J. Am. Ceram. Soc., 80 [4] 851–60 (1997)

High-Temperature, High-Pressure X-ray Investigation of Dicalcium Silicate Corinne Remy† and Denis Andrault ´ ´ ´ Departement des Geomateriaux CNRS-URA 734, Institut de Physique du Globe de Paris, 75252 Paris Cedex 05, France

Michel Madon ´ ´ ´ ´ ´ Laboratoire de Physique et Mecanique des Geomateriaux CNRS-URA 734, Universite de Marne-la-Vallee, 93166 Noisy le Grand Cedex, France

temperature;1–3,11 and finally a, the highest-temperature polymorph whose structure is still uncertain and has trigonal12,13 or hexagonal symmetry.14 The structures of all of these phases are built from isolated SiO4 tetrahedra. The differences come from the orientation of the SiO4 tetrahedra and the movements of calcium ions. Despite the numerous X-ray diffraction studies at elevated temperature, few papers include the investigation of all of the Ca 2 SiO4 polymorphs. Indeed, in most cases the starting material is either the g5,15 or the b form of Ca 2 SiO4 ,3,4 and because of the difficulty in reaching the highest temperatures, the a phase has scarcely been studied.2,16,17 It also appears that the thermal expansion data are not well-defined, in particular for a8H- and a-Ca 2 SiO4 . Authors generally report the unit-cell parameters or volume data only at selected temperatures.2–4 Furthermore, a great confusion still persists in the literature about the exact sequence of the pure Ca 2 SiO4 phase transformations with increasing temperature. The scheme usually proposed is that in Fig. 1 but other possibilities have been reported. For instance, another monoclinic form called a8m has been observed in the range 984–1252 K.19 Again, Sarkar suggested that a “transient phase” between g and a8L existed over the temperature range 1089–1183 K,5 and the existence of a cubic phase at temperatures higher than 1873 K was also mentioned.16 The characteristics of the starting material such as thermal history, impurities, or grain size appear to be important factors in determining this polymorphic phase transformation scheme. On the other hand, there has been relatively little highpressure research on Ca2 SiO4 until now. High-pressure data such as bulk moduli or axial compressibilities are absent. Moreover, some studies have revealed that g-Ca2 SiO4 transforms to b-Ca 2 SiO4 by cold compression,20–22 but no X-ray diffraction patterns collected from in situ high-pressure experiments and showing the progressive conversion were presented. In this study, powder X-ray diffraction experiments, at high temperature or high pressure and starting from well-characterized g and b polymorphs, are reported. The purpose of this work is (1) to measure the temperature dependence of the thermal expansion of each Ca 2 SiO4 polymorph, (2) to measure compressibility of g-Ca 2 SiO4 and estimate that of b-Ca 2 SiO4 , and (3) to reconsider the sequence of phase transformations on

Energy-dispersive X-ray powder diffraction experiments have been investigated at high temperature and room pressure, and at high pressure and room temperature, starting from either g- or b-Ca 2 SiO4 . High-temperature studies were performed up to 1980 K, using a versatile heating cell. The high-temperature phase transformations previously described were reexamined. Volume and linear thermal expansions were measured for each Ca 2 SiO4 polymorph, g, b, a*L , a*H , and a. Volume thermal expansion increases with increasing temperature except for a*H , whose thermal expansion tends to decrease at elevated temperature. Highpressure investigations were performed in the 0–15 GPa pressure range, using a diamond anvil cell, with silicon oil as the pressure-transmitting medium. The value of the roompressure bulk modulus K 0 , assuming a second-order Birch– Murnaghan equation of state with K*0 5 4, is 140(8) GPa for g-Ca 2 SiO4 . The g olivine form exhibits anisotropic compression, with the c axis as the most compressible. From such in situ high-pressure X-ray investigations, the g- → b-Ca 2 SiO4 phase transformation induced by cold compression is clearly evidenced and extends from 2 to about 5 GPa. I. Introduction ICALCIUM SILICATE (Ca 2 SiO4 ) is one of the most important constituents of Portland cement clinker and has therefore been extensively studied. Previous high-temperature X-ray investigations have demonstrated the existence of at least five polymorphs of Ca 2 SiO4 :1–5 g, thermodynamically stable under room conditions, with the orthorhombic olivine type of structure;6–8 b, a metastable monoclinic phase under room conditions;9,10 a8L and a8H orthorhombic phases stable at higher

D

P. K. Davies—contributing editor

Manuscript No. 191951. Received March 15, 1996; approved October 8, 1996. Based in part on the Ph.D. thesis by C. Remy in materials science, University of Paris VI, Paris, France, 1995. Supported in part by CNRS (URA 734). ´ ´ ´ † Present de Physique et Mecanique des Geomateriaux, ´ address: Laboratoire ´ Universite de Marne-la-Vallee, 93166 Noisy le Grand Cedex, France.

Fig. 1. Sequence of Ca 2 SiO4 phase transformations. After Niesel.18

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heating and show through in situ high-pressure studies the progressive g- → b-Ca 2 SiO4 phase transformation induced by static cold compression. II. Experimental Procedure The starting materials used in the high-temperature and highpressure X-ray diffraction experiments were the g and b forms of Ca 2 SiO4 . Powder samples were synthesized by solid-state reaction. Pure reagent oxides CaCO3 and SiO2 from Prolabo were intimately mixed in 2:1 stoichiometric proportion, both previously dehydrated at 823 and 1373 K, respectively. The g phase was obtained by slowly heating the mixture up to 1823 K and cooling was performed at the rate of 400 K/h. In the case of the b polymorph, the mixture was slowly heated up to 1473 K and quenched into water. Details of the sintering procedure are given elsewhere.23 The stoichiometry was verified by wetchemical analyses, and the reaction products were analyzed by X-ray powder diffraction and Raman spectroscopy, which confirmed that in both cases the final product was a single phase. X-ray data were measured using a powder diffractometer (with an internal standard) and CuKa radiation monochromated with graphite. The indexing of the patterns was effected by the use of JCPDS cards, and the cell parameters, refined with a least-squares method, are with the standard ˚ in good agreement ˚ ˚ A , c 5 11.227(2) data: 6–10 a 5 5.082(1) A, b 5 6.765(1) ˚ ˚ A for the g phase and a 5 5.504(1) A, b 5 6.753(1) A, c 5 ˚ 9.301(2) A, and b 5 94.56(2)8 for the b phase. The powder X-ray diffraction experiments were performed in an energy dispersive configuration, on the wiggler line of the DCI storage ring at the Laboratoire pour l’Utilisation du Rayonnement Electromagnetique (LURE) in Orsay, France. The diffracted beam was analyzed with a Canberra planar germanium detector at 2Q angles varying from 9.88 to 12.28 for energies ranging between 5 and 50 keV. The resolution was about 150 eV at 20 keV. In both cases, high-temperature or high-pressure experiments, the diffraction pattern collected under room conditions was used to determine the diffraction angle, taking into account the indexed d-spacings measured from the X-ray experiments performed on the starting materials, with a powder diffractometer. The indexing of the diffraction patterns (recorded at high temperature or at high pressure) was based on previously published data and JCPDS cards.2 The crystallographic axes for b-Ca 2 SiO4 have been chosen as follows: a , b , c, in accordance with the crystallographic convention for the monoclinic system (the b axis is the highestsymmetry axis), and they have been defined consequently in the orthorhombic g, a8L , and a8H phases so that equivalent axes bear the same label. Final values of the unit-cell parameters were refined with a standard least-squares method, which also gives an estimate of the standard deviation in those parameters. High-temperature experiments were performed using a heating cell described in detail elsewhere.24 Starting material was finally ground (1 mm mean size) and pressed into the 400 mm hole drilled at the center of a flattened area of a Pt 90%–Rh 10% wire. Temperatures were measured from the calibration curve obtained by reporting a series of melting points, well known for some silicates and salts, as a function of the power dissipated in the heating wire. Accuracy of the temperatures is about 610 K. The X-ray diffraction patterns were collected on heating only, over 100 K intervals (30 K around the phase transformations), from room temperature up to 1980 K. Indeed, strong orientation effects resulting from extensive recrystallization occurred on cooling from elevated temperature and spectra could not be interpreted. Acquisition times were about 6 min for the a phase, 8 min for the g, a8L , and a8H phases, and 12 min for the lowersymmetry b phase. High-pressure experiments were performed using a membrane-type diamond-anvil cell with 600 mm culet anvils.25 Fine-grained powder (1–5 mm sized) of g- or b-Ca 2 SiO4 was imbedded in the 200 mm hole of a stainless steel gasket with silicon oil (dimethylpolysiloxane) as the hydrostatic pressure

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medium. In this device, the errors on pressure measurements do not exceed 10%. The pressure was calibrated before each data collection using the ruby fluorescence method. The X-ray diffraction patterns were collected from room pressure up to 6 GPa (over 0.3 GPa intervals) and 15 GPa (over 5 GPa intervals), starting from g- and b-Ca 2 SiO4 , respectively. Acquisition times ranged between 45 min and 1 h for each pattern. The quality of the diffraction patterns collected at elevated pressure was lower than for those recorded from high-temperature experiments. III. Results (1) High-Temperature Experiments (A) Diffraction Patterns: The X-ray diffraction patterns collected on heating agree with those previously reported by Regourd et al. for the Ca 2 SiO4 polymorphs.2 Starting from the g phase, the g → a8L phase transformation developed sluggishly above 1073 K. The g phase was mostly present at 1115 K. At 1143 K, the mixture of g- and a8L-Ca 2 SiO4 was still observed. Above 1173 K, a8L-Ca 2 SiO4 was the only phase present. With increasing temperature, the a8L → a8H transformation occurred between 1413 and 1443 K. In Fig. 2, selected X-ray diffraction patterns are presented showing the progressive transformation. The X-ray diffraction patterns associated with the a8L and a8H phases are very similar. The main difference is the presence of weak additional reflections ˚ in the a8L-Ca 2 SiO4 spectra at 3.578, 3.092, 2.711, and 2.177 A (d-spacing values at 1329 K), which progressively disappear at the a8L → a8H transformation, as also mentioned by Regourd et al.,2 who observed five additional ˚ weak lines (one more at 2.658 A, value at 1273 K). The a8L polymorph is generally considered a superstructure of the a8H phase and two possibilities of indexing have been proposed. First, a8L can be described by doubling the a and c parameters of the a8H phase.2,4,13 The other possibility consists of tripling the b parameter of the a8H phase.3,26,27 In this work, we label these phases a8L (2a,b,2c) and a8L (a,3b,c), respectively, and two kinds of indexing were possible. On further heating, the a8H → a phase transformation was detected between 1723 and 1753 K. A mixture of the two phases was still observed up to 1753 K. Only the a phase was present above 1773 K and persisted at the highest temperatures reached in this study (1980 K). Starting from the b phase, the same sequence of phase transformations was observed on heating. Selected X-ray diffraction patterns associated with b-, a8L-, a8H-, and a-Ca 2 SiO4 polymorphs are plotted in Fig. 3. The b → a8L conversion occurred between 984 and 1005 K, and conversion was complete at 1032 K. The a8L → a8H and finally a8H → a phase transformations could be detected at similar temperatures when starting from the g-Ca 2 SiO4 polymorph. (B) Unit-Cell Parameters and Molar Volume: The crystallographic data at various temperatures are listed in Table I for all of the Ca2 SiO4 polymorphs. The unit-cell parameters associated with the a8L phase are mentioned in two possible ways. At a given temperature, the same unit-cell parameters were measured for a8L-, a8H-, and a-Ca 2 SiO4 , starting from either g- or b-Ca 2 SiO4 . These experimental data are consistent with some of the previous X-ray diffraction studies.2,4 The agreement, however, is less good with Saalfeld’s report,3 probably due to the lower accuracy of his measurements made with oscillation and Weissenberg photographs. The temperature dependence of the molar volume of the different Ca 2 SiO4 polymorphs is summarized in Table II. They are fitted by a second-order polynomial except for the a phase where a linear law is more acceptable, due to the narrow hightemperature range studied. The molar volume and unit-cell parameters of the Ca2 SiO4 polymorphs as a function of temperature are plotted in Fig. 4 and Figs. 5 and 6, respectively. Although there is some evidence for a superstructure in the a8L phase, the parameters of the simplest unit-cell are reported in Fig. 5, for the sake of graphical

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Figure 4 illustrates the large volume decrease across the g → a8L transformation, transformation which is also characterized by an increase of the a parameter and a marked decrease of the c parameter compared to the continuous b value, as plotted in Fig. 5. On the other hand, only small variations can be detected across the b → a8L phase transformation. However, the discontinuity observed in the evolution of the b angle (Fig. 6) clearly evidences the conversion into the orthorhombic structure. Also reported in Fig. 4, is the volume variation (about 12%) between the g- and b-Ca 2 SiO4 polymorphs at room conditions. The b axis, however, is preserved between the two structures. It is also preserved when the conversion into a8L occurs, starting from gor b-Ca 2 SiO4 (Fig. 5). Note finally that a8H-Ca 2 SiO4 is characterized by a pronounced curvature in the evolution of the molar volume compared to the other Ca2 SiO4 polymorphs (Fig. 4). (C) Thermal Expansion: The temperature dependence of the volume thermal expansion defined by a5

1 ­V V ­T

1 2

(1)

P

was measured for all of the Ca 2 SiO4 polymorphs. First, linear laws with temperature are proposed in Table III, except for a because of the narrow temperature range studied. The variations of the thermal expansion of both g- and b-Ca 2 SiO4 with temperature are rather similar. For a8L-Ca 2 SiO4 , the thermal expansion is approximately constant or increases slightly in its stability field. The thermal expansion of a8H-Ca 2 SiO4 decreases with increasing temperature. An average value of the volume thermal expansion is also given in Table III for all of the Ca 2 SiO4 polymorphs, to compare our results with those of previous investigators which give volume data only at distinct temperatures.3,4,28 It is defined by am 5

1 V 2 V0 V0 T 2 T0

1

2

(2)

with V0 , molar volume at T0 . The thermal expansions of both gand b-Ca 2 SiO4 are consistent with previous results (Table III). In contrast, strong discrepancies are observed for the a8L polymorph. Our data, however, are compatible with those of Barnes et al.4 The mean thermal expansion value increases from g, which is thermodynamically stable under room conditions, to a, which forms at the highest temperatures, except for a8H , whose average value is lower than that of a8L . Furthermore, one can compare thermal expansion of the two polymorphs which exist under room conditions, g- and b-Ca 2 SiO4 : the thermal expansion of g is lower than that of b. To complete this study, linear thermal expansions in the principal crystallographic directions Fig. 2. Selected energy dispersive X-ray diffraction patterns collected on heating, starting from g-Ca 2 SiO4 , and showing the progressive a8L → a8H phase transformation. Arrows underline weak peaks characteristic of the a8L polymorph. Indexing reported for a8L is related to a8L (2a,b,2c).

continuity. For the same reason, an orthohexagonal cell equivalent to the trigonal/hexagonal cell of the a phase was defined. The correspondence between the parameters is a o 5 a h , b o 5 c h , c o 5 Î3b h ; the subscripts h and o denote the hexagonal (trigonal) and orthorhombic structures, respectively. From Figs. 4 and 5, it is apparent that g-Ca 2 SiO4 is different from the other polymorphs and there is some evidence that b-, a8L-, and a8H-Ca 2 SiO4 have closely related structures because of the continuous evolution of the molar volume and unit-cell parameters with temperature. Discontinuities in the molar volume and a and b unit-cell parameters observed at the a8H → a transformation (strong increase of b 0 and decrease of a 0 , parameters associated with a) show that the a polymorph is somewhat different.

aa 5 ab 5 ac 5

1 ­a a ­T

1 2

1 ­b b ­T

1 2

1 ­c c ­T

(3a)

P

(3b)

P

1 2

(3c)

P

of the five Ca 2 SiO4 polymorphs are reported in Table IV and average values are compared with Forest’s study.28 (2) High-Pressure Experiments (A) Diffraction Patterns: Selected diffraction patterns, collected under pressure, which characterize the compression of g-Ca 2 SiO4 are reported in Fig. 7. No change is detected before 2 GPa except the shift of the g-Ca 2 SiO4 reflections due to the compression of this structure, and the progressive increase in the line width of the peaks. Above 2 GPa, the X-ray diffraction patterns exhibit new peaks of weak intensity, which cannot be indexed as g-Ca 2 SiO4 . These new reflections can be

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Fig. 3. Selected energy dispersive X-ray diffraction patterns collected on heating, starting from b-Ca 2 SiO4 .

˚ ˚ attributed to the b polymorph [103 (2.789 A) and 112 (3.042 A) reflections, d-spacing at room conditions]. The intensity of these new peaks increases at higher pressure. In an energy dispersive configuration, the relative intensity of peaks varies rapidly from one pattern to another. However, one can observe the progressive decrease in intensity of the peaks with increasing pressure˚ which can only ˚ be indexed ˚with the g structure ˚ [103 (3.013 A), 222 (1.911 A), 012 (4.325 A) and 110 (4.066 A), d-spacing under room conditions], whereas the intensity ˚of other peaks characteristic of the b polymorph [031 (2.185 A) ˚ and 021 (3.169 A)] increases. At 3.4 GPa, the g phase does not seem to be the most abundant. Note, in fact, that the severe overlap of X-ray diffraction peaks of both g- and b-Ca 2 SiO4 makes it difficult to quantify the proportion of each phase. At 5.2 GPa, the number of detectable reflections decreases but the X-ray diffraction pattern can be attributed to the b polymorph only. Thus, Fig. 7 clearly shows that the g- → b-Ca 2 SiO4 phase transformation is induced by cold compression. Starting from the b phase, few diffraction patterns as a function of pressure could be collected. However, as no highpressure X-ray data on this compound have been reported until now, it seems interesting to give an overview of the observations. No phase change was observed in the range from room

pressure to 15 GPa, as also mentioned by an in situ highpressure Raman spectroscopic study which demonstrates that b persists up to at least 24 GPa.22 (B) Unit-Cell Parameters and Molar Volume: The unitcell parameters and molar volume of the g- and b-Ca2 SiO4 phases at various pressures are listed in Table V. For the g phase, the unit-cell parameters were refined at pressures below 2.8 GPa. Above 2.8 GPa, the proportion of b-Ca2 SiO4 was too high and indexing of the reflections was not possible because of the severe overlap. The pressure dependence of the molar volume of g- and b-Ca 2 SiO4 phases is plotted in Fig. 8(A). The evolution of the unit-cell parameters of the g olivine phase as a function of pressure is also reported in Fig. 8(B). Unit-cell parameters vary smoothly as a function of pressure. (C) Compressibility: Based on the observed molar volumes with pressure, it was possible to derive the room-pressure bulk modulus K 0 at room temperature, using inversion fits with the following Birch–Murnaghan equation of state: 7/3

5/3

31 2 1 2 43

V0 3 P 5 K0 2 V

V0 2 V

2/3

11 2

V0 3 1 1 (K80 2 4) 4 V

24

21

(4)

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Table I. Unit-Cell Parameters and Molar Volumes of the Different Ca 2 SiO4 Polymorphs at Various Temperatures† T (K)

˚ a (A)

˚ b (A)

˚ c (A)

g, Pcmn6–8

298 536 921 1004 1115

5.082(1) 5.093(1) 5.108(1) 5.113(2) 5.120(3)

6.765(1) 6.785(1) 6.822(1) 6.829(2) 6.850(2)

11.227(2) 11.247(2) 11.283(2) 11.288(5) 11.294(5)

b, P21 /n9,10

298 508 649 835 938 984

5.504(2) 5.513(3) 5.519(6) 5.534(3) 5.544(5) 5.553(4)

6.753(2) 6.777(4) 6.785(4) 6.800(5) 6.810(7) 6.795(5)

9.301(3) 9.330(4) 9.351(6) 9.390(5) 9.403(6) 9.413(6)

a8L (2a,b,2c), Bm21 b 11 or Pmnb2,15 or Pcnb2

1005 1032 1260 1329 1382 1414

11.134(6) 11.140(4) 11.180(6) 11.196(2) 11.202(4) 11.202(4)

6.805(4) 6.825(3) 6.847(4) 6.849(1) 6.860(2) 6.861(2)

18.82(1) 18.79(1) 18.93(1) 18.990(4) 19.022(6) 19.048(4)

53.7(1) 53.7(1) 54.55(9) 54.81(3) 55.02(5) 55.10(5)

a8L (a,3b,c), P21 nb27 or Pmnb3

1005 1260 1329 1382 1414

5.565(4) 5.590(3) 5.599(1) 5.601(2) 5.601(2)

20.43(1) 20.54(1) 20.545(6) 20.58(1) 20.582(8)

9.412(7) 9.466(5) 9.495(2) 9.511(3) 9.524(3)

53.7(1) 54.55(9) 54.81(3) 55.01(6) 55.10(5)

a8H, Pmnb2,3

1445 1502 1553 1608 1689

5.605(1) 5.607(3) 5.607(3) 5.605(3) 5.611(5)

6.869(1) 6.875(3) 6.881(3) 6.891(3) 6.893(5)

9.537(1) 9.558(4) 9.563(4) 9.575(4) 9.575(7)

55.28(2) 55.47(7) 55.56(6) 55.68(7) 55.75(9)

a, P3m112,17 or P63 mc14

1774 1832 1895 1944

5.523(4) 5.531(3) 5.538(3) 5.543(2)

5.523(4) 5.531(3) 5.538(3) 5.543(2)

7.306(4) 7.322(4) 7.338(4) 7.351(4)

58.11(4) 58.41(3) 58.68(3) 58.89(2)

Polymorph

b (deg)

Vmol (cm3)

58.11(4) 58.50(4) 59.19(4) 59.33(6) 59.63(7) 94.56(3) 94.48(4) 94.32(5) 93.99(5) 93.75(5) 93.59(5)

51.88(4) 52.32(6) 52.57(8) 53.07(7) 53.33(8) 53.37(8)

† Values in parentheses represent estimated standard deviations. The space groups reported here correspond to our choice of crystallographic axes and may differ from those given in the original works.

Table II. Molar Volume Data as a Function of Temperature V (cm3) 5 f (T (K))

DT (K)

g

58.085 1 0.00137(T 2 273) 1 5.205 3 1027 (T 2 273)2

298–1073

b

51.827 1 0.00191(T 2 273) 1 4.527 3 1027 (T 2 273)2

298–973

a8L

51.212 1 0.00326(T 2 273) 1 1.377 3 10 (T 2 273)

2

1073–1373

a8H

44.842 1 0.01466(T 2 273) 2 4.899 3 10 (T 2 273)

2

a

51.117 1 0.00466(T 2 273)

Polymorph

27 26

1473–1693 1773–1973

V0 is the ambient pressure molar volume and K80 is the pressure derivative of the bulk modulus at room pressure. The quantity and resolution of the high-pressure data were not sufficient to determine K80 . Its value has thus been assumed to be 4, a value which is generally measured for compounds with the olivine structure (i.e., the g-Ca 2 SiO4 structure), for example, the forsterite Mg 2 SiO4 .29,30 This also permits one to simplify the Birch–Murnaghan equation for inversion fits. To a first approximation, this K80 value has been adopted for the b-Ca 2 SiO4 polymorph. The calculated bulk moduli are 140(8) GPa for the g olivine phase and 166(15) GPa for b. Axis linear compressibilities 1 ­a ba 5 2 a ­P

1 2 1 ­b b 52 1 2 b ­P

(5a)

T

b

(5b)

T

Fig. 4. Variation with temperature of the g-, b-, a8L-, a8H-, and a-Ca 2 SiO4 molar volume.

1 ­c bc 5 2 c ­P

1 2

T

(5c)

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Journal of the American Ceramic Society— Remy et al.

were also measured for the g olivine phase at room pressure: b a 5 1.25(10) 3 1023 GPa21, b b 5 1.70(10) 3 1023 GPa21, and b c 5 3.90(30) 3 1023 GPa21. The c axis has the highest compressibility, whereas compressibilities of the a and b axes are quite similar. IV. Discussion (1) Sequence of Phase Transformations with Increasing Temperature In this study, the sequence of phase transitions observed on heating is the same when starting from g- or b-Ca 2 SiO4 and agrees with previous investigations (for instance, Fig. 1).2,18 The phase transformation temperatures measured are also consistent

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with data found in the literature.1,4,6,31 From those results, three points may be underlined. First, several reports have mentioned the existence of an intermediate phase between g- and a8L-Ca 2 SiO4 on heating. Indeed, such a phase would exist in the temperature range 1089–1183 K,5 or 984–1252 K.19 With our experimental resolution limits, no transient phase could be clearly evidenced and it is observed that the a8L phase develops sluggishly over the temperature range 1073–1143 K, assuming that inhomogeneous temperatures over the powder grains are not too important. This work also strengthens the idea that additional reflections observed in the a8L-Ca 2 SiO4 X-ray diffraction patterns, when compared to the a8H phase, are superstructure lines. Indeed, in all of the runs performed, the a8L → a8H conversion is only characterized by the disappearance of several peaks of weak

Fig. 5. Variation with temperature of the g-, b-, a8L-, a8H-, and a-Ca 2 SiO4 unit-cell parameters.

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High-Temperature, High-Pressure X-ray Investigation of Dicalcium Silicate

Fig. 6. Variation with temperature of the b angle in the b- → a8L-Ca 2 SiO4 phase transformation.

intensity. The disappearance of the superstructure reflections above 1433 K was also observed by Regourd et al.,2 and Saalfeld.3 According to Saalfeld,3 a tilt mechanism of the SiO4 tetrahedra may account for the formation of this superstructure. However, the nature of these superstructures remains ambiguous. Indeed, both types of indexing, with a8L (2a,b,2c) or a8L (a,3b,c), were possible in this study. In contrast to those results, Barnes et al. pointed out that the additional reflections were still present above the transition temperature.4 Finally, the a phase was still present at the highest temperatures reached during the experiments (1980 K) and did not transform to a cubic form above 1873 K, as it has sometimes been observed.16 (2) Thermal Expansion In this study, volume and linear thermal expansions are given for each Ca 2 SiO4 polymorph. Excluding a8H-Ca 2 SiO4 , the mean

857

volume thermal expansion increase from g- to a-Ca 2 SiO4 may be attributed to the stability field temperature range of each polymorph. On the other hand, the higher molar volume of the g phase, which is about 12% greater than that of the b polymorph at room conditions, may explain why the thermal expansion associated with g-Ca 2 SiO4 is lower than that of b-Ca 2 SiO4 . The thermal expansion of the a8H phase exhibits a unique behavior and decreases linearly with increasing temperature (Table III). A similar trend was reported for the cubic b-cristobalite; for example, Swainson and Dove observe that the cubic lattice parameter increases on heating up to about 1273 K, but above this temperature the value of the lattice parameter remains constant.32 In this latter case, it is generally reported that two factors influence the thermal expansion: the expansion of the Si–O bonds, which gives rise to a positive contribution to the thermal expansion, and the rotations of the SiO4 tetrahedra as rigid units, which tend to decrease the volume. A similar explanation can be proposed for a8H-Ca 2 SiO4 . Indeed, Eysel and Hahn,14 and Smith et al.,6 described the a8H- → a-Ca 2 SiO4 transformation mechanism as implying rotation of half of the SiO4 tetrahedra so that their apices point in the opposite direction. These rotations may give a negative contribution to the thermal expansion. Note that the phase transformations occurring between the other Ca 2 SiO4 polymorphs (g and a8L , b and a8L or a8L and a8H ) only imply slight tilts of the SiO4 tetrahedra.6,14 (3) Volume Variation across the Phase Transformations A theoretical transition temperature at room pressure has been calculated for each phase transformation by solving DG 5 0, which characterizes the phase equilibria, with G the free energy defined by G(T) 5 G(T0 ) 1

E

T

2S(T8) dT8 (at constant pressure)

T0

(6) G(T0 ) 5 H(T0 ) 2 T0 S(T0 ) (H: enthalpy; and S: entropy) (7)

Table III. Volume Thermal Expansion as a Function of Temperature a 5 f (T(K))† (31025 /K)

Mean value (31025 /K)

DT (K)

Ref.

g

2.37 1 1.67 3 1023 (T 2 273)

3.09(30) 3.41

298–1073 298–948

This work 28

b

3.69 1 1.55 3 1023 (T 2 273)

4.28(40) 4.05 3.96

298–973 298–948 293–993

This work 28 4

a8L

6.39 1 8.61 3 1025 (T 2 273)

6.47(50) 3.53 10.68 6.53

1073–1373 953–1273 1073–1273 1043–1293

This work 28 3 4

a8H

25.3 2 1.68 3 1022 (T 2 273)

4.03(40)

1473–1693

This work

7.97(50)

1773–1973

This work

Polymorph

a †

a 5 (1/V)(­V/­T) P .

Table IV. Linear Thermal Expansion in the Principal Crystallographic Directions a a† (31025 /K)

a b‡ (31025 /K)

a c§ (31025 /K)

Mean value (31025 /K)

DT (K)

Ref.

g

0.88(10)

1.46(20)

0.75(10)

1.03 1.14

298–1073 298–948

This work 28

b

1.00(10)

1.25(10)

1.79(15)

1.35 1.35

298–973 298–948

This work 28

a8L

1.56(10)

1.34(10)

3.03(20)

1.98

1073–1373

This work

a8H

0

1.86(15)

2.34(15)

1.39

1473–1693

This work

a

2.16(15)

2.16(15)

3.68(20)

2.67

1773–1973

This work

Polymorph

a a 5 (1/a)(­a/­T) P . ‡a b 5 (1/b)(­b/­T) P . §a c 5 (1/c)(­c/­T) P .

†

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Journal of the American Ceramic Society— Remy et al.

Vol. 80, No. 4

For the b → a8L transformation, the volume increase calculated at the theoretical transition temperature (970 K) is very small, Vb 2 Va8L 5 0.18 cm3/mol. This change is in good agreement with previous investigations: 0.1728 or 0.19 cm3/mol.34 Despite this negligible volume increase, the transition may be considered as a first-order transformation and this confirms the study of Barnes et al.4 These authors observed a consistent evolution of the b angle up to the b → a8L transition, which was due to a gradual rotation of the SiO4 tetrahedra. Some earlier studies also reveal that this conversion involves rotation of the tetrahedra accompanied by the breaking of some Ca–O bonds.6,14 Across the a8L → a8H transformation, no volume change was detected. This indicates a second-order transformation and this result is also consistent with Barnes et al.’s observations.4 However, Barnes et al.’s4 results reveal a noticeable change in slope of the unit-cell parameters and volume graphs at 1393 K across the transition. In this present study, no change in slope is clearly evidenced (Figs. 4 and 5). According to Eysel and Hahn,14 only slight tilts of the SiO4 tetrahedra and small movements of the calcium ions take place, and the transformation is of the displacive type. The calculated volume increase across the a8H → a-Ca 2 SiO4 transformation at the theoretical transition temperature (1710 K) is Va 2 Va8H 5 2.02 cm3/mol, which indicates a first-order transformation. Eysel and Hahn designated this conversion as semireconstructive.14 As mentioned above, they described the transformation mechanism by involving a rotation of half of the SiO4 tetrahedra so that the apices point in opposite directions.

Fig. 7. Selected energy dispersive X-ray diffraction patterns under pressure, starting from g-Ca 2 SiO4 and showing the progressive g- → b-Ca 2 SiO4 phase transformation induced by cold compression. Stars show peaks characteristic of the g phase which disappear with increasing pressure, and arrows, those characteristic of the b phase.

Coughlin and O’Brien’s thermochemical data (enthalpies, entropies, and heat capacities) have been used.33 The calculated phase transition temperatures give systematically lower values compared to the experimental temperature data reported in this paper, but are in good agreement if we consider the measurements precision. The calculated volume variation at the theoretical transition temperature is thus an acceptable estimation. Starting from the g phase, the g → a8L transformation develops sluggishly over a large temperature range and the determination of a theoretical transition temperature was quite necessary in this case. The large volume decrease calculated at the theoretical transition temperature (1123 K) Vg 2 Va8L 5 5.54 cm3/mol indicates a first-order transformation, which is in agreement with earlier results. Indeed, it was classified as reconstructive by Eysel and Hahn,14 or semireconstructive by Smith et al.,6 and involves a change in the calcium coordination (6 for g, and 8 at least for a8L ) and a rotation of the SiO4 tetrahedra.

(4) Compression The bulk modulus K 0 has been measured for g- and b-Ca 2 SiO4 phases. The K 0 data for g-Ca 2 SiO4 , 140(8) GPa, are compatible with those generally measured for olivine compounds. For instance, K 0 values for monticellite (CaMgSiO4 ), forsterite (Mg2SiO4 ), and fayalite (Fe2SiO4 ), assuming a Birch– Murnaghan equation of state with K80 5 4, are 113,35 128,36 and 133 GPa,37 respectively. However, the general trend that K 0 V0 is roughly a constant for a given structure leads to a K 0 value of about 100 GPa for g-Ca 2 SiO4 .38 The high value of K 0 measured in this study for g-Ca 2 SiO4 compared to the general trend could be due to nonhydrostatic effects according to the scheme proposed by Meng et al.39 However, with the use of silicon oil as a hydrostatic pressure medium, such nonhydrostatic effects are negligible up to 10 GPa. Thus, another explanation may be the influence of the presence of b phase due to the progressive g- → b-Ca 2 SiO4 transformation starting from low pressure (around 2 GPa). Indeed, the large volume decrease (about 12%) produced across the phase transformation probably leads locally to a pressure decrease, lower than that measured. Thus, to compress the g structure which is still present, it is necessary to reach higher pressures than would be expected. As the bulk modulus characterizes the incompressibility of the structure, which is defined by K T 5 2V

­P

1­V2

(V: molar volume)

(8)

T

it clearly appears that the measured value for incompressibility may be overestimated because of the measured pressure. The bulk modulus K 0 associated with b-Ca 2 SiO4 was estimated to be about 166(15) GPa. Nonhydrostatic effects with increasing pressure cannot be ruled out in this case. However, the fact that the value of K 0 for b-Ca 2 SiO4 is higher than that for g is understandable because of the greater volume of g compared to that of b. Axial compressibilities were also measured for g-Ca2 SiO4 . The g polymorph exhibits compression anisotropy, the c axis being the most compressible (with our choice of crystallographic axes presented earlier). The axial compression ratios are (1.00:1.36:3.12) for this polymorph. Again, the significantly

April 1997

High-Temperature, High-Pressure X-ray Investigation of Dicalcium Silicate

859

Table V. Unit-Cell Parameters and Molar Volume of g- and b-Ca 2 SiO4 at Various Pressures†

†

˚ a (A)

˚ b (A)

˚ c (A)

Polymorph

P (GPa)

g, Pcmn6–8

0.0001 0.45 1.10 1.6 2.06 2.40 2.84

5.082(3) 5.081(4) 5.076(5) 5.075(5) 5.069(6) 5.067(6) 5.066(7)

6.765(4) 6.759(5) 6.753(5) 6.752(5) 6.741(7) 6.737(8) 6.732(8)

11.227(4) 11.213(11) 11.178(9) 11.150(9) 11.146(15) 11.125(20) 11.102(25)

b, P21 /n9,10

0.0001 4.6 10 14.7

5.504(5) 5.445(20) 5.407(10) 5.330(30)

6.753(4) 6.712(20) 6.642(10) 6.613(10)

9.301(6) 9.262(30) 9.108(30) 9.085(30)

b (deg)

Vmol (cm3)

58.11(8) 57.97(10) 57.69(15) 57.52(15) 57.34(20) 57.18(20) 57.00(25) 94.56(6) 94.69(20) 94.78(30) 94.86(35)

51.88(10) 50.79(50) 49.07(40) 48.04(50)

Values in parentheses represent estimated standard deviations.

Fig. 8. Variation with pressure of g- and b-Ca 2 SiO4 molar volume (A), and g-Ca 2 SiO4 unit-cell parameters (B).

greater compressibility of c compared to a is a general feature in silicate olivines.40 For instance, axial compression ratios for both silicate olivines,35 monticellite (CaMgSiO4 ) and forsterite (Mg2SiO4 ), are a:b:c 5 1.00:1.05:1.85 and 1.00:1.60:2.02, respectively. The high incompressibility of tetrahedra relative to octahedra may be the major cause of this phenomenon as suggested by Hazen.41 (5) Phase Transformation Induced by Cold Compression In situ high-pressure X-ray experiments show the progressive g- → b-Ca 2 SiO4 phase transformation induced by compression

at room temperature. The transformation is gradual and starts around 2 GPa. Hanic et al. indicate,20 from X-ray measurements on samples after pressure release, that the transformation begins around 1.7 GPa. A recent in situ high-pressure Raman spectroscopic study also reveals that the transition occurs between 1.9 and 2.1 GPa.22 The transition pressure measured in this present work is consistent with those previous investigations and demonstrates that the conversion extends over the pressure range 2–5 GPa. Note that the transformation of g into b requires only a small thermal activation, since it can be performed even at room

860

Journal of the American Ceramic Society— Remy et al.

temperature. Such a transformation can be related to the b- → g-Ca 2 SiO4 conversion which can occur totally or only partially on cooling from high temperatures. Two mechanisms have been proposed for this latter transformation: reconstructive14 or displacive.42,43 Our high-pressure experiments as well as those of Hanic et al.20 or Reynard et al.,22 all performed at room temperature, suggest that a mechanism with a low activation energy such as the displacive one is at least possible. Consequently, a strong relationship between the g-Ca 2 SiO4 structure and that of b may exist. V. Conclusion From in situ high-temperature powder X-ray experiments, all of the phase transformations occurring on heating, starting from g- or b-Ca 2 SiO4 , could be observed. Volume and linear thermal expansions were measured for each Ca 2 SiO4 polymorph, including a8H- and a-Ca 2 SiO4 , for which no available data existed until now. The decrease in a8H volume thermal expansion with increasing temperature may be explained by the rotation of half of the SiO4 tetrahedra, considered as rigid units, upon conversion into a-Ca 2 SiO4 which tend to decrease the volume. From in situ high-pressure powder X-ray experiments, axial compressibilities and bulk modulus of g-Ca 2 SiO4 were measured. The high incompressibility of the SiO4 tetrahedra may explain the compression anisotropy of this olivine. Moreover, the high K 0 value measured for g may be due to the presence of b-Ca 2 SiO4 , resulting from the progressive g → b phase transformation which occurs with increasing pressure, in the range 2–5 GPa. Acknowledgments:

C.R. thanks P. Richet for his help in the hightemperature experiments and his fruitful comments, and F. Guyot for his com` ments on this work. M. C. Sichere is acknowledged for the characterization by X-ray diffraction of the starting powders.

References 1 K. Niesel and P. Thormann, “The Stability Fields of Dicalcium Silicate Modifications” (in Ger.), Tonind.-Ztg., 91 [9] 362–69 (1967). 2 M. Regourd, M. Bigare, J. Forest, and A. Guinier, “Synthesis and Crystallographic Investigation of Some Belites”; pp. 44–48 in Proceedings of the 5th International Symposium on the Chemistry of Cement, Part I, Supplement Paper I-10 (Tokyo, Japan, 1968). Cement Association of Japan, Tokyo, Japan, 1969. 3 H. Saalfeld, “X-ray Investigation of Single Crystals of b-Ca 2 SiO4 (Larnite) at High Temperatures,” Am. Mineral., 60, 824–27 (1975). 4 P. Barnes, C. H. Fentiman, and J. W. Jeffery, “Structurally Related Dicalcium Silicate Phases,” Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr., 36, 353–56 (1980). 5 S. L. Sarkar, “Polymorphism of Dicalcium Silicate,” World Cem. Technol., [Jan.–Feb.] 20–33 (1980). 6 D. K. Smith, A. Majumdar, and F. Ordway, “The Crystal Structure of g-Dicalcium Silicate,” Acta Crystallogr., 18, 787–95 (1965). 7 R. Czaya, “Refinement of the Structure of g-Ca 2 SiO4 ,” Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem., 27, 848–49 (1971). 8 S. Udagawa, K. Urabe, M. Natsume, and T. Yano, “Refinement of the Crystal Structure of g-Ca 2 SiO4 ,” Cem. Concr. Res., 10, 139–44 (1980). 9 C. M. Midgley, “The Crystal Structure of b Dicalcium Silicate,” Acta Crystallogr., 5, 307–12 (1952). 10 K. H. Jost, B. Ziemer, and R. Seydel, “Redetermination of the Structure of b-Dicalcium Silicate,” Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem., 33, 1696–700 (1977). 11 K. Suzuki and G. Yamaguchi, “A Structural Study on a8-Ca 2 SiO4”; pp. 67– 72 in Proceedings of the 5th International Symposium on the Chemistry of Cement, Supplementary Paper (Tokyo, Japan, 1968). Cement Association of Japan, Tokyo, Japan, 1969. 12 M. A. Bredig, “Polymorphism of Calcium Orthosilicate,” J. Am. Ceram. Soc., 33, 188–92 (1950). 13 A. M. B. Douglas, “X-ray Investigation of Bredigite,” Mineral. Mag., 29, 875–84 (1952). 14 W. Eysel and T. Hahn, “Polymorphism and Solid Solution of Ca2GeO4 and Ca 2 SiO4 ,” Z. Kristallogr., 131, 322–41 (1970).

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