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Reciprocal to determine Miller indices

If we know the reciprocal space basis of a BCC lattice \begin{align}b_1=\frac{2\pi}{a}(\vec{x}+\vec{y}),b_2=\frac{2\pi}{a}(\vec{z}+\vec{y}),b_3=\frac{2\pi}{a}(\vec{x}+\vec{z})\end{align} how do we ...
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27 views

crystal momentum conservation

Electrons on 1D chain interacting with each other $$ H = \sum_{k_4,k_3, k_2, k_1} V(k_4-k_1) c_{k_4}^{\dagger}c_{k_3}^{\dagger}c_{k_2}c_{k_1}\delta_{k4+k3=k2+k1;\text{mod}~G}$$ where $G$ is ...
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0answers
38 views

Structure of Metallic Hydrogen [migrated]

I am simply curious what the theoretical arrangement of metallic hydrogen would be. I found this article which gives a picture, but I don't understand what the labels mean (e.g. is H5 an isotope, ...
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69 views

Calculation of the Madelung constant for a 2D Square Lattice of Ions

The question is Exercise 3.7 of Sidebottom's Condensed Matter textbook Fundamentals of Condensed Matter and Crystalline Physics: An Introduction. A link can be found below: http://goo.gl/WoBPnP I am ...
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3answers
54 views

Why are $2\pi$ factors included in the definition of the reciprocal lattice?

I would like to know where the $2\pi$ factors are coming from in the formula for reciprocal vectors in reciprocal lattices. For example, in a simple cubic lattice the primitive vectors are given by ...
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2answers
107 views

FCC lattice as a stack of triangular lattices

According to Marder, Condensed Matter Physics, Chapter 2: Within the planes normal to the vector [1,1,1], the atoms of an fcc lattice lie in a two dimensional triangular lattice However, he does ...
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26 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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1answer
42 views

How to prove Bloch function is periodic in reciprocal lattice?

How to prove Bloch function is periodic in reciprocal lattice? I saw in some textbooks this formula: $$ \Psi_{\mathbf{k}} (\mathbf{r}) = \sum_{\mathbf{G}} ...
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1answer
42 views

How is periodic potential approximation justified in semiconductor physics?

In semiconductor physics the usual approximation is that of infinite crystal. This seems to allow one to write Hamiltonian for electron subsystem (in adiabatic approximation) as having periodic ...
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0answers
10 views

magnetization of a infinite crystal lattice

Cosider a infinite crystal lattice with right face end at infinity and left face end at origin.my question is, consider this crystal is made of material which can be magnetized and if you magnetize ...
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2answers
128 views

Why do crystals grow in preferred directions?

I want to know why snowflakes (and other crystals) grow symmetrically and I find the leading answer to the established question to be entirely unsatisfactory. When water freezes, you get ice. ...
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1answer
34 views

neglect of lattice potential for conduction electrons

Why is it true that in nearly free electron compunds, complete neglect of the lattice potential is usually a good approximation as long as one considers crystal momenta remote from the boundaries of ...
2
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1answer
44 views

planewave Ansatz for modelling phonon dispersion in crystals

From Ashcroft's "Solid State Physics", for one-dimensional monatomic Bravais lattice, the equations of motion of ions are: \begin{equation} M\ddot u(na)=-K[2u(na)-u([n-1]a)-u([n+1]a)] \end{equation} ...
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1answer
20 views

Zero Diffraction Plates: Why do they give such low diffraction signals?

In our laboratory we use silicon plates named "Zero Diffraction Plates". They are named so because they give extremely low diffraction signals in an XRD instrument (reflection mode). But how are these ...
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2answers
44 views

What limits the doping concentration in a semiconductor?

Si and Ge can be blended in any ratio, $\mathrm{Si}_x\mathrm{Ge}_{1-x},\ 0\le x\le 1$. So do InxGa1-x. So what exactly causes doping impurities inside Si/Ge/etc. to saturate at $\sim 10^{-19}\ ...
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1answer
46 views

Difference in electrons excitation in Au (111) between perpendicular and diagonal orientation?

In Au (111) single crystalline as shown in attached file, is there a difference the way electrons are excited when they are excited from perpendicular and diagonal orientation as shown in the figure ...
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1answer
44 views

At which gravitational acceleration would a diamond crystal lattice break down?

Gravitational acceleration can be upto infinite (which is at the Event Horizon of a Black Hole). On which least acceleration, would crystal lattice of diamond break down? Update: Please, don't apply ...
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0answers
8 views

Phase Diagram of Polymorphs vs. Binding Energy

Phase diagrams show how various polymorphs are favored at specific temperatures and pressures. I am interested in a 3-axis diagram showing the binding energy on the third axis. Ideally there would ...
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1answer
100 views

Coordinate system for crystallographic groups

In the International Tables for Crystallography for each crystallographic group an asymmetric unit is supplied (mathematicians call this a fundamental domain of the group). This region is a bounded ...
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1answer
30 views

Why can the twin plane be uncoincide with the composition plane in reflection twin?

In the book Elements of X-Ray Diffraction, p67, I found the following sentence: In the case of a reflection twin, the composition plane may or may not coincide with the twin plane. But I think ...
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1answer
71 views

Why are (most) solids periodic?

Is there a rigorous proof that periodic arrangements minimize the energy of a group of particles?
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0answers
19 views

How many unique crystal faces does a given unit cell have?

I am not sure how to best approach this problem. "A diamond crystal is composed of an enormous number of cubic unit cells that are stacked to produce crystal faces. Stacking of cubes to produce an ...
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1answer
28 views

Crystal structure of Silicon

From what I was reading, Silicon has a FCC unit cell but they also said that the Silicon atoms form a tetrahedron at 109 degrees from each other. Then they said that the tetrahedron is formed by ...
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0answers
14 views

Binding forces in crystalline solids

I am referring to rocks in this instance. Individual crystals grow together in an igneous rock as it solidifies. I know that the SiO4 tetrahedron is the basic building unit of silicate minerals, and ...
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1answer
39 views

Can I tear apart a pipe with magnetostriction? And how big field should I use?

As I know, with magnetostriction we can "stretch" its unit cell. The stronger is the field, the more it expands the cell. Using alternating current in coils that induce magnetic field we can stretch ...
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0answers
26 views

Quantization in a 2D quasicrystal?

let be the Schroedinger equation with a potential in a quascristal $$ -( \partial _{x}^{2}+ \partial _{y}^{2}) \Psi (x,y)+ V(x,y)=E_{n} \Psi (x,y) $$ if we were in a crystal we could impose the ...
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1answer
52 views

How corner atom of a cube is shared by 8 atoms? [closed]

Since each atom is at the corner of a cube and 8 cubes meet at each corner. Therefore each atom is shared by 8 cubes. But I don't visualize it, so please tell how I Visualize it.
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1answer
40 views

Crystal lattices in solid state

I found this problem in Christman's book fundamental of solid state physics What is the Miller index for a plane parallel to both $3\vec{a}+\vec{c}$ and $\vec{b}$, in any lattice?
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2answers
853 views

How many atoms exist within a continuum body?

Materials, such as solids, liquids and gases, are composed of molecules separated by "empty" space. On a microscopic scale, materials have cracks and discontinuities. However, certain physical ...
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1answer
109 views

Does Graphene have a honeycomb lattice?

In my grand ignorance I would state that graphene has a honeycomb lattice. Some tend to agree with me and some others do not. I'm curious to know what members of the SE community think is the right ...
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1answer
62 views

Help needed to understand the dispersion curve of a 1D lattice with diatomic basis

I am trying to understand the dispersion curve (as shown below) of a 1D lattice with diatomic basis. Here are my questions: Can both optical and acoustic branch of phonon simultaneously exist in ...
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1answer
23 views

Why Nitrides have internal polarization?

Why GaN has internal polarization? I know that in wurtzite crystal structure, the atomistic bonds are not equivalent and as a result there appears a net dipole and consequently a polarization. But ...
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2answers
70 views

How many are the points which are $n$th nearest to a certain point in a hexagonal lattice

Suppose there are infinite points arranged as hexagonal lattice. The question is the one as the title. First we choose a point called $A$. Then when we count the $n$th nearest points to $A$, what ...
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1answer
83 views

Calculating number of atoms per cell in a crystal. Nonsense question in class

I don't agree at all with this question, and I think my teacher does not understand his topic. I hope you can prove me wrong. The question was this one: Potassium crystallises in a Body Centered ...
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0answers
39 views

Crystallography: relationship between side length and radius of atom

For a FCC the relationship between the radius and the side length 'a' is 4r=(2)^.5 a And this is derived by drawing a diagonal across one of the faces of the unit cell. However, is this meant to be ...
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0answers
34 views

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 ...
3
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1answer
107 views

Can you explain why crystals form without thermodynamics?

I know that the basic reason that solid crystals form is because it's the lowest energy configuration (i.e. this). I am looking for an intuitive explanation for this process, one that does not involve ...
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1answer
51 views

Why aren't base-centered orthorhombic Bravais lattice simple monoclinic?

I am learning 7 crystal systems and 32 Bravais lattices. I am quite confused about why a base-centered orthorhombic Bravais lattice is not a simple monoclinic one, if we take two edges and a half ...
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1answer
383 views

$c/a$ ratio for an ideal hexagonal close-packed (HCP) structure [closed]

Show that the $c/a$ ratio for an ideal hexagonal close-packed (HCP) structure is $\left(\frac{8}{3}\right)^\frac{1}{2} = 1.633$. I believe $a$ is the length of $a_1$ and $a_2$. I figured that ...
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0answers
15 views

What are some structures which minimize surface stress upon expansion

Intro I am currently researching into a problem involving the cyclical expansion and contraction of a 3 layered structure comprised of an internal metal encased by another metal encased in an outer ...
2
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2answers
82 views

Quantity to measure order in crystals

Imagine a cubic lattice for simplicity and put some atomic configuration inside of each unit cell. Lattice is of course a highly ordered entity (long range order). Please, how could I quantitatively ...
2
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2answers
68 views

What exactly are crystal planes and how do they reflect x-rays?

What exactly are crystal planes and how do they reflect x-rays? Are crystal planes real physical planes or just an abstract concept? What are these planes made of? If they are an abstraction, what ...
4
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1answer
239 views

Crystal Momentum in a Periodic Potential

I'm working through some basic theory on periodic potentials, and I would appreciate help in understanding the crystal momentum. Suppose we have a Bravais lattice with lattice vectors $\textbf{R}$. ...
3
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1answer
82 views

Lattice geometry and dispersion relation

Is there a general theorem which gives some information about which influence have the lattice geometry (for example sub-lattice structure, square lattice, honeycomb lattice, lattice symmetries, ...) ...
4
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1answer
57 views

What physical phenomenon occured in this experiment?

I noticed a strange behavior of my experiment. I have a glass container with a fully saturated solution of CuSO4, which I use to grow CuSO4 crystals, by waiting for the water to evaporate. Recently I ...
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0answers
31 views

Mixed-Alloy materials

Short version: Is it a physical problem (crystal structure/grains/redox/etc.) or just a logistics problem (keeping the solutes from homogenizing, molten/solid/temperature related problems) that keeps ...
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0answers
19 views

3-dimensional quasicrystals

As is well known, quasicrystals (i.e. their diffraction patterns) show patterns which can be deciphered and understood via the use Penrose tilings (and aperiodic tilings of the plane in general). ...
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0answers
98 views

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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2answers
176 views

Bloch theorem, Energy, Free electron

I'm trying to learn on my own a bit of solid physics to tackle semiconductors afterwards. I'm struggling with the Energy versus $k$ diagrams for a free electron which shows that for a single value of ...
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1answer
21 views

Effect of crystal growth on its scintillation

How does crystal growth affect its scintillation properties? What are possible ways in which growth of CaWO crystals grown via Chochralski method could be modified to avoid non-linearity in its ...