Phys Chem Minerals (2001) 28: 87±101

Ó Springer-Verlag 2001

ORIGINAL PAPER

T. Bo€a Ballaran á M. A. Carpenter M. C. Domeneghetti

Phase transition and mixing behaviour of the cummingtonite±grunerite solid solution

Received: 9 February 2000 / Accepted: 30 September 2000

Abstract Natural amphiboles with composition close to the binary join cummingtonite±grunerite and crystals of the same samples annealed at 700 °C for 55.5 h, in order to obtain di€erent degrees of non-convergent cation order, have been characterised by means of X-ray singlecrystal di€raction and IR spectroscopy. Long-range order parameters describing the non-convergent order of Mg/Fe among the di€erent octahedral sites have been calculated from the site occupancies of the investigated samples. Values of the O6-O5-O6 angles and of the hM4-Oi mean bond distances depend on the C2/ m ® P21/m phase transition for a given degree of order. In the IR spectra, only two phonon lines dominated by the bending of the tetrahedral chains are sensitive to the displacive phase transition and to the di€erent degree of cation order; all the other wavenumber shifts are correlated with compositional changes only. The local strains arising from the cation substitution, ordering and phase transition have been quanti®ed by means of the autocorrelation function. Very small local heterogeneities are associated with the Mg/Fe substitution and disordering in samples at intermediate composition. The displacive phase transition seems to occur in order to reduce local distortions and the P21/m samples are as homogeneous as orthorhombic anthophyllites. The orthorhombic structure, however, appears less ¯exible than the monoclinic in accommodating cations larger than Mg at the octahedral sites. T. Bo€a Ballaran (&) á M. A. Carpenter Department of Earth Sciences, Downing St., Cambridge, CB2 3EQ, UK e-mail: [email protected] Fax: +44-1223-333450 M. C. Domeneghetti Dipartimento di Scienze della Terra, Via Ferrata 1, 27100 Pavia, Italy Present address: T. Bo€a Ballaran Bayerisches Geoinstitut, UniversitaÈt Bayreuth, 95440 Bayreuth, Germany e-mail: tiziana.bo€[email protected]

Key words Cummingtonite á Solid solution á Cation ordering á Phase transition á IR spectroscopy

Introduction Local structural distortions can occur when a large cation is substituted for a smaller one in some solid solution or when some cation disorder between crystallographic sites is introduced on a unit-cell length scale. Microscopic or local strains associated with displacive or ordering processes may also correlate over a suciently large length scale to cause a phase transition. In both cases, however, the local distortions contribute substantially to the macroscopic elastic energy of the material. Evidence for the existence of these microscopic strains is provided by line broadening in vibrational spectra which can be quanti®ed by the autocorrelation method. This technique, developed in the past few years, has been used successfully to characterise several silicate solid solutions and to follow changes due to cationordering processes (Malcherek et al. 1995; Salje and Bismayer 1997; Bo€a Ballaran et al. 1998, 1999; Atkinson et al. 1999; Carpenter et al. 1999). From a microscopic perspective, the cummingtonite± grunerite (Mg, Fe2+)7Si8O22(OH)2 solid solution is of particular interest because of its di€erent features. The substitution of Mg for Fe can be expected to result in only a relatively small deviation from ideality, due to the small di€erence in size between the two cations. However, samples belonging to this system have di€erent structures depending on their Mg/Fe ratio. Mg endmember anthophyllites are orthorhombic with Pnma symmetry, Mg-rich cummingtonites are monoclinic P21/ m, and Fe-rich cummingtonite and grunerite end members are monoclinic C2/m (Cameron and Papike 1979; Hawthorne 1983). Although the monoclinic solid solution does not display obviously non-ideal changes in lattice parameters (Hirschmann et al. 1994, and references therein), implying that the macroscopic strain associated with the displacive C2/m ® P21/m phase

88

transition is small, there must be some microscopic strains associated with the transformation. Moreover, the displacive phase transition will be in¯uenced not only by variations in composition, but also by the cation ordering. It is well known that Mg and Fe order among the di€erent crystallographic sites, with Fe occupying preferentially the M4 site with respect to the M1, M2 and M3 sites (Hafner and Ghose 1971; Ghose and Weidner 1972; Hawthorne 1983; Yin et al. 1989; Hirschmann et al. 1994). The e€ect of cation substitution and state of order on the C2/m ® P21/m phase transition can be described with coupling terms between the order parameter Q associated with this transition, the compositional parameter XFe and the non-convergent order parameter Qt, respectively (Carpenter and Salje 1994, and references therein). It is therefore convenient to separate the total excess free energy DG into three parts:

All samples were examined by transmission electron microscopy (TEM) to check for the presence of exsolution lamellae. Specimens were ion beam-thinned and TEM observations were made in a JEOL 100CX electron microscope operating at 100 kV. A detailed list of microstructures, stacking faults, exsolution and twin lamellae observed is given in Table 1. In order to obtain samples with the same composition but di€erent distributions of Mg/Fe between the M1, M2, M3 and M4 sites, crystals were annealed at 700 °C, PH2 O ˆ 1:5 kb for 55.5 h, using the double-capsule method with a fayalite-magnetite-quartz bu€er to prevent the oxidation of iron. For iron-rich compositions, this temperature is within the stability ®eld of the C2/m structure. The detailed phase relations at the Mg-rich end of the anthophyllite±cummingtonite join remain a matter of speculation (Ghose 1981; Evans and Ghiorso 1995), but certainly the samples recovered as P21/m amphiboles were annealed at temperatures above the inversion to C2/m, and therefore they passed through the C2/ m ® P21/m transition on quenching. Recovered products always consisted of cummingtonite as the only phase.

DG ˆ G…Q† ‡ G…Q; Qt † ‡ G…Q; XFe † ;

X-ray di€raction data at room pressure were collected using a Philips PW1100 four-circle automated di€ractometer with graphite monochromated MoKa radiation. The equivalent pair hkl and hkl were measured in the h range 2±35° using the x-scan mode. Details of the analysis of the X-ray intensities and the absorption corrections are provided by Bo€a Ballaran et al. (2000). For only one of the three anthophyllite samples (G18691) was it possible to ®nd a crystal suitable for X-ray di€raction. Re¯ections with h ‡ k ˆ 2n ‡ 1 violating the C2/m space group were detected in the natural sample 1997-4 and in three annealed samples 1997-4, 118125 and Y42XB. Values of the equivalent pairs of re¯ections were averaged and the resulting discrepancy factors Rint are reported in Table 3. Weighted least-squares structure re®nements based on Fo2 were performed using the program SHELX93 (Sheldrick 1993) and carried out with space groups Pnma, C2/m and P21/m (Table 3). Atomic scattering curves (Ibers and Hamilton 1974) for completely ionised cations (Si4+, Fe2+, Mg2+ and Ca2+) were employed. For the anion positions, the O2) scattering curve was taken from Tokonami (1965). Anisotropic temperature factors were used for all atoms in all stages of the re®nements. The extinction parameters and the weighting scheme are de®ned in Bo€a Ballaran et al. (2000). As the X-ray scattering factors of Fe and Mn and of Mg and Al are similar, only Fe and Mg occupancies were re®ned at the M1, M2 and M3 sites, while Mg, Fe and Ca occupancies were re®ned at the M4 site. The resulting site distribution is given in Table 4. The short tetrahedral mean bond distances obtained (Table 5) provide no evidence for Al substitution at the tetrahedral sites (see also Ungaretti et al. 1981; Oberti et al. 1993; Tartarotti and Caucia 1993). During the structure re®nements, the A site was assumed to be vacant. Di€erence-Fourier maps were used to search for the hydrogen atoms of the hydroxyl groups and for possible occupancy of the A site. The hydrogen atom was found in all crystals as a distinct peak at a distance of 0.80±0.90 AÊ from O3, and was introduced in the last re®nement cycles with full occupancy and isotropic temperature factor. No signi®cant excess scattering density was detected at the A site. The re®nement of the data of the natural samples Nev1963 and 153620 yielded a discrepancy factor R1 of 5%, due to the poor quality of the crystals, which are all twinned. Examination of the re¯ections with the largest di€erences between Fo and Fc showed that, for the hk0 re¯ections, Fo was greater than Fc by a nearly constant factor. A relative scale factor was therefore included in further re®nements such that the Fc2 values of the hk0 re¯ections were multiplied by both relative and overall scale factors. The number of unique re¯ections, I, the discrepancy index, R1, based on Fo2 > 2r…Fo2 †, and the goodness of ®t, S, are reported in Table 3. Tetrahedral and octahedral mean bond distances and some geometrical parameters are reported in Tables 5 and 6, respectively. Data for samples Y42XB, BM93400, 1-K and 153620 have already been published in Bo€a Ballaran et al. (2000), and are reported here only to give a

where G…Q† ˆ 12 a…T Tc †Q2 ‡ 14 bQ4 ‡ 16 cQ6 is the change in energy associated with the displacive phase transition; G…Q; Qt † ˆ kt Qt Q2 is the coupling term between Q and Qt ; and G…Q; XFe † ˆ kX XFe Q2 is the coupling term between Q and composition. (Tc is the transition temperature; a, b and c are coecients of the polynomial expansion in Q and kt and kX are coupling coecients). The objectives of this study are: (1) to characterise the macroscopic and microscopic mixing behaviour of the cummingtonite±grunerite solid solution by means of single-crystal X-ray di€raction and IR spectroscopy, and (2) to de®ne the local strains due to cation substitution and ordering and their in¯uence on the C2/ m ® P21/m phase transition.

Experimental Samples The cummingtonite samples used in this study are listed in Table 1. They were selected on the basis of their Mg, Fe contents and their relatively low concentrations of components not belonging to the Mg7Si8O22(OH)2±Fe7Si8O22(OH)2 system. Compositions were determined by electron microprobe energy dispersive analysis with a CAMECA SX50 operating at 20 kV and 3 nA beam current, using a Link AN10000 system with ZAF4/FLS quantitative software. Up to 15 point analyses were obtained on several crystals (separated using heavy liquids) of each sample and averaged. Their structural formulae have been calculated on the basis of 23 oxygens (Table 2) and all the iron content was assumed to be Fe2+. Chemical analyses of samples Y42XB, BM93400, 1-K and 153620 are given by Bo€a Ballaran et al. (2000). The volcanic samples P1567 and Breccia have a very low Si content, which may suggest a high degree of Al substitution in the tetrahedra. However, from X-ray re®nements we obtained tetrahedral mean bond distances hT1-Oi which are consistent with a complete Si occupancy at the tetrahedral sites (see next section). The low Si content obtained by the microprobe analysis may, therefore, be due to the calculation used, based on 23 O, which is unsatisfactory when the OH content in the amphibole structure is lower than 2. The composition of the investigated samples is expressed as Fe XFe ˆ : Fe ‡ Mg

X-ray single-crystal re®nements

0.12

0.20

0.30 0.34

0.36

0.37

0.37

0.45

0.69

0.77

0.78

0.89

0.97

Lud5011

51332

G18691 1997-4

118125

P1567

Breccia

Y42XB

BM93400

Nev1963

35353

1-K

153620

Wabush iron formation, Labrador Vila Real, Portugal

MansjoÈ, Loos, Sweden

Central Massachusetts and Southwestern New Hampshire Cummington, Hampshire County, Massachusetts Cummington, Massachusetts

h/unit, Rotoiti breccia, New Zealand

Valle Antrona, Novara, Italy Bare Hills, Baltimore, Maryland Bare Hills, Baltimore, Maryland Rotoiti breccia, New Zealand

DuÈrrenstein, Austria

Unknown

Location

American Museum of Natural History

C. Klein

British Museum Neville collection Cambridge Harker collection

British Museum

P. Robinson

A. Ewart

C. Wilson

Smithsonian Institution

South Australia Museum Cambridge mineral collection

Cambridge, Harker collection

British Museum

Source

No microstructure

Two orientations of heterogeneously distributed exsolution lamellae up to 500 AÊ thick, with Guinier-Preston zones and precipitate free zones in between Isolated (100) twins, <0.4 lm thick

Rare and isolated lamellae a few 100 AÊ thick, probably (100) twins

Isolated (100) twins

Pervasive and uniform exsolution texture; exsolution lamellae parallel to (100), a few 100 AÊ apart, with thickness £50 AÊ. Appears to be clino host with ortho lamellae Anthophyllite with (100) stacking faults on spacing of 350±400 AÊ. One area of P clino found; no microstructure observed Anthophyllite with (100) stacking faults on spacing of 0.5 lm No exsolution or other pervasive microstructures. No obvious b-re¯ections in electron di€raction patterns Isolated lamellae a few 100 AÊ thick; probably (100) twins. Some rare (010) stacking faults Heterogeneous distribution of exsolution lamellae in two orientations, but plenty of clean grains with no microstructure. Very di€use b-re¯ections observed in overexposed electron di€raction patterns Appears to contain heterogeneously distributed exsolution lamellae with variable thicknesses up to 1000 AÊ. Exsolved phases perhaps represent a few % by volume, but this is not well constrained by a small number of observations No pervasive microstructure

TEM texture

[5]

[1] [5] [6]

[5]

[4] [5]

[2] [3]

[1]

Referencea

Reference [1] Hirschmann et al. (1994) and references therein; [2] Ewart (1968); [3] Buckley (1971); [4] Robinson and Ja€e (1969); [5] Bo€a Ballaran et al. (2000); [6] Klein and Waldbaum (1967)

a

XFe

Samples

Table 1 Sample descriptions

89

90 Table 2 Average electron microprobe analyses. Figures in brackets are 1r variations derived from counting statistics Wt%

Lud5011

51332

SiO2 TiO2 Al2O3 Cr2O3 FeO MnO MgO CaO Na2O K2O Cl

59.35 0.03 0.06 0.03 7.28 0.20 29.81 0.28 0.28 0.00 0.01

57.41 0.01 0.18 0.14 11.91 0.31 26.32 0.57 0.11 0.00 0.01

Total

97.32 (59)

Si Ti Al tot Cr Fe2+ Mn Mg Ca Na K XFe/(Fe+Mg) XAl+Na+Ca a

(41) (3) (5) (3) (18) (4) (25) (5) (5) (0) (1)

8.023 0.003 0.009 0.003 0.823 0.023 6.008 0.040 0.073 0.000 0.12 0.12

(10) (3) (8) (4) (24) (5) (25) (7) (14) (0)

(16) (1) (8) (6) (21) (5) (15) (4) (8) (0) (1)

96.96 (30) 7.979 0.001 0.030 0.015 1.384 0.036 5.452 0.086 0.029 0.000 0.20 0.14

G18691

1997-4

118125

P1567

56.15 0.01 0.04 0.03 17.35 0.39 22.50 0.41 0.19 0.00 0.00

55.60 0.01 0.25 0.02 19.20 0.32 20.77 0.62 0.39 0.00 0.01

55.53 0.01 0.13 0.01 20.43 0.60 19.80 0.73 0.25 0.01 0.01

53.61 0.27 1.11 0.01 19.51 1.63 18.63 1.91 0.54 0.02 0.03

(36) (2) (7) (3) (22) (8) (28) (4) (7) (1) (1)

97.07 (59)

(11) (1) (13) (6) (25) (6) (25) (7) (22) (0)

8.000 0.001 0.007 0.003 2.068 0.047 4.779 0.062 0.052 0.000 0.30 0.12

(16) (2) (12) (3) (23) (9) (44) (6) (20) (1)

(25) (2) (9) (2) (53) (9) (49) (10) (9) (0) (2)

97.18 (38) 7.992 0.001 0.043 0.002 2.309 0.039 4.449 0.096 0.107 0.000 0.34 0.25

(18) (2) (15) (3) (75) (11) (84) (15) (26) (1)

(24) (2) (6) (2) (27) (4) (25) (11) (10) (1) (1)

97.50 (44) 8.009 0.002 0.021 0.002 2.464 0.073 4.258 0.113 0.069 0.001 0.36 0.20

(7) (2) (11) (2) (32) (5) (54) (17) (28) (2)

(50) (11) (47) (2) (47) (12) (44) (60) (10) (3) (1)

Breccia

Nev1967

35353

53.17 0.29 1.34 0.03 19.49 1.57 18.44 2.07 0.45 0.01 0.04

50.21 0.02 0.04 0.01 39.57 1.03 6.47 0.19 0.09 0.01 0.01

50.29 0.04 0.30 0.02 39.64 0.99 6.09 0.49 0.21 0.00 0.05

(57) (11) (40) (3) (40) (6) (42) (58) (8) (2) (2)

97.24 (26)

96.86 (42)

7.821 0.030 0.190 0.001 2.380 0.201 4.051 0.299 0.153 0.004 a 0.370 0.64

7.791 0.032 0.232 0.004 2.388 0.195 4.028 0.325 0.129 0.003 a 0.372 0.69

(57) (13) (81) (2) (55) (15) (87) (94) (27) (6)

(57) (12) (70) (3) (43) (8) (78) (93) (23) (4)

(37) (3) (5) (3) (53) (6) (36) (5) (5) (1) (1)

97.64 (50) 7.996 0.003 0.007 0.002 5.270 0.139 1.535 0.033 0.027 0.002 0.77 0.07

(15) (3) (10) (3) (88) (8) (79) (8) (17) (2)

(47) (2) (14) (2) (47) (7) (21) (4) (10) (0) (3)

98.07 (81) 7.979 0.004 0.055 0.003 5.260 0.133 1.439 0.083 0.064 0.000 0.78 0.20

(21) (3) (25) (3) (78) (10) (41) (6) (29) (0)

The third ®gure has been considered only to distinguish between the two volcanic samples

Table 3 Re®nement parameters Samples

Space group

Rint

I

R1

S

G18691 nat. 1997-4 nat. 1997-4 ann. 118125 nat. 118125 ann. P1567 nat. P1567 ann. Breccia nat. Breccia ann. Y42XB nat. Y42XB ann. BM93400 nat. BM93400 ann. Nev1963 nat. Nev1963 ann. 35353 nat. 35353 ann. 1-K nat. 1-K ann. 153620

Pnma P21/m P21/m C2/m P21/m C2/m C2/m C2/m C2/m C2/m P21/m C2/m C2/m C2/m C2/m C2/m C2/m C2/m C2/m C2/m

4.11 2.73 2.08 1.42 2.26 1.69 2.23 2.02 3.45 2.07 3.66 2.01 2.09 3.38 2.66 2.39 2.29 1.86 2.12 3.68

4017 4012 4013 2013 4023 2027 2031 2027 2027 2026 4020 2050 2052 2054 2060 2056 2063 2077 2077 2077

3.95 3.00 2.70 2.03 3.15 2.51 2.90 2.67 3.42 2.50 3.29 2.83 2.50 4.31 2.77 2.96 2.63 2.20 2.55 4.06

0.897 0.875 0.942 0.985 1.120 1.046 0.982 1.037 0.987 1.010 0.821 0.974 0.972 1.006 0.935 0.931 0.940 0.965 0.967 0.930

complete overview of the behaviour of the solid solution. The positional and displacement parameters, as well as the observed and calculated structure factors, are available from the authors. IR measurements The cummingtonite samples were hand-ground in an agate mortar for a measured time (15 min). The pellet preparation follows a systematic methodology described by Bo€a Ballaran et al. (1998). Pellets of polyethylene, weighing 100 mg each and containing 2%

of sample, were used for the spectral region 50±500 cm)1. Pellets of CsI, weighing 300 mg each and containing 0.29% by weight of sample, were used for the spectral region 350±4500 cm)1. Spectra were collected under vacuum at room temperature with a resolution of 2 cm)1, using a Bruker 113 V FT-IR spectrometer for the FIR region and a Bruker 66 V FT-IR spectrometer for the MIR region. For all the experiments a DTGS detector was used. Every spectrum, recorded as absorbance, a ˆ log10 …Isample = Ireference †, where I is the single beam transmission intensity, was calculated by Fourier transformation of 512 interferometer scans.

Results Crystal structure The tetrahedral mean bond distances hT1-Oi and hT2-Oi of the investigated samples (Table 5) do not di€er from previous studies (Tartarotti and Caucia 1993; Hirschmann et al. 1994) and are practically constant along the solid solution (Fig. 1). As shown by Hirschmann et al. (1994), the M1, M2 and M3 mean bond distances correlate linearly with the mean ionic radius of the site occupants, but do not depend on the C2/ m ® P21/m phase transformation. Changes in other geometrical parameters are, instead, more important for describing the lowering in symmetry occurring in Mgrich cummingtonites; namely, the O6-O5-O6 kink angles (Yang and Hirschmann 1995) and the hM4-Oi mean bond distances. The variation in O6-O5-O6 angles as a function of composition is shown in Fig. 2. The angle in the C2/m cummingtonites is practically constant with composition

91 Table 4 Mg, Fe and Ca occupancies at the M1, M2, M3 and M4 sites from re®nements of X-ray single-crystal di€raction data. Standard deviations are 0.003 for the M1, M2 and M3 site occupancies and 0.006± 0.007 for the M4 site occupancies

Samples

M1

G18691 nat. 1997-4 nat. 1997-4 ann. 118125 nat. 118125 ann. P1567 nat. P1567 ann. Breccia nat. Breccia ann. Y42XB nat. Y42XB ann. BM93400 nat. BM93400 ann. Nev1963 nat. Nev1963 ann. 35353 nat. 35353 ann. 1-K nat. 1-K ann. 153620 nat.

M2

M3

M4

Mg

Fe

Mg

Fe

Mg

Fe

Mg

Fe

Ca

0.911 0.897 0.813 0.831 0.765 0.776 0.740 0.784 0.743 0.697 0.667 0.331 0.343 0.288 0.284 0.238 0.244 0.108 0.115 0.034

0.089 0.103 0.187 0.169 0.235 0.224 0.260 0.216 0.257 0.303 0.333 0.669 0.657 0.712 0.716 0.762 0.756 0.892 0.885 0.966

0.986 0.978 0.895 0.950 0.855 0.869 0.826 0.881 0.825 0.872 0.777 0.551 0.445 0.486 0.367 0.411 0.326 0.197 0.169 0.057

0.014 0.022 0.105 0.050 0.145 0.131 0.174 0.119 0.175 0.128 0.223 0.449 0.555 0.514 0.634 0.589 0.674 0.803 0.831 0.943

0.928 0.914 0.843 0.842 0.797 0.800 0.776 0.810 0.785 0.713 0.708 0.306 0.357 0.276 0.297 0.228 0.257 0.089 0.121 0.046

0.072 0.086 0.157 0.158 0.203 0.200 0.224 0.190 0.215 0.287 0.292 0.694 0.645 0.724 0.703 0.772 0.743 0.911 0.879 0.954

0.167 0.103 0.316 0.081 0.259 0.136 0.242 0.154 0.236 0.062 0.204 0.031 0.060 0.024 0.041 0.021 0.029 0.012 0.010 0.000

0.820 0.885 0.674 0.912 0.719 0.803 0.711 0.822 0.697 0.920 0.780 0.958 0.929 0.966 0.942 0.947 0.934 0.964 0.962 0.931

0.014 0.012 0.010 0.007 0.022 0.061 0.047 0.024 0.067 0.018 0.016 0.011 0.011 0.010 0.017 0.032 0.037 0.024 0.028 0.069

Table 5 Tetrahedral and octahedral mean bond distances Samples

hT1A-Oi

hT1B-Oi

G18691 nat. 1997-4 nat. 1997-4 ann. 118125 nat. 118125 ann. P1567 nat. P1567 ann. Breccia nat. Breccia ann. Y42XB nat. Y42XB ann. BM93400 nat. BM93400 ann. Nev1963 nat. Nev1963 ann. 35353 nat. 35353 ann. 1-K nat. 1-K ann. 153620

1.619 (3) 1.615 (3) 1.616 (2)

1.619 (3) 1.615 (3) 1.620 (2)

1.617 (2)

1.619 (2)

1.615 (3)

1.619 (3)

hT1-Oi

1.617 (1) 1.620 1.619 1.621 1.619 1.618

(1) (1) (2) (2) (1)

1.618 1.620 1.617 1.619 1.619 1.620 1.620 1.617 1.617

(1) (1) (2) (2) (2) (1) (1) (1) (3)

hT2A-Oi

hT2B-Oi

1.621 (3) 1.623 (3) 1.623 (2)

1.629 (3) 1.624 (3) 1.627 (2)

1.625 (2)

1.627 (2)

1.624 (3)

1.624 (3)

and degree of order (170±171°), in agreement with Yang and Hirschmann (1995). The same value is obtained by averaging the O6-O5-O6 angles of the A and B chains of the P21/m structure which have, however, an opposite behaviour. Whereas the B chains are more and more kinked with both increasing total Mg content and increasing Mg content at the M4 sites, the A chains ®rst straighten and then become S-rotated. The trend of the A chains of the P21/m annealed samples, which are Orotated for sample Y42XB, and S-rotated for samples 118125 and 1997±4, appears to be continuous. The simplest description of the behaviour of the P21/m chains is a linear ®t through the annealed data, which gives the evolution of the order parameter, perhaps as Q2, describing the displacive phase transition as a

hT2-Oi

1.626 (1) 1.626 1.624 1.625 1.626 1.626

(1) (1) (2) (2) (1)

1.627 1.627 1.626 1.627 1.627 1.627 1.627 1.625 1.627

(1) (1) (2) (2) (2) (1) (1) (1) (3)

hM1-Oi

hM2-Oi

hM3-Oi

hM4-Oi

2.092 2.091 2.096 2.094 2.098 2.096 2.096 2.095 2.096 2.100 2.099 2.114 2.115 2.116 2.118 2.118 2.117 2.126 2.123 2.130

2.084 2.088 2.092 2.089 2.093 2.089 2.091 2.089 2.091 2.089 2.092 2.104 2.112 2.108 2.116 2.111 2.116 2.124 2.123 2.129

2.079 2.084 2.086 2.088 2.088 2.087 2.086 2.086 2.086 2.092 2.088 2.109 2.106 2.109 2.111 2.113 2.110 2.120 2.117 2.120

2.273 2.283 2.273 2.284 2.276 2.294 2.291 2.295 2.290 2.282 2.275 2.285 2.287 2.287 2.290 2.290 2.292 2.295 2.293 2.299

(3) (3) (2) (1) (2) (1) (1) (2) (2) (1) (3) (1) (1) (2) (2) (2) (1) (1) (1) (3)

(3) (3) (2) (1) (2) (1) (1) (2) (2) (1) (3) (1) (1) (2) (2) (2) (1) (1) (1) (3)

(3) (3) (2) (1) (2) (1) (1) (2) (2) (1) (3) (1) (1) (2) (2) (2) (1) (1) (1) (3)

(3) (3) (2) (1) (2) (1) (1) (2) (2) (1) (3) (1) (1) (2) (2) (2) (1) (1) (1) (3)

function of composition for a given degree of non-convergent order. The linear ®t shown in Fig. 2 gives a critical composition (0.56 XFe), which de®nes the Fe content below which the P21/m phase is stable at room temperature for samples equilibrated at 700 °C. The kinking of the B chains of the Pnma crystal follows the trend of the P21/m data, while the kinking of the A chains has a di€erent behaviour due to the fact that, in the orthorhombic structure, both chains are O-rotated as in the C2/m structure. The M4 cations in the centred monoclinic structure have a 4 + 2 coordination given by two O2 and two O4 atoms at distances ranging between 1.98 and 2.17 AÊ, and two O6 atoms at about 2.68±2.78 AÊ (Table 5). In contrast, the M4 cations in the P21/m structure have a

92 Table 6 Selected geometrical parameters Samples

O6A-O5A-O6A

O6B-O5B-O6B

G18691 nat. 1997-4 nat. 1997-4 ann. 118125 nat. 118125 ann. P1567 nat. P1567 ann. Breccia nat. Breccia ann. Y42XB nat. Y42XB ann. BM93400 nat. BM93400 ann. Nev1963 nat. Nev1963 ann. 35353 nat. 35353 ann. 1-K nat. 1-K ann. 153620

171.0 (1) 173.7 (2) a 183.6 (1)

158.9 (1) 166.3 (2) 161.6 (1)

a

181.2 (2)

163.3 (2)

177.1 (2)

166.2 (2)

O6-O5-O6

169.9 (1) 169.9 170.4 169.8 170.3 170.4

(1) (1) (1) (2) (1)

171.1 171.2 171.4 171.2 171.2 171.1 171.2 171.2 171.1

(1) (1) (2) (1) (1) (1) (1) (1) (2)

T1A-O7A-T1A

T1B-O7B-T1B

141.7 (2) 141.8 (3) 142.3 (2)

138.2 (2) 140.5 (3) 139.4 (2)

142.0 (2)

140.3 (2)

142.3 (3)

141.7 (3)

T1-O7-T1

141.4 (1) 141.4 141.5 141.3 141.4 142.2

(1) (1) (1) (2) (1)

143.3 143.1 143.6 143.5 143.6 143.3 143.9 143.9 144.4

(1) (1) (2) (1) (2) (1) (1) (1) (2)

a

These tetrahedral A chains are S-rotated (cf. Yang and Hirschmann 1995), therefore the angles reported are expressed as 360°-(O6-O5O6) in order to be compared with the O-rotated chains

Fig. 1 Variation of the tetrahedral mean bond distances as a function of composition. These distances are practically constant across the solid solution and are consistent with rigid SiO4 tetrahedra. Open square: Pnma natural sample; open circles: C2/m natural samples; ®lled circles: C2/m annealed samples; open triangle: P21/m natural sample; ®lled triangles: P21/m annealed samples; open diamonds volcanic natural samples; ®lled diamonds volcanic annealed samples. The size of the symbols is of the order of the uncertainties

Fig. 2 Variation of the O6-O5-O6 kink angle as a function of composition. These angles are constant with composition and degree of order for the C2/m samples, but they are sensitive to the C2/m ® P21/m phase transition. Symbols as in Fig. 1. The solid lines through the annealed P21/m data are the least-squares best ®ts: O6A O5A O6A ˆ 202…4† 55…11†XFe and O6B O5B O6B ˆ 148…3† ‡ 40…8†XFe

4 + 1 + 1 coordination, due to the di€erent kinking angles of the two distinct tetrahedral chains, with four atoms (O2A, O2B, O4A and O4B) at distances between 2.00 and 2.15 AÊ, one (O6A) at 2.50±2.60 AÊ and one (O6B) at 2.75±2.83 AÊ. The orthorhombic Pnma sample G18691 also has a 4 + 1 + 1 coordination, though the two more distant anions are O5A at 2.42 AÊ, and O6B at 2.86 AÊ, while the O5B atom is at a distance of 2.90 AÊ.

Therefore, we can, in principle, consider two di€erent hM4-Oi mean bond distances, one describing the octahedral coordination around the M4 site (Fig. 3a) and the second obtained by averaging only the distances with the ®ve closer O atoms (for the C2/m samples only one of the two O6 is considered in the average) (Fig. 3b). In both graphs it is clear that the P21/m structure displays smaller bond distances, with respect to the C2/m struc-

93

ture, and that the volcanic cummingtonites plot o€ the general trend, due to their higher Ca content at the M4 sites. However, the average of only ®ve M4-O distances has a simpler behaviour (Fig. 3b). The C2/m crystals have a practically constant mean bond distance and the annealed P21/m samples show a unique trend as a function of composition. A linear ®t of these data can be used to describe the evolution of the order parameter (probably as Q2) as a function of composition for a given degree of non-convergent order. The estimate of the critical composition (at around 0.58 XFe) is close to that found by analysing the O6-O5-O6 angle variation. Bond distances for the Pnma structure plot on the same trend as the P21/m cummingtonites, but the ®ve coordinated oxygen atoms are O2A, O2B, O4A, O4B and O5A instead of O2A, O2B, O4A, O4B and O6A. The interchange between O6 and O5 in the coordination around the M4 site may be attributed to the di€erent rotations of the A chains in the orthorhombic and primitive monoclinic structures.

Fig. 3a, b Variation of the hM4-Oi mean bond distances as a function of composition calculated considering a the distances with six oxygen atoms in the highly distorted M4 octahedra, and b the distances with only the ®ve closer oxygen atoms (in the case of the C2/m cummingtonites only one of the two O6 atoms was considered). Symbols as in Fig. 1. The size of the symbols is of the order of the uncertainties. The solid line through the annealed P21/m bond distances is the least-squares best ®t to the data with: hM4-Oi ˆ 2.11(1) + 0.15(4)XFe. Note that as the displacive phase transition C2/m ® P21/m takes place, the hM4-Oi mean bond distances decrease

Cation ordering A general model for Mg/Fe ordering in cummingtonites is given by a four-site formulation (Ghiorso et al. 1995) with three independent order parameters Qt1, Qt2 and Qt3 (Bo€a Ballaran et al. 2000), which describe the ordering of Fe between M4 and M1, M4 and M2, and M4 and M3, respectively. A previous study (Hirschmann et al. 1994) and this X-ray study (Table 4) have shown that there is little evidence for a signi®cant Mg/Fe ordering between M1 and M3. This is clearly de®ned by the linear correlation, with a coupling coecient k close to 1, between Qt1 and Qt3 (Fig. 4a). As a ®rst approximation, Qt1 and, hence, Qt3 also can be considered as

Fig. 4a, b Correlation between the three order parameters, Qt1 , Qt2 and Qt3 , used to describe the non-convergent Mg/Fe order between M4 and M1, M4 and M2, and M4 and M3 octahedral sites, respectively. Symbols as in Fig. 1. To a ®rst approximation, both the correlations can be assumed to be linear

94

being linearly dependent on Qt2 (Fig. 4b). This means that the three order parameters do not in reality behave independently. It is therefore possible to de®ne a nonconvergent order parameter Qt according to a two-site model which involves the order between M4 and the combined M1, M2 and M3 (M123) sites. This can be expressed as:
1 M4 M1 M2 M3 XFe 5 2XFe ‡ 2XFe ‡ XFe
Qt ˆ M4 1 : M1 ‡ 2X M2 ‡ X M3 XFe ‡ 5 2XFe Fe Fe The coecient 1/5 takes into account the fact that the ratio of the number of sites among which the Mg/Fe order occurs is not 1:1. The values of Qt calculated for the investigated samples are reported in Fig. 5 as a function of composition. Mg7Si8O22(OH)2 and Fe7Si8O22(OH)2 end members have a value of only Qt ˆ 0 independently of the de®nition, because they contain either no Fe or only Fe; these values are represented on the graph (Fig. 5) as stars at XFe ˆ 0 and XFe ˆ 1. The solid line represents the maximum possible non-convergent order, Qmax , that the cummingtonite structure can achieve. t Since in our de®nition of Qt we choose to scale it with respect to the total amount of Fe, samples with XFe  2=7 can have any degree of order between zero and one, depending on their thermal evolution, and

Fig. 5 Variation with composition of the nonconvergent order parameter Qt that describes the order between M4 and the combined M1, M2 and M3 sites. The solid lines represent the maximum ideal order, with iron completely occupying the M4 site. The stars XFe ˆ 0 and XFe ˆ 1 represent the end members with Qt ˆ 0. Open square: Pnma natural sample; open circles: C2/m natural samples; ®lled circles: C2/m annealed samples; open triangle: P21/m natural sample; ®lled triangles: P21/m annealed samples; open diamonds volcanic natural samples; ®lled diamonds volcanic annealed samples; open downward triangles natural crystals from Hirschmann et al. (1994); ®lled downward triangles crystals annealed at 700 °C from Hirschmann et al. (1994); crosses MoÈssbauer data for natural and annealed at 700 °C by Seifert (1978) orthorhombic anthophyllites

therefore Qmax is always equal to one. When XFe > 2=7, t i.e. when the total Fe content is greater than the amount that can occupy completely the M4 sites, Qmax starts to t decrease until it reaches zero at the grunerite end. The di€erence between Qmax and the experimental Qt values t is a€ected, in the case of the natural samples, by the presence of Ca at the M4 site, which prevents complete Fe occupancy. The order parameters of the annealed samples follow the same trend as the order parameters calculated from data in the literature (Seifert 1978; Hirschmann et al. 1994) for crystals annealed at the same temperature, consistent with the view that, during the heating experiments, the equilibrium was reached. IR powder-absorption spectra IR powder absorption spectra of monoclinic natural samples are shown in Fig. 6 for the wavenumber region 50±1300 cm)1. Phonon bands can easily be followed across the solid solution at higher energies, whereas at

Fig. 6 Infra-red powder-absorption spectra recorded at room temperature for natural monoclinic cummingtonites as a function of composition. A spectrum of one of the volcanic samples studied is reported at the bottom of the ®gure. Line-broadening, due predominantly to a higher impurity content, can be observed in the latter

95

lower energies the changes in absorbance and peak position are not as easy to follow, although they still appear systematic. The spectrum of one of the two volcanic samples studied is shown at the bottom of Fig. 6 for comparison. Broadening of all the absorption bands is clearly visible in the latter. Comparisons of the spectra of natural and annealed Mg-rich and Fe-rich cummingtonites are shown in Fig. 7. The annealed sample of Mg-rich cummingtonite has P21/m symmetry. Its spectrum includes, in particular, peak splitting at 700 cm)1, the appearance of a small peak at 750 cm)1 and a change in the intensity ratio for the vibration bands at 1000 cm)1 with respect to the spectrum of the natural cummingtonite. In contrast, no changes are visible between the two spectra of the Ferich sample. The IR spectra of the orthorhombic Pnma samples are reported in Fig. 8. A spectrum of P21/m cummingtonite is shown at the top of Fig. 8 to stress the close similarity among the vibrational modes of the two structures, especially at the highest wavenumbers. Details of the lowest energy bands are shown in Fig. 9. Line widths and absorbances of the 140 cm)1 phonon line are practically constant for the Fe-rich amphiboles, whereas for Mg-rich monoclinic and orthorhombic samples they clearly depend on the degree of order. O-H stretching vibrations

amphiboles show only a single sharp band in this spectral region, the spectra of intermediate samples are more complex, due to cation substitution at the sites coordi-

Fig. 8 Infrared powder-absorption spectra recorded at room temperature for natural orthorhombic samples. The IR spectrum of a P21/m cummingtonite (top of the ®gure) presents features very similar to those observed in the spectra of the orthorhombic structures

The fundamental bands of the O-H stretching vibration occur in the spectra of amphibole between 3600 and 3700 cm)1 (Hawthorne 1981). Whereas end-member

Fig. 7 Infra-red powder-absorption spectra recorded at room temperature for natural (dotted lines) and annealed (solid lines) cummingtonites. Note that the IR spectrum of the annealed Mgrich sample has P21/m symmetry. There are no visible di€erences between the spectra of the Fe-rich annealed and natural cummingtonites

Fig. 9 Details of the lowest wavenumber vibrational band of the IR spectra of natural and annealed samples. This phonon line varies systematically with composition. Broadening of the phonon lines can be observed only for the annealed samples of Mg-rich cummingtonites

96

nated by the hydroxyl ion. In the case of cummingtonite there are eight possible ways of distributing Mg and Fe+2 over the three M sites (two M1 and one M3) coordinated by the hydroxyl group; however, their pseudo-trigonal arrangement introduces an accidental degeneracy to some bands, reducing the number of resolvable vibrations to four (Burns and Strens 1966; Hawthorne 1981). The O-H stretching region of natural (C2/m) and annealed (P21/m) 118125 sample is shown in Fig. 10. Only three of the expected four vibrational bands are observed in the spectrum of the natural cummingtonite because the probability of having a Fe+2 Fe+2 Fe+2 con®guration at the three M sites for this Mg-rich composition is practically negligible and therefore the lowest energy band which corresponds to this con®guration is not detected. In the P21/m phase the hydroxyl groups are not all equivalent, as in the highsymmetry phase, and splitting of the three stretching modes is observed in the spectrum of the annealed sample. Further investigation is being undertaken in order to correlate such peak splitting with the evolution of the displacive phase transition.

in previous studies (Kukovskii and Litvin 1970; Barabanov et al. 1974; Ishida 1990a, b). Here, we are only interested in distinguishing between vibrational modes at high energies (600±1300 cm)1), dominated by the vibrations of the tetrahedral chains, and lattice modes dominated by the vibrations of the cations in the octahedral cages. Following the literature assignments, the peaks numbered 1, 2, 3 and 4 in Fig. 6 correspond to Si-O vibrations (Fig. 11). Of these, only peak 2 varies linearly as a function of composition with a visible jump and change in slope of the data for the orthorhombic samples. The other vibrational modes are, instead, practically constant with respect to Mg/Fe substitution. Moreover, the Si-O peak positions do not depend on the degree of cation order nor are they sensitive to the C2/m ® P21/m phase transition. Also, the peak positions of the vibrational modes 7, 8, 9 and 10 vary simply as a function of composition (Fig. 12), with visible di€erences only between orthorhombic and monoclinic samples.

Wavenumber shift The wavenumber variations of the peaks numbered in Fig. 6 have been obtained using a computer routine which identi®es peak maxima by analysing the ®rst and second derivatives of the absorption signals. Such peaks have been chosen because they can be easily followed across the solid solution. Assignment of the vibrational bands of IR powder spectra of amphiboles has been done

Fig. 10 O-H stretching vibrations of natural C2/m and annealed P21/ m 118125 sample. Note the splitting of the absorbance bands due to the lowering of the symmetry

Fig. 11 Wavenumber shifts as a function of composition of the phonon bands at highest energies, dominated by the tetrahedral vibrations. Open squares: Pnma natural samples; ®lled squares: Pnma annealed samples; open circles: C2/m natural samples; ®lled circles: C2/m annealed samples; open triangle: P21/m natural sample; ®lled triangles: P21/m annealed samples; open diamonds volcanic natural samples; ®lled diamonds volcanic annealed samples. The size of the symbols is of the order of the uncertainties. Only peak 2 shows a linear correlation with composition, whereas the others are practically constant as the cation substitution occurs. These peak positions are not sensitive to the degree of cation order

97

Fig. 13a, b Wavenumber shifts as a function of composition of the vibrational bands dominated by bending of the tetrahedral chains. a Peak 5 depends on the non-convergent cation ordering but not on the displacive phase transformation. b Peak 6 splits into two peaks in the spectra of primitive cummingtonite and orthorhombic anthophyllites. Symbols as in Fig. 11. The solid lines shown are guides to the eye. The dotted line shows the nonlinear behaviour of the data of C2/m natural samples

Fig. 12 Linear shifts of the phonon bands in the spectral region 100± 700 cm)1. Symbols as in Fig. 11. Data for ordered and disordered samples plot on the same trend

Structural changes due to cation ordering and the displacive phase transition can be de®ned by the wavenumber shifts of peaks 5 and 6, respectively (Fig. 13a, b). Peak 5, assigned by Ishida (1990a, b) to a Si-O-Si stretching mode, has two di€erent trends for natural and annealed Mg-rich cummingtonites (Fig. 13a). Peak 6, assigned by Ishida (1990a) to OH librational vibrations, is one phonon line in the C2/m amphibole spectra but splits into two peaks in the spectra of primitive cummingtonites and orthorhombic anthophyllites (Fig. 13b). To quantify the peak splitting, the simple computer routine was considered inadequate due to peak overlap. Instead, the absorption signals of the P21/ m samples have been analysed by ®tting two Lorentzian pro®les (Salje and Bismayer 1997). The splitting of the peaks in the P21/m structure increases with increasing Q and is expected to scale with Q2 . Although the uncertainties of these peak positions are clearly large, the linear ®t shown in Fig. 13b gives a critical composition (0.60 XFe) relatively close to that found from the analysis of the structural parameters. One of the two

peaks in the orthorhombic structure follows the trend of the P21/m annealed data, whereas the other peak shift changes in slope with respect to the P21/m values. Autocorrelation analysis The autocorrelation function has been used in previous studies (Malcherek et al. 1995; Bo€a Ballaran et al. 1998, 1999; Atkinson et al. 1999) in order to quantify the variation of an e€ective line width of the phonon bands in a given spectral range and to avoid more or less arbitrary peak-®tting methods. This approach and its validity have been described in detail by Salje et al. (2000). In the present study, Dcorr values have been calculated for four di€erent ranges of each amphibole spectrum: 800±1200, 600±800, 320±580 and 100±250 cm)1. The results are shown in Fig. 14a±d. A common feature of the di€erent plots is that there is an evident broadening of the phonon lines in the IR spectra of Mg-rich annealed samples with decreasing cation order. The Dcorr values of C2/m amphiboles have practically a linear behaviour, except for the values calculated for natural samples in the region 320±580 cm)1. The Dcorr values decrease when the C2/m ® P21/m phase transition occurs, and the data for primitive cummingtonites are

98

close to the values obtained for the orthorhombic samples. As already observed in Fig. 9, the line width of the lowest energy band (Fig. 14d) is practically constant for the natural samples in spite of their space group, but

there is a signi®cant dependence on the degree of nonconvergent order for Mg-rich cummingtonites.

Discussion A description of the cummingtonite±grunerite solid solution must take into account the several variables that characterise the system: cation substitution and ordering, as well as displacive and reconstructive phase transitions. From a spectroscopic perspective, all the phonons of each recorded spectrum are a€ected to a greater or lesser extent by some or all these variables. At least qualitatively, however, it is possible to describe the di€erent e€ects separately. Cation substitution and disordering are known to give rise to local structural heterogeneities, causing linebroadening of the IR spectra. Some sharpening of the phonon lines of the Pnma and P21/m samples with respect to the C2/m crystals can also be expected, following the hypothesis that variations in line widths in IR spectra and variations in enthalpy are related (Bo€a Ballaran et al. 1998; Atkinson et al. 1999; Bo€a Ballaran et al. 1999; Carpenter et al. 1999). Mechanisms of solid solution formation

Fig. 14a±d Variation with composition of the Dcorr values obtained for the spectral intervals: a 800±1200 cm)1, b 600±800 cm)1, c 320± 580 cm)1, d 100±250 cm)1. Symbols as in Fig. 11. The solid lines are guides to the eye. The evolution of the Dcorr values of natural and annealed C2/m samples in the spectral region 320±580 cm)1 appear to be non-linear, suggesting a small degree of non-ideality of the C2/m solid solution. The Dcorr values of P21/m cummingtonites are lower than those of the C2/m samples and close to the values of the Pnma crystals. Note that the natural sample 118125 (XFe ˆ 0:36), although it has C2/m symmetry at the X-ray length scale, appears to be locally P21/m since its Dcorr values are lower than expected. The two anthophyllites with highest Mg content are exsolved, and this might explain the scatter of the Pnma data

The variation in composition of phonon bands of monoclinic C2/m cummingtonites at high energy (Fig. 6) is easy to follow across the solid solution, in contrast with the more complicated changes in the IR spectra of clino and orthopyroxenes (Bo€a Ballaran et al. 1998). While the tetrahedra in the pyroxene structure may deform as cation substitution and order occur at the octahedral sites, the SiO4 tetrahedra in the cummingtonite structure are relatively rigid and remain practically unchanged across the solid solution (Fig. 1). Thus, the highest energy modes, dominated by the stretching of the Si-O bonds, show the same constant trend as a function of composition and degree of order (Fig. 11). The other analysed peak positions correlate linearly with composition (Figs. 11 and 12). The linear behaviour of the Dcorr values relative to the Si-O vibrations (Fig. 14a, b) for the centred monoclinic samples implies that there is no evidence for non-ideality, at least with respect to the Si-O vibrations. However, a slightly non-linear behaviour can be observed for the wavenumber shift of peak 6 of natural C2/m samples (Fig. 13b) and for Dcorr values at lower wavenumbers (Fig. 14c). This is consistent with the presence of some heterogeneities in the intermediate cummingtonites at a length scale of a few unit cells and, therefore, some small positive excess enthalpy of mixing. The e€ects of composition on the orthorhombic and primitive monoclinic structures are more dicult to compare, in that the anthophyllite samples used here contained either pervasive exsolution or stacking faults which also give rise to line broadening. In addition, P21/m

99

cummingtonites with di€erent composition also have di€erent degrees of displacive order, as de®ned by the displacive order parameter, Q. Nevertheless, simply considering the Mg/Fe substitution, without taking into account the di€erent space groups, we can conclude that the general behaviour of the solid solution is pure one-mode behaviour (for a description of one-mode vs. two-mode behaviour see Hofmeister and Chopelas 1991, and references therein). If we considered in particular the lowest energy region (Fig. 9) where the e€ect of two-mode behaviour is more likely to be observed, we can notice not only a smooth and continuous dependence of the wavenumber shift on composition (Fig. 12), but also no signi®cant line-broadening for natural samples (Fig. 14d). Thus, the structural and IR data all point to Mg/Fe mixing in the C2/m structure of the (Mg, Fe2+)7Si8O22(OH)2 amphibole solid solution as being close to ideal. Some small excess enthalpy of mixing might be anticipated, but the e€ects of cation ordering, the displacive transition and the reconstructive clino « ortho transition are expected to be greater. Mechanism of cation ordering Structural changes associated with Mg/Fe ordering among the di€erent crystallographic sites in the C2/m structure are very small. This might simply be due to the small variation of Qt in Fe-rich cummingtonites, however (Table 4 and Fig. 5). Changes in phonon wavenumber do not re¯ect changes in Qt (Figs. 11 and 12), except for the case of peak 5 (Fig. 13a). This peak displays di€erent trends for natural and annealed Mg-rich samples, and appears to be una€ected by changes in space group (note that the P21/m cummingtonites and the orthorhombic G18691 plot on the same trends as the C2/m samples). A plateau of peak position can be observed at the grunerite end in the plot of peak 5 against composition (Fig. 13a), as Mg atoms are incorporated into the structure of the end member. The plateau is reminiscent of the plateau observed in the transition temperature of the solid solutions, and its magnitude, in terms of composition limits, is expected to correlate inversely with the magnitude of the strain ®elds around the impurity atoms (Salje et al. 1991; Carpenter 1992; Hayward and Salje 1996; Carpenter et al. 1999). The expectation is that properties of a pure crystal such as a phase transition temperature, or, in this case, phonon frequency, will remain constant when a second component of a solid solution is added so long as the microscopic strain ®elds around the substituted atoms do not overlap. A plateau of transition pressure has already been observed at the grunerite end of the cummingtonite±grunerite system (Bo€a Ballaran et al. 2000), and its composition limits are the same (10% Mg) as those of the plateau of phonon position observed here. The interpretation is that strain ®elds associated with Mg substitution into the grunerite structure are on the order of, or less than, one unit cell.

Since for a non-convergent ordering process there are no symmetry constraints, a change in wavenumber, D t, due to non-convergent order is expected to be proportional to the local non-convergent order parameter, qt. There are insucient data to test this hypothesis but, for example, the variation shown in Fig. 13a could be described by t ˆ to ‡ D tmix ‡ D tord , where D tmix is the wavenumber variation due to changes in composition and D tord is proportional to qt . To progress further with a comparison of the microscopic order parameter, qt , and the macroscopic order parameter, Qt , it will be necessary to de®ne the variation of to with composition. From a macroscopic perspective, ordering between M4 and M1 and between M4 and M3, as described by Qt1 and Qt3 , are linearly dependent (Fig. 4a), but natural and annealed samples show slightly di€erent trends for Qt1 as a function of Qt2 (Fig. 4b). In other words, the coecient for coupling between Qt1 and Qt3 is constant, while an additional higher-order term might be needed to relate Qt1 and Qt3 to Qt2 . The ordering relationship may not be strictly linear in detail, but, to a ®rst approximation, the cation ordering can be represented in terms of just one order parameter, Qt , depending only on the cation distribution between M4 and the combined M1, M2 and M3. We can hypothesise that the local strain ®elds associated with order/disorder at the M4 sites, though small, are large enough to in¯uence the M1, M2 and M3 topology suciently to ®x the values of the three order parameters Qt1 , Qt2 and Qt3 . Thus, the MoÈssbauer technique, which is unable to discriminate among M1, M2 and M3 Fe occupancies in anthophyllite, cummingtonite and grunerite spectra (Bancroft et al. 1967; Hafner and Ghose 1971; Ghose and Weidner 1972; Seifert 1978; Yin et al. 1989), gives a reasonable description of the Mg/Fe distribution. An estimate of the magnitude of the enthalpy variation associated with the non-convergent ordering process might, in principle, be obtained by analysing changes in line broadening as given by Dcorr values. These are practically the same for natural and annealed C2/m cummingtonites (Fig. 14). A small increase in Dcorr is, however, observed for the annealed sample BM93400 (XFe ˆ 0.69), with respect to the natural crystals, in the spectral region 320±580 cm)1 (Fig. 14c). The C2/m solid solution in this spectral region appears to be not perfectly ideal, and the deviation from ideality increases slightly as the cation order decreases. For Mgrich cummingtonites, the increase in Dcorr as Qt decreases is much more evident in all the spectral regions, but it cannot be ascribed directly to the change in Qt because all the annealed cummingtonites with XFe < 0.5 have P21/m symmetry and a di€erent value of Q. There is, instead, a direct correlation between cation disorder and increase in the Dcorr values for the orthorhombic structure for which no displacive phase transition occurs. Increasing the Fe content in M1, M2 and M3 gives rise to more local structural heterogeneities in disordered anthophyllites than in disordered cummingtonites.

100

In order to calibrate the e€ect of the local structural heterogeneity on the enthalpy, it would be necessary to develop a model which includes elastic constants. This is beyond the scope of the present paper, but some indication of the magnitude of the change in enthalpy associated to the local distortion arising from cation ordering can be obtained empirically using the results of Seifert (1978). According to his analysis, a change in Mg/Fe order between a natural anthophyllite and the same annealed at 700 °C would give an enthalpy change on the order of 2.7 kJ mol)1. According to Fig. 14, this change corresponds to a change in Dcorr of 6±7 units for the orthorhombic sample G18691 (XFe ˆ 0.30) with no exsolution. For C2/m cummingtonites it is possible to obtain enthalpy changes associated to the cation ordering from the enthalpy of mixing values reported in Fig. 10 of Ghiorso et al. (1995). This gives an approximate scaling of the Dcorr values for calculating enthalpy changes associated with Mg/Fe mixing and ordering and with the displacive phase transition, if local elastic distortions are the principal source of enthalpy variations. Displacive phase transition As already observed, few geometrical parameters are sensitive to the displacive C2/m ® P21/m phase transition. The main structural e€ects are seen in hM4-Oi mean bond distances and in the O6-O5-O6 kink angle. There are also few changes between P21/m and C2/m samples of the peak position of most of the IR modes (Figs. 11 and 12); only peak 6 has a behaviour similar to that of the O6-O5-O6 angles (Fig. 13b). The splitting of peak 6 can be explained following the assignment of Ishida (1990a): the hydroxyl groups equivalent under C2/m symmetry can be distinguished in O3A-H and O3B-H in the P21/m phase and might have a di€erent librational energy. The lowering in symmetry is associated with a reduction in phonon line broadening (Fig. 14). The phase transition might be thought of as providing a mechanism for reducing structural heterogeneities which arise in the C2/m structure as Mg is substituted in the grunerite end member (Fig. 14). The P21/m samples are, in fact, as homogeneous as the orthorhombic structure, and both are locally more homogeneous than the C2/m structure at Mg-rich compositions. The linear trends of the geometrical parameters (Figs. 2 and 3) and the IR vibrational modes (Figs. 13, 14d) for the annealed primitive samples are consistent with a phase transition which is continuous in character. The data are insucient to de®ne the thermodynamic character unambiguously, but linear variation of wavenumber and line width with composition are consistent with second-order character (Q2 / XFe ). It is also possible to estimate a critical composition (XFe  0:57±0.58) below which the P21/m phase is stable with respect to the C2/m phase for samples having a degree of cation ordering established at 700 °C.

Reconstructive phase transition It is noticeable that exsolution textures due to the Ca substitution (Table 1) and local structural heterogeneities due to Mg/Fe disordering are more likely to produce visible line-broadening of the IR phonons of Pnma samples with respect to those of the C2/m samples. This suggests that, from a microscopic perspective, the orthorhombic structure appears less ¯exible than the monoclinic in accommodating the cation substitution and ordering. Although the Mg-anthophyllite is more stable than the monoclinic analogue at low temperatures, this apparent lack of ¯exibility of the orthorhombic structure might explain the transformation to monoclinic as the Fe substitution takes place. It is also interesting to note that the trend of line-broadening of IR bands, for wavenumbers >300 cm)1, correlates with the expected enthalpy variations even for the reconstructive Pnma « P21/m transition. Being stable at the lowest temperature, the Pnma structure is expected to also have the lowest enthalpy ± it appears also to have the lowest degree of local structural heterogeneity. Acknowledgements We thank H. Buckley (British Museum), P. Dunn (Smithsonian Institution), A. Ewart, G. Harlow (American Museum of Natural History), C. Klein, A. Pring (South Australian Museum), P. Robinson and C. Wilson for kindly providing the samples used in this study. We thank M. Ghiorso and G. Della Ventura for their reviews, which improved our paper. X-ray singlecrystal di€raction data were collected at the CNR (Centro di Studio per la Cristallochimica e la Cristallogra®a) Pavia (MURST project Relation between structure and properties in minerals: analysis and applications.). This work has been supported by the Natural Environment Research Council (grant no. GR3/10917).

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