Isotopic Effect In Extended X-Ray-Absorption Fine Structure of Germanium

Extended x-ray absorption fine structure has been measured on two powdered samples of ${}^{70}\mathrm{Ge}$ and ${}^{76}\mathrm{Ge}$ as a function of temperature from 20 to 300 K. The effect of isotopic mass difference on the amplitude of relative atomic vibrations is neatly evidenced by the temperature dependence of the difference of Debye-Waller factors. The isotopic effect is also detected on the difference of nearest-neighbor average ineratomic distances, thanks to a resolution better than 10 fm.

Figure 1

Modulus of Fourier transforms for ${}^{70}\mathrm{Ge}$ at 20, 50, 100, 150, 200, 250, 300 K (from top to bottom in the upper panel) and comparison between the first-shell peak in the Fourier transforms of ${}^{76}\mathrm{Ge}$ (solid line) and ${}^{70}\mathrm{Ge}$ (dotted line) at 20 K.

Figure 2

Upper panel: EXAFS Debye-Waller exponents ${\sigma }^2$ as a function of temperature for the two isotopes ${}^{70}\mathrm{Ge}$ (squares) and ${}^{76}\mathrm{Ge}$ (circles). The lines, solid and dotted for ${}^{70}\mathrm{Ge}$ and ${}^{76}\mathrm{Ge}$, respectively, are the best fitting Einstein models. Lower panel: Difference of the Debye-Waller exponents of the two isotopes (diamonds); the solid and dashed lines are the differences between two Einstein models with the same (solid) and different (dashed line) values of the $k_0$ constant.

Figure 3

Difference of the nearest-neighbors average interatomic distance in ${}^{76}\mathrm{Ge}$ and ${}^{70}\mathrm{Ge}$, determined from EXAFS analysis (diamonds), compared with the difference of distance between average positions determined from x-ray backscattering [9] (open circles, containing the error bars).