An introduction to solid solutions
and disordered systems
MSSC2016 Torino
Ph.D’Arco
1
1
Institut des Sciences de la Terre de Paris (UMR 7193)
UPMC - Sorbonne Universit´
es, France
September 6, 2016
this talk is dedicated to Roberto Orlando
Ph.D’Arco
1
An introduction to solid solutions
and disordered systems
MSS
Goal of these presentations
give general idea to numerically study disordered systems
present unfamiliar application of the symmetry
introduce the techniques implemented in CRYSTAL
show few examples
CONFCNT
CONFRAND/RUNCONFS
Comparing computation and experiment is not straightforward
The same ideas or techniques are valid to study defects.
Ph.D’Arco
1
An introduction to solid solutions
and disordered systems
MSS
Non ideal crystalline systems
Using space group supposes that :
translational symmetry is strictly obeyed!
Some crystalline systems
cannot be strictly periodic at the ”atomic” scale !
Disordered materials
Solid solutions
Magnetic spin distribution
Ph.D’Arco
1
An introduction to solid solutions
and disordered systems
MSS
Disordered systems
Different atoms occupy positions that are equivalent at some temperature
Ex : Gehlenite Ca
2
Al
2
SiO
7
Space group :
P
¯
42
1
m
, a=7.6850
˚
A, c=5.0636
˚
A
atom
x
y
z
occ
Ca
.3389
.1611
.5104
AlT1
0
0
0
AlT2
.1434
.3556
.9540
.50
SiT2
.1434
.3556
.9540
.50
O1
.5
0
.1765
O2
.1427
.3573
.2835
O3
.0876
.1678
.8078
XRD cannot resolve atomic distribution over different positions
(sites)
Atoms are very similar (Si, Al)
Statistical disorder
Dynamical disorder
Ph.D’Arco
1
An introduction to solid solutions
and disordered systems
MSS
Textbook example of Disordered system
Normal to inverse spinel A
IV
B
VI
2
O
4
:
AB
2
O
4
↔
B (A,B) O
4
Symmetry remains cubic
→
statistical occupation of the octahedral
site! In general disordered over A and B sites : A
1
-
x
B
x
A
x
B
2
-
x
O
4
.
Non-converging disorder!
Ph.D’Arco
1
An introduction to solid solutions
and disordered systems
MSS
Solid solutions
Crystalline materials displaying large chemical variations without
apparent discontinuity.
Isostructural materials :
Alloys
Simple oxides : Al
2
O
3
-Cr
2
O
3
Complex silicates : NaAlSi
3
O
8
– KAlSi
3
O
8
Chemical variations are described on the basis of end-members
that are considered as pure compounds.
End-members may be stable or not : ZnS (Zincblende) -FeS
(NiAs).
The solution can be either continuous or partial between
end-members.
Ph.D’Arco
1
An introduction to solid solutions
and disordered systems
MSS
Macroscopic properties depend on composition/disorder
Melilite
Gehlenite
Ackermanite
Ca
2
Al
2
SiO
7
Ca
2
MgSi
2
O7
300
301
302
303
304
305
306
0
20
40
60
80
100
Volume/formula (A
3
)
Mol. per cent Ca
2
MgSi
2
O
7
Ge
Ak
11
12
13
14
15
0
20
40
60
80
100
Δ
H
sol
/formula (kcal)
Mol. per cent Ca
2
MgSi
2
O
7
Ge
Ak
Charlu et al, 1981, geochim. Cosmochim. Acta, 45, p1609-1617
Ph.D’Arco
1
An introduction to solid solutions
and disordered systems
MSS
Macroscopic properties depend on composition/order
ZnS-FeS system
Very large exces volume.
