High temperature structural and thermoelastic behaviour of mantle ...

ORIGINAL PAPER

High temperature structural and thermoelastic behaviourof mantle orthopyroxene: an in situ neutron powderdiffraction study

G. Diego Gatta Æ Romano Rinaldi Æ K. S. Knight ÆG. Molin Æ G. Artioli

Received: 5 October 2006 / Accepted: 6 December 2006 / Published online: 26 January 2007� Springer-Verlag 2007

Abstract The temperature induced structural evolu-

tion and thermoelastic behaviour of a natural (Pbca)

orthopyroxene (Opx), with chemical formulaM2(Mg0.856Ca0.025Fe2+

0.119) M1(Mg0.957Fe2+0.011Fe3+

0.016

Cr0.011Al0.005)Al0.032Si1.968O6, from a suite of high

pressure ultramafic nodules of mantle origin, have

been investigated by in-situ neutron powder diffraction

at several temperatures starting from 1,200�C down

to 150�C. Unit-cell parameter variations as a function

of T show no phase transition within this tempera-

ture range. The volume thermal expansion coefficient,

a = V –1(¶V/¶T) P0, varies linearly with T. The axial

thermal expansion coefficients, aj = lj–1(¶lj/¶T)P0, in-

crease non-linearly with T. The principal Lagrangian

unit-strain coefficients (e//a, e//b, e//c), increase

continuously with T. However, the orientation of the

unit-strain ellipsoid appears to change with T. With

decreasing T, the values of the unit-strain coefficients

along the b and c axes tend to converge. The orienta-

tion at DT = 1,080�C is maintained down to the lowest

temperature (150�C). The two non-equivalent tetra-

hedral chains, TAnOA3n and TBnOB3n, are kinked

differently. At room-T, the TBnOB3n chain is more

strongly kinked by about 23� than the TAnOA3n chain.

With increasing T, the difference decreases by 3� for

the TBnOB3n chain. The intersite cation exchange

reaction between M1 and M2 (Mg2+ and Fe2+) shows a

slight residual order at 1,200�C followed by reordering

with decreasing temperature although seemingly not

with a definite progressive trend. At the lowest tem-

perature reached (150�C), reordering has occurred

with the same value of partitioning coefficient KD as

that before heating. The absence of the expected phase

transition is most likely due to the presence of minor

amounts of Fe3+, Al, Ca and Cr which must play a

crucial role on the thermoelastic behaviour and phase

stability fields in natural Opx, with consequent impor-

tant petrologic and geological implications.

Keywords Orthopyroxene � High temperature �Neutron powder diffraction � Structural refinement �Thermoelastic behaviour � Cation-ordering

Introduction

Orthopyroxene (Opx) (Mg,Fe)2Si2O6, one of the most

common rock-forming minerals of the lithosphere and

a fundamental constituent of the Earth’s upper mantle,

G. D. Gatta (&) � G. ArtioliDipartimento di Scienze della Terra,Universita degli Studi di Milano,Via Botticelli, 23, 20133 Milano, Italye-mail: [email protected]

R. Rinaldi (&)Dipartimento di Scienze della Terra,Universita’ degli Studi di Perugia,06100 Perugia, Italye-mail: [email protected]

K. S. KnightISIS, Rutherford Appleton Laboratory,Chilton, Didcot, Oxon, UK

K. S. KnightDepartment of Mineralogy,The Natural History Museum,London, UK

G. Molin � G. ArtioliDipartimento di Mineralogia e Petrologia,Universita degli Studi di Padova, Padova, Italy

123

Phys Chem Minerals (2007) 34:185–200

DOI 10.1007/s00269-006-0138-2

has Pbca symmetry and its structure consists of alter-

nating tetrahedral and octahedral layers. The tetra-

hedral layer has two non-equivalent tetrahedra TA and

TB, TA being smaller and more distorted than TB,

parallel to c. The octahedral layer consists of zig-zag

chains of regular M1 octahedra also parallel to c,

joined by larger and distorted M2 octahedra (Fig. 1).

Si–Al substitution occurs only in TB (Tazzoli and

Domeneghetti 1987; Molin and Stimpfl 1994). Mg2+and

Fe2+ occupy the M1 and M2 sites. The M1 site is

smaller and nearly regular, whereas the M2 site is

larger and more distorted. The cation ordering is very

strong, with Mg preferring the M1 site and Fe the M2

site (Ghose 1965). A crystal chemical model for Pbca

Opx was proposed by Domeneghetti et al. (1995a)

based on the structure refinements of more than 200

natural Opxs. Because of its importance in the deter-

mination of cooling rates of host rocks and the excess

thermodynamic properties of the Opx solid solution,

the thermoelastic behaviour and the intracrystalline

Fe–Mg partitioning in Opxs have been extensively

studied (Ghose and Hafner 1967; Smith 1969; Smyth

1969, 1971, 1973; Pannhorst 1979; Virgo and Hafner

1969; Saxena and Ghose 1971; Besancon 1981; Chatil-

lon-Colinet et al. 1983; Anovitz et al. 1988; Molin 1989;

Saxena et al. 1989; Molin et al. 1991; Chopelas and

Boehler 1992; Shimobayashi and Kitamura 1993;

Sykes-Nord and Molin 1993; Yang and Ghose 1994a,

1995a; Zhao et al. 1995; Hugh-Jones 1997; Hugh-Jones

et al. 1997; Stimpfl et al. 1999; Camara et al. 2000;

Chopelas 2000; Jackson et al. 2001; Angel and Jackson

2002; Tribaudino and Nestola 2002; Nestola and Tri-

baudino 2003; Zema et al. 2003; Jackson et al. 2004;

Nestola et al. 2006). The exchange reaction:

Mg2+(M1)+Fe2+(M2), Mg2+(M2)+Fe2+(M1) depends

on temperature and chemical composition (Mg/Fe

ratio and AlVI content; Ganguly and Ghose 1979;

Domeneghetti et al. 1985; Tazzoli and Domeneghetti

1987; Molin 1989).

The accurate determination of the equilibrium

constant, KD and the kinetic constants of the intra-

crystalline Mg2+–Fe2+ exchange reaction between the

two inequivalent M1 and M2 sites as a function of

temperature are essential for thermodynamic calcula-

tions and the evaluation of the cooling history of the

host rocks (Ganguly 1982). Disequilibrium studies can

be used to obtain activation energies and reaction rates

of both ordering and disordering. Many heating

experiments followed by quenching carried out in the

past using X-ray diffraction techniques and Mossbauer

resonance to establish the structural changes induced

at high temperature, yielded wrong results due to the

speed of the reaction at temperatures above 1,000�C.

At high temperature, Opx has been reported to

transform reconstructively to different phases depend-

ing on the chemical composition. Enstatite, Mg2Si2O6,

transforms to protoenstatite with the space group Pbcn

at about 1,030�C (e.g., Smyth 1971, 1974; Murakami

et al. 1982), whereas ferrosilite, Fe2Si2O6, transforms

reversibly to clinoferrosilite with the space group C2/c

at the same temperature (Sueno and Kimata 1981;

Sueno and Prewitt 1983; Sueno et al. 1984, 1985).

Shimobayashi and Kitamura (1993) reported a phase

transition of orthoenstatite to high-clinoenstatite by in-

situ TEM study at high temperature. Intermediate

Opxs with Fe/(Fe + Mg) > 13% also show transfor-

mations to C2/c clinopyroxenes (Smyth 1969; Sueno

et al. 1985), the transition being irreversible and non-

topotactic, with transition temperatures decreasing

from approximately 1,230–980�C with increasing Fe

content. Upon cooling, the C2/c phase (‘‘high clino-

pyroxene’’) undergoes a reversible and displacive

phase transition to P21/c clinopyroxene (‘‘low clino-

pyroxene’’) (Smyth 1969; Smyth and Burnham 1972;

Sueno and Kimata 1981; Sueno and Prewitt 1983;

Sueno et al. 1985). Protoenstatite transforms to either

P21/c clinopyroxene or a mixture of P21/c clinopyrox-

ene and Opx, depending on kinematic factors (Smyth

1974; Lee and Heuer 1987; Schrader et al. 1990; Boysen

et al. 1991).

At temperatures above 1,100�C, Opx becomes

unstable and transforms into a protopyroxene with the

Pbcn structure (Smyth and Ito 1977). This phase is

unquenchable with a field of stability described by

Reid et al. (1974), who also report the formation of a

clinobronzite from the rapid cooling of a protobronzite

corresponding to a pyroxene composition similar to

that studied in the present work. The in-situ monitor-

ing of this phase transition is necessary to establish

crystallographic and thermodynamic parameters

Fig. 1 Crystal structure of orthopyroxene viewed down [001].The orientation of the Lagrangian unit-strain ellipsoid at DT =1,180�C (with e//a :e//b = 1:1.41) is shown

186 Phys Chem Minerals (2007) 34:185–200

123

relevant to the cooling history of the host rocks. Yang

and Ghose (1995a) carried out in-situ structure and

site occupancy refinements of a synthetic Opx,

(Mg0.75Fe0.25)2Si2O6, by single-crystal X-ray diffraction

at 23, 727, 827, 927, and 1,027�C (with reversals)

whereby they observed an anomalous intracrystalline

Fe–Mg equilibrium distribution above 927�C which

they ascribed to the existence of a ‘‘transitional state’’

before the HT phase transition to the protoenstatite

structure. In contrast, no transitional state was ob-

served for Mg2Si2O6 before the T-induced phase

transition to protoenstatite at 1,087�C (Yang and

Ghose 1995b). Single-crystal Brillouin scattering mea-

surements on a natural orthoenstatite [with the com-

position (Mg0.994Fe0.002Al0.004)2(Si0.996Al0.004)2O6] to

T = 1,350�C and room pressure (Jackson et al. 2004),

showed a significant softening of the elastic moduli

(C33 and C55) above 900�C leading to a rapid phase

transition with some hysteresis in the temperature

range, 1,090(10) < Ttr < 1,175(10)�C. No evidence for

any other transitions (i.e., to the protoenstatite struc-

ture) was observed at least up to T = 1,350�C. The

authors suggested that the displacive phase transition

would lead to an unreported pyroxene structure with

Cmca symmetry, at variance with the suggestion of a

different Pbca structure by Miyake et al. (2004) from

molecular dynamic simulations. Clearly, the crystal

structure of such a polymorph is still unknown, pending

confirmation of a very recent experimental report by

Ohi et al. (2006).

The transition temperature of orthoenstatite to a

high-temperature phase shows a broad range: from

~950�C (Smyth 1971) to ~1,230�C (Shimobayashi and

Kitamura 1993). It appears that the conflicting results

on the stability of the enstatite polymorphs can be

explained in terms of: small differences in chemical

composition of the samples, grain size, thermal history

or microstructures (Jackson et al. 2004 and references

therein).

We report an in-situ structural study by neutron

powder diffraction of a natural Opx from a suite

of high pressure ultramafic nodules from Victoria,

Australia (Molin and Stimpfl 1994, sample LE8) with

the origin representative of an Earth’s upper mantle

environment and with the chemical composition:M2(Mg0.856Ca0.025Fe2+

0.119)M1(Mg0.957Fe2+0.011Fe3+

0.016

Cr0.011Al0.005)Al0.032Si1.968O6.

The use of a natural sample was felt mandatory in

order to correlate more closely with the actual petro-

logical and geological problems linked with this kind

of investigation. Neutron Time-of-Flight (ToF) tech-

niques, profiting from the low attenuation for neutrons

of most materials (high penetration), allow the simul-

taneous collection of diffraction data from a wide

range of reciprocal space under non-ambient condi-

tions. Furthermore, the coverage of a wide range of

scattering vectors, resulting from the very short neu-

tron scattering lengths [of the order of 10–15 m (1 fm)

as compared with 10–10 m (1 A) for X-rays], leads to

insignificant variations of scattering amplitude with

scattering vector Q (i.e., Bragg angle); hence, neutron

diffraction enables the study of fine structural details

and allows an easier separation of the information on

thermal motion from that of site occupancy in structure

refinements (Dove 2002; Rinaldi 2002; Rinaldi et al.

2002).

The present work is aimed at providing a novel

approach on the question raised by Kroll et al. (1997),

regarding the need for new, accurate and consistent

site occupancies for Opx solid solutions and a full

description of the crystal structure for any high-T

polymorph of enstatite, in particular at T > 900�C

where conflicting behaviours have previously been

found. The role played by the minor amounts of Al,

Ca, Fe3+ and Cr on the thermoelastic behaviour and

phase stability fields of this mineral have also been

considered.

Experimental

The chemical composition and crystal chemistry of the

natural Opx used for the high temperature experiment

is detailed in Molin and Stimpfl (1994; sample LE8). As

reported by the same authors, the provenance from the

same xenolith ensures a high degree of chemical

homogeneity of the Opx crystals. Much care was taken

in separating the Opx from the coexisting phases

(olivine, clinopyroxene, spinel) by means of magnetic,

heavy liquid, and optical methods; only some olivine

remained at the level of a detectable phase in the

powder spectra and was estimated by a quantitative

Rietveld procedure to be less than 10% of the dif-

fracting sample. Neutron powder diffraction data were

collected at the Polaris ToF beam line of the ISIS

pulsed spallation neutron source of the Rutherford

Appleton Laboratory (UK). After collecting a pre-

liminary data set at RT, 12 data sets were collected at

different temperatures starting with the highest tem-

perature of 1,200�C. Each data collection was started

after a time interval well in excess of that needed for

the small crystals of the powdered sample to reach

equilibrium at each temperature according to previous

kinetic experiments based on quenching (Molin et al.

1991; Sykes-Nord and Molin 1993). Each data set was

collected for a total of 500 lA corresponding to an

Phys Chem Minerals (2007) 34:185–200 187

123

average data collection time of approximately 2.75 h

(ISIS was operating at around 180 lA with a Ta tar-

get). The data were collected at the following tem-

peratures (equilibrating times in brackets): RT (20¢)1,200�C (12¢) 1,175�C (12¢) 1,150�C (15¢) 1,125�C (15¢)1,100�C (15¢) 1,075�C (30¢) 1,050�C (45¢) 1,025�C (45¢)1,000�C (180¢) 975�C (180¢) 150�C. More time, of the

order of 15–30¢, was allowed in between runs for tem-

perature ramping (up for the first HT value, down for

the following) and temperature stabilization. Based on

previous reports, the highest temperature (1,200�C) was

selected to be well above possible reversible phase

transformation of the Opx used in the experiments.

A ~4 g coarse powder sample was vacuum sealed in

a silica glass vial together with a buffer (~1 g of iron/

wustite powder) to prevent oxidation, separated from

the sample by some silica glass wool. The chance of

oxidation was also minimized by the good operating

vacuum reached in the Nb furnace (10–5 to 7 · 10–7

mbar). Another phase appeared at high temperature,

supposedly from a partial crystallisation of the glass

vial to high-cristobalite (cubic), which remained at the

level of 1.5% wt until the high to low phase transition

was reached (at approximately 250�C) bringing the

amount of this phase up to 10%, consistent with the

thickness of the silica vial. The vial was suspended

within the furnace by means of a thin Ta wire mesh.

Temperature stability was estimated to be better than

±5�C during each run. The data collected covered the

range between 2,000 and 18,800 ls from detector bank

1 (at 2h = 90�), between 2,000 and 19,600 ls from

detector bank 2 (at 2h = 145�) and between 2,000 and

16,000 ls from detector bank 3 (at 2h = 35�) (Fig. 2) of

the POLARIS ToF diffractometer. Further details

concerning the experiments at room and high tem-

perature are reported in Table 1.

Structure refinements

Crystal structure refinements of Opx (+olivine + cris-

tobalite) at different temperatures were carried out

using the GSAS Rietveld refinement package (Larson

and Von Dreele 2001) starting with the structural

model of Molin and Stimpfl (1994). The neutron scat-

tering lengths were taken from the GSAS library. Scale

factor, background (modelled with a Chebyschev

polynomial), cell dimensions (Table 2), and peak-

profile [exponential pseudo-Voigt convolution, profile

function n. 3 in GSAS, Von Dreele 1990 (unpub-

lished)] were refined first. The atomic parameters

(position, occupancy and isotropic thermal displace-

ment) were refined next. Three different strategies of

structure refinement were tested to evaluate the

amount of possible bias from the correlation between

occupancy and thermal parameters. Due to the dif-

ferent neutron cross-sections of iron and magnesium

(11.24 · 10–24 cm2 for Fe; 3.631 · 10–24 cm2 for Mg),

their occupancy factors in the octahedral M1 and M2

sites of Opx were determined with good reliability. All

refinements converged to Rwp values between 3 and

4% (Table 1). The following three different strategies

of structure refinement were used:

Fig. 2 Experimental (crosses) and calculated (solid line) TOFneutron diffraction patterns from the three detactor banks forOpx (+olivine + cristobalite) at 1,200�C. Calculated peak posi-tions and difference plots are shown at the bottom of eachpattern


123

(i) refinement of Fe(M1) and Fe(M2) [with Fe(M1)

defined as (Fe2+ + Fe3+) in the M1 site] simulta-

neously with Uiso(M1) = Uiso(M2). This takes

care of the correlations at the expense of realistic

thermal parameters;

(ii) refinement of Fe(M1), Fe(M2), Uiso(M1), Uiso

(M2) in steps according to the following sequence:

(1) refinement of Fe(M1) and Fe(M2) with Uiso

(M1) = Uiso(M2),

(2) Fe(M1), Fe(M2) fixed at (1), Uiso(M1), Uiso

(M2) refined,

(3) Uiso(M1), Uiso(M2) fixed at (2), Fe(M1),

Fe(M2) refined and

(iii) refinement of Fe(M1), Fe(M2), Uiso(M1), Uiso

(M2) simultaneously varied. This naturally has the

largest correlation bias.

All refinements included: Cr(M1) = 0.01, Ca(M2) =

0.02, Fe(M1) + Fe(M2) = 0.15, Mg(M1) + Fe(M1) +

Cr(M1) = 1, Mg(M2) + Fe(M2) + Ca(M2) = 1.

The highest reliability was obtained in refinements

using strategy (ii) and the results are reported in

Table 3.

All structure refinements gave reasonable results in

terms of stability and precision, as shown in Tables 1,

2, 3 and 4. No stereochemical constraints were used for

the bond distances and no preferred orientation cor-

rection was applied. Convergence was rapidly achieved

after a first few cycles of refinement. In the last cycles,

the shifts in all parameters were less than their stan-

dard deviations. Refinement strategy No. (iii) gave

erratic occupancy parameters with very large error

bars. Such strategy, normally adopted in X-ray refine-

ments reported in the literature, should therefore be

considered with caution.

Refined atomic positions and thermal displacement

parameters are reported in Table 3 and bond distances

in Table 4. The Rietveld full-profile fits of Opx

(+ olivine + cristobalite) at 1,200�C are shown in Fig. 2

for each detector bank. For the olivine a pure Fo com-

position was found to provide the best fit as could be

expected from the low Fe content of this minor phase.

Results

Thermoelastic behaviour

The variation of the lattice parameters of Opx as

a function of T are shown in Fig. 3. Each trend is

Table 1 Experimental andinstrumental parameterspertaining to the datacollections and the Rietveldrefinements

Instrumental diffractometer POLARIS (neutron TOF powder diffract)Detector bank 1 ZnS scintillator—144 elements, 2h = 90�Detector bank 2 3He gas tubes—38 tubes, 2h = 145�Detector bank 3 3He gas tubes—80 tubes, 2h = 35TOF range (ms)/flight path (m):Bank 1 2.0–18.8/12.6030Bank 2 2.0–19.6/12.7794Bank 3 2.0–16.0/14.1402

Temperatures (�C)/equilibratingtimes (min)

20/20, 1,200/12, 1,175/12, 1,150/15, 1,125/15, 1,100/15,1,075/30, 1,050/45,

1,025/45, 1,000/180, 975/180, 150RefinementSpace group PbcaZ 8Unit cell refinement Whole patternObservations 9,200Refined parameters: 75 totalConstraints XCr(M1) = 0.01, XCa(M2) = 0.02,

XFe(M1) + XFe (M2) = 0.15,XMg(M1) +XFe (M1)+XCr(M1) = 1,XMg(M2) + XFe(M2)+XCa(M1) = 1,Uiso(SiA) = Uiso(SiB),Uiso(O1A) = Uiso(O1B) = Uiso(O2A) = Uiso(O2B)

= Uiso(O3A) = Uiso(O3B)Agreement factors wRp (20�C) = 0.0448; wRp (1,200�C) = 0.0290;

wRp (1,175�C) = 0.0294; wRp (1,150�C) = 0.0292;wRp (1,125�C) = 0.0288; wRp (1,100�C) = 0.0282;wRp (1,075�C) = 0.0297; wRp (1,050�C) = 0.0300;wRp (1,025�C) = 0.0291; wRp (1,000�C) = 0.0316;wRp (975�C) = 0.0318; wRp (150�C) = 0.0437;


123

continuous and non-linear showing no anomaly within

the T-range investigated. The evolution of the volume

thermal expansion coefficient, a = V–1 (¶V/¶T)P0, with

T is linear (Fig. 4). A weighted linear regression trough

the data points yields:

aT ¼ a0þ a1T ¼ 1:53ð1Þ� 10�5þ 2:10ð2Þ� 10�8 T ð�CÞ:

For the temperature range between 975 and 1,200�C,

the aT value increases from 3.57(8) to 4.05(11) ·10–5�C–1, respectively. These values agree with previ-

ously determined thermal expansion coefficients for

Pbca Opxs, although with different compositions, as

reported by Yang and Ghose (1994b, 1995a, b) and

reviewed by Yang and Prewitt (2000). The volumes at

temperatures above RT can be calculated from the

thermodynamic equation: VT = V0 exp�aT dT. For a

given T, or a small T-range of interest, aT can be

considered independent of the temperature and a VT

value can be determined as VT = V 0 exp[aT(T–T0)].

As observed for the unit-cell volume, the axial thermal

expansion coefficients, aj = lj–1(¶lj/¶T)P0, also increase

non-linearly with T. The best fit through the data was

found using the weighted quadratic regression equa-

tion: aTj = a0j + a1jT + a2jT2.

The refined values of the a0j, a1jand a2j for the a-, b-

and c-axis are reported in Table 2. At T = 1,000�C we

can calculate aT(a) = 0.93(6) · 10–5, aT(b) = 1.39(10) ·10–5and aT(c) = 1.28(14) · 10–5�C–1, with aT(a): aT

(b):aT(c) = 1:1.49:1.38, in good agreement with Smyth

(1973), Yang and Ghose (1995a) and Yang and Prewitt

(2000). Alternatively, the VTand lTj values can be easily

calculated on the basis of the simple weighted quadratic

regressions through the data point (VT = VT0[1 + a1

(T – T0) + a2(T – T0) 2], lT = lT0[1 + a1(T – T0) + a2(T –

T0)2]) reported in Fig. 3. However, on the basis of the

previous results reported by Yang and Ghose (1995a, b)

and Camara and Nestola (2006), who showed that the

lattice parameters of ortho-enstatites follow a linear

trend with T up to 900�C and then deviate from the

linearity at T > 900�C, the equations reported above

should be used only at 950 < T < 1,200�C.

The magnitudes of the principal Lagrangian unit-

strain coefficients (e//a, e//b, e//c), between room

Table 2 Lattice parameters, axial and volume thermal expansion coefficients and Lagrangian unit-strain coefficients in Opx at dif-ferent temperatures

T (�C) a (A) b (A) c (A) V (A3)

20 18.2429(5) 8.8171(2) 5.1894(1) 834.71(3)1,200 18.4588(5) 8.9638(2) 5.2848(1) 874.43(3)1,175 18.4517(5) 8.9612(2) 5.2797(1) 872.99(3)1,150 18.4450(5) 8.9589(2) 5.2749(1) 871.66(3)1,125 18.4378(5) 8.9555(2) 5.2711(1) 870.37(3)1,100 18.4314(5) 8.9520(2) 5.2674(1) 869.11(3)1,075 18.4244(5) 8.9481(2) 5.2639(1) 867.83(3)1,050 18.4197(5) 8.9449(2) 5.2609(1) 866.79(3)1,025 18.4125(5) 8.9408(2) 5.2577(1) 865.53(3)1,000 18.4047(5) 8.9366(2) 5.2543(1) 864.21(3)975 18.3995(5) 8.9329(2) 5.2519(1) 863.21(3)150 18.2513(5) 8.8274(2) 5.1929(1) 836.63(2)a0 (�C–1) 2.50(5) · 10–6 8.0(1) · 10–6 4.7(2) · 10–6 1.53(1) · 10–5

a1 (�C–2)a 8. 5(2) · 10–9 9.6(5) · 10–9 4.0(7) · 10–9 2.10(2) · 10–8

a2 (�C–3)a –1.8(2) · 10–12 –3.6(4) · 10–12 4.2(6) · 10–12 –

T–T0 (�C) e//a (�C–1) · 10–5 e//b (�C–1) · 10–5 e//c (�C–1) · 10–5 (e//a):(e//b):(e//c)

1,180 1.003b 1.410b 1.558b 1:1.41:1.551,155 0.991 1.415 1.507 1:1.43:1.521,130 0.980 1.423 1.458 1:1.45:1.491,105 0.966 1.420 1.425 1:1.47:1.481,080 0.957 1.417 1.392 1:1.48:1.451,055 0.943 1.408 1.361 1:1.49:1.441,030 0.941 1.407 1.338 1:1.50:1.421,005 0.925 1.396 1.310 1:1.54:1.42980 0.905 1.383 1.276 1:1.53:1.41955 0.899 1.375 1.261 1:1.53:1.40130 0.354 0.899 0.519 1:2.54:1.47

a Axial and volume thermal expansion coefficients according to: aTj = a0j + a1jT + a2jT2 (see text)

b The e.s.ds are less than 0.004


123

Table 3 Structural data for Opx at different temperatures

x y z Site occupancy KD Uiso · 100 (A2)

T = 20�CM1 0.3780(2) 0.6514(4) 0.8714(7) XFe = 0.023(6), XMg = 0.967(6) 0.159(42) 0.695(46)M2 0.3754(2) 0.4879(3) 0.3508(6) XFe = 0.127(6), XMg = 0.853(6) 1.089(54)Si(A) 0.2700(2) 0.3468(4) 0.0527(6) 0.153(11)Si(B) 0.4724(2) 0.3370(5) 0.7975(6) 0.153(11)O1(A) 0.1840(1) 0.3305(4) 0.0362(5) 0.218(12)O1(B) 0.5618(1) 0.3462(3) 0.7963(5) 0.218(12)O2(A) 0.3092(1) 0.5042(2) 0.0396(5) 0.218(12)O2(B) 0.4318(1) 0.4895(3) 0.6888(5) 0.218(12)O3(A) 0.3036(1) 0.2281(2) –0.1686(5) 0.218(12)O3(B) 0.4478(1) 0.1967(2) 0.6015(5) 0.218(12)

T = 1,200�CM1 0.3814(2) 0.6504(5) 0.8953(11) XFe = 0.071(6), XMg = 0.919(6) 0.881(100) 4.519(85)M2 0.3723(2) 0.4848(4) 0.3715(10) XFe = 0.079(6), XMg = 0.901(6) 5.034(112)Si(A) 0.2710(2) 0.3464(6) 0.0655(8) 1.735(26)Si(B) 0.4757(3) 0.3423(8) 0.7714(7) 1.735(26)O1(A) 0.1854(2) 0.3383(5) 0.0582(7) 1.959(29)O1(B) 0.5632(2) 0.3427(5) 0.7823(6) 1.959(29)O2(A) 0.3113(2) 0.5029(4) 0.0474(7) 1.959(29)O2(B) 0.4324(2) 0.4964(5) 0.7068(7) 1.959(29)O3(A) 0.3027(2) 0.2368(3) –0.1691(8) 1.959(29)O3(B) 0.4503(2) 0.2093(3) 0.5739(8) 1.959(29)




T = 1,100�CM1 0.3809(2) 0.6518(5) 0.8889(10) XFe = 0.065(6), XMg = 0.925(6) 0.739(86) 4.020(82)M2 0.3736(2) 0.4855(4) 0.3648(9) XFe = 0.085(6), XMg = 0.895(6) 4.412(104)


123

Table 3 continued


Si(A) 0.2712(2) 0.3475(5) 0.0612(8) 1.488(24)Si(B) 0.4751(3) 0.3392(7) 0.7769(7) 1.488(24)O1(A) 0.1853(2) 0.3386(5) 0.0516(6) 1.687(26)O1(B) 0.5627(2) 0.3429(5) 0.7863(5) 1.687(26)O2(A) 0.3112(2) 0.5045(4) 0.0467(7) 1.687(26)O2(B) 0.4321(2) 0.4934(5) 0.7026(6) 1.687(26)O3(A) 0.3026(2) 0.2348(3) –0.1702(7) 1.687(26)O3(B) 0.4499(2) 0.2061(3) 0.5792(7) 1.687(26)




T = 1,000�CM1 0.3801(2) 0.6525(5) 0.8848(9) XFe = 0.062(6), X Mg = 0.928(6) 0.677(80) 3.640(81)M2 0.3748(2) 0.4852(5) 0.3611(9) XFe = 0.088(6), XMg = 0.892(6) 3.988(104)Si(A) 0.2711(2) 0.3481(5) 0.0582(8) 1.347(23)Si(B) 0.4747(3) 0.3375(7) 0.7783(7) 1.347(23)O1(A) 0.1852(2) 0.3385(5) 0.0474(6) 1.531(26)O1(B) 0.5624(2) 0.3426(5) 0.7875(6) 1.531(26)O2(A) 0.3108(2) 0.5052(3) 0.0462(7) 1.531(26)O2(B) 0.4322(2) 0.4911(5) 0.7018(7) 1.531(26)O3(A) 0.3027(2) 0.2335(3) –0.1701(7) 1.531(26)O3(B) 0.4496(2) 0.2037(3) 0.5820(7) 1.531(26)

T = 975�CM1 0.3803(2) 0.6520(5) 0.8821(9) XFe = 0.063(6), XMg = 0.927(6) 0.697(82) 3.589(79)M2 0.3743(3) 0.4852(5) 0.3617(10) XFe = 0.087(6), XMg = 0.893(6) 3.947(102)Si(A) 0.2707(2) 0.3472(5) 0.0590(8) 1.273(22)Si(B) 0.4744(2) 0.3376(7) 0.7791(7) 1.273(22)O1(A) 0.1849(2) 0.3408(5) 0.0471(6) 1.450(25)


123

temperature and each measured T, were calculated

with the software STRAIN (Ohashi 1982) (Table 2).

The evolution of the principal unit-strain coefficients

with temperature is shown in Fig. 5 and the magnitude

of the strain coefficients at different (T–T0) values is

reported in Table 2. As shown in Fig. 5, each trend

appears to be continuous and the magnitude of all

three unit-strain coefficients increases with T. How-

ever, the orientation of the unit-strain ellipsoid appears

to change at different T regimes. At DT = 1,180�C, the

unit-strain ellipsoid is oriented with the major axis

parallel to c, being (e//a):(e//b):(e//c) = 1:1.41:1.55

(Fig. 1). With decreasing T, we observe a convergence

between the value of the unit-strain coefficients along

the b and c-axis (Table 2), being (e//a):(e//b):(e//c) =

1:1.47:1.48 at DT = 1,105�C. At DT = 1,080�C the

strain ellipsoid shows a different orientation with the

major axis parallel to b, with (e//a):(e//b):(e//c) =

1:1.48:1.45. The last orientation is maintained down to

the lowest temperatures. The structural reason of this

thermo-elastic behaviour is discussed in the following

paragraph.

Structural deformation at high temperature

The evolution of the unit-strain coefficients with T

(Fig. 5) shows that the main extensional deformation

mechanisms act along the b- and c-axis. However, it

appears that in the range between 1,100 and 1,200�C

the extensional strain along the c-axis is higher then

that along the b-axis. In contrast, at T < 1,100�C the T-

induced elastic strain is lower along the c-axis than

along the b-axis. The structural refinements performed

at different temperatures allow us to understand the

crystal chemical reason of such a behaviour.

The main mechanism responsible for the structural

expansion along the c-axis is the kinking of the TA-

nOA3nand TBnOB3n chains, represented by the varia-

tions of the O3A–O3A–O3A and O3B–O3B–O3B

angles. The TO4-tetrahedra in the pyroxene structure

do not expand significantly with increasing tempera-

ture (Cameron and Papike 1981), but the distortion

of the TB tetrahedron is stronger with increasing T

than that of TA (Table 5), in agreement with the

experimental findings of Yang and Ghose (1995a) for

En75Fs25. On the other hand, the structural extension

along the b-axis is mainly controlled by the M1 and M2

polyhedral edges that join the tetrahedral chains

(Fig. 6), and in particular by the M2 polyhedral edges

represented by the O3A–O1A, O2A–O1A, O3B–O1B

and O2B–O1B distances (Figs. 6, 7, Table 4). The

tetrahedral chains tend to extend monotonically with

increasing temperature, as shown by the evolution

of the angles O3A–O3A–O3A and O3B–O3B–O3B

(Table 4). In contrast, it appears that only the O3A–

O1A and O3B–O1B distances of the M2 polyhedral

edges increase with T, whereas the O2A–O1A and

O2B–O1B distances tend to remain almost constant

at the high temperature regime (Fig. 7, Table 4). This

behaviour leads to a more distorted configuration of

the M2 polyhedron at high temperature, as shown by

the polyhedral distortion coefficient in Table 5. The

extension of the tetrahedral chains gives rise to a

monotonic increase of the unit-strain coefficient along

Table 3 continued


O1(B) 0.5622(2) 0.3409(5) 0.7890(6) 1.450(25)O2(A) 0.3104(2) 0.5058(3) 0.0446(7) 1.450(25)O2(B) 0.4320(2) 0.4916(5) 0.7012(7) 1.450(25)O3(A) 0.3022(2) 0.2333(3) –0.1700(6) 1.450(25)O3(B) 0.4494(2) 0.2033(3) 0.5835(6) 1.450(25)

T = 150�CM1 0.3793(2) 0.6526(4) 0.8682(6) XFe = 0.018(6), XMg = 0.972(6) 0.118(40) 0.709(46)M2 0.3745(2) 0.4876(3) 0.3531(6) XFe = 0.132(6), XMg = 0.848(6) 0.974(52)Si(A) 0.2694(2) 0.3475(4) 0.0505(7) 0.361(13)Si(B) 0.4729(2) 0.3354(5) 0.7952(6) 0.361(13)O1(A) 0.1832(1) 0.3374(4) 0.0381(5) 0.447(14)O1(B) 0.5617(1) 0.3426(4) 0.7963(5) 0.447(14)O2(A) 0.3094(1) 0.5056(3) 0.0372(5) 0.447(14)O2(B) 0.4318(2) 0.4858(3) 0.6893(6) 0.447(14)O3(A) 0.3044(2) 0.2255(3) –0.1702(5) 0.447(14)O3(B) 0.4474(1) 0.1976(3) 0.6020(5) 0.447(14)

The fraction of Si and Al at the tetrahedral SiA and SiB sites were refined at 20�C. The refinement showed that the Al is mainly locatedat the SiB site, being X(AlB) @ 0.029, and a similar results was obtained at 1,200�C. Therefore, the fractions X(SiB) = 0.97,X(AlB) = 0.03 were fixed and not refined at any temperature


123

Ta

ble

4S

ele

cte

db

on

dle

ng

ths

(A)

an

da

ng

les

(�)

inO

px

at

dif

fere

nt

tem

pe

ratu

res

T(�

C)

20

1,2

00

1,1

75

1,1

50

1,1

25

1,1

00

1,0

75

1,0

50

1,0

25

1,0

00

97

51

50

M1

–O

1A

2.1

23

(5)

2.2

58

(6)

2.2

57

(6)

2.2

52

(6)

2.2

44

(6)

2.2

40

(6)

2.2

45

(6)

2.2

61

(6)

2.2

57

(6)

2.2

40

(6)

2.2

44

(6)

2.1

78

(5)

M1

–O

1A

2.0

82

(4)

2.1

69

(6)

2.1

71

(6)

2.1

64

(6)

2.1

62

(6)

2.1

57

(5)

2.1

54

(6)

2.1

39

(6)

2.1

35

(5)

2.1

31

(5)

2.1

30

(5)

2.0

61

(4)

M1

–O

1B

2.0

44

(4)

1.9

88

(5)

1.9

87

(5)

1.9

94

(5)

1.9

98

(5)

2.0

03

(5)

2.0

07

(5)

2.0

19

(5)

2.0

22

(5)

2.0

27

(5)

2.0

26

(5)

2.0

47

(4)

M1

–O

1B

2.2

16

(4)

2.2

13

(6)

2.2

15

(6)

2.2

10

(6)

2.2

12

(6)

2.2

04

(6)

2.1

97

(6)

2.1

90

(6)

2.1

81

(5)

2.1

92

(5)

2.1

84

(5)

2.1

68

(5)

M1

–O

2A

2.0

06

(4)

2.0

17

(5)

2.0

18

(5)

2.0

21

(5)

2.0

20

(5)

2.0

20

(5)

2.0

21

(5)

2.0

19

(4)

2.0

23

(4)

2.0

19

(4)

2.0

22

(4)

2.0

20

(4)

M1

–O

2B

1.9

74

(4)

1.9

45

(7)

1.9

53

(6)

1.9

58

(6)

1.9

60

(6)

1.9

66

(6)

1.9

67

(6)

1.9

52

(6)

1.9

57

(6)

1.9

64

(6)

1.9

64

(6)

1.9

87

(4)

ÆM1

–O

æ2

.07

42

.09

82

.10

02

.09

92

.09

92

.09

82

.09

82

.09

72

.09

62

.09

52

.09

52

.07

7M

2–

O1

A2

.16

0(4

)2

.15

0(6

)2

.15

1(6

)2

.14

2(6

)2

.15

2(6

)2

.15

1(6

)2

.14

1(6

)2

.11

3(6

)2

.12

1(6

)2

.13

9(6

)2

.13

3(6

)2

.10

1(4

)M

2–

O1

B2

.00

8(4

)2

.11

4(6

)2

.10

3(6

)2

.10

4(6

)2

.09

5(6

)2

.09

1(6

)2

.09

8(6

)2

.12

3(6

)2

.11

4(6

)2

.09

5(6

)2

.09

8(6

)2

.05

0(4

)M

2–

O2

A2

.02

2(4

)2

.05

6(6

)2

.04

3(6

)2

.04

3(5

)2

.03

7(5

)2

.04

0(5

)2

.04

1(5

)2

.05

9(6

)2

.05

0(5

)2

.05

1(6

)2

.04

7(5

)2

.03

2(4

)M

2–

O2

B2

.03

4(5

)2

.09

3(6

)2

.08

6(6

)2

.08

8(6

)2

.08

9(6

)2

.08

2(6

)2

.07

7(6

)2

.06

4(7

)2

.07

3(6

)2

.07

7(6

)2

.07

6(6

)2

.03

5(5

)M

2–

O3

A2

.31

3(4

)2

.37

5(5

)2

.37

7(5

)2

.37

6(5

)2

.37

3(5

)2

.37

4(5

)2

.37

0(5

)2

.36

9(5

)2

.36

8(5

)2

.36

8(5

)2

.36

6(5

)2

.27

8(4

)M

2–

O3

B2

.46

3(4

)2

.75

2(6

)2

.72

8(6

)2

.70

4(6

)2

.69

3(6

)2

.68

0(6

)2

.66

4(6

)2

.66

9(6

)2

.65

3(6

)2

.63

2(6

)2

.62

3(6

)2

.47

9(4

)(M

2–

O3

B¢)

3.1

67

(6)

3.0

52

(9)

3.0

63

(9)

3.0

74

(9)

3.0

79

(10

)3

.08

4(9

)3

.08

1(9

)3

.09

0(8

)3

.09

7(9

)3

.09

6(9

)3

.09

9(9

)3

.16

2(8

)ÆM

2–

Oæ

2.1

67

2.2

57

2.2

48

2.2

43

2.2

40

2.2

36

2.2

32

2.2

33

2.2

30

2.2

27

2.2

24

2.1

63

SiA

–O

1A

1.5

78

(4)

1.5

83

(5)

1.5

81

(5)

1.5

85

(5)

1.5

85

(5)

1.5

86

(5)

1.5

89

(5)

1.5

86

(5)

1.5

84

(5)

1.5

81

(5)

1.5

81

(5)

1.5

77

(4)

SiA

–O

2A

1.5

62

(4)

1.5

91

(6)

1.5

95

(6)

1.5

91

(5)

1.5

91

(5)

1.5

89

(5)

1.5

90

(6)

1.5

97

(6)

1.5

97

(5)

1.5

94

(5)

1.5

96

(5)

1.5

77

(4)

SiA

–O

3A

1.6

71

(4)

1.6

87

(5)

1.6

88

(5)

1.6

87

(5)

1.6

82

(5)

1.6

85

(5)

1.6

80

(5)

1.6

84

(5)

1.6

81

(5)

1.6

83

(5)

1.6

79

(5)

1.6

98

(4)

SiA

–O

3A

1.7

04

(4)

1.6

93

(6)

1.6

88

(6)

1.6

94

(5)

1.6

95

(5)

1.6

96

(5)

1.6

99

(5)

1.6

93

(5)

1.6

94

(5)

1.6

98

(5)

1.6

97

(5)

1.7

11

(4)

ÆSiA

–O

æ1

.62

81

.63

91

.63

81

.63

91

.63

81

.63

91

.63

91

.64

01

.63

91

.63

91

.63

81

.64

1O

3A

–O

3A

–O

3A

16

3.0

5(2

8)

16

9.7

9(3

8)

16

9.4

1(3

6)

16

8.6

3(3

1)

16

8.4

7(2

8)

16

8.1

8(3

1)

16

7.8

8(2

8)

16

7.8

5(3

0)

16

7.5

5(2

7)

16

7.1

4(2

8)

16

7.0

5(2

9)

16

1.0

5(2

7)

SiB

–O

1B

1.6

33

(4)

1.6

16

(6)

1.6

12

(6)

1.6

12

(6)

1.6

11

(6)

1.6

16

(5)

1.6

13

(6)

1.6

16

(6)

1.6

19

(5)

1.6

18

(5)

1.6

17

(5)

1.6

22

(4)

SiB

–O

2B

1.6

35

(5)

1.6

32

(7)

1.6

36

(7)

1.6

41

(7)

1.6

42

(7)

1.6

39

(7)

1.6

39

(7)

1.6

32

(7)

1.6

30

(6)

1.6

26

(6)

1.6

34

(6)

1.6

21

(5)

SiB

–O

3B

1.6

63

(4)

1.6

53

(6)

1.6

54

(6)

1.6

52

(6)

1.6

52

(6)

1.6

49

(5)

1.6

46

(6)

1.6

45

(6)

1.6

49

(5)

1.6

49

(5)

1.6

45

(5)

1.6

44

(4)

SiB

–O

3B

1.6

67

(4)

1.7

29

(5)

1.7

23

(5)

1.7

10

(5)

1.7

12

(5)

1.7

07

(5)

1.7

08

(5)

1.7

10

(5)

1.7

04

(5)

1.7

03

(5)

1.7

03

(5)

1.6

85

(4)

ÆSiB

–O

æ1

.64

91

.65

71

.65

61

.65

41

.65

41

.65

31

.65

11

.65

11

.65

01

.64

91

.65

01

.64

3O

3B

–O

3B

–O

3B

14

0.1

6(2

2)

14

9.1

3(2

8)

14

8.3

4(2

8)

14

7.5

0(2

6)

14

7.2

1(2

3)

14

6.7

7(2

4)

14

6.2

3(2

5)

14

5.7

5(2

6)

14

5.2

5(2

5)

14

4.9

3(2

6)

14

4.7

8(2

6)

14

0.7

8(2

4)

O3

A–

O1

A3

.67

0(5

)3

.77

5(8

)3

.76

2(8

)3

.74

5(7

)3

.74

8(7

)3

.74

1(7

)3

.71

9(8

)3

.70

1(7

)3

.69

8(8

)3

.70

2(7

)3

.69

5(6

)3

.59

9(6

)O

2A

–O

1A

2.8

79

(5)

3.0

07

(7)

3.0

11

(7)

3.0

08

(6)

2.9

98

(5)

2.9

92

(6)

3.0

05

(6)

3.0

13

(6)

3.0

05

(6)

2.9

91

(6)

2.9

94

(5)

2.9

32

(6)

O3

B–

O1

B3

.14

0(6

)3

.38

2(7

)3

.35

9(7

)3

.34

9(8

)3

.33

7(8

)3

.33

6(7

)3

.33

4(7

)3

.34

2(7

)3

.33

4(8

)3

.31

6(6

)3

.31

3(7

)3

.18

2(7

)O

2B

–O

1B

3.1

49

(6)

3.1

05

(6)

3.1

20

(8)

3.1

25

(8)

3.1

30

(7)

3.1

31

(7)

3.1

26

(7)

3.1

09

(8)

3.1

12

(6)

3.1

27

(6)

3.1

22

(6)

3.1

52

(6)

Th

ea

ve

rag

eÆM

2–

Oæ

dis

tan

ceis

calc

ula

ted

on

the

ba

sis

of

CN

=6


123

the c-axis within the T-range investigated. In contrast,

the counterbalancing effect of the M2-polyhedral

edges expansion along the b-axis gives rise to a satu-

ration effect in the unit-strain evolution along the

b-axis at the high temperature regime, implying a

cross-over between the unit-strain coefficient values

parallel to b and c at about 1,100�C.

The two non-equivalent tetrahedral chains, TAnO

A3n and TBnOB3n, are differently kinked in Pbca Opx.

At room temperature, the TBnOB3n chain is more

kinked by about 23� than TAnOA3n (Table 4). How-

ever, with increasing T this difference decreases, the

TBnOB3n chain being more kinked by about 20� than

Fig. 3 Evolution of Opx lattice parameters as a function oftemperature. Solid lines are the weighted quadratic fits throughthe data. The e.s.ds values are smaller than the size of the

symbols. On the basis of the previous results reported by Yangand Ghose (1995a) and Camara and Nestola (2006), theequations reported should be used only at 950 < T < 1,200�C

Fig. 4 Evolution of the volume thermal expansion coefficient(aT) with T Fig. 5 Magnitude of the three principal unit-strain coefficients

calculated at T-T0, where T is the temperature of interest and T0

is 20�C. Solid lines represent weighted quadratic fits of the data


123

TAnOA3n at 1,200�C. This trend (Fig. 8) appears to

confirm a general tendency for Opx at HT (Smyth

1973; Sueno et al. 1976; Yang and Ghose 1995a, b),

independent of chemistry, to reduce the difference in

kinking between the two tetrahedral chains toward the

HT phase transition, either to Pbcn (proto) or C2/c

(high clino), above which the two chains become

equivalent.

The values of the refined Mg/Fe fractions at the M1

and M2 sites at different temperatures, and the res-

pective equilibrium constants of the cation exchange

reaction, KD, expressed as:

KD ¼ Fe(M1) �Mg(M2)½ �= Fe(M2) �Mg(M1)½ �;

are reported in Table 3. The value of KD = 1 repre-

sents the state of total disorder, KD = 0 represents total

order. The KD value at RT agrees with that previously

obtained by Molin and Stimpfl (1994) by means of

single-crystal X-ray diffraction. The evolution of KD

with T is shown in Fig. 9. The KD value drastically

increases between RT and 975�C, confirming previous

studies of Mg–Fe order–disorder in Opx with T (Yang

and Ghose 1994a, 1995a, b; Stimpfl et al. 1999 and

references therein). A residual order remains even at

1,200�C. All refinements suggest a general trend to-

wards increasing order as the temperature is decreased

from 1,175�C all the way down, although seemingly not

following a definite progressive trend. At the lowest

temperature reached on the way down (150�C), the KD

has reached the same value determined by the refine-

ment at room temperature before the heating and

cooling cycle. In view of the extremely long times

Table 5 Polyhedral volumes and polyhedral distortion coefficient (n, according to Balic-Zunic and Vickovic 1996, and Makovicky andBalic-Zunic 1998) in Opx at different temperatures

T (�C) VM1 (A3) nM1 VM2(A3) nM2 VSiA (A3) nSiA VSiB (A3) nSiB

20 11.74(4) 0.0099 12.71(4) 0.0722 2.18(1) 0.0080 2.29(2) 0.00401,200 12.11(6) 0.0091 14.08(7) 0.0982 2.23(2) 0.0031 2.31(1) 0.00601,175 12.14(6) 0.0095 13.94(6) 0.0964 2.23(2) 0.0034 2.31(2) 0.00601,150 12.14(6) 0.0094 13.88(7) 0.0936 2.24(2) 0.0035 2.30(2) 0.00581,125 12.14(6) 0.0093 13.85(6) 0.0927 2.23(2) 0.0036 2.30(2) 0.00551,100 12.13(6) 0.0092 13.80(6) 0.0907 2.23(2) 0.0037 2.30(2) 0.00571,075 12.13(6) 0.0094 13.74(7) 0.0895 2.24(2) 0.0036 2.29(3) 0.00611,050 12.10(6) 0.0093 13.76(7) 0.0865 2.24(2) 0.0031 2.29(2) 0.00791,025 12.09(6) 0.0090 13.74(7) 0.0857 2.24(2) 0.0031 2.29(2) 0.00721,000 12.13(6) 0.0090 13.65(6) 0.0858 2.23(2) 0.0041 2.28(2) 0.0055975 12.09(6) 0.0089 13.65(7) 0.0840 2.23(2) 0.0034 2.28(2) 0.0062150 11.79(4) 0.0104 12.67(4) 0.0668 2.23(2) 0.0074 2.26(2) 0.0053

Fig. 6 Two clinographicviews of the crystal structureof Opx showing some selectedoxygen–oxygen distancespertaining to the M1 and M2polyhedra mentioned in the‘‘Discussion and conclusion‘‘and plotted in the followingFig. 7

Fig. 7 Evolution of some O–O distances versus T involving themost affected polyhedral edges (see Fig. 6)


123

expected for Opx to reach equilibrium at this temper-

ature, this may indicate that the equilibrium tempera-

ture of our natural sample was much higher than RT,

according with the volcanic history of the LE8 lherz-

olite xenolith ejecta associated with a basanitic lava. As

a matter of fact, the ‘‘closure temperature of ordering’’

(Tc) of our sample, calculated according to Stimpfl

et al. (2005), happens to be Tc = 648�C. Hence the low

temperatures reported in Fig. 9 (RT and 150�C) are to

be considered merely experimental temperatures,

representing a state of non-equilibrium in the mineral.

Furthermore, because of the complex crystal chemistry

of our sample (and possible interference on the Fe/Mg

partitioning) and because, as reported by Yang and

Ghose (1994a, 1995a), at T > 930–950�C the evolution

of KD with T follows an anomalous trend, if compared

to that at T < 930�C, due to structural rearrangements

for the impending phase transition, we avoid using the

KD values for a thermodynamic description of the HT

behaviour of Opx.

The thermal isotropic displacement parameters

(Uiso) for M1, M2 and T sites (we constrained Uiso

(TA) = Uiso(TB) in the structure refinements) increase

monotonically with T (with trends expressed by a

second-order polynomial, Fig. 10, Table 3), with Ui-

so(M2) > Uiso(M1) > Uiso(T). Also in this case,

no evidence of any anomalous behaviour within the

T-range investigated is observed.

Fig. 8 Top evolution of the kinking angles (O3A–O3A–O3A andO3B–O3B–O3B) of the tetrahedral chains TAnOA3n andTBnOB3n as a function of T. The kinking angle of the A-chain isplotted above 180�ð360� � \O3A--O3A--O3A�Þ and that of theB-chain below 180�, according to Sueno et al. (1976). Bottomevolution of D� ¼ ð\O3A--O3A--O3AÞ� � ð\O3B--O3B--O3BÞ�;which can be considered as an order parameter for a possible HT-phase transition. The solid lines represent the weighted quadraticregressions trough the data points

Fig. 9 Mg and Fe cation partitioning in M1 and M2 octahedralsites as a function of temperature expressed as KD versus Tin Opx. Total Mg/Fe disorder corresponds to KD = 1, totalorder corresponds to KD = 0 [with KD = (Fe(M1)Mg(M2))/(Fe(M2)Mg(M1))]. The two points at RT (before heating) and at150�C (after the heating cycle) are to be considered represen-tative of mere experimental temperatures. The effective ‘‘closuretemperature of ordering’’ (Tc) being in the 600–650�C range forthe two points (see text)

Fig. 10 Evolution with T of the isotropic thermal displacementparameters (Uiso) for the octahedral and tetrahedral sites[Uiso(M1), Uiso(M2) and Uiso(TA) = Uviso(TB)]


123

Discussion and conclusion

The HT structural behaviour of a natural Opx

(Wo1En91Fs~7) with minor amounts of Ca, Fe3+, Cr and

Al, was investigated by in-situ neutron powder dif-

fraction up to 1,200�C. The high quality of the neutron

data allowed a detailed description of the thermo-

elastic behaviour and a precise analysis of the T-

induced deformation mechanisms based on full-profile

fit Rietveld structure refinements.

Quite surprisingly, no evidence of a phase transition

was observed in the Opx within the temperature range

investigated, as confirmed by a careful inspection of the

diffraction patterns (no symmetry violating reflections

were observed), by the evolution of the lattice con-

stants and of the elastic and structural parameters

(thermal displacement coefficients, bond distances and

angles, polyhedral volumes) with T. The discrepancy

with respect to the previous HT-experiments on syn-

thetic or natural Opx is most likely due to the stabil-

ising effect of the minor amounts of Ca, Fe3+, Al and

Cr which played a crucial role.

Several studies have been devoted to the effect of

Ca and Al on the crystal chemistry, HT Fe/Mg order-

ing and kinetic processes, elastic and thermoelastic

behaviour of Opx (Chatillon-Colinet et al. 1983; Molin

1989; Domeneghetti et al. 1995a, b; Hugh-Jones et al.

1997; Stimpfl et al. 1999; Camara et al. 2000; Tribau-

dino and Nestola 2002; Nestola and Tribaudino 2003;

Zema et al. 2003; Nestola et al. 2006). In particular,

Nestola and Tribaudino (2003) studied the effect of Ca

on the orthoenstatite structure along the synthetic join

diopside (CaMgSi2O6)–enstatite (Mg2Si2O6), showing

that the Ca substitution into the Pbca structure of

orthoenstatite implies local distortions of the tetra-

hedral chains acting against the stability of the Pbca

symmetry. Consequently, the orthoenstatite structure

cannot contain more than 0.09–0.10 a.p.f.u. of Ca. For

an amount of Ca of about 0.15 a.p.f.u., the stable phase

is that of pigeonite with P21/c symmetry at room con-

ditions (Tribaudino and Nestola 2002). The effect of

Ca on the kinetics of the Fe–Mg disordering process in

a natural Opx (Wo4En60Fs36) was reported by Zema

et al. (2003) who carried out a study at 730�C. The

authors showed that the presence of Ca in the M2 site

of the Opx does not seem to have any influence on the

mechanism of the Fe–Mg intracrystalline exchange.

The experiments performed on Al-bearing Opxs at

high-it T by Domeneghetti et al. (1985), Tazzoli and

Domeneghetti (1987) and Molin (1989) showed that:

(a) Fe–Mg disordering occurs more quickly in Opx

containing less AlVI, hence AlVI(M1) hinders the ex-

change reaction; (b) AlVI, Cr3+and Fe3+ occupy the M1

site at both low- and high-T, whereas AlIV remains

completely ordered in the TB site.

The effect of Ca and Al on the P-induced struc-

tural evolution and on the elastic behaviour was

studied by Hugh-Jones et al. (1997) and by Nestola

et al. (2006). Hugh-Jones et al. (1997) showed that

chemical substitution of (0.04 + 0.03) a.p.f.u. of Al

and 0.006 a.p.f.u. of Ca into the structure of Opx

inhibits the initial rapid compression of M2–O3

bonds and the tetrahedral compression above 4 GPa

observed in synthetic (Mg,Fe)SiO3 samples. Nestola

et al. (2006) showed that a Ca substitution

(0.07 a.p.f.u.) into the pure orthoenstatite structure

gives rise to an increase of the bulk modulus (KT0)

and a decrease of its pressure-derivative (K¢) with

respect to the synthetic end-member [KT0(Mg2Si2O6) =

105.8(5) GPa, K¢(Mg2Si2O6) = 8.5(3); KT0(Ca0.07Mg1.93

Si2O6) = 110(1) GPa, K¢(Ca0.07Mg1.93Si2O6) = 6.6(4)].

In Opx along the En–Fs join, excluding the En end-

member, the rapid straightening of the TBnOB3n chain

at HT gives rise to a change in the topological config-

uration of the M2-polyhedron (Smyth 1973; Sueno

et al. 1976; Yang and Ghose 1995a, b). In fact, by

limiting the coordination shell within 3.0 A, at LT, the

M2 site in Opx is coordinated by O1A, O1B, O2A,

O2B, O3A and O3B. With increasing T up to 830–

930�C, previous studies on En75Fe25 Opx (Yang and

Ghose 1995a) showed that the coordination number of

M2 increases to seven, bonding also with the O3B¢oxygen. A further increase in T up to 1,030�C leads to a

new configuration with CN = 6, with the M2–O3B

distance longer than 3.0 A. The latter was considered

by Yang and Ghose (1995a) as a ‘‘transitional state’’

before the HT phase transition to the protoenstatite

structure. In contrast, the En100 does not show any

transitional state before the T-induced phase transition

to protoenstatite at 1,087�C (Yang and Ghose 1995b).

In this study, we do not observe any evidence of

anomalous behaviour with respect to the topological

configuration of the M2 polyhedron within the T-range

investigated. The M2–O3B¢ bond appears to be longer

than 3.0 A up to 1,200�C, although it slightly decreases

with increasing T (Table 4). In addition, the evolution

of the ‘‘order parameter’’ D (defined as the difference

between the O3–O3–O3 angles of the A and B chains,

Yang and Ghose 1995a) with T (Fig. 8) appears to be

smooth with a concave downward shape, less pro-

nounced than that observed for the En75Fs25 Opx at

HT (at the ‘‘transitional state’’). The absence of any

discontinuity confirms that no first-order phase transi-

tion occurs within the T-range investigated.

The experimental data reported in this study indi-

cate that the chemical substitution of a small amount of


123

Ca, Fe3+, Al and Cr can play a crucial role on the

thermoelastic behaviour and phase-stability fields of

Opxs with consequent important petrologic and geo-

logical implications, in particular on the thermody-

namic modelling of the Earth mantle processes.

Acknowledgments Financial support to the second author isacknowledged from MIUR (Italian Ministry of University andResearch; Grant No. 2004041033_4). The Italian National Re-search Council (CNR) is acknowledged for access to the ISISFacility through the mutual Agreement (No. 01/9001) betweenCNR and CCLRC. Many thanks are due to Subrata Ghose forprofitable discussion and critical reading of the manuscript be-fore submission. The authors thank the Editor M. Rieder, F.Nestola and an anonymous reviewer for their useful suggestions.

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