Precision Redetermination of Standard Reference Wavelengths for X-Ray Spectroscopy

Abstract

This investigation is designed to determine with high accuracy the wavelength ratios of 5 standard x-ray reference lines: Cr Ka2, Cu Kai, Mo Kai, Ag Kai, and W Kai. Most measurements were obtained with a double-crystal spectrometer in reflection. However, a few were taken with the instrument converted to a high-precision single-crystal spectrometer, and some tungsten determinations were made in transmission. Since estimated errors (± 1 ppm) are the lowest ever claimed for this type of work, the apparatus, including adjustment, calibration, and corrections, are described in considerable detail. Novel features include: use of a high-intensity, narrow-focus rotating-target tube for most measurements, calibration of the spectrometer circle to 0.1 sec with an angular interferometer, and a careful selection of 5 crystals (1 calcite, 2 quartz, and 2 silicon) from more than 100 samples tested. Bragg angles were determined for 20 different combinations of crystals and wavelengths. With an assumed wavelength value for one selected line, this gave an overdetermined set of 20 equations for 9 unknowns (4 wavelengths and 5 grating constants), which was solved by a least-squares adjustment. If the value for Mo Kai is provisionally taken as 707.831 xu, the resulting values for the other wavelengths are: Cr Ka 2 , 2288.854±0.003 xu; Cu Kai, 1537.370±0.002 xu; Ag Kai, 558.2486 ±0.0006 xu; W Kai, 208.5770±0.0003 xu. However, the primary quantities determined are the wavelength ratios, which are invariant with respect to a choice of the primary defining reference line. The question of adopting a definitive standard is left open for the present.

The double-crystal X-ray spectrometer: corrections, errors, and alignment procedure

“…We then obtain from equations (8), (17) and (6) (4), this must be subtracted from the apparent Bragg angle to obtain the true value. With a necessary change in sign convention, this is identical to that given by Bearden et al (1964). It is also in essential agreement with the work of Merrill & DuMond (1961), who restricted themselves to the first order case, but included terms in 62 .…”

“…between first and second order values; equation (19) shows that these should disagree if 62 caused a serious error. It should be noted here that the wavelength table of Bearden (1964 and the Bearden & Burr (1965 Note added in proof. '-It should be noted that the derivation in § 2-4 follows Schwarzschild and Schnopper in implicitly assuming that the angular intensity distribution I(u/) is completely defined by the slit system of Fig.…”

“…(5) Since the procedure outlined above was carefully followed in the precision wavelength measurements of Bearden et al (1964), it seems clear that misalignment and tilt errors were less than 1 p.p.m., far smaller than might be inferred from Schnopper's criticism. In the Bearden & Shaw (1935) measurements, misalignment effects may have been somewhat more serious; in this work tilts were reported to be limited to about 15 sec.…”

“…Following a proposal by DuMond (1937), several workers (Bollman, Bailey & DuMond, 1938;Renninger, 1955Renninger, , 1960Renninger, , 1967Bubakova, Drahokoupil & Fingerland, 1960, 1961 have used a three-crystal spectrometer for this purpose. On the other hand, Bearden, Marzolf & Thomsen (1968) have reported window functions obtained with the use of a virtually monochromatic ?,-ray source; they showed that for high quality crystals these profiles are closely represented by the Darwin-Prins theory.…”

“…Both the precision measurements and the test procedures discussed above have been carried out with a double-crystal spectrometer at The Johns Hopkins University (Bearden et al, 1964). It is easily adjusted with a tilting level.…”