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Mechanisms behind the spontaneous growth of Tin whiskers on the Ti2SnC ceramics
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Mechanisms behind the spontaneous growth of Tin whiskers on the Ti2 SnC ceramics Yushuang Liu , Chengjie Lu , Peigen Zhang , Jin Yu , Yamei Zhang , ZhengMing Sun PII: DOI: Reference:
S1359-6454(19)30866-3 https://doi.org/10.1016/j.actamat.2019.12.027 AM 15723
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Acta Materialia
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22 September 2019 15 December 2019 15 December 2019
Please cite this article as: Yushuang Liu , Chengjie Lu , Peigen Zhang , Jin Yu , Yamei Zhang , ZhengMing Sun , Mechanisms behind the spontaneous growth of Tin whiskers on the Ti2 SnC ceramics, Acta Materialia (2019), doi: https://doi.org/10.1016/j.actamat.2019.12.027
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Mechanisms behind the spontaneous growth of Tin whiskers on the Ti2SnC ceramics Yushuang Liu a,#, Chengjie Lu a,, Peigen Zhang a,*, Jin Yu a, Yamei Zhang b, ZhengMing Sun a, a
Jiangsu Key Laboratory of Advanced Metallic Materials, School of Materials Science and Engineering, Southeast University, Nanjing 211189, P. R. China
b
Jiangsu Key Laboratory of Construction Materials, School of Materials Science and Engineering, Southeast University, Nanjing 211189, P. R. China
Abstract The spontaneous growth of Tin whiskers has been a reliability issue in electronic assemblies for around 70 years, but the underlying physics is still ambiguous. Herein, Sn whiskers formed on the Ti2SnC, a layered ternary carbide ceramic MAX phase, were studied to trace the atomic motion in whisker growth process. Free Sn source was found to be necessary for the formation of Sn whiskers, however, the interface microstructure suggests that Sn atoms feeding whiskers are diffusing through the Ti2SnC lattice. According to the simulation results on the formation and migration energies of vacancies in Ti2SnC, a low diffusion barrier is expected for Sn atoms to diffuse along the basal planes. When Sn atoms diffuse out of the substrate, Sn whiskers bounded by low-energy planes form to minimize the total energy. In contrast, the whiskers maintain the striated morphology inherited from the whisker root in the environment containing oxygen, which is mainly attributed to the confinement of the oxide film on whisker surface. The findings will also shed new light on understanding the general whiskering problems found in other materials.
These authors contributed equally to this work. Corresponding authors. E-mail addresses: [email protected] (P. Zhang), [email protected] (Z.M. Sun).
Keywords: MAX phase; Sn whisker; Interface; DFT; HRTEM 1. Introduction Spontaneous Sn whisker growth on Sn and Sn alloys has attracted attention for approximately 70 years [1-3]. Sn whiskers pose a severe reliability risk in electronic assemblies as they can cause electrical failures [4]. To date, whisker-induced failures have involved almost all industry fields, including military, medical, aerospace, nuclear [5]. One of the most reliable and widely used strategies to mitigate Sn whisker growth is alloying Sn with Pb [6]. However, with the toxicity of Pb is being realized, the elimination of Pb from electronic devices is required according to RoHS and other Pb-free regulations. Therefore, Sn whisker growth has reemerged as a major reliability issue in electronic industry, and attracted increasing interest from both scientific and technical fields. To solve the problems associated with Sn whisker growth, a total understanding of the mechanisms behind is necessary. Therefore, many researches on different aspects have been performed in the past several decades, especially in recent years with the impact of lead-free movement. For example, Stein et al. [7] tried to understand the phenomenon by studying the growth directions of Sn whiskers. The whiskers were found to grow preferentially along low-index directions of β-Sn, which was explained by applying the concept of the periodic bond chains (PBCs) in a modified way. It was proposed that the whiskers preferred to grow along the directions of PBC vectors, which refer to chains of strong bonds running uninterruptedly through the crystal structure.
Jagtap et al. [8] tried to identify the locations of Sn whiskers by mapping the crystallographic microtexture of the electroplated Sn films. It was observed that Sn whiskers preferred to grow from low-index grains with (100) or near-(100) orientations that were surrounded by grains with similar orientations, which were then partially surrounded by grains with high-index orientations. The whisker growth was attributed to the high compressive stress around the whisker grain. Sun et al. [9] studied the microstructure between Sn whisker and the neighboring grains on SnAg micro-bumps. Dislocations and stacking faults were observed in both the whisker and the substrate, and twin boundary is determined between them, which was proposed to be the nucleation position of Sn whiskers. The authors suggested that the formation of Sn whiskers was realized by dislocation slip over the twin boundary. Illés et al. [10] investigated the relationship between the crystal structure of Cu-Sn intermetallic and Sn whisker growth on Sn film evaporated on Cu substrate. It was found that Sn whiskers preferred to grow in the regions where the IMC layer is composed of monocrystal grains. In addition, the corrosion of Sn and Sn alloys at elevated temperature and humidity conditions also reported to be responsible for Sn whisker growth [11]. Besides, interior microstructure of Sn whiskers was also studied [12]. The results revealed that Sn whiskers may consist of many side-by-side filaments, suggesting that a Sn whisker can grow from several adjacent grains with similar orientations. This assumption was further confirmed by the fact that the whisker diameters are larger than the underlying
film grains [13]. According to these reports, some new understandings about Sn whisker growth have been obtained. However, the underlying physics of Sn whisker growth remains ambiguous up to now. Essentially, Sn whisker growth is an atomic motion process. Therefore, in order to probe into the physics behind, it is necessary to understand the atomic motion behavior in whisker growth. However, investigation preformed from the point of atomic motion has been seldom reported up to date, which is mainly attributed to the difficulty in characterizing the Sn atom motion in Sn and Sn alloys. It is worthwhile pointing out that Sn whisker growth is not only limited to metals. MAX phases, a family of nanolaminate ternary carbide or nitride ceramics [14, 15], have also been reported to have such whiskering problems [16-19]. In addition, the pressure and temperature can effectively modulate the incubation period of A-element whisker growth on MAX phases by affecting the nucleation process [20]. It has been well-established that Sn whiskers grow by adding atoms to their bases [21, 22], therefore, the whiskers on MAX phases are considered to grow from a heterogeneous phase. Compared with the case of Sn and Sn alloys, it is more feasible to study the atomic motion behavior in whisker growth on MAX phases due to the crystal structure difference between the whisker and the substrate. Considering that Sn whiskers formed on different substrates share the same essence, it sheds new light on uncovering the physics behind the general whiskering phenomenon on Sn and Sn alloys by studying the
atomic motion behavior in Sn whisker growth on MAX phases. In the present work, Sn whiskers have been cultivated on Ti2SnC, which is a typical MAX phase. Interface microstructure between Ti2SnC and Sn whisker is characterized by high resolution transmission electron microscopy (HRTEM), in order to study the atomic motion. In addition, vacancy formation and migration energies are calculated based on Density Functional Theory (DFT) to explain the diffusion mechanism in Sn whisker growth. Afterwards, morphology analysis of Sn whiskers, together with surface energy calculation of β-Sn, are carried out to explain the morphology formation mechanism of Sn whiskers. 2. Experimental methods Predominantly single-phase of Ti2SnC was synthesized by pressureless sintering using stoichiometric powders of Ti (99.0%, 250 mesh), Sn (99.5%, 200 mesh), and graphite (99.85%, 500 mesh). The synthesis details have been described elsewhere [23]. Chemical etching was applied to remove residual free Sn in the as-synthesized Ti2SnC. Each portion of as-synthesized Ti2SnC around 5 g was immersed in diluted hydrochloric acid (1 mol/L, 50 mL) under magnetic stirring for 4 h. After that, Ti 2SnC powder without free Sn was collected by centrifugation, washed several times with deionized water, and finally dried in air at 60 °C. The as-synthesized and HCl etched Ti2SnC powders were ball-milled at 500 r/min for 1 h with the ball-to-powder weight ratio of 10:1 and then cold-pressed under 1000 MPa, respectively, to fabricate Ti2SnC bulk with
and without free Sn. The relative densities of un-etched and etched Ti2SnC samples were measured to be 85.2% and 84.1%, respectively. In addition, for the convenience of interface microstructure characterization, densified Ti2SnC bulk was fabricated by sintering the as-synthesized Ti2SnC at 1300 °C for 20 min under the pressure of 50 MPa using spark plasma sintering. Sn whisker growth on all the samples was performed at 210 °C in air or flowing argon atmosphere in a tube furnace. X-ray diffraction (XRD, Bruker D8 Discover) was performed to determine the phase composition of the samples, with Cu Kα radiation at a scanning step of 0.02° and scanning rate of 10°/min. In addition, the morphology was observed using a scanning electron microscope (SEM, FEI Sirion 200), and the chemical composition of the observed phases was determined by energy dispersive spectrometer (EDS, Oxford X-Max 50). Finally, the interface microstructure between Sn whisker and Ti2SnC substrate was studied using the combination of focused ion beam (FIB, FEI Helios G4) technique
and
transmission
electron
microscopy (TEM,
JEOL JEM-2100F)
characterization. 3. Calculation details First-principles calculations on the framework of the Density Functional Theory (DFT) were performed using the Vienna Ab-initio Simulation Package (VASP). The projector augmented wave method (PAW) and the generalized gradient approximation constructed by Perdew-Burke-Ernzerhof (GGA-PBE) for the exchange-correlation
energy function were used. In order to sample the k-mesh within the Brillouin zone, the
centered Monkhorst-Pack grids [24] were used. The total number of the k-points was determined to be k=40 for β-Sn and k=50 for Ti2SnC according to the convergence test, respectively, along with a plane-wave cutoff energy Ecutoff=480 eV, which made the accuracy within 1 meV/atom. The monovacancy structure of Ti2SnC is represented by a 2×2×1 supercell containing 31 atoms after removing one atom of each species, which is adequate to get a convincing result [25]. The formation energy ∆EV of monovacancy in Ti2SnC can be evaluated according to the equation:
EV =ETi2SnC+V ETi2SnC +V
(1)
where ETi2SnC+V is the total energy of the supercell containing a monovacancy, ETi2SnC is the total energy of the defect-free supercell, and V is the chemical potential in pure solid of each species, which can be approximated by the average atom energy of corresponding solid [26]. In addition, the self-diffusion barrier of Sn atoms in Ti2SnC substrate was studied by searching the transition state linking the two end defective models using the nudged elastic band (NEB) method, which was realized by neighboring vacancy jump along the basal plane. The typical slab model was used to calculate the surface energy of β-Sn, in which the periodic boundary conditions were applied to the surfaces and a vacuum region of 15 Å was applied to prevent unwanted interactions between the slab and its periodic
images along surface normal direction. For a given surface, the corresponding surface energy can be calculated according to the equation:
=
Eslab Ebulk Nslab 2 Aslab
(2)
where Eslab is the total energy of the slab model, Ebulk is the energy per atom of the bulk, Nslab is the total number of atoms in the slab model, the factor 2 accounts for the two surfaces in the slab model, and Aslab is the surface area. 4. Results 4.1. Sn whisker growth on Ti2SnC Phase composition of the Ti2SnC bulks was revealed by the XRD patterns. The upper curve in Fig. 1(a) shows the XRD pattern of the as-synthesized Ti2SnC bulk. It can be concluded that the Ti2SnC phase accounts for the majority of the bulk, together with a small amount of free Sn and TiC. The bottom curve shows the result of the Ti2SnC bulk followed by an HCl etching treatment. The peaks corresponding to Sn phase disappeared, while the peaks corresponding to Ti2SnC and TiC remained unchanged. Fig. 1(b) shows the microstructure of the Ti2SnC bulk with free Sn. Three phases with different contrasts can be observed in the image. The grey phase which accounts for the majority of the bulk is the Ti2SnC phase according to the XRD analysis. The chemical composition of the black phase is determined to be around Ti 40.12 at.%, Sn 2.21 at.%, C 57.66 at.% by EDS, and that of the white phase is about Ti 15.68 at.%, Sn 84.32 at.%, corresponding to TiC and Sn, respectively.
Fig. 1 Characteization of the substrates: (a) XRD patterns of the Ti2SnC bulk with and without free Sn; (b) BSE morphology of the Ti2SnC bulk with free Sn.
Fig. 2 shows the typical morphology of Sn whiskers on Ti2SnC substrate in air. After aging at 210 °C for 1 h, numerous filamentary Sn whiskers grew from the as-synthesized Ti2SnC bulk, as shown in Fig. 2(a). However, no whiskers were observed on the etched Ti2SnC substrate, even after the extension of aging time to 7 days, as shown in Fig. 2(b), suggesting that free Sn is necessary for the formation of Sn whiskers on Ti2SnC. The whisker diameter ranged from a few hundreds of nanometers to a few microns, and the length ranged from a few tens of nanometers to a few millimeters. Meanwhile, the morphology of the filamentary whiskers may be straight, kinked, and curved. Despite of the diverse morphologies, striations parallel to the whisker axis were observed on all of the whiskers, as typically displayed in the inset of Fig. 2(a). The random diameter and length, together with the diverse morphology and the striated surface of the Sn whiskers formed on Ti2SnC, are similar to the ones formed on Sn and Sn alloys [13, 27-29].
Fig. 2 Sn whisker growth behavior on Ti2SnC in air: (a) as-synthesized Ti2SnC after aging at 210 °C for 1 h, and the inset is the magnified view of a Sn whisker; (b) etched Ti2SnC after aging at 210 °C for 1 h, and the inset is the morphology after the extension of aging time to 7 days.
Thermodynamically, a crystal presents the morphology with lowest surface free energy when approaching equilibrium. Provided the surface energy of a crystal is generally anisotropic, the Sn whiskers are expected to display the morphology bounded by lower-energy planes. However, it is evident that the striated Sn whisker formed in air, as typically displayed in Fig. 3(a), is far away from the equilibrium morphology, which suggests that other factors affecting crystal morphology were involved during whisker growth. Therefore, Sn whisker growth was further carried out in argon atmosphere to simplify the growth environment. It is interesting that when the Ti2SnC was aged in argon, well-faceted Sn whiskers bounded by planar surfaces rather than the striated ones are formed, as shown in Fig. 3(b)-(d). According to the morphology diversity, most of the faceted Sn whiskers fall into two types: hexagonal (Fig. 3(b)) and quadrangular (Fig. 3(c) and (d)). Morphology formation mechanisms of the whiskers will be discussed in the following section in detail.
Fig. 3 Sn whiskers with different morphologies: (a) a striated Sn whisker formed in air; (b) a hexagonal Sn whisker formed in argon, and the inset is the magnified view of the whisker root; (c) and (d) quadrangular Sn whiskers formed in argon.
4.2. Microstructure at the base of Sn whiskers To study the microstructure at the base of the whiskers, FIB cross-sectioning at the root area of the whiskers was conducted. Fig. 4(a) displays a short Sn whisker grown on Ti2SnC. According to the corresponding cross-sectional morphology shown in Fig. 4(b), the whisker root with irregular shape is embedded in the substrate, and clear phase boundary between the whisker and the substrate was determined. Considering that Sn whiskers grow by adding atoms to their bases, it is reasonable to assume that the whiskers were developed from Sn grains located inside the Ti2SnC substrate. In addition, the whisker root is not connected with the free Sn distributed in the substrate. For a
more detailed understanding of the underlying microstructure, three dimensional morphology of a whisker root was reconstructed utilizing a series of cross-sectional images, one of which is shown in Fig. 4(c). According to the reconstruction result in Fig. 4(d), the whisker root is not in contact with free Sn in the substrate in three dimensions, which suggests that the Sn atoms feeding Sn whisker growth probably diffuse through the Ti2SnC lattice.
Fig. 4 Microstructure at the base of a Sn whisker: (a) a Sn whisker grown on Ti2SnC; (b) the cross-sectional morphology of the whisker in (a); (c) one cross-section of the Sn whisker to be reconstructed; (d) reconstruction result of the whisker root in (c).
For a precise characterization of the interface microstructure between Sn whisker and the Ti2SnC substrate, a TEM sample was fabricated around the interface using FIB technique. Fig. 5(a) shows the cross-sectional morphology of the chosen whisker. To
facilitate the fabrication process, the top part of the whisker was milled using FIB. BSE morphology of the fabricated sample is displayed in Fig. 5(b). Besides the sputtered Pt protective layer, three phases with different contrasts can be observed. The grey phase accounts for the major part of the sample, while there are also a small amount of light grey and dark grey phases. The light grey phase in the substrate shares similar contrast with the whisker. Afterwards, the element distribution of the TEM sample is given by STEM. Fig. 5(c) shows the STEM morphology of the sample and the corresponding distribution of the Ti, Sn, and C elements. It can be concluded from the figure that the grey phase composed of Ti, Sn, and C elements is Ti2SnC. Furthermore, the light grey phase is mainly composed of Sn element, while the dark grey phase is made up by Ti and C elements, which are deduced to be Sn and TiC, respectively.
Fig. 5 Characterization of the TEM sample: (a) initial morphology of the interface area; (b) BSE morphology of the TEM sample; (c) STEM morphology of the TEM sample, and the corresponding element distribution of Ti, Sn, and C elements, respectively.
5. Discussion 5.1. Interface microstructure of Ti2SnC/Sn The experimental results indicate that Sn whiskers grow on Ti2SnC. In addition, secondary phase of Sn was also detected in the Ti2SnC bulk. To trace the atomic motion in Sn whisker growth process, the interface microstructure of the two types of Ti2SnC/Sn interfaces was further investigated. Fig. 6(a) shows the TEM image of the interface area between Ti2SnC and free Sn in the substrate, which corresponds to the area marked in Fig. 5(c). The selected area electron diffraction (SAED) patterns of the two phases confirm that they are Ti2SnC and β-Sn, respectively. Fig. 6(b) shows the high resolution TEM (HRTEM) image of the interface. The lattice fringes with an interplanar spacing of 2.687 Å and 2.934 Å are determined to be the (101̅1) plane of Ti2SnC and the (200) plane of β-Sn, respectively. The HRTEM contrast also suggests a direct contact between Ti2SnC and the free Sn with no transition layer present.
Fig. 6 Interface microstructure between Ti2SnC and free Sn in the substrate: (a) TEM image of the interface, and the insets show the corresponding selected area electron diffraction (SAED) patterns; (b) high resolution TEM (HRTEM) image of the interface.
Fig. 7(a) shows the TEM image of the Ti2SnC/Sn whisker interface. According to the SAED patterns displayed, the two phases with distinct morphology are confirmed to be Ti2SnC and β-Sn, respectively. Fig. 7(a) together with the magnified image shown in Fig. 7(b) indicates that both the Sn whisker and the neighboring Ti2SnC are free of defects. Therefore, it is reasonable to assume that the presence of dislocations is not necessary for Sn whisker growth although dislocations and stacking faults within Sn whiskers has been previously observed [9, 30]. For a more detailed analysis of the interface microstructure, HRTEM images were recorded from the Ti2SnC/Sn whisker interface, as displayed in. Fig. 7(c) and (d). Measurements of the lattice fringes from the whisker and the substrate parts are consistent with those for (200) plane of β-Sn and (101̅ 2) plane of Ti2SnC, respectively. Different from the Ti2SnC/Sn interface in the substrate (Fig. 6), a nanometer-thick transition layer was observed at the Ti2SnC/Sn whisker interface. The transition layer has similar but less ordered atomic arrangement to (200) plane of the Sn whisker, and suggested to be diffused from the Ti2SnC substrate according to the interface morphology, as typically displayed in the insets in Fig. 7(c) and (d). All the coherent, semicoherent and incoherent interfaces can be observed between the transition layer and the whisker. Representative morphology of the three types of interfaces was marked in the HRTEM images. The coherent interface in area 1 exhibits a deflection of approximately 5 degrees, while the incoherent ones in area 3 and area 4 possesses totally interlaced atomic plane arrangement with same orientation. And
the semicoherent interface in area 2 is in between. Afterwards, the average interplanar spacing of the transition layer in area 1 to area 4 was measured to be 3.014 Å, 2.945 Å, 3.085 Å and 2.987 Å, respectively, as displayed in the corresponding area. Given that the interatomic distance of Sn in Ti2SnC crystal is 3.096 Å, and the measured interplanar spacing of the (200) plane of β-Sn is 2.926 Å, it can be concluded that the interplanar spacing of the transition layer is between the interplanar spacing of the (200) plane of β-Sn and the interatomic distance of Sn layer in Ti2SnC, which further suggests that the transition layer is diffused from the Ti2SnC. It was previously assumed that the atoms for metal whisker growth on MAX phases come from the corresponding elemental A [17], and the results in the present work also suggest the necessity of free Sn for the formation of Sn whiskers on Ti2SnC. However, the microstructure of the Ti2SnC/Sn whisker interface reveals that the atoms for Sn whisker growth have high possibility of diffusion through Ti2SnC lattice. To understand the diffusion behavior of Sn in Ti2SnC, the formation and migration energies of monovacancy in Ti2SnC are calculated. The vacancy formation energies are calculated as 3.75 eV, 1.72 eV and 2.89 eV for Ti, Sn and C monovacancy, respectively, indicating Sn vacancy is the most energetically favorable monovacancy in defective Ti2SnC. Assuming that the diffusion of Sn in Ti2SnC is sublattice-diffusion by neighboring vacancy jump along the basal plane, the migration energy is calculated to be 0.60 eV. Therefore, a low diffusion barrier is expected for Sn atoms to diffuse along
the Sn layer in Ti2SnC. As a result, Sn atoms in Ti2SnC can easily migrate outside and thus feed Sn whisker growth. The driving force for the mass transport of Sn atoms from Ti2SnC lattice to the whisker root is considered to be the concentration gradient. The Sn concentration in free Sn is much higher than that in Ti2SnC lattice, in consequence, Sn atoms from free Sn continuously diffuse into Ti2SnC. Therefore, the fundamental factor initiating the whiskering phenomenon on Ti2SnC is attributed to the interaction between Ti2SnC and Sn.
Fig. 7 Interface microstructure between Ti2SnC and Sn whisker: (a) TEM image of the interface, and the insets show the corresponding SAED patterns; (b) magnified view of the white rectangle area in (a); (c) and (d) HRTEM images of the interface.
5.2. Morphology formation mechanism of Sn whiskers In order to elucidate the morphology formation mechanism of Sn whiskers, surface energy calculation was performed for β-Sn. The low-indexed surfaces of (100), (112), (101), (001), (301), (110), (210), (211), (111) and (201) are selected. Both relaxed and un-relaxed surface energies for the surfaces are calculated, and the change in atomic
position of surface atoms was quantified by the relaxation factor. The results are listed in Table 1, in which the surfaces are arranged in an increasing order based on their un-relaxed surface energy. After relaxation, the order from smallest to largest surface energy changes slightly, but the surface energy of the relaxed surface is not significantly different from that calculated for the unrelaxed surface. The (100) surface was calculated to have the smallest relaxed surface energy, followed by (112), (101), (001), (301), (110), (111), (210), (211) and then (201). According to the calculation results, the surface energy of β-Sn is anisotropic, and (100), (112) and (101) surfaces are determined to possess the lowest energies. Table 1 Surface energy calculation results of β-Sn Surface
Un-relaxed surface energy (eV/Å2)
Relaxed surface energy (eV/Å2)
Relaxation factor
(100)
0.0241
0.0236
0.0215
(101)
0.0274
0.0256
0.0655
(112)
0.0276
0.0253
0.0844
(301)
0.0302
0.0275
0.0896
(110)
0.0306
0.0296
0.0329
(210)
0.0311
0.0301
0.0329
(001)
0.0325
0.0273
0.1614
(111)
0.0341
0.0300
0.1244
(211)
0.0345
0.0303
0.1213
(201)
0.0370
0.0309
0.1657
Afterwards, Sn whisker morphology was simulated according to the surface energy. It is worthwhile pointing out that the side surface of the whisker accounts for the majority of the total surface due to the fact that Sn atoms only feed Sn whisker growth
from the base. Therefore, the total surface energy of a given whisker is mainly determined by the energy of the side surface. The two kinds of faceted Sn whiskers, quadrangular and hexagonal whiskers, formed in argon atmosphere are matched well with the simulated configurations bounded by planar low-energy surfaces. As displayed in Fig. 8, the quadrangular Sn whisker is matched with the configuration bounded by r surfaces, and the hexagonal Sn whisker is consistent with the configuration bounded by {100} and {101} surfaces. It can be concluded that the low-energy surfaces will dominate the Sn whisker morphology when the Sn atoms diffuse out of the Ti2SnC substrate to minimize the total energy. As a consequence, Sn whiskers tend to appear as well-faceted prism bounded by low-energy surfaces.
Fig. 8 Experimental and corresponding simulated morphology of Sn whiskers: (a) and (b) quadrangular Sn whisker; (c) and (d) hexagonal Sn whisker.
It is worthwhile pointing out that the general Sn whiskers formed in air have striated rather than faceted appearance, which may be attributed to the oxidation of Sn whiskers. When exposed in air, whisker surface is immediately oxidized as they grow out. In consequence, the shape inherited from whisker root is restrained by the native oxide surface layer, and the Sn atoms would diffuse along the growth direction, forming the striations. This is supported by the microstructure of the whisker root presented in Fig. 3 and Fig. 5, that the shape of the studied whisker is consistent with its root. 6. Conclusions Spontaneous growth of Sn whiskers was studied on Ti2SnC at 210 °C in air and argon atmospheres, respectively. Sn whiskers were found to form only on Ti2SnC with free Sn, suggesting that free Sn is necessary for the formation of Sn whiskers on Ti2SnC. But the Sn whisker roots are not directly in contact with the free Sn in the substrate. Furthermore, a Sn transition layer diffused from the Ti2SnC substrate was observed at Ti2SnC/Sn whisker interface, which demonstrates that the Sn atoms feeding Sn whisker growth are diffusing through the Ti2SnC lattice. The feasibility of sub-lattice diffusion of Sn atoms along the basal planes of Ti2SnC is also supported by the lower formation and migration energies of Sn vacancies, which are calculated to be 1.72 eV and 0.60 eV, respectively. When Sn atoms diffuse out of the substrate, the low-energy surfaces dominate the Sn whisker morphology to minimize the total energy, which leads to the formation of faceted Sn whiskers. However, the general Sn whiskers formed in oxygen-containing atmosphere would be surrounded by the surfaces with high energies, due to the confining effect of the oxide film on whisker surface, leading to the formation
of the striated morphology. The findings reveal the atomic motion and the morphology formation mechanisms behind Sn whisker growth on Ti2SnC, which will assist the understanding of the general whiskering problems in other materials. Acknowledgements This work was supported by the Grants of National Natural Science Foundation of China (51731004, 51902051), and the Zhishan Youth Scholar Program of Southeast University. The author also acknowledges the funding from “International Postdoctoral Exchange Program” of Southeast University, and “the Fundamental Research Funds for the Central Universities”.
Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Graphical
Abstract
Mechanisms behind the spontaneous growth of Tin whiskers on the Ti2 SnC ceramics Yushuang Liu , Chengjie Lu , Peigen Zhang , Jin Yu , Yamei Zhang , ZhengMing Sun PII: DOI: Reference:
S1359-6454(19)30866-3 https://doi.org/10.1016/j.actamat.2019.12.027 AM 15723
To appear in:
Acta Materialia
Received date: Revised date: Accepted date:
22 September 2019 15 December 2019 15 December 2019
Please cite this article as: Yushuang Liu , Chengjie Lu , Peigen Zhang , Jin Yu , Yamei Zhang , ZhengMing Sun , Mechanisms behind the spontaneous growth of Tin whiskers on the Ti2 SnC ceramics, Acta Materialia (2019), doi: https://doi.org/10.1016/j.actamat.2019.12.027
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Mechanisms behind the spontaneous growth of Tin whiskers on the Ti2SnC ceramics Yushuang Liu a,#, Chengjie Lu a,, Peigen Zhang a,*, Jin Yu a, Yamei Zhang b, ZhengMing Sun a, a
Jiangsu Key Laboratory of Advanced Metallic Materials, School of Materials Science and Engineering, Southeast University, Nanjing 211189, P. R. China
b
Jiangsu Key Laboratory of Construction Materials, School of Materials Science and Engineering, Southeast University, Nanjing 211189, P. R. China
Abstract The spontaneous growth of Tin whiskers has been a reliability issue in electronic assemblies for around 70 years, but the underlying physics is still ambiguous. Herein, Sn whiskers formed on the Ti2SnC, a layered ternary carbide ceramic MAX phase, were studied to trace the atomic motion in whisker growth process. Free Sn source was found to be necessary for the formation of Sn whiskers, however, the interface microstructure suggests that Sn atoms feeding whiskers are diffusing through the Ti2SnC lattice. According to the simulation results on the formation and migration energies of vacancies in Ti2SnC, a low diffusion barrier is expected for Sn atoms to diffuse along the basal planes. When Sn atoms diffuse out of the substrate, Sn whiskers bounded by low-energy planes form to minimize the total energy. In contrast, the whiskers maintain the striated morphology inherited from the whisker root in the environment containing oxygen, which is mainly attributed to the confinement of the oxide film on whisker surface. The findings will also shed new light on understanding the general whiskering problems found in other materials.
These authors contributed equally to this work. Corresponding authors. E-mail addresses: [email protected] (P. Zhang), [email protected] (Z.M. Sun).
Keywords: MAX phase; Sn whisker; Interface; DFT; HRTEM 1. Introduction Spontaneous Sn whisker growth on Sn and Sn alloys has attracted attention for approximately 70 years [1-3]. Sn whiskers pose a severe reliability risk in electronic assemblies as they can cause electrical failures [4]. To date, whisker-induced failures have involved almost all industry fields, including military, medical, aerospace, nuclear [5]. One of the most reliable and widely used strategies to mitigate Sn whisker growth is alloying Sn with Pb [6]. However, with the toxicity of Pb is being realized, the elimination of Pb from electronic devices is required according to RoHS and other Pb-free regulations. Therefore, Sn whisker growth has reemerged as a major reliability issue in electronic industry, and attracted increasing interest from both scientific and technical fields. To solve the problems associated with Sn whisker growth, a total understanding of the mechanisms behind is necessary. Therefore, many researches on different aspects have been performed in the past several decades, especially in recent years with the impact of lead-free movement. For example, Stein et al. [7] tried to understand the phenomenon by studying the growth directions of Sn whiskers. The whiskers were found to grow preferentially along low-index directions of β-Sn, which was explained by applying the concept of the periodic bond chains (PBCs) in a modified way. It was proposed that the whiskers preferred to grow along the directions of PBC vectors, which refer to chains of strong bonds running uninterruptedly through the crystal structure.
Jagtap et al. [8] tried to identify the locations of Sn whiskers by mapping the crystallographic microtexture of the electroplated Sn films. It was observed that Sn whiskers preferred to grow from low-index grains with (100) or near-(100) orientations that were surrounded by grains with similar orientations, which were then partially surrounded by grains with high-index orientations. The whisker growth was attributed to the high compressive stress around the whisker grain. Sun et al. [9] studied the microstructure between Sn whisker and the neighboring grains on SnAg micro-bumps. Dislocations and stacking faults were observed in both the whisker and the substrate, and twin boundary is determined between them, which was proposed to be the nucleation position of Sn whiskers. The authors suggested that the formation of Sn whiskers was realized by dislocation slip over the twin boundary. Illés et al. [10] investigated the relationship between the crystal structure of Cu-Sn intermetallic and Sn whisker growth on Sn film evaporated on Cu substrate. It was found that Sn whiskers preferred to grow in the regions where the IMC layer is composed of monocrystal grains. In addition, the corrosion of Sn and Sn alloys at elevated temperature and humidity conditions also reported to be responsible for Sn whisker growth [11]. Besides, interior microstructure of Sn whiskers was also studied [12]. The results revealed that Sn whiskers may consist of many side-by-side filaments, suggesting that a Sn whisker can grow from several adjacent grains with similar orientations. This assumption was further confirmed by the fact that the whisker diameters are larger than the underlying
film grains [13]. According to these reports, some new understandings about Sn whisker growth have been obtained. However, the underlying physics of Sn whisker growth remains ambiguous up to now. Essentially, Sn whisker growth is an atomic motion process. Therefore, in order to probe into the physics behind, it is necessary to understand the atomic motion behavior in whisker growth. However, investigation preformed from the point of atomic motion has been seldom reported up to date, which is mainly attributed to the difficulty in characterizing the Sn atom motion in Sn and Sn alloys. It is worthwhile pointing out that Sn whisker growth is not only limited to metals. MAX phases, a family of nanolaminate ternary carbide or nitride ceramics [14, 15], have also been reported to have such whiskering problems [16-19]. In addition, the pressure and temperature can effectively modulate the incubation period of A-element whisker growth on MAX phases by affecting the nucleation process [20]. It has been well-established that Sn whiskers grow by adding atoms to their bases [21, 22], therefore, the whiskers on MAX phases are considered to grow from a heterogeneous phase. Compared with the case of Sn and Sn alloys, it is more feasible to study the atomic motion behavior in whisker growth on MAX phases due to the crystal structure difference between the whisker and the substrate. Considering that Sn whiskers formed on different substrates share the same essence, it sheds new light on uncovering the physics behind the general whiskering phenomenon on Sn and Sn alloys by studying the
atomic motion behavior in Sn whisker growth on MAX phases. In the present work, Sn whiskers have been cultivated on Ti2SnC, which is a typical MAX phase. Interface microstructure between Ti2SnC and Sn whisker is characterized by high resolution transmission electron microscopy (HRTEM), in order to study the atomic motion. In addition, vacancy formation and migration energies are calculated based on Density Functional Theory (DFT) to explain the diffusion mechanism in Sn whisker growth. Afterwards, morphology analysis of Sn whiskers, together with surface energy calculation of β-Sn, are carried out to explain the morphology formation mechanism of Sn whiskers. 2. Experimental methods Predominantly single-phase of Ti2SnC was synthesized by pressureless sintering using stoichiometric powders of Ti (99.0%, 250 mesh), Sn (99.5%, 200 mesh), and graphite (99.85%, 500 mesh). The synthesis details have been described elsewhere [23]. Chemical etching was applied to remove residual free Sn in the as-synthesized Ti2SnC. Each portion of as-synthesized Ti2SnC around 5 g was immersed in diluted hydrochloric acid (1 mol/L, 50 mL) under magnetic stirring for 4 h. After that, Ti 2SnC powder without free Sn was collected by centrifugation, washed several times with deionized water, and finally dried in air at 60 °C. The as-synthesized and HCl etched Ti2SnC powders were ball-milled at 500 r/min for 1 h with the ball-to-powder weight ratio of 10:1 and then cold-pressed under 1000 MPa, respectively, to fabricate Ti2SnC bulk with
and without free Sn. The relative densities of un-etched and etched Ti2SnC samples were measured to be 85.2% and 84.1%, respectively. In addition, for the convenience of interface microstructure characterization, densified Ti2SnC bulk was fabricated by sintering the as-synthesized Ti2SnC at 1300 °C for 20 min under the pressure of 50 MPa using spark plasma sintering. Sn whisker growth on all the samples was performed at 210 °C in air or flowing argon atmosphere in a tube furnace. X-ray diffraction (XRD, Bruker D8 Discover) was performed to determine the phase composition of the samples, with Cu Kα radiation at a scanning step of 0.02° and scanning rate of 10°/min. In addition, the morphology was observed using a scanning electron microscope (SEM, FEI Sirion 200), and the chemical composition of the observed phases was determined by energy dispersive spectrometer (EDS, Oxford X-Max 50). Finally, the interface microstructure between Sn whisker and Ti2SnC substrate was studied using the combination of focused ion beam (FIB, FEI Helios G4) technique
and
transmission
electron
microscopy (TEM,
JEOL JEM-2100F)
characterization. 3. Calculation details First-principles calculations on the framework of the Density Functional Theory (DFT) were performed using the Vienna Ab-initio Simulation Package (VASP). The projector augmented wave method (PAW) and the generalized gradient approximation constructed by Perdew-Burke-Ernzerhof (GGA-PBE) for the exchange-correlation
energy function were used. In order to sample the k-mesh within the Brillouin zone, the
centered Monkhorst-Pack grids [24] were used. The total number of the k-points was determined to be k=40 for β-Sn and k=50 for Ti2SnC according to the convergence test, respectively, along with a plane-wave cutoff energy Ecutoff=480 eV, which made the accuracy within 1 meV/atom. The monovacancy structure of Ti2SnC is represented by a 2×2×1 supercell containing 31 atoms after removing one atom of each species, which is adequate to get a convincing result [25]. The formation energy ∆EV of monovacancy in Ti2SnC can be evaluated according to the equation:
EV =ETi2SnC+V ETi2SnC +V
(1)
where ETi2SnC+V is the total energy of the supercell containing a monovacancy, ETi2SnC is the total energy of the defect-free supercell, and V is the chemical potential in pure solid of each species, which can be approximated by the average atom energy of corresponding solid [26]. In addition, the self-diffusion barrier of Sn atoms in Ti2SnC substrate was studied by searching the transition state linking the two end defective models using the nudged elastic band (NEB) method, which was realized by neighboring vacancy jump along the basal plane. The typical slab model was used to calculate the surface energy of β-Sn, in which the periodic boundary conditions were applied to the surfaces and a vacuum region of 15 Å was applied to prevent unwanted interactions between the slab and its periodic
images along surface normal direction. For a given surface, the corresponding surface energy can be calculated according to the equation:
=
Eslab Ebulk Nslab 2 Aslab
(2)
where Eslab is the total energy of the slab model, Ebulk is the energy per atom of the bulk, Nslab is the total number of atoms in the slab model, the factor 2 accounts for the two surfaces in the slab model, and Aslab is the surface area. 4. Results 4.1. Sn whisker growth on Ti2SnC Phase composition of the Ti2SnC bulks was revealed by the XRD patterns. The upper curve in Fig. 1(a) shows the XRD pattern of the as-synthesized Ti2SnC bulk. It can be concluded that the Ti2SnC phase accounts for the majority of the bulk, together with a small amount of free Sn and TiC. The bottom curve shows the result of the Ti2SnC bulk followed by an HCl etching treatment. The peaks corresponding to Sn phase disappeared, while the peaks corresponding to Ti2SnC and TiC remained unchanged. Fig. 1(b) shows the microstructure of the Ti2SnC bulk with free Sn. Three phases with different contrasts can be observed in the image. The grey phase which accounts for the majority of the bulk is the Ti2SnC phase according to the XRD analysis. The chemical composition of the black phase is determined to be around Ti 40.12 at.%, Sn 2.21 at.%, C 57.66 at.% by EDS, and that of the white phase is about Ti 15.68 at.%, Sn 84.32 at.%, corresponding to TiC and Sn, respectively.
Fig. 1 Characteization of the substrates: (a) XRD patterns of the Ti2SnC bulk with and without free Sn; (b) BSE morphology of the Ti2SnC bulk with free Sn.
Fig. 2 shows the typical morphology of Sn whiskers on Ti2SnC substrate in air. After aging at 210 °C for 1 h, numerous filamentary Sn whiskers grew from the as-synthesized Ti2SnC bulk, as shown in Fig. 2(a). However, no whiskers were observed on the etched Ti2SnC substrate, even after the extension of aging time to 7 days, as shown in Fig. 2(b), suggesting that free Sn is necessary for the formation of Sn whiskers on Ti2SnC. The whisker diameter ranged from a few hundreds of nanometers to a few microns, and the length ranged from a few tens of nanometers to a few millimeters. Meanwhile, the morphology of the filamentary whiskers may be straight, kinked, and curved. Despite of the diverse morphologies, striations parallel to the whisker axis were observed on all of the whiskers, as typically displayed in the inset of Fig. 2(a). The random diameter and length, together with the diverse morphology and the striated surface of the Sn whiskers formed on Ti2SnC, are similar to the ones formed on Sn and Sn alloys [13, 27-29].
Fig. 2 Sn whisker growth behavior on Ti2SnC in air: (a) as-synthesized Ti2SnC after aging at 210 °C for 1 h, and the inset is the magnified view of a Sn whisker; (b) etched Ti2SnC after aging at 210 °C for 1 h, and the inset is the morphology after the extension of aging time to 7 days.
Thermodynamically, a crystal presents the morphology with lowest surface free energy when approaching equilibrium. Provided the surface energy of a crystal is generally anisotropic, the Sn whiskers are expected to display the morphology bounded by lower-energy planes. However, it is evident that the striated Sn whisker formed in air, as typically displayed in Fig. 3(a), is far away from the equilibrium morphology, which suggests that other factors affecting crystal morphology were involved during whisker growth. Therefore, Sn whisker growth was further carried out in argon atmosphere to simplify the growth environment. It is interesting that when the Ti2SnC was aged in argon, well-faceted Sn whiskers bounded by planar surfaces rather than the striated ones are formed, as shown in Fig. 3(b)-(d). According to the morphology diversity, most of the faceted Sn whiskers fall into two types: hexagonal (Fig. 3(b)) and quadrangular (Fig. 3(c) and (d)). Morphology formation mechanisms of the whiskers will be discussed in the following section in detail.
Fig. 3 Sn whiskers with different morphologies: (a) a striated Sn whisker formed in air; (b) a hexagonal Sn whisker formed in argon, and the inset is the magnified view of the whisker root; (c) and (d) quadrangular Sn whiskers formed in argon.
4.2. Microstructure at the base of Sn whiskers To study the microstructure at the base of the whiskers, FIB cross-sectioning at the root area of the whiskers was conducted. Fig. 4(a) displays a short Sn whisker grown on Ti2SnC. According to the corresponding cross-sectional morphology shown in Fig. 4(b), the whisker root with irregular shape is embedded in the substrate, and clear phase boundary between the whisker and the substrate was determined. Considering that Sn whiskers grow by adding atoms to their bases, it is reasonable to assume that the whiskers were developed from Sn grains located inside the Ti2SnC substrate. In addition, the whisker root is not connected with the free Sn distributed in the substrate. For a
more detailed understanding of the underlying microstructure, three dimensional morphology of a whisker root was reconstructed utilizing a series of cross-sectional images, one of which is shown in Fig. 4(c). According to the reconstruction result in Fig. 4(d), the whisker root is not in contact with free Sn in the substrate in three dimensions, which suggests that the Sn atoms feeding Sn whisker growth probably diffuse through the Ti2SnC lattice.
Fig. 4 Microstructure at the base of a Sn whisker: (a) a Sn whisker grown on Ti2SnC; (b) the cross-sectional morphology of the whisker in (a); (c) one cross-section of the Sn whisker to be reconstructed; (d) reconstruction result of the whisker root in (c).
For a precise characterization of the interface microstructure between Sn whisker and the Ti2SnC substrate, a TEM sample was fabricated around the interface using FIB technique. Fig. 5(a) shows the cross-sectional morphology of the chosen whisker. To
facilitate the fabrication process, the top part of the whisker was milled using FIB. BSE morphology of the fabricated sample is displayed in Fig. 5(b). Besides the sputtered Pt protective layer, three phases with different contrasts can be observed. The grey phase accounts for the major part of the sample, while there are also a small amount of light grey and dark grey phases. The light grey phase in the substrate shares similar contrast with the whisker. Afterwards, the element distribution of the TEM sample is given by STEM. Fig. 5(c) shows the STEM morphology of the sample and the corresponding distribution of the Ti, Sn, and C elements. It can be concluded from the figure that the grey phase composed of Ti, Sn, and C elements is Ti2SnC. Furthermore, the light grey phase is mainly composed of Sn element, while the dark grey phase is made up by Ti and C elements, which are deduced to be Sn and TiC, respectively.
Fig. 5 Characterization of the TEM sample: (a) initial morphology of the interface area; (b) BSE morphology of the TEM sample; (c) STEM morphology of the TEM sample, and the corresponding element distribution of Ti, Sn, and C elements, respectively.
5. Discussion 5.1. Interface microstructure of Ti2SnC/Sn The experimental results indicate that Sn whiskers grow on Ti2SnC. In addition, secondary phase of Sn was also detected in the Ti2SnC bulk. To trace the atomic motion in Sn whisker growth process, the interface microstructure of the two types of Ti2SnC/Sn interfaces was further investigated. Fig. 6(a) shows the TEM image of the interface area between Ti2SnC and free Sn in the substrate, which corresponds to the area marked in Fig. 5(c). The selected area electron diffraction (SAED) patterns of the two phases confirm that they are Ti2SnC and β-Sn, respectively. Fig. 6(b) shows the high resolution TEM (HRTEM) image of the interface. The lattice fringes with an interplanar spacing of 2.687 Å and 2.934 Å are determined to be the (101̅1) plane of Ti2SnC and the (200) plane of β-Sn, respectively. The HRTEM contrast also suggests a direct contact between Ti2SnC and the free Sn with no transition layer present.
Fig. 6 Interface microstructure between Ti2SnC and free Sn in the substrate: (a) TEM image of the interface, and the insets show the corresponding selected area electron diffraction (SAED) patterns; (b) high resolution TEM (HRTEM) image of the interface.
Fig. 7(a) shows the TEM image of the Ti2SnC/Sn whisker interface. According to the SAED patterns displayed, the two phases with distinct morphology are confirmed to be Ti2SnC and β-Sn, respectively. Fig. 7(a) together with the magnified image shown in Fig. 7(b) indicates that both the Sn whisker and the neighboring Ti2SnC are free of defects. Therefore, it is reasonable to assume that the presence of dislocations is not necessary for Sn whisker growth although dislocations and stacking faults within Sn whiskers has been previously observed [9, 30]. For a more detailed analysis of the interface microstructure, HRTEM images were recorded from the Ti2SnC/Sn whisker interface, as displayed in. Fig. 7(c) and (d). Measurements of the lattice fringes from the whisker and the substrate parts are consistent with those for (200) plane of β-Sn and (101̅ 2) plane of Ti2SnC, respectively. Different from the Ti2SnC/Sn interface in the substrate (Fig. 6), a nanometer-thick transition layer was observed at the Ti2SnC/Sn whisker interface. The transition layer has similar but less ordered atomic arrangement to (200) plane of the Sn whisker, and suggested to be diffused from the Ti2SnC substrate according to the interface morphology, as typically displayed in the insets in Fig. 7(c) and (d). All the coherent, semicoherent and incoherent interfaces can be observed between the transition layer and the whisker. Representative morphology of the three types of interfaces was marked in the HRTEM images. The coherent interface in area 1 exhibits a deflection of approximately 5 degrees, while the incoherent ones in area 3 and area 4 possesses totally interlaced atomic plane arrangement with same orientation. And
the semicoherent interface in area 2 is in between. Afterwards, the average interplanar spacing of the transition layer in area 1 to area 4 was measured to be 3.014 Å, 2.945 Å, 3.085 Å and 2.987 Å, respectively, as displayed in the corresponding area. Given that the interatomic distance of Sn in Ti2SnC crystal is 3.096 Å, and the measured interplanar spacing of the (200) plane of β-Sn is 2.926 Å, it can be concluded that the interplanar spacing of the transition layer is between the interplanar spacing of the (200) plane of β-Sn and the interatomic distance of Sn layer in Ti2SnC, which further suggests that the transition layer is diffused from the Ti2SnC. It was previously assumed that the atoms for metal whisker growth on MAX phases come from the corresponding elemental A [17], and the results in the present work also suggest the necessity of free Sn for the formation of Sn whiskers on Ti2SnC. However, the microstructure of the Ti2SnC/Sn whisker interface reveals that the atoms for Sn whisker growth have high possibility of diffusion through Ti2SnC lattice. To understand the diffusion behavior of Sn in Ti2SnC, the formation and migration energies of monovacancy in Ti2SnC are calculated. The vacancy formation energies are calculated as 3.75 eV, 1.72 eV and 2.89 eV for Ti, Sn and C monovacancy, respectively, indicating Sn vacancy is the most energetically favorable monovacancy in defective Ti2SnC. Assuming that the diffusion of Sn in Ti2SnC is sublattice-diffusion by neighboring vacancy jump along the basal plane, the migration energy is calculated to be 0.60 eV. Therefore, a low diffusion barrier is expected for Sn atoms to diffuse along
the Sn layer in Ti2SnC. As a result, Sn atoms in Ti2SnC can easily migrate outside and thus feed Sn whisker growth. The driving force for the mass transport of Sn atoms from Ti2SnC lattice to the whisker root is considered to be the concentration gradient. The Sn concentration in free Sn is much higher than that in Ti2SnC lattice, in consequence, Sn atoms from free Sn continuously diffuse into Ti2SnC. Therefore, the fundamental factor initiating the whiskering phenomenon on Ti2SnC is attributed to the interaction between Ti2SnC and Sn.
Fig. 7 Interface microstructure between Ti2SnC and Sn whisker: (a) TEM image of the interface, and the insets show the corresponding SAED patterns; (b) magnified view of the white rectangle area in (a); (c) and (d) HRTEM images of the interface.
5.2. Morphology formation mechanism of Sn whiskers In order to elucidate the morphology formation mechanism of Sn whiskers, surface energy calculation was performed for β-Sn. The low-indexed surfaces of (100), (112), (101), (001), (301), (110), (210), (211), (111) and (201) are selected. Both relaxed and un-relaxed surface energies for the surfaces are calculated, and the change in atomic
position of surface atoms was quantified by the relaxation factor. The results are listed in Table 1, in which the surfaces are arranged in an increasing order based on their un-relaxed surface energy. After relaxation, the order from smallest to largest surface energy changes slightly, but the surface energy of the relaxed surface is not significantly different from that calculated for the unrelaxed surface. The (100) surface was calculated to have the smallest relaxed surface energy, followed by (112), (101), (001), (301), (110), (111), (210), (211) and then (201). According to the calculation results, the surface energy of β-Sn is anisotropic, and (100), (112) and (101) surfaces are determined to possess the lowest energies. Table 1 Surface energy calculation results of β-Sn Surface
Un-relaxed surface energy (eV/Å2)
Relaxed surface energy (eV/Å2)
Relaxation factor
(100)
0.0241
0.0236
0.0215
(101)
0.0274
0.0256
0.0655
(112)
0.0276
0.0253
0.0844
(301)
0.0302
0.0275
0.0896
(110)
0.0306
0.0296
0.0329
(210)
0.0311
0.0301
0.0329
(001)
0.0325
0.0273
0.1614
(111)
0.0341
0.0300
0.1244
(211)
0.0345
0.0303
0.1213
(201)
0.0370
0.0309
0.1657
Afterwards, Sn whisker morphology was simulated according to the surface energy. It is worthwhile pointing out that the side surface of the whisker accounts for the majority of the total surface due to the fact that Sn atoms only feed Sn whisker growth
from the base. Therefore, the total surface energy of a given whisker is mainly determined by the energy of the side surface. The two kinds of faceted Sn whiskers, quadrangular and hexagonal whiskers, formed in argon atmosphere are matched well with the simulated configurations bounded by planar low-energy surfaces. As displayed in Fig. 8, the quadrangular Sn whisker is matched with the configuration bounded by r surfaces, and the hexagonal Sn whisker is consistent with the configuration bounded by {100} and {101} surfaces. It can be concluded that the low-energy surfaces will dominate the Sn whisker morphology when the Sn atoms diffuse out of the Ti2SnC substrate to minimize the total energy. As a consequence, Sn whiskers tend to appear as well-faceted prism bounded by low-energy surfaces.
Fig. 8 Experimental and corresponding simulated morphology of Sn whiskers: (a) and (b) quadrangular Sn whisker; (c) and (d) hexagonal Sn whisker.
It is worthwhile pointing out that the general Sn whiskers formed in air have striated rather than faceted appearance, which may be attributed to the oxidation of Sn whiskers. When exposed in air, whisker surface is immediately oxidized as they grow out. In consequence, the shape inherited from whisker root is restrained by the native oxide surface layer, and the Sn atoms would diffuse along the growth direction, forming the striations. This is supported by the microstructure of the whisker root presented in Fig. 3 and Fig. 5, that the shape of the studied whisker is consistent with its root. 6. Conclusions Spontaneous growth of Sn whiskers was studied on Ti2SnC at 210 °C in air and argon atmospheres, respectively. Sn whiskers were found to form only on Ti2SnC with free Sn, suggesting that free Sn is necessary for the formation of Sn whiskers on Ti2SnC. But the Sn whisker roots are not directly in contact with the free Sn in the substrate. Furthermore, a Sn transition layer diffused from the Ti2SnC substrate was observed at Ti2SnC/Sn whisker interface, which demonstrates that the Sn atoms feeding Sn whisker growth are diffusing through the Ti2SnC lattice. The feasibility of sub-lattice diffusion of Sn atoms along the basal planes of Ti2SnC is also supported by the lower formation and migration energies of Sn vacancies, which are calculated to be 1.72 eV and 0.60 eV, respectively. When Sn atoms diffuse out of the substrate, the low-energy surfaces dominate the Sn whisker morphology to minimize the total energy, which leads to the formation of faceted Sn whiskers. However, the general Sn whiskers formed in oxygen-containing atmosphere would be surrounded by the surfaces with high energies, due to the confining effect of the oxide film on whisker surface, leading to the formation
of the striated morphology. The findings reveal the atomic motion and the morphology formation mechanisms behind Sn whisker growth on Ti2SnC, which will assist the understanding of the general whiskering problems in other materials. Acknowledgements This work was supported by the Grants of National Natural Science Foundation of China (51731004, 51902051), and the Zhishan Youth Scholar Program of Southeast University. The author also acknowledges the funding from “International Postdoctoral Exchange Program” of Southeast University, and “the Fundamental Research Funds for the Central Universities”.
Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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