Talk:Kapustinskii equation

Assumptions/Derivation from Born-Landé equation

I've got a list of three assumptions used to form the Kapustinskii equation from the Born-Landé equation in my first-year undergraduate lecture notes (handwritten by me, so no copyright issues). Shall I put them up to improve the article? Brammers (talk) 15:23, 30 April 2009 (UTC)[reply]

Coefficients

The equation is given thus (delinked).

$U_{L}=-1202.5\cdot {\frac {\nu \cdot |z^{+}|\cdot |z^{-}|}{r^{+}+r^{-}}}\cdot {\biggl (}1-{\frac {0.345}{r^{+}+r^{-}}}{\biggr )}$
... It is important to remember that the units of the radii in this equation are Ångström, and the lattice energy is given in kJ/mol.

It's more usual to write something like

$U_{L}=-{a}\cdot {\frac {\nu \cdot |z^{+}|\cdot |z^{-}|}{r^{+}+r^{-}}}\cdot {\biggl (}1-{\frac {b}{r^{+}+r^{-}}}{\biggr )}$

and then define the constants a & b in terms of appropriate units. The question is what we should use as coefficients, a & b or something else. We then don't have to "remember" to use these units or those.

Looking at this, K and d seem decent labels for the coefficients.

We thus get:

U_{L}=-{K}\cdot {\frac {\nu \cdot |z^{+}|\cdot |z^{-}|}{r^{+}+r^{-}}}\cdot {\biggl (}1-{\frac {d}{r^{+}+r^{-}}}{\biggr )}

where	K = 1.2025×10⁻⁴ J·m·mol⁻¹
	d = 3.45×10⁻¹¹ m
	ν is the number of ions in the empirical formula,
	z⁻ and z⁺ are the numbers of elementary charge on the anion and cation, respectively, and
	r⁻ and r⁺ are the radii of the anion and cation, respectively.

JIMp_talk·cont 22:10, 24 June 2009 (UTC)[reply]