二维氯化钠型结构马德隆常数的求算

Calculation of Two Dimensional Madelung Constant for NaCl Type Crystal

本文对二维氯化钠型结构的马德隆常数进行求算。首先确定其无穷级数的具体形式,为: 4-1/2^(1/2)-4/2+8/5^(1/2)-4/8^(1/2)+…并将其整理成通式: 4 sum from k=1 to π (-1)^(k=1) 1/k-4/2^(1/2) sum form =1 to π 1/k+8 sum from =2 to π sum from I=1 to k=1 (-1)^(+I-1) 1/(K^2+I^2)^(1/2) 然后分别求算通式中每一项的收敛值。这些收敛值之和为1.6152,此即二维氯化钠型结构的马德隆常数。

In this paper, the two dimensional Madelung constant for the NaCl type structure is calculated. The infinite series is of the form 4-1/2^(1/2)-8/4^(1/2)+8/5^(1/2)-4/8^(1/2)+… which is generalized to the following expression 4 sum from k=1 to n(-1)^(k-1)1/K-4/2^(1/2) sum from k=1 to n 1/K+8 sum from k=2 to n sum from I=1 to k-1 (-1)^(k+I-1)1/((k^2+I^2))^(1/2) The convergence values for every term in the general expression is then determined. The calculation shows that the infinite series converges to 1.6152, which is thus the value of the two dimensional Madelung constant for the NaCl type structure.