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Estimation of the Hydrogen Debye-Waller Factor


Hydrogen Debye-Waller Factor

In order to fit neutron diffraction data on hydrogenated GIC's (see Section gif), it is necessary to have an estimate of the hydrogen Debye-Waller factor. The C4KHx inelastic neutron scattering data of Kamitakahara, Doll, and Eklund,[218] were employed here to make an estimate of BH using a procedure suggested by Kamitakahara.[122]

Kamitakahara, Doll, and Eklund[218] report that the hydrogen vibrational mode in C4KH0.8 has a frequency of 93 meV in-plane and 71 meV out-of-plane. The Debye-Waller factor corresponds approximately to the mean-square vibrational amplitude of the atom.[10] Semiclassically, a harmonic oscillator has energy

where m is the mass of the oscillator, Omega its characteristic frequency, and < x2 > its mean-square displacement, the quantity of interest. Plugging in the numbers for the out-of-plane vibration, the one relevant to (00l) diffraction patterns, gives < x2 > = 0.058Å2.

The Debye-Waller factor is actually 8 pi2 < x > 2 due to corrections that come into play in an exact calculation.[10] From the value of < x > 2, the final result is BH = 4.58 Å2. (Alison Chaiken)
Wed Oct 11 22:59:57 PDT 1995