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.

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Kronig-Penney model

I am studying the Kronig-Penney model as treated in the book by Kittel: Introduction to Solid State Physics. In this model one considers a period potential which is zero in the region $[0,a]$ (...
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Bloch's theorem

I am studying Bloch's theorem, which can be stated as follows: The eigenfunctions of the wave equation for a period potential are the product of a plane wave $e^{ik \cdot r}$ times a modulation ...
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Why does a halocline form?

I was doing an experiment over the last couple of days to try to crystallize alum using a thermal gradient. The idea was that solute at the bottom of my container would be dissolved at a higher ...
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Why a mono-atomic crystal layer (2D) can't be stable?

According to Peierls and Landau, 2D crystals were thermodynamically unstable. They can't exist! Of course, this theory was disapproved in 2004 (example: graphene). What is the general definition of ...
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Pseudocubic unit cells: how to construct one?

I keep coming across the term pseudocubic unit cell while reading about orthorhombic perovskite structures. No clear explanation ...
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How can one reasonably theoretically model polycrystalline materials?

Many techniques are taught in advanced solid state courses but they are almost all derived for perfectly crystalline materials. For example, band structure really only appears theoretically when you ...
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Reciprocal Lattice of a non-bravais lattice

Is a reciprocal lattice defined for non-Bravais lattices? I'm trying to work out one for HCP structure and not figuring it out.
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Why can't a dislocation terminate in the bulk?

We are told that they can only terminate on surfaces, grain boundaries or other dislocations but we are not told why they can't terminate inside the crystal.
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What does (001) Silicon mean?

If someone gives me a thin film of Si, and they tell me it's (001) Si, does that mean that the (001) planes of Si are the ones making up the surface of the film?
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Translation invariance in crystals

Context: solid state physics - dynamics of atoms in crystals. Coupling constants are defined as: \begin{align*} \frac{\partial^2\Phi}{\partial r_{nai}\partial r_{mbj}} = \Phi_{nai}^{mbj} \end{align*...
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273 views

Ashcroft Mermin Solid State Eq. 22.15

I recently read a paper on Specific heat of a Classical Crystal: Dulong-Petit law. In Eq. 22.15, I don't understand why the ionic displacement $\mathbf{u}$ and ...
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Conductivity of a crystalline solid

In a crystalline solid each atomic level 'splits' into n levels (n = number of atoms in the system). When the number of atoms is large each level becomes replaced by a band of closely spaced levels. ...
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317 views

Difference in chemical potential in supersaturated solutions

I have been more or less struggeling to understand an equation that is apparently used in almost all books covering crystals in any way. Basically every book that I have found explains the following: ...
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Experimental Evidence of Random Tiling Limit Shapes

In the area of random tilings, there are many results that fall under the term "Arctic Circle Theorems." This roughly means that if one chooses a tiling of a specific region uniformly at random, then ...
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Point group symmetries and unit cell

I was wondering if the unit cell (of a given lattice) had to have every point group symmetries of the lattice it defines ? I guess there is no unique way to define a unit cell and that it may not have ...
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345 views

Atomic nearest neighbor notation

I recently got a correction to a paper that I am writing. The correction references a section in which I talk about nearest neighbors. The comment says: Do you mean NN, NNN, etc., or NN, 2NN, 3NN? ...
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How does a liquid crystal on Silicon affect the phase of incident light?

When a polarized light beam is directed to a phase-only LCoS system how is the phase modulated ? What is the physical effect behind ? Does voltage modulation has an impact on birefringence ?
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531 views

Overview and doubts about Bloch's theorem and the concept of partial density of states

So I have a large confusion with QM as applied to solid state. The following is a summary of what I know, what I think I know, and what I know I don't know. I hope to stir a discussion that will help ...
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How strong is electron degeneracy pressure?

I'm trying to get some specific numbers for electron degeneracy that I can understand, using a concrete example. Take for example this portion of carbon crystal: Exactly how much energy would be ...
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What groups of symmetry are most suited for filling uniformely a spherical 3D space, whilst possessing the lowest possible surface-to-volume ratio?

I am looking for the closest known approximate solution to Kelvin foams problem that would obey a spherical symmetry. One alternative way of formulating it: I am looking for an equivalent of Weaire–...
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Topological Insulators: is HgX a special case?

I got confused by reading this article: Francois Virot, Roland Hayn, Manuel Richter, and Jeroen van den Brink. “Engineering topological surface-states: HgS, HgSe and HgTe.” arXiv preprint arXiv:...
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How does a vacancy become mobile during annealing?

The Nitrogen Vacancy (NV) centre is a defect in diamond consisting of a substitutional nitrogen atom accompanied by a vacant nearest-neighbour lattice site. Substitutional nitrogen impurities are ...
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Are synthetically-produced diamonds as hard as natural diamonds?

I was having a discussion with my friend about the intrinsic worthlessness of diamonds (DeBeers and whatnot) and how synthetic diamonds haven't caught on, again because of the marketing/propoganda ...
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345 views

Simplest derivation of Fourier transform for periodic functions (in crystal lattice)?

What is the simplest derivation of the following two well-known formulas that work for crystal lattice [1]: $$ F[f(\mathbf{x})] \equiv \tilde f(\mathbf{G}) = {1\over\Omega_\mathrm{cell}} \...
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262 views

How to derive inverse Fourier transform for periodic functions (in crystal lattice)?

I would like to derive the following two well-known formulas that work for crystal lattice [1]: $$ F[f(\mathbf{x})] \equiv \tilde f(\mathbf{G}) = {1\over\Omega_\mathrm{cell}} \int_{\Omega_\...
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995 views

Bloch wave function orthonormality?

there is this text book that is giving me a hard time for a while now: It shows that Bloch wave functions can be written as $$\Psi_{n\vec{k}}\left(\vec{r}\right) = \frac{1}{\sqrt{V}}e^{i\vec k \vec r}...
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Interpretation Born-Von Karman boundary conditions

The cyclic Born-Von Karman boundary condition says that if we consider a one dimensional lattice with length $L$, and if $\psi(x,t)$ is the wavefunction of an electron in this lattice, then we can say ...
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332 views

Interpreting a Hamiltonian in terms of 'hopping' operators

I am having some trouble interpreting a Hamiltonian in terms of "hopping" operators. The Huckel model for nearest neighbour interaction in graphene is given by $$H=-t\sum_\vec{R}|\vec R\rangle\...
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342 views

Dispersion relation of silicon

In the case of dispersion relation of silicon having crystal plane orientation 111; what is the Sellmeier's equation for refractive index $n$ of silicon orientation 111 & what it's extinction ...
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Lattice theory in mathematics and physics [closed]

I have undertaken a project examining lattice model and trying to construct algorithm that could work on all lattice (in physical sense, or crystal structure). I notice there is a branch in ...
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166 views

Structure factor of crystals (X-ray crystallography)

How can one prove that the degree of each node in a distance graph must be at least four in order to obtain a unique solution to an exact distance geometry problem with sparse distance data? The ...
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366 views

Anisotropic refractive index with isotropic components?

In relation to my question here I wanted to make sure that my physical argument was not flawed. Anisotropic properties, (especially refractive index) is characteristic of a well-ordered solid (...
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262 views

Bloch's theorem and Bloch's state

The question is not so much about the theorem, but more about what it means in this context: see this link. So yes, because of Bloch's theorem the Hamiltonian eigenstates in a crystalline system can ...
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What is the physical meaning of group velocity for elastic waves through crystals?

In a chapter about phonons they define group speeds for elastic waves in crystals as the derivative of the dispersion relation: $$v_g = \frac{d{\omega}}{d{k}} $$ I wonder though how they come to ...
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What are degenerate transversal oscillation modes?

This is just a question about terminology that is used in the beginning of a chapter about phonons. In a simple cubic crystal, we can consider elastic oscillations in f.i. the [100] direction. In ...
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What determines Phonon - Phonon collisions?

I was in Solid State Physics lecture yesterday and we BRIEFLY went over what causes phonons to collide with one another. Things such as crystal imperfections, boundaries, Temperature, but I was ...
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Is there a derivation of all possible Bravais lattices in 2D and 3D?

Do any of you know a (possibly elegant) derivation of all possible Bravais Lattice and the Crystallographic Group of Lattices in 2 and 3 dimensions? Group theory /abstract nonsense approaches are ...
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136 views

Plane Wave expansion method

I really don't know if this is the right forum to ask the question...but please help me if you can!! I was going through the Plane Wave Expansion Method Derivation...But to be honest I could not find ...
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How should I think about reciprocal lattice and Miller indices?

When I hear someone talking about a (100) plane or a (111) plane or an (hkl) in general, my first thought is, is the system cubic. The reason I think this is because I tend NOT to think of the planes ...
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Why does ice have a lower density than water?

Can someone explain me why is ice less dense than water? As I know, all solids are usually denser than the liquids (correct me if I am wrong).
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How to demonstrate that there are just 14 types of Bravais lattice?

Is it possible to demonstrate that there are just 14 types of Bravais lattice without the knowledge of group theory?
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Why do some things crystallize? (And others don't, for that matter.)

Ice, for example, will form a crystal when frozen under certain circumstances. Why is this the case for ice? While on the subject of water crystallization, why do snowflakes usually form in base 6 ...
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Regarding Bravais lattices

There is 'End-Centered' Orthorhombic lattice . Why this type is not in 'Cubic' lattice ? On which basis did Bravais propose his theory ?
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Methods for determination of crystal lattice's homogeneity

I know of X-Ray diffraction, which produces a pattern corresponding to the inverse Fourier Transform of the lattice (reciprocal lattice). While this method is widely employed, it provides more ...
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Molecule vs Crystal

Feynman mentions in his lectures: ...the concept of a molecule of a substance is only approximate and exists only for a certain class of substances. It is clear in the case of water that the ...
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Should a polyatomic crystal behave similarly to the bulk of each/either of its constituent elements?

Generally, metals are usually fairly conductive, but their oxides aren't. I know conductivity is just one attribute, but in general, should you expect a, say, diatomic bulk crystal's properties to be ...
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Do indirect optical transitions “cool” the material a little?

So I'm reading in Ashcroft and Mermin about indirect optical transitions: So, a photon comes in, and it only excites the electron across the indirect band gap if a phonon with the appropriate wave ...
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The boundary between polycrystalline and crystalline

My current understanding of solid crystalline-like materials (please correct me if I'm wrong!) is that it is a continuum in terms of crystallinity, from amorphous (basically no periodicity) to single ...
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951 views

gaussian fitting of xrd peaks

I am reading a paper regarding the nano crystalline material with hexagonal crystal structure. In that paper in order to find out lattice parameter of hexagonal crystal structure they have fitted a ...
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How to homegrow large, momocrystalline water ice crystals

This is a follow up to this question:Can one get clear ice crystals from a dirty suspension?. How could one grow a large - meaning visible with the naked eye - water ice crstal with common household ...