| Abstract: | The ratio of 6·(1/2m)·(E
0/c)2 of 12.9 meV at E
0=4 keV to k
B
D
of 2.27 meV for hcp-4He in the exponent 2M=6·(1/2m)·(E
0/c)2/k
B
D
]· (t)sin2
B
of the Debye-Waller factor D=exp(–2M) becomes 5.7, because of the small atomic mass m and the low Debye temperature
D
. Conversely that of the heavy atom crystals becomes smaller than 1. An experiment on hcp-4He as an example of a light atom crystal at low temperature limit of (t) 1 reveals that not only the maximum value of D is significantly reduced below 0.249 (=e
–1.395) but also the values of D for all other Laue spots except the following observed six spots are crowded into a range of D<0.05. Therefore, only the six Laue spots of
at 11.2 keV, (0002) at 20.3 keV,
and
at 14.4 keV and
and
at 23.9 keV in a low angular range of
B 10.22° were observed over low values of e
–1.395>D e
–3. At high angle of
B
45°, the values of E
0 for the above six Laue spots are assigned to the region below 4.07 keV from the Bragg condition under constant values of D. Therefore, detection of them over the higher angular range of
B
45° is not impossible but quite difficult at low temperature X-ray diffraction, considering X-ray absorption by multi-thermal shields of the refrigerator, the thick sample holder as a pressure vessel and massive air in space. Generally this means that the large reduction of the Debye-Waller factor of hydrogen and helium drastically encloses the diffraction intensity and the number of observable Laue spots within lower bounds. This is the reason why definite Laue spots in the light atom crystals of hcp-4He could be observed only by forward X-ray diffraction. Conversely the recoil fraction of the diffuse scattering expressed by 1–D concomitantly increases as a major part of the total scattering. A proposal to measure thermal diffuse scattering as well as pressure experiments will provide insight into the wave-like character of constituent atom in solid helium. |
