Aluminum substitution mechanisms in perovskite-type MgSiO3: an investigation by Rietveld analysis

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: [email protected]

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


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


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


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)


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)


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)


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


123

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Documents

Aluminum substitution mechanisms in perovskite-type MgSiO3: an investigation by Rietveld analysis