根据压电本构方程和细观力学统计平均法,采用X射线衍射(XRD)测量Pb(Zr0.52Ti0.48)O3(PZT)铁电薄膜的残余应力。考虑激光沉积生长过程中,薄膜相变应力、热应力和本征应力对自由能的贡献,分析薄膜晶胞在晶体坐标系上的应力应变状态。由坐标转换将晶胞残余应力从晶体坐标系转换到样品坐标系得到任意取向晶粒的残余应力,通过取向平均得到薄膜样品坐标系上的残余应力。用脉冲激光沉积法(PLD)制备了不同厚度的PZT薄膜。利用X射线衍射分别采用细观力学统计平均法和传统sin2ψ法测量了PZT薄膜的残余应力。结果表明,两种结果在数值上是比较接近的(绝对差范围0.3～16.6 MPa),残余压应力随着膜厚的增加从96 MPa左右减少到45 MPa左右。最后讨论了细观力学统计平均法的优缺点。

Based on piezoelectric constitutive equations and statistic average of micro-mechanics, residual stresses in Pb(Zr0.52Ti0.48)O3 (PZT) ferroelectric thin films were measured by X-ray diffraction (XRD). Theoretically, it is considered that the intrinsic stress, thermal stress and transformation stress contribute to the minimum energy principium. The stress-strain relationship of the uint cell in the crystallite coordinate is studied. Residual stresses in any oriented crystallites are obtained via the transformation matrix from the crystallite coordinate to the sample coordinate, and residual stresses in thin films are statistically averaged by orientations. Experimentally, residual stresses in PZT thin films prepared by pulsed laser deposition (PLD) were evaluated by the statistic average of micro-mechanics and conventional sin2ψ method. The results evaluated by two models are very close, with absolute errors ranging from 0.3 MPa to 16.6 MPa. The residual stresses of PZT thin films are compressive and decrease from about 96 MPa to 45 MPa with the increase of the thickness. The measured results and advantages of the statistic average model of micro-mechanics are discussed.