= Crystal X-ray spectrometer
A <crystal X-ray spectrometer> selects a narrow <wavelength> interval by <diffraction> at known <interplanar spacing> $d$ and <Bragg angle> $\theta$. For fixed <diffraction order> $n$, a known $d$ lets an angular measurement determine $\lambda=2d\sin\theta/n$. This reverses the <crystallography> problem of finding $d$ from a known <wavelength>.
Siegbahn's laboratory developed <X-ray tubes> and evacuated spectrographs for longer <wavelengths>. Rotating the <crystal> selected reflections; <photographic plates> recorded positions. Opposite-side exposures measured angles on both sides of the direct beam. Later tube instruments mounted a beam-defining slit opposite the plate holder. A separate double instrument compared two reflected beams with two <ionization chambers>. These were different instruments, not one universal assembly.<Manne Siegbahn, His Research by Hugo Atterling>[Hugo Atterling, Manne Siegbahn: Development of precision spectroscopy; Work at Uppsala 1923–1927]{ref}
The Nobel biography describes constant-<temperature> spectrographs and a precision angular scale read by diametrically opposed microscopes.<Nobel Lectures, Physics 1922–1941/Manne Siegbahn - Biographical>[Nobel Lectures, Physics 1922–1941; Biographical, paragraph beginning As a measure of the high precision; inspected collected volume pp. 90–91]{ref} <Temperature> control matters because <thermal expansion> changes $d$; an accurately read angle cannot compensate for an unknown <interplanar spacing>.
\Image[/siegbahn-crystal-spectrometer-functions.png]
{title=Functions of a <crystal X-ray spectrometer>}
{id=image-siegbahn-crystal-spectrometer-functions}
{description=Original functional schematic, not a reconstruction of a particular Siegbahn instrument. Two slits illustrate <collimation>; the selected incident direction, rotatable <crystal> and movable readout define the geometry. The <Bragg angle> $\theta$ is measured from the <lattice planes>; the beam deflection is $2\theta$. The <photographic plate> and scanning <ionization chamber> are alternative readouts. Component sizes, angles and positions have no historical scale.}
The schematic separates preparation, selection and readout. An <X-ray tube> target supplies <Characteristic X-rays> with a possible <bremsstrahlung> background. A <collimator> limits incident directions; evacuation reduces air <X-ray attenuation>. Rotating the <crystal> brings different <wavelengths> into reflection. A <photographic plate> stores line positions over an exposure, whereas an <ionization chamber> can measure collected <electric charge> at successive angles. Neither readout alone establishes absolute <wavelength>: an angular zero, angular-scale calibration, <diffraction order>, $d$ and any required <refraction> correction enter the inference. Narrower slits reduce accepted angular spread but also reduce signal; a weak line can become harder to locate despite a narrower instrumental response.
A control reported in Siegbahn's lecture photographed a line system with copper-sulphate and calcium-sulphate <crystals>. Irregular relative shifts around copper's characteristic <frequency> supported <anomalous dispersion>; the arrangement excluded differing absorption across that <frequency> as the explanation.<Nobel Lectures, Physics 1922–1941/The X-ray Spectra and the Structure of the Atoms by Karl Manne Georg Siegbahn>[Nobel Lectures, Physics 1922–1941; Printed pp. 88–89, final experiment]{ref} A finer angular scale alone cannot remove this physical <refraction> correction.
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