The Polyol Process and the Synthesis of ζ Intermetallic Compound Ag5Sn0.9

The present work concerns the intermetallic compound (IMC) existing in the Ag–Sn system and its potential use in electronics as attachment materials allowing the adhesion of the chip to the substrate forming the power module. First, we present the synthesis protocol in polyol medium of a compound with the chemical formula Ag5Sn0.9 belonging to the solid solution of composition located between 9 and 16 at.% Sn, known as solid solution ζ (or ζ-Ag4Sn). This phase corresponds to the peritectic invariant point at 724 °C. Differential thermal analysis and X-ray dispersive analysis confirm the single-phased (monocrystalline) nature of the Ag5Sn0.9 powder issued after synthesis. Scanning electron microscopy shows that Ag5Sn0.9 particles are spherical, and range in submicronic size of around 0.18 μm. X-ray diffraction analysis reveals that the ζ phase mostly exists under the two allotropic varieties (orthorhombic symmetry and hexagonal symmetry) with however a slight excess of the hexagonal variety (60% for the hexagonal variety and 40% for the orthorhombic variety). The lattice parameters resulting from this study for the two allotropic varieties are in good agreement with the Hume-Rothery rules.


Introduction
Historically, in power electronics, lead solders based mainly on Sn-Pb alloys were used as attachment joints because of their stable behavior [1]. To obtain the power module, a joint based on a lead alloy with a general eutectic composition is interposed between the various components to be assembled. The entire device is then brought to a temperature slightly above the melting point of the eutectic and then cooled slowly. This brazing process allows the diffusion of the elements of the alloy to the different components and leads to their assembly. However, the European Restriction of the use of certain Hazardous Substances in electrical and electric equipment (RoHS) directive dating from 2002 forbade the use of lead and certain harmful substances such as mercury, cadmium, etc.; and thus intended to gradually replace Sn-Pb alloys in current applications. In this context, great effort was deployed to propose alternative lead-free binary or ternary eutectic alloys, such as Sn-Zn [2,3], Sn-Sb [2,4], Sn-Ag [5][6][7] and SnAgCu [8,9]. However, all of these alloys have relatively low melting points (between 80 • C and 240 • C), which make them unsuitable for electronic power components intended for applications in extreme conditions (high temperature, etc.) such as electric aircraft for the aeronautical industry, the electrification of vehicles in the automotive, or the rail sector [3].
Faced with these limitations, a significant number of studies has been devoted to the development of new processes for assembling the components of power modules. In this context, several works have been devoted in recent decades to the use of silver as an attachment material, the assembly being carried out by means of the sintering acetate, nitrates, hydroxides and oxides, etc.). By heating at moderate temperature we can favor reduction or forced hydrolysis resulting in the formation of metals, oxides or hydroxides via the nucleation and growth stages. The competition between the reduction and hydrolysis reactions is controlled by the hydrolysis rate, which is defined as the ratio of the number of moles of water to that of metal cation. The reduction reaction is favored when the hydrolysis rate is low or even zero.
The polyol solvent can also be a surfactant which is adsorbed on the surface of the particles to prevent their agglomeration by steric gene (as a stabilizer that limits particle growth and prevents agglomeration [23,[30][31][32]). In addition, their high boiling point (of the solvents) allows them to solubilize a large number of metal salts and to activate reactions such as the oxidation of the polyol and consequently the formation of metals by reduction.
In the present work, the polyol process was extended to the elaboration of the solid solution and particularly the phase ζ with the chemical formula Ag 5 Sn 0.9 . In addition, it is possible to conduct these syntheses on a semi-pilot scale and thus have enough material for the die-bonding process. As will be shown hereafter, this phase has a very close structural filiation with the intermetallic compound Ag 3 Sn and therefore X-ray diffraction analysis does not allow its unambiguous characterization. During this study, thermal (DTA) as well as chemical (EDX) analyses were essential for a precise characterization of these phases. The results of these analyses are compared with the expected phases according to the equilibrium diagram and confirm that the obtained phase belongs to ζphases and corresponds to the chemical formula Ag 5 Sn 0.9 .

Materials
The materials used in this study to synthesize the Ag 5 Sn 0.9 particles were tin (II) chloride (SnCl 2 , 99%, Honeywell, Charlotte, NC, USA), silver nitrate (AgNO 3 , >99%) and ethylene glycol (EG) (VWR, 98%, Radnor, PA, USA) (Alfa Aesar, 99%, Haverhill, MA, USA). This latter is used as a solvent and a reducing agent for silver ions. Sodium borohydride (NaBH 4 ) was selected as a reducing agent for tin ions. A surface stabilizer, PVP (Alfa Aesar), was used to prevent particles from coalescing. A distillation device [21] was chosen to achieve a lower hydrolysis rate and obtain the metallic particles. Note that all the chemical products were used as received, without any further purification.

Synthesis
The synthesis was carried out using a distillation assembly comprising a heating mantle, a temperature probe, a temperature regulator, a three-necked flask, a stirring shaft and a distillation column [21]. A volume of 200 mL of EG was poured into a 500 mL threenecked flask. The polyol was under an ambient atmosphere and underwent mechanical stirring at 350 revolutions per minute (rpm). Table 1 resumes the optimal conditions to obtain the Ag 5 Sn 0.9 phase. At 50 • C, 1.43 g of PVP58000 were added and dissolved in the polyol medium. Subsequently, 1.43 g of AgNO 3 were added at 70 • C to form a mass ratio of PVP/AgNO 3 = 1. The solution became yellowish after dissolution of the precursors. The rate of temperature increase was set at 5 • C./min. After a plateau of 5 min at 160 • C, 1.4 g of SnCl 2 were added to the polyol to constitute a molar ratio n (Ag/Sn) = 1.14. After an additional 5 min at 160 • C, stirring was stopped and a mass of 5.478 g of NaBH4 corresponding to a molar ratio of NaBH 4 /Sn = 19.6 was slowly added to the medium. Then, the solution was brought to 180 • C with a plateau of 1 h maintained at this temperature while it was stirred mechanically. At the end of the reaction, the solution was cooled by water quenching (the heating mantle was removed from the experimental device). The powder was then isolated by centrifugation at 12000 rpm for 10 min and washed with ethanol and acetone, alternately. These steps were necessary in order to remove the remains of the polyol. Washing was stopped when the float became colorless. Finally, the powder was dried in an oven at 70 • C for 12 h. It is interesting to note that the as-produced powder was in a metastable state in comparison with the predictions of the equilibrium diagram of the Ag-Sn system. Table 1. Protocol of the synthesis of ζ-Ag 5 Sn 0.9 particles in polyol medium.

Characterizations
The crystal structure of the synthesized powder was determined by x-ray diffraction (XRD) (20 • < 2θ <120 • and ∆2θ = 0.03 • ), using Co Kα1 radiation (Kα1 = 1.78897 Å) on an INEL Equinox 1000 X-ray diffractometer. XRD characterization was performed by using two softwares: Match3 (version 3.14, CRYSTAL IMPACT, Bonn, Germany) was used for the phase identification, and material analysis using diffraction (Maud) (version 2.993, L. Lutterotti, University of Trento, Trento, Italy) was used to perform the Rietveld refinement analysis. The background and incident intensity factors were refined first; lattice constants were refined in a second step. Additional characteristics such as texture, crystallite size, strain and atomic positions of silver and tin were refined in followed steps. When necessary, phase percentages are refined as well. In addition, phase identification was carried on by differential thermal analysis (DTA) using Labsys TG-D747 instrument. The morphological observations and the particle/grain size were achieved by scanning electron microscopy (SEM), using a field emission gun scanning electron microscopy (FEG-SEM) model ZEISS TM SUPRA 40 VP.

DTA and EDX Analysis
The thermogram of Figure 1 indicates the formation of the ζphase which is characterized by the endothermic peak at around 728 • C, characteristic of the peritectic transformation (at 724 • C) due to the fusion of the ζ phase (Equation (1)): Solid solution (11.5 at.% Sn) + Liquid (19.5 at.% Sn).
As shown in Figure 2, the particles obtained are spherical, submicronic and nonaggregated, with an average size equal to 175 nm.
The chemical composition of the ζ phase has been precisely determined using the scanning transmission electron microscopy/high-angle annular dark-field imaging technique (STEM/HAADF). Observations and analysis were carried out on two different areas ( Figure 3). As shown in Figure 2, the particles obtained are spherica non-aggregated, with an average size equal to 175 nm. The chemical composition of the ζ phase has been precisely d scanning transmission electron microscopy/high-angle annular dark nique (STEM/HAADF). Observations and analysis were carried out eas ( Figure 3).
Chemical imaging analysis revealed a homogeneous distributio As shown in Figure 2, the particles obtained are spherical, submicronic and non-aggregated, with an average size equal to 175 nm. The chemical composition of the ζ phase has been precisely determined using the scanning transmission electron microscopy/high-angle annular dark-field imaging technique (STEM/HAADF). Observations and analysis were carried out on two different areas ( Figure 3).
Chemical imaging analysis revealed a homogeneous distribution of silver and tin in all the particles ( Figure 3). The composition is, however, variable from one area to another but remains within a relatively narrow range close to 1.3% (Table 2). Indeed, for silver, the percentage varies between 84.90% and 86.22% and for tin it varies between 15.10% and 13.78%. Based on this, the average chemical composition for the ζ phase can be estimated at 85.56 at.% Ag and 14.46 at.% Sn. This chemical composition indicates the formation of a ζ phase with a chemical formula close to Ag5Sn (Ag5Sn0.9) and not Ag4Sn.   Finally, we conducted XRD analysis on our sample powder. As a reminder, the DTA and EDX analyses show that the obtained phase corresponds to the ζ phase. As seen in Figure 4, and as discussed above as well as in the previous work on Ag3Sn [22], the diffractogram is substantially identical between the Ag3Sn and the ζ phases and cannot discriminate between them. This point will be taken up in the following discussion. The Chemical imaging analysis revealed a homogeneous distribution of silver and tin in all the particles (Figure 3). The composition is, however, variable from one area to another but remains within a relatively narrow range close to 1.3% (Table 2). Indeed, for silver, the percentage varies between 84.90% and 86.22% and for tin it varies between 15.10% and 13.78%. Based on this, the average chemical composition for the ζ phase can be estimated at 85.56 at.% Ag and 14.46 at.% Sn. This chemical composition indicates the formation of a ζ phase with a chemical formula close to Ag 5 Sn (Ag 5 Sn 0.9 ) and not Ag 4 Sn. Finally, we conducted XRD analysis on our sample powder. As a reminder, the DTA and EDX analyses show that the obtained phase corresponds to the ζ phase. As seen in Figure 4, and as discussed above as well as in the previous work on Ag 3 Sn [22], the diffractogram is substantially identical between the Ag 3 Sn and the ζ phases and cannot discriminate between them. This point will be taken up in the following discussion. The crystallite size calculated by MAUD (174 nm) is very close to the size of the particles deduced from SEM observations, indicating that the particles obtained are monocrystalline and probably formed by a mechanism involving Ostwald ripening.

Structural Hypothesis for the ζ Phase
As pointed out above, the characterization of the elaborated phase was carried out essentially on the basis of the DTA and EDX analysis based on the reading of the equilibrium diagram of the Ag-Sn system. Indeed, XRD analyses are not suitable for this purpose because of the similarity of the diffractograms of the two phases Ag3Sn and ζ-Ag4Sn (or Ag5Sn0.9). An attempt to explain this similarity is proposed in the following paragraphs.

Review on the Structure of the Ag3Sn Phase
The Ag3Sn phase exists in two allotropic varieties with a phase transition at 395 °C [33,34]. The high temperature variety has hexagonal symmetry (Space Group P63/mmc). The low-temperature variety has orthorhombic symmetry (Space Group Pmmn) and results from a distortion of the hexagonal variety. Figure 5 shows the correspondence diagram between the two cell parameters, taking into account the permutation of the axes carried out by Rossi et al. [33]. In this case, the orthorhombic lattice parameters ( , , ) derive from those of the hexagonal lattice ( , ) by the following relations (Equation (2)):

Structural Hypothesis for the ζ Phase
As pointed out above, the characterization of the elaborated phase was carried out essentially on the basis of the DTA and EDX analysis based on the reading of the equilibrium diagram of the Ag-Sn system. Indeed, XRD analyses are not suitable for this purpose because of the similarity of the diffractograms of the two phases Ag 3 Sn and ζ-Ag 4 Sn (or Ag 5 Sn 0.9 ). An attempt to explain this similarity is proposed in the following paragraphs.

Review on the Structure of the Ag 3 Sn Phase
The Ag 3 Sn phase exists in two allotropic varieties with a phase transition at 395 • C [33,34]. The high temperature variety has hexagonal symmetry (Space Group P6 3 /mmc). The low-temperature variety has orthorhombic symmetry (Space Group Pmmn) and results from a distortion of the hexagonal variety. Figure 5 shows the correspondence diagram between the two cell parameters, taking into account the permutation of the axes carried out by Rossi et al. [33]. In this case, the orthorhombic lattice parameters (a 0 , b 0 , c 0 ) derive from those of the hexagonal lattice (a h , c h ) by the following relations (Equation (2)): Materials 2022, 15, x FOR PEER REVIEW 8 of 15 Figure 5. Diagram of correspondence between the two hexagonal and orthorhombic crystal systems.

Structural Hypothesis for the ζ Phase
The solid solution ranging from 9 to 16 at.% Sn (ζ) also has hexagonal symmetry and belongs to the same space group (P63/mmc) as the high temperature variety of the Ag3Sn phase. In addition, the lattice parameters of the Ag4Sn phase representative of this family are close to those of the high temperature Ag3Sn phase (Ag4Sn: a = 2.9658 Å, c = 4.7842 Å; Ag3Sn: a = 2.9863 Å, c = 4.7840 Å) [34,37].
It should be noted that, to our knowledge, only the hexagonal variety has been reported for this solid solution (ζ). However, as for the Ag3Sn phase, the diffractogram cannot be explained by the existence of this allotropic variety alone due to the splitting of most of the peaks (except two).
We therefore hypothesized the existence of an orthorhombic variety for this phase, isostructural of that of the Ag3Sn phase. Because Ag3Sn and Ag4Sn exhibit the same structures at high temperature, the orthorhombic distortion of the lattice observed for Ag3Sn can reasonably occur for the ζ phase. Moreover, it was observed that a prolonged heating of the compound Ag3Sn at 320 °C leads to the formation of the solid solution ζ (Ag4Sn) [38]. It can therefore be assumed that this transformation is carried out by a mechanism of tin depletion concomitant with enrichment in Ag of the lattice of the Ag3Sn phase.
Since tin totally occupies the 2a site (1/4 1/4 z = 0.1700) in the case of Ag3Sn (Pmmn group) [39], this mechanism allowing the transformation of Ag3Sn into Ag4Sn will likely occur via progressive substitution of Sn by Ag in the 2a site as shown in the Table 3. The occupancy rates of both elements of the 2a site are calculated based on EDX analysis so that the chemical formula of the obtained phase can be written Ag3.4Sn0.6 and corresponds to the compound obtained during this work: Ag85Sn15 (or Ag5Sn0.9). We therefore carried out refinements in the three hypotheses: (i) hexagonal variety alone, (ii) orthorhombic variety alone and (iii) presence of both varieties ( Figure 6). The starting cell parameters and atomic positions were those given by King et al. for Ag0.8Sn0.2 [37] in the case of the hexagonal variety and those given by Fairhurst and al for the orthorhombic variety [39]. Thermal agitation (Biso) was fixed at 0.6 and not refined. In the orthorhombic Ag5Sn0.9 we imposed for the tin site (2a site) an occupancy rate equal to 0.6 for tin and occupancy rate equal to 0.4 for silver. The final atomic positions in hypothesis (iii) are reported in Table 3. Those for hypotheses (i) and (ii) are almost identical to those of hypothesis (iii) and therefore not shown. The refined diffractograms given in Figure 6 and Table 4 indicate the results of the refinements (cell parameters and reliability factors) in the three hy- As noted above, Ag 3 Sn has been synthesized by the polyol process. The refinements of its X-ray patterns were more satisfactory when the hexagonal phase is taken into consideration. The low-temperature variety with orthorhombic symmetry was certainly the majority (89%) but the high-temperature (hexagonal) variety is still present in a non-negligible amount (11%) [22]. The presence of both varieties at room temperature is likely due to the nature of the polyol process. Indeed, it has been shown that this method belongs to the soft chemistry routes which enable the formation of metastable phases along with stable ones [35,36].

Structural Hypothesis for the ζ Phase
The solid solution ranging from 9 to 16 at.% Sn (ζ) also has hexagonal symmetry and belongs to the same space group (P6 3 /mmc) as the high temperature variety of the Ag 3 Sn phase. In addition, the lattice parameters of the Ag 4 Sn phase representative of this family are close to those of the high temperature Ag 3 Sn phase (Ag 4 Sn: a = 2.9658 Å, c = 4.7842 Å; Ag 3 Sn: a = 2.9863 Å, c = 4.7840 Å) [34,37].
It should be noted that, to our knowledge, only the hexagonal variety has been reported for this solid solution (ζ). However, as for the Ag 3 Sn phase, the diffractogram cannot be explained by the existence of this allotropic variety alone due to the splitting of most of the peaks (except two).
We therefore hypothesized the existence of an orthorhombic variety for this phase, isostructural of that of the Ag 3 Sn phase. Because Ag 3 Sn and Ag 4 Sn exhibit the same structures at high temperature, the orthorhombic distortion of the lattice observed for Ag 3 Sn can reasonably occur for the ζ phase. Moreover, it was observed that a prolonged heating of the compound Ag 3 Sn at 320 • C leads to the formation of the solid solution ζ (Ag 4 Sn) [38]. It can therefore be assumed that this transformation is carried out by a mechanism of tin depletion concomitant with enrichment in Ag of the lattice of the Ag 3 Sn phase.
Since tin totally occupies the 2a site (1/4 1/4 z = 0.1700) in the case of Ag 3 Sn (Pmmn group) [39], this mechanism allowing the transformation of Ag 3 Sn into Ag 4 Sn will likely occur via progressive substitution of Sn by Ag in the 2a site as shown in the Table 3. The occupancy rates of both elements of the 2a site are calculated based on EDX analysis so that the chemical formula of the obtained phase can be written Ag 3.4 Sn 0.6 and corresponds to the compound obtained during this work: Ag 85 Sn 15 (or Ag 5 Sn 0.9 ). We therefore carried out refinements in the three hypotheses: (i) hexagonal variety alone, (ii) orthorhombic variety alone and (iii) presence of both varieties ( Figure 6). The starting cell parameters and atomic positions were those given by King et al. for Ag 0.8 Sn 0.2 [37] in the case of the hexagonal variety and those given by Fairhurst and al for the orthorhombic variety [39]. Thermal agitation (B iso ) was fixed at 0.6 and not refined. In the orthorhombic Ag 5 Sn 0.9 we imposed for the tin site (2a site) an occupancy rate equal to 0.6 for tin and occupancy rate equal to 0.4 for silver. The final atomic positions in hypothesis (iii) are reported in Table 3. Those for hypotheses (i) and (ii) are almost identical to those of hypothesis (iii) and therefore not shown. The refined diffractograms given in Figure 6 and Table 4 indicate the results of the refinements (cell parameters and reliability factors) in the three hypotheses.     As we can see, the refinement based on the presence of the two allotropic varieties leads to slightly better results (lower reliability factors and lower difference between calculated and observed XRD patterns as shown in the continuous background below the corresponding refinement). As shown for Ag 3 Sn, the synthesis in polyol medium leads to the formation of both allotropic varieties. However, it can be seen that high temperature variety remains predominant (59.9%) for the studied phase, whereas for Ag 3 Sn this allotropic variety represents the lower amount (11%).

Discussion
Jo et al. [40] used the polyol process to produce particles existing in the Ag-Sn system. In their protocol, the polyol (1,5-pentandediol) only plays the role of solvent allowing the synthesis to be carried out at 180 • C. Ag-Sn alloys are obtained via two steps: (i) obtaining Sn particles by the action of the NaBH 4 reducing agent of the Sn 2+ ions, and (ii) reduction of the Ag+ ions adsorbed on the Sn particles by the galvanic reaction (Equation (3)): 2Ag + + Sn 0 → Sn 2+ + 2Ag 0 (3) Since no complementary analyses were used, authors concluded on the basis of X-ray diffraction, that the two phases (Ag 3 Sn and Ag 4 Sn) are present along with tin as impurity [40].
As for the synthesis of Ag 3 Sn [22], we took advantage of the reducing character of the polyol to carry out the synthesis by permuting the two steps described by Jo et al. First, metallic silver particles were obtained by reduction of Ag+ ions by simple action of the polyol. In a second step, the Sn 2+ ions added to the medium were adsorbed on the surface of the silver particles. They then underwent a reduction thanks to the controlled addition of a strong reducing agent NaBH 4 . The formed tin atoms then diffused inside the silver particles to form submicron particles of the intermetallic compounds Ag 3 Sn [22] or ζ phase in the present study. It is worth noting that the main parameter governing the nature of the obtained phase is the amount of the reducing agent NaBH 4 . A high amount (NaBH 4 /Sn) of around 30 favors Ag 3 Sn formation whereas a lower amount (19.6) favors the phase rich in silver, namely ζ-Ag 5 Sn 0.9 .
During the investigation of the Ag-Sn system, appropriate analysis techniques such as DSC and EDX were necessary to qualify the formed phase (Ag 3 Sn or the ζ phase) (in our case the chemical formula is close to Ag 5 Sn). Indeed, the two phases have structural relationships leading to very similar diffractograms. Like us, several authors have reported similar diffractograms for samples qualified as Ag 3 Sn or the ζ phase (Ag 4 Sn) on the basis of EDX analysis [41,42].
We have proposed in this work a structural hypothesis to explain the similarity of the diffractograms observed for the two phases. It assumes that the Ag 3 Sn phase can evolve towards a phase richer in silver (ζ phase) thanks to a partial substitution of tin by silver on the 2a site of the Pmmn space group. This topotactic reaction is facilitated because the ζ phase and the high temperature variety of the Ag 3 Sn phase have the same symmetry and belong to the same space group (P6 3 /mmc) with very close cell parameters.
Both Ag 3 Sn and ζ phases are classified as Hume-Rothery compounds [43]. Their structure and lattice parameters depend on the electron concentration per atom (e/a) [44]. To calculate the ratio e/a, silver involves one electron and tin involves four electrons. Figure 7 gives the evolution of (e/a) for the series of compounds existing in the Ag-Sn system. As can be seen, the concentration (e/a) increases with the molar fraction of tin present in the compound. silver on the 2a site of the Pmmn space group. This topotactic reaction is cause the ζ phase and the high temperature variety of the Ag3Sn phase h symmetry and belong to the same space group (P63/mmc) with very clos ters.
Both Ag3Sn and ζ phases are classified as Hume-Rothery compoun structure and lattice parameters depend on the electron concentration per a To calculate the ratio e/a, silver involves one electron and tin involves four Figure 7 gives the evolution of (e/a) for the series of compounds existing system. As can be seen, the concentration (e/a) increases with the molar present in the compound.  Table 5 compares the lattice parameters found during this work with t in the literature for these compounds.   Table 5 compares the lattice parameters found during this work with those available in the literature for these compounds.
It has been shown that for the phases of hexagonal symmetry, contrary to the parameter c h , the parameter a h increases with the concentration (e/a) [43]. The lattice parameters determined for the Ag 3 Sn phase and the ζ phase (Ag 5 Sn 0.9 ) are in good agreement with this correlation (Figure 8); they increase when the concentration (e/a) increases. Figure 9 represents the evolution of the orthorhombic lattice parameter b 0 as a function of (e/a). This parameter actually derives from the a h parameter as a result of the orthorhombic distortion (b o ≈ 2a h ). Similar to a h for the hexagonal varieties, b o also increases with the concentration (e/a).   For the ζ phase (Ag 5 Sn 0.9 ), we hypothesized the existence of an orthorhombic symmetry as for Ag 3 Sn. The lattice parameter b 0 obtained in this hypothesis is in good agreement with the predictions of Hume-Rothery [43]. In fact, its value correlates well with the concentration (e/a) for this chemical formula.
In addition, one notices that the e/a ratio has an influence on the compactness of the lattice. Indeed, c/a and the corresponding ratio in an orthorhombic system deviate from the hexagonal close packed (hcp) value, namely 1.633: it decreases when the electron density per atom (e/a) increases (see Table 5, column 7).

Conclusions
The Ag-Sn system presents an intermetallic compound of defined composition Ag 3 Sn with a non-congruent melting point at 480 • C and a solid solution called ζ phase extending over a restricted range of composition (9-16 at.% Sn) with a melting point that is also non-congruent but at a higher temperature (724 • C). This solid solution is also considered an intermetallic compound. This work has been devoted to the synthesis of an intermetallic compound belonging to the ζ-phases by the polyol process. This ζ phase corresponds to the chemical formula Ag 5 Sn 0.9 . The particle's size is close to 180 nm. The size of the crystallites is very close to that of the particles showing a monocrystalline character.
Despite different chemical compositions and melting temperatures, the two compounds exhibit substantially identical diffractograms. Ag 3 Sn exists in two allotropic varieties: one hexagonal existing at high temperature and the other with orthorhombic symmetry existing at low temperature. The two varieties have been the subject, in the literature, of structural studies showing a filiation between these two structures resulting from the orthorhombic distortion of the hexagonal symmetry with the relation b 0 ≈ a h √ 3 (b 0 being the parameter b of the orthorhombic cell). For the ζ phase, only a variety of hexagonal and isostructural with the formula Ag 3 Sn is reported in the literature (same space group and close lattice parameters). This variety does not allow a satisfactory explanation of the diffractogram observed for this phase. Pending a precise structural determination, it was necessary to admit the existence, for this phase, of an allotropic variety with orthorhombic and isostructural variants of the compound Ag 3 Sn. Taking into account this variety alongside the hexagonal variety leads to a better accounting of the results of the X-ray diffraction analysis. The lattice parameters obtained are in line with the Hume-Rothery rules.