Born lande equation
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It allows lattice energy calculation from the knowledge of geometry of a crystal, Madelung constant, inter atomic distance, and charge of the ions.
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The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound. In 1918. Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term.
E
=
−
N
A
M
z
+
z
−
e
2
4
π
ϵ
0
r
0
(
1
−
1
n
)
{\displaystyle E=-{\frac {N_{A}Mz^{+}z^{-}e^{2}}{4\pi \epsilon _{0}r_{0}}}\left(1-{\frac {1}{n}}\right)}
where:
NA = Avogadro constant;
M = Madelung constant, relating to the geometry of the crystal;
z+ = numeric charge number of cation
z− = numeric charge number of anion
e = elementary charge, 1.6022×10−19 C
ε0 = permittivity of free space
4πε0 = 1.112×10−10 C2/(J·m)
r0 = distance to closest ion
n = Born exponent, typically a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.[3]
E
=
−
N
A
M
z
+
z
−
e
2
4
π
ϵ
0
r
0
(
1
−
1
n
)
{\displaystyle E=-{\frac {N_{A}Mz^{+}z^{-}e^{2}}{4\pi \epsilon _{0}r_{0}}}\left(1-{\frac {1}{n}}\right)}
where:
NA = Avogadro constant;
M = Madelung constant, relating to the geometry of the crystal;
z+ = numeric charge number of cation
z− = numeric charge number of anion
e = elementary charge, 1.6022×10−19 C
ε0 = permittivity of free space
4πε0 = 1.112×10−10 C2/(J·m)
r0 = distance to closest ion
n = Born exponent, typically a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.[3]
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