I recently came across the concept of skin-depth of an conductor in Electromagentism , which says that after the skin depth distance below the surface , the eloectromagnetic waves eventually die out( exponentially it becomes 1/e after this distance).
We explain X-Ray Bragg defraction using planes of atoms and find out a condition of maximum diffraction of the light from two planes.
So how do I explain a Xray diffraction of a conductor, which as per Maxwell's equations should not allow penetration of electric field/light ?
In addition to what has been said before, you may want to visit the website linked below, it is a public server where you can calculate (for estimations which work pretty well, in my experience) optical properties of solids in the x-ray range. This is only concerned with non-resonant processes, though.
I have attached a figure generated on that site, showing the x-ray absorption length of Au in the 5keV-10keV range. At 8keV, we get about 2.5 microns. That will yield a largely enough number of unit cells for very sharp diffraction peaks.
A small correction to Alexander's post: it is not the refractive index being very small in the x-ray range but its departure from unity. It is then usually expressed as 1+delta, delta being a small number (which will actually turn negative at high frequencies).
http://henke.lbl.gov/optical_constants/atten2.html
The dielectric constant, because of which there is a skin-depth has frequency dependence. At high frequencies, and especially the frequency of X-rays, it is extremely small. In particular, this is manifested in a practically zero X-ray refractive index.
With decreasing frequency dielectric constant increases, the refractive index becomes not negligible and the concept of skin - depth becomes valid.
Dear Hrushikesh,
From the practical view:
as you shurely know, X-ray diffration on electrical conductors (metals) is possible and is done on the daily basis. It's a fact that XRD radiation do not penetrate metals deeply - for the reasons you (and Alexander) mentioned and also by scattering incident wave on atoms (involwing diffraction and interference). The practical approach to this problem is solved by special preparations of samples, mainly by low energetical grinding. In this way (powder diffraction) X-ray wave can penetrate also material that is normally in the deep midle (inside) of the sample.
For single crystals wave in fact does not travel deeply inside sample, so the diffration is made mainly in few first layers of material and mainly the reflection method is used.
Konrad
Dear Hrushikesh,
1) skin depth d~sqrt(2/conductivity×dielectric ×frequncy),1/e is for light.
2)Gold is conductor and its XRD is done,shows that it is FCC.
3)The dimension ofunit cell of gold is of the order of A, and therefore diffraction from fewlayer is sufficient for XRD,you can also use powder method for XRD.
Titov is quite right. Also note that there is a maximum frquency if electroagnetic radiation/ phonons which does not peetrate into a given metal. This plasma frequency is in the visible phonon range,,thtat is the reason for metallic shine. X-ray reguencies are wel above plasma frequency.
An electrical conductor is a solid material if not amorphous is crystalline. In this case it can be characterized by crystallographic diffraction methods.
X-ray diffraction deals with strong emission (CuK-alfa, for example) it can penetrate the bulk of very thick sample? no matter that some weak electromagnetic field cannot. So I do not see any problems in this
in may opining X-ray diffraction have relation with the organisation of matter. the quality of you diffracto in powder or your single crystal measurement depend of this organisation of matter when you do your synthesis and not dependent of the nature of your compound if it s conductor or semi conductor. the Brillouin zone is responsible to diffraction
In addition to what has been said before, you may want to visit the website linked below, it is a public server where you can calculate (for estimations which work pretty well, in my experience) optical properties of solids in the x-ray range. This is only concerned with non-resonant processes, though.
I have attached a figure generated on that site, showing the x-ray absorption length of Au in the 5keV-10keV range. At 8keV, we get about 2.5 microns. That will yield a largely enough number of unit cells for very sharp diffraction peaks.
A small correction to Alexander's post: it is not the refractive index being very small in the x-ray range but its departure from unity. It is then usually expressed as 1+delta, delta being a small number (which will actually turn negative at high frequencies).
http://henke.lbl.gov/optical_constants/atten2.html
as said Professor Amigo in his in his commentary: An electrical conductor is a solid material if not amorphous is crystalline. In this case it can be characterized by crystallographic diffraction methods. simply the difference between the compound is the quality of structure....
I
Just some personal observations and notes about this discussion:-)
https://www.researchgate.net/post/What_depths_can_one_typically_probe_with_XRR_X-ray_Reflectivity_Reflectometery?_tpcectx=profile_questions
Hrushikesh Sable has posted a very interesting question. If we examine the two skin effects separately (the confinement of high frequency electric current near the surface of conductors; and the confinement of X-Ray Diffraction to the near surface layers, specially in high absorbent materials) no correlation is to be expected. Only is valid the question about if the skin characterized by XRD is the same as the skin in which take place the electric current. But, what could be expected if an XRD pattern is obtained when a high frequency current IS FLOWING-THROW a piece of metal? It should be an interesting experiment, because the XRD pattern is created by the scattering of electrons, and the free electrons in this case are no more moving chaotically, but in an ordered (collective) way. I have not more than a few doubts that very amazing things may arise, perhaps a new way to characterize surfaces.
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