Measurement of thin film elastic constants by X-ray diffraction

Faurie, D.; Renault, P.-O.; Bourhis, E. Le; Villain, P.; Goudeau, P.; Badawi, F.

doi:10.1016/j.tsf.2004.08.097

Cited by 35 publications

(27 citation statements)

References 17 publications

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“…Thus, the present experiments exemplify a significant dependency of the effective experimental electrocapillary coupling parameter on the roughness. In situ uniaxial tensile testing and X-ray diffraction experiments 44 have determined the value of Poisson's ratio n as 0.421 for gold thin films deposited on polyimide substrates, similar to our samples. We insert this Poisson's ratio of the gold thin film and the value of roughness factor calculated above from AFM data into the correction equation (eqn (10)).…”

Section: B Electrocapillary Coupling Coefficientsupporting

confidence: 80%

Electrocapillary coupling at rough surfaces

Deng

Gosslar

Smetanin

et al. 2015

Phys. Chem. Chem. Phys.

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We investigate the impact of the surface roughness on the experimental value of the electrocapillary coupling coefficient, B. This quantity relates the response of electrode potential, E, to tangential elastic strain, e, and also measures the variation of the surface stress, f, with the superficial charge density, q. We combine experiments measuring the apparent coupling coefficient B eff for gold thin film electrodes in weakly adsorbing electrolyte with data for the surface roughness determined by atomic force microscopy and by the capacitance ratio method. We find that even moderate roughness has a strong impact on the value of B eff . Analyzing the mechanics of corrugated surfaces affords a correction scheme yielding values of B that are invariant with roughness and that agree with expectations for the true coupling coefficient on ideal, planar surfaces. The correction is simple and readily applied to experiments measuring B eff from surface stress changes in cantilever bending studies or from the potential variation in dynamic electrochemo-mechanical analysis.

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Section: B Electrocapillary Coupling Coefficientsupporting

confidence: 80%

Electrocapillary coupling at rough surfaces

Deng

Gosslar

Smetanin

et al. 2015

Phys. Chem. Chem. Phys.

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“…Destructive techniques generally involve design of test apparatus or applying load to execute the measurement on thin films, such as tensile test [2][3][4][5], bulge test [6][7][8], bending test [9] and nanoindentation [10,11]. Among those techniques, nanoindentation is the most popular one that can simultaneously determine both hardness and elastic constant of a thin film.…”

Section: Introductionmentioning

confidence: 99%

Determination of average X-ray strain (AXS) on TiN hard coatings using cos2αsin2ψ X-ray diffraction method

Wang

Chuang

et al. 2015

Surface and Coatings Technology

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Keywords:Average X-ray strain (AXS) Average effective X-ray elastic constant (AEXEC) Cos 2 αsin 2 ψ method High energy X-ray Laser curvature method TiN hard coating For stress measurement on thin films and coatings using X-ray diffraction (XRD) methods, the uncertainty is commonly acknowledged to be from elastic constants. However, the uncertainty can be due to the statistical fluctuation of strain measured by XRD. In this study, we proposed a method where the average X-ray strain (AXS) was determined using cos 2 αsin 2 ψ XRD technique at several rotational (ϕ) angles to improve the accuracy of the measurement of X-ray stress or X-ray elastic constants (XECs). The major concept was to increase sampling volume by measuring X-ray strain at multiple rotational angles. TiN hard coating on Si (100) substrate was selected as the model system, where the residual stress was determined by laser curvature technique and the accompanying lattice strain was measured by cos 2 αsin 2 ψ method. The average effective elastic constant (AEXEC) could be attained by substituting the residual stress into the slope of AXS vs. cos 2 αsin 2 ψ plot. The AEXEC was served as an indicator to validate the AXS measurement. By substituting AEXEC in conventional sin 2 ψ XRD stress measurement, the deviation of the result from the stress obtained by laser curvature method was less than 7%, indicating that AXS effectively reduced the uncertainty in XECs and thus increased the accuracy of stress measurement. The concept of increasing sampling volume was also confirmed using synchrotron X-ray source, where the statistical fluctuation in X-ray strain could be further reduced by performing the measurement at all azimuthal direction. The experimental results showed that the uncertainty on XEC measurement by sin 2 ψ method was less than 10%, if sufficient sampling volume was provided. Furthermore, using AXS and elastic constant measured by nanoindentation (E NIP ) to calculate X-ray stress, the stress deviation from that by laser curvature method could be substantially reduced even down to 3% with sufficient sampling points. Therefore, AXS may serve as a convenient parameter, when combining with E NIP , in X-ray stress measurement, by which residual stress of hard coatings comparable to that by laser curvature method can be obtained without using XECs.

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“…A variety of techniques have been employed to measure the elastic constants of thin films, for example, tensile test [7][8][9], substrate curvature technique [10][11][12][13], bulge test [14][15][16][17], microbeam bending or deflection technique [18,19], nanoindentation (NIP) [20][21][22][23][24][25][26][27], resonant ultrasound spectroscopy [28][29][30], surface guided wave technique [31][32][33], X-ray diffraction (XRD) technique [34,35], combination of 2 sin ψ X-ray diffraction and laser curvature methods [36,37], combination of acoustic microscopy and nanoindentation method [38,39]. Among the above-mentioned methods, it is available in a few cases that the methods are able to simultaneously determine the Poisson's ratio and Young's modulus of elasticity for functional thin films and thin film structures, but usually either Poisson's ratio or modulus of elasticity should be assumed a priori for determining the other one.…”

Section: Introductionmentioning

confidence: 99%

A practical method for simultaneous determination of Poisson’s ratio and Young’s modulus of elasticity of thin films

et al. 2011

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In this paper, based on the exact analytical solution of axisymmetric deformation of the circular membrane fixed at its edge under the action of uniformly-distributed loads, we propose a new method to be able to simultaneously determine Poisson's ratio and Young's modulus of elasticity for thin films. We also present a set of exact formulas used for simultaneously determining Poisson's ratio and Young's modulus of elasticity for free-standing thin films or coating thin films without residual stresses or pre-tension. This method has the advantages of simplicity and reliability, and it doesn't involve the substrate effect.

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Measurement of thin film elastic constants by X-ray diffraction

Cited by 35 publications

References 17 publications

Electrocapillary coupling at rough surfaces

Electrocapillary coupling at rough surfaces

Determination of average X-ray strain (AXS) on TiN hard coatings using cos2αsin2ψ X-ray diffraction method

A practical method for simultaneous determination of Poisson’s ratio and Young’s modulus of elasticity of thin films

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