Question
In: Mechanical Engineering
Consider a two-dimensional triangular lattice described by the two primitive vectors (in an orthogonal coordinate system...
Consider a two-dimensional triangular lattice described by the two primitive vectors (in an orthogonal coordinate system
Find the two primitive lattice vectors describing the reciprocal lattice. Find the area of the 1st
Brillouin zone and its relation with the area of the direct lattice unit cell.
Solutions
samet mamat answered 1 year agoRelated Solutions
Of the seven three-dimensional primitive lattices, which ones have a unit cell where all three lattice vectors are of the same length?
Of the seven three-dimensional primitive lattices, which ones have a unit cell where all three lattice vectors are of the same length?
"Draw the first 5 Brillouin zones of a two-dimensional cubic primitive reciprocal lattice." When we covered...
"Draw the first 5 Brillouin zones of a two-dimensional cubic
primitive reciprocal lattice."
When we covered this in in an engineering class lecture it
seemed like we were just drawing lines on a 2d dotted graph and I
couldn't understand what we were doing.
A) Create two vectors in R3 ( 3D vectors) such that they are orthogonal. b) Using...
A) Create two vectors in R3 ( 3D vectors) such that they are
orthogonal.
b) Using the two vectors from a) above, determine the cross
product of the two vectors
c)Is it possible to write the vector [0,0,1] using scalar
multiples of these vectors?
In a two-dimensional Cartesian coordinate system the y-component of a given vector is equal to that...
In a two-dimensional Cartesian coordinate system the y-component
of a given vector is equal to that vector's magnitude multiplied by
which trigonometric function, with respect to the angle between
vector and y-axis?
Consider a two-dimensional hexagonal lattice: (a) Draw the free electron Fermi surface in the reduced zone...
Consider a two-dimensional hexagonal lattice:
(a) Draw the free electron Fermi surface in the reduced zone
scheme when the lattice points are occupied by atoms with: i. One
valence electron/atom. ii. Two valence electrons/atom.
Consider a two-dimensional ideal flow in the x-y plane (with radial coordinate r2 = x2 +...
Consider a two-dimensional ideal flow in the x-y plane (with
radial coordinate r2 = x2 + y2). Given the velocity potentials of
1) a uniform flow, 2) a source φ = (q/2π) ln r, and 3) a dipole φ =
−d · r/(2πr2):
a) Using the principle of superposition, construct a linear
combination of the ingredients above that gives the flow past an
infinite cylinder. [10 points]
b) Sketch the streamlines of the flow everywhere in space. [10
points]
Consider a one-dimensional lattice with a basis of two non-equivalent atoms of masses M_1and M_2. 1....
Consider a one-dimensional lattice with a basis of two
non-equivalent atoms of masses M_1and M_2.
1. Find the dispersion relations (ω versus k).
2. Sketch the normal modes in the first Brillouin zone.
3. Show that the ratio of the displacements of the two atoms u/v
for the k = 0 optical mode is given by:u/v=-M_2/M_1
Consider a two-dimensional hexagonal lattice: (a) Find Fermi wave vector of the free electron circular Fermi...
Consider a two-dimensional hexagonal lattice:
(a) Find Fermi wave vector of the free electron circular Fermi
surface in reciprocal space. (b) Draw the free electron Fermi
surface in the reduced zone scheme when the lattice points are
occupied by atoms with: i. One valence electron/atom. ii. Two
valence electrons/atom
Consider a two-dimensional hexagonal lattice: (a) Find Fermi wave vector of the free electron circular Fermi...
Consider a two-dimensional hexagonal lattice:
(a) Find Fermi wave vector of the free electron circular Fermi
surface in reciprocal space.
(b) Draw the free electron Fermi surface in the reduced zone
scheme when the lattice points are occupied by atoms with:
i. One valence electron/atom.
ii. Two valence electrons/atom.
Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal....
Consider the one dimensional model of one-particle-in-a-box. Under
what condition the two quantum levels are orthogonal. Namely, find
the relation between m and n so that < m | n > = 0
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