Monday, April 6, 2009

effective charge





















Born and ionic effective charge:

Compound
q/e
qB/e

NaCl
1.16
0.80





MgO
1.26
0.77





GaAs
1.48
0.34



















The data shown in the upper table is calculated from the data of ε(0), ε(∞), ωTO found in and Ashcroft[1] and Kittel[2].

The formulas used are:
For Born effective charge
q_B^2=\epsilon_0mV\omega_{TO}^2[\varepsilon(0)-\varepsilon(\infty)]


eq=q_B^2=\epsilon_0mV\omega_{TO}^2[\varepsilon(0)-\varepsilon(\infty)]



For ionic effective charge
q^2=\epsilon_0mV\frac{\omega_{TO}^2[\varepsilon(0)-\varepsilon(\infty)]}{\eta^2[\varepsilon(\infty)+1/\eta-1]^2}



eq=q^2=\epsilon_0mV\frac{\omega_{TO}^2[\varepsilon(0)-\varepsilon(\infty)]}{\eta^2[\varepsilon(\infty)+1/\eta-1]^2}




I only showed a couple of examples for typical materials, basically, as long as you have the data of ε(0), ε(∞), ωLO, you can calculate ionic and Born effective charge.

Here m is the reduced mass, V is the volume of the oscillator, η is the depolarization factor (for cubic system it is 1/3). The formula is in SI units.

[1] N. W. Ashcroft and N. D. Mermin, Solid state physics (Holt, Rinehart and Winston, New York, 1976).
[2] C. Kittel, Introduction to solid state physics (Wiley, New York, 1966).


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