Extra Negative Term in the Incoherent Part of the Diffuse Scattering of X-Rays from Neon-Like Crystals

Following the suggestion of Harvey, Williams and Jauncey that experimental evidence for the need of the Waller-Hartree extra negative term which arises from the Pauli exclusion principle can best be obtained in the diffuse scattering of x-rays from crystals, careful measurements of the $S_{\exp }$ values for NaF, MgO and SiC have been made at 295°K using the method of Jauncey and Claus. Various precautions are described. Since the theoretical $S_{\mathrm{th}}$ values depend somewhat critically upon the characteristic temperature $\Theta$ for a given crystal, a discussion of the determination of $\Theta$ from specific heat data is given. It is shown that for x-ray purposes the proper value for $\Theta$ is that obtained from specific heat data for fairly low temperatures even though the temperature at which x-ray scattering occurs may be fairly high. Tables of quantum-mechanical $f$ and $\Sigma {E_r}^2$ values extend only to $\left(sin \frac{\phi }{2}\right)\lambda =1.1\mathrm{}$. Beyond this the crystals approach neon gas in their scattering and it was found that Brown's analytical formula for neon gives better agreement with experiment than does Froman's extrapolation formula. The experimental results showed excellent agreement with the Waller-Hartree theory and thus give definite evidence for the operation of the Pauli exclusion principle on the outer shell electrons. Some remarks on the classical analog of the extra term are included. A special discussion of the results for SiC is given.