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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Does positronium have a stable crystalline phase?

This is a long shot, but while the 100YSS conference is going on at Houston, i haven't been able to get a grip on myself and think in other, more mundane and short-term rewards as normal people do. ...
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84 views

Neutron diffraction on Salty Ice VII

Can someone explain in layman's term how this figure shows the presence of Cl and Li ions in Ice VII ? What can we deduce about the crystal from this data ? The whole figure and caption are ...
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52 views

Lattice parameters and basis vectors of crystal lattice structures

Does someone know where I can find lattice parameters and basis vectors of crystal lattice structures (Strukturbericht Designation) for different materials? In particular I am searching the lattice ...
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37 views

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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What is the the real world interpretation of the high dimensionality of quasicrystals?

One of the examples of the problems of 5-fold symmetry is that pentagons tiled on a 2D plane do not completely fill that plane, leaving voids. This may be solved by "folding" it into 3D space, and ...
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Why is there a 'loophole' in Mermin Wagner for rotations?

I'm just starting out in my mathematics career by looking at some simple stuff on broken symmetries in statistical mechanics. Since 3D is 'hard' it would be very nice to look at 2D toy models of ...
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198 views

Bandgap Spacing in Photonic Crystals

I am doing some self-study on photonics and have encountered the following question: We know that amorphous electronic crystals such as amorphous silicon have a bandgap. Can amorphous photonic ...
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23 views

Deriving Reciprocal Lattice Definition

The derivation of reciprocal lattice vectors in terms of the direct space lattice vectors starts by applying expanding a translationally invariant lattice function $f(\bf{R_k}+r)$ in plane waves $f_k ...
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34 views

Crystals in piezoelectricity

I was reading about piezoelectricity and crystals and found such a statement (on Wikipedia) : For example, a 1 cm3 cube of quartz with 2 kN (500 lbf) of correctly applied force can produce a voltage ...
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52 views

Proof that magnetic Bloch waves are almost periodic in the reciprocal index

I would like to prove that the magnetic Bloch waves change by a phase factor if you shift their crystal momentum by a reciprocal lattice vector. That is, if $u_{n,\mathbf{k}}(\mathbf{r})$ is a Bloch ...
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25 views

What is crystal “supermodulation”?

I am researching the pair density wave in cuprates, and during my reading I came across a term "crystal supermodulation". I believe it relates to BSCCO. Can anyone give me a definition or give me a ...
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46 views

Estimate Uncertainties in Rietveld Refinement

I have the output of an x-ray diffraction experiment made on a thin film. Here I report the output of the experiment (I analyzed those data using powdercell and coloured regions have been excluded ...
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217 views

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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115 views

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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244 views

Discrete sum over an exponential with imaginary argument, considering only every second lattice site?

Let's say I sum an exponential function $e^{\imath \left(k-k^{\prime}\right) x_{i}}$ over a chain system where every member of the chain is of the same type, e.g., A-A-A-...-A-A (total of N sites) ...
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27 views

High pressure deformation of metals

Does copper undergo elastic recovery after being exposed to high pressures (above 30 GPa in a diamond anvil) at room temperature?
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27 views

Lattice sums (solid state physics)

The potential in a crystal doesn't only depend on the distance between 2 atoms, but also with the interaction to all $j^{th}$ neighbour-atoms. The Lennard-Jones-Potential then becomes $U(R_j)=\...
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44 views

Space groups and crystals. Simple example for the diamond structure

I try to learn the basis notions in crystallography and space group. But I already fail at the beginning. Let me give you an example: Consider the diamond structure (space group $Fd\overline 3 m$, ...
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33 views

Dopants vs impurities

The question is related to terminology. What is the difference between dopants and impurities in condensed matter (semiconductor) physics?
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30 views

Structure Factor for a Simple BCC Lattice

This is an example of a general misunderstanding I am having. The structure factor is given by $$S=\sum_{j}f_je^{i\mathbf{G}.\mathbf{x_j}}$$ where the index $j$ denotes a sum over the atoms within a ...
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74 views

Coulomb potential of a periodic crystal in reciprocal space

Usually the Coulomb potential (electron-electron interaction) can be Fourier transformed (aside from prefactors) like that: $$ \frac{1}{|\vec r_1 -\vec r_2|} = \int \frac{\text d ^3 k}{(2\pi)^3} \frac{...
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85 views

Activation energy of luminescence

Assuming that activation energy is constant for some range of temperature, it can be determined from the slope of the plot: $$\ln{I}=A-\frac {E_a}{k_bT}$$ where $I$ - intensity , $E_a$ - activation ...
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68 views

Four dimensional Bravais lattice

I am wondering if there are any reference on four dimensional Bravais lattice and their primitive vectors, even an example will help.
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45 views

Sum in the reciprocal lattice

I have to use this property but I don't understand at all the deduction, so I was wondering if someone could help me. We have a crystal lattice with vectors to each atom from one of them $R_j$, and ...
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77 views

Is there an intuitive reason for why the reciprocal lattice of FCC is BCC and vice versa?

This can be proved using formulae for generating reciprocal lattice vectors from direct lattice vectors. But does this result have more to it than meets the eye?
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65 views

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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331 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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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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143 views

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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156 views

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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427 views

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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47 views

pressure required for displacing a single electron off a crystal

I need to know this for my project- "power generation using the pressure applied on a keypad of a mobile electronic device". How much pressure does it take to displace a single electron off its ...
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389 views

What defines the thickness of a Nomarski prism?

Lets say I want to design a Nomarski prism that would split the ordinary and extraordinary beam by an angle of 0.32 mrad. I used a raytracer to find the internal angle between the quartz wedges. ...
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12 views

How exactly to build the band diagram for photonic crystal?

How to build a band structure for the photonic crystal? I'd like to understand the full train of thought. I understand that we go on the perimeter of irreducible first Brillouin zone and somehow copy ...
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23 views

The d-orbital splittings in WS2 monolayer

According to this paper (and many others), the formely degenerate $d$ orbitals of the tungsten atoms in the $WS_2$ monolayer are split into three groups: (1) $d_{z^2}$, (2) $d_{x^2-y^2}, d_{xy}$ and (...
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30 views

Miller indices and distance between parallel planes in a cubic lattice

I have been learning about the Miller indices of a lattice plane and how to use them to find the distance to the nearest parallel lattice plane in a Cubic lattice but I must be getting something wrong....
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18 views

How one can count how many phonon modes is there in the crystal?

I'm reading the review on phonon and Raman scattering in 2D transition metal dichalcogenides (2D TMDCs). At the beginning of Section 2.1 it is said that, since there are two X-M-X units in the crystal'...
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24 views

crystal lattice modification

Can the lattice of a copper with FCC structure be altered, even microscopically? Copper has 0.361 nm lattice constant but can it be altered by external force, say neutron impact?
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23 views

Occupancies of atoms in a crystalline structure from wyckoff positions of space groups

I am trying to fit an XRD pattern using the ILL program: FullProf and in one of the codes I have to enter the positions and occupancies of the atoms in the unit cell. I am working on the YSZ ($Y_xZr_{...
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17 views

Construction of a lattice structure and the Wyckoff positions

I would like to build a unit cell of a Cmcm (no. 63) lattice structure. It is a orthorhombic crystal and my lattice vectors are $\vec a_1 = (1,0,0)\,,\; \vec a_2 = (0,3,0)\,, \;\vec a_3 = (0,0,2)\,.$ ...
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38 views

Explanation of crystal formation in a Fitzroy's storm glass with the change in weather conditions

I was recently reading about Admiral Robert FitzRoy's storm glass and how it was used to predict the weather conditions based on the formation of camphor crystals in a sealed glass tube containing ...
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12 views

What is the growth mode of thermal-evaporated aluminum on organic subtrates?

Does aluminum grow in an island mode or layer-by-layer mode on organic substrates which is amorphous? For example, on PMMA, fullerene or surfactant thin films. Can I predict the mode by comparing the ...
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18 views

Commutation of photonic crystal master equations

In studies of photonic crystal's, there are two "master equations" for the electric and magnetic fields: $$\mathcal{L}_\mathbf{E}\mathbf{E}=\frac{1}{\epsilon(\mathbf{r})}\nabla\times\nabla\times\...
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23 views

Analytical derivation of photonic bandstructure in photonic crystal

It seems the usual way to find the photonic bands of a photonic crystal is to setup the "master equation" $$\nabla\times\left(\frac{1}{\epsilon(\mathbf{r})}\nabla\times\mathbf{H}(\mathbf{r}) \right)=...
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32 views

Using Huygen's principle to draw diagram of wave propagation within uniaxial crystal?

"A beam of unpolarised plane wave is incident normal to the surface of a slab of the crystal, with optics axis 45 degrees to the surface. Based on Huygens’ principle, draw the beams propagating in the ...
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Which crystal defects might single, very bright Reflexes in Laue Images indicate?

In a Laue X-ray crystallography , if you observe a single Laue reflex very bright, which is not one of the main reflexes, can that indicate a certain crystal defect or is it a peculiarity in the ...
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How to determine the basis of any crystal

In the following example, I have a rutile TiO2. Here the basis of O with respect to Ti is (0.3*x, 0.3*y, 0*z), where a,b,c are the lattice vectors. So in order to build a crystal, I need the basis and ...
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What is temperature dependence (Schottky defects)?

The problem requires us to use the following property to determine the temperature dependence: For a system in thermal equilibrium in a heat bath at temperature $T$ the Helmholtz free energy is a ...
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162 views

Calculating potential energy per ion of an one dimensional ionic crystal

The problem states to calculate "the potential energy, per ion, for an infinite 1D ionic crystal with separation $a$"; the crystal is a 1D lattice of alternating charges, likes so: $$...+-+-+-+-+-...$...
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Whether raman spectroscopy is dependent on crystallographic orientation

If I have three bars of Si, and each has the (100) (110) and (111) surface pointing up at the laser respectively, will I get a different raman spectra for each of them? In my opinion, I shouldn't ...