On Jan 24, 2007, at 11:04 AM, Bart Hazes wrote:
Carlos Frazao wrote:
Hi,
I have once heard and recently read that "the diffraction event
results from the fact that both the X-rays wavelength and the
atomic distances are of the same magnitude". Although such a
relation seems appealing I am unsure if this is not a mere
coincidence. Could someone clarify or lead me to a relevant reading.
Cheers,
Carlos
The diffraction event does not <<< result from >>> the fact that
both wavelength and atomic differences are of the same magnitude.
But as many interestingly different yet related answers have
indicated you need such a wavelength to resolve the atomic details
you are interested in. Another way to think about it, the phase
difference between the scattering of two atoms at distance d
depends on d, the wavelength, and the angle of diffraction. If the
wavelength is long relative to d then the phase difference becomes
too small and you can thus not resolve the small details (I believe
in microscopy the smallest visible detail is the wavelength divided
by 2 or the square root of 2 depending on the method of illumination)
From the Wikipedia entry entitled "Diffraction" (http://
en.wikipedia.org/wiki/Diffraction)
"Diffraction refers to various phenomena associated with wave
propagation, such as the bending, spreading and interference of waves
emerging from an aperture. It occurs with any type of wave, including
sound waves, water waves, electromagnetic waves such as light and
radio waves, and matter displaying wave-like properties according to
the wave–particle duality. While diffraction always occurs, its
effects are generally only noticeable for waves where the wavelength
is on the order of the feature size of the diffracting objects or
apertures.
The most conceptually simple example of diffraction is single-slit
diffraction in which the slit is narrow, that is, significantly
smaller than a wavelength of the wave. After the wave passes through
the slit a pattern of semicircular ripples is formed, as if there
were a simple wave source at the position of the slit. This
semicircular wave is a diffraction pattern."
A nice pictorial representation can be found at the following web site:
http://www.phy.hk/wiki/englishhtm/Diffraction.htm
And if you think about the Bragg equation,
mλ = 2dsinθ
where
λ is the wavelength,
d is the distance between scattering centers,
θ is the angle of diffraction
and m is an integer known as the order of the diffracted beam.
then yes, the wavelength of the incident radiation is on the order of
the "distance between the scattering centers," or in our case, the
typical interatomic distance.
This is typically how I explain to visiting high school science
teachers and students why we use x-ray wavelengths (as opposed to
microwaves, for example) in our diffraction studies of protein crystals.
Diana
* * * * * * * * * * * * * * * * * * * * * * * * * * * *
Diana R. Tomchick
Associate Professor
University of Texas Southwestern Medical Center
Department of Biochemistry
5323 Harry Hines Blvd.
Rm. ND10.214B
Dallas, TX 75390-8816, U.S.A.
Email: [EMAIL PROTECTED]
214-645-6383 (phone)
214-645-6353 (fax)
