Force constants radial

Chadi and Martin (1976) used essentially the same LCAO parameters that are given in the Solid State Table to obtain the energies at the two special points in the Brillouin Zone. They then redetermined the wave numbers of the special points for the distorted crystal and recalculated the energy. The clastic distortion which they used is a shear strain, in which there is no change in bond length to first order in the strain thus the radial force constant ofEq. (8-1) docs not enter the calculation. That strain can be written as... 

In the zincblende structure, with three independent elastic constants, the use of a model with only two parameters will allow a test and also allows alternate ways of obtaining the parameters. We obtain the radial force constant from a uniform compression, e, = = Cj = r, from which we obtain a change in energy per bond... 

We note first that the radial force constants are quite large and only qualitatively follow the d trend that would correspond to the d bulk modulus variation discussed in Chapter 7. There is a weak tendency for Cq to decrease both with mctallicity and with polarity. 

The term E oh is the observed cohesive energy it will not interest us here. The constant Cq is called the radial force constant. Its value is about forty to fifty electron volts for most semiconductors and will be tabulated later. In this chapter, we focus on angular distortions and add this empirical radial interaction where it is needed. 

V,e define the second order radial force constant 6.- as ... 

Fig. 21a-c. Cu(lOO) c(4x2) PF3. Surface phonon dispersion measured with HATOF (a) isolated PF3 molecules (exposure 0.4 langmuirs PF3), (b) c(4x2) PF3 overlayer, (c) results of a LDM assuming the bulk radial force constant between nearest neighbour substrate atoms [99Bra]. 

---