Laurent Puech
email: puech@icmcb-bordeaux.cnrs.fr

Christophe Cantau

Philippe Vinatier

Gwenaëlle Toussaint

Philippe Stevens

Elaboration and Characterization of a Free Standing LiSICON Membrane for Aqueous Lithium-Air Battery

Keywords: Metal-air battery, Lithium anode, Li 2 O -Al 2 O 3 -TiO 2 -P 2 O 5 system, LiPON, Solid electrolyte

In order to develop a LISICON separator for an aqueous lithium-air battery, a thin membrane was prepared by a tape-casting of a Li 1.3 Al 0.3 Ti 1.7 (PO 4 ) 3 -AlPO 4 based slip followed by a sintering step. By optimizing the grain sizes, the slip composition and the sintering treatment, the mechanical properties were improved and the membrane was reduced to a thickness of down to 40 μm. As a result, the ionic resistance is relatively low, around 38 Ω for a 55 μm membrane of 1 cm 2 . One side of the membrane was coated with a lithium oxynitrured phosphorous (LiPON) thin film to prevent lithium metal attack. Lithium metal was electrochemically deposited on the LiPON surface from a saturated aqueous solution of LiOH. However, the ionic resistance of the LiPON film, around 67 Ω for a 1.2 μm film of 1 cm 2 , still causes an important ohmic loss contribution which limits the power performance of a lithium-air battery.

Introduction

Metal-air batteries are based on the use of a metal negative electrode in combination with an oxygen positive electrode. Such a positive electrode theoretically has an infinite capacity, because the active material -the oxygen gas-is not stored in the battery, only the product of the reaction is. Among the different metals, lithium is very interesting because of its high theoretical capacity (around 3 800 Ah/kg) and the favourable oxydo-reduction potential of the Li + /Li couple versus these of the oxygen: ∆E = 3.4 V for aqueous oxygen electrodes and ∆E = 3.0 V for non-aqueous oxygen electrodes. As a result, lithium-air batteries have a high theoretical energy density at more than 10 000 Wh/kg, comparable to that of gasoline (13 000 Wh/kg). However, this density is only related to the mass of lithium and does not include the other components of the battery: the air electrode, its discharge product, the liquid and solid electrolytes and the package. Moreover, the practical useable energy density and the power density of the battery are limited by the ohmic loss caused essentially by the electrical resistance of the solid electrolytes. As a result, an energy density of 500 Wh/kg may be considered to be a more realistic but still very interesting objective.

The first rechargeable lithium-air battery was made by Abraham and Jiang [1] in 1996. It consisted of a Li metal foil as anode, an organic polymer membrane as solid elec-trolyte and a thin carbon composite exposed to pure oxygen as the oxygen electrode. Such a battery based on nonaqueous electrolyte is generally limited by the formation of Li 2 O 2 inside the pores of the oxygen electrode and by the decomposition of the organic solvent resulting from the formation to a super-oxide radical [2]. Aqueous lithiumair batteries using an aqueous electrolyte such as LiOH solution do not have these problems. The product of the reaction (LiOH,H 2 O) is stored as a solid in the aqueous compartment and not in the electrode [3]. Moreover, the use of a polymeric anion-exchange membrane in the oxygen electrode prevents LiOH precipitation inside the electrode, but also the formation of Li 2 CO 3 . Such a cathode can run with untreated air. Among the other main limitations, the oxygen electrode has a poor reversibility. It can be destroyed by the oxygen evolution during the charge of the battery. Toussaint et al. [4] proposed an oxygen bielectrode: during the charge, a stainless steel electrode in the aqueous electrolyte shunts the porous air electrode to play the role of an oxygen evolution electrode.

A watertight protection of the lithium electrode is however necessary to prevent its oxidation by the water. This protective barrier needs to be stable to the aqueous electrolyte. Aono et al. [5] proposed a water-stable NaSICONlike electrolyte: Li 1+x Al x Ti 2-x (PO 4 ) 3 (LATP). For x ∼ 0.3, this LiSICON offers a good ionic conductivity, close to 7 × 10 -4 S/cm. Thokchom and Kumar [6] proposed a way to elaborate a membrane based on 14Li 2 O -9Al 2 O 3 -38TiO 2 -39P 2 O 5 (LATP-AP), a composite of LATP and AlPO 4 . This stoichiometry was chosen by these authors because of the reproducibility of its synthesis and its good ionic conductivity, similar to that of LATP. The solid electrolyte should also be protected from attack by lithium metal. This can be done using a lithium-stable electrolyte as a lithium oxynitrured phosphorous glass (LiPON) as proposed by Bates et al. [7]. This can be obtained as a thin film by the sputtering of a Li 3 PO 4 target under a nitrogen discharge. Its low thickness compensates its relative low ionic conductivity, close to 2 × 10 -6 S/cm. Alternatively, a liquid organic electrolyte such as 1 M LiClO 4 in ethylene carbonate/dimethyl carbonate can be used between the LiSICON membrane and the lithium metal as proposed by Wang et al. [8]. The liquid acts as an interface between the lithium and the LiSICON, but the formation of lithium dendrites will eventually come in contact with and attack the ceramic electrolyte to destroy it. A very good electrode/electrolyte interface can also be obtained by using a stainless steel thin film (0.3 μm) as current collector, coated onto the LiPON thin film protection [9]: the lithium metal is then electrochemically deposited between the LiPON and the current collector from a saturated lithine solution during first charge process after the battery manufacture.

In a previous study [3], an aqueous lithium-air battery was made using an oxygen bi-electrode (see figure 1). On the anode side, the solid electrolyte consisted to a glass-ceramic LiSICON membrane supplied by Ohara [10] coated by a protective LiPON film. As descripted above, the lithium electrode was electrochemically deposited after the battery manufacture. However, the thickness of the Ohara membrane (160 μm) was still too high and induced a resistance of around 160 Ω for one cm 2 area. Such a resistance causes an important ohmic loss which limits the performances of the battery.

The aim of this work was to improve the lithium halfcell with a thinner membrane, less than 50 μm, and based on a ceramic LATP-AP powder, chosen for the reproducibility of its synthesis and its high conductivity. This membrane should be sufficiently strong to be free standing and to be manipulated. The lithium half-cell built with this membrane was then characterized by electrochemical analyses by depositing a lithium electrode and evaluated.

Experimental

Synthesis of LATP-AP Powder and its Characterizations

As proposed by Thokchom and Kumar [6], a LATP-AP glass was prepared by melting a Li 2 CO 3 , Al 2 O 3 , TiO 2 and NH 4 H 2 PO 4 mixture at 1450 • C followed by tempering on a steel plate heated close to 500 • C. The glass was then milled by planetary ball milling to obtain a powder. The LATP-AP glass was crystallised by heating at 900 • C for 10 hours. In order to obtain submicronic and homogeneous grain size powder, attrition milling was performed during 5 hours using ethanol as a solvent.

Thermal dilatometric analyses were done using a Netzsch 402ED dilatometer. These consisted in measuring variations in the length of pellets with the furnace temperature using a saphir reference. The thermal treatment constituted in heating at 10 • C/min from room temperature to 1200 • C, followed by cooling of the furnace to room temperature.

The X-ray diffraction analyses were performed using a Philips X'Pert Powder diffractometer equipped with a Cu anode (λ = 1.5418 Å).

Elaboration of the Lithium Half-Cell

A ceramic LATP-AP powder based slip was made with ethanol and xylene as solvents, menhaden oil as dispersant, benzyl-butyl phtalate (BBP) and poly-ethylene glycol (PEG) as plasticizers, and poly(vinyl-butyral-co-vinylalcohol-co-vinyl-acetate) (PVB-VA-VAc) as binder. The slip composition needs to be adjusted to optimize its rheological properties depending on the grain size of the ceramic powder and to improve the mechanical properties of the membrane before and after the sintering.

A raw membrane was prepared by a tape casting of the slip with a thickness of 0.15 mm on a silicone coated Mylar sheet. After the elimination of the solvents at room temperature, this membrane was peeled off and disposed between two silica glass plates to conserve its flatness. The organic additives were eliminated during a slow heating step (+0.25 • C/min) followed by a 1 hour plateau at 450 • C. The membrane was then sintered with a rapid heating rate (+7.2 • C/min) and a 1 hour plateau at 1080 • C.

For the LiPON deposit, a Li 3 PO 4 target was made from milled β-Li 3 PO 4 powder. In order to avoid that the β → γ phase transition at 500 • C occurs during the sintering step, the powder was heated at 850 A γ-Li 3 PO 4 based pellet was prepared with a 5 cm diameter and a 4 mm thickness, and sintered at 620 • C during 12 hours. The target was then glued onto a copper backing plate using a silver epoxy glue.

LiPON and the stainless steel current collector (SSCC) thin films were deposited by RF magnetron sputtering using a Plassys MP 300 T apparatus opening in a dry box under argon with the parameters listed on the table 1. In the two cases, the pressure was kept during the deposition at 1 Pa using a Vat vacuum valve and a Vat PM-3 pressure controller.

The negative compartment was then built under normal laboratory air.

Impedance Measurements and Electrochemical Analyses

Two SSCC thin films were deposited by RF magnetron sputtering on the two side of a 56 μm LATP-AP membrane. Impedance measurements were performed using a Solartron 1260 impedance analyser, with a 10 mV amplitude and a frequency varying between 1 Hz and 10 MHz. In order to measure the impedance of a 0.75 μm LiPON film, a SSCC/LiPON/SSCC sandwich structure was deposited by RF magnetron sputtering on a glass substrate with an overlap area of 0.04 cm 2 . Impedance measurements were performed with a 50 mV amplitude and using the same impedance analyser and the same frequency range as those of LATP-AP.

To evaluate its performances during the charge process, the lithium half-cell was disposed vertically in contact with an aqueous 2 M LiOH solution and a stainless steel counter electrode. The working electrode potential was measured using a Hg/HgO/KOH (1 M) reference electrode. The cyclic voltammogram was performed using a Biologic VMP3 potentiostat at a scan rate of 20 mV/s between -0.5 and -3.5 V versus Hg/HgO/KOH (1 M).

Results and Discussion

Synthesis of the LATP-AP membrane

After treating the glassy LATP-AP powder at 900 • C for 10 hours, the X-ray diffractrogram is typical of a crystallized sample (see figure 2). As a result, we can consider this powder to be a ceramic powder elaborated from a glass-ceramic process. As proposed by Wong et al. [11], the most intensive peaks can be identified as a NASICONlike structure: LiTi 2 (PO 4 ) 3 (LTP) [12] with a change of the cell volume. The laser granulometry results varying with the duration of the attrition milling (see figure 3) show drastic decreases of both the median grain size D V (50%), close to 0.4 μm after 2 hours, and the diameters D V (10%) and D V (90%) -the diameter D V (n) is the maximal size of the smallest grains constituting the volume ratio n of the powder. These decreases are also visible by scanning electron microscopy (see figure 4). Moreover, we can note an improvement of the homogeneity of the grain sizes: the ratio of D V (90%) versus D V (10%) decreases from up to 20 to near 5 after a 5 hours attrition milling.

Optimization of the sintering is an important key to improve the density and to obtain a strong and efficient membrane. To evaluate effects of optimized milling on the sintering, thermal dilatometric analyses of ceramic LATP-AP powder were performed before and after the attrition milling. We notice a higher shrinkage for the milled powder (see figure 5a). Before the attrition milling, according to the shrinkage rate curve (see figure 5b), the sintering is broken down into three steps corresponding to the three local maximums of the rate: 870 • C, 915 • C and 1065 • C. This may be the consequence of the heterogeneity of the grain sizes. After a five hours attrition milling, the shrinkage rate curve only presents a peak at 1080 • C. This is coherent with the improvement of the grains size homogeneity. Moreover, this analysis enabled us to define the optimal temperature of sintering at 1080 • C for a maximal shrinkage. This helped us to reduce the membrane thickness without losing its mechanical properties.

Because of the increase in the powder specific surface, the slip constituents and their concentrations needs be adapted: the solvents proportions should be increased to keep the rheological properties of the slip. Moreover, it is necessary to increase the binder ratio to facilitate the removal of the raw membrane from the Mylar sheet. However, too high proportion of organic additives may cause kracks during the sintering. The proposed slip composition (see table 2) improved the mechanical properties of the raw membrane and helped us to reduce its thickness, and also kept its cohesion after the sintering.

As a result, we obtained a free standing and handleable membrane (see figure 6). Its thickness is closed to 40 μm according to the section measurement by SEM (see figure 7). Its density is estimated to be around 2.8 g/cm 3 by buoyancy measurements into diethylphtalate and water. This value is close to the LATP-AP theoretical density, between 2.7 and 2.8 g/cm 3 . However, as volume loss induced by open pores is not taken account by buoyancy measurements, we can estimate that the compactness is below one. We notice the presence of pores on the crosssection views (see figure 7b), which probably results from the gas evolution during the elimination of the organic constituents. Inside the pores, the grains have a cushion-like shape, whereas on the fracture, its have a more angular shape resulting from the optimized sintering.

Impedance Measurements

Impedance measurements were performed on a ceramic LATP-AP membrane (see figure 8). Its electrical behaviour is modelled by a parallel circuit consisting of a resistance R LATP and a constant phase element CPE LATP . As proposed among others by Hamon et al. [13], a serial resistance R S1 and a serial constant phase element CPE S1 should be use to model the electrical behaviour of the

) LATP circuit Serial circuit R LATP (Ω) 39 R S1 (Ω) 7.2 Q LATP (F) 2.5 × 10 -7 Q S1 (F) 1.6 × 10 -6
P LATP 0.87 stainless steel electrodes. R S1 accounts for the current collector resistance and a CPE is used because the current collector is not a perfectly blocking electrode. The CPE impedance Z CPE is a function of a capacity Q and a potency P (0 < P < 1):

P S1 0.92 b) LiPON circuit Serial circuit R LiPON (Ω) 1820 R S2 (Ω) 260 Q LiPON (F) 8.1 × 10 -9 Q S2 (F)
Z CPE = 1 Q (iω) P (1)
As a result, the impedance Z LATP of the equivalent circuit is expressed by:

Z LATP = 1 1 RLATP + Q LATP (iω) PLATP + R S1 + 1 Q S1 (iω) PS1 (
2) The ohmic resistance of the LATP-AP membrane can be identified with R LATP . As a result, the determination of equivalent circuit parameters (see table 3) enabled us to estimate the ionic conductivity of the membrane at 1.8 × 10 -4 S/cm. Similar impedance measurements were performed on a LiPON film (see figure 9). According to previous studies including those of Hamon et al. [13], the impedance Z LiPON can be expressed by:

Z LiPON = 1 1 RLiPON + Q LiPON (iω) PLiPON +R S2 + 1 Q S2 (iω) PS2
(3) As above, the resistance of the LiPON film can be identified with R LiPON . We calculated the ionic conductivity to be close to 1.8 × 10 -6 S/cm at 298 K using the equivalent circuit parameters (see table 3).

Electrochemical Analyses

A gradually increasing reduction potential E we was applied on the working electrode of the half-cell and measured with a Hg/HgO/KOH (1 M) reference electrode, up to -3.5 V (see figure 10). Between -1.5 and -1.9 V, the local current peaks are probably due to the electrochemical reduction of impurities as adsorbed water. This artefact produced low currents which suggested that these impurities was present in low quantities: they did not seem to have destructive effect on the half-cell. Once the reduction potential of Li + is reached at -3.3 V, a rapid increase in current is observed due to the lithium metal electroplating. When reversing the cycle by decreasing the applied potential between -3.5 V and -3.0 V, the electrochemically deposited lithium metal is consumed by electrochemical oxidation of lithium metal to Li + . Between -3.0 V and -3.5 V, the cyclic voltametry curve presents a straight shape which corresponds to a reversible phenomenon. We can estimate a resistance close to 105 Ω for one cm 2 area from the slope of this straight curve. If we calculate the membrane ohmic resistance by the addition of the resistance of a 55 μm LATP-AP membrane, 38 Ω.cm 2 , and the resistance of a 1.2 μm LiPON thin film, 67 Ω.cm 2 , we obtain the same value. This demonstrates that the electrochemical lithium metal deposition during charge and the lithium consumption during discharge are limited only by the lithium ion conduction through the solid electrolyte. As a result, we can conclude that the interface resistances are negligible compared to the membrane resistance. The absence of a large water reduction peak in the voltamogram also shows that the LATP-AP membrane appears to be watertight.

Discussion about the protective coating

We can note that the LiPON resistance, 67 Ω for a one cm 2 area of a 1.2 μm film, contributes for a large part to the total membrane resistance, as a result of its low conductivity (1.8 × 10 -6 S/cm). On the surface of the membrane (see figure 11), we can observe pores with a size close to 1 μm. As a consequence, a LiPON film of more than 1 μm is necessary to compensate for the membrane roughness. This is caused by the micron size grains which constitute 10% in volume according to the measurement of the grain size distribution (see figure 3) and by the evolution during the elimination of the organic additives.

One solution to reduce the LiPON thickness would be to reduce the roughness of the ceramic membrane. This could be done by the elaboration of a membrane using smaller grains. Instead of a solid state reaction followed by a milling step, some authors [14,15] mentioned the possibility to synthesizing smaller LATP grains by using soft chemistry processes: this route enabled Wu et al. [16] to elaborate micronic LATP film.

An other solution could be to replace the LiPON film by a lithium-stable Li + ionic conductor. Xu et al. [17] reported on the good stability of the interface between Li 1.5 Al 0.5 Ge 1.5 (PO 4 ) 3 -0.05 Li 2 O and a lithium metal anode. Moreover, this ceramic had a higher conductivity than LiPON, around 5 × 10 -3 S/cm according to Thokchom et al. [18]. However, the interface with a lithium anode introduced an important ohmic loss, around 20 kΩ, according to impedance plots from Xu et al. [17] and our own studies. Deiseroth et al. [19] presented Li-argyrodite materials, Li 6 PS 5 X (X ≡ Cl or Br), with a conductivity close to 10 -3 S/cm. Moreover, Stadler and Fietzek [20] announced that this material have good stability in contact with lithium anode. Recently, a new lithium superionic conductor, Li 10 GeP 2 S 12 , was reported by Kanno et al. [21] with a conductivity higher than 10 -2 S/cm and a good electrochemical stability front of a lithium anode.

Conclusion

An optimized milling, an optimized slip composition and an optimized sintering enabled us to prepare a ceramic LATP-AP membrane which was sufficiently strong to be free standing and handleable. This membrane was sufficiently thin to minimize its ionic resistance and therefore significantly reduced the ohmic loss in an aqueous lithiumair cell. Moreover, electrochemical analyses in contact with an aqueous solution showed that this membrane was watertight. Finally, growth of lithium from an aqueous solution was demonstrated in a lithium half-cell using a thin LATP-AP membrane. However, this study pointed out the limiting effect of the protective LiPON thin film, with an ionic resistance higher than that of the LATP-AP membrane. As a result, for a current density of 10 mAh.cm -2 , a 1 V ohmic loss through the membrane can be estimated. This value is too high to reach a good energy density and power density. Further studies should be performed to reduce the LiPON thickness, for example by reducing the roughness of the membrane surface, or to substitute the LiPON by a better ionic conductor. This study of a thin LiSICON membrane was an important step to demonstrate the feasibility of an aqueous lithium-air battery and to solve its main limitations.

Figure 1 :

 1 Figure 1: Aqueous lithium-air battery as proposed by P. Stevens et al. [3]. a: O 2 reduction electrode with a polymeric anion-exchange membrane; b: O 2 evolution electrode (stainless steel grid); c: LiSI-CON membrane; d: protective LiPON thin film; e: stainless steel current collector (thin film); Li film: electrochemically deposited after the battery manufacture.

Figure 2 :Figure 3 :

 23 Figure 2: X-ray diffractrograms of the synthesized ceramic LATP-AP powder; unmarked peaks are attributed to Li 1.3 Al 0.3 Ti 1.7 (PO 4 ) 3 .

Figure 4 :

 4 Figure 4: Ceramic LATP-AP powder after (a) and before (b) the attrition milling by SEM.

Figure 5 :

 5 Figure 5: Thermal dilatometric analyses of ceramic LATP-AP before (dotted lines) and after (solid lines) the attrition milling; the arrows indicate temperature evolutions versus time: increasing until 1200 • C then decreasing.

Figure 6 :

 6 Figure 6: Resulting free standing LATP-AP membrane.

Figure 7 :

 7 Figure 7: Cross-section of LATP-AP membrane by SEM.

  a

Table 3 :Figure 8 :

 38 Figure 8: Cole-cole plot of LATP-AP membrane and its equivalent electrical circuit.

Figure 9 :Figure 10 :

 910 Figure 9: Cole-cole plot of LiPON thin film at 298 K and its equivalent electrical circuit.

Figure 11 :

 11 Figure 11: Surface of sintered LATP-AP membrane by SEM.

Table 1 :

 1 Parameters of the thin film deposition; SSCC: stainless steel current collector; SCCM: cm 3 /min at 25 • C and 1 bar.

	Film	LiPON	SSCC
	Thickness	1.6 μm	0.3 μm
	Target	Li 3 PO 4	Stainless steel
	Gas	N 2	Ar
	Flow	45 SCCM	50 SCCM
	Pressure	1.0 Pa	1.0 Pa
	Power	40 W	50 W
	Duration	8 hours	20 minutes

• C during 12 hours.

  The constants a and c can be estimate to 8.501 Å and 20.82 Å respectively, instead of 8.513 Å and 20.878 Å for LTP. These values are very closed to those determined by Aono et al.[5] for Li 1+x Al x Ti 2-x (PO 4 ) 3 with x ∼ 0.3. Because of the aluminium substitution, the cell volume decreases: the Al 3+ radius (0.535 Å) is inferior than the Ti 4+ radius (0.605 Å). According to Wong et al.[11], other peaks can be attributed to AlPO 4 and rutile (TiO 2 ). These results are in accordance with the composition of LATP-AP: 14Li 2 O -9Al 2 O 3 -38TiO 2 -39P 2 O 5 may correspond to Li 1.3 Al 0.3 Ti 1.7 (PO 4 ) 3 -(∼ 0.5) AlPO 4 -(∼ 0.06) TiO 2 . Beside these structures, two peaks, 39.64 • and 46.12 • , are unattributed.

Table 2 :

 2 Optimized slip composition.

Acknowledgement

The authors acknowledge financial support provided by the french national agency for research (ANR) under the STOCK-E program, LIO and LIO2 project.


S Couillaud

E Gaudin

F Weill

S Gomez

C Stan

D Planté

S Miraglia

J L Bobet
email: bobet@icmcb-bordeaux.cnrs.fr

Structure of a new ternary compound with high magnesium content, so-called Gd 13 Ni 9 Mg 78

Keywords: Rare-earth intermetallics, Magnesium, Nanocrystallite, Hydrogen storage

The magnesium metal rich composition Gd 13 Ni 9 Mg 78 was synthesized from the elements in sealed tantalum tubes in an induction furnace. According to the X-ray diffraction, the EPMA analyses and the dark field images obtained by TEM, a new compound with a composition ranging from Gd 10-15 Ni 8-12 Mg 72-78 and low crystallinity was brought to light.

In order to increase the crystallinity, different experimental conditions were investigated for numerous compounds with the initial composition Gd 13 Ni 9 Mg 78 . Also, several heat treatments (from 573 K to 823 K) and cooling rates (from room temperature quenched down to 2 K/h) have been tested. The best crystallinity was obtained for the slower cooling rates ranging from 2 to 6 K/h.

From the more crystallized compounds, the structure was partially deduced using the transmission electron microscopy and an average cubic structure with lattice parameter a = 4.55 Å could be assumed. A modulation along both a*and b* axis with vectors of modulation q1 = 0.42a* and q2 = 0.42b* was observed. This compound so-called Gd 13 Ni 9 Mg 78 absorbs around 3 wt% of hydrogen at 603 K, 30 bars and some fair reversibility is possible, because after the first hydrogenation, irreversible decomposition into MgH 2 , GdH 2 and NiMgH 4 has been shown. The pathway of the reaction is described herein. The powder mixture after decomposition shows an interesting kinetics for magnesium without ball milling.

Introduction

The RE-TM-Mg systems (with RE = rare earth and TM = Transition Metal) have been intensively investigated in recent years. Several systems were already identified such as:

(i) the compounds with the higher RE content: RE 4 NiMg (with RE = Y, Pr-Nd, Sm, Gd-Tm, Lu) [1] crystallizing in the large cubic structure, a =13-14 Å, space group F-43m.

(ii) the compounds with the higher TM content : RENi 4 Mg (with RE = La, Ce, Nd, Gd and Y) [2][3] which crystallize in the F-43m space group (cubic MgCu 4 Sn structure type, known as C15b), with a lattice parameter from 7.03 to 7.18 Å, (iii) the equiatomic compounds: RENiMg (with RE = La and Ce) [4] crystallizing in orthorhombic structure (Ima2 space group) with the lattice parameters a ≈ 8.54 Å, b ≈ 13.10 Å and c ≈ 7.36 Å, (iv) and other compounds with, for example, the composition RETMMg 2 , RE 2 TM 3 Mg 3 , RE 2 TM 2 Mg, RETM 9 Mg 2 , RETM 2 Mg,… [4].

More recently, the Mg rich part of ternary diagrams has also been studied. Solokha et al. have identified 2 new ternary phases with high magnesium content :

-RECuMg 4 (with RE = La, Tb, Y) [5][6] However the Mg rich part of the ternary diagrams RE-TM-Mg is still not well known. As it is now established that these compounds can have interesting mechanical properties [8,9] and good hydrogenation properties [10], the study of the system Gd-Ni-Mg (rich Mg part) was the aim of this work.

First, a new compound was identified with a low crystallinity for the initial composition

Experimental details

Starting materials for the preparation of the sample were gadolinium pieces (Stream Chemicals, > 99.9 %), nickel rod (Stream Chemicals, > 99.9 %), and magnesium rod (alpha Aesar, > 99.8 %). To avoid oxides impurities, the surfaces of the magnesium and gadolinium pieces were cleaned in the glove box. Elemental pieces were then weighed in the appropriate amounts and sealed in tantalum ampoules under an argon pressure of ca. 800 mbar. The argon used was purified before with magnesium sponge (673 K). Then, the ampoules were heated at about 1373 K (high frequency furnace or resistance furnace) and kept at this temperature for 2-10 min. The ampoules were then placed in a quartz tube and sealed under vacuum to be annealed at different temperature (from 573 K to 823 K) for two weeks. No reaction with the tantalum tubes was observed. The polycrystalline samples were found to be stable in air.

All polycrystalline samples were characterized with X-ray powder diffraction using a Philips PW 1050 diffractometer with CuKα radiation (λ = 0.15405 nm). These patterns were scanned by steps of 0.02° (2θ) from 5° to 80° with a constant counting time of 30 s.

The bulk samples were investigated by electron probe microanalyses (EPMA) with metallic Gd (L α ), Ni (K α ) and Mg (K α ) as standards. The bulk samples were embedded in a methylmetacrylate matrix and the surface was polished with different silica and diamond pastes. The surface remained unetched for the EPMA measurements. The quantitative analyses were in good agreement with the initial compositions.

TEM images and electron diffraction experiments were performed using respectively JEOL 22200 FS and JEOL 2000 FX microscope equipped with double tilt specimen holder.

It was used at an accelerating voltage of 200 kV. The powder was ground in ethanol and a droplet of this suspension was then deposited on a carbon -formvar copper grid.

Hydrogen kinetics sorption were investigated by use of an automatic Sievert-type volumetric apparatus (HERA, Hydrogen Storage System) in the temperature range from room temperature to 603 K and with 10 bar and 0.2 bar of H 2 for absorption and desorption respectively [11].

Results and Discussion

Effects of experimental conditions on the crystallinity of Gd 13 Ni 9 Mg 78 compound

The X-Ray powder pattern of 13Gd + 9Ni + 78Mg melted (called Gd 13 Ni 9 Mg 78 in this paper) is shown in figure 1. Few diffraction peaks and a broad amorphous peak (in the range 22° ≤ 2θ ≤ 40°) are observed. The low signal/background ratio indicates that the crystallinity of the as-cast sample is poor. Nevertheless, the major peaks can be indexed with a facecentered cubic structure (FCC) with a ≈ 4.55 Å, but some peaks (marked with a star on figure 1) remain not indexed. However, this hypothesis agrees well with a hypothetic theoretical FCC structure. Indeed, if the stoichiometry and the metal radii of each element in the compound are considered, an average metallic radius of 1.59 Å is obtained (e.g. 0.13r Gd + 0.09r N i + 0.78r Mg ). This value leads to a lattice parameter a = 4.5 Å if a perfect contact between atoms in FCC stacking is considered.

Therefore, the crystallinity is too weak to go further on the structure of the compound.

For that purpose, the experimental conditions have been optimized to increase the crystallinity. Two parameters were selected:

-the heat treatment temperature from 573 K to 823 K for 2 weeks -the rate of cooling from air quenched down to 2 K/h. All the tested experimental conditions are reported in table 1. The samples are numbered from 1 to 13 with the initial name GNM (e.g. for Gd-Ni-Mg ternary compounds).

The X-Ray patterns of each sample are given in figure 2. The major diffraction peaks observed in figure 1 are visible for each X-ray pattern. However, some differences allow to separate the X-Ray patterns into two groups:

-Group I: The samples which are cooled quickly (almost air-quenched) and heat-treated at temperature higher than 673 K (i.e. GNM1-8). For these samples, the major part of diffraction peaks can be indexed with the FCC structure with a lattice parameter a ≈ 4.55 Å. Moreover, as observed for the first sample (fig. 1), the low signal/background ratio indicates a bad crystanility for these samples.

-Group II: The samples which are cooled slowly down to 673 K, 573 K or 323 K (i.e. GNM9-13). As for compounds of group I, the major part of diffraction peaks can be indexed with FCC structure (i.e. a ≈ 4.55 Å). However, the signal/background ratio is higher and at least two new peaks appear. The one at 2θ = 48.5° can be indexed with the (112) plan of the cubic structure which induces a loss of F mode. To explain the peak, around 8°, the hypothesis of a superstructure (confirmed latter by TEM analysis) with lattice parameter a ≈ 22.8 Å (i.e. a*5), can be done.

To simplify the discussion, only the sample GNM1, GNM2 of group I and GNM12, GNM13 of group II are going to be considered in the following. The X-ray patterns of these 4 samples are isolated and presented in figure 3. From the higher peak of each X-ray pattern (i.e. around 34°), the crystallite size was estimated using Scherrer's formula and given in table 2. Even if the absolute value must be considered with caution, the values can be compared between each over. The crystallite sizes are going from 32 nm to 49 nm and increase (i) slightly when the heat treatment temperature decreases and (ii) more significantly when the rate of cooling decreases. It should be concluded that the rate of cooling is probably the predominant factor to increase the crystallinity.

All compounds have been characterized by EPMA (figure 4). Two different microstructures are observed : (i) GNM1 and GNM2 can be described as a mixture of two phases with 2 compositions slightly different and of both sides of the initial composition (e.g. Gd 16 Ni 12 Mg 72 and Gd 11 Ni 8 Mg 81 for GNM2), (ii) for GNM12 and GNM13 only one phase exists with the composition Gd 11±0.5 Ni 8±0.5 Mg 81±0. 5 . For GNM12, it could be possible to highlight two different contrasts but each of then correspond to the same composition for more than fifty points measured. For GNM13 the picture given in figure 4 presents the worst areas where some gadolinium oxides were observed which explain the slightly lower gadolinium content of the ternary phase. From this figure 4, it is clear that the cooling conditions strongly affect the microstructure. Moreover, the EPMA analyses demonstrate the existence of different compositions going from 10 to 15 %at. for Gd, from 8 to 12 %at. for Ni and from 72 to 78 %at. for Mg (i.e. Gd 10-15 Ni 8-12 Mg 72-78 ) while the X-Ray patterns are similar. It means that the new compound with the initial composition Gd 13 Ni 9 Mg 78 exist in a large domain. Nevertheless, we will continue to name it Gd 13 Ni 9 Mg 78 in the following.

The TEM dark field pictures given in figure 5 highlights another difference between samples of group I (i.e. GNM1 and 2, figure 5.a-b) and sample of group II (i.e. GNM13, figure 5-c). For samples of group I, the crystallites (which appear bright on the picture) are distributed randomly in the sample with a size ranging from 1 to 10 nanometer. For GNM13 compound (and also for GNM12 not show here) larger crystallites of about 200 nm are observed. This observation agrees well with the information deduced from X-Ray pattern (table 2).

Selected area electron diffraction patterns for GNM1 and GNM2, confirm the low crystallinity as it has not been possible to select one single crystallite (because of the limit dimension of the diaphragm). So, for both samples the electron diffraction patterns obtained are characteristic of a polycrystalline sample, which explain the existence of some spot of diffraction. The presence of more defined spots of diffraction for GNM2 is due to the domains of crystallinity which are bigger. Moreover, both show amorphous halos which confirm the low crystallinity of the samples. However this information could be distorted by the sample holder in carbon. The higher crystallinity of the group II samples allow to make electron diffraction patterns usable to get structural information.

Information on crystal structure of Gd 13 Ni 9 Mg 78 compound

According to the previous results, efforts were focussed on the groupe II samples. The TEM was then a unique tool according to the relative low crystallinity of the sample. Both samples (i.e. GNM12 and 13) have the same metric and the same symmetry. In figure 6, some electron diffraction patterns are presented. The picture 6.b was obtained on GNM12 sample while the others (figure 6.a,c-d) were obtained from GNM13 sample.

In figure 6.a and 6.b, it is possible to observe both the 4 fold and 3 fold symmetry axis. Both are coherent with the hypothetic cubic structure. Moreover, the most intense spots can be indexed considering a lattice parameter a ≈ 4.55 Å. The electron diffraction patterns presented on figures 6.c and 6.d, are respectively obtained by rotating the crystallite along a* and b* axis with the same angle in accordance with a cubic symmetry. This observation is an additional proof of the cubic symmetry.

The projection of the cubic symmetry with lattice parameter a ≈ 4.55 Å is drawn on the figure 6.a and the unindexed spots of diffraction can be taken into account by considering a superstructure with a'= 5a as previously considered to explain the peak at about 8° on XRD powder patterns. To confirm this hypothesis, the evolution of spots intensity observed along one direction (from figure 6.d) was studied (figure 7). In figure 7, it appears that the spots of the superstructure are not equidistant (as shown by the red arrows on figure 7). To index all spots along this direction, it is necessary to introduce a modulation vector q1 = 0.42a*. The spots observed between the more intense spots are the satellites of order 1 or 2 (sometimes 3) and the indexation is proposed on figure 7. As the modulation vector is slightly higher than 0.4 (the one for a 5a superstructure) the distance between the more intense spot and the two subsequent is smaller. For the 3 rd order, it is even possible to see a shoulder (i.e. leading to an asymmetry of the peak). The same information was obtained along axis b*. Unfortunately and because of the small size of the crystallites, it has not been possible to get information along the c* axis. However the spots observed between two planes on the electron diffraction patterns (shown by red arrows on the figure 6.c-d) could be induced by the same modulation along c*.

On all electron diffraction patterns (figure 6) a diffusion phenomenon is observed and confirms the low crystallinity of the sample. So, the Gd 13 Ni 9 Mg 81 compound has a long range order characterized by the modulation and a crystallographic disorder characterized by the diffusion. The disorder is confirmed by the high resolution picture (figure 8), where ordered and disordered areas are observed. Moreover, the periodic repartition of the intensity found on the ordered areas confirms the cubic structure of lattice parameter a ≈ 4.55 Å. Complex crystal structures were also observed for other rich magnesium compounds (e.g. LaMg ~11 , Mg 35 Zn 3 RE 4 , Mg 29 Zn 3 RE 4 ), which present long-range order [12,13]

Preliminary hydrogenation behaviour

Gd 13 Ni 9 Mg 78 (sample GNM12) has been subjected to hydrogen pressure at different temperatures in the range from room temperature to 603 K. At first, at 603 K and under 30 bars, the full absorption is obtained after 5h. Such low kinetic is assumed to be due to the existence of oxides layers. X-Ray diffraction performed after absorption (figure 9) shows that Gd 13 Ni 9 Mg 78 compound is decomposed into GdH 2 , MgH 2 and Mg 2 NiH 4 . A same effect has already been reported for the ternary compound LaCuMg 8 which decomposes irreversibly into LaH 3 , MgCu 2 and MgH 2 after 20h [14].

After the desorption at 573 K under 1.10 -4 bar of H 2 , the X-Ray pattern presented in figure 9 highlights the presence of 3 phases: GdH 2 , Mg 2 Ni and Mg proving that the ternary compound no longer exist. The decomposition is then irreversible and only Mg 2 Ni and Mg phases will react further with hydrogen. The reaction path of hydruration could then be written as follows:

(i) First step reaction (irreversible)

In order to test the reversibility of the second step reaction, absorption/desorption cycles were done at 573 K on the powder decomposed, called "Gd 13 Ni 9 Mg 78 activated powder" (figure 10). The sample absorbs about 3%wt of hydrogen with good kinetics (i.e. full absorption after 10 min). This capacity agrees well with the theoretical capacity of 3.4%wt deduced from the reaction 2. For desorption, all hydrogen (i.e. 3%wt) is released in less than 3 min. So, the second step reaction is fully reversible and a good sorption kinetic is obtained.

The subsequent kinetics of the absorption and desorption at different temperatures are given in figure 11 and figure 12 respectively. As expected, it is shown that decreasing the temperature leads to a decrease of the kinetic but also of the maximum capacity. Nevertheless, the absorption is possible at room temperature and a full desorption is also observed at temperature as low as 533 K. These kinetics are comparable with the ones obtained by So, it could be concluded that "Gd 13 Ni 9 Mg 78 activated powder" exhibit a good kinetics without any ball milling. Moreover, the results confirm the interest of the decomposition under hydrogen of the ternary compounds to obtain highly reactive powder [17].

Conclusion

The new compound so-called Gd

  crystallizing in tetragonal structure (a = 10.39 Å, c = 4.51 Å) for La compound and orthorhombic structure (a = 13.5 Å, b = 20.3 Å, c = 3.9 Å) for Tb and Y -Tb 2 Ni 2 Mg 3 [7] which crystallizes with an orthorhombic structure, with the lattice parameters a = 3.978 Å, b = 21.203 Å, c = 3.6583 Å.

Gd 13 Ni 9

 9 Mg 78. Other tests with composition close to this nominal composition (e.g. Gd 11.8 Ni 5.8 Mg 82.4 and Gd 13.4 Ni 12.2 Mg 74.4 ) lead to the same results in terms of structure meaning that the compounds can exist in a certain range of composition. These new phases are referred to in the text as Gd 13 Ni 9 Mg 78 . In this paper we report (i) the crystallographic properties of Gd 13 Ni 9 Mg 78 and (ii) the relationship between experimental conditions and crystallinity and (iii) the hydrogen sorption properties.

  Zaluska et al.[15] and Li et al.[16] on ball milled MgH 2 + Mg 2 NiH 4 . Indeed for a mixture milled in the proportion 65-35%wt, Zaluska et al. get a good kinetic and a desorption temperature reduced from 100 K versus pure MgH 2 . They explain this improvement by the presence of Mg 2 NiH 4 . A same observation was done on the mixture Mg + Ni-Y (20%wt) milled 40h. In this case the improvement of the kinetics is explained by the dual catalytic effect of YH 3 and Mg 2 NiH 4

13 Ni 9

 9 Mg 78 was discovered in the Gd-Ni-Mg system. In fact, this compound exists in a large domain going from 10 to 15 for Gd, from 8 to 12 for Ni and from 72 to 78 for Mg (i.e. Gd 10-15 Ni 8-12 Mg 72-78 ). The low crystallinity of the compound has been improved with different heat treatments and rate of cooling. The best crystallinity was obtained for the samples which were cooled slowly (i.e. 2-6 K/h). According to the TEM measurements and in agreement with the preliminary XRD powder studies, Gd 13 Ni 9 Mg 78 crystallizes in an average cubic structure a ≈ 4.5 Å with a modulation along both axis a* and b* with vectors q1 = 0.42a* and q2 = 0.42b*. Gd 13 Ni 9 Mg 77 absorbs hydrogen at 603 K and 10 bars, but the absorption leads to an irreversible decomposition into MgH 2 , GdH 2 and Mg 2 NiH 2 . Reversibility of the reaction was observed for both couples: Mg/MgH 2 and Mg 2 Ni/Mg 2 NiH 4 with kinetics and temperatures comparable with the ones obtained on ball milled MgH 2 + Mg 2 NiH 4 . Indeed, the absorption is possible at room temperature and a full desorption is also observed at temperature as low as 533 K. It makes such compound very promising for several hydrogen applications.

Figure 1 :

 1 Figure 1 : Hydrogen absorption kinetics under 10 bar of H 2 and 300 °C, for LaCuMg 8 as-cast (black circle) and for LaCuMg 8 cold-rolled 20 (red square) and 150 times (blue triangle).

Figure 2 :

 2 Figure 2: Hydrogen absorption kinectics for "LaCuMg 8 actived powder" under 10 bar of H 2 and 100 °C (blue triangle), 200 °C (green circle) and 300 °C (black square). The dashed lines show theoretical hydrogen uptakes according to reaction (2) and (3), of 3.6 wt% and 2.9 wt% respectively.

Figure 3 :

 3 Figure 3: Hydrogen desorption for "LaCuMg 8 actived powder" under 0.2 bar of H 2 and 280 °C (red circle) and 300 °C (black square).

Figure 4 :

 4 Figure 4 : PCT curves of "LaCuMg 8 activated powder" under hydrogen at 300 °C (black square) and 350 °C (blue circle).

Figure 5 :

 5 Figure 5 : Calculated Van't Hoff plots of the various reactions for the destabilization of magnesium hydride.

PressureFigure 6 :

 6 Figure 6 : In-situ synchrotron X-Ray diffraction of "LaCuMg 8 activated powder" during the desorption step (from 25 °C to 300 °C at 10 °C/min) under argon flow (500 mL.m -1 ). The figure b and c are the enlarged portions of figure a indicated by hatched zones.

Figure 7 :

 7 Figure 7 : In-situ synchrotron X-Ray diffraction of "LaCuMg 8 activated powder" during the absorption step (from 300 °C to 25 °C at 10 °C/min) under 30 bar of hydrogen. The figure b and c are the enlarged portions of figure a indicated by hatched zones.

Figure 8 :

 8 Figure 8 : ln(-ln(1-F)) versus ln(t) plot for the absorption kinetics at 300 °C (a) and 100 °C (b) of "LaCuMg 8 activated powder".

Figure 9 :

 9 Figure 9 : Arrhenius plot for the determination of the activation energy of "LaCuMg 8 activated powder".

Figure 10 :

 10 Figure 10 : Scheme describing the mechanism of the transformation Mg 2 Cu/MgCu 2 during sorption cycles.

Table 1 :Figure 11 :

 111 Figure 11 : SEM pictures (secondary electron) of "LaCuMg 8 activated powder" after decomposition (a) and after 4 absorption/desorption cycles (b, c, d).

Figure 12 :

 12 Figure 12: EPMA analysis of one grain of "LaCuMg 8 activated compound" after four absorption/desorption cycles. The three first pictures represent the repartition of one element (i.e. Cu, Mg, La) inside the grain. The last one is the BSE picture.

  Gd 13 Ni 9 Mg 78 + 91 H 2  13GdH 2 + 9Mg 2 NiH 4 + 60 MgH 2 Mg 2 NiH 4 + 60 MgH 2  13 GdH 2 + 9 Mg 2 Ni + 60 Mg + 78H 2

	(ii) Second step reaction (reversible)
	13GdH 2 + 9
	(1)


Antoine Boutet

Hyoungshick Kim

Eiko Yoneki

What's in Your Tweets? I Know Who You Supported in the UK 2010 General Election

Nowadays, the use of social media such as Twitter is necessary to monitor trends of people on political issues. As a case study, we collected the main stream of Twitter related to the 2010 UK general election during the associated period. We analyse the characteristics of the three main parties in the election. Also, we propose a simple and practical algorithm to identify the political leaning of users using the amount of Twitter messages which seem related to political parties. The experimental results showed that the best-performing classification method -which uses the number of Twitter messages referring to a particular political party -achieved about 86% classification accuracy without any training phase.

Introduction

We are interested in how to measure the authority of political parties and the political leaning of users from social media. To illustrate the practicality of our analysis, we used a dataset formed of collected messages from Twitter related to the 2010 UK general election which took place on May 6th, 2010.

We examined the characteristics of the three main parties (Labour, Conservative, Liberal Democrat) and discussed the main differences between parties in term of structure, interaction, and contents.

Through this intensive analysis about the users with political interests, we develop a simple and practical algorithm to identify the political leaning of users in Twitter -the messages expressing the user's political views (e.g. tweets referring to a particular political party and retweets from users with known political preferences) are used to estimate the overall political leaning of users. To demonstrate the effectiveness of the proposed heuristic model, we evaluated the performance of the proposed classification method. The experimental results showed that the proposed classification method -which uses the number of tweets referring to a particular political party -achieved about 86% classification accuracy using all trials without any training phase, outperforming existing heuristics (Pennacchiotti and Popescu 2011a;[START_REF] Zhou | Classifying the political leaning of news articles and users from user votes[END_REF] that require expensive costs for tuning of parameters to construct classifier.

Our approach has two key advantages: (1) as we only process the messages relevant to a particular event rather than the whole dataset at one time, it drastically reduces the computation costs of constructing a classifier compared with existing approaches which may indeed be unacceptable for online classification; (2) it also has potential: we can discover the temporal trends of a user's political views by analysing her political leaning over time.

Party Characteristics

To analyse the characteristics of the Labour, Conservative and Liberal Democrat (LibDem) parties to identify the relevant features for user's party affiliation, we collected all tweets published on the top trending topics related to the UK election between the 5th and 12th of May, and kept only the 419 topics which have over 10,000 tweets. The resulting dataset gathers more than 220,000 users for almost 1,150,000 tweets. For these users, we also collected their profiles and about 79,000,000 following/follower relationships. Some user profiles can be used to identify their political party affiliation. We manually identified the 356 Labour, 159 Conservative and 169 LibDem self-identified members as a ground truth dataset.

With this ground truth dataset, we detected the communities associated to each political party using a well-known technique called label propagation method [START_REF] Raghavan | Predicting elections with twitter : What 140 characters reveal aboutpolitical sentiment[END_REF]. Here, the label propagation method spreads affiliations from ground truth users called seeds throughout the retweet graph. We label a user with the party affiliation according to seeds who have reached it. We need to set the maximum propagation distance to k to avoid tie-breaking cases (i.e. multiple nearest nodes with different party memberships exist at the same time). We performed the label propagation until the propagation distance is greater than k. When k = 2, we detected 5,878 Labour, 3,214 LibDem and 2,356 Conservative candidates with a high accuracy of 0.77, 0.78 and 0.90 respectively for an average at 0.82. With these candidates, we analysed the following characteristics of each party: (i) structure/interaction and (ii) content features.

Structure and Interaction

We studied the differences between the political parties in network structure and inter-action patterns. The interaction patterns between members within a party reflects a level of party cohesion while the interaction patterns between different communities reflect the exchanges (i.e. conflict or collaboration) between them.

We particularly observed the amount of interactions between the political parties by counting the number of exchanged retweets (forward messages to its followers) and mentions (direct messages to another user) between them during the election period. According to the detected communities described above, we can see that there was no retweet exchanged between different political parties. In contrast, the mentions between different parties were more frequently used. We can also see that few interactions have been observed between the Labour and Libdem members, in opposition to the high rate of interactions between Conservative and both Labour and LibDem. We surmise that the suggested coalition between Conservative and LibDem generated more discussions among members of both parties than between Labour and LibDem.

Content We analysed the contents of tweets by counting the number of hashtags (tags used to define topics) and URLs used in tweets for each party. Political parties showed a similar behaviour for the number of used URLs while Labour members used various hashtags in their tweets compared to the other parties. The usage rates of neutral hashtags indicating the UK election remained at a similar level between all parties while non-neutral hashtags were more or less used depending on their underlying meaning.

We also analysed the hashtag similarity between users to evaluate the content homogeneity of each party. For a user, we define a vector containing the frequencies of hashtags used in the user's tweets and then we computed the cosine similarity between each pair of all users. The average similarity is overall low regardless of political party affiliation. That is, these results imply that Twitter users have heterogeneous behaviour in the use of hashtag.

By analysing the URLs mentioned in tweets, we can identify the preferred websites of each party. LibDem members more frequently referred to Financial Times, The Independent and The BBC compared with the other party members.

We also particularly observed the blogs which are usually more politically oriented. We observed very few overlaps of the referenced blogs between the parties. This result may confirm the high segregated structure of the blogosphere according to political parties reported in [START_REF] Adamic | The political blogosphere and the 2004 u.s. election: Divided they blog[END_REF].

Finally, we measured the volume of references to a specific party included in tweets. We considered only the tweets referring to one name of party or its leader as such tweets are more likely to reflect the allegiance or interest of the users. The analysis clearly shows that users were more likely to frequently refer to their own preferred party or leader.

User Classification

For user classification, our goal is to the party to which a user belongs. We particularly focused on developing a classification method to process the dynamically updated statistics on users; user's tweet activities are sequentially observed over time.

Bayesian Classification

Without loss of generality, we assume that a sequence of tweet activities (e.g. retweets or references to a specific party/leader in tweets) by a user is divided into n subsequences, where the kth subsequence corresponds to the tweet activities during the kth time interval. For a user u, we use A k (u) and M i k (u) to denote the kth subsequence (i.e., the tweet activities performed by the user u during the kth time interval) and the 0-1 binary variable indicating user u's membership for the party i after the kth time interval (i.e., M i k (u) = 1 when u is a member of the party i), respectively where 1 ≤ k ≤ n and i ∈ {labour, libdem, conservative}. We also use P (M i k (u)) to denote the probability of user u to be a member of the party i after the kth time interval. We assume that all users should be included to one of parties;

i P (M i k (u)) = 1. After the nth time interval, we classify the user u as a member of the party j where P (M j n (u)) = max i {P (M i n (u))}. For example, when the affiliation probability distribution for the user u after the nth time interval is given as [0.7, 0.2, 0.1], we classify the user u as a member of the Labour party. We randomly choose the user u's party in case of equiprobability distribution.

We now focus on how to compute P (M i k (u)). At each time interval, for each i ∈ {labour, libdem, conservative}, P (M i k (u)) is updated stochastically according to its probability distribution relying on the user's tweet activities during the time interval.

Before the first inference step, the initial prior affiliation probability of the user u is set uniformly: P (M i 0 (u)) = 1 3 , ∀i. After the kth time interval, P (M i k (u)|A k (u)) can be calculated by using Bayes' theorem as follows:

P (M i k (u)|A k (u)) = P (A k (u)|M i k (u))P (M i k (u)) j P (A k (u)|M j k (u))P (M j k (u)) where P (M i k (u)|A k (u)) is the posterior of user u, the un- certainty of M i k (u) after A k (u) is observed; P (M i k (u)) is the prior, the uncertainty of M i k (u) before A k (u) is observed
; and

P (A k (u)|M i k (u)) P (A k (u))
is a factor representing the impact of A k (u) on the uncertainty of M i k (u). To calculate P (A k (u)|M i k (u)), we consider two tweet activities for A k (u), respectively, based on the observation in the previous section: (1) retweeting the messages from the members of each political party and (2) referring to political parties in tweets.

We can see that tweets generated by users supporting the same political party were more frequently retweeted. For this activity, we assume P (A k (u)|M i k (u)) can be calculated as follows:

P (A k (u)|M i k (u)) = v∈RT P (M i (k-1) (v)) |RT | (1)
where RT is the set of the users included in retweets as the source or the destination of information.

We use Bayesian-Retweet to denote the Bayesian classification where P (A k (u)|M i k (u)) is defined in (1). The other important tweet activity is to generate a tweet referring to the political party (or party leader) that the user u will support after the kth time interval since party members are more likely to make reference to their own party than another. For this activity, we assume P (A k (u)|M i k (u)) can be calculated as follows:

P (A k (u)|M i k (u)) = t∈T V i (t) |T | (2)
where T is the tweets of the current user during the period and V i (t) is equal to 1 if the tweet t does a reference to the political party i, 0 otherwise.

We use Bayesian-Volume to denote the Bayesian classification where

P (A k (u)|M i k (u)) is defined in (2).

Evaluation

The aim of our experiment was to demonstrate feasibility and effectiveness of the proposed classification approach compared with the other popularly used classification methods. For comparison, we also tested the performance of the following classification methods:

• Volume classifier: We counted the frequencies referencing parties (or party leaders) in a user's tweets and then assigned the most frequently referenced party to the user's political party. • Retweet classifier: This approach detects the communities of users using a label propagation method [START_REF] Raghavan | Predicting elections with twitter : What 140 characters reveal aboutpolitical sentiment[END_REF] on the retweet graph. In the label propagation process, each user's party is classified with the majority party in the user's neighbours. Ties can be broken according to the volume of references to party.

From the initial seed users (self-identified members), we iteratively this process until all users' parties are classified. • SVM classifier: Support Vector Machine (SVM) is known as one of the best supervised learning techniques for solving classification problems. We constructed a SVM classifier using the following six features of a user proposed in (Pennacchiotti and Popescu 2011a;2011b): (i) the number of followers, (ii) the number of replied users, (iii) the number of retweeted users, (iv) the number of used words in the user's tweets, (v) the number of used hashtags in the user's tweets, and (vi) the average emotion over the user's tweets.

To show the performance of a classifier, we measured the accuracy of the classifier for the self-identified users. The classification accuracy is defined as the ratio between the number of correctly predicted samples and the total number of testing samples.

For the classifiers requiring the training samples (Retweet, SVM, and Bayesian-Retweet), one-tenth of the ground truth users was used to construct the classifiers and the rest was reserved for out-of-sample testing. We have seen that the accuracy of these classifiers can be changed with the set of training samples. We used the most influential users with the highest number of followers since these training samples provide the best accuracy compared to the most active users with the highest number of generated tweets or random users. The Bayesian-Volume produced the best results: the measure accuracy (0.86) is significantly higher compared to other classification methods. In addition, this classification benefits from two advantages. Firstly, it requires to maintain only the affiliation probability of each user without massive training overheads and secondly, as the information about references to a party or a leader in tweets is only needed, incremental computation is significantly faster. These important advantages make it possible to use this solution in real time. Unlike our expectations, SVM which involves an expensive tuning phase, did not outperform other algorithms.

We also analysed how the number of partisans of each party and the accuracy of the proposed Bayesian classifiers, respectively, changes with time. The results are shown in Figure 2. Conservative members outnumbers the Labour and LibDem members at the end of the election. Inherently, the accuracy of Bayesian-Volume and Bayesian-Retweet starts at 1/2 (equiprobability), continuously increases with time, and achieved at 0.86 and 0.64, respectively. These results imply that the proposed Bayesian approach is proper to understand users' political leaning over time. However, the accuracy for Bayesian-Retweet increases more slowly than Bayesian-Volume. Even if a retweet graph generally presents a high segregated structure, latency might be expected to sufficiently propagate retweets over the graph. In contrast, Bayesian-Volume, which uses only the tweets pub-lished by users during the current time interval, achieves accurate prediction without latency caused by message propagation between users.

Related Work

The exponential growth of social media has attracted much attention. Different approaches have been proposed for classifying users in many directions. [START_REF] Lin | The multirank bootstrap algorithm: Self-supervised political blog classification and ranking using semi-supervised link classification[END_REF] presented a semi-supervised algorithm for classifying political blogs. [START_REF] Zhou | Classifying the political leaning of news articles and users from user votes[END_REF]) also applied three semi-supervised algorithms for classifying political news articles and users, respectively. On the other hand, [START_REF] Adamic | The political blogosphere and the 2004 u.s. election: Divided they blog[END_REF] studied the linkage patterns between political blogs and found that the blogosphere exhibits a politically segregated community structure with more limited connectivity between different communities. Recently, [START_REF] Conover | Political polarization on twitter[END_REF]) observed a similar structure in a retweet graph of Twitter in politic context. Other classifications used machine learning methods to infer information on users. (Pennacchiotti and Popescu 2011a) demonstrated the possibility of user classification in Twitter with the three different classifications: political affiliation detection, ethnicity identification and detecting, affinity for a particular business. (Pennacchiotti and Popescu 2011b) used Gradient Boosted Decision Trees which is a machine learning technique for regression problems, which produces a prediction model in the form of an ensemble of decision trees.

Several studies have addressed to characterise user behaviour or personality in social networks [START_REF] Benevenuto | Characterizing user behavior in online social networks[END_REF][START_REF] Quercia | The personality of popular facebook users[END_REF]. However few works have tried to study the characteristics of politic parties and the interaction structure between parties. [START_REF] Livne | The party is over here: Structure and content in the 2010 election[END_REF]) studied the usage patterns of tweets about the candidates in the 2010 U.S. midterm elections and showed stronger cohesiveness among Conservative and Tea party.

Other studies have addressed the predictive power of the social media. [START_REF] Livne | The party is over here: Structure and content in the 2010 election[END_REF]) has investigated the relation between the network structure and tweets and presented a forecast of the 2010 midterm elections in the US, and (Tumasjan et al. 2010;[START_REF] Gayo-Avello | Limits of electoral predictions using twitter[END_REF] discussed the relevance of Twitter as a valid indicator of political opinion. [START_REF] O'connor | From tweets to polls: Linking text sentiment to public opinion time series[END_REF]) used sentiment analysis to compare Twitter streams with polls in different areas and showed the correlation on some points. [START_REF] Diakopoulos | Characterizing debate performance via aggregated twitter sentiment[END_REF] showed that tweets can be used to track real-time sentiment about candidates' performance during a televised debate.

Conclusion

As a case study, we first analysed the characteristics of the political parties in Twitter during the 2010 UK General Election and identified the two main ways to differentiate political parties: (i) the retweet graph presented a highly segregated partisan structure, and (ii) party members were more likely to make reference to their own party than another.Through these party characteristics, we built two classification algorithms based on Bayesian framework. The experimental results showed that the proposed classification method is capable of achieving an accuracy of 86% without any training which make it a perfect solution for real time classification.

Figure 1 :

 1 Figure 1: Exchanged messages between parties

Figure 2 :

 2 Figure 2: Dynamic changes of the Bayesian classifiers.

Table 1 :

 1 Performance according with approach.

	Classifier	Accuracy
	Volume	0.60
	Retweet	0.73
	SVM	0.63
	Bayesian-Retweet	0.64
	Bayesian-Volume	0.86


Antoine Boutet
email: antoine.boutet@inria.fr

Anne-Marie Kermarrec
email: anne-marie.kermarrec@inria.fr

Erwan Le Merrer
email: erwan.lemerrer@technicolor.com

Alexandre Van Kempen
email: alexandre.vankempen@technicolor.com

On The Impact of Users Availability In OSNs

Keywords: C 2.1 [Network Architecture and Design]: Network Topology; C 2.0 [General]: Data Communications Availability, Time Varying Graphs, Information Spreading, Centrality

Availability of computing resources has been extensively studied in literature with respect to uptime, session lengths and inter-arrival times of hardware devices or software applications. Interestingly enough, information related to the presence of users in online applications has attracted less attention. Consequently, only a few attempts have been made to leverage user availability pattern to improve such applications. Based on an availability trace collected from MySpace, we show in this paper that the online presence of users tends to be correlated to those of their friends. We then show that user availability plays an important role in some algorithms and focus on information spreading. In fact, identifying central users i.e. those located in central positions in a network, is key to achieve a fast dissemination and the importance of users in a social graph precisely vary depending on their availability.

Introduction

Online Social Networks (OSNs) now attract hundreds of millions of users around the world and represent a crucial place to gather data with countless possibilities of analysis, ranging from extracting user habits to influencing recommendation systems. Information on the availability of re-Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SNS'12 April 10, 2012, Bern, Switzerland Copyright c 2012 ACM ACM 978-1-4503-1164-9/12/04. . . $10.00 sources are usually of crucial importance to build reliable applications in computer systems. While this availability has been extensively measured, studied and leveraged for computers and application runtimes [START_REF] Blond | Finding good partners in availability-aware p2p networks[END_REF][START_REF] Mickens | Exploiting availability prediction in distributed systems[END_REF][START_REF] Rhea | Handling churn in a dht[END_REF][START_REF] Saroiu | A measurement study of peer-to-peer file sharing systems[END_REF], we know little about the online presence patterns of users and their impact on specific features in the case of OSNs [START_REF] Benevenuto | Characterizing user behavior in online social networks[END_REF][START_REF] Gyarmati | Measuring user behavior in online social networks[END_REF]. In this paper, we show that online presence is very heterogeneous among users, and that complex interactions may influence it. This constitutes a significant difference with studies about computing devices. More specifically, observing device uptime patterns only allows coarse grain observations such as extracting the correlation between day and night patterns or between the presence of users and the occurrences of significant worldwide events (sport event, holidays, etc). On the opposite, the online presence of users on a given OSN enables to extract finer characteristics and correlations such as the simultaneous presence of users with respect to their friends.

This availability information can be of particular interest to various practical functionalities such as efficient information spreading and influence in OSN [START_REF] Tang | Analysing information flows and key mediators through temporal centrality metrics[END_REF], load prediction on the service provider's platform [START_REF] Pujol | The little engine(s) that could: scaling online social networks[END_REF], or resource management in distributed social networks. In addition, while the 'who-knows-who" relations of OSN structures are inherently time varying graphs [START_REF] Casteigts | Time-varying graphs and dynamic networks[END_REF], extracting at a fine granularity the user presence is interesting. Indeed, some recent works emphasize the fact that graph analysis aggregating the interactions usually miss the time dimension [START_REF] Casteigts | Time-varying graphs and dynamic networks[END_REF][START_REF] Kim | Temporal node centrality in complex networks[END_REF][START_REF] Tang | Analysing information flows and key mediators through temporal centrality metrics[END_REF].

In this paper, we investigate the dynamic nature of OSNs, based on a trace we have extracted from Myspace1 . This trace contains both the social network structure (friendship relations), as well as availability information in each timeslot. While a majority of related works [START_REF] Benevenuto | Characterizing user behavior in online social networks[END_REF][START_REF] Gyarmati | Measuring user behavior in online social networks[END_REF] focus on models that fit session lengths, inter-arrival times or rely on browsing habits of users, here we are interested in studying the correlations between users availability and those of their friends and its impact on information spreading. From our analysis, we conclude that the availability of a user is highly correlated with that of her friends: on average a user is 42% more likely to be online when 50% of her friends are connected. In addition, leveraging this availability information to spread information in the network leads to an 8.5% increase in the number of nodes reached by the information during the dissemination, while speeding up the whole process.

User availability in MySpace

Accurate information on user activity on a given social platform can only be obtained by the service operator or the ISP. Given the fact that we did not have direct access to this information, we used the online status information displayed on the user profile in MySpace.

Measurement and methodology

We first crawled MySpace for a few weeks and collected for each user, her profile and the one of her explicit friends in the OSN. From this first dataset, we only kept the users who were online at least once during the crawling period. There are two kinds of profile in the MySpace OSN: regular and music band. We conducted an analysis on standard users, by removing the band profiles. In addition, in order to obtain a connected component (friendship relations are non symmetrical in MySpace) and to observe the availability of users over a subset of the MySpace network, we selected the most active French users in the same weakly connected component during this first period. This represents 833 users. In MySpace, the list of online friends of a specific user is available on a dedicated webpage (possibly including band profiles). We collected that information for each of these 833 preselected users from that webpage, yielding about 180, 000 tracked MySpace users. The period of observation was 17 days, in May 2011. For each user, we collected availability information every 10 minutes.

Surprisingly, although consistent with observations made in [START_REF] Gyarmati | Measuring user behavior in online social networks[END_REF] on the loss of interest of users after an initial adoption period, only 13, 286 among those 180, 000 users had been indicated as online at least once. Yet, a potential second reason for the unavailability may also come from the fact that a user can hide her availability information for privacy purposes.

The resulting graph used in this study contains 13, 286 users, along with 68, 064 friendship relations 2 . This graph can be observed, as traditionally, in a static aggregated view, or in a more realistic time varying manner with nodes and edges appearing and disappearing at a 10-minute granularity.

Static vs time varying MySpace graph

In contrast to a static graph which aggregates the users and relations observed at least once during the whole crawling period, the time varying graph reflects actual availability for 2 We make this graph publicly available on request. each of the 2, 500 timeslots of 10 minutes. Table 1 and Figure 1 show the structural properties of both directed graphs, as well as the associated degree distribution (the SNAP library 3 has been used for the graph statistics presented in this paper).

We observe that the 90-percentile effective diameter [START_REF] Faloutsos | On power-law relationships of the internet topology[END_REF] for the time varying graph is significantly spread around its average. In addition, the average degree for the time varying graph is reduced by almost 40% when compared to the value depicted for the static graph. As shown in Figure 1, the distribution degrees for the static graph and the aggregate of all time varying graphs are also notably different. These observations confirm the relevance of considering a time varying graph in the particular context of OSNs, thus providing more information.

User availability on the platform

This section presents statistics on users availability during the observed period: (i) the number of users connected over time, (ii) the number of sessions, (iii) the session length and (iv) the inter-arrival times. The number of sessions shows the number of connections for each user to her account. The session lengths captures how long users remain online each time they get connected and inter-arrival times illustrates the interval between the moment a user departs and her next arrival. Figure 2 depicts the distribution of those availability statistics.

We observe that the availability patterns of users connected at the same time vary according to the instant in the day and week. The number of users connected simultaneously does not exceed 4, 800 and is relatively stable over time. This can be explained by the fact that selected users are from the same country (France) but their friends may come from various countries on different time zones. However, daily patterns are clearly observable on the figure. The Cumulative Distribution Functions (CDF) show that 50% of users have less than 50 different sessions during the observed period (an average of 1.6 sessions per day) while most of the sessions are short. In fact 60% of the sessions last less than 10 minutes. In addition, more than 80% of inter-arrival times are shorter than 2 hours. Note that these observations are consistent with measures previously made in [START_REF] Benevenuto | Characterizing user behavior in online social networks[END_REF].

Correlation between friends

Social networks like MySpace enable users to interact with each other. These interactions may influence the behavior of users such that they do not behave independently. For example, an application such as the instant messaging service offered by MySpace may push users to share some connection patterns (by chatting together). The goal of this section is to evaluate to what extent the uptime patterns of users are correlated with those of their friends on our dataset. The underlying question is to evaluate if friends are connected at the same time and thus characterize how active are the links between them.

We define the notion of availability correlation between two users as a measure on how similar their availability patterns are. This correlation is evaluated using a cosine similarity metric, which is frequently used when trying to determine similarity between documents, user profiles, or in our case availability patterns. The availability of each user is represented as a vector of a predefined size. For each timeslot, the corresponding vector entry is set to 1 if the particular user was online at that time and 0 otherwise. As uptime sessions are relatively short, we choose a ten-minute timeslot in order to capture all the connection events. More formally, let -→ A x and -→ A y be the availability vector of respectively user x and y. In practice, the cosine similarity S x,y is modelled as the cosine of the angle between the two vectors -→ A x and -→ A y .

S x,y = (

-→ A x • -→ A y -→ A x • -→ A y ) • S x,y = 1 : Perfect uptime correlation between x & y • S x,y = 0 : No uptime correlation between x & y
Note that a correlation implicitly exists at the dataset level as users of the same country tend to connect during daytime for example. However in order to check if explicitly declaring friends had an impact on this correlation, we computed the correlation between each user and her friends. For comparison purposes, we also computed the correlation between a user and a given number of friends, chosen randomly in the dataset; this dissociates the behavior of friends, allowing us to measure the impact of friendship on uptime correlation. As MySpace offers the possibility to declare top friends, we finally computed the correlation for each user with her top friends.

The cumulative distribution functions of correlation values are plotted in Figure 3. The first observation is that correlation values are rather low with random friends as well as with friends and top friends. Even if the correlation with top friends is the best one, we note that there is almost no differ-ence between the correlation with friends and top friends. However we clearly see that the correlation with explicit friends is higher than with random ones (twice as much), thus showing the impact of friendship on availability correlation.

In the previous experiment we studied the correlation at the user level i.e. between pairs of user. To go further we also evaluated how this correlation between a user and her friends impacts the probability for this user to be connected by taking into account the aggregated behavior of her friends. In other words, we wanted to answer the following question: is the probability of a user to be connected at a given time impacted by the fact that her friends are also connected at this particular time or are these two independent events? For example if 50% of her friends are connected, what is the statistical probability that she is also connected?

In order to estimate this impact, we computed for each user the probability to be connected depending on the proportion of her friends being effectively connected. For the sake of clarity we distinguished two cases, one when less than 50% of her friends are connected, and the other when more than 50% are online. This probability is simply evaluated using conditional probabilities. More formally, let U P be the event "User is UP", and M ore50 be the event "More than 50% of her friend are U P " then:

Pr(U P | M ore50) = Pr(U P ∩ M ore50) Pr(M ore50)
where Pr(U P ∩ M ore50) is the number of timeslots when the user and more than 50% of her friends are connected, normalized by the total number of timeslots. Pr(M ore50) is the number of timeslots when 50% of her friends are connected, normalized by the total number of timeslots.

Results are plotted on Figure 4. The cumulative distribution function of all a priori probabilities to be connected is also plotted as a means of comparison. In absolute term, all these probabilities are rather low. However, results clearly show that users are more likely to be online when their friends are, and on the contrary this probability decreases when the majority of their friends are not connected.

This correlation between friends' behavior may have a direct impact on applications requiring the computation of metrics like centrality (i.e. reflecting the importance of a given user in the graph) for example. In fact even if a user is qualified as central according to the static graph, her centrality may not be representative if she is never connected when her friends are. In other words the availability knowledge of users is an important aspect when looking for central nodes in a social graph.

Impact of Availability on Information Spreading

Users which are able to spread information quickly to a large number of users are commonly identified using centrality measures [START_REF] Merrer | Centralities: capturing the fuzzy notion of importance in social graphs[END_REF][START_REF] Santoro | Time-varying graphs and social network analysis: Temporal indicators and metrics[END_REF][START_REF] Tang | Analysing information flows and key mediators through temporal centrality metrics[END_REF] (including degree, betweenness or eigenvector centralities). In this section we evaluate the impact of the availability of users on information spreading.

To this end, we compared the spreading process depending on the (importance of the) user that initiates the dissemination (seed user). We ranked seeds based on their centrality extracted from both the static and the time varying graphs. Note that in this section, measures and analysis are conducted over the undirected version of the graph. This undirected graph models a bidirectional communication channel between users as a chat application for instance. Every second timeslot in the interval [0 : 500], a seed s was elected to spread a message in the network. A user u was infected by a message m once she was connected at one timeslot to a user who get already infected by the message m. A total of 250 messages were thus injected in the system offering about 3, 250, 000 of possible infections if each user received each message.

We measured both the size and the spreading time by observing the number of users reached by a new message from every user. We also looked at the time needed by an injected message at a seed to propagate and to be received by reachable users in the time varying graph. For instance, assuming the seed s injected the message m at the timeslot t, and a user u connected to s in the time varying graph and online for the first time at the timeslot t + α, the reception time of m for this user is equal to α. We believe this simple model fits the example of live news propagation.

We then compared different seed selections. The seed was selected among the online users at each timeslot, based on its centrality measure on the actual graph (we use the betweenness centrality [START_REF] Brandes | A faster algorithm for betweenness centrality[END_REF]), or simply randomly chosen. In order to evaluate the impact of the availability of users, we compared this approach against the one selecting the most central node in the static graph as an initial seed. In addition, in order to model multiple channels of communications, in case of the static graph, the seed was chosen randomly among the 10 users with the higher centrality measure.

Figure 5 depicts the number of infections over time according to the seed selection. Results show that seeds selected the time varying centrality measures increase the dissemination process by 8.5% at the end of the experiment and by 7% at the timeslot 1000, when compared to a selection based on the static graph. It is interesting to note that only about half of the users were infected at the end of the experimentation (1, 600, 000 against 3, 250, 000). In addition, we show that random selection reduces by more than 50% the spreading as compared to the selection based on the time varying graph.

We now consider the infection speed. Figure 6 depicts the additional infections of the time varying centrality based selection and the one based on the static centrality and randomly according to the latency of the infection. Results show that the highest number of additional receptions is mainly achieved quickly after the injection from the seeds. This phenomenon highlights the importance of selecting initial seeds according to the current topology of the social network taking into account the availability of users for a fast and efficient dissemination. Indeed, seeds connected to more people or better placed in the time varying graph, infect more users directly and meanwhile reduce the infection latency. Almost 20, 000 direct additional infections are achieved thanks to seeds selected according to their time varying centrality measure, as compared to the static one. Only 2, 000 additional infections are made possible with a latency of 1 (infection 10 minutes after the injection). In addition, latency is drastically reduced as compared to random seeds with al- most 200, 000 additional direct infections using seed selection in the time varying graph.

Related Works

There have been several studies on availability of computing resources, mainly in the field of distributed and peer-to-peer systems. When resources availability patterns (mostly on/off patterns) are well understood, prediction systems can bring significant gains on reliability, load balancing, resources savings in terms of bandwidth and storage space [START_REF] Blond | Finding good partners in availability-aware p2p networks[END_REF][START_REF] Mickens | Exploiting availability prediction in distributed systems[END_REF][START_REF] Rhea | Handling churn in a dht[END_REF][START_REF] Saroiu | A measurement study of peer-to-peer file sharing systems[END_REF]. Interestingly enough, availability patterns of users on online applications have been far less considered, while we believe such studies can yield interesting and new insights. In [START_REF] Gyarmati | Measuring user behavior in online social networks[END_REF], the time spent online by users of Bebo, Myspace, Netlog and Tagged has been studied through statistical analysis; authors discovered that a Weibull distribution accurately models the behavior of 80% of users. Session lengths, as well as the number of sessions, follow power law distributions. Notably, authors note a clear loss of interest for part of the users over a short time period (they do not reconnect frequently afterwards, or simply leave), after a few initial days of activity when registering to the service. This remark underlines the fact that analysis should not be conduced on a basic aggregated friendship, as user access to the service is fairly variable. Paper [START_REF] Benevenuto | Characterizing user behavior in online social networks[END_REF] studies Orkut, MySpace, LinkedIn and Hi5 OSNs. Authors concluded that session lengths follow a heavy-tailed distribution, while inter-arrival times a Lognormal distribution. It also describes browsing habits of users on their friends' pages. Our work is complementary to those findings, as we address the impact of users sessions over information spreading and study the correlation between uptime periods of friends.

The general Time Varying Graph notion captures in a framework the dynamics of such a complex system [START_REF] Casteigts | Time-varying graphs and dynamic networks[END_REF][START_REF] Santoro | Time-varying graphs and social network analysis: Temporal indicators and metrics[END_REF]. While dynamic objects that are currently considered are the relations between people or computers (i.e. the graph edges), node dynamics can be trivially added to fit the framework. This would allow traditional algorithms to be expressed or redesigned in the context of inherently non static networks, as for instance dissemination algorithms [START_REF] Censor-Hillel | Fast information spreading in graphs with large weak conductance[END_REF]. As we provide the dataset along with this paper, it could be leveraged for future research on time varying graphs. Paper [START_REF] Tang | Analysing information flows and key mediators through temporal centrality metrics[END_REF] studies the varying importance of persons in a network (with the help of the centrality toolbox). The Enron dataset (mail exchanged within the company) is used as a basis for analysis, and to point out that temporal metrics should be designed instead of the static known ones. Two new centralities are defined, in order to better reflect the varying importance of individuals as a function of their actual interactions over time in the network. We choose to study in this paper if similar conclusions could be highlighted when considering an explicit online social network.

Conclusion

It has been well understood that the availability of resources that a computer system relies on is critical for both reliability and performance. In this paper, we have shown that the information of the availability of users in online social networks has also an important impact. More specifically, results demonstrate that users availability may also be leveraged in order to provide a more efficient information dissemination. This confirms the need to take into account this crucial time varying metric when developing online applications. Secondly, we have shown that users availability is not only dependent of the daytime, but also correlated to the presence of their friends on the platform. This observation may serve in future works for the development of more accurate and fine-grained models of users' behavior on specific online applications.

Figure 1 :

 1 Figure 1: Degree distribution: static vs the aggregate of time varying graphs.

Figure 2 :

 2 Figure 2: Information about the availability of users (1 unit equals 10 minutes).

Figure 3 :

 3 Figure 3: Correlation between the user's availability and the one of their friends.

Figure 4 :

 4 Figure 4: Users are more likely to be online if their friends are present.

Figure 5 :

 5 Figure 5: Number of infected nodes, depending on the seed selection method (centrality computed on the static graph, on the time varying graph, or randomly on the time varying graph).

Figure 6 :

 6 Figure 6: Seed selection using the centrality metric, computed on the time varying graph, speeds up the spreading (normalized comparison).

Table 1 :

 1 Structural properties: static vs time varying graph.

		Characteristic			Static		Time Varying
							min	avg	max
			Nodes			13,286	2214	3668	3997
			Edges			68,064	5764	11706	13858
		Avg degree			9.60	5.20	6.30	7
	90-percentile effective diameter	5.80	5.50	6.15	8.21
	Average Clustering Coefficient		0.131	0.117	0.130	0.1482
	CDF	0 0.1 0.2 0.3 0.4 0.5 0.9 1 0.8 0.7 0.6	1	10 Average degree	0 10 2 4 6 8	100 Time Varying Static 1000 Static Time varying	10000
						Degree

http://www.myspace.com

Acknowledgments

This work was partially funded by the ERC Starting Grant Gossple number 204742 [1].