Applications of Raman spectroscopy to the study of ...
41
Olivier Beyssac & Michele Lazzeri CNRS IMPMC Paris (olivier.beyssac or michele.lazzeri @impmc.upmc.fr) Applications of Raman spectroscopy to the study of graphitic carbons in the Earth sciences The Raman spectrum of graphitic carbons: Theory Characterizing graphitic carbons by Raman spectroscopy: Methodology
Transcript of Applications of Raman spectroscopy to the study of ...
Oli
vie
r B
ey
ssa
c &
Mic
he
le L
azz
eri
CN
RS
IM
PM
C P
ari
s
(oli
vie
r.b
eys
sac
or
mic
he
le.l
azz
eri
@im
pm
c.u
pm
c.fr
)
Ap
pli
cati
on
s o
f R
am
an
sp
ect
rosc
op
y t
o t
he
stu
dy
of
gra
ph
itic
ca
rbo
ns
in t
he
Ea
rth
sci
en
ces
Th
e R
am
an
sp
ect
rum
of
gra
ph
itic
ca
rbo
ns:
Th
eo
ry
Ch
ara
cte
rizi
ng
gra
ph
itic
ca
rbo
ns
by
Ra
ma
n s
pe
ctro
sco
py
: M
eth
od
olo
gy
1.
Intr
od
uct
ion
2.
Th
e R
am
an
sp
ect
rum
of
gra
ph
itic
ca
rbo
ns:
Th
eo
ry
2
.1.
Wh
y a
re t
he
D a
nd
2D
pe
aks
so
`u
niq
ue
'?
2
.2.
Ba
sic
con
cep
ts o
f q
ua
ntu
m m
ech
an
ics
an
d p
ert
urb
ati
on
th
eo
ry
2
.3.
Ele
ctro
nic
ga
p a
nd
re
son
an
t R
am
an
2
.4.
Fo
urt
h-o
rde
r p
ert
urb
ati
on
an
d d
ou
ble
re
son
an
t R
am
an
2
.5.
Ele
ctro
nic
str
uct
ure
an
d p
ho
no
n d
isp
ers
ion
in
gra
ph
en
e/g
rap
hit
e
2
.6.
Do
ub
le r
eso
na
nce
in
gra
ph
ite
2
.7.
Att
rib
uti
on
of
the
Ra
ma
n p
ea
ks
2
.8.
Sh
ap
e a
nd
wid
th o
f th
e 2
D p
ea
k
2
.9.
Inte
nsi
ty o
f th
e D
pe
ak
an
d t
he
Tu
inst
ra-K
oe
nig
re
lati
on
3.
Me
tho
do
log
y:
cha
ract
eri
zin
g g
rap
hit
ic c
arb
on
s b
y R
am
an
mic
rosp
ect
rosc
op
y
3
.1.
Ra
ma
n s
pe
ctro
sco
py
is
a s
urf
ace
an
aly
sis
of
gra
ph
itic
ca
rbo
ns
3
.2.
An
aly
tica
l st
rate
gy
an
d s
am
ple
pre
pa
rati
on
: h
ow
to
min
imiz
e a
na
lyti
cal
art
ifa
ct?
3
.3.
Th
e a
nis
otr
op
ic s
tru
ctu
re o
f g
rap
hit
ic c
arb
on
s a
nd
po
lari
zati
on
eff
ect
s
3
.4.
Dis
pe
rsiv
ity
of
the
de
fect
pe
aks
an
d c
ho
ice
of
a l
ase
r w
ave
len
gth
3
.5.
Fit
tin
g s
pe
ctra
: h
ow
to
re
trie
ve q
ua
nti
tati
ve i
nfo
rma
tio
n o
n t
he
str
uct
ure
of
gra
ph
itic
ca
rbo
ns?
3
.6.
Th
e i
ntr
insi
c st
ruct
ura
l h
ete
rog
en
eit
y o
f n
atu
ral
gra
ph
itic
ca
rbo
ns
4.
Ap
pli
cati
on
s o
f R
am
an
sp
ect
rosc
op
y t
o t
he
stu
dy
of
na
tura
l g
rap
hit
ic c
arb
on
s
4
.1.
Ca
rbo
niz
ati
on
/gra
ph
itiz
ati
on
du
rin
g t
err
est
ria
l d
iag
en
esi
s/m
eta
mo
rph
ism
4
.2.
Gra
ph
itic
ca
rbo
ns
an
d f
luid
-ro
ck i
nte
ract
ion
s
4
.3.
Gra
ph
itic
ca
rbo
ns
as
tra
ces
of
life
in
th
e g
eo
log
ica
l re
cord
4
.4.
Gra
ph
itic
ca
rbo
ns
an
d c
osm
och
em
istr
y
4
.5.
Gra
ph
itic
ca
rbo
ns
an
d e
nv
iro
nm
en
tal
Sci
en
ces
5.
Co
ncl
usi
on
B
eys
sac
& L
azz
eri
EM
U N
ote
s in
Min
era
log
y 2
01
2
Gra
ph
itic
ca
rbo
ns
are
am
orp
ho
us-
lik
e o
r tu
rbo
stra
tic
or
mic
rocr
yst
all
ine
or
Mo
no
cry
sta
llin
e…
op
aq
ue
(h
igh
ext
inct
ion
co
eff
icie
nt
for
vis
ible
lig
ht)
=>
Lo
w p
en
etr
ati
on
of
lase
r, <
20
0 n
m (
Lesp
ad
e e
t a
l. 1
98
4)
an
iso
tro
pic
(in
cre
asi
ng
an
iso
tro
py
wit
h g
rap
hit
iza
tio
n)
=>
Po
ssib
le e
ffe
ct o
f sa
mp
le o
rie
nta
tio
n v
s la
ser
po
lari
zati
on
fra
gil
e (
ea
sily
cle
ave
d a
lon
g t
he
gra
ph
en
e l
aye
rs)
he
tero
ge
ne
ou
s (i
n t
erm
s o
f st
ruct
ure
an
d c
he
mis
try
)
Ch
em
ica
l a
nd
str
uct
ura
l
evo
luti
on
of
carb
on
ace
ou
s
ma
teri
al
du
rin
g b
uri
al
Re
vie
w b
y
Va
nd
en
bro
uck
e &
La
rge
au
,
Org
an
ic G
eo
che
mis
try (
20
07
)
Ferr
ari
and R
obert
son, P
hys. R
ev. B
, 2000
Quantify
ing t
he d
egre
e o
f gra
phitiz
atio
n
Tuin
str
a &
Koenig
, J. C
hem
. P
hys., 1
970
For
a r
evi
ew
: B
eys
sac
& L
azz
eri
EM
U N
ote
s in
Min
era
log
y 2
01
2
Pro
tocol fo
r R
am
an a
naly
sis
of gra
phitic
carb
on m
ate
rials
Ra
ma
n s
pe
ctro
sco
py
is
a s
urf
ace
an
aly
sis
for
gra
ph
itic
ca
rbo
ns
Dis
pe
rsiv
ity
of
the
de
fect
ba
nd
s =
> c
on
sta
nt
lase
r l
(5
14
.5 n
m)
Lase
r-in
du
ced
he
ati
ng
=>
lo
w-l
ase
r p
ow
er
(<0
.5m
W @
51
4.5
nm
)
Sa
mp
le o
rie
nta
tio
n v
ers
us
lase
r p
ola
riza
tio
n =
> n
ot
a p
rob
lem
exc
ep
t fo
r
gra
ph
ite
mo
no
crys
tals
Str
uct
ura
l d
efe
cts
ind
uce
d b
y s
am
ple
pre
pa
rati
on
(e
.g.
po
lish
ing
) =
> a
na
lysi
s b
elo
w
a t
ran
spa
ren
t m
ine
ral
wit
hin
th
e t
hin
-se
ctio
n t
hic
kn
ess
Intr
insi
c st
ruct
ura
l h
ete
rog
en
eit
y o
f n
atu
ral
gra
ph
itic
ca
rbo
ns
=>
to
be
do
cum
en
ted
Ext
ract
ing
qu
an
tita
tive
in
form
ati
on
fro
m t
he
Ra
ma
n s
pe
ctra
=>
Pe
ak
fit
tin
g
…
Se
e B
eys
sac
& L
azz
eri
, E
MU
No
tes
in M
ine
ralo
gy
an
d r
efe
ren
ces
the
rein
Dis
pe
rsiv
ity
of
the
de
fect
ba
nd
s: p
ract
ica
l co
nse
qu
en
ces
po
siti
on
an
d r
ela
tive
in
ten
siti
es=
f(l
lase
r)
Fro
m P
ime
nta
et
al.
(2
00
7)
Ca
nca
do
et
al.
(A
pp
lie
d P
hys
ics
Lett
ers
20
06
)
Dis
pe
rsiv
ity
of
the
de
fect
ba
nd
s: p
ract
ica
l co
nse
qu
en
ces
po
siti
on
an
d r
ela
tive
in
ten
siti
es=
f(l
lase
r)
Sp
ect
ra t
o b
e c
om
pa
red
MU
ST
be
ob
tain
ed
at
the
ve
ry s
am
e l
ase
r w
ave
len
gth
51
4 n
m
10
00
1
50
0
20
00
2
50
0
30
00
Ba
sal
pla
ne
Ed
ge
pla
ne
ll
Ed
ge
pla
ne
^
15
82
16
24
1
36
6
27
27
32
48
24
40
78
0 n
m
10
00
1
50
0
20
00
2
50
0
30
00
15
80
13
22
86
3
16
15
26
46
32
44
63
3 n
m
Ra
ma
n S
hif
t (c
m-1
)
10
00
1
50
0
20
00
2
50
0
30
00
15
81
13
44
16
49
16
20
24
54
26
85
23
28
86
4
Sa
mp
le o
rie
nta
tio
n v
ers
us
lase
r p
ola
riza
tio
n
Tan
et
al.
20
04
No
sig
nif
ica
nt
eff
ect
@ 5
14
nm
fo
r g
rap
hit
ic C
/ m
icro
crys
tall
ine
gra
ph
ite
For
gra
ph
ite
mo
no
crys
tal,
use
a c
ircu
lar
po
lari
zati
on
fo
r th
e l
ase
r a
nd
me
asu
re s
am
e
ori
en
tati
on
Str
uct
ura
l d
efe
ct i
nd
uce
d b
y s
am
ple
pre
pa
rati
on
(p
oli
shin
g,
cru
shin
g,
che
mis
try
…)
e.g
. P
ast
eri
s (A
pp
lie
d S
pe
ctro
sco
py 1
98
9),
Be
yssa
c e
t a
l. (
20
03
)
Gra
ph
itic
ca
rbo
ns
are
bla
ck,
op
aq
ue
ma
teri
als
, a
nd
as
such
ha
ve a
hig
h e
xtin
ctio
n
coe
ffic
ien
t fo
r v
isib
le l
igh
t. T
he
dir
ect
co
nse
qu
en
ce i
s th
at,
in
th
e v
isib
le r
an
ge
, th
e
pe
ne
tra
tio
n o
f th
e l
ase
r in
gra
ph
itic
ca
rbo
ns
is v
ery
lo
w.
Usi
ng
C f
ilm
s w
ith
a w
ell
con
stra
ine
d t
hic
kn
ess
de
po
site
d b
y c
he
mic
al
vap
or
de
po
siti
on
on
a c
oru
nd
um
sub
stra
te,
Lesp
ad
e e
t a
l. (
19
84
) e
stim
ate
d t
he
arg
on
la
ser
(2.4
1e
V,
51
4 n
m)
pe
ne
tra
tio
n d
ep
th a
t a
bo
ut
10
0-2
00
nm
.
Str
uct
ura
l d
efe
ct i
nd
uce
d b
y s
am
ple
pre
pa
rati
on
(p
oli
shin
g,
cru
shin
g,
che
mis
try
…)
Tra
nsp
are
nt
min
era
l g
rap
hit
e
lase
r la
ser
po
lish
ed
N
on
po
lish
ed
A
na
lysi
s b
elo
w a
tra
nsp
are
nt
min
era
l w
ith
in t
he
th
in-s
ect
ion
thic
kn
ess
Þ N
o s
tru
ctu
ral
ma
pp
ing
on
po
lish
ed
sa
mp
le.
Na
sda
la e
t a
l. (
EM
U n
ote
s 2
00
4)
Be
rna
rd e
t a
l. (
EP
SL
20
07
)
Eve
rall
et
al.
(C
arb
on
19
91
)
Lase
r-in
du
ced
he
ati
ng
Ph
oto
-oxy
da
tio
n o
f g
rap
hit
ic C
un
de
r th
e l
ase
r in
air
Do
wn
shif
tin
g o
f G
an
d D
po
siti
on
Þ M
ust
use
lo
w-l
ase
r e
ne
rgy
(< 0
.5m
W @
51
4.5
nm
)
Ra
ma
n s
pe
ctro
sco
py
of
gra
ph
itic
ca
rbo
ns
1st
an
d 2
nd o
rde
r
G b
an
d v
s. D
efe
ct b
an
ds
Do
ub
le-r
eso
nn
an
ce R
am
an
th
eo
ry f
or
the
de
fect
Ba
nd
s (T
ho
mse
n &
Re
ich
20
00
; se
e B
eys
sac
& L
azz
eri
EM
U n
ote
s in
Min
era
log
y f
or
a r
ev
iew
)
Beyssac
&Lazzeri
EM
UN
ote
s2012
Ra
ma
n v
ers
us
XR
D (
tra
ckin
g 3
D o
rde
rin
g)
Lesp
ad
e e
t a
l. (
Ca
rbo
n 1
98
4)
Pim
en
ta e
t a
l. (
20
07
)
Sp
liti
ng
of
the
2D
ba
nd
in
dic
ate
s
Loca
l 3
D A
BA
B s
tack
ing
Ra
ma
n v
ers
us
XR
D (
tra
ckin
g 3
D o
rde
rin
g)
Wo
pe
nka
& P
ast
eri
s (A
m M
in 1
99
3)
Be
rna
rd e
t a
l. (
Ca
rbo
n 2
01
0)
+ S
TX
M-X
AN
ES
At
the
C k
-ed
ge
Sadezky e
t al.,
Carb
on, 2005
Schopf et
al. (
Astr
obio
logy 2
005)
Bonal et
al. (
GC
A 2
006)
Zic
kle
r et
al. (
Carb
on 2
006)
Fit
tin
g s
pe
ctra
of
gra
ph
itic
ca
rbo
ns
Fit
ing
sp
ect
ra o
f
gra
ph
itic
ca
rbo
ns
Exa
mp
les
of
pe
ak
-fit
tin
g p
roce
du
res
for
Ra
ma
n s
pe
ctra
of
gra
ph
itic
carb
on
s. a
) P
ea
k-f
itti
ng
in
ca
se o
f a
very
dis
ord
ere
d g
rap
hit
ic c
arb
on
usi
ng
5 b
an
ds
wit
h p
ure
Lo
ren
tzia
n
sha
pe
. b
) P
ea
k-f
itti
ng
in
ca
se o
f a
gra
ph
itic
ca
rbo
n u
sin
g 3
ba
nd
s w
ith
Vo
igt
pro
file
(m
ix G
au
ssia
n-
Lore
ntz
ian
). N
ote
th
at
in a
ll c
ase
s
no
a p
rio
ri r
est
rict
ion
is
imp
ose
d o
n
the
ba
nd
po
siti
on
, F
WH
M o
r
inte
nsi
ty.
Th
ick
gre
y l
ine
is
the
me
asu
red
sp
ect
rum
, b
lack
lin
e i
s
the
mo
de
led
sp
ect
rum
, g
rey
da
she
d
lin
es
are
th
e p
ea
ks m
od
ele
d.
Ext
ract
ion
of
qu
an
tita
tive
pa
ram
ete
rs (
FW
HM
, p
osi
tio
n,
aa
tio
s…)
Ca
uti
on
wit
h I
D /
IG r
ati
o
Be
yssa
c e
t a
l. 2
00
3;
Be
yssa
c &
La
zze
ri 2
01
2
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hνL/c
hνS
//
hνS/c
hνq
//
�q
^'
hνL/c=
hνS/c+
�νq
νL=
νS+νq
q
<-&*"2,#$%&'&($)*#+,-&$
B5%'>$B5B5':Y;$
Γ'P
EJ'
='W_ <'
=@'`';"+8?SB+C%+'a'1)A)5'
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B5%'>$B5B5':];$
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$B5B5':
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'%Q#"?)IB58'
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L%+I#)&'?+)58"IB5'!
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BA%5?GA'
i$)?'"8')5'%&%#?+B5"#'%Q#"?)IB5j'
ǫq
q
4'P5%+JK''XX'A
BA%5?GA':'
hνq
//
�q
hνL
//
hνL/c
9'
D.&(,.'$'
#+"&(2+)3$7&)2+$+/(+#*,)$
P&%A%5?)+K'
%Q#"?)IB58'
"5')'8B&"C'
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' S>$B5B5"#'
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@'%5%+JK'
ǫa
=+BG5C'8?)?%'!
'%Q#"?)IB58'
hνq
//
�q
hνL
//
hνL/c
|a〉=
|νL〉
⊗|ph〉
⊗|el〉
1)A)5@'
!'
|i〉=
|νL〉
⊗|G〉
⊗|G〉
|f〉=
|νS〉
⊗|νp〉
⊗|G〉
g'
E#-,.-7&8/($,"#/-4$FG),$/-H#-I$
,5?%+)#IB5'>B?%5I)&''''!
'4%7J7@'%&%#?+B5X&"J$?k'
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%&%#?+B5XC%D%#?8:'
VPif
4[+)58"IB5'>+BF)F"&"?K:'
;%+A
"'=B&C%5'+G&%'
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L'"8'8A
)&&:'
〈fVi〉
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%%5'"')5C'D'
4&"5%)+'"5'L'!
'<8?'B+C%+:'
δ(ǫ)=
0for
ǫ�=
0⇒
ǫi=
ǫf
4#B58%+6)IB5'BD'%5%+JK:'
Pif=
2π �|〈iVf〉|2δ(ǫ
i−
ǫf)
l'
E#-,.-7&8/($,"#/-4$FJ-H$/-H#-I$
∑ a
@2GA'B5')&&'?$%'>B88"F&%'%Q#"?)IB58'
' @2A)&&'+%)&'5GAF%+'
γ
iW10,0=@',5'&"?%+)?G+%'?$"8'"8'#)&&%C'`'c+8?SB+C%+'a'1)A)5'
1)A)5'8#)R%+"5J'4B5%':Y;'>$B5B5:'
^'#B58%#GI6%'`'6"+?G)&'?+)58"IB58'a@'
i→
aa→
bb→
f
Pif=
2π �
∣ ∣ ∣ ∣ ∣ ∣∑ a,b
〈iVa〉〈aVb〉〈bVf〉
(ǫi−
ǫa−
iγ)(ǫi−
ǫb−iγ)
∣ ∣ ∣ ∣ ∣ ∣2
δ(ǫ
i−
ǫf)
("J$?')F8B+>IB5'
4%&%#?+B5X$B&%'#+%)IB5:'
P&%#?+B5X>$B5B5'8#)R%+"5J'
4>$B5B5'%Q#"?)IB5:'
("J$?'%A"88"B5'
4%&%#?+B5X$B&%'+%#BAF"5)IB5:'
m'
ǫq
q
E#-,.-7&8/($,"#/-4$FK,"$/-H#-I$
Pif=
2π �
∣ ∣ ∣ ∣ ∣ ∣∑ a,b,c
〈iVa〉〈aVb〉〈bVc〉〈cVf〉
(ǫi−
ǫa−iγ)(ǫi−
ǫb−
iγ)(ǫi−
ǫc−iγ)
∣ ∣ ∣ ∣ ∣ ∣2
δ(ǫ
i−
ǫf)
:$
L:$
i→
aa→
b
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b'`'6"+?G)&'?+)58"IB58'a@'
("J$?')F8B+>IB5'
P&%#?+X>$B5'8#)R%+"5J'
("J$?'%A"88"B5'
O%D%#?'8#)R%+"5J'
b→
cc→
f
b→
c
P&%#?+B5X>$B5B5'8#)R%+"5J'
[MB'>$B5B58'SH/H@'
<e'
E&-8&9$).''&-43$
-%+?G+F)IB5'?$%B+K'48?)5C)+C'?%Q?FBBV'?BB&:@'
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b?$'B+C%+'!'%Q#"?)IB5'BD'?M
BS>$B5B58'
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i$K')+%'?$%'OXEO'>%)V8'8B'"5?%58%j'
i$K')+%'?$%K'8A)&&SM
"C?$'M%&&'C%c5%C'>%)V8j'
i$K'CB'?$%K'C"8>%+8%'M"?$'?$%'()8%+'%5%+JKj'
OBGF&%'+%8B5)5#%'4[$BA8%5'd'1%"#$/'-1('Eeee:'
<<'
%#)/(&(,$%&'&($
Pif=
2π �
∣ ∣ ∣ ∣ ∣ ∣∑ a,b
〈iVa〉〈aVb〉〈bVf〉
(ǫi−
ǫa−
iγ)(ǫi−
ǫb−iγ)
∣ ∣ ∣ ∣ ∣ ∣2
δ(ǫ
i−
ǫf)
!"'4%&%#?+B5"#'J)>:@'A
"5"A
GA'%5%+JK'DB+'%&%#?+B5"#'%Q#"?)IB5'
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<E'
ǫq
q
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PA>?K'
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=+)>$%5%XJ+)>$"?%@'6%+K'8"A
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g
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g
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g
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KK
Energy
(1)
(2)
(3)
(4)
*
kk+q
k!
k!*
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KK
Energy
(1)
(2)
(3)
(4)
*
kk+q
k!
k!*
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KK
Energy
(1)
(2)
(3)
(4)
*
kk+q
k!
k!*
' 4<: ("J$?')F8B+>IB5'
4E: P&%#?+B5'8#)R%+"5J'M"?$')'C%D%#?'
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4b: ("J$?'%A"88"B5'
O'>%)V'
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b?$'B+C%+'>+B#%88:'
ǫk,π
∗−
ǫk,π
=hνL
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∗=
ǫk,π
∗
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KK
Energy
(1)
(2)
(3)
(4)
*
kk+q
k!
k!*
<g'
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KK
Energy
*
q
hL
KK
Energy
*
q’
hL’
<l'
M5-27.8/($/0$,"#$%&'&($*#&B)$
KK
Energy
*
KK
Energy
*K
K
Energy
*
KK
Energy
*
40
0
80
0
12
00
16
00
Phonon frequency (cm-1
)
KM
D'
D'
DD
D''
KK
<m'
Energy
KK
K
Energy
*
KK
M5-27.8/($/0$,"#$%&'&($*#&B)$
=+)>$"?%'A
B5B#+K8?)&'
O"8B+C%+%C'J+)>$"?%'
OTO__'
EO_'
40
0
80
0
12
00
16
00
Phonon frequency (cm-1
)K
M
D'
D'
DD
D''
(BM%8?SB+C%+@'
='!
'<fle'#A
S<'
' OBGF&%'+%8B5)5?@'
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λ('Y'f<b'5A'
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16
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ID
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ID/IG∝
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