Questions tagged [crystals]
Crystals are solid material whose constituents, such as atoms, molecules or ions, are *arranged in a highly ordered microscopic pattern*, a crystal lattice that extends with regularity in all directions. Use for all crystallography and ordered structure topics.
1,086 questions
2
votes
1
answer
112
views
Can diamonds be annealed like silicon?
Annealing is an important step in semiconductor fabrication. The doping of silicon crystals is done by ion implantation which creates a lot of defects in the crystal lattice. Heating the crystals for ...
- 2,641
3
votes
0
answers
73
views
Spread functional of maximally localized generalized Wannier functions
I am reading the 'Maximally localized generalized Wannier functions for composite energy bands' by Marzari and Vanderbilt (DOI: https://doi.org/10.1103/PhysRevB.56.12847, https://arxiv.org/abs/cond-...
- 31
4
votes
1
answer
181
views
Phase in translation operator
I was reading a paper by J. Zak on Magnetic Translation Group (Zak J 1964 Phys. Rev. 134 A1602). Where I came across the following expression (the paper defined the operator $\tau$ and later said this ...
2
votes
2
answers
170
views
Free Electron theory and fermi surface
I am trying to figure out following statement:
For noble metals, the free-electron picture would predict that the Fermi sphere does not reach the boundary of the first Brillouin zone. In reality, ...
- 21
1
vote
0
answers
74
views
Deriving the full crystal Hamiltonian from a Lagrangian density
I'm trying to understand the connection between field-theoretic Lagrangians and the standard Hamiltonians used in solid-state physics. In particular, consider a full crystal Hamiltonian of the form:
$ ...
2
votes
1
answer
153
views
What is a $k$-point physically — beyond its use in computational methods? [closed]
To my understanding, a $k$-point (or wavevector) is a point in reciprocal space that can be used as the “spawning” point of plane waves. These plane waves are then used as a basis set to describe a ...
- 21
3
votes
1
answer
292
views
How is the separation between core and valence electrons justified?
The full crystal Hamiltonian, strictly speaking, depends on all electrons, protons, and neutrons. Even before applying the Born–Oppenheimer approximation, one typically assumes — implicitly — that the ...
- 310
0
votes
1
answer
58
views
Dipole moment operator and $C_{1h}$ point group symmetry
Why does the dipole moment have to be perpendicular to the mirror plane in systems with $C_{1h}$ point group symmetry? I am trying to understand the dipole emission of point defects in solid-state ...
- 1
0
votes
0
answers
52
views
Particle-Hole Symmetry in Bloch Hamiltonians and Fock Space
I am having trouble understanding how Charge Conjugation is defined in Fock Space and in particular when applied to Bloch Hamiltonians.
In particular I would start by defining the PH operator ($P$)in ...
2
votes
0
answers
88
views
Confusion in the implications of Bloch's Theorem [duplicate]
I am a beginner in condensed matter physics and I am reading Bloch's Theorem from a book by Ashcroft & Mermin. It is saying that
because the set of all wave functions and energy levels for two ...
- 172
0
votes
0
answers
96
views
Are $(2,1,0)$ and $(-2,-1,0)$ Miller indices different planes or the same plane seen from opposite sides?
I’m learning about Miller indices and I’m a bit confused about how to interpret negative indices.
For example, consider the (210) plane in a cubic lattice:
If I take intercepts x=1a, y=2b, z=infty, I ...
- 11
1
vote
0
answers
100
views
Do Miller indices always need to be reduced to the smallest integers?
I’m studying crystallography and I’m confused about the convention for Miller indices vs. plane spacing.
If the intercepts are m=1/4,n=1/2,p=infty,
then by taking reciprocals I get (hkl)=(4,2,0).
...
- 11
0
votes
1
answer
160
views
How many Nitrogen-Vacancies (NV) can there be in a NV-diamond?
I read on the internet that Nitrogen-Vacancies (NV) diamonds can be made as large as $\approx$ 1 gram, so I guess they can be somewhat macroscopic. But how many NV centers there can be in a diamond? ...
- 1,111
1
vote
1
answer
128
views
On the Separability of the Coulomb Interaction into Ionic and Electronic Components within the Ewald Summation
Background and Context:
In calculations for periodic systems, such as ab initio MD, the Ewald method is employed to compute the Coulomb interaction. A known issue with the Ewald method is the ...
- 11
0
votes
1
answer
183
views
Why in the derivation of Bragg's law, the incident angle = scattered angle? [duplicate]
In the derivation of Bragg's law in Wikipedia here, they assumed that the incident angle is equal to the scattered angle. But every layer of atoms should act like a diffraction grating. Is somehow in ...
- 59