]
[21] Feng D 1998 Metal Physics (Beijing:Science Press) p1 (in Chinese) [冯端 1998 金属物理学(北京: 科学出版社) 第1页]
[22] Pugh S F 1954 Philos. Mag. 45 823
[23] Cornish L A, Svss R, Douglas A, Chown L H, Glaner L 2009 Platinum Metals Rev. 53 2
[24] Zhang K, Jiang Y Y, Li K S, Li H, Yu D B 2014 J. Alloy. Compd. 611 386
[25] Wei Z, Zhai D, Shao X H, Lu Y, Zhang P 2015 Chin. Phys. B 24 043102
[26] Akola J, Jones R O 2009 Phys. Rev. B 79 134118
[27] Zhou W, Wu H, Yildirim T 2007 Phys. Rev. B 76 184113
[28] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
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[1] Yamabe-mitarai Y, Ro Y, Maruko T, Harada H 1998 Metall. Mater. Trans. A 29 537
[2] Ohriner E K 2008 Platinum Met. Rev. 52 186
[3] Xiang C S, Ge Y, Zhang H L, Li Z F, Huang Y P, Tang H P {2009 Mater. Rev. 23 7 (in Chinese) [向长淑, 葛渊, 张晗亮, 李增峰, 黄愿平, 汤慧萍 2009 材料导报 23 7]
[4] Chen K, Zhao L R, Tse J S, Rodgers J R {2004 Phys. Lett. A 33 400
[5] Sekido N, Hoshino A, Fukuzaki M, Maruko T, Yamabe-Mitarai Y 2011 J. Phase Equilib. Diff. 32 219
[6] Li D H, Su W J, Zhu X L 2012 Acta Phys. Sin. 61 23103 (in Chinese) [李德华, 苏文晋, 朱晓玲 2012 61 23103]
[7] Wang Y, Lu T C, Wang Y Z, Yue S L, Qi J Q, Pan L 2012 Acta Phys. Sin. 61 167101 (in Chinese) [王颖, 卢铁城, 王跃忠, 岳顺利, 齐建起, 潘磊 2012 61 167101]
[8] Chen S, Lu J S, Xie M, Xia L, Pan Y, Hu J Q {2015 Rare Metals 39 276 (in Chinese) [陈松, 陆建生, 谢明, 夏璐, 潘勇, 胡洁琼 2015 稀有金属 39 276]
[9] Liu Y C, Zhou D W, Gao L J, Peng P 2013 Rare Metal Mat. Eng. 42 578 (in Chinese) [刘友成, 周惦武, 高丽洁, 彭平 2013 稀有金属材料与工程 42 578]
[10] Wang L X, Yao S, Wen B {2014 J. At. Mol. Phys. 31 305 (in Chinese) [王兰馨, 姚山, 温斌 2014 原子与分子 31 305]
[11] Liu Y C, Zhou D W, Gao L J {2013 Rare Metals and Cemented Carbides 41 47 (in Chinese) [刘友成, 周惦武, 高丽洁 2013 稀有金属与硬质合金 41 47]
[12] Chen L {2012 Rare Metal Mat. Eng. 41 290 (in Chinese) [陈律 2012 稀有金属材料与工程 41 290]
[13] Ding Y C, Xiao B 2011 Acta Phys. Chim. Sin. 27 1261 (in Chinese) [丁迎春, 肖冰 2011 物理化学学报 27 1261]
[14] Wang Y L, Cui H L, Yu B R, Chen X R 2008 Commun. Theor. Phys. 49 489
[15] Hartnett T M, Maguire E A, Gentilman R L, Corbin N D, Mccauley J M 1982 Cera. Eng. Sci. Proc. 3 67
[16] L L H 2013 M. S. Dissertation (Kunming: Kunming University of Science and Technology) (in Chinese) [吕连灏 2013 硕士学位论文 (昆明: 昆明理工大学)]
[17] Wang P 2014 M. S. Dissertation (Kunming: Kunming University of Science and Technology) (in Chinese) [王鹏 2014 硕士学位论文 (昆明: 昆明理工大学)]
[18] Hu J Q 2012 M. S. Thesis (Kunming: Kunming Institute of Precious Metals) (in Chinese) [胡洁琼 2012 硕士学位论文 (昆明:昆明贵金属研究所)]
[19] Liu Y, Chen D Q, Chen J L, Dai H, Li Z L, Luo X M, Li W, Xu K 2014 Precious Metal. 35 40 (in Chinese) [刘毅, 陈登权, 陈家林, 戴华, 李泽丽, 罗锡明, 李伟, 许昆 2014 贵金属 35 40]
[20] Wen X Z 1996 Crystal Defects and Metal Strength (Changsha: Central South University Press) p55 (in Chinese) [文先哲 1996 晶体缺陷与金属强度 (长沙: 中南大学出版社)第55页]
[21] Feng D 1998 Metal Physics (Beijing:Science Press) p1 (in Chinese) [冯端 1998 金属物理学(北京: 科学出版社) 第1页]
[22] Pugh S F 1954 Philos. Mag. 45 823
[23] Cornish L A, Svss R, Douglas A, Chown L H, Glaner L 2009 Platinum Metals Rev. 53 2
[24] Zhang K, Jiang Y Y, Li K S, Li H, Yu D B 2014 J. Alloy. Compd. 611 386
[25] Wei Z, Zhai D, Shao X H, Lu Y, Zhang P 2015 Chin. Phys. B 24 043102
[26] Akola J, Jones R O 2009 Phys. Rev. B 79 134118
[27] Zhou W, Wu H, Yildirim T 2007 Phys. Rev. B 76 184113
[28] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
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