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本文从晶体结构的角度,证明等结构化合物晶胞边长、晶胞体积与离子半径之间存在以下关系:(1)多元化合物A_mB_m…X_p的晶胞体积V与某种阳离子如A的半径之间有关系式:V=(a+br_A)(r_X+r_A)~3 (a,b为常数)。(2)对于二元化合物关系式为:V=K(r_X+r_A)~3 (K为常数)。(3)由以上关系式可推得二元化合物V与_A~3r成近似直线关系,多元化合物V与r_A~3之间易表现为曲线关系,但r_A变化不大时仍近似为直线,另外V与r_A也成近似线性关系。(4)二元化合物品胞边长与r_A成线性关系,多元化合物无此线性关系。
In this paper, from the perspective of the crystal structure, it is proved that there are the following relations among the unit cell side length, the unit cell volume and the ionic radius of the isostructural compound: (1) the unit cell volume V of the plural compound A_mB_m ... X_p and the radius Between the relations: V = (a + br_A) (r_X + r_A) ~ 3 (a, b is a constant). (2) For the binary compounds the relationship is: V = K (r_X + r_A) ~ 3 (K is a constant). (3) From the above relation, it can be deduced that the binary compound V has approximately linear relationship with _A ~ 3r, and the relationship between the compound V and r_A ~ 3 tends to be a curve. However, when the change of r_A is not large, In addition, V and r_A also become approximately linear. (4) There is a linear relationship between cell length and r_A in binary compound, and there is no linear relationship between multiple compounds.