Coulabilité des poudres cohésives : mesures aux faibles contraintes ...
Progrès dans l’affinement de structures sur poudres : contraintes rigides et molles · 2006. 3....
56
March 2006 Rencontres LLB-SOLEIL: Diffraction de Poudres Progrès dans l’affinement de structures sur poudres : contraintes rigides et molles Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), CEA/Saclay Institut Laue-Langevin, Grenoble (from 1-March-2006)
Transcript of Progrès dans l’affinement de structures sur poudres : contraintes rigides et molles · 2006. 3....
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Pro
grès
dan
s l’
affi
nem
ent
de
stru
ctu
res
sur
pou
dre
s :
contr
ainte
sri
gides
et
mol
les
Juan
Rod
rígu
ez-C
arva
jal
Lab
orat
oire
Léo
n B
rillou
in (
CE
A-C
NR
S),
CE
A/S
acla
yIn
stit
ut
Lau
e-L
ange
vin, G
renob
le (
from
1-M
arch
-200
6)
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
()
hh
hc
ii
iy
IT
Tb
=Ω
−+
∑
Con
tain
s st
ruct
ura
l in
form
atio
n:
atom
pos
itio
ns,
mag
net
ic m
omen
ts, e
tc(
)h
hI
II
=β βββ
(,
)h
Pix
Ω=Ω
β βββC
onta
ins
mic
ro-s
truct
ura
l info
rmat
ion:
inst
r . r
esol
uti
on, d
efec
ts, c
ryst
allite
siz
e, ..
.
()
Bi
ib
b=
β βββB
ack
grou
nd:
noi
se, d
iffu
se s
catt
erin
g, ..
.
The
pro
file
of
pow
der
dif
frac
tion
pat
tern
s
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Th
e R
ietv
eld
Met
hod
con
sist
of
refi
nin
g a
crys
tal
(an
d/o
r m
agn
etic
) st
ruct
ure
by
min
imis
ing
the
wei
ghte
d s
qu
ared
dif
fere
nce
bet
wee
n t
he
obse
rved
an
d t
he
calc
ula
ted
pat
tern
aga
inst
th
e p
aram
eter
vec
tor:
β βββ
{}2
2
1
()
n
ii
ci
i
wy
yχ
β=
=−
∑
21 iiw
σ=
2 iσ
: i
s th
e va
rian
ce o
f th
e "ob
serv
atio
n"y i
The
Rie
tvel
d M
ethod
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Lea
st s
quar
es:
Gau
ss-N
ewto
n (
1)
Min
imum
nec
essa
ry c
ondit
ion:
A T
aylo
r ex
pan
sion
of
a
round
a
llow
s th
e ap
plica
tion
of
an ite
rati
ve p
roce
ss. T
he
shif
ts t
o be
appli
ed t
o th
e par
amet
ers
at e
ach c
ycle
for
impro
ving χ χχχ
2ar
e ob
tain
ed b
y so
lvin
g a
linea
r sy
stem
of
equat
ions
(nor
mal
equat
ions)
2
0∂
=∂χ χχχ β βββ
()
icyβ βββ
0β βββ
0
00 0
()
()
()
()
Ab
icic
kli
ik
l
ick
ii
ic
ik
yy
Aw
yb
wy
yββ β
=
∂∂
=∂
∂
∂=
−∂
∑ ∑
β βββδ δδδ
ββ
ββ
ββ
ββ β βββ
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Lea
st s
quar
es:
Gau
ss-N
ewto
n (
2)
The
new
par
amet
ers
are
consi
der
ed a
s th
e st
arti
ng
ones
in t
he
nex
t cy
cle
and t
he
pro
cess
is
repea
ted u
nti
l a
conve
rgen
ce
crit
erio
n is
sati
sfie
d. T
he
vari
ance
of
the
adju
sted
par
amet
ers
are
calc
ula
ted b
y th
e ex
pre
ssio
n:
The
shif
ts o
f th
e par
amet
ers
obta
ined
by
solv
ing
the
nor
mal
equat
ions
are
added
to
the
star
ting
par
amet
ers
givi
ng
rise
to
a new
set
01
0=
+β βββ
ββ
δβ
βδ
ββ
δβ
βδ
1(
)(
)A
kkk
N-P+C
22 ν
22 ν
σβ
χ
χχ
−=
=
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
,,
h
()
hh
cii
iy
sI
TT
bφ
φφ
φ
=Ω
−+
∑∑
Sev
eral
phas
es (φ φφφ
= 1
,nφ φφφ)
con
trib
uti
ng
to t
he
dif
frac
tion
pat
tern
,,
h
()
hh
pp
pp
p
cii
iy
sI
TT
bφ
φφ
φ
=Ω
−+
∑∑
Sev
eral
phas
es (φ φφφ
= 1,n
φ φφφ) c
ontr
ibuti
ng
to s
ever
al (p=1,np)
dif
frac
tion
pat
tern
s
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Lea
st s
quar
es:
a lo
cal
opti
mis
atio
n m
ethod
•T
he
leas
t sq
uar
es p
roce
dure
pro
vides
(w
hen
it
conve
rges
) th
e va
lue
of t
he
par
amet
ers
const
ituti
ng
the
loca
l m
inim
um
clo
sest
to
the
star
ting
poi
nt
•A
set
of
good
sta
rtin
g va
lues
for
all p
aram
eter
s is
nee
ded
•If
the
init
ial m
odel
is b
ad f
or s
ome
reas
ons
the
LSQ
pro
cedure
wil
l not
con
verg
e, it
may
div
erge
.
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Impor
tant
ques
tion
s …
�What is the effect of resolution and the peak shape
systematic errors in the structural parameters?
�To what extend powder diffraction can provide
precise structural results? Are the structural
parameters chemically meaningful?
�How reliable is m
y refinement? Are the R-factors
good indicators of the quality of a structural model?
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Com
ple
xity
of
a st
ruct
ura
l pro
ble
m:
effe
ctiv
e
num
ber
of
refl
ecti
ons
and s
olva
bilit
y in
dex
If one is interested in “structural parameters” the number of independent
observations is notthe number of points in the patternN.
What is the number of “independent” observations?(No rigorous answer …)
Points to be considered:
•Signal-to-noise ratio, statistics.
•Number of independent Bragg reflections: NB
•Number of structural free parameters: NI = N
f
•Degree of reflection overlap: resolution versus separation
between consecutive reflections.
•Effective number of observations (resolution weighted): N
eff
•“Solvability” index: ratio between the effective number of
observations and the number of structural parameters: r = N
eff/N
I
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Eff
ecti
ve n
um
ber
of
refl
ecti
ons Neff
Two reflections separated by ∆ ∆∆∆(Q) can be
discriminated properly if the following relation
holds:
∆ ∆∆∆(Q) = 2π πππ2j/(Q
2Vo) ≥ ≥≥≥p D
Q
DQis the FWHM in Q-space, p is of the order of the
unity
A single reflection at Qocontributes to N
effas
1/(1+Nn), where N
nis the number of reflections in
the neighbourhood of Qo, verifying:
Qo-p D
Q≤ ≤≤≤Qn≤ ≤≤≤Qo+ p D
Q
1,
1
1B
eff
iN
i
NN
=
=+
∑The formula for calculating N
effis:
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Plo
t of
∆ ∆∆∆Q
and D
Qve
rsus
Q
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Sim
ula
tion
of
syst
emat
ic e
rror
s in
Rie
tvel
d
refi
nem
ents
Met
hod
:
1.G
ener
ate
det
erm
inis
tic
pat
tern
s w
ith d
iffe
rent
scal
e fa
ctor
s (c
ounti
ng
tim
es)
and a
dd a
Poi
sson
ian
noi
se.
2.E
ach p
atte
rn is
refi
ned
by
the
RM
by
usi
ng
eith
er t
he
“tru
e” m
odel
or
a bia
sed m
odel
(e.
g. w
rong
pea
k s
hap
e).
3.T
he
valu
es o
f th
e re
fined
par
amet
ers
are
then
com
par
ed t
o th
e tr
ue
valu
es (
bia
s an
d d
isper
sion
).
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Res
ult
s of
sim
ula
tion
s:
Ref
inem
ents
of
sim
ula
ted p
owder
dif
frac
tion
pat
tern
s usi
ng
corr
ect
and b
iase
d p
eak s
hap
e m
odel
s
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
0
2000
4000
6000
8000
1000
0
0.0
25.0
50.0
75.0
100.
012
5.0
150.
0
Ref
inem
ent
of s
imul
ated
pat
tern
wit
h bi
ased
pea
k s
hape
and
cor
rect
stru
ctur
al m
odel
.N
Intd
p=39
, Npr
of=
5, N
ref=
1507
Nef
f=(7
0, 1
37, 2
48)/
Sol
v=(1
.8,3
.5,6
.4)
Intensity (a.u.)
2Θ ΘΘΘ (
°)
RM
(sy
stem
atic
err
ors)
: B
iase
d p
eak s
hap
e+
corr
ect
stru
ctu
ral m
odel
NI=
39 +
bad
res
olu
tion
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
0
4000
8000
1200
0
0.0
25.0
50.0
75.0
100.
012
5.0
150.
0
Ref
inem
ent
of s
imul
ated
pat
tern
wit
h bi
ased
pea
k s
hape
and
cor
rect
stru
ctur
al m
odel
.N
Intd
p=39
, Npr
of=
5, N
ref=
1507
Nef
f=(1
85, 3
52, 6
11)/
Sol
v=(4
.8,9
.0,1
5.7)
Intensity (a.u.)
2Θ ΘΘΘ (
°)
RM
(sy
stem
atic
err
ors)
: B
iase
d p
eak s
hap
e+ c
orre
ct
stru
ctu
ral m
odel
NI=
39 +
bet
ter
reso
luti
on
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Beh
avio
ur
of R
ietv
eld
R-f
acto
rs, a
nd o
ther
indic
ator
s,
vers
us
counti
ng
stat
isti
cs f
or
per
fect
and b
iase
d p
eak s
hap
e m
odel
s
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
RM
(sy
stem
atic
err
ors)
: B
ehav
iou
r of
RW
Pfa
ctor
s ve
rsu
s co
un
tin
g ti
me
(bia
sed
pea
k s
hap
e)
0
10
20
30
40
50
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
R-f
act
ors
(R
WP)
Rw
pcR
wp
Rw
p(B
)cR
wp(B
)
RWP
(%)
Lo
g(C
ou
nti
ng
Tim
e)
NIn
tdp
=16
, N
pro
f=8, N
ref=
393
Neff
=(1
73, 24
4, 3
01)
Bia
sed p
ea
k s
hap
e
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
02468101214
2,0
2,5
3,0
3,5
4,0
4,5
5,0
5,5
R-f
acto
rs (
RB
ragg
and
RF)
Rb
RF
R(%)
Log
(Cou
ntin
g T
ime)
NIn
tdp=
16, N
prof
=8,
Nre
f=39
3N
eff=
(173
, 244
, 301
)B
iase
d pe
ak s
hape
RM
(sy
stem
atic
err
ors)
: B
ehav
iou
r of
RB
ragg
and
RF
fact
ors
vers
us
cou
nti
ng
tim
e (b
iase
d p
eak s
hap
e)
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
0
10
20
30
40
50
60
2,0
2,5
3,0
3,5
4,0
4,5
5,0
5,5
R-f
act
ors
(χ χχχ2)
Chi2
Chi2
(B)
Reduced χχχχ2
Lo
g(C
ou
nti
ng
Tim
e)
NIn
tdp=
16, N
pro
f=8, N
ref=
393
Neff
=(1
73, 244, 301)
Bia
sed p
eak
shape
RM
(sy
stem
atic
err
ors)
: B
ehav
iou
r of
red
uce
d
Ch
i-sq
uar
e ve
rsu
s co
un
tin
g ti
me
(bia
sed
pea
k s
hap
e)
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Ato
m c
oord
inat
es v
ersu
s re
solu
tion
(“s
olva
bilit
y in
dex
”)r = Neff / NI
Cor
rect
pea
k s
hap
e m
odel
s
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
RM
(sy
stem
atic
err
ors)
: P
osit
ion
al p
aram
eter
s N
I=39
, Cou
nti
ng
Tim
e: 1
2500
(co
rrec
t m
odel
, r=
3.5)
-0,0
40
0
-0,0
20
0
0,0
00
0
0,0
20
0
0,0
40
0
05
10
15
20
25
30
35
40
NIn
tdp=
39,
Np
rof=
5, N
ref=
150
7
Ne
ff=
(70
, 1
37
, 24
8)/
So
lv=
(1.8
,3.5
,6.4
)C
orr
ect
mod
el-
(Coun
tin
g t
ime
:1250
0)
Delta (Å)
Posi
tio
na
l P
ara
me
ter
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
-0,0
400
-0,0
200
0,0
000
0,0
200
0,0
400
05
10
15
20
25
30
35
40
NIn
tdp=
39, N
pro
f=5, N
ref=
1507
Neff
=(1
02, 192, 362)/
Solv
=(2
.6,4
.9,9
.3)
Corr
ect
model-
(Counti
ng t
ime:1
2500)
Delta (Å)
Posi
tional P
ara
mete
r
RM
(sy
stem
atic
err
ors)
: P
osit
ion
al p
aram
eter
s N
I=39
, Cou
nti
ng
Tim
e: 1
2500
(co
rrec
t m
odel
, r=
4.9)
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
RM
(sy
stem
atic
err
ors)
: P
osit
ion
al p
aram
eter
s N
I=39
, Cou
nti
ng
Tim
e: 1
2500
(co
rrec
t m
odel
, r=
9)
-0.0
400
-0.0
200
0.0
000
0.0
200
0.0
400
05
10
15
20
25
30
35
40
NIn
tdp=
39, N
pro
f=5, N
ref=
1507
Neff
=(1
85, 352, 611)/
Solv
=(4
.8,9
.0,1
5.7
)
Corr
ect
model-
(Counti
ng t
ime:1
2500)
Delta (Å)
Posi
tional P
ara
mete
r
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Ato
m c
oord
inat
es v
ersu
s st
atis
tics
(co
unti
ng
tim
e)co
rrec
t pea
k s
hap
e m
odel
, N
I=72
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
RM
(sy
stem
atic
err
ors)
: P
osit
ion
al p
aram
eter
s N
I=72
, Cou
nti
ng
Tim
e: 1
25 (
corr
ect
mod
el, r
=5.
1)
-0,3
00
0
-0,2
00
0
-0,1
00
0
0,0
00
0
0,1
00
0
0,2
00
0
0,3
00
0
010
20
30
40
50
60
70
80
NIn
tdp=
72
, N
pro
f=5,
Nre
f=39
60
Ne
ff=
(18
8,
368
, 7
26
)/S
olv
=(2
.6,5
.1,1
0.1
)C
orr
ect
mode
l-(C
oun
ting
tim
e:1
25)
Delta (Å)
Posi
tio
na
l P
ara
me
ter
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
RM
(sy
stem
atic
err
ors)
: P
osit
ion
al p
aram
eter
s N
I=72
, Cou
nti
ng
Tim
e: 1
250
(cor
rect
mod
el, r
=5.
1)
-0,1
00
0
-0,0
50
0
0,0
00
0
0,0
50
0
0,1
00
0
010
20
30
40
50
60
70
80
NIn
tdp=
72
, N
pro
f=5,
Nre
f=39
60
Ne
ff=
(18
8,
368
, 7
26
)/S
olv
=(2
.6,5
.1,1
0.1
)C
orr
ect
mo
de
l-(C
ounti
ng
tim
e:1
250)
Delta (Å)
Posi
tio
na
l P
ara
me
ter
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
RM
(sy
stem
atic
err
ors)
: P
osit
ion
al p
aram
eter
s N
I=72
, Cou
nti
ng
Tim
e: 1
2500
(co
rrec
t m
odel
, r=
5.1)
-0,1
00
0
-0,0
50
0
0,0
00
0
0,0
50
0
0,1
00
0
010
20
30
40
50
60
70
80
NIn
tdp=
72
, N
pro
f=5,
Nre
f=39
60
Ne
ff=
(18
8,
368
, 7
26
)/S
olv
=(2
.6,5
.1,1
0.1
)C
orr
ect
mo
del-
(Cou
nti
ng t
ime:1
25
00
)
Delta (Å)
Posi
tio
na
l P
ara
me
ter
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
RM
(sy
stem
atic
err
ors)
: P
osit
ion
al p
aram
eter
s N
I=72
, Cou
nti
ng
Tim
e: 1
2500
0 (c
orre
ct m
odel
, r=
5.1)
-0,1
00
0
-0,0
50
0
0,0
00
0
0,0
50
0
0,1
00
0
010
20
30
40
50
60
70
80
NIn
tdp=
72
, N
pro
f=5,
Nre
f=39
60
Ne
ff=
(18
8,
368
, 7
26
)/S
olv
=(2
.6,5
.1,1
0.1
)C
orr
ect
mod
el-
(Coun
tin
g t
ime:1
25
000
)
Delta (Å)
Posi
tio
na
l P
ara
me
ter
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Ato
m c
oord
inat
es v
ersu
s re
solu
tion
(r=Neff / NI)
(bia
sed p
eak s
hap
e, N
I=39
)
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
-0,1
000
-0,0
500
0,0
000
0,0
500
0,1
000
05
10
15
20
25
30
35
40
NIn
tdp=
39, N
pro
f=5, N
ref=
1507
Neff
=(1
85, 352, 611)/
Solv
=(4
.8,9
.0,1
5.7
)B
iase
d p
eak
shape-(
Counti
ng t
ime:1
2500)
Delta (Å)
Posi
tional P
ara
mete
r
RM
(sy
stem
atic
err
ors)
: P
osit
ion
al p
aram
eter
s N
I=39
C
oun
tin
g T
ime:
125
00 (
bia
sed p
eak s
hap
e, r
=9)
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
RM
(sy
stem
atic
err
ors)
: P
osit
ion
al p
aram
eter
s N
I=39
C
oun
tin
g T
ime:
125
00 (
bia
sed p
eak s
hap
e, r
=4.
9)
-0,1
000
-0,0
500
0,0
000
0,0
500
0,1
000
05
10
15
20
25
30
35
40
NIn
tdp=
39, N
pro
f=5, N
ref=
1507
Neff
=(1
02, 192, 362)/
Solv
=(2
.6,4
.9,9
.3)
Bia
sed p
eak
shape-(
Counti
ng t
ime:1
2500)
Delta (Å)
Posi
tional P
ara
mete
r
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
-0,1
00
0
-0,0
50
0
0,0
00
0
0,0
50
0
0,1
00
0
05
10
15
20
25
30
35
40
NIn
tdp
=39,
Np
rof=
5, N
ref=
15
07
Neff
=(7
0,
137
, 24
8)/
Solv
=(1
.8,3
.5,6
.4)
Bia
sed p
eak
sh
ape
-(C
ounti
ng t
ime:1
2500
)
Delta (Å)
Posi
tion
al P
ara
mete
r
RM
(sy
stem
atic
err
ors)
: P
osit
ion
al p
aram
eter
s N
I=39
C
oun
tin
g T
ime:
125
00 (
bia
sed p
eak s
hap
e, r
=3.
5)
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Con
clusi
ons
(sim
ula
tion
s)
(1)For complex structures high statistical accuracy and high resolution
is requiredfor getting the true parameter values even is the refined
model is unbiased. Suggestion: the solvability index (r = Neff/Nffor
p=1/2) should be largely greater than 4-5to be sure that the structural
parameters are accurate enough. More experience is needed to
establish precise rules.
(2)The absolute value of the profile R-factors has little significance
because their values depend on the quality of the data as well as on the
goodness the structural model. The R-factors obtained by a Le Bail fit
provide the “expected” values for the best structural model.
(3)Well behaved peak shape could be more important than resolution
in some cases.
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
What
to
do
when
th
e in
form
atio
n in
the
pow
der
dif
frac
tion
pat
tern
is
not
en
ough
?r = Neff / NI<
4
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Con
stra
ints
:re
duce
the
nu
mber
of
free
par
amet
ers
(rig
id b
ody
refi
nem
ents
)
Res
trai
nts
:sa
me
nu
mber
of
free
par
amet
ers
+ a
ddit
ional
obse
rvat
ions
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
New
ver
sion
of
EdP
CR
allo
ws
an e
asy
edit
ion o
f R
igid
Bod
ies
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
PC
R f
ile
gener
ated
by
EdP
CR
!-------------------------------------------------------------------------------
! Data for PHASE number: 1 ==> Current R_Bragg for Pattern#
1: 4.95
!-------------------------------------------------------------------------------
C5H4NO(CH3) ,ESRF 10K
! !Nat Dis Ang Pr1 Pr2 Pr3 Jbt Irf Isy Str Furth ATZ Nvk Npr More
120 0 0 0.0 0.0 1.0 4
0 0 1 0 929.020 0 7 0
! P 41 <--Space group symbol
!Atom Typ x y z B Occ P6
THETA PHI
Spc
! r/xc/rho the/yc/phi phi/zc/z
X0 Y0 Z0
CHI
P16:SAT DEG KIND
PI1 N 0.65457 0.83848 0.58247 3.83061 1.00000 1.00000 -176.735 -35.488
0 #CONN C C 0 1.8
0.00 0.00 0.00 0.00 0.00 0.00 111.00 121.00
1.38667 0.000 0.000
0.65878 0.83502 0.65264 -57.933
0.000 1 0
0.00 0.00 0.00 351.00 361.00 371.00 131.00
PI2 O 0.65070 0.84127 0.51616 3.71433 1.00000
0 0 0 0 #CONN C N 0 1.8
0.00 0.00 0.00 0.00 0.00
2.69269 0.000 0.000
0.00 0.00 0.00
PI3 C 0.68712 0.76540 0.61290 2.83613 1.00000
0 0 0 0 #CONN O N 0 1.8
0.00 0.00 0.00 0.00 0.00
1.40761 58.805 -90.000
0.00 0.00 0.00
PI4 C 0.62593 0.90874 0.61882 2.83613 1.00000
0 0 0 0 #CONN D C 0 1.2
0.00 0.00 0.00 0.00 0.00
1.40761 58.805 90.000
0.00 0.00 0.00
. . . . .
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
How
to
gen
erat
e re
stra
ints
for
Fu
llP
rof?
1: Calculating distances
from
FullProf
2: Using Bond_Str
importing a CIF file
Both programs
generate a file called
CFML_Restrains.tpcr
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
How
to
gen
erat
e re
stra
ints
for
Fu
llP
rof?
List of possible restraints:
At1 At2 ITnum T1 T2 T3 DIST SIGMA
O1 N1 1 0.00000 0.00000 0.00000 1.3393 0.0047
O1 C1 1 0.50000 -0.50000 0.00000 2.2874 0.0045
O1 C1 -2 0.25000 -0.25000 0.50000 3.3163 0.0041
O1 C2 -4 1.00000 -0.25000 -0.25000 3.1481 0.0046
O1 H1 1 0.50000 -0.50000 0.00000 2.5023 0.0051
. . . .
Lines to be pasted into the PCR file
DFIX 1.33935 0.00467 O1 N1
DFIX 2.28738 0.00455 O1 C1_9.545
DFIX 3.31627 0.00413 O1 C1_24.545 In CFL format
DFIX 3.14808 0.00457 O1 C2_6.644
DFIX 2.50228 0.00510 O1 H1_9.545
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
A p
ract
ical
cas
e:
Low
tem
per
ature
phas
e of
the
met
hyl
pyr
idin
e-N
-oxi
de
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
4-m
eth
ylpyr
idin
e-N
-oxi
de
(4M
PN
O)
At RT, free rotation of methyl
around C-C bound.
At 4K, methyl group ~ light
quantum rotor.
Four tunnelling transitions on
INS spectrum linked with local
topology (crystal structure).
C5H4NO(CH3)
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Syn
chro
tron
pat
tern
s RT
T=
110K
T=
25K
Ph
ase
tran
siti
ons
in 4
MP
NO
(S
NB
L-E
SR
F)
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
T=
80 K
T=
105
K
T=
280
KI41/amd
Fddd
Wh
at is
the
cell
an
d s
ymm
etry
of
the
LT
ph
ase?
Ph
ase
tran
siti
ons
in 4
MP
NO
as s
een
by
lon
g w
avel
engt
h (λ λλλ≈ ≈≈≈
3.13
Å)
neu
tron
s
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
250K
str
uct
ure
Neutron pow
der diffraction results
using a rigid-body and TLS matrices
c
b
a
I41/amd, Z = 8
a = b = 7.941Å
c = 19.600Å
3T2 -LLB
Fourier map of
methyl group
D atoms are omitted for clarity
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
250K
str
uct
ure
usi
ng
free
ato
ms
and A
DP
’s
=> Total number of "independent" reflections: 520
Effective number (account for resolution) of reflections:
at level p=1.00 : 124.5 r=2.3
at level p=0.50 : 200.1 r=3.6
at level p=0.25 : 306.3
r=5.6
=> WARNING!:
Eclectic-view-ratio is TOO LOW (<4), if there is no constraint
your intensity-dependent parameters could be rather inaccurate !
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
100K
str
uct
ure
c
a
b36.8°
Fddd, Z = 16
a = 12.138Å
b = 10.237Å
c = 19.568Å
3T2 -LLB
Fourier map of
methyl groupD
atoms are omitted for clarity
Neutron pow
der diffraction results
using a rigid-body and TLS matrices
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
100K
str
uct
ure
usi
ng
free
ato
ms
and A
DP
’s
=> Total number of "independent" reflections: 973
Effective number (account for resolution) of reflections:
at level p=1.00 : 151.6 r=2.0
at level p=0.50 : 264.9 r=3.6
at level p=0.25 : 415.8
r=5.6
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
10K
stru
cture
…??
?
Neutron data is toocomplex!
3T2 -LLB
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Low
tem
perature synchrotron data is
man
dat
oryto determine :
�Cell parameters
�Space group
Molecules positions and orientations
can be obtained using either
synchrotron or neutron data from
G42
10K
str
uct
ure
…
BM1 –
ESRF SNBL
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
10K
str
uct
ure
–w
ork
ing
wit
h s
ynch
rotr
on d
ata
or w
ith h
igh r
esol
uti
on low
-Q n
eutr
on d
ata
(G4.
2, λ≈λ≈λ≈λ≈3.
13Å
Cell parameters from
DicVol:
a = b = 15.410Å
, c = 19.680Å
, tetragonal!
Possible space groups :
derived from
subgroups of I41/amd: P41,
P -4 m 2, etc…
Positions and orientations of molecules:
Simulated Annealing with FullProf
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Sim
ula
ted a
nnea
ling
in
FullP
rof
�Integrated intensities extracted from a
LeBailfit on 25K
synchrotron data
�In P41: search for 8 x 6parameters
8 rigid independent
molecules
x, y, z (position of centre of mass )
Θ,
Θ,
Θ,
Θ, ϕ ϕϕϕ, , , , χ χχχ( (((orientation of molecule, Euler)
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
10K
str
uct
ure
: P
4 1, Z
=32
Positions and orientations of the 8 molecules can be successfully determined
from the synchrotron data or low-Q high resolution neutron data.
c
b
a
M1
M2
M3
M4
M5
M6
M7
M8
HTT-phase
ITO-phase
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
10K
str
uct
ure
: m
ethyl
rot
ors
Neutron data shows that D atoms are
localised and that rotors order at low
temperature
3T2 -LLB
10K
P41
a= b= 15.410Å
c= 19.680Å
z = 32
a
b
Fourier map
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Syn
chro
tron
dat
a at
25K
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
10K
str
uct
ure
: R
GB
-rin
gs,
free
met
hyl
gro
ups
and D
Better refinement can be performed but
a deformation of the molecules occurs
3T2 -LLB
-
Mar
ch 2
006
Ren
contr
esL
LB
-SO
LE
IL:
Dif
frac
tion
de
Pou
dre
s
Con
clu
sion
s
�R
efin
emen
t of
com
ple
x st
ruct
ure
s re
quir
es v
ery
good
re
solu
tion
, abse
nce
of
syst
emat
ic e
rror
s an
d s
olva
bilit
y in
dic
es m
uch
hig
her
than
6-7
�In
pra
ctic
e th
e re
finem
ent
may
be
mor
e dif
ficu
lt a
nd
tedio
us
than
sol
ving
the
stru
cture
due
to t
he
intr
insi
c lo
st o
f in
form
atio
n in
pow
der
dif
frac
tion
com
par
ed t
o si
ngl
e cr
ysta
ls
�It
is
bet
ter
to u
se c
onst
rain
ts/r
estr
aints
eve
n if
the
Rie
tvel
d r
efin
emen
t is
wor
se
