crystal lattice Definition and Topics - 8 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
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n
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a
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n
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n
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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.
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
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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...
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)...
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...
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 Equations
The Attempt at a Solution
Part(a)[/B]
I'm quite confused as to what they mean by 'principal axes'.
For...
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...