以六硼化镧粉末作为标准样品,根据衍射拟合结果分离出任意角度下的仪器宽化值。对焙烧后的氧化铝样品进行X射线衍射分析,结果表明该氧化铝样品为α晶型结构。对样品因素（晶粒细化、微观应变）引起的宽化值分别使用高斯分布法和Hall法进行拟合,计算出氧化铝样品的平均晶粒尺寸。将计算结果与谢乐公式计算出的各晶面晶粒尺寸值进行对比,表明Hall法测试平均晶粒尺寸更加准确,衍射峰晶粒细化和微观应变引起的宽化函数遵循柯西函数关系,确认该氧化铝样品的平均晶粒尺寸为155 nm。

As a classic analytical technique,X-ray diffraction （XRD） method is applied in a board range of fields,such as phase analysis,grain size calculation,structure analysis,etc.The grain size is important to characterize the physical and mechanical properties of alumina materials.Here,the grain size of nano-materials based on the XRD characteristic technique.Firstly,the calcined alumina sample was qualitatively analyzed by XRD,and the α crystal structure of the sample was confirmed by matching with the standard pattern.Gaussian distribution method and Hall method were used to fit the broadening values caused by sample factors（grain refinement and micro strain）.The instrument width value at any angle was calculated according to the diffraction fitting results of the NIST LaB₆ powder and the broadening influence was eliminated.Compared with the grain size values of each crystal plane obtained by the Scherrer formula,the calculated results indicated that the Hall method value was more accurate and the broadening function caused by grain refinement and micro-strain follows the Cauchy function.It was confirmed that the average grain size of the alumina sample was 155 nm.