Hydrogen Debye-Waller Factor

In order to fit neutron diffraction data on hydrogenated
GIC's (see Section ), it is necessary to
have an estimate of the hydrogen Debye-Waller factor. The
C_{4}KH_{x} inelastic neutron scattering data
of Kamitakahara, Doll, and Eklund,[218] were employed here to make an
estimate of B_{H} using a procedure suggested by
Kamitakahara.[122]

Kamitakahara, Doll, and Eklund[218] report that the hydrogen
vibrational mode in C_{4}KH_{0.8} 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 < x^{2} > its
mean-square displacement, the quantity of interest. Plugging
in the numbers for the out-of-plane vibration, the one
relevant to (00*l*) diffraction patterns, gives <
x^{2} > = 0.058Å^{2}.

The Debye-Waller factor is actually 8 *pi*^{2}
< x > ^{2} due to corrections that come into
play in an exact calculation.[10] From the value of < x
> ^{2}, the final result is B_{H} = 4.58
Å^{2}.

alchaiken@gmail.com (Alison Chaiken)

Wed Oct 11 22:59:57 PDT 1995