How is the microscopic crystal structure visible?

[znbhckcs]

I just noticed that it's often taken for granted that a macroscopic crystal has a similar geometric structure as in the atomic scale.
What is the physical explanation for this (assuming it is true)?

 

[cgk]

Who is taking that for granted?

Note that this topic is nothing which *needs* taking anything for granted, because you can easily measure the geometric structure down from the single atom level (with scanning tunneling microscopy or high-resolution transmission electron microscopy) up to the 1mm scale. And from around 2nm to 2mm you can even do this smoothly (i.e., with all resolutions in between) with a scanning electron microscope.

That being said, the structure on the atomic scale is often only a minor player in the structure and properties of a real crystal. For example, plasticity and most other mechanical and magnetic properties of metals are determined mainly by crystal defects (dislocations and grain boundaries, in particular).

 

[znbhckcs]

Ok, perhaps taking for granted was not a good way of putting it. I was trying to say this is a phenomenon to which I have never really given much thought.

My question is what is the physical mechanism by which the microscopic structure is visible on a macroscopic scale?
I am not talking about defects... I just can't see why, for example, a cubic lattice on the atomic scale should be cubic on a macroscopic one.

 

[johng23]

When you say "cubic on the macroscopic scale", what do you mean? Its physical shape?

 

[znbhckcs]

Yes. I mean the physical shape... for example look at this http://commons.wikimedia.org/wiki/File:Rock_salt_crystal.jpg" .
And remember that NaCl is a cubic (fcc) lattice.

 

[ZapperZ]

Yes. I mean the physical shape... for example look at this http://commons.wikimedia.org/wiki/File:Rock_salt_crystal.jpg" .
And remember that NaCl is a cubic (fcc) lattice.

One can do an x-ray diffraction, which is one of the most common methods to determine the crystal structure. Doing such a thing, one can get the crystal structure in the reciprocal space, and consequently, the crystal structure in real space. So no, none of these were accepted without any direct empirical evidence.

Zz.

 

[Dr Lots-o'watts]

My question is what is the physical mechanism by which the microscopic structure is visible on a macroscopic scale?
I am not talking about defects... I just can't see why, for example, a cubic lattice on the atomic scale should be cubic on a macroscopic one.

I also find macroscopic cubic crystals fascinating. Pyrite is another good example:
http://innumerablegoods.typepad.com/innumerable_goods/2007/05/pyrite.html

Fundamentally, I can imagine arriving atoms statistically depositing on the rough edges before starting a new (001) layer, so this would give out a prism. Now if atoms come in from all directions equally-the crystal generally bathes in the required gas-you'll tend to get cubic rather than rectangular. That should at least be a first approximation to the exact process.

 

[johng23]

There are generally certain sets of crystal planes which cleave easier than others, and the arrangement of these planes will have the same symmetry as the unit cell, so that's why if the entire material is a single crystal and you break it apart, it will share some of the symmetry of the microscopic structure, and if you try to cut it along these particular planes, it will cut easily and will not have a rough surface.

Don't know if that helps.

 

[znbhckcs]

But if the symmetry is visible because the crystal breaks only along these special plains, that would mean that the macroscopic crystal surface should be smooth to a very very high degree: almost to the level of a single atom. Is that true?

 

[DrDu]

Usually, the habitus of a crystal from a cubic system is not a cube. It may also be a tetrahedron an octahedron a truncated octahedron or something much more complicated.
For all crystal systems it is possible to derive from the angles between the faces the angles between the basis vectors spanning elementary cell and the ratios of their lengths a:b:c.