10
votes
Why does x ray diffraction take place in crystals as it seems to violate the law of conservation of energy?
For your concerns about energy conservation, the issue here is that you are considering the electron as essentially free, whilst in reality it is tightly bound to the crystal structure. The crystal ...
- 9,450
8
votes
Accepted
Medical X-Ray - why no diffraction?
Since the lattice spacing is about eight angstroms, the issue isn't any sort of unusual lattice spacing. Instead, the issue is that bones are thick.
[Another answer points out that the crystals are ...
rob♦
- 94.2k
6
votes
Distance between adjacent planes in a crystal
In answer to the question: adjacent planes are planes that are closest to one another when distance is measured along the normal to the plane. It is important to understand that every lattice point ...
- 141
6
votes
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What did Feynman say about cesium chloride and body-centered cubic structure?
A Google search turned up the May 2016 IAS article Errors in The Feynman Lectures on Physics; Symmetry and Crystals by Rajesh Prasad, which I think explains the remark. In Vol. II, Section 30.4 of the ...
- 8,517
6
votes
Interplanar distance in FCC and BCC
The formula $d_{hlk} = \frac{a}{\sqrt{h^2+k^2+l^2}}$ is a special case of the general formula:
$$d_{hkl} = \frac{2\pi}{|\vec{G}|}$$
for a reciprocal lattice vector $\vec{G}$ to the case of a cubic ...
- 4,574
6
votes
What is the unit and dimension of a matrix operator in quantum mechanics?
In scattering theory, $\hat V$ is a potential and has units of energy, while the Green's function is
$$
\hat G_0=(E-\hat H_0+i0^+)^{-1}
$$
has units of the inverse of an energy.
Therefore, there isn't ...
- 12.1k
6
votes
Determining Brillouin Zone for a crystal with multiple atoms
Lattice and crystal structure are two different things.
A crystal structure is a convolution of a (Bravais) lattice with a basis (an atom or a group of atom).
A lattice is a collection of geometrical ...
- 566
5
votes
Accepted
Determining Brillouin Zone for a crystal with multiple atoms
Option 2 is essentially the correct approach. Just as in the your Bravais lattice example, you begin by writing down the lattice vectors $\mathbf{a}_i$ of the real-space lattice. The lattice vectors ...
- 2,749
4
votes
Accepted
How can a monochromatic X-Ray tube produce a spectrum in XPS?
Because the X-rays, in the Photoelectron spectroscopy device, excite the electrons from the individual core levels out and as we know the electrons from the individual core levels reside in different ...
- 1,398
4
votes
Accepted
Is the Compton effect observed during regular x-ray diffraction?
Yes, in fact Compton scattering is often an annoyance in x-ray diffraction when you want to study the diffuse background from crystal defects and disorder. The amount of Compton scattering is highly ...
- 8,129
4
votes
Accepted
What is an example of an actual crystal with a primitive cell containing more than one atom?
Diamond and any diamond-like materials (silicon, GaAs, etc.). The most transparent example is probably graphene (since it is two-dimensional) - its primitive cell contains two atoms (referred to as A ...
- 65k
3
votes
Accepted
Structure factor calculation for non-cubic lattices
The common (at least in my field...) definition for the structure factor is
$$
S({\vec q}) = \frac{1}{\sum_{j}b_j^2} \sum_{j} \sum_{k} b_j b_k \mathrm{e}^{-i{\vec q}\cdot({\vec r}_j - {\vec r}_k)}
$$
...
- 1,235
3
votes
How can a monochromatic X-Ray tube produce a spectrum in XPS?
Monochromatic X-rays produce electrons from a multiplicity of orbitals,
producing a range of electron kinetic energies. One can analyze the outgoing electron
energy to produce a spectrum. It's a ...
- 10.2k
3
votes
Why are X rays in X ray crystallography diffracted by the electron clouds rather than nuclei?
Contemplate the difference in "size" of electron orbitals to the nucleus that is contained in the center:
Atomic sizes are on the order of 0.1 nm = 1 Angstrom = 10^-10 m
Nuclear sizes are on the ...
- 235k
3
votes
Accepted
Why the first peak in the X-ray diffraction of an amorphous solid has significantly high, in terms of intensity than the second peak?
In a perfectly crystalline solid the distances between the scattering planes are precisely defined so the scattering angles are precisely defined. In principle the XRD spectrum would show an ...
- 363k
3
votes
Accepted
Relation between $(hkl)$ indices and the integers $m_i$ in $\vec{G}=\sum_i m_i\vec{b}_i$?
A crystal plane with Miller indices $(hkl)$ is orthogonal to the reciprocal lattice vector $\vec G = h \vec b_1 + k \vec b_2 + l \vec b_3$.
- 71.3k
3
votes
Accepted
Can X-ray diffraction be applied to liquids, gasses or non-crystalline materials?
(I'm going to focus on protein crystallography here)
Yes, in fact Small-angle X-ray Scattering, in which (usually) proteins are not in the crystalline state, is used extensively in biochemistry, ...
- 1,175
3
votes
Accepted
What kind of material could be used as a diffraction grating for Xrays?
You can use whatever single crystal you have. The cheapest high quality single crystals are Si wafers.
Another more DIY-type option might be taking an old GPU or CPU die and grinding it off somewhat ...
- 1,831
3
votes
Accepted
Do neutrons change their wavelengths when diffracted?
X- rays can be treated with classical electromagnetic equations, and diffraction presupposes elastic scattering, so no (or very small) loss in energy.
Neutrons are quantum mechanical entities and the ...
- 235k
3
votes
Number of Possible Primitive Vectors and Primitive cells in a Bravais Lattice
Consider any lattice with primitive vector triplet ($\vec{x},\vec{y}, \vec{z})$. Any lattice vector $\vec{v}$ can be written as
$\vec{v} = v_x \vec{x} + v_y \vec{y} + v_z \vec{z}$
where $v_x, v_y, v_z$...
- 304
3
votes
Accepted
Physical meaning of Laue's condition for diffraction from crystals
But how can a 'particular vector' equal a set of vectors=
Of course it is mathematical nonsense to say,
a particular vector $\Delta\mathbf{k}$ is equal to a set of vectors.
$$\Delta\mathbf{k} = \{ \...
- 41k
3
votes
Accepted
Book recommendation on X-ray diffraction
Two of the books in my collection:
"Principles of Protein X-ray Crystallography" by Jan Drenth
This book focuses on the application of X-ray diffraction to the study of proteins. It ...
2
votes
Structure Factor for a Simple BCC Lattice
The Wigner-Seitz cell of a bcc lattice is not cubic, i.e. the angles $\alpha$, $\beta$, $\gamma$ are not 90°. They are actually around 109.3°. Therefore you have to build your reciprocal lattice with ...
2
votes
Accepted
How do visualization programs generate electron density meshes?
Starting from the end:
map → isosurface
If you have electron density values in the form of 3D discrete scalar field
(i.e. values on a 3D grid) you can use a computer graphics algorithm,
such as ...
- 215
2
votes
Why are X rays in X ray crystallography diffracted by the electron clouds rather than nuclei?
I agree with Pieter (but I do not have enough reputation to comment yet). And as pointed out by Physicist137, they actually scatter elastically both to electrons and nuclei. (see this paper on ...
- 181
2
votes
Noncentrosymmetric crystal symmetries; list of polar and chiral space groups
A space group is non-centrosymmetric if it doesn't contain centers of inversion.
To check for centers of inversion, you need to look at the full Hermann-Mauguin symbol.
If the symbol contains
(a) ...
2
votes
Accepted
How to find the Miller indices for a family of planes?
Assume a 3D lattice and denote its reciprocal lattice basis vectors as $\vec{b}_{1,2,3}$. The symbol $\left(h,k,l\right)$ stands for all the planes orthogonal to the vector $h\vec{b}_{1}+k\vec{b}_{2}+...
- 4,239
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