57Fe Mössbauer spectrometry: A powerful technique to analyze the magnetic and phase characteristics in RE–Fe–B permanent magnets

This review summarizes the recent advances on the application of ⁵⁷Fe M?ssbauer spectrometry to study the magnetic and phase characteristics of Nd–Fe–B-based permanent magnets. First of all, the hyperfine structures of the Ce₂Fe₁₄B,(Ce,Nd)₂Fe₁₄B and MM₂Fe₁₄B phases are well-defined by using the model based on the Wigner-Seitz analysis of the crystal structure. The results show that the isomer shift δ and the quadrupole splitting ?EQ of those 2:14:1 phases show minor changes with the Nd content, while the hyperfine field Bhfincreases monotonically with increasing Nd content and its value is influenced by the element segregation and phase separation in the 2:14:1 phase. Then, the hyperfine structures of the low fraction secondary phases are determined by the ⁵⁷Fe M?ssbauer spectrometry due to its high sensitivity. On this basis,the content, magnetic behavior, and magnetization of the REFe₂ phase, the amorphous grain boundary(GB) phase, and the amorphous worm-like phase, as well as their effects on the magnetic properties, are systematically studied.     

判断直线与椭圆位置关系的一种方法

在平面解析几何中，判断直线与圆的位置关系主要有两种方法：方法卫是从代数角度，即从直线方程与圆方程联立所得的方程组的解的个数来判断；方法2是从几何角度，即从圆心到直线的距离与半径的大小关系来判断．在解题中，常用方法2．对直线与椭圆位置关系的判断，目前只有一种方法，就是从直线方程与椭圆方程联立得到的方程组的解的个数来判断，它是从直线与圆的位置关系的判断方法1，通过类比而得到的．那么，我们自然要问：对直线与椭圆的位置关系的判断，能否有类似于上述判断方法2的结论呢？几经探求，笔者得出了如下结论：定理若椭圆E…     

一个最值问题的多种解法

题已知ａ、ｂ是不相等的正数,试求函数ｙ＝ａｃｏｓ２ｘ＋ｂｓｉｎ２ｘ＋ａｓｉｎ２ｘ＋ｂｃｏｓ２ｘ的最值．文［１］认为,此题用通常解法不仅繁而且难,并给出了一种明快和直观的几何解法．笔者通过多角度、多层次的分析,发现此题有多种解法,是一道难得的好题．现介...