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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Have I found all of the zero order laue zone points for an FCC crystal being imaged along the [111] zone axis?

Since the equation for laue zones is hu+kv+lw=0 and the electron beam is incident in [uvw]=[111] can I say that the first order laue zone points are [hkl]=[-110],[1-10],[-101],[10-1],[0-11], and ...
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Honeycomb Bravais Lattice with Basis

I just had my second solid state physics lecture and we were talking about bravais lattices. As far as I understand a Bravais lattice is an infinite network of points that looks the same from each ...
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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 ...
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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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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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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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32 views

How does the surface of a material always break inversion symmetry?

I am trying to visualize this for an HCP structure. Take the profile view as such: just working in 2d. So my understanding is if we can take a point (x,y) -> (-x,-y) and get the same crystal than ...
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FCC-to-BCC phase transition in NaCl, Buckingham or Lennard-Jones potentials?

Background The transformation from B1 (face centered cubic (FCC) type) to B2 (body centered cubic (body centered cubic (BCC) type) structures is one of the best documented high pressure phase ...
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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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39 views

Hartree-Fock orbitals of a periodic crystal -> Bloch waves?

I am wondering how I can see that the Hartree-Fock orbitals of a periodic crystal obey the Bloch theorem? My problem is that the Hartree-Fock Hamiltonian does not have the form $-\frac 1 2 ...
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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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Commutation of photonic crystal master equations

In studies of photonic crystal's, there are two "master equations" for the electric and magnetic fields: ...
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30 views

Would High Explosive helped free Shackleton's ship, trapped in pack ice?

This question is based on physical concepts regarding presssure waves and crystallography, but I thought it might be helpful to include a brief historical context first. From Wikipedia: Loss of Polar ...
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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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31 views

Nonzero stress on crystal at equilibrium volume?

Using a first principles computational method such as DFT, you can calculate the energy of a unit cell at different volumes to obtain a parabolic energy vs. volume curve. The minimum of this curve ...
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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}) ...
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82 views

Physical meaning of crystal momentum

I am familiar with some of the definitions of crystal momentum and I am familiar with how it is related to Bloch's theorem. I also am familiar that crystal momentum is not the momentum of each ...
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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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Number of atoms in HCP unit cell

Whenever the atomic packing factor for the hexagonal close-packed (HCP) crystal structure is discussed, such as in this wikipedia article, it is stated that the (effective) number $N$ of atoms in a ...
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43 views

Is it possible to see a diffraction pattern from a BCC crystal made of 2 randomly-distributed species?

Suppose I have a 50-50 mix of two different kinds of atoms in a crystal. The crystal is BCC and the atoms have different scattering factors $f$. I know that if the crystal is organized in the regular ...
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Is it possible for a crystal to have different structures at different temperatures?

For instance, suppose it is a 50-50 alloy of two metals that is BCC at room temperature $T_0$. If I raise (or lower) the temperature, is it possible for the bonds in the crystal to rearrange and form ...
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31 views

Understanding FCC and BCC Bravais Lattices

A book I am reading states that one possible definition of a Bravais Lattice is that the surroundings will look the same from whichever lattice point you observe from. Consider for example the simple ...
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26 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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If pencil tip is heated why doesn't it write?

Why doesn't a pencil write if its tip is heated in a candle flame?
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Bloch Functions as an implication of the Crystallographic Restriction Theorem?

I'm studying Bloch Functions and it seems to me safe to assume that they are the most general Eigenfunction of a Hamiltionian with the crystal periodicity. Now the only considerations made in deriving ...
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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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24 views

Can a piezoelectric material only vibrate at one frequency?

Given a material X with piezoelectric properties which is used in a ultrasonic transducer, what determines the working frequency of said transducer? If hypothetically such a transducer is specified ...
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99 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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7 views

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 ...
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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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3D Bravais Lattices in terms of $\mathbb{Z}^3$

I am looking at the definitions of Bravais Lattice on Wikipedia and I find that I can describe many of them in terms of a mathematical lattice $\mathbb{Z}^3$. cubic $\mathbb{Z}^3$ body-centered ...
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Electrode configuration when radially poling piezoelectric material?

All the information on the web I have come across WRT poling piezoelectric material usually assumes a uniform field (such as between two plates). I would like to pole a cylinder so that the reverse ...
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Are There Any Theories To Explain Why Ice Freezes in Orthogonal Patterns on Surfaces Such as Glass

If one examines the following image: One will notice that the ice is freezing in this characteristic criss-cross pattern. Are there any theories to explain this behavior? I've seen this on car ...
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How do atoms scatter X-rays?

I am learning the theory behind X-ray diffraction but I have a question. According to the textbook I am using, X-ray tubes (in diffractometers) produce near monochromatic X-rays. In other words, they ...
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40 views

How can we prove that each point (hkl) in the reciprocal lattice corresponds to a set of lattice planes (hkl) in the real space lattice?

In crystallography, we always speak about the direct and reciprocal lattice spaces. One property about these spaces in mentioned here, as follows: Each point (hkl) in the reciprocal lattice ...
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How to understand the simplified tight-binding representation on square lattice?

I have read a paper in this website:http://cmt.nbi.ku.dk/student_projects/bsc/Haider_Moradi_BSc_thesis.pdf I am curious about how to understand the simplified tight-binding representation on square ...
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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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74 views

Space group setting of a crystal structure

I was reading a PDF of a crystal phase in order to draw its structure, when I noticed that it was, apparently, ambiguously described. The PDF lists two descriptions of the monoclinic structure: 1) ...
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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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Twin and Detwin Crystals [closed]

Hello i would like to ask , what are twin and detwin monocrystals? what has to do with their crystalographic symmetry? any consequences ? any image also would be really helpfull! Thank you
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Process of x-ray crystallography

This is a pretty basic question but I would just like some confirmation of what I suspect is true. As I understand it, the basic idea behind x-ray crystallography is that we take our crystal and hit ...
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Solving Bloch Waves for Potentials with Few Fourier Components

Suppose we have a potential in 1D $$U(x) = 2A\cos(\frac{2\pi}{a} x)$$ Let $G_\alpha$ be reciprocal lattice coordinates $$G_\alpha = \frac{2\pi \alpha}{a},\;\;\;\;\alpha\in \mathbb{Z}$$ As in Ashcroft ...
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What are gyrotropic crystals?

I am reading a paper about spin photocurrents that talks about gyrotropic crystals, but I do not find any good explanation what gyrotropy is or how to find out whether a crystal belongs to the ...
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621 views

Why are HCP materials brittle whie FCC materials are ductile?

Why are hexagonal close packed materials brittle, While face centered cubic is ductile. Is it related to crystal planes?
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81 views

crystal structure of metals

I am studying solid state physics and I'm a complete newbie in that sense. I know that semiconductors and group IV elements bond themselves in the FCC structure with covalent bonds which satiate the ...
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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} ...
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Reduce integration over crystal to integration over unit cell

I am wondering when I can reduce integrals over a periodic crystal to a an integral over the unit cell. Especially I consider the following two-electron integral $$ I=\langle \varphi_i \varphi_j | V | ...
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Might a diamond with impurities (doped) be less brittle than a pure diamond?

Diamonds are extremely hard (resistant to pressure) but quite brittle (susceptible to shock). Sufficient impurity will compromise hardness, but I am finding it difficult to find out the effect on ...