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不完全极图的应用导致在缔合勒让德函数中失去正交性关系,而且需要确切计算这些函数乘积的积分。所需要的缔合勒让德函数及其乘积的不定积分已对立方晶体的对称性和正交物理对称性计算到第十六阶。对{200},{222}和{110}背反射极图的解法进行了详细讨论,在那里的数据被限制在不超过板法线方向60°的范围内。用低锰钢板样品所得到的数据来说明本方法,并将其结果与用相同材料的组合样品所得到的全极图的结果相比较。所描述的——用抛光和腐蚀逐次对样品进行减薄,在表面上测量一系列极图——方法使得能够把晶体取向分布做为板面距离的函数来研究。
The application of the incomplete polar diagram leads to the loss of orthogonality in the associated Legendre function and requires the exact calculation of the integral of the product of these functions. The required integrating Legendre function and the product of its indefinite integral have been calculated to the sixteenth order for the symmetry and orthogonal physical symmetry of the cubic crystal. The solution to the {200}, {222}, and {110} back-reflector maps is discussed in detail, where the data is limited to no more than 60 ° of the normal of the plate. This method is illustrated by the data obtained for a sample of a low manganese steel plate and the results are compared with the results obtained for a total polar figure with a combined sample of the same material. Described - Sequential thinning of specimens with polishing and etching to measure a series of polar diagrams on the surface - The method enables the study of the crystal orientation distribution as a function of plate surface distance.