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We present a theoretical analysis on the applicability of Vegards linear rule in InxAl1-xN alloys in relation to strain related elastic and piezoelectric properties. We derive the elastic stiffness constants and biaxial coefficients, as well as the respective deviations from linearity (Vegards rule) by using ab initio calculations. The stress-strain relationships to extract composition from the lattice parameters are derived in different coordinate systems for InxAl1-xN with an arbitrary surface orientation. The error made in the composition extracted from the lattice parameters if the deviations from linearity are not taken into account is discussed for different surface orientations, compositions and degrees of strain in the InxAl1-xN films. The strain induced piezoelectric polarization is analyzed for InxAl1-xN alloys grown pseudomorphically on GaN. The polarization values are compared with those obtained from our experimental data for the lattice parameters. We establish the importance of the deviation from linearity to correctly determine the piezoelectric polarization and also a smooth, not particular piezoelectric response at GaN lattice matched conditions.<p>Funding Agencies|Swedish Research Council (VR)|2010-3848|Swedish Governmental Agency for Innovation Systems (VINNOVA) under the VINNMER international qualification program|2011-03486|FCT Portugal|PTDC/FIS/100448/2008|Linkoping Linnaeus Initiative on Nanoscale Functional Materials (LiLiNFM)||</p

physical review. b, condensed matter and materials physics

Elastic constants, composition, and piezolectric polarization in In<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mi>x</mml:mi></mml:msub></mml:math>Al<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math>N: From<i>ab initio</i>calculations to experimental implications for the applicability of Vegard's …

Elastic constants, composition, and piezolectric polarization in InxAl1−xN: Fromab initiocalculations to experimental implications for the applicability of Vegard's …