X-Ray Wavelength Conversion Factor Λ(λgλs)

Abstract

A new experimental value of the x-ray conversion factor $\ensuremath{\Lambda}$ (m\AA{}/xu) has been obtained through a precision experiment on calcite crystals, and a recommended value of $\ensuremath{\Lambda}$ adopted based on this and other data. Nine selected crystals were used and the principal impurities determined by spectrochemical analysis. Grating constants were measured with the Cu $K{\ensuremath{\alpha}}_{1}$ and Ag $K{\ensuremath{\alpha}}_{1}$ emission lines, and the density of each crystal obtained by hydrostatic weighing in ethylene bromide. The product $\ensuremath{\rho}{d}^{\ensuremath{'}3}$ for an ideal impurity-free crystal was then computed by a linear extrapolation, with a least-squares adjustment to determine coefficients. The geometrical volume factor $\ensuremath{\Phi}$ was found by experimental measurement of dihedral angles on five of the crystals. Combining these data with the best available values for atomic weight and Avogadro's number yields $N{\ensuremath{\Lambda}}^{3}=(6.05972\ifmmode\pm\else\textpm\fi{}0.00015)\ifmmode\times\else\texttimes\fi{}{10}^{23}$ ${(\mathrm{g}\mathrm{mole})}^{\ensuremath{-}1}$ ${(\mathrm{m}\mathrm{\AA{}}/\mathrm{x}\mathrm{u})}^{3}$ and $\ensuremath{\Lambda}=1.002055$ m\AA{}/xu, where the x unit is based on ${\ensuremath{\lambda}}_{\mathrm{Cu}K{\ensuremath{\alpha}}_{1}}=1537.400$ xu. Taking a weighted average of this result and other high-precision data on $\ensuremath{\Lambda}$ has led to the adoption of $\ensuremath{\Lambda}=(1.002056\ifmmode\pm\else\textpm\fi{}0.000005)$ m\AA{}/xu expressed on the same basis. The result becomes $\ensuremath{\Lambda}=(1.002076\ifmmode\pm\else\textpm\fi{}0.000005)$ m\AA{}/xu when referred to an x-unit scale on which ${\ensuremath{\lambda}}_{\mathrm{W}K{\ensuremath{\alpha}}_{1}}=208.5770$ xu. This last wavelength then becomes ${\ensuremath{\lambda}}_{\mathrm{W}K{\ensuremath{\alpha}}_{1}}=0.2090100$ \AA{}, which value has been adopted by the author as a wavelength standard.

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