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)

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 J&middot;m&middot;mol−1
 * ||d = 3.45 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.
 * }
 * || 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.
 * }
 * || r− and r+ are the radii of the anion and cation, respectively.
 * }

J IM ptalk·cont 22:10, 24 June 2009 (UTC)