## X-Ray Data Booklet

## Section 4.2
Specular Reflectivities for Grazing-Incidence Mirrors

Eric M. Gullikson

The specular reflectivity of six common materials is given in Figs.
4-4 and 4-5 for photon energies between 30 eV and 30 keV. The reflectivity
for a perfectly smooth surface and for s-polarization is

_{}
(1)

where

_{}

The grazing angle *q* is measured from the plane of the mirror
surface. The normal components of the incident and transmitted wave vectors
are *k*_{iz}_{ }and
*k*_{tz}, respectively. The complex index
of refraction *n* is obtained from the
average atomic scattering factor of the material, as described in Section 1.7
and in Ref. 1.

The effect of high-spatial-frequency roughness on the reflection
coefficient of an interface can be approximated by the multiplicative factor

_{}
(2)

where *r*_{0}*
*is the complex reflection coefficient of a perfectly smooth interface and
*s*
is the rms roughness. For updated values of the atomic scattering factors and
for on-line reflectivity calculations, see http://www-cxro.lbl.gov/ optical_constants/.

REFERENCE

1. B. L. Henke,
E. M. Gullikson, and J. C. Davis, “X-Ray Interactions: Photoabsorption, Scattering,
Transmission, and Reflection at *E*
= 50–30,000 eV, *Z* = 1–92,” *At. Data Nucl. Data Tables* **54,** 181 (1993).

**Fig.
4-4.** Specular reflectivities of
carbon (r = 2.2 g/cm^{3}), silicon (r = 2.33 g/cm^{3}),
and silicon dioxide (r = 2.2 g/cm^{3}). The reflectivity is calculated for s-polarization
at grazing angles of 0.5, 1, 2, 4, 6, 8, 10, and 20 degrees.

**Fig.
4-5.** Specular reflectivities of
nickel (r = 8.90 g/cm^{3}), ruthenium (r = 12.41 g/cm^{3}),
and gold (r = 19.3 g/cm^{3}). The reflectivity is calculated for s-polarization
at grazing angles of 0.5, 1, 2, 4, 6, 8, 10, and 20 degrees.