María Barrio

Philippe Négrier

Josep Ll Tamarit
email: jose.luis.tamarit@upc.edu.

Luis C Pardo

Denise Mondieig

Marı ´a Barrio

Philippe Negrier

Josep Ll

Tamarit

Universitat Polite

Multiple Crossed Isopolymorphism: Two-Component Systems CCl 4 + CBr 2 Cl 2 and CBrCl 3 + CBr 2 Cl 2 ; Inference of a Metastable Rhombohedral Phase of CBr 2 Cl 2

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Orientationally disordered (hereafter abbreviated by OD) crystalline phases show three-dimensional long-range order in respect to the molecular positions and extreme disorder in the orientational degrees of freedom of molecules at each lattice point. Such OD phases are typically found in "globular" compounds. 1,[START_REF] Parsonage | Disorder in Crystals[END_REF] The halogenomethane compounds, CX n Y m , (n, m ) 0, ..., 4; n + m ) 4; X, Y ) F, Cl, Br, I) are compounds formed by molecules of more or less globular shape, providing little steric hindrance for reorientational processes and, thus, giving rise to the existence of OD phases as introduced by Timmermans. 1 The phase relations as a function of temperature at normal pressure for the compounds of the aforementioned family seem, however, quite different on account of the difference in size of the chlorine and bromine atoms. [START_REF] Ohta | [END_REF][4][5][6][7][8][9] Another family, closely related to the halogenomethane compounds is that of methylchloromethane compounds, (CH 3 ) 4-n CCl n , n ) 1, ..., 4. The phase behavior of this family has been extensively studied. As for the OD state, they exhibit a polymorphic nature such that at least two OD forms are involved, the symmetry of which are rhombohedral (R) or cubic (FCC or SC). Upon cooling, compounds corresponding to n ) 2, 3, and 4 solidify into a cubic phase [FCC for n ) 3 and 4, and simple cubic for n ) 2], and then transform to an OD R structure with further cooling. When heated, phase R melts without passing back through the cubic phase. When cooling is limited so that the cubic phase is formed, the cubic phase melts. Then, the cubic phase is metastable with respect to the former R phase and behaves monotropically at ordinary pressure. The melting pressuretemperature curve of these compounds (n ) 2, 3, and 4) is rather convex, indicating that there should be no triple point involving liquid and R and cubic OD solid phases (at positive pressure), an evidence that we are dealing with a cubic metastable state at any pressure. 7,11,[23][24][25]32 This case, which is known as overall monotropic behavior, is schematized in the pressure-temperature (p-T) diagram of Figure 1a. For such a case, R-FCC-L triple point is invariably located in the negative pressure domain.

As for the remaining compound, n ) 1, only one facecentered cubic (FCC) OD phase is observed at normal pressure. Nevertheless, when polymorphism analysis is extended to the high-pressure domain, a new OD phase, which has been demonstrated to be of rhombohedral symmetry, appears in the positive pressure domain. 33,34 It means then that intermolecular interactions combined with steric conditions reach the necessary requirements to stabilize the R phase at high pressures. It should be noticed that the R-FCC-L triple point can make then a physical appearance in the positive pressure domain, as displayed in Figure 1c, or in the negative domain, as for n ) 1. 34 As for the halogenomethane CBrCl 3 compound, the enantiotropic behavior between a cubic (FCC) and R phases has been recently stated at ordinary pressure [START_REF] Ohta | [END_REF][4][5] and extension at highpressure has shown that pressure-temperature phase diagram belongs to the type displayed in Figure 1b. 6 This provides evidence for the disappearance of FCC phase at pressures higher than the triple point sharing liquid and R and FCC OD phases (31 MPa, 278.7 K). It should be emphasized that, first, according to the p-T diagram, the extrapolation of melting curve of the R phase at normal pressure gives the temperature at which R phase would melt if the FCC phase would not exist and, second, that such an extrapolated value falls in the temperature stability domain of OD FCC phase at normal pressure. It is obvious that depending on the thermodynamic properties of the OD phases, which all of them are a consequence of a balance between intermolecular interactions and steric conditions, an additional case, shown in Figure 1c, can appear. In such a case, the topology of the two-phase equilibria generates R-FCC-L and Or-R-FCC triple points (Or, being the low-temperature ordered phase) on the positive pressure domain (Figure 1c). This is in contrast to the previous case (Figure 1b) for which the triple point between the low-temperature ordered phase and the OD phases (FCC and R) falls at negative pressures (as for the CBrCl 3 ). 6 The polymorphism of CBr 2 Cl 2 at normal pressure has been studied by several methods. [START_REF] Ohta | [END_REF][4][5] The crystal structure of the low-temperature ordered form is monoclinic C2/c with Z ) 32 as inferred from neutron powder diffraction. 4 At 259 K, monoclinic phase transforms into an OD phase, the symmetry of which is FCC. The latter phase is stable up to the melting at ca. 294 K. [START_REF] Ohta | [END_REF] The crystal structures of the ordered and OD phases of CBrCl 3 were attempted by Binbrek et al. 4 They described the structure of the phase III of CBrCl 3 , from neutron powder diffraction, in terms of the C2/c space group with Z )32, on the basis of the hypothesis of the isostructural character with CBr 4 and CCl 4 . Thus, as far as the low-temperature ordered phases are concerned, for the three compounds involved in this work, CBrCl 3 , CBr 2 Cl 2 , and CCl 4 , all of them are isostructural (monoclinic C2/c, Z ) 32). This experimental fact enables the possibility of continuous formation of mixed crystals in such an ordered state.

Because the polymorphic behavior of CBr 2 Cl 2 at normal pressure does not display the existence of an OD R phase, we have explored the possibility of combining the results obtained for the binary systems sharing pure compounds displaying several of the described topological p-T phase diagrams to unravel the physical appearance of the rhombohedral phase, which seems to be a "common" possibility of these kinds of compounds concerning a spatial long-range ordering with orientational disorder.

This work is then mainly concerned with the manifestation of the metastable transitions for two-component systems (CCl 4 + CBr 2 Cl 2 and CBrCl 3 + CBr 2 Cl 2 ) sharing compounds displaying the phase behavior of the schemes depicted in Figure 1a (CCl 4 ) 35 and 1b (CBrCl 3 ) 6 to contribute to the understanding of the metastable behavior of a possible rhombohedral phase of CBr 2 Cl 2 at normal pressure by the influence of the stability at high-pressure. The phase behavior of the two systems is examined from the viewpoints of crystallography and thermodynamics. With regard to the thermodynamic analysis a main part is devoted to the phenomenon of crossed isopolymorphism. 23,36 The present paper underlines their importance and at the same time provides new experimental evidence.

To unravel the characteristics of the two-component systems we have then used three strongly complementary techniques, the differential scanning calorimetry, which enables us to characterize the phase transitions of the mixed crystals; the X-ray powder diffraction, which accounts for the lattice properties of each phase as well as assures the one-or two-phase domains in the binary systems; and, finally, the thermodynamic analysis of each particular system, which permits us to coherently rationalize the thermodynamic data, to account for the stability/ metastability of the phases and to derive the excess properties of the solid phases.

Experimental Section

2.1. Materials. The chemicals CCl 4 and CBrCl 3 were obtained from Across with purity of 99+% and 99%, respectively. They were used as received since the measured melting points agreed well with the ones reported earlier. [START_REF] Ohta | [END_REF]6 CBr 2 Cl 2 was obtained from Aldrich and fractionally distilled, the final compound showing a melting temperature which agrees with previous works.

Binary mixtures were prepared at room temperature, i.e., in the liquid state, by mixing the materials in the desired proportions.

Thermal Analysis.

A low-temperature equipped Perking-Elmer DSC-7 differential scanning calorimeter was used to conduct calorimetric measurements, performed with Perkin-Elmer high-pressure stainless-steel pans to prevent reaction with the container. Heating and cooling rates of 2 K'min -1 and sample masses around 15 mg were typically used.

X-ray Powder Diffraction.

High-resolution X-ray powder diffraction patterns using the Debye-Scherrer geometry and transmission mode were recorded with a horizontally mounted INEL cylindrical position-sensitive detector (CPS-120) made of 4096 channels (angular step ca. 0.029 °(2θ)). 37 Monochromatic Cu KR 1 (λ ) 1.54059 Å) radiation was selected by means of an asymmetrically focusing incident beam curved quartz monochromator. The generator power was set to 40 kV and 30 mA. Low-temperature measurements were achieved with a liquid nitrogen 600 series Cryostream Cooler from Oxford Cryosystems.

External calibration using Na 2 Ca 3 Al 2 F 4 cubic phase was performed to convert channels to 2θ degrees by means of cubic spline fittings to correct the deviation from angular linearity in PSD 38 and the peak positions were determined by pseudo-Voigt fittings. After indexing the patterns lattice parameters of the OD phases were refined while patterns of the low-temperature ordered phases were submitted to a Rietveld profile refinement by means FullProof program. [START_REF] Rodriguez-Carvajal | Laboratoire Le'on Brillouin[END_REF] Details of the procedure are given in Section 3.2.

Liquid samples were placed into 0.3 mm-diameter Lindemann capillaries at room temperature and were rotated perpendicularly to the X-ray beam during data collection to improve averaging of the crystallites. Acquisition times were around 60 min for measurements in the OD phases and no less than 120 min for the low-temperature ordered phases.

Results

Differential Scanning Calorimetry.

The thermodynamic properties of the phase transitions for the pure halogenomethane compounds are given in Table 1. At present only values corresponding to phase changes between phases denoted by the superscript (s), which correspond to the experimental available transitions, should be considered. Such values match quite well with previously reported values.

The reader must pay attention to some evidence, which will be of importance for the following sections describing the twocomponent systems. Both CCl 4 and CBrCl 3 compounds display stable OD phases with rhombohedral symmetry, while the OD FCC phase is stable for CBrCl 3 and metastable (but experimentally available) for CCl 4 . The OD stable phase for the compound CBr 2 Cl 2 has FCC symmetry.

The DSC output was used to establish the complete melting and solid-solid transition temperatures, as well as the concomitant heat effect, both as a function of composition. To determine the stable phase diagram, mixed samples were cooled from room temperature down to at least 180 K at 2 K'min -1 and heated back to room temperature. In fact, the information on the systems comes from combining X-ray diffraction as a function of temperature and composition, with differential scanning calorimetry, the former being detailed later.

In Figure 2 the characteristic temperatures of the two-phase equilibria are shown as a function of composition for both CCl 4 + CBr 2 Cl 2 and CBrCl 3 + CBr 2 Cl 2 two-component systems. The results of the enthalpy of the solid-solid-phase transitions and melting obtained for both systems are shown in Figure 3.

Experimental evidence shared by the two-component systems is the existence of continuous OD FCC mixed crystals. It should be noticed that such mixed crystals for the (CCl 4 ) 1-X (CBr 2 Cl 2 ) X two-component system can be classified into two different categories: (i) mixed crystals with molar compositions within the 0.40 < X < 1 composition range for which the phase transitions appearing upon cooling are liquid to FCC and FCC to R or to M, all of them being reversible and thus evidenced the enantiotropic relation between both OD phases in this composition range, (ii) for mixed crystals with molar composition lower than ca. 0.40, two phase transitions involving OD occur upon cooling while only one occurs upon heating back a The stable and metastable transitions are denoted by superscripts (s) and (m), respectively. M refers to the low-temperature monoclinic (C2/c) phase of CCl4, CBrCl3, and CBr2Cl2, and R and FCC for the rhombohedral and face-centered cubic OD phases. b The small disagreement (<5%) for the ∆H M-FCC value of this work to that obtained by means adiabatic calorimetry could be ascribed to the addition by the authors of ref 3 of some pretransitional effects appearing at the M to FCC transition as superimposed to the vibrational heat capacity in the monoclinic phase (see Figure 1 to room temperature. The sequence upon cooling (as revealed by X-ray diffraction measurements) is related to the liquid-FCC and FCC-R phase transitions. The R mixed crystals do not revert to the FCC phase upon heating back and only melting of the R phase is found. When cooling is limited such the FCC phase is formed, this phase melts upon heating without transformation to the R phase, as it occurs for the CCl 4 pure compound. Thus, the same monotropic behavior between R and FCC phases is found for that composition range of mixed crystals.

As far as mixed samples of the CBrCl 3 + CBr 2 Cl 2 system are concerned, it appears that the FCC mixed crystals are stable for the whole range of composition.

Another relevant fact (as we will demonstrate in the crystallographic section) is the existence of continuous formation of low-temperature monoclinic mixed crystals whatever the system. This makes evident the isomorphism relation between the lowtemperature ordered phases of all the compounds involved in this work and, confirms the results obtained by Binbrek et al., 4 who determined the structure of CBr 2 Cl 2 in terms of the C2/c space group by postulating that all the members of the CBr n Cl 4-n (n ) 0, ..., 4) were isostructural and assuming that the molecules are disordered so that sites have equivalent fractional occupancies for chlorine and bromine atoms.

According to the described thermal analysis measurements, the enthalpy changes associated with the melting of the FCC mixed crystals were measured continuously for the whole composition range in both binary systems (Figure 3). As far as the melting of the R mixed crystals is concerned, direct information is only obtained from the CCl 4 + CBr 2 Cl 2 system for the 0 < X < 0.40 composition range. In spite of such a limited availability, the complete variation of the melting enthalpy of R mixed crystals can be obtained by adding the heat of the R to FCC transition to the melting of the FCC mixed crystals. Such a calculation is based on the following equation: applied for φ ≡ R, γ ≡ L and R ≡ FCC. This equation assumes that the specific heats of both φ and R phases are close, as is the case for both OD FCC and R phases. In this way, extrapolation at X ) 1 of the melting enthalpy change of the R mixed crystals provides the heat effect associated with the melting of a virtual R (metastable) phase of the CBr 2 Cl 2 compound. The obtained value is ∆ R L H ) (2.36 ( 0.15)kJ'mol -1 . To end this section, we would like to point out that the extrapolation of the [R + FCC] two-phase equilibrium as well as the associated enthalpy change at X ) 1 (CBr 2 Cl 2 ) enables us to infer the characteristic values of a virtual transition between a metastable R phase to the stable FCC phase for the CBr 2 Cl 2 compound (T R-FCC ) 243.6 ( 2.0 K and ∆ R FCC H ) (0.436 ( 0.080)kJ'mol -1 ). Such value can be physically interpreted as the extrapolation at normal pressure of a high-pressure twophase equilibrium between R and FCC phases as indicated in Figure 1c. It should be noticed that the T R-FCC value falls into the temperature stability domain of the low-temperature ordered (monoclinic) phase ruling out the pressure-temperature daigram displayed in Figure 1d. It is also noteworthy that with increasing mole fraction of the [R + L] melting equilibrium of the CCl 4 + CBr 2 Cl 2 system would end (at X ) 1) at the nonexperimentally available melting temperature of phase R of CBr 2 Cl 2 , T R-L . Finally, with the same coherence as for the previous transitions, a M to R solid-solid transition (T M-R ) appears for the CBr 2 Cl 2 compound.

Crystallographic Characterization.

The isomorphism relationships between the isostructural phases have been shown by determining the continuity of the lattice parameters as a function of composition by means of X-ray powder diffraction studies at different temperatures.

3.3. Monoclinic Mixed Crystals. X-ray powder diffraction measurements were undertaken at 220.2 K for the monoclinic (C2/c, Z ) 32) mixed crystals in both two-component systems for several compositions. To carry out the analysis of the X-ray patterns of these "ordered" mixed crystals, we have performed a Rietveld profile refinement by means of Fullprof software. [START_REF] Rodriguez-Carvajal | Laboratoire Le'on Brillouin[END_REF] The process was successfully followed for the CCl 4 +CBrCl 3 mixed crystals in a previous work 8 and consists mainly on the procedure described by Binbrek et al. for pure compounds CBrCl 3 and CBr 2 Cl 2 . 4 As the starting configurations we used the atomic coordinates of the four molecules in the asymmetric unit of CCl 4 or CBrCl 3 (for the CCl 4 + CBr 2 Cl 2 and CBrCl 3 + CBr 2 Cl 2 mixed crystals, respectively). Fractional occupancies of the halogen sites were set according to the composition of the analyzed mixed crystal and molecules were represented by a rigid body with tetrahedral symmetry. Varying slightly the fractional occupancies around the values of the exact composition determined by the chlorine and bromine atoms participating in the mixed crystal did not result in a substantial decreasing of the related R-factors, precluding then a partial "ordering" of the mixed crystals in regard to the halogen disorder described for pure compounds. 4,8 Two representative examples of the experimental and calculated profiles for two mixed crystals (CCl 4 ) 0 51 (CBr 2 Cl 2 ) 0 49 and (CBrCl 3 ) 0 55 (CBr 2 Cl 2 ) 0 45 are given in Figure 4 together with that of the CBr 2 Cl 2 pure compound.

Following the same procedure for several mixed crystals with molar fractions distributed along the whole concentration range, the lattice parameters vs concentration were determined and are shown in Figure 5. The continuous variation of the lattice parameters with concentration establishes the existence of an isomorphism relationship between the low-temperature ordered phases of the three pure compounds involved, confirming the structural results found for CBrCl 3 and CBr 2 Cl 2 from neutron powder diffraction on the hypothesis that both compounds were isostructural to CCl 4 and CBr 4 . It is to be noticed that lattice parameters of both series of mixed crystals nicely converge at the same values for X ) 1, i.e., the CBr 2 Cl 2 pure compound. In addition, monoclinic lattice parameters of CBr 2 Cl 2 determined at 220. ∆H φfγ ) ∆H φfR + ∆H Rfγ (1) ranges for the enantiotropic or monotropic behavior as well as the limit of metastability for which FCC mixed crystals obtained by cooling from the liquid were clearly stated for the CCl 4 + CBr 2 Cl 2 system. Such a procedure enabled to measure at 241.2 K for the whole concentration range the variation of the lattice parameter vs mole fraction in the aforementioned system, with the exception of the pure compound CBr 2 Cl 2 for which the quoted value was obtained by extrapolation of the cubic parameter as a function of temperature. As for the CBrCl 3 + CBr 2 Cl 2 system, the OD FCC mixed crystals display a complete stable domain as regard to the composition, so they were crystallographically characterized in that region at 265.2 K. The results for both systems are shown in Figure 6. The continuity of both curves demonstrates the isomorphism relationship between the monotropic FCC of CCl 4 and the enantiotropic FCC phases of CBr 2 Cl 2 and CBrCl 3 .

3.4.2. Rhombohedral Mixed Crystals. In this case, Lindemann capillaries were cooled down to the stable low-temperature monoclinic phase and heated again up to the temperature at which the measurements were carried out. This path ensures that stable R mixed crystals are formed. Figure 6 shows the variation of the R lattice parameters as a function of the mole fraction at 243.2 and 253.2 K for the CCl 4 + CBr 2 Cl 2 and CBrCl 3 + CBr 2 Cl 2 systems, respectively. By assuming the existence of a metastable R phase for CBr 2 Cl 2 compound, it can be inferred that a "virtual" continuous series of mixed crystals in the R phase would give rise to an isomorphism relationship. The lattice parameters for that metastable R phase of CBr 2 Cl 2 compound can be obtained with more accuracy at 243.2 K from the extrapolation performed in the CCl 4 + CBr 2 Cl 2 system (a R (243.2 K) ) 14.772(15) Å, R R (243.2 K) ) 89.44-(2)°).

3.5. Thermodynamic Analysis Procedure. The purpose in this section is to bring together the experimental data of both systems and to subject them to a thermodynamic analysis. Next, we explore the possibility of combining the results obtained for each individual system to a coherent and unifying descrip- tion, in particular with regard to the inference of thermodynamic properties of a virtual R phase of CBr 2 Cl 2 compound.

3.5.1. Thermodynamic Formulation. We have reported in detail on the thermodynamic formalism we use in other works. 8,[23][24][25] Here, we repeat only the pertinent information for the sake of completeness. To follow the used thermodynamic analysis procedure, it is expedient then to describe the case referred to as crossed isopolymorphism 23,36 sketched in Figure 7. The form R is stable for component A, while the form β is stable for component B (β is metastable for A and R is metastable for B), γ being stable for both components. The "stable" phase diagram can be looked upon as the stable result of two crossing two-phase loops. The two crossing loops imply a stable three-phase equilibrium (R + β + γ), which, in the case of Figure 7, is peritectic.

Any phase φ we consider in which (1 -X) mole of component A mixes with X mole of component B, is characterized by its own Gibbs function where T stands for the thermodynamic temperature, R the gas constant, µ k *,φ (T), k ) A, B denote the molar Gibbs energies of the components, and G E,φ (T, X) denotes the excess Gibbs energy which accounts for the deviation of the mixture in the φ phase from ideal-mixing behavior produced by interactions between molecular species A and B with regard to the interactions between molecules of the same species (A-A and B-B).

To determine the two-phase equilibrium region between two phases (φ and γ), i.e., the concentration limits of the loop for the coexisting phases, the well-known equilibrium rule minimizing the Gibbs energy of the mixed crystal A 1-X B X at each temperature, which consists on the common tangent to both Gibbs energies characterizing the phases of the corresponding equilibrium, G φ (T, X) and G γ (T, X), must be determined. For this task, the molar Gibbs energies of the pure compounds A and B as well as the excess properties for each phase are required. Because of the lack of data on µ k *,φ , k ) A, B and φ ) R, β, γ the simplified treatment of the equal-Gibbs curve-(EGC-) method will be used. [START_REF] Oonk | Phase Theory: The Thermodynamics of Hetereogeneous Equilibria[END_REF] To do so, the difference between the Gibbs energies of phases φ and γ is written as where ∆ φ γ µ k / (T) is µ k *,γµ k *,φ (k ) A, B) and ∆ φ γ G E (T, X) is the excess Gibbs energy difference between the considered phases, i.e., G E,γ (T, X) -G E,φ (T, X).

Because the existence of equilibrium at a given temperature necessarily implies that the Gibbs functions of the φ and γ phases intersect, it follows that the locus of the points of intersection in the TX plane (the EGC) will be the result of this equation:

By neglecting the heat capacities differences between both phases, ∆µ k / (T) can be approximately written as

∆ φ γ S k / (T k φfγ - T), being T k
φfγ the temperature of the φfγ transition for the component k, the EGC temperature can be deduced from eq 4 as shown:

where ∆ φ γ H k / and ∆ φ γ S k / are the enthalpy and entropy changes of the φfγ transition for the component k. The first term of the right side of eq 5 represents the EGC temperature for the [φ + γ] equilibrium when the excess Gibbs energy difference is zero and is only pure component-dependent and thus can be obtained from pure component data. Nevertheless, some of the metastable G φ (T, X)

) (1 -X)µ A *,φ (T) + Xµ B *,φ (T) + RT[X ln(X) + (1 -X)ln(1 -X)] + G E,φ (T, X) (2) ∆ φ γ G(T, X) ) G γ (T, X) -G φ (T, X) ) (1 -X)∆ φ γ µ A / (T) + X∆ φ γ µ B / (T) + ∆ φ γ G E (T, X) (3) ∆ φ γ G(T EGC , X) ) 0 (4) T EGC ) (1 -X)∆ φ γ H A / + X∆ φ γ H B / (1 -X)∆ φ γ S A / + X∆ φ γ S B / + ∆ φ γ G EGC E (X) (1 -X)∆ φ γ S A / + X∆ φ γ S B / (5)
properties as heats of transition and transition points have to be obtained in an indirect manner when a crossed-isomorphism is considered.

A first estimation of the EGC curve can be done from the experimental data of the two-phase equilibrium. An iterative procedure performed by means of the WINIFIT program [START_REF] Daranas | Polythecnic University of Catalonia[END_REF] based on Oonk's method and on the well-known LIQFIT program [START_REF] Jacobs | A Computer Program for the Thermodynamic Assessment of T-X Liquidus or Solidus Data[END_REF] enables one to obtain reasonable values of the excess Gibbs energy differences at the EGC temperature by means of eq 5. More details on the computational procedure can be found in ref 45. Because of the lack of the thermodynamic excess properties of the liquid phase, only excess Gibbs energy differences (∆ φ γ G E ) have been determined. In this framework, the description of the excess Gibbs energy difference was given by a two-parameter function in the form of a Redlich-Kister polynomial which in the lack of strong local anomalies is fairly adequate and physically understandable: ∆ φ γ G 1 expresses the magnitude of the excess Gibbs energy difference at the equimolar composition and ∆ φ γ G 2 , gives account for the asymmetry of such a function with respect to X ) 0.5. In addition, we consider the ∆ φ γ G 1 and ∆ φ γ G 2 coefficients to be temperature-independent due to the small range of temperature in which two-phase equilibria exists.

The Simple [FCC + L] Two-Phase Equilibria.

In the case of the two-component systems analyzed here, the CBr 2 Cl 2 component displays a stable OD FCC phase, which according to the calorimetric and crystallographic characterization is isomorphous to the metastable OD FCC phase of CCl 4 and to the stable OD FCC phase of CBrCl 3 .

The temperatures and enthalpy changes corresponding to the FCC melting of the pure compounds (see Table 1), all of them experimentally available, and the temperature data of the equilibrium were used for the thermodynamic assessment. It results in the excess Gibbs energy differences expressed by the Redlich-Kister coefficients given in Table 2.

Crossed Isopolymorphism: [R + FCC], [M + R] and [M + FCC] Two-Phase Equilibria.

As for the equilibria involving R, FCC and M phases, the nonexistence of an OD R phase for the CBr 2 Cl 2 compound forces to an estimation of the thermodynamic properties of a such virtual phase (isomorphous to the R phase of both CCl 4 and CBrCl 3 compounds) for that compound. Such an estimation is performed by the metastable extensions of the [R + FCC] loops which ends (at X ) 1) in the theoretical metastable R to FCC transition point of the pure CBr 2 Cl 2 . Such estimation is nicely performed simultaneously for the two systems. As can be seen in Figure 8, extrapolations of the [R + FCC] loops converge into the same virtual temperature (T CBr 2 Cl 2 R-FCC ) 243.6 ( 2.0 K). As far as the associated enthalpy change ∆ R FCC H, extrapolation of the values for the R to FCC phase transition (see Figure 3), some of them being calculated from eq 1, provides, within the experimental error, a virtually equal value for both systems (∆ R FCC H ) 0.436 ( 0.080 kJ'mol -1 ).

It should be mentioned here that the R to FCC transition for the pure CCl 4 it is not experimentally available. Owing to the monotropic character of the FCC phase with respect to the R phase, such a transition would appear in the stability domain of the liquid phase. The properties of such transition were determined in some previous works 8,[START_REF] Barrio | [END_REF] and thus, details of the procedure to determine the temperature as well as the enthalpy change will be omitted here. Values are listed in Table 1.

The next step in the thermodynamic assessment of the twocomponent systems consisted on the evaluation of the required data for the analysis of the [M + R] equilibria. Experimental phase diagrams (Figure 2) make evident that composition extension of such equilibria are large enough to determine the temperature for the virtual M to R phase transition for the pure component With the temperature and enthalpy change calculated values together with the experimental solvus temperatures, the [R + FCC] and [M + R] phase equilibria were computed by using the crossed isodimorphism procedure.

As for the [M + FCC] equilibria, their relevance on the thermodynamic assessment is smaller than the previous ones. Thus properties of the virtual phase transitions as M to FCC for CCl 4 and CBrCl 3 were estimated according to the state function character of the enthalpy and entropy magnitudes. Once the described equilibria were calculated and the excess Gibbs a The [R + L] equilibrium does not make a physical appearance in the CBr2Cl2 + CBrCl3 two-component system, but excess Gibbs energy difference is given for completeness. energy differences between the involved phases determined, straightforward calculations were performed for the additional equilibria appearing in both phase diagrams. The obtained excess Gibbs energy differences in the form of Redlich-Kister polynomial coefficients are compiled in Table 2.

TABLE 2: ∆ R β G 1 ) G 1 β -G 1 R and ∆ R β G 2 ) G 2 β -G 2 R
CCl4 + CBr2Cl2 CBr2Cl2 + CBrCl3 equlibrium R β ∆ R β G1 J'mol -1 ∆ R β G2 J'mol -1 TEGC(X ) 0.5) K ∆ R β G1J'mol -1 ∆ R β G2 J'mol -1 TEGC(X ) 0.5) K [FCC + L] FCC L -
∆ φ γ G E (X) ) X(1 -X)[∆ φ γ G 1 + ∆ φ γ G 2 (1 -2X)] (6)
It should be noticed that an individual experimental temperature point may deviate from the mean trend to a maximum of about 1 K for the melting and [R + FCC] equilibria while and no more than about 2 K for the equilibria involving the lowtemperature monoclinic phase.

Another observation that can be made is related to the existence of a maximum and a minimum in the [R + FCC] two-phase equilibrium of the CCl 4 + CBr 2 Cl 2 system. In the field of molecular materials, phase diagrams with a maximum are unusual although they seem to appear when chlorine or bromine atoms and methyl groups are combined. [START_REF] Barrio | [END_REF]46 The closely related two-component system CCl 4 + (CH 3 ) 3 CBr shows also a [R + FCC] two-phase equilibrium with a minimum and a maximum. [START_REF] Barrio | [END_REF] As it can be seen from Figure 8, and taking into account all the thermodynamic properties for the transitions between the M, R, FCC, and L phases, a simple calculation provides the properties for the melting of the R phase of CBr 2 Cl 2 . Values are presented in Table 1.

The complete phase diagrams resulting from the described thermodynamic assessment together with the experimental values are shown in Figure 8. This figure includes also the metastable parts of the loops. The comparison of calculated and experimental results provides us with reassurance about the robustness of the procedures here employed since the former is shown to account for most of the subtleties brought in by the details of the experimental equilibria. Particularly noteworthy is the evidence for the common inferred metastable temperatures by means of the extrapolation of the two-phase equilibria. Thus, in particular, experimentally "hidden" transitions for CBr 2 Cl 2 compound emerge and their fundamental properties (temperature and enthalpy change) are obtained.

The temperature and the mole fractions of the peritectic and eutectic invariants characterizing the three-phase equilibria are compiled in Table 3 for both systems.

Discussion

According to the described polymorphism of the materials involved in the two-component systems, it is straightforwardly seen that OD mixed crystals between the compounds showing, at normal pressure, a monotropic phase (CCl 4 ) or showing exclusively enantiotropic phases (CBrCl 3 and CBr 2 Cl 2 ) can be of two types, either R or FCC. It necessary appears then that a two-phase region (demixing region) between both OD phases will be present in the phase diagrams. Once Rudman et al. 7 proved the rhombohedral lattice symmetry for the stable OD phase of CCl 4 , the same molecular arrangement was found for several related methylchloromethane compounds ((CH 3 ) 4-n CCl n ), at normal pressure (n ) 2, 3, 4) 11,18,20,47 or at high pressure (n ) 1). 33,34 Recently, such lattice symmetry was disclosed for CBrCl 3 halogenomethane at normal pressure 6,8 and, the present work proves that a rhombohedral phase makes its (metastable) appearance also for CBr 2 Cl 2 material. How the rhombohedral phase would be placed on the pressure-temperature phase diagram can be looked upon as sketched in Figure 1c and by "ordering" the phase transition temperatures obtained for CBr 2 Cl 2 (Table 1): By considering the equivalence of symbols in Figure 1c, R ) FCC, β ) R, and Or ) M, the temperatures of the stable and metastable phase transitions order as

T S FCC-L > T m R-L > T m M-R > T S M-FCC > T m R-FCC ,
which are in perfect agreement with the obtained values (293.7 > 280.7 > 262.0 > 258.8 > 243.6 K). Then, the stability hierarchy of the OD phases and the thermodynamic conditions of their existence can be determined trough a topological representation without regarding the details of the specific values for locating triple points.

As far as crystallographic properties of the inferred rhombohedral phase of CBr 2 Cl 2 are concerned, coherence should be also found. Figure 9 shows the packing coefficient for the ordered and OD mixed crystals. This coefficient is defined as η ) V m /(V/Z), where V m is the molecular volume and V/Z is the unit-cell volume (V) divided by the number of the molecules (Z) in the unit cell. As usual, molecular volumes of the pure compounds were calculated using van der Waals radii and interatomic chemical bonds according to the Kitaigorodsky's method. [START_REF] Kitaigorodsky | Mixed Crystals[END_REF] Values following such procedure are 87.72, 94.29, and 100.86 Å 3 for CCl 4 , CBrCl 3 , and CBr 2 Cl 2 , respectively. The packing of the mixed crystals was determined by means of the simplest way, i.e., by setting for a mixed crystal of molar composition X a linear contribution of the molecular volumes of the A and B molecules shared in the mixed crystal, V m (X) ) (1 -X)V m (A)+ XV m (B). As expected, the highest packing coefficient corresponds to the low-temperature monoclinic phase (for which strongest interactions and thus greatest density appear). In addition, whatever the degree of stability at normal pressure, the packing of the OD R phase for pure compounds as well as for mixed crystals is higher than that of the OD FCC taking into account the temperature at which values have been determined. Thus, coherent packing coefficient values for the R phase of CBr 2 Cl 2 are obtained from the extrapolation of OD R mixed crystals in both two-component systems.

Upon increasing mole fraction of CBr 2 Cl 2 , whatever the phase and whatever the mixed crystals are, packing coefficient increases. Such effect cannot, a priori, be related to either the existence of the R phase at high-pressure nor to the dipole moment of the CBr 2 Cl 2 molecule, which is virtually the same as for CBrCl 3 molecule (≈0.2 D). In a robust way the evidence of the coherence of the extrapolated crystallographic properties of the OD R phase of CBr 2 Cl 2 is shown in Figure 10, corresponding to the OD R lattice parameter and packing coefficient for the halogenomethane compounds for which such phase exists. From that figure noteworthy is the possibility of an OD R phase for compounds CBr 3 Cl and CBr 4 . Thus, although for the first one there is not available information in the literature (synthesis of this compound seems to be difficult), [START_REF] Ohta | [END_REF][START_REF] Miller | [END_REF] for the tetrabromomethane, it has been well established the cubic symmetry of the OD phase at normal pressure, but a highpressure OD phase has been reported. 50 The existence of highpressure OD R phases for several members of the family goes along with the normalized slopes of the packing coefficient (1/ η(n ) 0)(∂η/∂n) ) 0.041) and molecular volume (1/V m (n ) 0)(∂V m /∂n) ) 0.073) as a function of n: They indicate that unitcell volume as a function of n increases slower than molecular volume and thus, the highest packing for high n values will be compatible with high-pressure phases. For both, CBr 2 Cl 2 and CBr 4 high-pressure neutron scattering measurements will be done to determine the coherence of the correlation disclosed by Figure 10. Molecular dynamic studies of the liquid state for the methylchloromethane compounds ((CH 3 ) 4-n CCl n ), 26,27 have shown some peculiarities which make difficult to rationalize the net effect of the dipole moment and the polarization. In particular, electrostatic energy for those compounds shows a very low contribution vs nonelectrostatic contribution. In fact, it has been found that in the liquid-state, polarizability for nonpolar molecules (as C(CH 3 ) 4 and CCl 4 ) has no effect on the structural properties in spite that polarizability are about a factor 7 higher than that of the water. Then, induction effects coming from charge flow within the molecule have been shown to give rise to substantial induced dipole moments for polar molecules. 26 A different work describing the thermodynamic excess properties of the OD mixed crystals between methylchloromethanes, has also revealed the role of the polarizability, which is there called "dipole dilution effect". 31 When a mixed crystal is formed between a molecule displaying dipolar moment and a molecule devoid of permanent dipole moment, it appears as a supplementary positive excess enthalpy to that inherently present from steric factors (evaluated from the mismatch in molecular size). Although for the twocomponent systems described in this work, excess properties, read Gibbs energy and enthalpy, of the liquid mixtures have not been reported in the literature, some evidence can be obtained by considering differences, particularly those between the R and FCC OD phases. Figure 11 shows the excess enthalpy differences between the OD phases and the liquid state (experimen-tally available from the heat effect measured in the melting process) together with those between OD phases and lowtemperature monoclinic phase. The values have been parametrized by using two-coefficient (∆ φ γ H 1 , ∆ φ γ H 2 ) Redlich-Kister polynomials (as eq 6 for the excess Gibbs energy difference). It should be kept in mind that excess enthalpy are the result of a number of successive arithmetical operations with data that have been determined in a direct experimental way or in an indirect manner, including extrapolations. Thus, some reserve must be exercised in drawing conclusions with regard to a desired finetuning. Nevertheless, within the described ubiquitous limiting conditions, some general trends can be achieved. It has been shown [51][52][53] that the geometric mismatch between the molecules of the two components of a given system plays a key role to account for the excess properties. Such a mismatch is parametrized by m, defined as the quotient between the difference between molar volumes of the components (∆V) and their mean (V m ), i.e., m ) ∆V/V m . As for methylchloromethane compounds, an additional role is played by the dipolar nature of the shared molecules. 31 More into specifics, it has been demonstrated that equimolar excess enthalpy of the OD phases (H E,OD (X ) 0.5)) increases when the geometric mismatch increases and that an additional common value (ca. 0.125 kJ'mol -1 for the equimolar composition) must be added for two-component systems sharing a polar and a nonpolar molecule (according to the effect that the authors called "dipole dilution"). 31 The mismatch parameters for OD phases of the two-component systems are calculated from the crystallographic results and are as follows: (i) CCl 4 + CBr 2 Cl 2 : m FCC ) 0.0584; m R ) 0.0693; (ii) CBrCl 3 + CBr 2 Cl 2 : m FCC ) 0.0327 ; m R ) 0.0341. Although the established correlation cannot be quantitatively verified for the two-component systems of this work due to the lack of excess properties for the liquid mixtures, it is straightforward, as seen from Figure 11, that for both R and FCC OD phases, the highest deviation from ideal behavior corresponds to OD mixed crystals having the highest value of geometric mismatch parameter. In addition, assuming that deviation from ideality of liquid mixtures is smaller than for the OD phases (as it is commonly found), the excess enthalpy of OD phases for the polar + nonpolar system (CCl 4 + CBr 2 Cl 2 ) is noticeably higher than that which would correspond to the values of the m parameter, which means that the dipole dilution effect appears. We also note that in spite of uncertainties of the experimental excess enthalpy values, the asymmetry of the excess enthalpy functions (commonly expressed by the quotient of the two parameters of the Redlich-Kister expression for the excess enthalpy) is in line with the degree of asymmetry shown by the majority of the mixed crystal systems (ca. -0.2). [52][53][54] It is of interest to note the small excess Gibbs energy difference between the OD and M phases especially for the twocomponent system CBr 2 Cl 2 + CBrCl 3 (Table 4). Two factors are invoked to account for such effect. First, the close similarity in volume (difference is around 6.5%) and symmetry (C 3V ) between the molecules should generate resemblance between A-B interactions when compared to A-A or B-B. Second, the inherent disorder introduced by the substitution process. 55 Note that although the symmetry of both molecules (C 3V ) does not fulfill the symmetry requirements of the C2/c lattice site (T d ), a symmetry simulation is generated by the appearance of an orientational disorder or by the change of the occupancy of the chlorine and bromine atoms as it has been demonstrated for both pure compounds as well as for mixed crystals by means of the structural refinement. Direct evidence for such a disorder has been obtained by heat capacity measurements 3 as well as by dielectric spectroscopy measurements, 56 both characterizing a glass transition at ca. 90 K associated to the freezing of the molecular disorder within the monoclinic phase. The linear dependence of the packing coefficient of the monoclinic phase as a function of the molar composition (Figure 10) goes along the ideal behavior of the low-temperature monoclinic mixed crystals.

Conclusions

The stable as well as the metastable parts of the twocomponent systems CCl 4 + CBr 2 Cl 2 and CBrCl 3 + CBr 2 Cl 2 have been determined by means of calorimetry and X-ray powder diffraction. The thermodynamic assessment coherently reproduces all the equilibria involved in both phase diagrams. Particularly noteworthy is the evidence for the common inferred metastable temperatures by means of the extrapolation of the two-phase equilibria, hardly obtained when the thermodynamic assessment is performed uniquely with one two-component system. These results suggest that the virtual character of such metastable transitions must be correlated with a physical reality. Thus, as it has been demonstrated in some previous works, 6,8,34,41 such transitions make appearance and acquire physical evidence when the extrapolation of high-pressure transition lines are considered. Then, detailed and coherent thermodynamic analyses of two-component systems can provided much more information than that typically obtained (as excess properties of the mixed crystals), in particular, for the pure components taking part in the binary system. In the present case, the existence of an orientational disordered high-pressure rhombohedral phase for the halogenomethane CBr 2 Cl 2 has been disclosed and a pressuretemperature topological diagram is inferred.

From the well-established crossed isopolymorphism we can conclude the existence of several isomorphism relationships (i) between the OD R stable phases of CCl 4 and CBrCl 3 and the OD R metastable (at normal pressure) phase of CBr 2 Cl 2 , (ii) between the OD FCC phase of CCl 4 (metastable), the OD FCC stable phase of CBrCl 3 and OD FCC stable phase of CBr 2 Cl 2 , and (iii) between the low-temperature monoclinic phases of the three pure compounds involved in this study.

Interesting to note that this family of halogenomethane constitutes a remarkable case study because they are all molecules of almost identical geometry, with both polar and nonpolar species, with orientationally disordered phases and with glass transitions in the low-temperature "ordered" phase, which make a systematic comparison possible. As regard to the glass transition associated to the freezing of the disorder generated by the fractional occupancy of the chlorine and bromine atoms, dielectric spectroscopic and nuclear quadrupole resonance experiments have been undertaken around and below the glass transition temperature (ca. 90 K).

Figure 1 .

 1 Figure 1. Temperature-pressure diagrams involving stable (continuous lines) and metastable (dashed lines) two-phase equilibria involving liquid (L), OD R and β, and ordered (Or) phases.

  of ref 6) c Values obtained from the extrapolation of experimental values. d Values obtained from fundamental thermodynamics (see text).

Figure 2 .

 2 Figure 2. Temperature-composition CCl4 + CBr2Cl2 and CBrCl3 + CBr2Cl2 two-component systems showing the stable (continuous line) two-phase equilibria. The metastable part of the [FCC + L] equilibrium for the CCl4 + CBr2Cl2 system is also displayed as a dashed line.

  2 K (a ) 20.872(4) Å, b ) 11.747(2) Å, c ) 20.434(4) Å, β ) 111.19(1)°, V/Z ) 146.0 Å 3 ) agree quite well with those previously published. 4 3.4. OD Mixed Crystals. 3.4.1. Face-Centered Cubic Mixed Crystals. From previous DSC experiments, the concentration

Figure 3 .

 3 Figure 3. Experimental enthalpies (full symbols) of melting of FCC (b) and R ([) and for the R to FCC (9) and the M to R (2) or FCC (1) transitions as a function of the mole fraction. Empty symbols are obtained either by extrapolation of the curves or by eq 1 (see text).

Figure 4 .

 4 Figure 4. Experimental (o) and theoretical (black line) diffraction patterns along with the difference profile of monoclinic phase at 220.2 K (blue line at the bottom of each panel) for (A) CBr2Cl2 pure compound (Rp ) 7.08%, Rwp ) 9.88%) and (B) (CCl4)0.51(CBr2Cl2)0.49 (Rp ) 5.32%, Rwp ) 7.42%) and (C) (CBrCl3)0.55(CBr2Cl2)0.45 (Rp ) 5.30%, Rwp ) 7.23%) mixed crystals. Each inset corresponds to a five times expanded vertical scale for the 40-60°2θ-range.

Figure 5 .

 5 Figure 5. Lattice parameters as a function of the mole fraction for the low-temperature monoclinic mixed crystals at 220.2 K of the CCl4 + CBr2Cl2 (full symbols) and CBrCl3 + CBr2Cl2 (empty symbols) twocomponent systems.

Figure 6 .

 6 Figure 6. Lattice parameters as a function of the mole fraction for the OD FCC (A1 and B1) and R (A2 and B2) mixed crystals. Temperature at which they were measured is detailed inside each panel. Full square for the FCC lattice parameter a at 241.2 K comes from the extrapolation of the lattice parameter variation with temperature for the pure compound CBr2Cl2.

Figure 7 .

 7 Figure 7. Solid and dashed curves represent stable and metastable behavior, respectively. Full and open circles represent the stable and metastable transition points, respectively The small-circle lines represent the EGC-curves.

  CBr 2 Cl 2 (T CBr 2 Cl 2 M-R ) 262.0 ( 2.0K).

  Figure 3 provides directly the associated enthalpy change (∆ M R H ) 4.80 ( 0.18 kJ'mol -1 ).

  Parameters of the Redlich-Kister Polynomial for the Excess Gibbs Energy Difference between the Involved Phases in the CCl 4 + CBr 2 Cl 2 and CBr 2 Cl 2 + CBrCl 3 Two-Component Systems Together with the Equimolar Equal-Gibbs Temperature (T EGC (X ) 0.5)) for Each of the Assessed Equilibria

Figure 8 .

 8 Figure 8. Calculated equilibria (red and blue dotted lines), experimental points and stable equilibria (black line).

Figure 9 .

 9 Packing coefficient of the monoclinic (squares), rhombohedral (diamonds), and face-centered cubic (circles), mixed crystals. Full diamonds correspond to extrapolated values.

Figure 10 .

 10 Figure 10. Packing and lattice parameter of the rhombohedral phase as a function of the number n of Bromine atoms for the halogenomethane CBrnCl4-n series. Normalized slopes: Packing: 1/(η(n ) 0)) (∂η/∂n) ) 0.041; molecular volume: 1/(Vm(n ) 0)) (∂Vm/∂n) ) 0.073.

Figure 11 .

 11 Figure 11. Excess enthalpy differences for the OD phases with respect to the liquid state (left panel) and for the monoclinic phase with respect to the OD phases (right panel) for the two-component systems CCl4 + CBr2Cl2 (circles) and CBrCl3+ CBr2Cl2 (squares). Full symbols correspond to direct experimental values while empty symbols correspond to values determined by means of eq. 1 Dashed lines are for the Redlich-Kister polynomials. The excess enthalpy difference H E,L -H E,R has been estimated by the using eq 1.

TABLE 1 : Temperatures and Enthalpy and Entropy Changes Associated with the Phase Transitions of CCl 4 , CBrCl 3 , and CBr 2 Cl 2 Obtained in This Work and from Previously Reported Adiabatic Calorimetry 3,a

 1

		transition	T /K	∆H/kJ'mol -1	∆S/J'mol -1 'K -1	reference
	CCl4	M S f R S	225.9	4.68	20.72	8
			225.35	4.581	20.33	19
			225.70 ( 0.01	4.631 ( 0.020	20.52	20
		R S f L S	250.3	2.52	10.06	8
			250.3	2.515	10.05	19
			250.53 ( 0.01	2.562	10.23	20
		FCC m f L m	245.8	1.82	7.42	8
			246.01 ( 0.01	1.830 ( 0.070	7.44	20
		R m f FCC m	262.9 d	0.69 d	2.64 d	8
			258.0 c	0.66 c	257 c	40
	CBrCl3	M S f R S	238.1	4.58	19.23	8
			238.19	4.618	19.40	3
		R S f FCC S	260.3	0.52	1.98	8
			259.34	0.527	2.03	3
		FCC S f L S	267.1	2.03	7.61	8
			267.9	2.032	7.59	3
		R m f L m	265.7 c	2.55 c	9.58 c	8
			265.5 c	2.55 c	9.59 c	41
	CBr2Cl2	M S f FCC S	258.8	5.22 b	20.19	this work
			258.8	5.431	21.06	3
		M S fR m	262.0 c	4.80 c	18.32 c	this work
		FCC S f L S	293.7	2.30	7.82	this work
			294.4	2.308	7.89	3
		R

m f FCC S 243.6 c 0.436 c 1.79 c this work R m f L m 280.7 c 2.36 c 8.40 c this work

TABLE 3 : Calculated Temperatures and Mole Fractions Characterizing the Three-Phase Equilibria for the Two-Component Systems CCl 4 + CBr 2 Cl 2 and CBrCl 3 + CBr 2 Cl 2

 3

	invariant	CCl4 + CBr2Cl2 CBrCl3 + CBr2Cl2
	eutectoid [M + R + FCC] T/K	264.6	252.5
	XM	0.844	0.652
	XN	0.898	0.704
	XP	0.851	0.659
	peritectic [R + FCC + L] T/K	262.5
	XM	0.434
	XN	0.479
	XP	0.477

TABLE 4 :

 4 ∆ R β H 1 ) H 1 β -H 1 R and ∆ R β H 2 ) H 2 β -H 2 R Parameters

of the Redlich-Kister Polynomial for the Excess Enthalpy Difference between the Involved Phases in the CCl 4 + CBr 2 Cl 2 and CBr 2 Cl 2 + CBrCl 3 Two-Component Systems for Each of the Assessed Equilibria, Together with the Quotient H 1 OD /H 2 OD assuming Ideal Behavior in the Liquid State

					CCl4 + CBr2Cl2			CBr2Cl2 + CBrCl3
	equlibrium	R	β	∆ R β H1 J'mol -1	∆ R β H2 J'mol -1	H 2 OD /H 1 OD	∆ R β H1 J'mol -1	∆ R β H2 J'mol -1	H 2 OD /H 1 OD
	[FCC + L]	FCC	L	-1516	540	-0.356	-147	39	-0.265
	[R + L ]	R	L	-326	28	-0.086	-229	67	-0.293

Acknowledgment. This work was supported by the Spanish Ministry of Education and Science (MEC) under project FIS2005-00975 and by the Catalan government by grant SGR2005-00535. We thank Dr. S. Coco at the Chemical Physics Department, University of Valladolid, for providing us with the pure CBr 2 Cl 2 used in this work.


Mike Chiasson
email: m.chiasson@lancaster.ac.uk

Ola Henfridsson
email: ola.henfridsson@chalmers.se

Researching the Future: The Information Systems Discipline=s Futures Infrastructure

This proceedings for the IFIP 8. 2 working conference on Researching the Future is an attempt to pull together some of our research community=s best ideas about how to research the future. The choice of conference theme should be seen as a way to solicit work that can help in building the information system discipline=s futures infrastructure. Such an infrastructure is one that provides an initial and developing set of intellectual structures from which IS research can respond to the needs of our future society.

Researching the future is important. As researchers within a discipline focused on the design, adoption, utilization, and effects of information and communication technologies (ICT), we should be well-positioned to contribute to the future shaping of ICT-based practices. If anticipating and influencing the future is something qualitatively different than immediate research relevance, we must then ask whether and how our approaches to inquiry can affect our ability to do so. Such reflection would be valuable in shaping a discipline that is progressive and confident about its role in dealing with questions about the future. Drawing on a healthy debate about research relevance, it is now time to explore, develop, and substantiate how our field can shape and influence the future of ICT-based practices.

The papers covered in this volume are the result of such reflection. Reflecting differences in philosophical foundation, theoretical orientation, and topical emphasis, each deals with the future of ICT in both traditional and novel ways, in illustrating the process and outcomes of ICT applications in contemporary and emerging social settings, as individuals, collectives, firms, and institutions seek to change their future worlds.

2

Toward a Futures Infrastructure for IS Research Some of the ongoing digitally enabled transformations in business, institutions, and societal practices dazzle us with possibilities for improving social welfare, while others suggest that social inequality may be increasing and preserving the status quo. Still, there is little doubt that we live in a time when anticipating the future is becoming increasingly difficult. Technologies converge [START_REF] Lyytinen | Research Commentary: The Next Wave of Nomadic Computing[END_REF]; product life cycles shrink [START_REF] D=aveni | Hypercompetition: Managing the Dynamics of Strategic Maneuvering[END_REF]; institutions evolve [START_REF] Porter | Redefining Health Care: Creating Value-Based Competition on Results[END_REF]; new learning cultures are born (Thomas and Brown 2011). The multitude of ongoing and parallel changes is vast, which makes the governance of not only enterprises but also some of our society=s basic institutions, such as the educational and healthcare systems, increasingly challenging. There are many indications that this complex web of socio-technical changes will continue to evolve as digital technology becomes ever more woven into the fabric of everyday life. As a result, successful businesses of our time are shifting attention from decision-making, planning, and control toward enactment, improvisation, and empowerment. This shift is manifested in attempts to build platform-centric strategies [START_REF] Ciborra | The Platform Organization: Recombining Strategies, Structures, and Surprises[END_REF][START_REF] Tiwana | Platform Evolution: Coevolution of Platform Architecture, Governance, and Environmental Dynamics[END_REF], where the focus is on creating and nurturing the socio-technical capabilities needed for being responsive to emerging opportunities. Such capability-creation seems doubly distributed across two dimensions: control and knowledge [START_REF] Yoo | The New Organizing Logic of Digital Innovation: An Agenda for Information Systems Research[END_REF]. First, the control over innovation resources is increasingly distributed across actors and stakeholders. Second, the heterogeneity of knowledge sources is increasingly apparent, where digital technology multiplies the space of possible pockets of innovation.

In this period of social transformation, it seems increasingly important for our research discipline to be more than by-standers as our object of study changes the world. To be participants in this change, learning how to research the future is a key ingredient.

Just as the businesses of our time are becoming increasingly infrastructurecentric, it may be time to reflect upon the futures infrastructure of IS researchCthe practices, logics, and approaches to our research which enable our ability to contribute to the future of IS practice. Important questions arise from this reflection. What can we do in order to be more aware, resilient, and capable of responding and prompting changes in and through our research? How can we adopt infrastructural thinking for making us capable of enacting, improvising, and empowering futures that are responsive to the future needs of our society?

While these are issues partly covered in this book, there are at least three issues that are worth exploring further as we seek to research the future. First, as manifested in the papers included in this volume, we need new conceptual and practical resources for IS research to help us understand what lies ahead. Some argue that our best chance to understand the future lies in understanding the past. Others propose that the adoption of new research methods, especially tailored for future studies, is important. Without a coherent and unambiguous road ahead, a first step toward a futurology of IS is to expand and treat common and unusual positions as resources to engage in the conceptualization, design, and execution of our research.

Second, an IS futures platform would possibly investigate and use the boundary resources of other disciplines. Just as the meanings of a smartphone multiply with infrastructural thinking (not just a phone, but also a navigation system, remote, camera, blood pressure instrument, and so on), it seems likely that the research ecosystem is enriched through the concepts and practices of unrelated disciplines. Neuroscience [START_REF] Dimoka | What Does the Brain Tell Us About Trust and Distrust? Evidence from a Functional Neuroimaging Study[END_REF]) and ecological sustainability (e.g., [START_REF] Watson | Information Systems and Environmentally Sustainable Development: Energy Informatics and New Directions for the IS Community[END_REF] are recent examples. Moreover, in affecting the future, an IS futures infrastructure also offers its boundary resources to emerging knowledge bodies, making it possible for them to tap into our ecosystem (e.g., recent eHealth special issues in IS journals).

Third, an IS futures infrastructure rethinks the prevalent assumption about the individual research hero and the increasing subspecialization prompted by small and isolated collectives. Just as infrastructure owners deal with numerous and emerging networks of stakeholders, a resilient research infrastructure would increasingly be ready to respond to the increasing diversity and changing configuration of the research participants and stakeholders in the future, while still preserving a distance and level-headedness that isn=t swept along by fashions and fads. In our view, this suggests the need to think about how to prepare IS researchers for this future, and how the infrastructure for IS research may be able to foster both theoretical stability and practical application as researchBparticipant collectives regroup around important issues emerging in the wake of increasing societal change.

The Review Process

A total of 36 papers were submitted. The papers were submitted from all three AIS regions, with 7 papers from region 1 (Americas), 24 from Region 2 (Europe, Middle East, and Africa), and 5 from region 3 (Asia and the Pacific). Using a three-tier review structure, all papers went through a rigorous review process where feedback was provided by at least four independent referees including the editorial by one of the program cochairs. While the program chairs managed the 38 papers together, any conflicts-of-interest with a cochair was managed by assigning sole responsibility to the other program chair.

Considering the reviews of members of the program committee, we accepted 16 papers. We also accepted three panels and one workshop presentation on methods for studying the future. The program also includes three plenary sessions with invited speakers.

4

Overview of the Book

Keynotes

We would like to show our appreciation of the efforts of our three invited keynote speakers.

Yrjö Neuvo=s topic is AUnfogging the Future.@ He was vice president and chief technology officer for Nokia during the years it was establishing itself as the world=s leading mobile phone manufacturer. For many decades, he has been a very influential voice in European research initiatives. Now retired from Nokia, he is based at Aalto University.

The topic of Judith Gregory presentation is ADesign for Participation and Negotiation across Logics and Knowledge Communities.@ She is, and for over 30 years has been, a key figure in the participatory design community. In other words, she engages in making the future together with others. With a very international past, she is currently based at the Illinois Institute of Technology.

Our third keynote speaker is Youngjin Yoo, with a topic AAfter the Promised Land: What Do We Do Now?@ He is an associate professor in Information Systems and an IBIT Research Fellow at the Fox School of Business and Management at Temple University. His research and teaching interests include digital innovation, experiential computing, design, knowledge management, and virtual teams. You can read his reflections on technology, design, and innovation in everyday experiences in his blog at youngjinyoo.com.

Papers

We wish to thank the authors for the range of approaches taken to the topic of researching the future of information systems. We grouped the articlesCsomewhat imperfectlyCinto particular methodological, theoretical, and/or practical approaches to the theme.

We grouped a number of paper focused specifically on how the future and the past are connected and inter-related. Sewchurran and Brown explore the importance of metaphor and analogy across theory and as-lived experience, in transforming the future of IT project management theory and practice, and IS research generally. In a complementary contrast, Aanestad considers how the durability of the past and present is important in understanding and anticipating what the future may hold, and which futures we may wish to hold. Finally, Wynn examines how the future is made Apresent-at-hand@ in corporate projects, and how the future is produced from revisiting the past and realizing its presence within the present. All three papers provide an interesting starting point for thinking about the issues that research about the future may conceptually need to consider.

Another grouping of papers focused on a critical view of the future. Stahl examines discourses emerging from 11 discussions about future ICTs and, by highlighting particular assumptions in the discourse, goes on to critique the implied assumptions in each. In doing so, he provides a basis for examining the unrealized futures beyond these assumptions, which we may wish to pursue instead. Brown examines and explores the people who anticipate and shape the future in organiza-tionsCforecastersCand how the supposed foolishness of their activities, as defined within the mathematical forecasting literature, may be seen as an alternative rationality of dealing with the uncertainties of the future in organizations.

Another group of papers examines particular technological futures. Stahl examines the difficulty (if not impossibility) of anticipating specific technological futures, and moves on to consider the need and possibility for participation in shaping the collective future of technology, through approaches such as participatory technology assessment. In contrast to Stahl=s epistemology, Andreev, Duane, and O=Reilly examine how perceptions of trust and ease-of-use in m-payment systems affect individuals= willingness to pay and transact using m-payment systems. By examining a future technology using more traditional research approaches, the paper provides an important point of contrast to the open-ended possibilities of Stahl=s critique. In a similar vein, Ou, Leung, and Davison examine the growing use of instant messaging tools used in organizations for knowledge management and team performance. Again, as a specific example of researching the future about an important information technology using traditional research methods, the paper provides an important and complementary perspective on futures research about particular types of IT, complementing and adding to the debate in this session on the shaping and co-shaping of information systems.

A group of papers examines the future of information technology and workrelated practices in health care. Litchner and Venters lead off the health care session using science fictionCa relatively rare approach to researching the future in IS research. They employ science fiction to make a futuristic sense of the evaluation of an electronic prescription system implementation in the national health service (NHS) in the United Kingdom. Pedersen, Ellingsen, and Monteiro consider how the future is standardized through the enactment of both topBdown and bottomBup processes in nursing work, and the performativity of standardization beyond the traditional dichotomous view of top-down or futile (bottom-up) views of standardization. Finally, Petrakaki, Cornford, Hibberd, Lichtner, and Barber propose a framework for considering how ICT could affect worker=s professional standing in terms of both increasing and decreasing autonomy and capability depending on the effect of ICT on professional roles, work practices, and jurisdictions.

A group of papers examines the future of industrialBinstitutional practices and outcomes through information technology. Nylén and Holmström consider how latent capabilities in the computing in forestry machinery could transform it into a service sector organization, through the possibilities of open innovation. They make a general claim that open innovation possibilities in an embedded ICT could enable transformation in a number of industrial settings. Crowston examines how insights from the open source community and their use of ICTs may tell us something general about the future of knowledge workCthe organization and incentives produced through ICT. Kautz, Bunker, Rab, and Sinnet consider the relations and actions among various companies involved in the production, standardization, and customization of a CRM system, and their use of various open and proprietary positions in producing various niches. They illustrate the range of organizational positions needed to create a rich interorganizational ecosystem around a technological platform, and point to the future of the software industry.

A final group of papers examines the future of critical realism in IS research. Vega and Brown employ critical realism to examine the production and effects of government programs on the diffusion of IT in small and medium sized companies. They illustrate how the social complexity of IS diffusion in the future can be better understood through critical realism (CR). Carlsson explores the past, present, and future use of critical realism in information systems research. Given the position of fallibility in any particular method and study, CR opens the door to many current and future approaches to IS research, and to a never-ending future for IS research practice. A more than fitting conclusion to a special issue on researching the future in IS research.

Panels and Workshop

We have three panels and one workshop in the conference. The first panel by Sawyer, Iivari, Venkatesh, Light and Urquhart examines how our conceptual apparatus for systems design needs to be changed to consider the future of building social software (e.g., online communities) as opposed to role-based software within a single organization. Two questions considered in their panel and discussion are: How do designers deal with the tensions of developing more socially complex users of social software versus traditional role-based users, and how do designers grapple with the need to design systems to address social needs versus only functional work activities? Our second panel by Carmel, Avital, Gray, Kallinikos, and King focuses on the importance and relevance of teaching foresight and futuristic thinking in a university curriculum. Their panel focuses on particular controversies in attempting to do so. Our final panel, with Alter, Korpela, Petkov, and Russo, considers the viability of revisiting and reinfusing socio-technical principles and practices in systems development. The panel, through its various questions about the strengths and weaknesses of current approaches, possible extensions, and the current and future trends and issues in design, considers the future form and application of socio-technical approaches in systems development. Our workshop with Gray and Hovav considers three rigorous approaches to futures research in information systems that move beyond simple extrapolation of the present. A fitting conclusion to our volume on the future of IS research about the future.

Conclusion

In responding to the future of information systems research about the future, the comprehensive and creative response to the call is represented in this volume. However, as a project to produce the infrastructure for futures research in information systems, it is only a beginning within other attempts to tackle the IS researcher=s role in shaping the future. Whether it is speculating on particular technological futures, exploring the philosophical for futures research, or critiquing the limited possibilities in visions of the future, the future of IS practice is both potentially limitless and unnecessarily limited. Our only enduring role in the future may be the unstable mixing of observing and understanding what we think is endurable, critiquing what we come to realize is unnecessarily durable, and considering and prompting the IS futures worth having. Our infrastructure for thinking, observing, writing, and participating in dealing with the future may, therefore, be open to continuous exploration and experimentationCa wonderful future indeed!