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推导出几何平均模型并使用这个模型计算了Cu和TiN的弹性矩阵和x射线弹性常数,计算的结果处于Voigt和Reuss模型所定义的多晶材料弹性常数的有效区间内,与Hill、Kroner模型的计算结果的最大相对误差小于4%,TiN[422]方向杨氏模量的计算值为424.3GPa,与其实验值411土45Gpa基本一致.

参考文献

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[3] V.M.Hauk, Stress Evaluation on Materials Having Non-Linear Lattice Strain Distributions, Adv. In X-rayAnal, 27, 101(1983)
[4] 于力根,白辰东,陈华,徐可为,何家文,薄膜应力分析中的应力梯度的影响,薄膜科学与技术,6(3),173(1993)(YU Ligen, BAI Chendong, CHEN Hua, XU Kewei, HE Jiawen, Effect of the Stress Gradient on X-ray Stress Analysis of Thin Films, Scinece and Technology of Thin Film, 6(3), 173(1993))
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[6] 张铭,何家文,具有丝织构TiN薄膜弹性常数的计算,自然科学进展,11(2),169(2001)(ZHANG Ming, HE Jiawen, Calculation of the Elastic Constants of TiN with the Fiber Texture, Progress in Natural Science, 11(2), 169(2001))
[7] 于利根,何家文,B.C.Hendrix,择尤取向对X射线应力测试的影响,金属学报,34(6),667(1998)(YU Ligen, HE Jiawen, The Effect of Preferred Orientation on X-ray Stress Measurement, Acta Metallurgica Sinica, 34(6), 667(1998))
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[12] W.Kress, P. Roedhammer, H.Bilz, W.Teuchent, A.N.Christensen, Phonon Anomalies in Transition-Metal Nitride: TiN, Phys. Rev., 17, 111(1978)
[13] D.S.Rickerby, A.M.JonesM, B.A.Bellamy, Internal Stress in Titanium Nitride Coatings: Modeling of Complex Stress Systems, Surf. Coat.Technol., 36, 661(1988)
[14] J.A.Sue, X-ray Elastic Constants and Residual Stresses of Textured Titanium Nitride Coatings,Surf. Coat. Techn., 54, 154(1992)
[15] 于利根,择优取向材料弹性参量计算及薄膜应力测定,博士学位论文,西安交通大学(1995)(YU Ligen, Calculation for elastie constants of texture material and measurement for residnal stresses of thin films, Doctor thesis, Xi'an Jiaotong University(1995))
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