A sample of palladium deuteride,

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Solid State Physics, Ch Diffraction as measurement: form factors, thermal motion and refinement

Problem

\mathrm{PdD_{0.6}}

, of volume

1.0\,\mathrm{cm^3}

is available for a diffraction study whose aim is to locate the deuterium sublattice relative to the palladium lattice. The X-ray form factor of palladium at

Q=0

equals its atomic number,

f_{\rm Pd}(0)=46

; a deuterium atom contributes only its one electron,

f_{\rm D}(0)=1

. The neutron coherent scattering lengths are

b_{\rm Pd}=5.91\,\mathrm{fm}

and

b_{\rm D}=+6.67\,\mathrm{fm}

. Three instruments are on offer: a laboratory X-ray powder diffractometer, a synchrotron X-ray powder diffractometer, and a reactor-based neutron powder diffractometer, which needs at least

1.0\,\mathrm{cm^3}

of sample to reach useful counting statistics in a reasonable time. ((a)) Compare the scattered amplitude from a Pd atom with that from a D atom, for X-rays at

Q=0

and for neutrons, and turn each amplitude ratio into an intensity (contrast) ratio. ((b)) State which technique can locate the deuterium positions and whether the available sample meets the requirement of that technique.

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