Theoretical investigation of the inversion parameter in Co
3 - s
Al
s
O
4
(s =0–3)
spinel structures
F. Tielens
a,b,
⁎, M. Calatayud
c,d
, R. Franco
e
, J.M. Recio
e
, J. Pérez-Ramírez
f
, C. Minot
c,d
a
UPMC Univ Paris 06, UMR 7609, Laboratoire de Réactivité de Surface, Tour 54-55, 2ème étage—Casier 178, 4, Place Jussieu, F-75005 Paris, France
b
CNRS, UMR 7609, Laboratoire de Réactivité de Surface, Tour 54-55, 2ème étage—Casier 178, 4, Place Jussieu, F-75005 Paris, France
c
UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, 4, Place Jussieu, F-75005 Paris, France
d
CNRS, UMR 7616, Laboratoire de Chimie Théorique, 4, Place Jussieu, F-75005 Paris, France
e
MALTA-Consolider Team, Departamento de Química Física y Analítica, Universidad de Oviedo E-33006, Oviedo, Spain
f
ICREA and Institute of Chemical Research of Catalonia (ICIQ), Avinguda Països Catalans 16, E-43007 Tarragona, Spain
abstract article info
Article history:
Received 30 June 2008
Received in revised form 27 October 2008
Accepted 30 March 2009
Available online xxxx
Keywords:
Spinels
DFT
Inversion parameter
Co
2
AlO
4
CoAl
2
O
4
The structural, energetic, and thermodynamic properties of the Co
3 -s
Al
s
O
4
(s =0, 1, 2, and 3) crystal family
are studied using periodic DFT calculations. We provide a quantitative discussion of the cation distribution
effect on the cell parameter, the oxygen Wyckoff position, the interatomic distances and the energies of the
structures. It is demonstrated that the low cobalt containing CoAl
2
O
4
spinel is the most stable structure of the
Co
3 -s
Al
s
O
4
(s =0, 1, 2, and 3) crystal family.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
The spinel structure receives its name from the mineral MgAl
2
O
4
and can be considered as very common and widely spread mixed
oxide with more than one hundred varieties known [1]. The crystal-
line lattice is essentially a compact cubic pilling of divalent anions (e.g.
O
2-
, S
2-
, Se
2-
) and divalent and trivalent cations occupying
tetrahedral and octahedral sites [2]. Depending on the oxidation
state of the cations, different types of spinels can be formed, namely:
the 2,3 type such as MgAl
2
O
4
, the 4,2 type such as TiMg
2
O
4
, the 1,3,4
type such as LiAlTiO
4
, the 1,3 type such as Li
0.5
Al
2.5
O
4
, the 1,2,5 type
such as LiNiVO
4
, and the 1,6 type such as Na
2
WO
4
.
The possibility to alter the distribution of cations situated in
tetrahedral and octahedral sites opens interesting routes to design
compounds with a priori selected properties. This switch between
cation coordination can theoretically reach two extreme situations:
the normal spinel in which the divalent cations are situated in the
tetrahedral sites (e.g. MgAl
2
O
4
) and the inverse spinel in which the
divalent cations occupy half of the octahedral sites and the tetrahedral
sites are occupied by the trivalent cations (e.g. MgFe
2
O
4
). Between
these two extremes, intermediate distributions can be found which
are characterized by the so-called degree of inversion parameter, x,
defined as the fraction of divalent metal cations that moves to
octahedral sites:
A
1 -x
B
x
ð Þ A
x
B
2 -x
½ X
4
ð1Þ
Cations in tetrahedral and octahedral surroundings are denoted
with the round ( ) and square [ ] brackets, respectively. In Eq. (1), X
is a divalent anion, and A and B represent divalent and trivalent
cations, respectively. In normal spinels x = 0, while inverse spinels
have x =1. When the degree of inversion is equal to 2/3, the di- and
trivalent cations are distributed in a way that both, the O
h
and T
d
positions have an equal proportion of interchanged cations, i.e. the
ratio of trivalent/divalent cations is two in both interstices. This
spinel structure is referred to as random since the number of
possibilities to reach this distribution leads to a maximum in the
configurational entropy [3].
The cation distribution in spinels is a function of the combina-
tion and nature of the cations, and is also influenced by pressure and
temperature. The structural factors that determine the inversion
parameter of a certain spinel are the ionic/covalent character, the
ion size, and most importantly the crystal field stabilization [4,5].
This cation distribution, among tetrahedral and octahedral sites,
can be modified by means of adequate changes in chemical com-
position, which leads to changes in physical and chemical proper-
ties of the resulting materials [6]. It has been possible to force
Solid State Ionics xxx (2009) xxx–xxx
⁎ Corresponding author. UPMC Univ Paris 06, UMR 7609, Laboratoire de Réactivité de
Surface, Tour 54-55, 2ème étage—Casier 178, 4, Place Jussieu, F-75005 Paris, France.
E-mail address: frederik.tielens@upmc.fr (F. Tielens).
SOSI-11552; No of Pages 6
0167-2738/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.ssi.2009.03.023
Contents lists available at ScienceDirect
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journal homepage: www.elsevier.com/locate/ssi
ARTICLE IN PRESS
Please cite this article as: F. Tielens, et al., Solid State Ionics (2009), doi:10.1016/j.ssi.2009.03.023