Experimental Charge Density of Copper

The first six charge-density form factors of crystalline copper have been measured by Bragg scattering of $\mathrm{Cu}K\alpha$ and $\mathrm{Mo}K\alpha$ x rays from copper-powder samples. Detailed studies of both the samples and the x-ray beam parameters have reliably established the experimental error at about 1%. The measured form factors are in best agreement with an augmented-plane-wave (APW) self-consistent-field calculation of Snow using $X\alpha$ Slater exchange for a value of $\alpha$ between 0.70 and 0.75. They are in poor agreement with an APW calculation using the Chodorow potential but agree well with a calculation by Wakoh using Slater exchange and a self-consistent procedure. It is concluded that form-factor measurements of high accuracy are a sensitive and useful test of band wave functions and crystalline potentials.