Week 5 Lattice Vibrations Flashcards

1
Q

what are the two main dynamics of a solid

A

vibrational motion

motion of valence electrons

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2
Q

what is the Einstein model of lattice vibrations

A

vibrational motion of a lattice as many independent simple harmonic oscillators

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3
Q

what is unique of vibrations in solids

A

the lattice has both transverse and longitudinal vibrations

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4
Q

what is the longitudinal vibration relation in 1D chain equation

A

mω^2 = 4k(sin(ka/2))^2

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5
Q

what is the general rule for dealing with longitudinal vibrations of a diatomic chain

A

focus on the basis

view from perspective of both atoms

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6
Q

what is the dispersion (square) relation for a diatomic chain

A

ω^2 = K(M+m)/Mm +- K[μ^2 - 4Mm * (sin(ka/2))^2]^1/2

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7
Q

what are the small k conditions for the diatomic chain

A

for small k
ω^2 –> K(M+m)/Mm +- K(M+m)/Mm
ω = SQRT[2K/M] for + and 0 for -

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8
Q

what are the boundary conditions for the diatomic chain

A

as k –> π/a
ω^2 –> K(M+m)/Mm +- K(M-m)/Mm
ω = SQRT[2K/m] for + and SQRT[2K/M] for -

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9
Q

what do the +- solutions of diatomic chain lead to

A

+ upper band is optical

- lower band is acoustic

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10
Q

why is the upper band referred to as the optical band

A

optical band because it is the only one that responds to optical light

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11
Q

how many different vibrational modes are there in a single brillouin zone and where are they

A
4 different modes
1 peak of optical band
2 trough of acoustic band
3 at boundary of optical
4 at boundary of acoustic
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12
Q

what is true of transverse oscillations and what is the difference between acoustic and optical

A

vibrations are perpendicular to propagation
acoustic both atoms oscillate in phase
optical different classes of atoms vibrate out of phase

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13
Q

what is a phonon

A

quasi-particles corresponding to quantum states of vibrations

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14
Q

what is true of the energy of a normal mode of a lattice vibration and its equation

A

the energy is discrete

E(k) = (n + 1/2)ħω(k)

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