What is Crystal lattice: Definition and 31 Discussions
In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (1850), is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by:
R
=
n
1
a
1
+
n
2
a
2
+
n
3
a
3
{\displaystyle \mathbf {R} =n_{1}\mathbf {a} _{1}+n_{2}\mathbf {a} _{2}+n_{3}\mathbf {a} _{3}}
where the ni are any integers and ai are primitive vectors which lie in different directions (not necessarily mutually perpendicular) and span the lattice. The choice of primitive vectors for a given Bravais lattice is not unique. A fundamental aspect of any Bravais lattice is that, for any choice of direction, the lattice will appear exactly the same from each of the discrete lattice points when looking in that chosen direction.
The Bravais lattice concept is used to formally define a crystalline arrangement and its (finite) frontiers. A crystal is made up of a periodic arrangement of one or more atoms (the basis or motif) at each lattice point. The basis may consist of atoms, molecules, or polymer strings of solid matter.
Two Bravais lattices are often considered equivalent if they have isomorphic symmetry groups. In this sense, there are 14 possible Bravais lattices in three-dimensional space. The 14 possible symmetry groups of Bravais lattices are 14 of the 230 space groups. In the context of the space group classification, the Bravais lattices are also called Bravais classes, Bravais arithmetic classes, or Bravais flocks.
When light passes through Calcite it is split into two beams opposite polarizations, doubling the image, and this sounds very similar to the Stern-Gerlach experiment where atoms are split into two beams with opposite polarizations
The difference is that with light the opposite polarizations are...
I have trouble researching whether valence-electrons take part in electrical conductivity. Some sources say that a lower amount of valence electrons lead to an higher electrical conductivity, whilst others say the opposite. And each have their different reasons, for example, lower valence...
Hi,
I'm looking into how phonon dispersion changes with pressure analytically and need to know how the atomic spacing in copper changes with pressure in order to model the crystal. I can't find any helpful papers online :(
Any help would be appreciated
thanks
e
Homework Statement
Homework Equations
I'm not sure.
The Attempt at a Solution
I started on (i) -- this is where I've gotten so far.
I am asked to compute the Fourier transform of a periodic potential, ##V(x)=\beta \cos(\frac{2\pi x}{a})## such that...
Hello,
Sorry if this is a rather basic question, but my memories of solid-state chemistry are a bit rusty. Basically I'm trying to predict new crystal structures. I understand the crystallographic aspects quite well and know that at given external temperature and pressure the most stable...
Homework Statement
Which cannot be the structure of two acoustic branches, nor three acoustic branches?
Simple cubic, FCC, BCC, diamond cubic, NaCl lattice
Homework Equations
N/A
http://solid.fizica.unibuc.ro/cursuri/solid_en/curs_solid_EN.pdf#page=61...
Homework Statement
The only things you know about the sample are: (i) it has some kind of cubic lattice, and (ii) it is a pure element. Identify the element in the crystalline sample.
SC: R = 0.5a
FCC: R = 0.25a√2
BCC: R = 0.25a√3
Distances from Bragg peaks:
d1 = 0.2037 nm
d2 = 0.1746 nm
d3...
Hi all,
I’m brushing up my skills on solid state physics and I have a few questions about crystal lattices:
1. What’s the spacing between allowed kx, ky, and kz states for a lattice of dimensions La x Lb x Lc?
My attempt:
The spacing is kx, ky, and kz:
k_x = \frac{2\pi}{L_a}, \qquad k_y =...
Homework Statement
Silicon crystalises in a cubic structure whose lattice is face-centred, with a basis [000],[1/4,1/4,1/4].
How many optic/acoustic modes are to be found in the phonon dispersion diagram for silicon. How many distinct branches would you expect along the [100] direction...
Homework Statement
This is just a problem to help me understand. Determine the dispersion relations for the three lowest electron bands for a 1-D potential of the form
##U(x) = 2A\cos(\frac{2\pi}{a} x)##
Homework Equations
I will notate ##G, \,G'## as reciprocal lattice vectors.
$$\psi_{nk}(x)...
Homework Statement
Use a computer to calculate numerically the potential energy, per ion, for an ifinite 2D square, ionic crystal with separation a; that is, a plane of equally spaced charges of magnitude e and alternating sign.
Homework EquationsThe Attempt at a Solution
The closest I can...
Taken from http://dao.mit.edu/8.231/BZandRL.pdf
BCC
In real space, it has a simple cubic lattice with one basis in the centre. Total number of atoms per unit cell = 2. Volume of primitive unit cell is then ##\frac{1}{2}a^3##.
In reciprocal space, BCC becomes an FCC structure. It has a simple...
Why are atoms taken to be spheres, and not of some other shape, in the calculation of the packing fraction of different crystal lattices?
In other words, what experimental evidence and theoretical reasoning motivates this form of the atomic shape?
Homework Statement
[/B]
(a) Show Compression of FCC leads to BCC.
(b) State rules for X-rays reflection in FCC.
(c) What are the new Miller Indices after compression?
Homework EquationsThe Attempt at a Solution
Part(a)[/B]
I'm quite confused as to what they mean by 'principal axes'.
For an...
why the solution for energy levels of electron in 1D crystal lattice as solved in Kronig penny model has used wave vector k differently then the Schrödinger equation solved for a free particle.
(only the conditions in the equation has changed not the maths...so the "USE" of wavevector 'k' must...
Homework Statement
A crystal lattice consists of a spin 1 particle at each lattice point. Spin 1 particles can have z-components of magnetic moment that take on the values +μZ, 0, and -μZ. In an external magnetic field B, each spin can have an energy U = -μZB, so the possible energies are...
what is this
answer choices:
a. Primitive cubic with an octahedral hole
b. Body centered cubic with an octahedral hole
c. Face centered cubic with an octahedral hole
d. None of the above
e. Not enough information to determine
We didn't talk about this in class, and this was a question...
Homework Statement
A two-dimensional rectangular crystal has a unit cell with sides a 6.28Å and
b 3.14Å. A beam of monochromatic neutrons of wavelength 5.0 Å is used to
examine the crystal.
Using either the Laue condition for diffraction or Bragg's Law, determine
whether it would be...
Bear with me (Two part question),
In the ideal case, an electron in a lattice under the influece of a static force will undergo bloch oscillations.
A simple hamiltonian for this system would be:
H=H° +Fx and V(x+d)=V(x)
If I used the kronig-Penney Model would I be able to derive...
What decides that which salt will take up which crystal lattice?
Some salts have cubic lattice , some have hexagonal , some have orthorhombic - but what factor decides which crystal system the salt will take over. Most of the examples i have seen consist of cubic lattice system. Is it becasue...
Homework Statement
Be the vectors a, b, c such as:
| a | = | b | = | c | = 10.5 Angstron
The angles between these vectors are:
alpha = beta = gamma = 109.5 degree
These vectors represent the lattice vectors of a crystal.
Find out their components (a_1, a_2, a_3, b_1...
I'm not sure what is the correct equation for motion of electron in a crystal
lattice under the influence of magnetic force. On may easily proof that for
electric force the following equation holds (the proof might be found in
http://ajp.aapt.org/resource/1/ajpias/v54/i2/p177_s1" [Broken] )...
Homework Statement
Using the powder XRD data below, show that the substance has a face centred cubic structure. (xray lamda = 0.154056 nm)
Peak No.------2(theta)
1 -------------38.06
2 -------------44.24
3 -------------64.34
4 -------------68.77
5 -------------73.07
Homework...
Can entangled protons be maintained in a crystal lattice for an indefinite period of time?
The following papers seem to support this contention.
I need the help of the Forum’s readers to critique this research and the assertions the authors are making.
Dr. Francois Fillauxa and Dr Alain...
Homework Statement
The atomic mass number of copper is A = 64. Assume that atoms in solid copper form a cubic crystal lattice. To envision this, imagine that you place atoms at the centers of tiny sugar cubes, then stack the little sugar cubes to form a big cube. If you dissolve the sugar, the...
friends i studied abt the crystalline structures of compounds but i am just failing to understand the defects of the crystal lattice so i hope some one will help me in sorting out this problem of mineo:)
I know this might be a really stupid question, but to convert a crystal lattice 2D representation to a 2D reciprocal lattice do you justdo you just invert the scaling. I know this is a pretty poor explanation so I will try and illustrate what I mean.
Let's say that you have a reciprocal lattice...
hey guys...im stuck with this experiment of an Electrical Analogue Simulating a crystal Lattice...could anyone explain me the whole concept of relating a set of LC filters to a crystal lattice?
Hello, my name is Kenichi, from japan.
Inorder to draw Crystal Lattice 3D Structures, what libraries for free out there to be used with C programming language ? I am still a C novice.
I wonder, in chemical simulation research do you also program using C language plus some libraries to...