X unit

A unit of length used to specify the wavelength of x rays. Symbol, X, Xu or xu. Also known as a siegbahn. The length of the X unit was set at ¹/3029.04 of the spacing of the (200) planes of calcite at 18°C.¹ This value was chosen with the intention of making the X unit one-thousandth of an angstrom, or 10⁻¹³ meters, but more recent measurements show it is about 2 parts per thousand larger than that.

The original definition of the X unit (Siegbahn, 1919) depended on crystals of rock salt, not calcite, and defined the unit as ¹/2814.00 of the lattice spacing. Switching to calcite improved the definition of the spectral lines. In the 1930’s, experiments with ruled gratings yielded new values for x-ray wavelengths that were about 0.2% greater than those obtained from calcite crystals. Ultimately the discrepancy was traced² to an error in Milliken’s determination of the charge on the electron, due to his using a mistaken value for the viscosity of air, which led to an error in Siegbahn’s calculation of Avogadro’s number.

The copper x unit is based on taking the wavelength of the Kα1 line of copper to be exactly 1537.400 xu. According to the 1986 CODATA recommendations, it is equal to 1.002 077 89 × 10⁻¹³ meters with a one-standard-deviation uncertainty of ± 0.000 000 70 × 10⁻¹³ meter (relative uncertainty, 0.70 parts per million).³ Its symbol is xu(CuKα1).

The molybdenum x unit is based on taking the Kα1 line of molybdenum to be exactly 707.831 xu.4 According to the 1986 CODATA recommendations, it is equal to 1.002 099 38 × 10⁻¹³ meters with an uncertainty of ± 0.000 000 45 × 10⁻¹³ meter (relative uncertainty, 0.45 parts per million).³ Its symbol is xu(MoKα1).

Around 1965 some workers began to use the A* unit in place of the X unit.

According to the current national standard in the United States⁵, the X unit is not to be used. The meter should be used instead.

1. Manne Siegbahn.
“Röntgenspektroskopische Präzionsmessungen. (Erste Mitteilung).”
Annalen der Physik. 4th series, volume 59, page 56.
Leipzig: Verlag von Johann Ambrosius Barth, 1919.

M. Siegbahn.
Spektroskopie der Röntgenstrahlen.
Berlin: Springer-Verlag, 1931.

Pages 42-44.

2. For this detective story, see: E. R. Cohen and J. W. M. DuMond.
Handbuch der Physik, vol 35, page 1.
Berlin: Springer-Verlag, 1957.

3. E. Richard Cohen and Barry N. Taylor.
“The 1986 CODATA recommended values of the fundamental physical constants.”
Journal of Research of the National Bureau of Standards, volume 92, no. 2, page 1. (March-April 1987)

Table 3.

4. John J. Merrill and Jesse W. M. DuMond
Precision Measurement of the L X-Ray Spectra of Uranium and Plutonium.
Physical Review, vol 110, pages 79-84. (April 1, 1958)

See “Appendix I. Definition of the X-unit as used in this article”, which in addition to defining the molybdenum x unit, contains a concise history of the x unit.

To tie down the precision results of the present article in the most definite way possible we therefore adopt, for the purpose of defining what we mean in this paper by the term one “x-unit,” the convention that the central wavelength value of the Mo Kα1 line profile (determined by means of the median points of chords across it as explained in this paper) shall be 707.8490 “x-units.” Should a later change in the convention modify this number it will be a simple matter for anyone to modify all our observed tabular wavelengths herein reported by the same proportional amount to suit the change in the definition of the unit. We are aware, of course, that the conventional number we have here adopted for Mo Kα1 differs slightly from the value in x-units (707.831) frequently quoted and tabulated for this line. The difference is in fact 25.4 parts per billion. Our primary reason for our particular numerical choice is because it is consistent with assigning the conventional value of the effective grating space in the first order, d1 = 3029.040 x-units to the pair of calcite crystals we have used in this research. Since our particular pair of crystals might b

J. J. Merrill and J. W. M DuMond.
Annals of Physics (New York) vol 14, page 166.

5. IEEE/ASTM SI 10™-2002.
American National Standard for Use of the International System of Units (SI): The Modern Metric System.
New York: IEEE, 30 December 2002.

See Section 3.3.3.

The symbol “Xu” is found in

National Research Council.
A Glossary of Terms in Nuclear Science and Technology.
New York: American Society of Mechanical Engineers, 1955.

Page 187.


The value of the Avogadro number which is recommended by Taylor, Parker and Langenberg in their recent survey of fundamental constants¹ has been obtained indirectly through a least squares adjustment of some highly selected data. Accurate direct measurements, such as those by Bearden² and Hemins and Bearden³ do not determine an absolute value for the Avagadro number but rather the product of N and Λ³, the Ångstrom-kilo x-unit conversion factor. This results from the use of x-ray crystallographic measurements of the lattice spacing of a crystal in x-units, a unit of length defined in terms of the wavelength of an x-ray emission line. As pointed out by Cohen and Dumond in 1965 ⁴, at least two inconsistent working definitions of the x-unit have been used, resulting in ambiguous interpretation of most of the early precision x-ray measurements.

1. Taylor, B. N., Parker, W. H., and Langenberg, D. N., Rev. Mod. Phys. 41 375 (1969).

2. Bearden, J. A., Phys. Rev. 137, B455 (1965).

3. Henins, I, and Bearden, J. A., Phys. Rev. 135, A890 (1964)

4. Cohen, E. R., and Drummond, J. W. M., Rev. Mod. Phys. 37, 537 (1965).

I. Curtis, I. Morgan, M. Hart and A. D. Milne.
A New Determination of Avogadro's Number.
United States Dept. of Commerce; Nat'l Bureau of Standards.
Precision Measurement and Fundamental Constants. Proceedings of the International Congress…
D. N. Langenberg and B. N. Taylor, editors.
National Bureau of Standards Special Publication 343.
Washington: U.S.G.P.O., August 1971.
Page 285.

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