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)]
For ionic effective charge
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).
No comments:
Post a Comment