Phonon 6
Sunday, October 07, 2007
6:09 PM
Phonon 7
Sunday, October 07, 2007
6:11 PM
Phonon 8
Sunday, October 07, 2007
6:13 PM
Phonon 9
Sunday, October 07, 2007
6:14 PM
Inelastic phonon scat.
Thursday, February 01, 2007
10:56 AM
Phonons in crystals
1.For a harmonic lattice (phonons have infinite
lifetime) the neutron energy has to match the
lattice dispersion for one-phonon scattering to
occur
2.Anharmonic effects modify the cross-sections
in a non-trivial manner
3.Multiphonon process are significant at
intermediate and large scattering vectors and
contribute to the structure of the one-phonon
processes
Assume crystal has N-atoms with 3N
modes.
Omro mind each atomis
a
}
ohm omit
Initial state, D. described by a set of
quantum I's (nynz,ns.. ..n3N)
final state, I, described lay n! nr... nor
The scattering is classified according to the change
in quantum numbers:
Elastic, Ni In: where i is oscillator index
One-phonon, Ni = Ni or all i except a
no In # f
Two-phonon, nil In: except for 2, B
oscillators
no Inx II n'p=np=c
where phonons can be created or absorbed
if we consider that the atoms are moving in a
coherent way producing normal modes, then
possible to get inelastic phonon scattering
The displacement of an atom is
given by will) l-lattice site
Position vector of atom is
harmonic oscillator
t-=-kx.
Ck-spring constant)
Reft Ute)
One would need to then solve the
Hamiltonian for the equation
of motion
H = PI r KK } very
simplified!
2m
From this obtain lattice dispersion
frequencies
wigs where j has 3 values
(b/c of what?)
2B.
long.
Iran.
Example of an fcc lattice:
W ^ went. : I I
: as
II!
_ 2th a To
This is along (100)
W ^ ; reclined | w ^ \
long transverse
I|
'g
This is along (101)
$
extend to the next
Britain gone
of
Phonon 11
Sunday, October 07, 2007
10:43 PM
Phonon 12
Sunday, October 07, 2007
10:59 PM
Detailed balance
Sunday, October 07, 2007
11:00 PM
Let's consider the case where neutron loses energy in
the scattering process
trio = alias this contributes to SCtr,w)
E
lattice
os is @
neutron
Let's consider the case where neutron gains energy in
the scattering process
of at
Thw
thew
this contributes to S (-15>-20)
neutron lat
sc-ixia) = eon
tire
w
SCia,w)
There is less chance for the system to be in the higher
energy state
initially and then undergo a transition to the lower state.
This is
why Sinew) is multiplied by E Btw term.
If Detailed balance correction
Phonon 14
Sunday, October 07, 2007
11:02 PM
Phonon 15
Sunday, October 07, 2007
11:03 PM
Phonon 16
Sunday, October 07, 2007
11:05 PM
Phonon 17
Sunday, October 07, 2007
11:07 PM
Phonon 18
Sunday, October 07, 2007
11:09 PM
Phonon 19
Sunday, October 07, 2007
11:11 PM
Phonon 20
Sunday, October 07, 2007
11:19 PM
Debye-Waller factor
Sunday, October 14, 2007
12:43 PM
DW 2
Sunday, October 14, 2007
12:45 PM
DW 3
Sunday, October 14, 2007
12:47 PM
DW 4
Sunday, October 14, 2007
12:48 PM
DW 5
Sunday, October 14, 2007
12:49 PM
Phonon 23
Sunday, October 07, 2007
11:24 PM
MgB2 has a very simple crystal structure where the
boron atoms form graphite-like sheets separated
by hexagonal layers of Mg atoms.
Types of phonon modes (active)
Harmonic Zone-Center Modes
E1u (at 40.7 meV)
A2u (at 49.8 meV)
B1g (at 87.1 meV)
Anharmonic In-Plane Boron Modes
E2g (at 74.5 meV)
E2g (at 74.5 meV)
In-plane boron breathing mode
Phonon 24
Sunday, October 07, 2007
11:26 PM
If
From specific heat, obtain average values of s for
all the normal modes. But from neutron
experiment, obtain details of the frequency as a
function of q.
INS 1
Sunday, October 14, 2007
11:45 PM
INS 2
Sunday, October 14, 2007
11:47 PM
Ins 3
Sunday, October 14, 2007
11:49 PM
Ins 4
Sunday, October 14, 2007
11:51 PM
ins5
Sunday, October 28, 2007
7:55 PM
INS 6
Sunday, October 28, 2007
7:56 PM
INS 7
Sunday, October 28, 2007
8:02 PM
INS 8
Sunday, October 28, 2007
8:04 PM
INS 9
Sunday, October 28, 2007
8:08 PM
INS 10
Sunday, October 28, 2007
8:19 PM
INS 11
Sunday, October 28, 2007
8:47 PM
INS 12
Sunday, October 28, 2007
8:50 PM
INS 13
Sunday, October 28, 2007
8:51 PM
INS 14
Sunday, October 28, 2007
8:55 PM
INS 15
Sunday, October 28, 2007
8:57 PM
INS 16
Sunday, October 28, 2007
9:00 PM
INS 17
Sunday, October 28, 2007
9:02 PM
Summary INS 1
Sunday, October 28, 2007
11:48 PM
Summary 2
Monday, October 29, 2007
12:00 AM
Summary 3
Monday, October 29, 2007
12:01 AM
Summary 4
Monday, October 29, 2007
12:02 AM
Summary 5
Monday, October 29, 2007
12:03 AM
Summary 6
Monday, October 29, 2007
12:04 AM
Summary 7
Monday, October 29, 2007
12:04 AM
Summary 8
Monday, October 29, 2007
12:06 AM
Summary 9
Monday, October 29, 2007
12:07 AM
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