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ORIGINAL PAPER
Aluminum substitution mechanisms in perovskite-type MgSiO3:an investigation by Rietveld analysis
Hiroshi Kojitani Æ Tomoo Katsura Æ Masaki Akaogi
Received: 10 June 2006 / Accepted: 15 January 2007 / Published online: 17 February 2007� Springer-Verlag 2007
Abstract Al-containing MgSiO3 perovskites of four
different compositions were synthesized at 27 GPa and
1,873 K using a Kawai-type high-pressure apparatus:
stoichiometric compositions of Mg0.975Si0.975Al0.05O3
and Mg0.95Si0.95Al0.10O3 considering only coupled
substitution Mg2+ + Si4+ = 2Al3+, and nonstoichio-
metric compositions of Mg0.99Si0.96Al0.05O2.985 and
Mg0.97Si0.93Al0.10O2.98 taking account of not only the
coupled substitution but also oxygen vacancy substi-
tution 2Si4+ = 2Al3+ + VO. Using the X-ray diffraction
profiles, Rietveld analyses were performed, and the
results were compared between the stoichiometric and
nonstoichiometric perovskites. Lattice parameter–
composition relations, in space group Pbnm, were
obtained as follows. The a parameters of both of the
stoichiometric and nonstoichiometric perovskites
are almost constant in the XAl range of 0–0.05, where
XAl is Al number on the basis of total cation of two
(XAl = 2Al/(Mg + Si + Al)), and decrease with further
increasing XAl. The b and c parameters of the stoi-
chiometric perovskites increase linearly with increasing
Al content. The change in the b parameter of the
nonstoichiometric perovskites with Al content is the
same as that of the stoichiometric perovskites within
the uncertainties. The c parameter of the nonstoi-
chiometric perovskites is slightly smaller than that of
the stoichiometric perovskites at XAl of 0.10, though
they are the same as each other at XAl of 0.05. The
Si(Al)–O1 distance, Si(Al)–O1–Si(Al) angle and min-
imum Mg(Al)–O distance of the nonstoichiometric
perovskites keep almost constant up to XAl of 0.05, and
then the Si(Al)–O1 increases and both of the Si(Al)–
O1–Si(Al) angle and minimum Mg(Al)–O decrease
with further Al substitution. These results suggest that
the oxygen vacancy substitution may be superior to the
coupled substitution up to XAl of about 0.05 and that
more Al could be substituted only by the coupled
substitution at 27 GPa. The Si(Al)–O1 distance
and one of two independent Si(Al)–O2 distances in
Si(Al)O6 octahedra in the nonstoichiometric perovsk-
ites are always shorter than those in the stoichiometric
perovskite at the same Al content. These results imply
that oxygen defects may exist in the nonstoichiometric
perovskites and distribute randomly.
Keywords Perovskite � Aluminum substitution �High-pressure � X-ray diffraction � Rietveld analysis
Introduction
It is widely accepted that (Mg, Fe)SiO3 perovskite is a
major constituent mineral in the Earth’s lower mantle.
High-pressure experiments on pyrolitic mantle sug-
gested that most of aluminum is incorporated in the
(Mg, Fe)SiO3 perovskite (e.g., Irifune 1994). To
examine effects of the aluminum substitution in
MgSiO3 perovskite on its elastic properties, many
researchers have performed determination of equation
of state (Zhang and Weidner 1999; Kubo et al. 2000;
H. Kojitani (&) � M. AkaogiDepartment of Chemistry, Faculty of Science,Gakushuin University, 1-5-1 Mejiro,Toshima-ku, Tokyo 171-8588, Japane-mail: hiroshi.kojitani@gakushuin.ac.jp
T. KatsuraInstitute for Study of the Earth’s Interior,Okayama University, 827 Yamada, Misasa,Tottori 682-0193, Japan
123
Phys Chem Minerals (2007) 34:257–267
DOI 10.1007/s00269-007-0144-z
Andrault et al. 2001; Daniel et al. 2001; Walter et al.
2004; Yagi et al. 2004) and Bullouin spectroscopy
(Jackson et al. 2004) on Al-containing MgSiO3 per-
ovskites.
In considering the aluminum substitution mecha-
nism in MgSiO3 perovskite, there are two types of
possible substitution. One is a Tschermakite-like cou-
pled substitution:
Mg2þ þ Si4þ ¼ 2Al3þ: ð1Þ
Al-containing MgSiO3 perovskite only by this
substitution has a stoichiometric composition. The
other is an oxygen vacancy substitution:
2Si4þ ¼ 2Al3þ þV€o; ð2Þ
where VO means an oxygen vacancy. Most of Al sub-
stitutions in MgSiO3 perovskite have been investigated
by taking only the coupled one into account. Lattice
parameter–composition relations of perovskite solid
solutions in the MgSiO3–Mg3Al2Si3O12 system have
been reported by Weng et al. (1982), O’Neill and
Jeanloz (1994), Irifune et al. (1996), Kubo and Akaogi
(2000), and Walter et al. (2004). Their results indicated
that, in space group Pbnm, a-axis generally kept con-
stant within scatter of the data and that b- and c-axes
increased with increasing Al component. In the three
axes, an increasing rate of the c-axis was the highest.
XAFS study by Andrault et al. (1998) and NMR
investigation by Stebbins et al. (2001) suggested that
Al3+ was accommodated in both Mg2+ and Si4+ sites.
Kesson et al. (1995) mentioned the existence of
nonstoichiometric Al-containing MgSiO3 perovskites,
which show smaller oxygen numbers than three on the
basis of total cation of two, in recovered samples of la-
ser-heated diamond anvil cell experiments at 55 GPa
with starting composition of MgSiO3 : MgAl2O4 =
77:33 in mol ratio. In the experiments of high-pressure
phase relations in the MgSiO3–Mg3Al2Si3O12 system by
Kubo and Akaogi (2000), coexistence of stishovite with
perovskite was observed in recovered samples from 25
to 27 GPa and 1,873 K of multi-anvil experiments,
implying that the Al-containing MgSiO3 perovskite had
a Si-poor composition that could not be explained only
by the coupled substitution. Finally, it was shown by
Navrotsky et al. (2003) that nonstoichiometric Al–
MgSiO3 perovskite could be synthesized in high-pres-
sure multi-anvil experiments at 27 GPa and 1,873 K
along the MgSiO3–MgAlO2.5 join taking the oxygen
vacancy substitution into account. Theoretical studies of
Al-containing MgSiO3 perovskites by first-principle
calculation (Brodholt 2000; Yamamoto et al. 2003) and
by energetic calculation (Akber-Knutson and Buko-
winski 2004) suggested that the coupled substitution was
more favorable than the oxygen vacancy substitution at
pressure higher than about 30 GPa.
The nonstoichiometric Al–MgSiO3 perovskites
indicate Mg-rich and Si-poor compositions, and oxygen
numbers smaller than three on the basis of total cation
of two. NMR studies (Stebbins et al. 2003, 2006)
showed that Al occupancy of octahedral site is much
higher than that of eightfold coordination site in non-
stoichiometric Al–MgSiO3 perovskites in contrast to
the same Al occupancy of both sites in stoichiometric
Mg0.95Si0.95Al0.1O3 perovskite (Stebbins et al. 2001). A
partial oxygen vacancy substitution can explain these
compositional characters of the nonstoichiometric
perovskite. If a nonstoichiometric perovskite contains
oxygen vacancies, it is expected that there are some
structural differences between nonstoichiometric and
stoichiometric perovskites at the same Al content. In
this study, structure refinements of both nonstoichio-
metric and stoichiometric Al–MgSiO3 perovskites have
been made using Rietveld method. Obtained structures
are compared for better understanding of the alumi-
num substitution mechanisms in MgSiO3 perovskite,
particularly the behavior of oxygen vacancies.
Experimental methods
High-pressure synthesis
Samples for Rietveld analysis were prepared as fol-
lows. Targeted compositions of Al-containing MgSiO3
perovskites were MgSi0.95Al0.05O2.975, MgSi0.90Al0.10
O2.95, Mg0.975Si0.975Al0.05O3, and Mg0.95Si0.95Al0.10O3.
Starting materials were the mixtures of MgO, Al2O3,
and silicic acid (SiO2�11 wt.% H2O) with the desired
compositions. Extra SiO2 of 10 mol% was added in the
syntheses of stoichiometric perovskites with
Mg0.975Si0.975Al0.05O3 and Mg0.95Si0.95Al0.10O3 compo-
sitions to prevent possible production of nonstoi-
chiometric perovskite, because nonstoichiometric
Al-containing MgSiO3 perovskite could be synthesized
in MgO-saturated bulk composition (Navrotsky et al.
2003). These oxide powders were mixed in an agate
mortar under ethanol for 1 h, and then heated at
1,273 K for 3 h to remove water in the silicic acid and
organic impurities. Starting material for pure MgSiO3
perovskite was synthetic MgSiO3 orthoenstatite.
The high-pressure and high-temperature syntheses
of perovskites with MgSi0.90Al0.10O2.95, Mg0.975Si0.975
Al0.05O3, Mg0.95Si0.95Al0.10O3, and MgSiO3 composi-
tions were performed using a Kawai-type multi-anvil
258 Phys Chem Minerals (2007) 34:257–267
123
high-pressure apparatus at Gakushuin University.
Tungsten carbide anvils with a truncated edge length
(TEL) of 1.5 mm were used. A pressure medium was a
semi-sintered MgO octahedron. A cylindrical LaCrO3
sleeve for thermal insulator was placed in the central
part of the pressure medium. A cylindrical Re heater
was inserted into the LaCrO3 sleeve. Sample powder
was put directly into the Re heater. MgO plugs were
stuffed at both ends of the heater. Thin Pt discs sepa-
rating the sample from the MgO plugs were inserted to
prevent any reaction between them. Temperature was
measured by a Pt/Pt–13%Rh thermocouple, hot junc-
tion of which was positioned in the central part of the
heater. Starting materials were held at 27 GPa and
1,873 K for 3–5 h. After quenching under pressure, the
samples were recovered to the ambient conditions. In
each composition, three recovered samples (total
weight of about 2 mg) were used for an X-ray dif-
fraction (XRD) measurement.
The synthesis of MgSi0.95Al0.05O2.975 perovskite was
performed using a Kawai-type multi-anvil high-pres-
sure apparatus at Institute for Study of the Earth’s
Interior, Okayama University. The synthesis method
was the same as that described above, except for use of
tungsten carbide anvils with TEL of 3 mm, a sleeve
and plugs made of ZrO2, and thin Re discs. The
starting material was held at about 26 GPa and 1,873 K
for 4 h. The samples used for XRD measurement were
synthesized in two experimental runs (total weight of
about 4.5 mg). These samples were the same as those
used in 27Al-NMR measurement of nonstoichiometric
perovskite by Stebbins et al. (2006).
Compositions of the synthesized samples were ana-
lyzed using an electron probe microanalyzer (EPMA)
(JEOL JXA-8800) at Tokyo Institution of Technology.
An acceleration voltage and a filament current were
10 kV and 9 nA, respectively. The spot size of electron
beam was 1 lm. Synthetic MgSiO3 orthoenstatite was
used as a standard for magnesium and silicon. A single
crystal of corundum was used as a standard for alu-
minum. Composition of MgSiO3 perovskite was ana-
lyzed using a scanning electron microscope (JEOL
JSM-6360) with energy dispersive spectrometer (OX-
FORD INCA X-sight) (SEM-EDS) at Gakushuin
University. Acceleration voltage and probe current
were 15 kV and 0.44 nA, respectively. The synthetic
MgSiO3 orthoenstatite was used as a standard of the
SEM-EDS analysis for magnesium and silicon.
Rietveld refinement
The synthesized samples were crushed in a tungsten
carbide die at the liquid nitrogen temperature to prevent
potential amorphization. The powdered sample was
mounted on a nonreflective quartz holder with acetone.
A Rigaku RINT2500V diffractometer with monochro-
matized Cr Ka radiation (45 kV, 250 mA) at Gakushuin
University was used for the powder XRD measurement.
XRD profiles were collected by the step scanning
method in the 2h range of 20�–140�. The step size and
counting time were 0.02� and 25 s per step, respectively.
Rietveld analysis was made with the RIETAN-2000
program (Izumi and Ikeda 2000). Peak profiles were
fitted with the pseudo-Voigt function. The preferred
orientation was corrected by the March–Dollase func-
tion (Dollase 1986). All of XRD profiles were analyzed
with the crystal structure model of GdFeO3-type
perovskite in space group Pbnm. Site occupancies were
calculated based on the results of composition analysis.
In the case of Mg0.975Si0.975Al0.05O3 and Mg0.95Si0.95
Al0.10O3 perovskites, when all isotropic atomic dis-
placement factors were refined, those of oxygens
showed unusual values. Therefore, they were fixed at
0.9, which was the average value of those for nonstoi-
chiometric perovskites. When detectable amounts of
impurities (stishovite, Re, ReO2, or WC) were included
in the samples, the refinements were made as multi-
phase samples including the impurities.
Results and discussion
Compositions
The results of composition analysis of synthesized
perovskites are indicated in Table 1. Average grain size
of the perovskites was 5 lm · 10 lm to 10 lm · 20 lm
in all observed samples. Since larger grains were
chosen in the EPMA measurement, it is believed that
obtained compositions are those of only perovskite
phase. It was confirmed that all synthesized perovskites
contained desired amounts of Al within the measure-
ment errors.
Both of synthesized perovskites from the starting
compositions of MgSi0.95Al0.05O2.975 and MgSi0.90
Al0.10O2.95 considering perfect oxygen vacancy substi-
tution do not show the same compositions as the
starting materials. However, calculated oxygen num-
bers of the perovskites are still obviously less than
three on the two total cation basis. Therefore, they are
called as ‘‘nonstoichiometric’’. Although an Al-con-
taining MgSiO3 perovskite only by the oxygen vacancy
substitution should have Mg number of unity, those of
the nonstoichiometric perovskites are smaller than
unity beyond the analytical errors. Also, their Si com-
ponents are richer than those expected by the perfect
Phys Chem Minerals (2007) 34:257–267 259
123
oxygen vacancy substitution. These suggest that Al in
the nonstoichiometric perovskites seems to be substi-
tuted not only by the oxygen substitution but also by
the coupled substitution. In the nonstoichiometric
perovskite with XAl of 0.05, where XAl is Al number on
the basis of total cation of two and is calculated as
twice of mol fraction of Al, XAl = 2Al/(Mg + Al + Si),
the Mg number of 0.99 implies that Al of XAl = 0.02 is
substituted by the coupled substitution and that the
rest of Al of XAl = 0.03 might be substituted by the
oxygen vacancy substitution. Similar calculation sug-
gests that Al in the nonstoichiometric perovskite with
XAl of 0.10 can be resolved into two substitution
components, XAl by the coupled substitution of 0.06
and XAl by the oxygen vacancy substitution of 0.04.
Synthesized perovskites from the starting composi-
tions of Mg0.975Si0.975Al0.05O3, and Mg0.95Si0.95Al0.10O3
only by the coupled substitution show almost the same
compositions as desired ones and calculated oxygen
numbers of three within the errors on the basis of total
cation of two. Similarly to ‘‘nonstoichiometric’’ per-
ovskites, these are referred as ‘‘stoichiometric’’
perovskite.
Lattice parameters
Obtained lattice parameters are shown in Table 1. The
results of the Rietveld analyses are shown in Table 2
and Fig. 1. In this study, lattice parameters of pure
MgSiO3 perovskite were also determined in addition to
Al-containing MgSiO3 perovskites for the internal
consistency of data. Our lattice parameters of the
MgSiO3 perovskite are the same as those by Ross and
Hazen (1989), Mao et al. (1991), and Dobson and
Jacobsen (2004) within the errors.
The relationships between lattice parameters and Al
content are plotted in Fig. 2. The a-axis of the stoi-
chiometric perovskites of this study is almost constant
in the XAl range of 0–0.05 and decreases with further
increasing Al content. The b- and c-axes of the stoi-
chiometric perovskites increase almost linearly with
increasing Al content in the XAl range of 0–0.10. Our
lattice parameters of the stoichiometric perovskites are
compared with those by previous works in Table 3 and
Fig. 2. O’Neill and Jeanloz (1994) and Irifune et al.
(1996) reported that a-axis increases with increasing Al
content. The a-axes of Weng et al. (1982) and Walter
et al. (2004) are almost independent of Al content. Al-
containing MgSiO3 perovskites with XAl of 0.10 and
0.20 reported by Kubo and Akaogi (2000) have a-
parameters of 4.7697(13) and 4.7726(5) A, respectively.
Kubo and Akaogi (2000) did not determine lattice
parameters of MgSiO3 perovskite. If our MgSiO3
perovskite data are combined with their data, negative
change of a-axis is observed. It is noteworthy that
simple extrapolation of our a-axis length–Al content
relation to XAl of 0.5 which is equal to pyrope com-
position gives a value of 4.7644 A close to that of
Mg3Al2Si3O12 perovskite (4.771 A) by Ito et al. (1998).
The increasing rates of both b- and c-axes for our
stoichiometric perovskites show very good agreement
with those of previous studies (Weng et al. 1982;
O’Neill and Jeanloz 1994; Irifune et al. 1996; Walter
et al. 2004).
Lattice parameters of the nonstoichiometric per-
ovskites are compared with those of the stoichiometric
perovskites in Fig. 2. The a-axis change of the non-
stoichiometric perovskites is very similar to that of the
stoichiometric perovskites. The b- and c-axes of the
nonstoichiometric perovskites increase with increasing
Table 1 Lattice parameters,volumes and compositions ofMgSiO3 and Al-containingMgSiO3 perovskites
XAl: Aluminum cationnumber on the basis of totalcation of two defined by theequation XAl = 2Al/(Mg + Si + Al)a Total cation numbers werenormalized to two
MgSiO3 pv Nonstoichiometric pv Stoichiometric pv
XAl 0.00 0.05 0.10 0.05 0.10
Lattice parameters and unit cell volumea/ A 4.7784(2) 4.7785(1) 4.7769(1) 4.7783(1) 4.7767(1)b/ A 4.9303(1) 4.9326(1) 4.9336(1) 4.9327(2) 4.9342(2)c/ A 6.8990(2) 6.9059(1) 6.9085(2) 6.9051(2) 6.9130(2)V/ A 3 162.53(1) 162.77(1) 162.82(1) 162.75(1) 162.93(1)
Composition/wt.%SiO2 59.9(6) 57.6(10) 55.5(5) 57.9(9) 57.3(2)MgO 40.1(2) 39.7(4) 38.5(3) 38.6(2) 38.1(2)Al2O3 – 2.5(8) 5.2(3) 2.5(3) 5.1(2)Total 100.0 99.8 99.2 99.0 100.5
Atomic ratioa
Si 1.002(4) 0.963(16) 0.933(8) 0.971(10) 0.946(3)Mg 0.998(9) 0.988(10) 0.964(8) 0.979(5) 0.955(5)Al – 0.049(16) 0.103(6) 0.050(6) 0.098(4)O 3.001 2.987 2.985 2.996 2.995
260 Phys Chem Minerals (2007) 34:257–267
123
Al content. They show very good agreement with those
for the stoichiometric perovskites at XAl of 0.05. The b-
axis of the nonstoichiometric perovskites is also com-
parable to that of the stoichiometric perovskites at
XAl = 0.10 within the uncertainties of twice the stan-
dard deviations. On the other hand, the c-axis of the
nonstoichiometric perovskites is smaller than that of
the stoichiometric perovskites at XAl of 0.10. Our
volume differences between the stoichiometric and
nonstoichiometric perovskites are relatively smaller
than that suggested by Walter et al. (2004) in which
nonstoichiometric perovskites data by Navrotsky et al.
(2003) were compared with stoichiometric perovskites
data by them and also previous studies. Considering
Table 2 Fractional atomic coordinates and isotropic displacement factors of Al-containing MgSiO3 perovskites refined by rietveldanalysis
Atom Site x y z Biso/ A2 g
Nonstoichiometric perovskite with XAl = 0.05RWP = 6.44%, RB = 2.50%, RF = 2.11%, Re = 4.39%, S = 1.47Mg 4c 0.9863(3) 0.0530(2) 1/4 1.00(5) 0.99Al 4c 0.9863(3) 0.0530(3) 1/4 1.00(5) 0.01Si 8d 0 1/2 0 0.36(5) 0.96Al 8d 0 1/2 0 0.36(5) 0.04O1 4c 0.1006(4) 0.4662(5) 1/4 1.05(8) 0.995O2 4b 0.6983(3) 0.2958(3) 0.0538(2) 0.85(6) 0.995
Nonstoichiometric perovskite with XAl = 0.10RWP = 7.30%, RB = 7.65%, RF = 5.27%, Re = 5.88%, S = 1.24Mg 4c 0.9886(6) 0.0561(4) 1/4 0.30(9) 0.97Al 4c 0.9886(6) 0.0561(4) 1/4 0.30(9) 0.03Si 8d 0 1/2 0 0.15(8) 0.93Al 8d 0 1/2 0 0.15(8) 0.07O1 4c 0.1058(8) 0.4628(9) 1/4 0.82(13) 0.993O2 4b 0.6983(6) 0.2967(6) 0.0533(4) 0.65(11) 0.993
Stoichiometric perovskite with XAl = 0.05RWP = 9.71%, RB = 5.08%, RF = 2.47%, Re = 7.62%, S = 1.27Mg 4c 0.9848(5) 0.0556(4) 1/4 0.69(7) 0.975Al 4c 0.9847(5) 0.0548(4) 1/4 0.69(7) 0.025Si 8d 0 1/2 0 0.76(6) 0.975Al 8d 0 1/2 0 0.76(6) 0.025O1 4c 0.1058(6) 0.4640(7) 1/4 0.9 1.0O2 4b 0.6944(5) 0.2986(5) 0.0529(4) 0.9 1.0
Stoichiometric perovskite with XAl = 0.10RWP = 10.12%, RB = 12.10%, RF = 6.10%, Re = 6.92%, S = 1.46Mg 4c 0.9727(7) 0.0462(7) 1/4 0.59(12) 0.95Al 4c 0.9727(7) 0.0462(7) 1/4 0.59(13) 0.05Si 8d 0 1/2 0 0.34(11) 0.95Al 8d 0 1/2 0 0.34(11) 0.05O1 4c 0.1079(11) 0.4481(14) 1/4 0.9 1.0O2 4b 0.6955(8) 0.2978(9) 0.0570(6) 0.9 1.0
Space group: Pbnm
XAl: Aluminum number on the basis of total cation of two defined by the equation XAl = 2Al/(Mg + Si + Al)
Isotropic atomic displacement factor = exp[–Biso(sin h/k)2]
g: Site occupancy
RWP ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
i wi yi oð Þ � yi cð Þ½ �2P
i wi yi oð Þ½ �2
s
; RB ¼P
k Ik oð Þ � Ik cð Þj jP
k Ik oð Þ ; RF ¼
P
k Ik oð Þ½ �1=2 � Ik cð Þ½ �1=2�
�
�
�
�
�
P
k Ik oð Þ½ �1=2;
Re ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
N � PP
i wiy2i
s
; S ¼ RWP
Re;
where yi(o) and yi(c)
are observed and calculated intensities at profile point i, respectively
wi is a weight for each step i
Ik(o) and Ik(c) are observed and calculated integrated intensities, respectively
N and P mean numbers of all data and of parameters used for refinement, respectively
Phys Chem Minerals (2007) 34:257–267 261
123
that the lattice parameter–Al content relations of
nonstoichiometric perovskites of Navrotsky et al.
(2003) are almost the same as those of stoichiometric
perovskites of this study and previous works as shown
in Table 3, it is likely that Al content values might be
confused in the comparison by Walter et al. (2004)
because they adopted a mol fraction of Al which is a
half of XAl, used in Navrotsky et al. (2003) as well as
this study, at the same Al content. It is expected that
the differences in b- and c-axes between the stoichi-
ometric and nonstoichiometric perovskites are proba-
bly caused by some structure differences derived from
the two aluminum substitution mechanisms.
Crystal structures
More detailed crystallographic data are useful to
understand how the structure of MgSiO3 perovskite
changes with Al substitution. Interatomic distances and
bond angles of the stoichiometric and nonstoichio-
metric perovskites are shown in Table 4 and Figs. 4, 5,
and 6 together with pure MgSiO3 perovskite data
which were calculated by combining our lattice con-
stants with atomic position parameters of Dobson and
Jacobsen (2004), because their lattice parameters of
MgSiO3 perovskite (a = 4.7780(2) A, b = 4.9298(3) A,
and c = 6.8990(3) A) are the same as ours within the
errors and atomic positions were most accurately
determined by them among several previous studies.
An effect of the Al substitution on shapes of SiO6
octahedra can be observed in interatomic distances
between Si and O. The Si(Al)–O1 distance of the
stoichiometric perovskites increases with increasing Al
content. The Si(Al)–O1 distance of the nonstoichio-
metric perovskites is constant at 0 £ XAl £ 0.05 and in-
creases with further Al content. The increasing rate for
the nonstoichiometric perovskites at 0.05 £ XAl £ 0.10
is lower than that for the stoichiometric perovskites.
Fig. 1 Results of Rietveld refinement: a Mg0.99Si0.96Al0.05O2.985
perovskite, b Mg0.97Si0.93Al0.10O2.98 perovskite, c Mg0.975Si0.975
Al0.05O3 perovskite, and d Mg0.95Si0.95Al0.10O3 perovskite. XAl isan aluminum number on the basis of total cation of two,XAl = 2Al/(Mg + Si + Al). Crosses and lines indicate observedand calculated X-ray diffraction profiles, respectively. Verticalbars under the profile are peak positions of phase(s) used in
refinement. Four steps of bars in a show peak positions ofperovskite, ReO2, Re, WC in turn from the top. Bars in b arepeak positions of perovskite. Similarly, bars in c are perovskite,stishovite, and those in d are perovskite, stishovite, and Re foreach step. The plot at the bottom represents the difference ofintensity between observed and calculated patterns
262 Phys Chem Minerals (2007) 34:257–267
123
There are two independent Si(Al)–O2 distances, i.e.,
Si(Al)–O2(i) and Si(Al)–O2(ii) as shown in Table 4
and Fig. 3. The Si(Al)–O2(i) of the stoichiometric
perovskites increases slightly with increasing Al con-
tent, and that of the nonstoichiometric perovskites
keeps almost constant within the errors (Fig. 4). In the
Si(Al)–O2(ii) distance, both the stoichiometric and
nonstoichiometric perovskites show almost constant
values within the errors. Therefore, it is suggested that
averaged Si(Al)O6 octhahedra in both the stoichiom-
etric and nonstoichiometric perovskites are slightly
extended to the direction of Si(Al)–O1 with the Al
substitution, though the degree of extension in the
Si(Al)–O1 direction of the nonstoichiometric per-
ovskites is smaller than that of the stoichiometric per-
ovskites.
Si(Al)–O1–Si(Al) and Si(Al)–O2–Si(Al) bond an-
gles are given in Table 4 and in Fig. 5 to show degree
of tilting of Si(Al)O6 octahedra. The Si(Al)–O1–Si(Al)
angle in the stoichiometric perovskites decreases more
rapidly with increasing Al content than that of the
nonstoichiometric perovskites. While Si(Al)–O2–
Si(Al) angle in the stoichiometric perovskites de-
creases with increasing Al content, that in the non-
stoichiometric perovskites shows no change. These
indicate that the tilting of the Si(Al)O6 octahedra is
promoted with Al substitution in both of the per-
ovskites and that the degree of tilting in the stoichi-
ometric perovskites is larger than that in the
nonstoichiometric perovskites at the same Al content.
In the eightfold coordination site, replacement of
Mg2+ for Al3+ may result in reduction of size of the site
due to the smaller ionic radius of Al3+ than that of
Mg2+. Generally, an average of interatomic distances
between a cation and coordinating oxygens is used to
estimate the size change of such a cation site as the
Si(Al)O6 octahedra. However, when the method is
applied to the eightfold coordination site of the per-
ovskites of this study, average Mg(Al)–O distances in
both the nonstoichiometric and stoichiometric per-
ovskites show no difference within uncertainties cal-
culated from the propagation of errors of eight
Mg(Al)–O distances (Table 4). This is because some
Mg(Al)–O distances decrease but the others increase
or keep almost constant with increasing Al content and
also because the Mg(Al)–O distances have values in a
wide range. Since it is expected that the distance be-
tween Mg(Al) and oxygen closest to Mg(Al) in the
eightfold coordination site may be most affected by
substitution of Mg by Al, here we pay attention espe-
cially to minimum Mg(Al)–O distance instead of the
average Mg(Al)–O distance. The relation between
minimum Mg(Al)–O distance and Al content is shown
in Fig. 6. The minimum Mg(Al)–O distance in the
stoichiometric perovskites decreases with increasing Al
content. That in the nonstoichiometric perovskites is
almost constant up to XAl of 0.05, and then decreases
with further Al content. These changes are similar to
those observed in the Si(Al)–O1–Si(Al) angle and the
Si(Al)–O1 distance for both the perovskites. The fact
suggests that the degree of tilting of Si(Al)O6 octahe-
dra might be connected with the change in average
cation size in the eightfold coordination sites. The al-
most linear decreasing relation in the stoichiometric
Fig. 2 Lattice parameters of Al-containing MgSiO3 perovskites.Solid squares, open squares, and solid triangles show the data ofMgSiO3 perovskite, stoichiometric Al–MgSiO3 perovskites, andnonstoichiometric Al–MgSiO3 perovskites, respectively. Solidlines and solid curves indicate a linear fitting of the stoichiometricperovskite data (labeled as ‘‘S’’) and a quadratic fitting of thenonstoichiometric perovskite data (labeled as ‘‘NS’’) by theleast-squares method, respectively. Dashed lines are the resultsby previous studies: Wn Weng et al. (1982), O-J O’Neill andJeanloz (1994), I Irifune et al. (1996), K-A Kubo and Akaogi(2000), Wt Walter et al. (2004). XAl is an aluminum number onthe basis of total cation of two, XAl = 2Al/(Mg + Si + Al)
Phys Chem Minerals (2007) 34:257–267 263
123
perovskites can be explained by decrease of the aver-
age cation size in the eightfold coordination site due to
the exchange of Mg2+ for Al3+ by the coupled substi-
tution (Mg2+ + Si4+ = 2Al3+). Similarly, in the nonsto-
ichiometric perovskites, the constant minimum
Mg(Al)–O distance in the XAl range of 0–0.05 might
imply that Mg2+ is hardly replaced by Al3+ because of
the oxygen vacancy substitution (2Si4+ = 2Al3+ + VO),
and that decrease in the relation at XAl larger than 0.05
may correspond to the coupled substitution similarly to
the stoichiometric perovskites.
Atomic position of the eightfold coordination site in
the stoichiometric perovskite with XAl of 0.10 ((x, y,
z) = (0.9727, 0.0462, 0.25)) slightly differs from that of
the pure MgSiO3 perovskite (0.9862, 0.0559, 0.25)
determined by Dobson and Jacobsen (2004). On the
other hand, the atomic position of the eightfold coor-
dination site in the nonstoichiometric perovskite with
XAl of 0.10 (0.9886, 0.0561, 0.25) is considerably close
to that of pure MgSiO3 perovskite. These comparisons
suggest that the decrease of average ionic size in the
eightfold coordination site by the coupled substitution
affects not only the degree of tilting of Si(Al)O6
octahedra but also the position of the eightfold coor-
dination site. A wider range of the Mg(Al)–O distances
of the stoichiometric perovskite with XAl of 0.10
(Table 4) indicates that the eightfold coordination sites
in the stoichiometric perovskites have more deformed
Table 3 Comparison of lattice parameter–composition relations of Al-containing MgSiO3 perovskites
a (A) b (A) c (A) Reference
0.00198XAl + 4.780a 0.0419XAl + 4.935a 0.115XAl + 6.907a a0.016(8)XAl + 4.779(1)a 0.043(7)XAl + 4.932(1)a 0.143(11)XAl + 6.900(2)a b0.019(7)XAl + 4.777(1)a 0.077(10)XAl + 4.925(2)a 0.142(13)XAl + 6.899(2)a c–0.040(3)XAl + 4.7784b 0.029(2)XAl + 4.9303b 0.155(4)XAl + 6.8990b d–0.001(2)XAl + 4.7784b 0.038(1)XAl + 4.9303b 0.143(2)XAl + 6.8990b e–0.014(2)XAl + 4.7784(2) 0.041(2)XAl + 4.9303(1) 0.137(3)XAl + 6.8990(2) f0.003(20)XAl + 4.7782(5)c 0.056(8)XAl + 4.9306(4)c 0.149(10)XAl + 6.8998(7)c g
XAl: Aluminum number on the basis of total cation of two, XAl = 2Al/(Mg + Si + Al)
a Weng et al. (1982), b O’Neill and Jeanloz (1994), c Irifune et al. (1996), d Kubo and Akaogi (2000), e Walter et al. (2004), f Thisstudy (Stoichiometric perovskites), and g Navrotsky et al. (2003)a Slope is a half of the original valueb Equation was obtained by combining with MgSiO3 perovskite data of this studyc Nonstoichiometric perovskite
Table 4 Interatomicdistances and bond angles ofMgSiO3 perovskite and Al-containing MgSiO3
perovskites
XAl: Aluminum cationnumber on the basis of totalcation of two defined by theequation XAl = 2Al/(Mg + Si + Al)a Values were calculatedusing lattice parameters ofthis study and atomiccoordinates of Dobson andJacobsen (2004)
MgSiO3 pva Nonstoichiometric pv Stoichiometric pv
XAl 0.00 0.05 0.10 0.05 0.10
Interatomic distance/ ASi(Al)–O octahedronSi(Al)–O1 · 2 1.800 1.800(1) 1.809(1) 1.808(1) 1.822(2)–O2(i) · 2 1.795 1.797(2) 1.794(3) 1.803(2) 1.807(4)–O2(ii) · 2 1.783 1.779(2) 1.782(3) 1.779(2) 1.785(4)Average 1.793 1.792 1.795 1.797 1.805
Mg(Al)–O polyhedronMg(Al)–O1 2.017 2.020(3) 1.991(5) 2.008(4) 2.060(7)–O2 · 2 2.055 2.055(2) 2.069(3) 2.048(3) 1.982(5)–O1 2.098 2.110(2) 2.083(4) 2.096(4) 2.086(6)–O2 · 2 2.282 2.273(2) 2.276(4) 2.283(3) 2.253(5)–O2 · 2 2.425 2.446(2) 2.433(3) 2.428(3) 2.496(5)Average 2.205 2.210 2.204 2.203 2.201
Bond angle/�O1–Si–O2(i) 91.5 92.1(1) 91.6(2) 91.2(2) 93.3(2)O1–Si–O2(ii) 91.3 89.0(1) 88.0(2) 88.2(1) 86.9(3)O2(i)–Si–O2(ii) 90.6 89.4(1) 90.6(1) 89.5(1) 89.2(1)Si–O1–Si 146.8 147.2(1) 145.4(2) 145.5(2) 143.2(3)Si–O2–Si 147.2 147.5(1) 147.5(2) 146.8(2) 145.8(2)
264 Phys Chem Minerals (2007) 34:257–267
123
shape than that of the nonstoichiometric perovskites.
This result can be used for interpretation of the dif-
ference in 27Al-NMR signals between stoichiometric
and nonstoichiometric perovskites, in which the non-
stoichiometric perovskite showed slightly lower CQ
value of 7.5 ± 0.5 MHz for the ‘‘A site’’ (Stebbins et al.
2003) than that of the stoichiometric perovskite of
10 MHz (Stebbins et al. 2001), where synthetic condi-
tions and a starting material to synthesize the nonsto-
ichiometric perovskite samples with XAl of 0.10 for the
XRD measurement in this study were completely the
same as those of nonstoichiometric perovskite samples
used in the 27Al-NMR measurement by Stebbins et al.
(2003).
The changes in the lattice parameters can be ex-
plained by considering the relation between lattice
parameters and degree of tilting of BX6 octahedra in a
GdFeO3-type ABX3 orthorhombic perovskite.
According to O’Keeffe et al. (1979), axis lengths of the
orthorhombic perovskite are calculated using tilting
angle /, which is a rotation angle of BX6 octahedron
on the [111] axis of a cubic perovskite, as follows:
a ¼ dffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
8 cos /;p
ð3Þ
b ¼ dffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
8 2þ cos2 /ð Þ=3q
; ð4Þ
c ¼ dffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
48= 1þ 2= cos2 /ð Þq
; ð5Þ
where d is an interatomic distance between cation B
and anion X. These equations mean that a larger /results in a smaller axis length when d is constant. Sinceffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
8 2þ cos2 /ð Þ=3p
andffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
48= 1þ 2=cos2 /ð Þp
parts in the
Eqs. 4 and 5 do not contribute so much to decrease in
lengths of b- and c-axes, respectively, the b- and c-axes
of the Al–MgSiO3 perovskites may increase due to the
increase of d, i.e., the Si(Al)–O distance with increas-
ing Al content. The shorter Si(Al)–O1 distance of
the nonstoichiometric perovskite than the stoichio-
metric perovskite can explain the shorter c-axis of the
Fig. 3 Crystal structure of perovskite-type MgSiO3 shown by theSi–O framework. Bars represent bonds between silicon andcoordinate oxygens
Fig. 4 Interatomic distances in Si(Al)O6 octahedra: a Si(Al)–O1distance, b Si(Al)–O2(i) distance, and c Si(Al)–O2(ii) distance.Solid squares, open squares, and solid triangles show the data ofpure MgSiO3 perovskite, stoichiometric Al–MgSiO3 perovskites,and nonstoichiometric Al–MgSiO3 perovskites, respectively. XAl
is an aluminum number on the basis of total cation of two,XAl = 2Al/(Mg + Si + Al)
Phys Chem Minerals (2007) 34:257–267 265
123
nonstoichiometric perovskite than that for the stoichio-
metric perovskite at XAl of 0.10. On the a-axis, the
effect of cos / in the Eq. 3 is more considerable thanffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
8 2þ cos2 /ð Þ=3p
andffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
48= 1þ 2=cos2 /ð Þp
: Therefore,
it depends on the competition between / and d
whether the a-axis length increases or decreases. It is
considered that the decrease of a-axes of both the
nonstoichiometric and stoichiometric perovskites may
be caused by more effect of / change than that of d.
Conclusions
In the stoichiometric perovskites, both the Si(Al)–O1
and Si(Al)–O2(i) distances in Si(Al)O6 octahedra in-
crease with increasing Al content. On the other hand,
in the nonstoichiometric perovskites, the constant
Si(Al)–O1, Si(Al)–O2(i), and Si(Al)–O2(ii) distances
up to XAl of 0.05 suggest that Si(Al)O6 octahedra ob-
served by XRD do not expand with the substitution of
Al for Si, even though the nonstoichiometric per-
ovskites may include more Al in the octahedral sites
than the stoichiometric perovskites at the same Al
content. This implies that the effect of ‘‘AlO6’’ octa-
hedra on average size of Si(Al)O6 octahedra in the
nonstoichiometric perovskites might be offset by oxy-
gen defects. All of the Si(Al)–O1, Si(Al)–O2(i), and
Si(Al)–O2(ii) distances, the Si(Al)–O1–Si(Al) and
Si(Al)–O2–Si(Al) angles, and the minimum Mg(Al)–O
distance in the nonstoichiometric perovskites indicate
no change up to XAl of 0.05. With further Al substi-
tution, the Si(Al)–O1 distance increases, and the
Si(Al)–O1–Si(Al) angle and minimum Mg(Al)–O dis-
tance decrease. These suggest that the oxygen vacancy
substitution is superior to the coupled substitution in
the XAl range of 0 to ~0.05 in the nonstoichiometric
perovskites, and that the coupled substitution may
occur at XAl larger than ~0.05. This substitution
mechanism expected from the structure refinement is
consistent with that considered from the compositions
of the nonstoichiometric perovskites as described
above. Thus, it is concluded that the maximum solu-
bility of Al in the MgSiO3 perovskite only by the
oxygen vacancy substitution is at most XAl of ~0.05,
and further Al is accommodated by the coupled sub-
stitution at 27 GPa. No change in the Si(Al)–O1,
Si(Al)–O2(i), and Si(Al)–O2(ii) distances in the non-
stoichiometric perovskites up to XAl of 0.05 suggests
the random distribution of oxygen defects, that is
consistent with the results of 27Al-NMR measurement
by Stebbins et al. (2006).
Acknowledgments We thank J.F. Stebbins for useful commentson interpretations of NMR data, E. Takahashi, T. Sugawara andT. Suzuki for helping compositional analyses by EPMA, A.Navrotsky for helpful discussion, D. Andrault and an anonymousreviewer for careful review. We are grateful to M. Matsui foreditorial handling and useful comments. This work was sup-ported in part by Grants-in-Aid for Scientific Research, (C)18540478 to H. Kojitani and (A) 15204049 to M. Akaogi, fromthe Japan Society for the Promotion of Science.
Fig. 5 Bond angles indicating degree of tilting of Si(Al)O6
octahedra: a Si(Al)–O1–Si(Al) and b Si(Al)–O2–Si(Al). Solidsquares, open squares, and solid triangles show the data of pureMgSiO3 perovskite, stoichiometric Al–MgSiO3 perovskites, andnonstoichiometric Al–MgSiO3 perovskites, respectively. XAl isan aluminum number on the basis of total cation of two
Fig. 6 Relationship between minimum Mg(Al)–O distance andAl content. A solid square, open squares, and solid triangles showthe data of pure MgSiO3 perovskite, stoichiometric Al–MgSiO3
perovskites, and nonstoichiometric Al–MgSiO3 perovskites,respectively. XAl is an aluminum number on the basis of totalcation of two
266 Phys Chem Minerals (2007) 34:257–267
123
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