III. RESULTS AND DISCUSSION

Figure 1 shows the seven most representative XRD patterns of milled samples. The precursor material was identified as the β-Sn structure, space group I41/amd (141), which is in excellent accordance with ICSD database ¹⁶ card 43,613.

FIG. 1.

XRD patterns measured with increase of milling time.

The peaks centered at 2θ ∼ 27.7° and 2θ ∼ 28.9° are indicative of Bi₂Sn₂O₇, space group Fd-3m (227), in small amount. This phase was identified using the Bruker's Eva software in conjunction with the 2007 PDF-2 ICDD card 00-056-0657. ¹⁷ This type of impurity is usually added to Tin to suppress the allotropic phase transition which occurs at 13.2 °C ^{Reference Gialanella, Deflorian, Girardi, Lonardelli and Rossi18} and, therefore, it was not considered in this paper.

The high-energy ball milling process introduces high densities of structural defects in metals and alloys, besides a reduction in the average crystallite sizes. Generally, when the sample components are fragile, it is common to observe a lot of the material in the grain boundaries. ^{Reference Chookajorn, Murdoch and Schuh19,Reference Poffo, de Lima, Souza, Trichês, Grandi and de Biasi20} However, when the components are ductile, it is expected that such effect occurs in a less pronounced way.

In Fig. 1, the gradual increase of the baseline shows that successive collisions between spheres and particles produce large quantity of defects when stearic acid is present. In fact, PCAs containing carbon, hydrogen, and oxygen (such as stearic acid) are prone to introduce oxygen and carbon in the surface of the powder particles, resulting in the formation of oxides and carbides evenly dispersed in the matrix. ^{Reference Suryanarayana21} In turn, hydrogen can act as a surfactant and does not participate in the alloy formation process. On the other hand, it is known that hydrogen induces embrittlement in several metal alloys. In particular, Muktepavela et al. ^{Reference Muktepavela, Vasylyev, Czerwinski and Rogulski22} reported that the embrittlement of Sn–Al alloy, during contact with water vapors, happens mainly due to interaction of hydrogen with the tin surfaces forming SnH₄ hydrides. The formation of SnH₄ occurs only upon the fulfillment of two conditions ^{Reference Samsonov23} : the presence of atomic hydrogen and of free bonds of tin. Indeed, the dissociation of the stearic acid and tin deformations, during milling processes, satisfies these two conditions. The authors also affirm that SnH₄ shows instability and decomposes at room temperature.

The baseline profile can be seen in more detail in the inset of Fig. 1. This profile is characteristic of amorphous structures and the broad band, extended from 2θ = 20–40°, corresponds to x-ray scattering from atomic distribution of first neighbors. As this broad band is an atomic distribution of distances of the disordered structure, Gaussian functions are applied to fit the shape of the amorphous halo. A good fit is achieved only when two Gaussians are considered. Thus, the interatomic distances r of this structure can be estimated by applying the Ehrenfest formula ^{Reference Rachek24} :

where λ is the wave length of x-rays and θ is the half angle of diffraction. The first Gaussian, with smaller area, is centered at 2θ = 26.4°, whereas the second, bigger and more relevant, is centered at 2θ = 31.1°. So, according to Ehrenfest formula, the interatomic distances are 4.1 and 3.5 Å. Using the same methodology applied to the x-ray diffraction pattern reported in Ref. Reference Idota, Kubota, Matsufuji, Maekawa and Miyasaka25 for the amorphous tin oxide, an interatomic distance of 4.0 Å was obtained, which the authors of the referred work claim to be the distributions of distances of Sn–Sn pairs. On the other hand, we observe a gradual enlargement of diffraction lines of the crystalline component indicating a gradual reduction in average crystallite sizes.

All patterns were simulated using the Rietveld structural refinement procedure through the GSAS code and the data given in the ICSD code. Good simulations were obtained only by choosing the Chebyschev function with ten parameters to fit the background, reaching R _w and R _wp factors smaller than 10%. Figure 2 depicts the experimental and simulated XRD patterns of the powder after 28 h of milling, where one can see an excellent agreement as it is shown by the difference curve (bottom).

FIG. 2.

XRD pattern of the sample milled for 28 h (black line) and its Rietveld simulation (red line). The bottom line represents the difference between the experimental and the simulated pattern.

The average crystallite sizes and microstrain can be estimated from the simulated XRD pattern taking into account the line broadening caused by both crystallite size and microstrain by the equation ^{Reference Strand26}

where θ is the diffraction angle, λ is the x-ray wave length, β_t is the total broadening measured at the full-width at half-maximum (FWHM) of the peak (in radians), d is the crystallite size, σ _p is the strain, and K is a constant dependent on the measurement conditions and definition of β_t and d. Here, K is assumed to be 0.91 as usual in the Scherrer's formula. Graphical linearization of the above relationship, i.e., plotting ${\rm{\beta }}_{\rm{t}}^{\rm{2}} \cos ^2 {\rm{\theta }}/{\rm{\lambda }}^2$ versus $\sin ^2 {\rm{\theta }}/{\rm{\lambda }}^2 ,$ yields the average crystallite size free from strain effects and the strain. The GSAS code generates the β_t and 2θ positions for all the simulated peaks. Thus, considering these values in Eq. (2), the mean crystallite sizes of the samples' crystalline phase for all milling times were obtained and are shown in Fig. 3. In the first 2 h of milling, a decrease of approximately 49% in the mean crystallite size was observed; whereas after 28 h, this decrease becomes approximately 84% relative to the precursor tin powder.

FIG. 3.

Mean crystallite size as a function of milling time.

Recently, Gialanella et al. ^{Reference Gialanella, Deflorian, Girardi, Lonardelli and Rossi18} applied mechanical milling in Sn using 2 wt% of graphite as PCA in a mill similar to the one used in the present work. Upon 16 h of milling, they did not observe any significant reduction in average crystallite sizes. In this work, in 16 h of milling, we have observed a reduction of around 75%, as shown in Fig. 3. Therefore, the nature of the PCA may be an important variable to the crystallite reduction efficiency.

The obtained microstrains for all milling times were less than 1.0% with fluctuation at about 0.3%. This result is not a surprise, once Sn is notoriously ductile. For example, Hotta et al., ^{Reference Hotta, Matsumoto, Murakami, Narushima and Ouchi27} in a study about dynamic and static restoration behaviors of tin and lead, in the ambient temperature range, reported relatively low activation energy of structural restoration, around 50 kJ/mol, which is half the energy of atomic self diffusion. So, in spite of the severe plastic deformations during ball milling, we observe a low microstrain value which can be understood by the successive deformation/restoration processes undergoing during milling. In other words, the energy originated from the collisions is sufficient to deform and to restore the tin structure at the same time.

Figure 4 shows some DSC measurements performed with a heating rate of 10 °C/min. The measurement for the precursor powder is indicated as 0 h (black curve), and it shows a practically constant baseline with an endothermic reaction in 235 °C, which corresponds to the complete fusion of the β-Sn crystalline structure. ^{Reference Hansen28}

FIG. 4.

DSC thermograms measured with increase of milling time.

After milling, a wide exothermic band is observed starting approximately at 140 °C and overlapped by β-Sn melting. Owing to these simultaneous exothermic and endothermic processes, the determination of T _onset of the β-Sn was affected. However, the difference between the T _peak of precursor Sn and that of Sn milled for 28 h was less than 2%. Immediately after the melting of Sn, appears a new exothermic broad band followed by the elevation of the baseline, usually associated with variation in the specific heat. For example, the specific heats of β-Sn, SnO, and SnO₂ in the room temperature are 26.943, 50.089, and 64.224 J/mol K, ²⁹ respectively. There exists no data about the amorphous SnO specific heat. Therefore, this pronounced baseline variation after the oxides nucleation may be associated with the existence of these new phases.

After 16 h of milling, a second endothermic peak around 229 °C was observed whose resolution increases after 20 h of milling and it enhances with larger milling times, until the amplitude of the nanocrystalline Sn melting point is reached, as shown in the inset of Fig. 4. Part of the explanation may be found in Sn–Al phase diagram. ^{Reference Hansen28} Once aluminum pans were used in DSC measurements, there is a eutectic reaction in 228 °C for a compound with 97.6 wt% of Sn and Al, which explains the observed phenomenon. However, this reaction is only noticeable in the thermogram when the mean crystallite size is smaller than 60 nm, indicating that the surface energy plays an important role in the activation process of such reaction.

To investigate the exothermic processes, DSC measurement was performed at a reduced rate, 2 °C/min. The result is shown in Fig. 5. Now it is possible to distinguish clearly the two processes separated by the nanocrystalline β-Sn melting: the first one around 196 °C and the second one at 287 °C. Based on these features, two heat treatments were carried out under the same conditions in the sample milled for 28 h. The first annealing was performed at 240 °C and the second at 350 °C, both for 20 min.

FIG. 5.

DSC thermogram of the sample milled for 28 h at a rate of 2 °C/min. The exothermic peak at 196 °C has been associated with nucleation of tetragonal crystals of SnO. The exothermic peak at 287 °C corresponds to SnO₂ tetragonal phase.

In Fig. 6, the XRD patterns for the annealed samples at 240 °C (red curve) and 350 °C (black curve) are shown together with the 28 h as-milled sample (gray curve). The peaks appeared at 240 °C have been associated with tetragonal crystals of SnO, space group P4/nmm (ICSD: 26,597). Once the heat treatment was hermetic, the appearance of these crystals is explained by the crystallization of the amorphous phase present in the sample.

FIG. 6.

XRD patterns measured for the annealed samples at 240 and 350 °C and the 28 h as-milled sample.

After the second annealing, new and enlarged peaks were observed. These peaks correspond to two new phases: the SnO₂ tetragonal phase and an indeterminate phase, indicated by asterisks.

Legendre et al. ^{Reference Legendre, Poissonnet and Bonnaillie30} produced SnO₂ tetragonal phase powders with crystallite size smaller than 10 nm, at room temperature by reactive milling of metallic tin (Sn) powder under pure oxygen medium in a vertical planetary ball-mill. The authors have concluded that the significant agglomeration level of the powder attenuates the benefits of the decrease of the crystallite size and they suggest the addition of a PCA in the mill to work around this problem.

Some authors have reported the nucleation of a high pressure SnO₂ orthorhombic phase in monoxide Sn when mechanically milled and heat treated at 575 °C. ^{Reference Lamelas31} Also, the mechanochemical processing of SnCl₂ and Na₂CO₃ resulted in the formation of nanocrystalline SnO during milling and oxidized to SnO₂ after heat treatment at 700 °C in an air atmosphere. ^{Reference Cukrov, Tsuzuki and McCormick32} However, none of the high pressure phases of SnO₂ (Pnnm, Pbcn, Pa-3, Pbcn, Fm-3m, and Pnam) ^{Reference Gracia, Beltrán and Andrés33} could be successfully indexed to the unknown phase present in the sample milled for 28 h and heat treated at 350 °C.

Figure 7 shows the x-ray pattern for the sample annealed at 350 °C, the total Rietveld refinement (red curve), and its deconvolution for 12 wt% of Sn, SnO 47 wt%, and 41 wt% of SnO₂ phases. This deconvolution makes evident the presence of different degrees of crystallinity between the phases. While the β-Sn phase has narrow peaks, the peaks of SnO₂ are considerably broadened. The calculated mean crystallite size for SnO₂ phase is about 8 nm. The crystallographic parameters obtained are shown in Table I.

FIG. 7.

XRD pattern for the sample annealed at 350 °C, total Rietveld refinement, and the deconvolutions of Sn, SnO, and SnO₂ phases.

TABLE I.

Crystallographic parameters obtained by Rietveld refinement for the sample milled for 28 h and annealed at 350 °C.