Elodie Chevereau

Stéphanie Kodjikian

Philippe Lacorre

Gwenaël Corbel

Topological metastability and oxide ionic conduction in La 2-x Eu x Mo 2 O 9

published or not. The documents may come

Topological metastability and oxide ionic conduction in

La2-xEuxMo2O9

and Eu 2 O 3 were calcinated in air for 12 h at 1000 °C to remove adsorbed water and carbon dioxide. The stoichiometric mixture of La 2 O 3 , Eu 2 O 3 , and MoO 3 was first heated in an alumina crucible at 500 °C for 12 h (heating and cooling rates of 2 °C/min). Then, several annealings with regrindings in acetone in between were necessary to obtain a pure single phase. The final firing temperatures were 1000 and 1050 °C (heating and cooling rates of 5 °C/min) for europium content lower and higher than x ) 0.20, respectively.

2.2. Europium Valence Determination. To determine the valence of europium cation in the La 2-x Eu x Mo 2 O 9 series, all compositions were excited by a short-wavelength 254 nm ultraviolet lamp at room temperature. All substituted samples exhibit an intense red emission characteristic of trivalent europium ion 9 (Figure S1 in the Supporting Information). The isovalent nature of the substitution is confirmed: the balance between oxygen and vacancy in the structure is kept constant.

2.3. Structural Characterization. After completion, X-ray powder diffraction patterns were recorded at room temperature on a θ/θ Bragg-Brentano Philips X'pert MPD PRO diffractometer (Cu KR 1+2 radiations) equipped with the X'celerator detector. The powder was dusted through a 63 µm sieve on a glass holder. Diffractograms were collected during 400 min in the [5-130°] scattering angle range, with a 0.0084°step. The program FullProf 10 was used for Le Bail's fits.

Thermodiffractograms were collected on the same diffractometer equipped with an HTK 1200 Anton Paar chamber using an Al 2 O 3 sample holder cup. Diffractograms were recorded under air flow from room temperature (RT) to 950 °C (heating rate of 10 °C/min, temperature stabilization for 20 min with temperature correction after calibration). 11 A [9-130°] or [15-130°] scattering angle range with a 0.0084°step was used for europium contents of lower or higher than x ) 0.20, respectively. The thermal evolution of the (231) diffraction line of x ) 0.15 and 0.2 pellet samples was recorded from RT to 950 °C in the [46-48.75°] scattering angle range (counting time of 11 min).

The electron microscopy study was performed with a 200kV JEOL 2010 TEM equipped with a side entry (30°double-tilt specimen holder. The raw powder was ground in absolute ethanol, and one droplet was deposited on a carbon-coated holey film supported by a copper grid. This microscope is coupled with a KEVEX energy dispersive spectroscopy analyzer.

2.4. Thermal Analysis. Thermal analyses were performed on raw powders with a TGA/DTA Q600 SDT TA Instuments apparatus (Pt crucibles, Al 2 O 3 as a reference) under air flow (100 mL/min).

For x e 0.20, thermograms were collected on ∼20 mg samples in the RT-1000 °C range (heating/cooling rate of 10 °C/min). For x > 0.20, DTA measurements were carried out on ∼50 mg samples with 3 heating/cooling cycles from RT to 800 °C (20 °C/min).

2.5. Transport Properties. Pellets with high relative density (>95% of theoretical density) were obtained from fine grain powders (∼1 µm). Grain size reduction was performed by ballmilling using a FRITSCH planetary micromill pulverizette 7 apparatus. Typically, 900 mg of raw powder were placed into a 45 cm 3 agate bowl with six 12 mm diameter agate balls (ball-to-powder mass ratio of around 16:1) and covered with ethanol. Milling conditions were four alternations of 15 min milling sequences at 700 rpm with 15 min pause in between. Milled powders were then dried slowly at 100 °C. Polyvinyl alcohol ((C 2 H 4 O) n in water solution) was used as bending agent. The compaction into pellets (5 mm in diameter and 3-5 mm in thickness) was achieved by uniaxial hydraulic pressing (500 MPa load), followed by a final RT isostatic pressing (550-580 MPa) in a Top Industrie apparatus. The axial shrinkage was continuously recorded up to the synthesis temperature (to prevent decomposition) with a vertical dilatometer SETARAM TMA Setsys Evolution 16 (20 mL/min air flow, heating/cooling rate of 5 °C/min). After the sample was sintered, the phase purity was checked on the pellet by X-ray diffraction.

Thin Pt film electrodes were deposited by magnetron sputtering on both flat faces of the sintered pellets. Two-probe electrical conductivity measurements were carried out using a Solartron 1260 frequency response analyzer connected to a Solartron 1296 dielectric interface over the 10 MHz to 0.05 Hz range (ac voltage of 50mV, 40 points/decade). Complex impedance spectra were recorded under dry air flow every 25 °C (35 min thermal equilibration) over the temperature range of 300-725 °C for all compositions, except those containing an europium content of x e 0.25. For these latter compositions, additional spectra were collected every 5 °C in the intermediate range of 550-600 °C. Impedance diagrams plotted in the Nyquist complex plane present a spike at the low-frequency side characteristic of the electrode polarization phenomenon. This spike was fitted with a Warburg element with the Z-view 2.8d software. 12 In the 300-475 °C range, high frequency and lower frequency semicircles were observed and least-squares fitted with a series combination of two (R//CPE) elements. On the basis of the values of capacitance (∼1.10 -11 F), the former arc was assigned to the bulk response, while the latter (∼4.10 -9 F) was associated to the grain boundaries contribution. Above 475 °C, only one semicircle was distinguished.

Results and Discussion

Phase Existence Domain and Structural Evolution

with Europium Content. The room-temperature X-ray diffraction patterns of La 1.95 Eu 0.05 Mo 2 O 9 and La 1.9 Eu 0.1 Mo 2 O 9 clearly exhibit the peak splitting characteristic of the slight monoclinic distortion and the 2 × 3 × 4 superstructure peaks at low 2θ scattering angle relative to the β-La 2 Mo 2 O 9 form (Figure 1). 2 This was confirmed by DT analysis (Figure 2):

(9) (a) Neeraj, S.; Kijima, N.; Cheetham, A. K. an endothermic peak upon heating up, associated to the reversible R f β structural phase transition, was seen around 570-580 °C. With increasing europium content, a slight shift of this transition toward higher temperatures is observed (Table 1). The reduction in intensity of the thermal peak upon substitution is consistent with the slightly smaller monoclinic splitting of the pseudocubic (231) diffraction line. The broadening of the peak (increase of the difference between the temperature at the onset point and at the peak maximum in Table 1) reflects the increase of cationic disorder introduced by the europium substitution. Above an europium content of x ) 0.25, the stabilization of the cubic β-phase at room temperature occurs. These results are in agreement with the investigations of Marrero-Lo ´pez et al. 8 undertaken on samples elaborated from freeze-dried precursors.

For two intermediate compositions, x ) 0.15 and x ) 0.2, Figure 1 shows that the (231) cubic reflections are widened and less intense than those of the x ) 0.25, 0.3, and 0.4 samples. Furthermore, a weaker peak at lower scattering angle (not attributed to the asymmetry effect) was observed for the La 1.85 Eu 0.15 Mo 2 O 9 sample (see the arrow in Figure 1). DTA thermogram collected on the x ) 0.15 sample upon heating reveals the existence of a broad endothermic peak around 580 °C at the first-order R/β transition, whereas a subtle break is detected for the x ) 0.15 and x ) 0.2 samples at lower temperatures. These measurements carried out on two different as-prepared samples were reproducible. For both samples, the occurrence of these transitions evoked the coexistence of the two polymorphs (R + β). This assumption would explain the presence of (231) overlapping peaks belonging to R and β forms noted for the La 1.85 Eu 0.15 Mo 2 O 9 sample. The ratio (low-temperature form R/high-temperature form β) tends to decrease as x increases because this overlapping is not detected for x ) 0.2.

To confirm the biphasic feature of the La 1.85 Eu 0.15 Mo 2 O 9 sample, room-temperature electron diffraction patterns were collected on 11 different crystallites. At first, the elemental composition of each crystallite was checked by energy dispersive X-ray spectroscopy analysis. No significant variation in La and Mo content was detected between crystallites. For 5 of the 11 crystallites, the presence of the monoclinic superstructure relative to the cubic β phase was confirmed. As shown in the selected area electron diffraction pattern along [100] (Figure 3a), the tripling and quadrupling of cell parameter characteristic of the ×2×3×4 superstructure of R-La 2 Mo 2 O 9 is clearly found. For the 6 latter crystallites, all SAED patterns exhibit elongated Bragg reflections that can be all indexed onto a cubic cell with a parameter of ∼7.14 Å. It must be mentioned that the zone axis orientation of ED patterns cannot be determined because of the cubic symmetry. Note that in Figure 3b, the diffuse scattering is oriented along one diagonal of the basal plane. This implies that the statical disorder is limited to layers perpendicular to [110], [101], or [011] direction. Unfortunately, the tilting angle of the specimen holder is limited to (30°making a reconstruction of the total reciprocal lattice impossible. However, this experiment has shown that the coexistence of the two polymorphs (R + β) within the sample of La 1.85 -Eu 0.15 Mo 2 O 9 is not involved by any gradient of composition.

As it will be demonstrated in Section 3.3 thanks to in situ high-temperature X-ray diffraction, the presence of the subtle break around 450 °C in the DT thermograms of both the La 1.85 Eu 0.15 Mo 2 O 9 and La 1.8 Eu 0.2 Mo 2 O 9 samples originates from the metastability of β-phase, which transforms back to stable R phase.

Unit cell parameters were obtained by the pattern-matching fit of diffractograms either in a single monoclinic subcell (space group P2 1 (No. 4)) for x e 0.15 or in a cubic cell (space group P2 1 3 (No. 198)) for x g 0.2. Along the series, the linear reduction of the unit cell volume with increasing the europium content x (usual Vegard's law, Figure 4) reflects that trivalent europium cation (ionic radii ) 0.947 (CN ) 6), 1.12 Å (CN ) 9)) 13 is much smaller than lanthanum ion (ionic radii ) 1.032 (CN ) 6), 1.216 Å (CN ) 9)). 13 The formation of a partial solid solution is then established in the whole composition range, all the studied samples being pure. Moreover, this work shows that the composition range explored by Marrero-Lo ´pez et al. 8 can be extended at least up to an europium concentration of x ) 0.4. This is in good agreement with previous studies carried out on trivalent samarium-14 or gadolinium-substituted 4 LAMOX samples.

Sintering Process.

At first, the thermal instability of ball-milled powders was determined from TG analysis. A continuous weight loss takes place above 1100 °C before the lanthanum molybdate starts to melt. It must be noted that the abrasion of agate balls during milling can introduce a weak SiO 2 contamination. When a sintering temperature of 1075 °C was applied (higher than the synthesis temperature of raw powders, i.e., 1000-1050 °C), a clear increase of the bulk resistance above 560 °C was observed by complex impedance spectroscopy. This decrease of the bulk conductivity cannot be attributed to oxygen losses involving the partial reduction of molybdenum cation (mixed valence) because the resulting electronic contribution would increase the total conductivity. 15 Although consecutive X-ray diffraction did not reveal any extra diffraction peaks, the presence of an insulating phase at the grain boundaries of the pellet (either from LAMOX decomposition or reaction with silica contaminant) cannot be ruled out.

A method to sinter europium-substituted samples, while preventing any decomposition or any formation of an insulating phase, was to apply an isothermal treatment for 3 h at the final synthesis temperature of corresponding raw powders (Table 2). All results reported hereafter were obtained on ceramic samples sintered under these conditions. No increase of the bulk resistance was observed by complex impedance spectroscopy as shown in Figure 6. It is worth noting that the conductivity curve that we reported for La 1.75 -Eu 0.25 Mo 2 O 9 is identical to the curve presented by Marrero-Lo ´pez et al. This result is important because these authors have elaborated at 500 °C the nanocrystalline powder used to prepare the pellet sintered at 950 °C. In our study, the possible SiO 2 contamination introduced by the ball milling stage and the possible molybdenum oxide losses during the sintering were then considered as negligible. Furthermore, despite the reduction of the sintering temperature to the synthesis temperature, all sintered pellets exhibit relative densities F higher than 96% (Table 2). This can be explained by the fact that an isotherm at lower temperature slows down the densification and minimizes the separation of pores from the boundaries (trapping of pores inside large grains when the grain growth is faster than the pore motion). 16 X-ray diffraction patterns show that all sintered pellets are pure. The linear shrinkage, ∆l/l 0 , values as a function of the temperature for several compositions are shown in the Supporting Information.

Thermal Stability and Charge Transport versus Composition.

A previous study showed correlations between oxide-ion conduction increase and thermal expansion in the LAMOX family. 7 The thermal stability of all members of the solid solution La 2-x Eu x Mo 2 O 9 was investigated by using in situ high-temperature X-ray powder diffraction performed in air. From the Le Bail's fit of high-temperature patterns, the thermal evolution of the single-cell volume is determined and given in Figure 5. In the linear regimes, data were fitted with a linear regression to deduce the average thermal expansion coefficient reported in Table 3. The relative thermal expansion ∆l/l 0 curves of air-sintered ceramic pellets of La 2-x Eu x Mo 2 O 9 are reported in Figure S3 of the Supporting Information. Finally, Figure 6 shows the dependence of their total ionic conductivity in the temperature range of 300-725 °C. Data relative to pure La 2 Mo 2 O 9 are also added in Figures 5,S3, and 6, for reference. We will first examine low Eu content samples (x ) 0.05, 0.1), then the high content The La 1.9 -Eu 0.1 Mo 2 O 9 powder sample displays a 0.8% abrupt cell volume expansion, larger than the one observed for pure lanthanum molybdate (0.53%), at the structural R/β phase transition (Figure 5). This jump in the thermal expansion is lowered to 0.2% when the samples of La 2 Mo 2 O 9 , La 1.95 Eu 0.05 -Mo 2 O 9 , and La 1.9 Eu 0.1 Mo 2 O 9 are shaped into the form of a dense pellet (Figure S3). The difference between the volume expansion measured on a pellet by dilatometry and on a powder by XRD can originate from the difference in measurement techniques, but it might also be a sign of the effect of sample shaping on the equilibrium of point defects. In the low-temperature range, the average thermal expansion coefficient of R-La 1.9 Eu 0.1 Mo 2 O 9 and R-La 2 Mo 2 O 9 are almost equal (Table 3). This was confirmed by dilatometry (Figure S3) because the ∆l/l 0 curves are perfectly superimposed below 580 °C regardless of the europium content considered. Above 580 °C, slight decreases of the R coefficient (Table 3) and of the relative expansion ∆l/l 0 (Figure S3) are noted for β-La 1.9 Eu 0.1 Mo 2 O 9 .

The thermal dependencies of the total conductivity of the La 1.95 Eu 0.05 Mo 2 O 9 and La 1.9 Eu 0.1 Mo 2 O 9 samples are consistent with temperature-controlled diffraction data. The conductivity jump of about 1 order of magnitude, when the first order R/β phase transition takes place in La 2 Mo 2 O 9 , did not change significantly with the europium concentration. However, when x increases, the transition temperature T R/β is progressively shifted toward the low-temperature region (Figure 6). Correlatively, the narrow peak in plots of the first derivative of the conduction with respect to temperature (Figure 6), associated to the first-order transition of La 2 Mo 2 O 9 , is broadened and less intense as the europium content increases. Note that an opposite evolution of T R/β has been shown on powder samples by differential thermal analysis. This difference could arise from the dynamic character of DTA measurement or from sample shaping. In the temperature range of 300-500 °C, conductivity curves have been fitted with an Arrhenius-type law σT ) σ 0 exp(-E a /RT) (thermally activated anionic mobility) with an activation energy E a of 1.1 eV regardless of the value of x (Figure 7a). In the hightemperature region, the bulk conductivity is not enhanced significantly through La 3+ /Eu 3+ substitution.

It must be underlined that this observation is not consistent with results published on this series by Marrero-Lo ´pez et al. 8 These authors have measured an increase by an order of magnitude, in the whole temperature range explored, of the ionic conductivity of La 2 Mo 2 O 9 when a fraction, x ) 0.05, of lanthanum is substituted with europium. However, the authors attributed this increase of conductivity to the sample microstructure because the sintered pellet of La 1.95 Eu 0.05 -Mo 2 O 9 exhibits the higher relative density (98%) among all substituted samples. Note that, in our series, all relative densities are in the range of 96-99% (Table 2). Moreover, another discrepancy with the Marrero-Lo ´pez et al. results concerns the x ) 0.1 europium sample. The conductivity curve of La 1.9 Eu 0.1 Mo 2 O 9 they reported looks like the curve of a cubic member, whereas DTA thermogram clearly shows an endothermic peaks attributed to the R f β phase transition. An attempt to explain these contradictory results will be given in Section 3.3.3.

La 2-x Eu

x Mo 2 O 9 with 0.25 e x e 0.4. As shown by room-temperature diffraction, the last three members of this series have a cubic symmetry. The thermal behavior of these compositions is similar to that previously shown for cubic members of the LAMOX family. 7,17 Cell volume evolutions (Figure 5) and relative thermal expansions ∆l/l 0 (Figure S3) present a departure from linearity above 400-450 °C. However, the values of the thermal expansion coefficients (TEC) (Table 3), calculated in the linear part of the cell volume evolution, remain almost constant and comparable to that of R-La 2 Mo 2 O 9 . It is worth noting that by DT analysis performed on all cubic samples (see the experimental conditions), a wide endothermic event around 450 °C (onset point) is detected upon heating, whereas a diffuse bump is noted during cooling (Figure 8). No evolution of these thermal events were noted when two additional cycles of heating-cooling were performed. In the same way, a deviation from a pure Arrhenius-type behavior, below 1000/T ≈ 1.35 K -1 , is noted on conductivity curves regardless of the value of x (Figure 6).

This change in the conduction mechanism has been interpreted as resulting from a transition toward a Vogel-Tammann-Fulcher (VTF) regime. [17][18] Recently, a mathematical analysis 7 of the flexibility of the anti-polyhedral framework 5 of the β-La 2 Mo 2 O 9 crystal structure was undertaken. The extra thermal volume expansion, observed above 450 °C, was interpreted as originating from the opening up of tunnels through cooperative rotations of anti-tetrahedra [O1La 3 Mo]. Since mobile O2 and O3 oxide ions are located in these tunnels, the ionic migration would then be thermally assisted by the host matrix distortion/libration. As shown in Figure 6, total conductivity was fitted with a conventional Arrhenius law in the linear part at low temperature and with the empirical Vogel-Tammann-Fulcher (VTF) model when departure from linearity is observed at higher temperature. The VTF equation has three adjustable parameters: σ 0 is the pre-exponential factor, B a pseudoactivation energy, and T 0 the temperature at which oxide ion disordering becomes dynamic. Values of the Arrhenius and of VTF parameters for all compositions are presented in Figure 7.

In the Arrhenius-type regime, the values of the activation energy E a and of the pre-exponential factor σ 0 for β-La 2-x -Eu x Mo 2 O 9 (x ) 0.15-0.4) samples are much larger than values obtained for R-La 2-x Eu x Mo 2 O 9 (x ) 0, 0.05, 0.1) samples. Above x ) 0.15, E a and σ 0 decrease linearly when the europium concentration increases. This significant increase of σ 0 between the Rand β-type phases could reflect that, in the latter, the diffusion of defects (vacancy migration entropy) and the concentration of defects allowing a hopping of mobile species is larger than in the vacancy ordered R-phase.

In the high-temperature regime (VTF), an increase of the temperature T 0 and a decrease of σ 0 and B with increasing x (taking into account the x ) 0.2 composition described in the next paragraph) are observed, both followed by a kind of leveling off above x ) 0.3 (Figure 7). Note, that the pseudoactivation energy we find for x ) 0.4 is comparable to values determined for crystallized fast silver ion conductors Ag 7 GeS 5 I (0.06 eV) and R-AgI (0.06 eV). 19 One possible explanation of the evolution of T 0 is that oxygen vacancies 0 present intrinsically in β-La 2 Mo 2 O 9 0 (LPS concept) 20 could be trapped around substituting cations. The average coordination of lanthanum ions determined from the partial occupancy of O2 and O3 sites in the β-form is 10. This oxygen vacancies/Eu 3+ ions association is plausible since the trivalent europium cation, smaller in size than lanthanum, adopts generally surroundings with lower coordinence number. In crystal structures of europium molybdates, the rare earth ion is eight-fold coordinated within a distorted square antiprism. 21 For reference, lanthanum is nineor ten-fold coordinated in the structures of Rand β-La 2 -Mo 4 O 15 . 22 In our analysis of the VTF behavior, we consider that T 0 is the transition temperature from a static to dynamic disordered states of oxide ions. Thereby, an increase of the number of vacancies trapped as the amount of europium increases could explain that the transition toward a dynamic disordered state occurs at higher temperature. However, the range of lanthanum substitution investigated here is rather limited. As a matter of fact, this oxygen vacancies/Eu 3+ ions association might be small and is consistent with the weak incidence on ionic conductivity noted. But, it is amazing that a 0.2 variation of the europium content induces a shift of T 0 larger than 100 K. It must be noted that, whatever the value of x, the departure from linearity (Arrhenius/VTF transition) starts at around 695 K. As shown in Figure 7, a substantial decrease of the difference between T Arr/VTF and T 0 occurs upon substitution.

In the assumption of mobility assisted by the libration of the matrix, a question can be raised: do the relative volume expansion and the VTF parameters σ 0 and B have an identical composition dependence? A conduction activation energy is the sum of the strain energy required to dilate or distort the network to allow a mobile ion to hop from one site to another and the energy binding an ion to one equilibrium site (related to the bond dissociation energy). As shown in Figure 7, the relative volume expansion [V 950°C -V 25°C ]/ V 25°C (or % unoccupied volume ) [V 25°C -V ions /V 25°C ) of cubic Eu members is constant regardless of the europium fraction. Because the expansion of the host matrix behaves the same way, despite the reduction of the unit cell volume as the europium content increases (Figure 5), the strain energy might not change within the series. The average bond energy of mobile anion is dependent on its cationic neighborhood. It is worthy to note that the strength of Eu-O bond (479(10) kJ/mol) [START_REF] Kerr | CRC Handbook of Chemistry and Physics 1998-1999[END_REF] is smaller than the strength of La-O bond (799(4) kJ/mol). [START_REF] Kerr | CRC Handbook of Chemistry and Physics 1998-1999[END_REF] It gives an explanation of the evolution of the pseudoactivation energy with the substitution level since the higher the europium content, the lower the average bond energy, and the easier the diffusion of oxide ions. However, the ionic conductivity did not reflect this trend.

To understand, let us analyze the evolution of σ 0 . Because the pre-exponential factor σ 0 is proportional to the concentration of defects allowing a hopping of mobile species, the continuous decrease of this concentration as increasing the europium content up to x ) 0.3 could be ascribed to the progressive trapping of oxygen vacancies around Eu 3+ ions assumed previously. Note, that the magnitude of the variation of σ 0 is similar to that found in the Arrhenius-type regime. The kind of leveling off above x ) 0.3 would mean that a maximum of oxygen vacancies and Eu 3+ ions associated is probably reached for the x ) 0.4 sample. Thereby, the europium substitution has two antagonistic effects: it lowers the activation energy but favors the trapping of oxygen vacancies.

Metastability and Sample Shaping:

The Case of La 1.85 Eu 0.15 Mo 2 O 9 and La 1.8 Eu 0.2 Mo 2 O 9 . In section 3.1, room-temperature diffraction and DT analysis have shown that the x ) 0.15 and 0.2 compositions stand apart from the others. Indeed, the two polymorphs (R + β) coexist at ambient temperature for La 1.85 Eu 0.15 Mo 2 O 9 . It was also supposed that the RT β-phase obtained for both samples was not the most stable form. This narrow substitution range (0.1 < x < 0.25) probably forms a border region between single monoclinic phase and cubic phase existence domains. A deeper insight of the system was achieved thanks to temperature-controlled X-ray powder diffraction. These measurements, performed on raw powder samples, revealed a series of structural transitions upon heating (Figure 5). The insets in Figure 5 show the evolution of the pseudocubic (231) reflection with increasing temperature.

At first, let us focus on La 1.8 Eu 0.2 Mo 2 O 9 . Upon heating, the raw powder sample exhibits a complete conversion to monoclinic R-form in a limited thermal range, ∼450-560 °C, before undergoing the R/β transition, like in pure La 2 Mo 2 O 9 . The single cell volume relative to the transient R-phase is found to be slightly smaller than the one of the β-phase before the inverse β/R transition. These doublereversed transitions indicate that the initial β-phase, when the powder sample is cooled from 1000 °C at 5 °C/min (sample 1), is metastable in nature. According to Turnbull, 24 metastability may be: (1) morphological when it arises from a decrease of the particule size (nanocrystalline anatase), 24 (2) topological when it arises from an increase of disorder leading to alternate crystalline or amorphous phases, or (3) compositional when it arises from an increase of solute trapping leading to extended solid solution.

Here, the metastability is topological since the metastable β-form is a disordered version of the room-temperature stable R-phase. In such a case, the slower the cooling rate, the smaller the proportion of metastable β-form. To highlight this behavior, sample 2 has been prepared starting from sample 1 annealed at 500 °C for 12 h (heating rate 5 °C/ min) and cooled slowly at 0.5 °C/min. Figure S4 displays the room-temperature X-ray powder diffraction pattern of sample 2. One can notice that the stabilization of the monoclinic R-form at room temperature occurred since all diffraction lines are broadened and superstructure peaks at low 2θ scattering angle appeared. Single monoclinic subcell parameters a ) 7.1356(1) Å, b ) 7.1434(1) Å, c ) 7.1444-(1) Å, β ) 89.733(1)°, and V ) 364.16(1) Å, 3 determined from Le Bail's fit disclose the weak distortion of the structure, while retaining the cell volume almost constant after the transformation (See Figure 4). A diffraction study of the thermal evolution of the (231) line was carried out upon heating up to 950 °C (Figure 5). Powder of sample 2 behaves the same way as La 2 Mo 2 O 9 with the occurrence of the first-order transition around 580 °C (Figure S4).

At this stage, it seems clear that a competitive phase selection problem takes place in La 1.85 Eu 0.15 Mo 2 O 9 because the two polymorphs (R + metastable β) coexist at room temperature. The crystallization kinetics for the monoclinic and cubic phases are all the more competitive than these phases are oxygen/vacancy ordered and disordered versions of the same structure. Figure 5 shows that a smooth curvature of the cell volume expansion is noted below 400 °C for this sample, whereas the thermal expansion was linear in this temperature range for the europium-richer composition x ) 0.2. Then, in the thermal range of ∼450-560 °C (in red color in Figure 5), La 1.85 Eu 0.15 Mo 2 O 9 has a monoclinic symmetry, as previously observed for La 1.8 Eu 0.2 Mo 2 O 9 . The continuous decrease of the slope, upon heating to 450 °C, for La 1.85 Eu 0.15 Mo 2 O 9 could reflect a progressive conversion of the metastable β-phase into R-form with a slightly smaller cell volume. Note, that the conversion taking place at 450 °C for La 1.8 Eu 0.2 Mo 2 O 9 is sudden. Hayward et al. [START_REF] Hayward | plots of ∆l/l 0 as a function of temperature, and stabilization of R-La 1.8 Eu 0.2 Mo 2 O[END_REF] have shown that a continuous evolution of the cell parameter a across the transition can be observed for La 2 Mo 2 O 9 when a powder sample is quenched from high temperature above 580 °C. In such a situation, the transition is thermodynamically second order.

The electrical property of the x ) 0.15 and 0.2 compositions was measured from pellets prepared with powders cooled down at 5 °C/min. The evolution of the conductivity with temperature is reported in Figure 6. Contrary to all expectations, the curve of La 1.8 Eu 0.2 Mo 2 O 9 did not show any thermal instability and looks like the curve of a cubic member. In contrast, the successive transitions highlighted by temperature-controlled X-ray diffraction on La 1.85 Eu 0.15 -Mo 2 O 9 powder sample remain present in the temperature dependence of conductivity. To elucidate this singular difference, the evolution of the (231) diffraction line upon heating to 950 °C was recorded on both samples, shaped as a pellet. Large pellets (13 mm in diameter and 0.8 mm in thickness) were prepared starting from ball-milled powder and sintered in the conditions determined previously. The diffractograms are displayed in Figure 9. Diffraction revealed that only the x ) 0.2 sample is sensitive to sample shaping because the cubic β-phase is henceforth stable in the whole temperature range explored. These results are in perfect agreement with conductivity measurements.

This metastable behavior and the stabilization of the cubic β-form through sample shaping as a pellet was recently evidenced in the aliovalent substituted lanthanum molybdate La 1.92 Ca 0.08 Mo 2 O 8.96 . 26 At first, one could have speculated that this metastability arises from the change of oxygen/ vacancy balance through calcium substitution in La 2 Mo 2 O 9 . This work demonstrates that such a behavior can also be encountered in an isovalent substituted molybdate La 1.8 Eu 0.2 -Mo 2 O 9 . However, a difference exists with La 1.92 Ca 0.08 -Mo 2 O 8.96 because, in this last composition, a substitute depletion/recombination process occurs above 640 °C, which is not observed here.

In the light of what we observed for La 1.8 Eu 0.2 Mo 2 O 9 , a way to explain the Marrero-Lo ´pez et al. conduction measurement performed on nanocrystalline R-La 1.9 Eu 0.1 Mo 2 O 9 (≈30 nm) is to consider that the phase stability of Eu-substituted compounds is also sensitive on grain size. As a matter of fact, the compositional range where metastability takes place for our samples would be extended to lower europium content when the samples are elaborated from freeze-dried precursors. This assumption would explain the coexistence of Rand β-phases that Marrero-Lo ´pez et al. observed in an extended range of composition 0.1 e x < 0.25. The metastability would also be morphological. 24 3.3.4. Metastability and Arrhenius/VTF Transition. The effect of repeated thermal cycles on the phase stability of La 1.85 Eu 0.15 Mo 2 O 9 and La 1.8 Eu 0.2 Mo 2 O 9 (previous samples 1 and 2) was then investigated by DT analysis. Three cycles of heating/cooling at a rate of 20 °C/min were performed on ∼50 mg of powder. All DTA thermograms of the x ) 0.15 analogue exhibit, upon heating, the sequence of phase transitions previously observed (Figure 10). However, a widening of the endothermic event around 580 °C occurs between the two first cycles. This signal remains unchanged during cycle 3. This broadening, induced by the first rapid cooling, suggests that the fraction of coexisting phases (R + β metastable) changes before reaching an equilibrium after cycle 2. This is the reason why the successive β metastable f R f β phase transition remains present during the cycle 3 (Figure 10). The higher the cooling rate, the larger the proportion of β metastable form. A comparison between diffraction pattern of the (231) line collected before DTA measurement (Figure 2) and after the last cycle (Figure 10) shows that the weaker peak at lower scattering angle (arrow in inset) becomes very diffuse. This is consistent with a slight decrease of the amount of the monoclinic phase.

For sample 1 of La 1.8 Eu 0.2 Mo 2 O 9 (Figure 10), the amount of the monoclinic phase is suspected to be lower than the amount present in La 1.85 Eu 0.15 Mo 2 O 9 . The second peak at around 580 °C has completely disappeared after the first cooling at 20 °C/min. This illustrates the decreasing tendency of the β metastable disordered phase to order with increasing cooling rate. DTA thermograms recorded during cycles 2 and 3 look like the curve of a cubic europium substituted samples with the Arrhenius/VTF transition at around 450 °C (Figure 8 and 10). Bearing in mind that a monoclinic symmetry at room temperature was identified on the powder diffraction pattern collected on the slowly cooled sample 2, the reminiscence of β-metastable/R transition upon the first heating up at 20 °C/min is surprising. It shows that the cooling rate of 0.5 °C/min used to prepare sample 2 is not slow enough to obtain a pure R-type phase at room temperature. A part of the β-metastable phase is retained in quantity too weak to be detected by powder diffraction (Figure S4). The two thermograms recorded during the next cycles 2 and 3 are similar to the curves of sample 1. The conversion into a single cubic phase seems to be effective as soon as the first rapid cooling down is performed.

Conclusion

In this paper, the solid solution La 2-x Eu x Mo 2 O 9 was reexamined to obtain a deeper insight into the influence of trivalent europium on the crystal structure, thermal stability, and electrical properties. As mentioned by Lubomirsky,[START_REF] Lubomirsky | [END_REF] collective effects induced by interacting point defects occur in fast ion conductor because the concentration of point defects is very high. When a partial substitution is performed in a solid such as La 2 Mo 2 O 9 , the equilibrium of point defects is naturally affected in a different manner depending on the substitution level. Below an europium content of x ) 0.1, the interaction of point defects (substitute/oxygen vacancies) leads to an order-disorder transition (R f β) associated with a sudden volume expansion (spontaneous strain). However, this study reveals that the situation could be more complex when the europium increases up to x ) 0.2, since the enthalpy of such a transition is greatly lowered by the random cationic substitution (see for instance DT thermograms).

Thereby, many factors as the thermal history (temperature, heating and cooling rates), the external stress (pressure), and the internal strain induced by sample shaping change the equilibrium of point defects. Indeed when a cooling rate of 5 °C/min is used for the preparation of La 1.85 Eu 0.15 Mo 2 O 9 and La 1.8 Eu 0.2 Mo 2 O 9 samples, the low temperature R-form and a pseudo-β-form can coexist at room temperature while preserving a homogeneous europium distribution within the sample. The stress induced by cooling allows the existence of a pseudo-β-form with a 2D disordering of the oxygen sublattice (TEM study), intermediate situation between the complex ordering in the R-phase, and 3D disordering in the β-phase. A relaxation of the system occurs upon heating leading to a release of topological metastability (successive β/R/β phase transitions). The decrease of the enthalpies associated to the (metastable β)/R and R/β transitions with increasing the europium content up to x ) 0.2 makes the permanent stabilization of the β phase possible, thanks to mechanical constraints such as sample shaping.

Above an europium content of x ) 0.2, increasing the substitution rate favors the interactions of points defects (substitute/oxygen vacancies). As pointed out by Greenberg et al., 28 the development of such a chemical strain effect could be accompanied by a large change in specific volume. In Bi 2 O 3 -based oxide ion conductors, 29 the clear increase of thermal expansion coefficient around 500 °C is ascribed to the disordering of oxide ions at high temperature. The extra volume expansion measured above 450 °C, which characterizes all cubic LAMOX members, could also be seen as a clear manifestation of this phenomenon. However, the pronounced curvature of the thermal volume expansion and of the conductivity thermal evolution would indicate that the reaction of defect association/dissociation upon heating is complex. This is the reason why, upon substitution, the trapping of oxygen vacancies around europium cannot decrease significantly the anionic conductivity because a lowering of the average bond energy occurs in parallel.

Figure 1 .

 1 Figure 1. RT X-ray diffraction patterns of La2-xEuxMo2O9 raw powder samples. The insets show the disappearance of the monoclinic splitting upon europium substitution through the evolution of the (231) pseudocubic lines.

Figure 2 .

 2 Figure 2. DTA thermograms upon heating (10 °C/min) in air of La2-xEuxMo2O9 raw powder samples.

Figure 3 .

 3 Figure 3. Typical SAED patterns of R-La1.85Eu0.15Mo2O9 along [100] (a) and of the β-type phase (b).

Figure 4 .

 4 Figure 4. Variations of the unit cell parameters and volume of La2-xEuxMo2O9 with x. Error bars are approximately the size of the data points.

Figure 5 .

 5 Figure 5. Temperature dependencies of the single cell volume of La2-xEuxMo2O9 raw powder samples determined from temperature-controlled X-ray diffraction data. To compare with La1.9Eu0.1Mo2O9, the thermal volume expansion of La2Mo2O9 is added as red (R-form) and black (β-form) solid lines for reference. The insets display the thermal evolution of the (231) pseudocubic reflection line for La1.85Eu0.15Mo2O9 and La1.8Eu0.2Mo2O9.

Figure 6 .

 6 Figure 6. Temperature dependencies of the electrical conductivity measured in air on dense ceramics of the La2-xEuxMo2O9 series, fitted with a conventional Arrhenius law in the linear part at low temperature (dashed black lines) and with a VTF model when departure from linearity is observed at higher temperature (solid black lines). At the bottom of each graph, plot of the first derivative of the conduction with respect to temperature is shown. The conductivity curve of La2Mo2O9 is added as solid red line for reference.

Figure 7 .

 7 Figure 7. Evolution with europium content x of (a) activation energy Ea (points) and pre-exponential factor σ0 (triangles) of the Arrhenius law determined in the temperature range of 300-500 °C for 0 e x e 0.1 and in the temperature range of 300-425 °C for x g 0.15 and (b) of the VTF parameters and the relative volume expansion [V950°C -V25°C]/V25°C. The constant Arrhenius/VTF transition temperature (from DTA signal, conductivity curves, and thermal expansion) is added as a dashed line.

Figure 8 .

 8 Figure 8. DTA thermograms of β-La2-xEuxMo2O9 raw powder samples.

( 26 )

 26 Selmi, A.; Corbel, G.; Lacorre, P. Solid State Ionics 2006, 177, 3051.

Figure 9 .

 9 Figure 9. Thermal evolution of the (231) diffraction line of dense pellet samples of La1.85Eu0.15Mo2O9 (a) and La1.8Eu0.2Mo2O9 (b) upon heating.

Figure 10 .

 10 Figure 10. Consecutive DTA measurements during repeated thermal cycles (3 loops of heating at 800 °C and cooling to 160 °C, rate of 20 °C/min) performed on powder samples of La1.85Eu0.15Mo2O9 (red line) and La1.8Eu0.2Mo2O9 (black lines, samples 1 and 2). The insets show the (231) cubic diffraction line recorded after the cycle 3. For arrow, see text.

  Vol. 46, No. 16, 2007 6403

Table 1 .

 1 First-Order Transition Temperatures of Raw Powder of La2-xEuxMo2O9 Determined by DTA in Air

		R f β transition	β f R transition
		temperature (°C)	temperature (°C)
	x	onset	peak max	onset	peak max
	0	568	571	558	548
	0.05	572	577	542	534
	0.1	573	581	537	503
	0.15	565	580	a	a
	0.2	562	580	a	a

a Too diffuse to be detected

Table 2 .

 2 Sintering Conditions and Relative Densities of La2-xEuxMo2O9 Pellets

		sintering	relative density
	x	temperature	F (%)
	0 0.05 0.1 0.15 0.2 0.25 0.3 0.4	1000 °C 1000 °C 1000 °C 1000 °C 1000 °C 1025 °C 1050 °C 1050 °C	96(1) 96(1) 97(1) 97(1) 98(1) 98(1) 99(1) 99(1)

La 2-x Eu x Mo 2 O 9 Inorganic

Chemistry, Vol. 46, No. 16, 2007 6399

Table 3 .

 3 Average

	0	R T -580	15.7
		580-1000	20.1
	0.1	RT-580	16.0
		580-1000	19.2
	0.15	570-1000	20.6
	0.2	RT-410	16.5
		570-1000	20.5
	0.25	RT-420	16.0
	0.3	RT-420	15.7
	0.4	RT-420	16.0

Thermal Expansion Coefficients of La2-xEuxMo2O9 Samples Determined by Temperature-Controlled X-ray Powder Diffraction x temperature range (°C) R (×10 -6 °C-1 )

Inorganic Chemistry,Vol. 46, No. 16, 2007

Inorganic Chemistry,Vol. 46, No. 16, 2007

Inorganic Chemistry,Vol. 46, No. 16, 2007


Georgios Kanakis
email: georgios.kanakis@jku.at

Stefan Fischer
email: stefan.fisher@jku.at

Djamel Eddine Khelladi
email: djamel-eddine.khelladi@irisa.fr

Alexander Egyed
email: alexander.egyed@jku.at

Supporting A Flexible Grouping Mechanism for Collaborating Engineering Teams

Keywords: collaboration, collaborating groups, software engineering, change propagation

Most engineering tools do not provide much support for collaborating teams and today's engineering knowledge repositories lack flexibility and are limited. Engineering teams have different needs and their team members have different preferences on how and when to collaborate. These needs may depend on the individual work style, the role an engineer has, and the tasks they have to perform within the collaborating group. However, individual collaboration is insufficient and engineers need to collaborate in groups. This work presents a collaboration framework for collaborating groups capable of providing synchronous and asynchronous mode of collaboration. Additionally, our approach enables engineers to mix these collaboration modes to meet the preferences of individual group members. We evaluate the scalability of this framework using four real life large collaboration projects. These projects were found from GitHub and they were under active development by the time of evaluation. We have tested our approach creating groups of different sizes for each project. The results showed that our approach scales to support every case for the groups created. Additionally, we scouted the literature and discovered studies that support the usefulness of different groups with collaboration styles.

I. INTRODUCTION

A multitude of engineering tools exist, covering the diverse needs of engineers, during the different phases of the software and systems engineering life cycle. These needs are spread throughout every phase of the software engineering process. There are tools for requirement engineering, architecture & design modeling, implementation, and beyond covering other engineering disciplines [START_REF] Holzner | Eclipse: A Java Developer's Guide[END_REF]. However, nearly all engineering tools are tailored to the needs of individual engineers and rarely to the needs of a collaborating group of engineers. Yet, collaborative engineering is the norm and the group of engineers play a vital role in this engineering process.

The importance of collaboration for software engineering groups has been recognized very early and has been an active research field since the beginnings of the 90's [START_REF] Grudin | Groupware and social dynamics: Eight challenges for developers[END_REF]. Collaboration has been described in taxonomies [START_REF]Computer-supported cooperative work: history and focus[END_REF], [START_REF] Cruz | Towards an Overarching Classification Model of CSCW and Groupware: A Socio-technical Perspective[END_REF] -within the software engineering domain and with other engineering disciplines (e.g., between mechanical engineers and software engineers) [5]. However, today's engineering tools usually focus on individual engineers who capture and handle artifacts locally on their workstation. In doing so, these tools fail to address many collaboration needs: such as the sharing of artifacts or changes at arbitrary times with arbitrary engineers in the same collaborative group.

As a consequence, explicit collaborative tools have emerged to address the lack of tooling support. However, all mainstream approaches, such as Git [START_REF] Loeliger | Version Control with Git: Powerful Tools and Techniques for Collaborative Software Development[END_REF], SVN [START_REF] Collins-Sussman | Version Control with Subversion[END_REF], support a single style of asynchronous group collaboration. They have limited means of sharing artifacts with some engineers (i.e., as desired in feature-driven engineering [START_REF] Turner | A conceptual basis for feature engineering[END_REF]) or no means of sharing artifacts' changes continuously (i.e., as required by pair programming [START_REF] Beck | Extreme programming explained: embrace change[END_REF], [START_REF] Martin | Agile software development: principles, patterns, and practices[END_REF]). A flexible collaboration approach, as we discuss in this paper, could help to overcome these limitations. Furthermore, a systematic mapping study by Portillo Rodriguez et al. showed that there is a lack of tools supporting collaboration in groups with different modes [START_REF] Rodriguez | Tools used in global software engineering: A systematic mapping review[END_REF].

Our experience, supported by literature [START_REF] Harvey | Cognitive, social, and environmental attributes of distributed engineering collaboration: A review and proposed model of collaboration[END_REF], suggests that the collaboration among engineers rarely follows limited groups, tools, timing intervals. Moreover, collaborating engineers may use the same tools (e.g., a group of programmers using the same programming tool) or different tools (e.g., a designer and a programmer working together). There are hardly any restrictions on who needs to collaborate with whom, when, and how. Thus, the collaborative groups can apply uniform artifact sharing mode or they may require different modes from each group member. An extension with a grouping mechanism to our previous flexible collaboration framework is proposed and discusses in this paper.

The contributions of this paper are as follows: First, we present scenarios that engineering groups can use to collaborate and propagate their changes. Second, we present a collaboration language that allows engineers to specify their desired collaboration style, both among individual members and in addition to collaborate within their group. Third, we present a change propagation algorithm that enforces the engineers' desired collaboration's parameters in respect to change propagation within groups. Fourth, a cloud-based prototype demonstrates a working implementation. There, the cloud serves as a change propagation facilitator. Lastly, to ensure the principles of the collaboration as defined by the language, we created a model using Alloy. The model verifies that the restrictions and parameters required for the data propagation stand for the applied change propagation algorithm.

We assessed the feasibility and scalability of our approach using four open source projects found on Github. The projects are: Google's SyzKaller, Amazon Web Service Javascript SDK, Facebook's RockSDB and Microsoft Visual Studio. We implemented them using our proposed collaboration language and tested them using their collaboration history (as available through commits). We performed experiments subdividing the engineers of these projects into groups of different sizes. For both collaboration modes, synchronous and asynchronous, we found that the number of engineers in a group had an impact on the time required to propagate all the changes. Furthermore, we compared these propagation times, from collaborating in groups, with scenarios in which engineers collaborate directly with each other without groups. Our experiments showed that the collaboration in groups propagated the same amount of changes significantly quicker than when all engineers collaborate individually with each other.

The rest of the paper is structured as follows: Section II provides the motivating examples and their challenges. Section III discusses our approach and a mixed collaboration scenario for group collaboration. Later, Section IV presents the evaluation of our approach, Section V explores the related work and lastly Section VI has our concluding remarks and future work.

II. MOTIVATING EXAMPLES

Collaboration among engineers is inevitable in modern engineering. Furthermore, it is essential for engineers to form groups within a project. Imagine a number of engineers that need to create two different groups. Naturally, each engineer has his own private workspace which contains his own artifacts. The engineer has also his/her own view of the artifacts within his/her tool's view. This information needs to be shared among the other four engineers in different ways based on the role of each engineer. This can occur through a shared workspace that every group member can have access to.

The core of this section presents three examples of engineers collaborating in groups using two different collaboration modes. The first mode is synchronous collaboration where a change made by an engineer is propagated instantly to the group and the collaborating engineers. The second mode is asynchronous which requires trigger actions of the engineers to propagate their changes to the group and the collaborating engineers. Finally, we describe when these two different collaboration modes are being mixed together.

A. Synchronous Group Collaboration

In this example, we use the synchronous collaboration mode, from now on, we call it Instant mode to present the collaboration among the different engineers within groups.

Figure 1 presents three engineers form a collaborating group (Alice, Bob and Charlie). These engineers are collaborating by sharing artifacts to their group workspace instantly. Imagine Alice creating changes in her private workspace, then these changes are instantly shared to the group workspace, from where they are instantly propagated to the private workspaces of Bob and Charlie. Similarly, Bob could make another change in his private workspace and share it instantly with the group workspace allowing all engineers to receive the changes instantly. This scenario is used for engineers that want to collaborate in a similar way as in GoogleDoc.

B. Asynchronous Group Collaboration

In this example, we use the asynchronous collaboration mode, from now on we call it Triggered mode. We will apply change propagation with the use of trigger actions between the private workspaces and the group workspace and vice versa. Figure 2 presents the scenario where an arbitrary number of engineers forming a group that shares information asynchronously. As in the previous scenario, Alice creates a change in her private workspace at one point, then she needs to perform a trigger action to propagate her changes to the group workspace. Similarly, Bob and Charlie are required to perform a trigger action on their side to receive Alice's changes to their

C. Mixed Use of Collaboration Modes

This motivating example is more complex since it uses both collaboration modes, instant and triggered in the same group collaboration. This scenario assumes that engineers would like to apply different collaboration modes per engineer.

Figure 3 presents different engineers with different collaboration preferences working together in the same collaboration group. In this scenario, Alice is the main developer of the project and she wants to share her changes instantly to the group as well as instantly receive theirs. While Bob is responsible for component integration and wants to receive only production ready artifacts and then share the completed integration work to the group thus prefers only triggered collaboration. Charlie is a test engineer and want to receive production ready code for black box testing while he shares his unit tests immediately with the group for Alice to receive these tests.

Hence, we see that different engineers and roles within group require different collaboration modes. Varying engineer's needs come also with different challenges in order to provide a collaboration framework to support them.

D. Challenges and Objectives

To date, tools supporting group collaboration usually follow asynchronous (GIT, SVN) or synchronous (Collabode [START_REF] Goldman | Collabode: Collaborative coding in the browser[END_REF], [START_REF]Real-time collaborative coding in a web ide[END_REF], GoogleDocs) collaboration mode. At most, some tools may support the change from one collaboration mode to the other (Cloud9 [START_REF] Fylaktopoulos | An overview of platforms for cloud based development[END_REF], ATCoPE [START_REF] Fan | Atcope: any-time collaborative programming environment for seamless integration of real-time and non-realtime teamwork in software development[END_REF]). The main challenge of a collaboration framework is to be able to support different collaboration modes within the same group of collaborators. An even more advanced challenge is not only supporting different collaboration modes for each engineer but also for each direction from and towards the group workspace as presented in Section II-C.

Furthermore, when a collaboration framework succeeds in providing mixed collaboration modes, it has to ensure that the changes are propagated correctly according to the collaboration styles. For example, an engineer with triggered collaboration mode should not receive a change unless he/she makes the necessary triggering actions to receive the change. Next, this framework should ensure that all data is transferred to the collaborating private workspaces regardless of the collaboration modes selected by the engineers. This requires all data to be able to be transferred instantly to these engineer selecting instant collaboration mode and the same data must be available for those engineer which selected triggered mode.

III. METHOD

This section presents our approach for a collaboration framework that supports group collaboration. The work presented in this paper focuses on the propagation of changes between collaborating engineers within groups. Services beyond the sharing of artifacts, for instance communication between engineers, are out of the scope of this work.

Our collaboration framework provides instant and triggered mode and also the ability to mix these modes based on the individual engineers needs. Additionally, our framework is tool independent since it can be applied to different kinds of artifacts. It allows to define the change propagation between the group workspace and the individual private workspaces (for the collaborations between individual engineers). Our approach consist of i) the configuration language to define the collaboration, and ii) the algorithm to propagate the changes within a group according to the defined collaboration.

A. Configuration language

The configuration language defines the syntax and semantics on how engineers are allowed to configure their collaboration. It allows engineers to select Instant or Triggered mode and the collaborating parties. In our approach the collaboration is established between two workspaces and it is uni-directional between these workspaces. Figure 4 illustrates the configuration language as it is represented in a meta model representation. The main elements of the configuration language are the CollaborationPrimitive which contains the information that is needed to establish the collaboration between the workspaces, the CollaborationType, the Trigger, the Change, the Workspace.

We define the CollaborationPrimitive as a tuple C = {T,S,R} such that • T is the CollaborationType.

• S is the sending Workspace.

• R is the receiving Workspace. We define CollaborationType (Ct) as an object such that Ct.Type ∈ {Instant, Triggered}. Workspace is defined as a tuple Ws = {Owner, Collabora-tionPrimitives, Changes, Trigger} such as

• Owner is a string. • CollaborationPrimitives is a set of CollaborationPrimi- tive. • Changes is a set of Change.
• Trigger is an action for starting change propagations when type=Triggered. To establish the group collaboration, we define the Group Workspace as an extension to the workspace element that inherits the owner field but it does not set it with a value(i.e., remains NULL).

Finally, we define a Change as an element to represent the changes made to an artifact by an engineer through a given tool (i.e., described by a workspace). The engineer who made the change is considered the change initiator.

The configuration of the group collaboration is the same as the configuration of individual collaboration since the group workspace is an extension of the workspace element. Based on the definition of the collaboration primitive, the engineer defines a sender and a receiver of the change propagation and the type of the collaboration. This allows the engineer to define the mixed mode of collaboration even between his/her relationship to the group.

As an example consider the scenario presented in Figure 3. Using our configuration language we would define six collaboration primitives, three with the engineers' workspaces as senders and the group workspace as receiver and three with the group workspace as sender and receivers each one of the three engineers' workspace. For each one of the primitive, we can define its type separately. Figure 5 presents an instance of our configuration language for the mixed scenario with six collaboration primitives for three engineers and the group workspace. We see that "Charlie" can define his collaboration with the group differently when he makes a change and when a change is propagated from the group workspace. Furthermore, Alice and Bob can work with their own individual styles within the same collaborative group.

B. Change Propagation

The behavioral aspect of the configuration language is the change propagation algorithm which is depicted in Algorithm 1. The algorithm takes as input either a change or a trigger (usually not both). The changes correspond to creations, modifications, and deletions of artifacts' elements within tools. The triggers denote events when engineers want to propagate these changes to and from a group. They are relevant in case of triggered collaborations only and ignored otherwise. In case a change is passed, the algorithm checks for each collaboration primitive defined by the change initiator (workspace), whether the collaboration primitive is instant and, if true, forwards the change to the defined receiver. In case the receiver is a group workspace, the same propagation algorithm is called, so the changes are propagated through all the collaboration primitives of type instant that have the group workspace as sender. As was discussed above, the receiver then synchronizes these changes with its respective tool normally a tool adapter, completing the change propagation. In case a trigger is passed, the algorithm checks for collaboration primitives in the sender of the trigger (also a workspace), that are of type triggered, and forwards the change to the defined receiver.

Imagine Alice making a change to her artifacts. The propagation algorithm is called (line 1). Automatically, the algorithm takes the change and retrieves its initiator collaboration set (algorithm line 3). It checks collaboration primitives that are of type instant and it will recover the collaboration primitive with the group workspace propagating the change to it (lines 4-5). Then, the group workspace initiates the propagation algorithm and checks its list of collaborations for instant collaborations (lines 6-11). In the scenario depicted in Figure 3 there are not any available. Thus, the algorithm terminates.

Later, Charlie wants to make a change to his code. Therefore, he needs to receive the latest code shared in the group to avoid introducing possible conflicts. He initiates the change propagation algorithm with a trigger that set the sender being the group workspace (line 1 and lines 12 -15). The group workspace recovers its set of collaborations that are triggered and selects the one that has the engineer who triggered the propagation (i.e., Charlie) as receiver (line 17). When found, the changes submitted by Alice will be passed to Charlie (Line 18). The sender is the group workspace but the initiator of the trigger is an engineer by creating and setting the trigger's sender and initiator field.

Similar, actions will occur when Bob needs Alice's changes. To call the change propagation algorithm from the group workspace, the trigger is instantiated with sender being the group workspace and Bob as its initiator. Then, Bob would be able to receive the changes made by Alice. The lines 22 to 24 are applied when a trigger has propagated changes to the group workspace from a private workspace and the group has collaborations that are of type instant with other private workspaces. In our scenario, if Bob wants to share his changes into the group. He needs to initiate the change propagation algorithm by sending a trigger. Then, the algorithm will retrieve his defined collaboration primitive with the group and it will propagate his changes to the group workspace.

C. Method's Verification

In order to verify our collaboration framework, we also built an Alloy model using the configuration language and the change propagation algorithm 1. In the Alloy model, we define the required predicates based on the requirement of the change propagation algorithm. The Alloy model allowed us to verify the soundness of our approach in respect to the required change propagation among defined collaboration primitives within Alloy model's scenarios.

D. Implementation

As a proof of concept, we have implemented our collaboration framework (configuration language and change propagation algorithm) in our platform called DesignSpace [START_REF] Demuth | Designspace: an infrastructure for multi-user/multitool engineering[END_REF]. We have set up change propagation in triggered and instant mode using both JUnit tests as well as actual tools to propagate changes among the engineers workspaces. To interact with the DesignSpace platform, we have built tool adapters for Eclipse, Microsoft Visio [START_REF] Helmers | Microsoft Visio 2016 step by step[END_REF] and others. The Alloy model has verified a number of properties with its implementation. However, we decided also to test this in the proof of concept implementation making changes to the defined collaboration primitives. During operation, we changed the receiver, in another case, we switched the collaboration primitive's type. After these changes, we observed the behavior of the system. The behavior of the system was as expected and verified by the Alloy model.

IV. EVALUATION

This section presents the evaluation of our approach for group collaboration between the different engineers. A main concern that the propagation algorithm may rise is its ability to scale. Thus, this section will answer that question. Does the approach scales with real projects? We also present our exploration for the usefulness of this approach to the different collaboration styles proposed by the literature and applied from different tools.

A. Evaluating Scalability

To evaluate the scalability of our approach we took real projects of different sizes and emulated their sizes in terms of engineers and average changes per engineer. We evaluated the scalability of our approach using four open source projects that are actively developed on GitHub. The selected projects are:

1) Google SyzKaller Project end if 33: end function 2) Amazon Web Services SDK for Javascript language 23) Facebook RockSDB Project3 4) Microsoft Visual Studio 4These projects have different sizes concerning the number of engineers that collaborate in them. The smallest, Google Syzkaller, has 73 contributors as by 07/01/2019 and the largest has 790 as by 07/01/2019. We consider these projects adequate for the scalability test since they are large enough and contain a significant number of engineers working on them. We also chose these projects since they are active and growing projects where a large number of changes occurred by their collaborating engineers.

For each project, we examined a set of 70 commits and we extracted the average number of changed files within these commits. This gives us the average number of changes an engineer performs for our framework to replicate these projects' collaboration behavior using our group collaboration framework. However, since we cannot deduct from GitHub the group sizes of collaborating engineers within these projects, we decided to emulate different sizes of group for every project. The groups sizes we decided to emulate are 5, 10, 20, 50, 100 and all engineers of a project in a group.

For the scalability study, we performed the measurements within a Windows Core-I7, 8GB ram computer, using the Eclipse platform to build unit tests. Each unit test is considered a test case where we spawned the required number of collaborators and we filled their workspaces with instances of changes. Then, within the test, we started the data exchanges. The measurements were performed within the JUnit environment and the number of runs were five per test case. From these five runs, we report their average time in the tables.

Table I summarizes the sizes of the projects selected for the scalability testing of our approach. The number of engineers per project are reported in the second column, the average changes an engineer performs in the project is reported in the third column. The forth column provides the total number of changes that will be propagated within the project. In each project, we are going to create groups of different sizes ranging from 5 engineers per group until all engineers belonging to one group. The last group may have a slightly less engineers, those remaining, than the rest of the groups. We measured the time required for all groups to transfer all changes among the group engineers. The time is measured within the JUnit [START_REF] Massol | JUnit in Action[END_REF] framework of Eclipse IDE [START_REF] Holzner | Eclipse: A Java Developer's Guide[END_REF].

Table II shows the time required for the propagation of changes among the collaborating engineers in all different groups in instant mode. The second column of Table II presents the time required to propagate all changes created by the engineers in a group of five engineers for all created groups. We see that regardless of the project's size the groups of five engineers require the same amount of time, as expected since the sizes of the groups are the same despite the total number of engineers. The third column presents the time required to propagate the changes engineers made within groups of 10 engineers. We see that doubling the size of the group does not seem to have an impact on the time required to propagate their changes remaining at 16ms. Only when the size of the groups becomes 20 or 50 engineers per group does the time increase to 30ms as seen in columns four and five in Table II. For the project Google Syzkaller, we could not perform the test with 100 engineers per group since there are not enough engineers in total in this project. For the rest of the projects, we see that adding 100 engineers in a group does not have significant impact in the time measurement for instant mode. When we created a single group with all engineers for the test case projects, we see that for the two smaller projects the time remains around 20ms. However, when the number of collaborating engineers in a single group is getting larger, the time also increases from 20ms in the Amazon Web Services (112 engineers) to 60ms for the Microsoft Visio project (790 engineers). The Facebook RockSDB project (414 engineers) requires 40ms time in the single group with all engineers.

From the measurements of Table II, we can conclude that the number of created groups does not really affect the time of propagation for the changes engineers are making in instant mode. However, the number of engineers per group is the key factor that affects the time any number of changes to be propagated among the collaborating engineers.

Table III shows the time measurements for the test cases of our approach using the triggered mode of collaboration.

Similarly, with the instant mode, we performed tests dividing the engineers into groups with different sizes. Note, that in our experiments we performed the triggering sequentially from all engineers of a group in order to assess the worst possible case of change propagation. We observed that the number of groups existing does not create significant changes to the time required to propagate the changes. The smallest project requires 16ms while the largest project requires 32ms for the group with size of five engineers. The time is two times higher between the two projects for the groups of 5 engineers but the number of engineers in the largest project is 10 times higher than the smallest project (73 engineers -790 engineers). This difference on the number of engineers, requires almost 10 times more groups in the largest project but only two twice the time to propagate the changes among all groups.

In contrast to the small effect of the number of groups required, we see that the number of engineers per group has a strong effect on the time measurement. In Table III, we observe that for the triggered mode of collaboration, the larger the group is, the more time it requires to propagate the changes of all members of the group to the remaining engineers in the group. This behavior is expected since the number of triggers that are required to be executed is larger. Again for the smallest test project, the Google SyzKaller, we could not perform the 100 engineers per group test. In almost all cases the time is smaller than a second. The cases with all engineers in one group for the two largest projects (Facebook RockSDB and Visual studio projects) are exceptions with times four second for the RockSDB and 21 seconds for the Visual studio.

Additionally, we see that the number of changes each engineer performs has an impact on the result but does not significantly affect the scalability of the approach. We presented the average changes per engineer in Table I where we see Amazon Web services project has 14 changes per engineer while the Google SyzKaller only three changes per engineer. Even though, the difference of the number of engineers between the two projects is only 39 engineers, the time measurements were twice as high which is explained by the different number of propagated changes.

B. Comparing Groups to Single Collaborations

We also consider the performance benefit of using groups in our approach instead of creating individual collaboration between each engineer. Thus, we performed also tests creating collaboration primitives between the workspaces of each engineer. We used the same test case projects and the same number of changes as presented in Table I.

Table IV presents the time measurements to propagate a number of changes without using group workspaces at the time of writing of this paper. We only create collaborations among the engineers of each project. The results for the instant collaboration mode using the created collaborations is presented in column five while column six presents the same set up using triggered collaboration mode. Column one to three contains the projects and their characteristics again to remind the reader the corresponding sizes. We observe that using a group among all engineers is significantly faster than creating individual collaborations among the different engineers of the project. We see that the benefit of applying groups increases, with the number of collaborators in a project. In the smallest project, without a group collaboration, we measured around 0.04s for instant and 0.08s for the triggered collaboration mode. The same project have around 0.02s and 0.07s time to propagate changes when the group collaboration was applied. For the largest project, we measured 0.25s for the instant collaboration mode and around 47s for triggered mode while using a group collaboration the measurements are 0.06s and 21s respectively.

Similarly, we observe benefit when using the group collaboration for the two intermediate projects, Amazon WS SDK and Facebook RockSDB. Thus, we can conclude that the use of groups can improve the change propagation within the team when applied compared to establishing individual collaborations among the team members.

C. Usefulness of Group Collaboration

Until this point, we demonstrated that our approach is scalable using real open source projects to evaluate it. The discussion about the usefulness will take part in this subsection. Even though, we have not explicitly done an experiment to evaluate the usefulness of group in collaboration, we researched for other works that have evaluate the usefulness of group collaboration. Cook et al. [START_REF] Cook | A user evaluation of synchronous collaborative software engineering tools[END_REF] presented a user evaluation of collaborative tools for software engineering. They used a post experiment questionnaire to evaluate the experiments qualitative aspects. The experiment consisted of tools with asynchronous/triggered collaboration mode and synchronous/instant collaboration mode. The usefulness of both modes in the distributed setting was 15.7 out of 20 in the survey climax with 20 being highest and 1 being lowest. The instant mode scored 14.8 and the general source code sharing scored 16.4 out of 20. Furthermore, the rapid use of Git in developing new open source projects as described in Barr et al. [START_REF] Barr | Cohesive and isolated development with branches[END_REF] is a good indication of the usefulness of groups within software engineering. They also performed a semi-structured interview with six people in four different projects to assess the need and usefulness of branches and revision control systems. The interviews revealed that engineer in collaborating groups require cohesion and isolation during development but also easy merge of work. These features made GIT a successful tool among developers. Therefore, as we argue that we can simulate the GIT collaboration style, we provide the benefits of GIT to collaborating engineers in a group.

D. Limitations

This work is limited to explore the information exchange between the collaborating parties and does not focus on the collaboration awareness and communication between the collaborating parties. The goal of our evaluation was to provide the evidence for the scalability of our approach. For the awareness among collaborating parties, we have built a graphical user interface. It is linked to our cloud platform and adds collaboration management and awareness functionality to our framework.

V. RELATED WORK

Mcguire et al. [START_REF] Mcguire | Shade: Technology for knowledge-based collaborative engineering[END_REF] had proposed a framework called SHADE that tried to be flexible in exchanging the different engineering knowledge among defined producers and consumers. SHADE framework did not have any selection or suggestion to allow engineers to define the synchronous or asynchronous mode of the knowledge exchange. Our approach has these modes in the center of its implementation.

Steinfield, Jang and Pfaff [START_REF] Steinfield | Supporting virtual team collaboration: The teamscope system[END_REF] had proposed the Team-SCOPE system to support the needs of distributed team of a project. TeamSCOPE implements features to support communication awareness and artifact sharing. The artifact sharing feature is a stand-alone application which has a preset way for the members of the team to exchange their artifacts. In our approach, engineers can define their mode of collaboration based on their individual needs. Also, our approach is not a specific tool but a framework that can be implemented in different tools and for different artifacts.

Li et al. [START_REF] Li | Supporting ad-hoc collaboration with group-based rbac model[END_REF] proposed on their work a permission driven collaboration scheme. The permission scheme requires any sharing of information to be explicitly defined with a permission role towards the accessed data. Their work utilizes virtual groups to address problems within multi-domain environments where different engineering knowledge must be shared among different groups. Their work differs from ours since they do not discuss the change propagation in respect to the different collaboration modes but they describe a mechanism to manage the distribution of members among the groups.

M. Pasqual and O. Weck [START_REF] Pasqual | Multilayer network model for analysis and management of change propagation[END_REF] present on their work the notion of change propagation and a model to efficiently propagate change requests to the different groups of engineers within a project. This work or any related to it differs significant from our work since they discuss the propagation of change as a change request from external source. Whereas we discuss the change propagation as a change made by the engineers to the artifacts one created.

Fylaktopoulos et al. [START_REF] Fylaktopoulos | An overview of platforms for cloud based development[END_REF] presented an overview of the platforms for cloud based development that most of them support groups with instant or triggered collaboration mode but none of them support the possibility of mixing these modes for the individual engineer. In some cases, the engineers can switch the group collaboration from one mode to the other but they cannot choose individually within the group or per direction, the mode they prefer.

VI. CONCLUSION

In today's software engineering landscape, collaboration is an essential part of the software engineering process. It enables engineers to overcome the limitations of capabilities of single humans and to resolve complex and difficult tasks. Teams are the core form of collaboration among engineers. Collaborative teams can vary on the how, when and what engineers collaborate with. Tools exist that provide group collaboration. However, they provide limited options for flexibility to engineers to apply their preferred styles. Our approach proposed a framework that can allow engineer form collaborating groups the way they decide. Simultaneously within the group, we can have engineers collaborating instantly or with triggered mode allowing them to apply their individual work style or the style that their role in the project requires. We ensure that these conditions are holding within the group by formally verifying our collaboration language and its change propagation algorithm using Alloy. Later, we present evidence of the scalability of our approach using four real large open source projects. These projects were found on GitHub and were actively developed at the time of writing. These projects had between 73 and 790 engineers working on them. We divided these engineers into different groups ranging in size from five engineers, and increased these numbers until all engineers were in one group. Furthermore, we compared the group usage with the individual collaboration among all engineers in the projects. This allowed us to observe the benefits of using the group collaboration over the individual interlinked collaboration. We plan to examine the ability to extend our framework and implement workspace and group hierarchies to provide further collaboration possibilities.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Instant Group Collaboration Scenario

Fig. 3 .

 3 Fig. 3. Mixed Mode Group Collaboration Scenario

Fig. 4 .

 4 Fig. 4. High Level Model For The Configuration Language

Fig. 5 .

 5 Fig. 5. Illustration of Mixed Scenario with Our Approach as Model Instance

SKD-JS's GitHub page: https://github.com/aws/aws-sdk-js

RockSDB's GitHub page:https://github.com/facebook/rocksdb

Visual Studio's GitHub page: https://github.com/Microsoft/vscode

ACKNOWLEDGMENT

The research leading to these results was funded by the Land of Upper Austria -Joint International PhD Program in Informatics under the grant number Wi-2014-202477/6. Funded by the JKU Linz Institute of Technology (LIT) the state of Upper Austria, grant no. LIT-2016-2-SEE-019 and Pro2Future, a COMET K1-Center of the Austrian Research Promotion Agency (FFG), grant no. 854184.