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中文摘要：
近年来，在纳米尺度的研究中应用到很多表面的技术和概念．然而，以往针对表面的研究中对象为单晶块体样品，这些研究结果将不再适用纳米材料．为了研究表面对纳米体系弹性响应的影响，选取较为简单的铜纳米薄片为研究对象，构建了铜（111）面和（001）面的薄片模型，使用第一性原理方法计算了铜纳米薄片的双轴泊松比，分析了纳米薄片与体材料的差异，研究不同厚度纳米薄片中表面对内层原子的影响．计算结果显示，表面原子层的双轴泊松比大于内部原子层，并且其收敛速度和数值大小均和薄片取向有关．根据双轴泊松比随厚度的变化特性，可以得到不同取向的纳米薄片中表面对弹性响应的临界厚度．
英文摘要：
Recently, with the development of nanotechnology, some surface techniques and concepts are being used to nanoscale objects. In the last decades, it has focused on surfaces of macroscopic single crystal samples. The measurement, the definition, and calculation of these quantities were based on two assumptions： strained surface atoms and strain-free substrates. Nanomaterials have different elastic properties from the bulk, and surface atoms have large effects on interior region. The elastic energy of a biaxial strained material depends on both the magnitude and the direction of the applied biaxial strain. The Poisson ratio and elastic energy of copper slabs under biaxial strain in （111） and （001） direction are studied by density-functional theory calculations. The results show that the changes in biaxial Poisson ratios depend on the orientation thickness, and the values of surface layers are larger than those of inner layers. The different critical thickness of the nano-sheet biaxial Poisson＇s ratio can be obtained by different orientations and thickness. The surface effect is significant if the thickness is smaller than the critical thick- ness.
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