Consult the books Small-Angle Scattering of X-Rays, by André Guinier and Gérard Fournet (John Wiley & Sons, New York, 1955), Structural Analysis by Small-Angle X-Ray and Neutron Scattering, by L.A. Feigin and D.I. Svergun, edited by George W. Taylor (Plenum Press, New York, 1987), and the lecture Small-Angle Scattering: Basics and Applications, by Yoshiyuki Amemiya and Yuya Shinohara (2010), the link to which I present below. The theoretical details in this lecture are almost verbatim reproduction of those in the above-mentioned two books.

In essence, SAXS and WAXS are the same thing, however given the wavelength λ of the incident X-ray, they look at the system under investigation at different length scales, the former at large (molecular) and the latter at small (atomic) scales. In principle one would be able to achieve with WAXS what is achievable by SAXS were it not for the strong absorption of X-ray at relatively long wavelengths; thus SAXS bypasses one of the limitations of nature. For clarity, consider the Bragg law. With 2θ being the scattering angle, for the Bragg condition one has:*

n λ = 2d sin(θ)

where n is referred to as the order of reflection. Identifying n with 1 and assuming θ to be small, so that to a good approximation sin(θ) ≈ θ, from the Bragg condition one obtains:

d ≈ λ /(2θ).

Expressing θ in degrees (instead of radians), one has:

d ≈ (90/π) λ /θ = 28.647... λ /θ ≈ 30 λ /θ.

For θ = 1 (0.1) degree d is therefore some 30 (300) times the wavelength of the incident X-ray; for λ = 10 nm, d is approximately 300 nm (3000 nm). See the figure on page 8 of the above-mentioned lecture by Amemiya and Shinohara.

Incidentally, one should be mindful that the above arguments are order-of-magnitude arguments, the more so by the fact that the systems investigated are not infinitely large and periodic (as a result, the Fourier transforms of the relevant functions are not discrete; most evidently, surface effects play an important role here). For a precise discussion, one will have to consider the continuous Fourier transforms of the structures/functions one intends to investigate. For the details, consult the references that I have given above, where one sees that the authors appropriately discuss the relevant issues in terms of the continuous Fourier transform of the charge density and the auto-correlation of this function.

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* Consult Chapter 6 of the book Solid State Physics, by Ashcroft and Mermin.

http://cheiron2010.spring8.or.jp/text/lec/18_Small-angle_Scattering_Y.Amemiya.pdf

Read these and all will become clear.

1) O. Glatter and O. Kratky. Small Angle X-ray Scattering. Academic Press,111 Fifth Avenue, New York, NY 10003, 1982.

2) A. Guinier, G. Fournet, C. Walker, and K. Yudowitch. Small-Angle Scattering of X-rays. John Wiley and Sons, Inc., 1955.