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运用柯亨最小二乘法完整地推导了七种晶系点阵常数测定的计算公式,并指出正则方程的形式与所选用的外推函数无关,从而使推得的正则方程适用于任意一种外推函数(但在实际工作中,人们一般选用cos~2θ和cos~2θ(1/(sinθ)+1/θ)作为外推函数)。然后将推导的正则方程程序化后,计算了贮氢材料ZrCo及LaNi_(5-x)M_x(M=Al,Mn)的点阵常数。计算表明,本程序计算点阵常数快速、准确,可用在任何需要测定点阵常数的场合,具有较大的应用前景。计算也同时表明,对LaNi_5合金,当原子半径比Ni大的元素(如Mn,Al等)置换部分的Ni后,其点阵常数均随之增大,而且对于同一种置换元素Al,随着置换Ni的Al含量增大,其点阵常数也相应增大。这与理论相一致。
The calculation formulas of the lattice constant constants of seven kinds of crystal system are deduced completely by Cohen ’s least square method. It is pointed out that the form of regular equation has nothing to do with the chosen extrapolation function, so the deduced regular equation can be applied to any kind of outside In practice, however, people generally choose cos ~ 2θ and cos ~ 2θ (1 / (sin θ) + 1 / θ as an extrapolation function). Then, the lattice regularities of hydrogen storage materials ZrCo and LaNi_ (5-x) M_x (M = Al, Mn) were calculated after programming the regular equations. The calculation shows that the program calculates the lattice constant quickly and accurately and can be used in any occasions where the lattice constant needs to be measured and has great application prospect. The calculations also show that for LaNi_5 alloys, the lattice constants of LaNi_5 alloy increase with the substitution of Ni with larger atomic radius than Ni (eg, Mn, Al, etc.), and with the same replacement element Al, Al substitutional Ni content increases, the lattice constant is also increased accordingly. This is consistent with the theory.