Å* unit

A very small unit of length used to measure the wavelengths of X rays and the distances between atoms in crystals (such distances are measured by shining X rays through the crystal). Symbol, Å* (no period). The unit is read as “angstrom star”.

J. A. Bearden¹ introduced this unit in 1965 to replace the X unit, defining its length by taking the wavelength of the tungsten Kα1 line as exactly 0.209 010 0 Å*, a value chosen to make 1 Å* equal to 1 angstrom within 5 parts per million. To quote Bearden:

This numerical value of the wavelength is now proposed for use with the W Kα₁ line to define the x-ray wavelength standard by the relation

λW kα1 = 0.20290 10 0 Å*.

This is a new unit of length which may differ from the angstrom by ±5 ppm (probable error), but as a wavelength standard it has no error. In order to clearly indicate that this unit is not exactly an angstrom, it is suggested that it be designated Å*.

Later work has shown that the Å* unit is about 15 parts per million bigger than an angstrom. The value of the unit according to the 1986 CODATA recommendations is 1.000 014 81 × 10⁻¹⁰ meters, with a one-standard-deviation uncertainty of ± 0.000 000 92 × 10⁻¹⁰ meters.²

By 1970, this unit was clearly obsolescent, because:

(1) the availability of nearly perfect synthetic crystals such as silicon which have lattice parameters uniform to parts in 10⁸ or better throughout a macroscopic portion of the crystal, and (2) combined optical and X-ray interferometers which enable a crystal lattice spacing to be determined directly in metres. The potential accuracy of lattice parameter measurements with such combined interferometers is at least parts in 10⁸.

B. N. Taylor.
Report on the International Conference on Precision Measurement and Fundamental Constants.
Metrologia, vol 7, no 1, 1971.
Page 41.

1. J. A. Bearden.
Selection of the W Kα₁ as the X-Ray Wavelength Standard.
Physical Review 2nd series, volume 137, no. 2B, pages 455B – B461 (1965).

2. 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.


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 interpretaion of most of the early precision x-ray measurements.

Some of the inconsistencies have been eliminated with the introduction by Bearden of a newly defined unit—Å* in terms of which he has measured a complete range of x-ray wavelengths⁵. Unfortunately, this is also essentially an independently defined unit which is known no better with respect to the fundamental standard of length than the earlier x-unit.

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).

5. Bearden, J. A., Rev. Mod. Phys. 39 78 (1967).

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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