Variation of electrical conductivity in enstatite with oxygen partial pressure: Comparison of observed and predicted behavior

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Physics of the Earth and Planetary Interiors, 17 (1978) P34—P40 © Elsevier Scientific Publishing Company, Amsterdam — Printed in The Netherlands

LETTER SECTION VARIATION OF ELECTRICAL CONDUCTIVITY IN ENSTATITE WITH OXYGEN PARTIAL PRESSURE: COMPARISON OF OBSERVED AND PREDICTED BEHAVIOR RL. STOCKER Department of Geology, Arizona State University, Tempe, AZ 85281 (U.S.A.) (ReceivedNovember 8, 1977; revised and accepted July 24, 1978)

Stocker, R.L., 1978. Variation of electrical conductivity in enstatite with oxygen partial pressure: comparison of observed and predicted behavior. Phys. Earth Planet. Inter., 17: P34—P40. Oxygen partial pressure influences the electrical conductivity of cnstatitc because it affects the point-defect concentrations in enstatite. The behavior of the defect concentrations with P 0 axe obtained for open and partially closed conditions. On the basis of the defect variations, models for the effect of oxygen pressure on the conductivity can be constructed. The first-order models, which assume one defect type transporting all the charge, predict log(P~2)vs. log(conductivity) slopes that are not in agreement with slopes derived from measurements on natural single crystals of enstatite. The disagreement could result from: (1) more defect species being present than the assumed chargeneutrality condition gives, or (2) the charge is transported by two or more defect types. The data suggesting the latter is the cause of the disagreement, and hence the experimentally derived activation energies must be treated carefully.

1. introduction A general and fundamental expression for the electrical conductivity of silicates is: 11e’ + F[h] Ph’ + F ~ [MM]P MM + F~Z~ [j] ~ a = FEe’] (1)

Electrical conductivity is denoted by a, Faraday’s constant by F, molar concentrations by square brackets, mobilities by p, and the valence of the ith ionic-defect species by Z~e’ represents conductionband electrons, h holes in the valence band,M~a transition metal having a different than normal valence, and i the ith ionic-defect species. The first three terms in eq. 1 give the electronic components of the electrical conductivity and the fourth term the ionic cornponents. The term containing [M~] describes the contribution arising from the hopping motion of electrons between ions of variable valence, the most notable of which are the transition metals. Each of the concentrations is potentially sensitive to P02 which implies that the electrical conductivity could be a rather complex function of P02.

With regard to conductivity the oxygen pressure is important for two reasons. As mentioned above defect concentrations and hence the magnitude of conductivity are potentially dependent on P0 making this thermodynamic-state important in geophysical processes. The change variable in electrical conductivity with F 02, measured under laboratory conditions, can be of diagnostic value in determining the mechanism operating at the atomic level. Duba et al. (1973, 1976) have measured the conductivity of natural enstatite single crystals. The purpose of this paper is to examine the implications of Duba et al.’s data for the mechanism(s) of conduction in enstatite. To do this the variation of the defect concentrations with P0 are derived for two physically distinct situations. In the first all the elements in enstatite have sufficient mobility to be freely exchangeable with other phases in the system; the number and chemistry of these phases is such as to define the compositional part of the thermodynamic state of enstatite. This is the open-system case. When only some of the elements are mobile then enstatite behaves as a partially closed system. The experiments were conducted on single crystals of enstatite surrounded by an

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ambient atmosphere having a well-defined P02. Assuming no differential volatility of the cations, one would treat enstatite in these circumstances as a partially closed system with oxygen the single mobile species. However, as will be shown, enstatite can be driven out of its phase field by changes in F0 the system switches to open conditions when this occurs, Secondly, some of the samples containedinclusions which may have led to an open system. The behavior of defects in enstatite with P0 2 can be found from purely formal arguments for both open and partially closed situations. The procedure has been discussed in detail (Stocker and Smyth, 1978; Stocker, 1978); the point-defect notation used here is also presented in those papers. However, to limit the possible charge-neutrality conditions, use has to be made of indirect information on the favorable point-defect species. Section 2 contains that discussion, Sections 3 and 4 models for the oxygen pressure variation, and Section 5 a comparison of data and models.

tion have necessarily small equilibrium constants. One is left with the intrinsic ionization reaction, the ionization of Fe on an Ml or M2 site, or the Mg or Fe Frenkel reactions, having the greatest equilibrium constant in stoichiometric enstatite. The reflectance study of Nitsan and Shankland (1976) yielded a band gap of approximately 8.5 eV for two Mg-rich orthopyroxenes (93 en and 96 en). A band gap of this magnitude rules out the intrinsic ionization reaction. On the other hand, in the enstatite structure octahedral sites, which are normally vacant and of about the right size for Mg or Fe ions, are present. Interstitial ions of these two elements pose no space problems, as do oxygen interstitials, and so these reactions are the likely candidates. The Fe ionization reaction is also a likely possibility since only a fraction of the full band-gap energy is r~cessaryfor the thermal removal of an electron from the Fe ion to the conduction band. A resolution of this matter will only be possible by further experimentation. 3. Effect of P0 under open-system conditions 2

2. The energetically favorable point defects in enstatite The nature of the energetically favorable point defects in enstatite must be inferred from crystallographic-bonding considerations plus analogies with other materials since little relevant experimental data exists at present. In detail, enstatite has a complex crystal structure (Papike and Cameron, 1976). In broad outline, the crystal structure may be viewed as a distorted close packing of oxygen ions with systematically occupied and vacant interstitial sites. Two types of larger sites, denoted Ml and M2, occur; cations in the Ml site are octahedrally coordinated with oxygen, and cations in the M2 site are either in six- or eight-fold coordination, depending on the size of the cation. No sites large enough to accomodate either an oxygen atom or oxygen ion are present. This lack of normally vacant interstitial sites with appropriate size means that oxygen interstitials are almost certainly unfavorable defects and4’~ion hence from their tetrahedral concentration is small. coordination Removal of acreates Si with oxygen a severe disruption of the Si—O framework in enstatite, and therefore Si vacancies

The effect of oxygen pressure on the defect concentrations in an open-system setting (all elements mobile) is obtained from the set of mass-action expressions corresponding to the defect reactions and the major defect species. Table I gives the P02 dependencies of the various point-defect species in enstatite for a variety of stoichiometric and non-stoichiometric chargeneutrality conditions. The three non-stoichiometric conditions all arise from a stoichiometric excess of silica in enstatite. Examination of Table I reveals the magnitudes of the P02 dependencies, ranging from unity for Si vacancies and interstitials, when the chargeneutrality condition is [Feb] = [e’], to zero for the ionic defects under several approximate chargeneutrality conditions. The smallest non-zero dependence is 1/6, and several defect species vary in this manner when vacant octahedral sites and Fe(III) on octahedral sites are present in the two largest concentrations. 4. Effect ofF 0 2 under partially closed conditions

should have a large enthalpy. With 0 interstitials and Si vacancies being unfavorable defect species, the silicon and oxygen Frenkel reactions and the Schottky reac-

4.1. Single-phase region The effect ofF0 2 on the defect concentrations,

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TABLE I Effect of oxygen partial pressure on defect concentrations: equllibrium with external phases Charge-

Mg

VM”

Si1”

V5i”

01”

Vo”

FeM’

Fe1” Fe1”

e’

—

—

—

—

—

—

+1/4

—

+1/2 —1

+1

+1/2 —1/2

—

—

—

—

—

—

—

+1/4

+1/4 —1/2 —1/2 — +1/4

—1/4 +1/4

—1/2

—1/4

+1/4

— —1/6

— — +1/6 ‘—1/3

— +1/3

— — +1/4 +1/6 —1/6 +1/6

— +1/4 —1/6 —

—1/4 +1/6 +1/4 —1/6

1’’

h’

neutrality condition

[VM”l= [Mg1’‘1 [FeM’]= [e’] [VM”] = 2[Si1”] [YM”] ==[V0”] 2[VM”] [FeM’]

—

when only oxygen is transferable between enstatite and the ambient atmosphere, can be obtained from the defect reactions for the oxygen addition and oxygen removal. The two choices for oxygen removal which do not create unfavorable defects are: ~ ~

+ V0” +

Mg~~( + FeM” +

+

2Si1”

2e’

(2)

2Sis~”+

+ 302 +

Mg1”

*

12e’

+ Fe1” +

(3)

The loss of oxygen creates oxygen vacancies and free electrons in the first reaction and cation interstitials plus free electrons in the second. No distinction is made between the Ml and M2 sites; together they are denoted by the subscript M. This grouping is permissible for the purpose of discussing the P0 2 variations although there are certainly enth’alpic differences. Three choices exist for the addition of oxygen to enstatite: 2FeMx

+

V0”

+

~02 0k”

00X

2FeM’~+ ~02

*

8FeM’~+ 202

* 400x +

+

+

2FeM’

(4)

2FeM’ 2VM”

(5) +

~

‘H,

+

8FeM’ (6)

Oxygen addition generates Fe(III) on octahedral sites in all cases and, depending on the reaction, consumes oxygen vacancies or leads to either oxygen interstitials or vacant M sites. Eqs. 2—6, in conjunction with the defects occurring in the largest concentrations, lead to the functional relationship between the defect concentrations and Po 2 (Stocker, 1978). In some circumstances not only must

—

the majority defects be specified, but also the defect pair present in the next higher concentrations. As shown in Table II, this arises when [VM“1 = [Mg 1”] or [FeM’] = [e’] dictates the charge-neutrality regime. Table II shows that the magnitude of the defect variations with P02 ranges from a maximum power of 3/2 to a minimum of zero. The smallest non-zero power is 1/14; oxygen vacancies and interstitials possess this power when the approximate charge-neutrality condition is [VM”] = [Mg1”], and the next most prominent defects are Fe(III) on octahedral sites and Si vacancies or free electrons and Si interstitials. 4.2. Multiphase region The activities of silica and magnetite in enstatite are not constant for a partially closed system, but rather vary with temperature and pressure and can vary with oxygen pressure. As a result enstatite can be driven to a phase boundary with the precipitation of other phases. First consider Fe-free enstatite. At the phase boundaries the phase having the next higher Si02 content (one of the Si02 polymorphs) is exsolved if the activity of silica in the enstatite is increasing, or the phase of next lower Si02 content (olivine) is exsolved if the activity of silica is decreasing with P02. The reactions and mass-action expressions for the four possibilities are: (1) Activity of silica increasing with increasing F02: Si5~”+ MgSiO3 +

2h”

+

~0~ ~ 2Si02

+ Mg1” + V”~ +

(7)

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~.

‘.Q ‘.0

~.

en en en en

—

‘.0’.0 — ,~

—

II ,~.

‘.0

~.

-.~

lilt

o

—

liii

I

ii

,+ -.4

00

00

C~1 (‘i

el

ei

~l

‘.0 ‘.0

—

— -4

— -4

.—

—

— -4

—

— -4

— -4

— -4

—

e~

el

r~ r-~

‘.0 ‘.0

— -4

~-

—iii —

—

~-4

— -4 ii— -4

el

‘~

~

el

—

i

—

++

—

~.

~.

el

—

,~ 00

00

—

— +

— — — -4liii — -4

-.-. -4

(_.l

~ ‘—4

el

I

—

I

‘.0 ‘.0 — —

~ .

—

-4

—.

el — Iii —

+++

el I

I

— en

I

—

en en en — ~en ~en

— en

-.~ —

ii

=

I

C-~ —

~— — en en en —~ en ++en

.~

++

‘.0

enenenm~

~.

III

liii

III

—

—

++,-,

‘+

—

— — en en en +++

~.~ ++ .~

e~ ~

~

— en — en -~ en

—

ill

.—

— —

ii

~

a

en en

—

liii

en

—

I++

en en

—‘

ii

+

Ii

I

‘0

a o

C.) =

, , H) — II..

‘.0’.o ,..,

-.enen -.--

~

— en

111111

enen — —

Ii

Iii

I

III

0 U

—

en en en en — I+++++~

H)

—

,

++

0, ‘.0’.0 — ..

a I

H)

—.. — en en I++

11111

o

— enen —

~.

— en -.en I++

1+en

el

——

•

‘.4

—S

1+—

‘+‘~1.

en

enen 555

—S

Ii

III

555

Ii

.~

a -

,~. —

I

0

a

‘‘~‘

Ii— H

II

,~‘~aa ‘_~400,~,

~.

~

~-r”~

—

‘—fl’’

~

v~

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[Mg1 ‘] [Vsi,,,, ] [h’ ~2

=

K1F0

(8)

1/2

(2) Activity of silica decreasing with decreasing F02: 2MgSiO3 ~ Mg2SiO~+ 02 + Si1” 4 =K [Si1””] [c’] 2Po2_1~~’2

+

4e’

(9)

its stability limit, silica and magnetite are exsolved; if enstatite is reduced, free Fe and silica precipitate. Writing the reactions, we have: (1) oxidation of enstatite: 4FeM’~+ (Mg,Fe)Si206

(10)

+

~g~X

+

2FeM’

+

02 ~ 2SiO2

+

+

Fe3O4

+

(16)

It

2Sio (3) Activity of silica increasing with decreasing F02: MgSiO3

Si02 2= K

*

[Mg1”] [e’]

+ ~ 0~+

Mg1”

+

2e’

(11) (12)

3F02_hh’2

(4) Activity of silica decreasing with increasing F02: +

MgSiO3

2h’ 2 [VM”][h’]

+ ~ 0~ *

Mg2SiO4

+ YM” +

(13)

+

K

[FeM‘]2 VM”

=

K5P0 a

(2) reduction of enstatite: (Mg,Fe)Si206 * 2Si02 2 =K [Mg1”] [e’] 6P0’

+

Fe

+

02

+

Mg1”

+

2e’ (18) (19)

The reactions above refer to enstatite with an Fe/Mg ratio of unity. The P0 dependence of the defects is a function of the Fe/Mg ratio, as can be shown by formulating the reduction reaction for Mg/Fe ratio of9: 10(Mg09Fe01)Si03

The major defects present in enstatite at the phase boundary determine whether the activity of silica is in2 creasing decreasing activity of reacsilica in enstatite,orderived fromwithP0 a possibleThe incorporation tion, is: .

[VM”] [V K

(17)

(14)

4P02’/2

0”]

2aFe3 04

(15)

The major defects govern the variation of VM” and v0” with P1-1 and hence the activity of silica. As an

*

1OSiO2

+ Fe +

502

+ 9Mg1” +

+ 1 8e’ (20) 5 (21) [e’]18 [Mg1” ]9 = K7P02 In this case, assuming conduction-band electrons and Mg interstitials are the major defects:

[e’]

=

2[Mg1”]

~xp0~5/27

while for the Fe/Mg ratio of unity:

,

‘—3

example, assume the major defects in the chargeneutrality regime adjacent to the phase boundary being FeM’ and VM”. Then [YM”] is independent of P02 and [V0”] ~ p0 —1/2 so the activity of silica is proportional toP0 2 1/22 that is, the activity of silica is increasing with decreasing P03. Therefore, category (3) above would describe the situation, and that mass-action cxFession should be used. Once in the two-phase region the Pn dependencies are exactly those for the open‘-3 system case if the major defects are the same in both situations, the reason being enstatite is now in equilibrium with an external phase or phases. So far only Fe-free enstatite has been examined. If enstatite contains Fe, several new features appear. At the limits of the single-phase region, two solid phases separate simultaneously. if enstatite is oxidized beyond

[e’] = 2[Mgi”] czP0il~ For this reaction the magnitude of the P0 dependencies of the dominant defects increase ~vithincreasing Mg/Fe ratio. In the limit of no Fe, the previous analysis shows: [e’] = 2 [Mg1”] ~ p0’1/6 Once the enstatite coexists with silica and either free Fe or magnetite, the variation of the point defects with P02 becomes that for an open equilibrated system.

5. Comparison with experimental results Duba et al. (1973, 1976) measured the high-

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temperature AC electrical conductivity of natural enstatite single crystals using a two terminal technique

because the slopes were reasonably constant over a range ofF02 broader than one would expect from this

with Pt electrodes. Three crystals contained inclusions while the fourth sample, of gem quality, was inclusion free. Each of the three inclusion-bearing crystals exhibited a minimum in conductivity as a function ofF02, and had alog a—log P02 slope of about —1/30 in the n-type region and a slope of + 1/30 in the p-type region. The gem-quality enstatite exhibited a slope of —1 / 12 in the n-type region over a more limited range of P0. In pure enstatite, one or possibly more of the following defects plays a major role in the conduction process: (1) Mg interstitials; (2) Mg vacancies; (3) Fe(III) on M1—M2 sites, this is the defect necessary in the electron hopping process; and (4) conduction-band electrons. These are the likely carriers either because of their expected high mobility, i.e. conduction-band electrons and electrons hopping between Fe atoms, and/or their relatively large concentration, i.e. Mg vacancies and interstitials. However, referring to Tables I and II, none of these defects possesses the observed P03 dependencies. Table II, valid for partially closed conditions, should apply to the gem-quality single crystal granting no differential loss of the cationic species. Table I, valid for open conditions, would apply to the crystals with inclusions provided the inclusions had the appropriate composition to fix activities and the mobility of the elements was sufficient for equilibration, Several reasons are possible for the lack of agreement between experiment and theory. The results in Table 1 are based on the assumption that two defect species are present in the charge-neutrality condition. Similarly the underlying assumption in Table II is that two or three defect types exist in concentrations much greater than any other point defect. These are reasonable assumptions in the middle of a charge-neutrality regime (Stocker and Smyth, 1978), but cannot be valid near the boundaries. For example, three defects would be present in roughly equal concentrations, the largest concentrations over a range of thermodynamic states spanning the boundary between charge-neutrality conditions for an open system. The P02 variation of the defects would not be that of Table I or Table II, but instead would be transitional between the variation in the two charge-neutrality regimes. It is unlikely that the experimental results can be interpreted in this manner

effect. The variation of the electrical conductivity with oxygen fugacity is only identical to the P0 variation of a given defect as long as that defect carries the great majority of the charge. If two or more defects each transport a significant quantity of change, the oxygen partial pressure becomes the weighted average of the P03 dependencies for the defects, the weighting being in accordance with their fractional contribution to the conductivity. When such is the case, no meaningful activation energy can be extracted from the data. Bender (1976) demonstrated a mixed conduction in olivine (Fo90). However, one can, as yet, only propose that a several species conduction occurs in enstatite. Both a slope of 11/30 I and —1/12 could arise from mixed conduction. A slope of 1/12 could also represent the transition zone from a regime where the concentration of the charge carrier varied more strongly than 1/12 to a regime where it varied less strongly. Again, for this situation, any derived activation energy would be difficult to interpret (Stocker, 1978). Duba et al.’s (1973, 1976) results cannot be explained in any direct way on the basis of impurities, i.e. elements other than Fe, Mg, Si or 0. Supposing that an acceptor ion and the complementary defect electron were the major defect pair, and one or both defects carried the current, then the conductivity would be P~independent. Exactly the same would be true if a donor and the conduction-band electron were the major defects. A combination of defects arising from impurities, and native defects could certainly be constructed that would have the same P0 dependence as that measured. In summary, the measured electrical conductivity vs. P02 relationships in enstatite do not permit a unique conduction model at present. Conduction involving two defects is indicated, but the two defects cannot be identified. References . . . Bender, N., 1976. Electrical conductivity of smgle crystals of Mg, 8Fe0 2SiO4. Erlangen Res. Abstr. Mater. Sd., I/TR 33. Duba, A., Boland, J.N. and Ringwood, A.E., 1973, The electrical conductivity of pyroxene. J. GeoL, 81: 727.

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Duba, A., Heard, H.C. and Schock, R.N., 1976. Electrical conductivity of orthopyroxene to 1400°Cand the resulting selenotherm. Univ. Calif. Radiat. Lab., No. 77655 (preprint). Nitsan, U. and Shankland, T.J., 1976. Optical properties and electronic structure of mantle sllicates. Geophys. J.R. Astron. Soc., 45: 49. Papike, J.J. and Cameron, M., 1976. Crystal chemistry of

silicate minerals of geophysical interest. Rev. Geophys. Space Phys., 14: 37. Stocker, R.L., 1978. Influence of oxygen pressure on defect concentrations in olivine with a fixed cationic ratio. Phys. Earth, Planet. Inter., 17: 118 (this volume). Stocker, R.L. and Smyth, D.M., 1978. Effect of enstatite activity and oxygen partial pressure on the point-defect chemistry of olivine. Phys. Earth Planet. Inter., 16: 145.