Measuring atom positions in a crystal

[Lojzek]

I heard that it is possible to measure positions of individual atoms in a crystal. Is this true?

I understand the principle of measuring crystal orientation and base vectors of Bravais lattice with X-ray, but I have no idea how positions of individual atoms can be obtained. I suppose it is only possible to measure the geometry of Bravais lattice of each small piece of the crystal, assuming that the small piece has aproximately periodic structure over many atom distances.
But what about the areas with lots of defects (for example grain boundaries) or large deformations? Is it possible to obtain information about the positions of individual atoms in those parts of the crystal?

 

[nasu]

I heard that it is possible to measure positions of individual atoms in a crystal. Is this true?

I understand the principle of measuring crystal orientation and base vectors of Bravais lattice with X-ray, but I have no idea how positions of individual atoms can be obtained. I suppose it is only possible to measure the geometry of Bravais lattice of each small piece of the crystal, assuming that the small piece has aproximately periodic structure over many atom distances.
But what about the areas with lots of defects (for example grain boundaries) or large deformations? Is it possible to obtain information about the positions of individual atoms in those parts of the crystal?

If the atoms are on the surface you can do if with Scanning Tunneling Microscopy (STM) or Atomic Force Microscopy (AFM). Both require ultrahigh vacuum and ultra-pure samples.

 

[f95toli]

And if you have a thin slice of the material you can use TEM (which is almost like a SEM, but works in transmission mode).

If you are looking for a e.g. a single "distinct" dopant which is somewhere near (but not necessarily on) the surface there are also techniques that can "penetrate" the surface a few nm or so.

 

[Gokul43201]

But what about the areas with lots of defects (for example grain boundaries) or large deformations? Is it possible to obtain information about the positions of individual atoms in those parts of the crystal?

When you talk about the "positions of atoms", do you mean a knowledge of positions relative to some external frame, or only relative to atoms in the neighborhood of those that you are studying.

If you are looking for the latter, then XRD (or micro-XRD, if you want to zoom in) will still give you relative positions (averaged over the region under illumination) so long are there is sufficient crystallinity in that region.

Very rarely does anyone need to know the positions of atoms relative to say, a lab frame. All one typically cares about is the arrangement of atoms relative to each other.

 

[Astronuc]

I'm a little puzzled by the OP question.

Positions of atoms will vary in solids via diffusion, which is temperature dependent. Certainly some materials, e.g. ceramics (e.g. metal oxides) or intermetallic compounds (e.g. silicides) have very low self-diffusion rates.

Grain boundaries certain see a departure from the regular lattice order. Within a lattice, the dislocations move or glide, especially when the material is under load, and especially where there is a stress gradient.

I believe that in order to observe the position of an atom, the sample must be 'chilled'.

Considering there is on the order of 10²² atoms/cm³ it is not practical to know exact position of an atom in a crystal, especially given the grain boundaries in a polycrystalline material, and the distribution of grain sizes and orientation. If the material is an alloy, then there are substantial compositional variations within a crystal.

FYI - http://www.zurich.ibm.com/nano/exhibits_atoms.html

 

[ZapperZ]

Still, it is possible to know the "coordination number" of these atoms that make up a solid, and definitely a crystal. If not, there is no way we can have the ability to know the crystal structure and the Bravais lattice, and there is no way we can derive theoretically the band structure. The fact that we can implies that we have the ability to know the position of these atoms that make up a solid.

Zz.

 

[f95toli]

Grain boundaries certain see a departure from the regular lattice order. Within a lattice, the dislocations move or glide, especially when the material is under load, and especially where there is a stress gradient.

But the atoms do not neccesarily move THAT much and it also depends on the material. There are quite a few paper where people have done TEM studies of small artificiall grain boundary junctions (I am familiar with some work on perovskites: YBCO, LSMO etc). Starting from with a small junction made from an epitaxial film (lets say a junction a few tens of monolayers thick and 200 nm wide) it is possible to use a FIB to make a "slice" that can be studied using TEM.
Now, I am not 100% sure you can actually see the atoms but you can certainly see the layers; and since the junction is only a couple of hundred unit cells wide to start with one should -at least in principle- be able to "count" the unit cells around the GB. The GB is certainly stable enough to allow us to image it without problem.

However, in order to get atomic-scale resolution when imaging a surface it certainly help to cool the sample; although there are plenty of low-temperature STMs around so that is not a big problem anymore (and you only need to cool it to say 6-7K; which is easy and can be done using e.g. a flow cryostat).

 

[Lojzek]

To be more precise, I would like to know the positions of atoms to determine stress tensor in any point in the material (not necessary near the surface).

It seems straightforward to calculate strain tensor from the deformation of base vectors of Bravais lattice, but I'm not sure if they can be measured with sufficient accuracy.

Also, is it possible to get any information about stress tensor in areas with a lot of defects?

 

[alxm]

It seems to me you're asking for things that are at odds with each other.
On one hand, you're talking about the strain tensor, a bulk property, and such things as imperfections, grains, and such macroscopic properties.
On the other hand, you're talking about measuring individual atoms in the crystal lattice.

Now, you can model the latter (say using a DFT method) and get pretty accurate results for the microscopic scale, and using periodic boundary conditions, you can scale that up to _homogeneous_ macroscopic properties.

Or, you work at the macroscopic level and have some more empirical model that takes into account grains and that sort of thing. I'm no materials scientist but I'm sure there are approximate models that deal with it.

But if you're asking about how to model bulk properties of an inhomogeneous material all the way down to the level of individual atoms, I'm afraid I just don't think that can be done at present.

 

[Lateralis]

As a surface physicist with experience in scanning probe microscopies, I feel it is my duty to correct some details in this thread before people get the wrong idea! Even if these points strictly fall outside the scope of the (refined) question.

Firstly, scanning tunnelling microscopy (STM) DOES NOT give you atomic positions. STM is a probe of local electron density in teh vicinity of the Fermi level. In some cases where electron density is highly localised around an atomic site - in the case of strongly covalent III-V semiconductors - you can glean some basic information on relative atomic positions. However, this information is limited and one should not be seduced by the images one can sometimes obtain. However, in the case of metals, electrons slosh around more freely than in semiconductors, leading to much lower corrugations in electron density. In this way "Friedel oscillations" and other surface effects may in fact dominate STM signals leading to misleading images.

Similarly with AFM, you are not measuring the forces between a single atom on the surface and one on the tip. Whilst resolutions with AFMs are getting better all the time - and the very best can see features which are angstroms in size - one must always remember that the image obtained is a convolution between the tip (shape) and surface (features). This is true to all scanning probe microscopies, yet is a point that is often overlooked.

Next, AFM and STM do not necessarily require the use of ultra high vacuum (UHV). You use UHV with STM principally due to contamination of your sample. See Modern Techniques of Surface Science (Woodruff and Delchar) for more information on the deposition rate of 1 monolayer/unit time for a given pressure. However, I have done STM on graphene at room temperature and pressure (just to check the thing was working correctly before I took the time to pump out and bake the chamber), so it is possible. Moreover, AFM is often performed in atmospheric conditions, although AFMs that operate under a rough vacuum are becoming more popular. However, an AFM mounted on a fuly fledged UHV system leads to all sorts of complications one would not deal with if one did not have to!

As for TEM, it is possible to obtain atomic positons from diffraction images, but electrons interact strongly with matter and as such, a multiple-scattering algorithm should be used to determine anything quantitative.