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X-ray Standing Wave Studies of Minerals and Mineral Surfaces: Principles and Applications

¹ Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois, 60208, U.S.A.
² Materials Science Division
³ Environmental Research Division, Argonne National Laboratory, Argonne, Illinois, 60439, U.S.A.

The first 20% of the full text of this article appears below.

	INTRODUCTION

 
With a penetration depth ranging from microns to millimeters, Ångstrom-wavelength X-rays are an ideal probe for studying atomic-scale buried structures found in the natural environment, such as impurities in minerals and adsorbed ions at mineral-water interfaces. But this penetration depth also makes an X-ray beam inherently less useful as a spatially localized probe. Using the superposition of two coherently coupled X-ray beams, however, makes it possible to localize the X-ray intensity into interference fringes of an X-ray standing wave (XSW) field, as illustrated in Figure 1, and thereby attain a spatially localized periodic probe with a length scale equivalent to the XSW period. The XSW period is

View larger version (33K):   Figure 1. Top: A standing wave field formed from the superposition of two traveling plane waves of wavelength and intersection angle (scattering angle) 2. The standing wave period is D as defined in Equation (1). Bottom: The two traveling planes waves are represented in reciprocal space by wave vectors K0 and KR. K0 = KR = 1/. The standing wave is defined by standing-wave vector Q defined in Equation (2).

(1)

where is the X-ray wavelength and 2 is the scattering angle or angle separation between the two coherently coupled wave vectors K_R and K₀. In reciprocal space, the scattering vector, or wave vector transfer, is defined as

(2)

Q is in the direction perpendicular to the equal-intensity planes of the XSW and has a magnitude that is the reciprocal of D. Thus, Q is also referred to as the standing wave vector.

An X-ray standing wave can be used as an atom-specific probe via the photoelectric effect, which can be observed by photoelectron emission, fluorescence, or Auger electron emission. There are a number of mechanisms for generating an XSW. The simplest and perhaps most practical method for producing an XSW . . . [Full Text of this Article]

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