Determination of the thickness of titanium films on glass substrate by nanoindentation tests
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termination of the thickness of titanium films on glass substrate by nanoindentation tests Tao Wen School of Engineering and Technology, China University of Geosciences at Beijing, Beijing 100084, People’s Republic of China; and State Key Laboratory of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of China
Jianghong Gong State Key Laboratory of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of China
Zhijian Penga) School of Engineering and Technology, China University of Geosciences at Beijing, Beijing 100084, People’s Republic of China
Danyu Jiang Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, People’s Republic of China
Chengbiao Wang and Zhiqiang Fu School of Engineering and Technology, China University of Geosciences at Beijing, Beijing 100084, People’s Republic of China
Hezhuo Miao State Key Laboratory of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of China (Received 7 May 2010; accepted 4 October 2010)
We reported a simple and convenient method to determine the film thickness by nanoindentation tests. This method starts from the analysis of the unloading portion of the measured nanoindentation loaddisplacement curves according to a quadratic polynomial, P 5 a(h hf)2 P0, where P is the indentation load, P0 is the virtual load used to consider the effect of the residual contact stress, h is the indenter displacement (penetration depth), hf is the final displacement after complete unloading which should be determined by curve fitting, and a is a constant. Then the best-fit value of the parameter P0 is plotted as a function of the maximum penetration depth, hmax. Such a P0 versus hmax curve may pass through a minimum, and hmax corresponding to this minimum would be equal to the film thickness value.
The nanoindentation test has been established as an important and powerful tool for characterizing the nearsurface mechanical properties of solid materials. There has been extensive literature concerning the application of nanoindentation tests, and almost all the studies have centered on the determination of hardness, H, and elastic modulus, E, for the test materials.1–5 In this communication, a fresh application of nanoindentation tests in the film-substrate system will be reported. We will show below that the film thickness can be extracted by analyzing the nanoindentation load-displacement curve. Similar to the conventional applications of the nanoindentation test, our study will also start from the analysis a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2010.56 J. Mater. Res., Vol. 26, No. 3, Feb 14, 2011
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of the unloading portion of the indentation load-displacement curve. The most frequently used function
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