Nucleation and growth of Ag 3 Sn in Sn-Ag and Sn-Ag-Cu solder alloys

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Introduction
Silver is a key component in many electronic solder alloys.In the era of leaded solders, Sn-3.5Ag was used in applications where Sn-37 Pb was unsuitable including when soldering to thick-film silver conductors.During the transition to Pb-free solders, the use of Sn-3.5Ag has continued and new Ag-containing solders have become widespread, often based on Sn-Ag-Cu (SAC) compositions due to the ubiquity of copper substrates.These include the first generation Pb-free solders SAC387 and SAC305 [1,2], the second generation alloys SAC0307 and SAC105 [3][4][5], and emerging third generation alloys which typically add Bi and/or Sb to near-eutectic Sn-Ag-Cu compositions [6][7][8][9].In all these solders, the intermetallic compound (IMC) Ag 3 Sn forms during solidification in a eutectic reaction and, sometimes, also as a primary solidification phase.Since all these solders are eutectic or hypoeutectic compositions, the formation of primary Ag 3 Sn occurs when the liquid supercools with respect to the β-Sn liquidus due to nucleation difficulties of the β-Sn phase [10][11][12].
Extensive work has explored the formation of eutectic Ag 3 Sn and three types of morphologies have been identified: plate-like, needle-like and spheroidal Ag 3 Sn.One body of work has applied unidirectional solidification under controlled conditions to show that there is a plate to rod eutectic growth transition with increasing growth velocity [13][14][15][16][17]. Another body of work has shown that cooling rate in castings and solder joints [18][19][20][21][22] plays a significant role in the size and morphology of Ag 3 Sn: a fine distribution of spheroidal Ag 3 Sn particles was observed at higher cooling rate (17~24 • C/s) while coarse needle-like and plate-like Ag 3 Sn were formed at low cooling rate (~0.1 • C/s).Increasing the volume fraction of eutectic Ag 3 Sn provides enhanced strength [23] and improves resistance to creep and thermal fatigue [24][25][26][27][28], and a finer eutectic Ag 3 Sn lengthscale improves creep resistance further [29,30].
The role of primary Ag 3 Sn plates on solder joint reliability is less clear than for eutectic Ag 3 Sn.Some investigators found large primary Ag 3 Sn to be detrimental to mechanical performance [11,[31][32][33].Other studies have indicated that the role of large Ag 3 Sn plates depends on their location in the joint: they are detrimental when aligned in the direction of crack propagation, whereas large plates can enhance thermal fatigue life when aligned such that they block or arrest an advancing crack [34].An additional factor is that the solubility of Ag is negligible in the β-Sn and Cu 6 Sn 5 phases [35].Thus, almost all Ag atoms go into Ag 3 Sn and the formation of primary Ag 3 Sn ties up Ag atoms that would otherwise form small eutectic Ag 3 Sn [36], reducing the volume fraction of effective strengthening particles.
Prior work has focussed on finding ways to prevent the formation of primary Ag 3 Sn plates [37][38][39].Reducing the Ag content in the alloy is a simple method to prevent their formation; with a silver content less than 3 wt.% in SAC alloys large Ag 3 Sn formation can be substantially reduced even under extremely slow cooling conditions (0.02 • C/s) [37].
However, Ag contents of 3 wt.%or higher may be desirable for performance in thermal cycling [5].Primary Ag 3 Sn can also be reduced or completely supressed at sufficiently high cooling rate in freestanding solder balls with near-eutectic ternary Sn-Ag-Cu composition [37,38], although there is often limited scope for altering the cooling rate in a soldering process.Since primary Ag 3 Sn forms as the liquid supercools with respect to the β-Sn liquidus, primary Ag 3 Sn plates can also be suppressed by additions that promote the nucleation of the β-Sn phase [39].For example, Kang et al. [38] demonstrated that dilute Zn additions to Sn-3.8Ag-0.7Cureduce the undercooling for β-Sn and prevent Ag 3 Sn formation in alloys with near-eutectic Ag content and low cooling rate (0.02 • C/s).
For Sn-Ag-Cu solders, primary Ag 3 Sn typically grows with a faceted plate morphology [12,[40][41][42][43]. Kim et al. [40] observed Ag 3 Sn plates at the top of the interfacial reaction layer with different growth stages varying from faceted dendrites to hopper crystals and simple plate morphologies in Sn-3.9Ag-0.6Cusolder joints.Gong et al. [42] reported that Ag 3 Sn plates in Sn-3.8Ag-0.7Cu/Cujoints nucleate preferably near the solder/substrate interface.Through in-situ synchrotron X-ray imaging of Sn-3.5Ag/Cu joints, Ma et al. [44] proposed three growth patterns for Ag 3 Sn plates: linear, Y and X shape.It was interpreted later by Mueller et al. [45] that the multiplate formations do not necessarily develop into all six directions.Mueller et al. [45] also observed star-shaped Ag 3 Sn morphology in Sn-5Ag solders which they attributed to its pseudo-hexagonal structure with the main plate facet and two perpendicular in-plane growth directions indexed using a hexagonal unit cell.However, the detailed mechanisms affecting the formation of these Ag 3 Sn morphologies remain ambiguous, and the difference in Ag 3 Sn nucleation and growth between freestanding balls and solder joints is also unclear.
This work was conducted to build a deeper understanding of the nucleation and growth of primary Ag 3 Sn crystals in solder balls and in joints on Cu substrates.We first study binary Sn-Ag solder balls and focus on (i) the nucleation undercooling for Ag 3 Sn, (ii) the Ag 3 Sn nucleation location, and (iii) the influence of melt undercooling on the growth of Ag 3 Sn crystals.We then explore how factors (i)-(iii) are affected by the presence of Cu solute, pre-existing Cu 6 Sn 5 primary crystals, a Cu 6 Sn 5 reaction layer, and the nucleation of β-Sn.

Sample preparation
Sn-5Ag, Sn-3.5Ag,Sn-3Ag-0.5Cu,Sn-3Ag-1Cu and Sn-4Ag-0.5Cu(wt.%) alloys were made by melting 99.999% Sn with 99.9% Ag and Sn-10 wt.% Cu master alloy.The mixture was heated to 300 • C in a claybonded graphite crucible in a resistance furnace.After holding for 2 h, the melt was stirred with an Al 2 O 3 rod and then poured into a steel mould.Alloys were rolled to ~30 µm foils, punched into Ø 1.6 mm discs and reflowed in a ROL-1 tacky flux on a hotplate at 280 • C to form ~500 μm diameter spheres due to surface tension.The balls were then used in one of three forms: (i) as freestanding balls, (ii) as single balls soldered to a copper substrate on one side, or (iii) as a 2 × 2 ball array joining copper to copper.

Differential scanning calorimetry (DSC)
To apply controlled cooling conditions and measure the nucleation temperature of the Ag 3 Sn and β-Sn phases, the 500 µm balls and joints were melted and solidified in a Mettler Toledo DSC in aluminium pans under a nitrogen atmosphere.The standard reflow profile used was to heat to a peak temperature of 280 • C for Sn-5Ag and 230 • C for all other solder compositions, hold for 10 min, and then cool at a rate of 5 K/min.>20 samples were studied for each composition.In Sn-5Ag, >80 samples were studied to obtain data on the distribution of undercoolings and to explore the undercooling-microstructure relationship for primary Ag 3 Sn over a wide range.
The liquidus temperature of Ag 3 Sn in Sn-5Ag was measured by cyclic DSC using a method similar to that in previous studies [35,[46][47][48].The system was heated at 1.2 K/min to a temperature where a mixture of liquid and Ag 3 Sn is known to exist (242 • C), and was then isothermally held for 30 min.The system was then heated at 1.2 K/min to 280 • C and cooled at 5 K/min to 150 • C, ending the first cycle.The isothermal holding temperature for the subsequent cycle was set to be 2 • C higher than the previous one.The presence of an endothermic peak on heating was taken to indicate that some Ag 3 Sn remained at the prior isothermal holding temperature.The absence of an endothermic peak on heating indicated all Ag 3 Sn had melted at the prior isothermal holding temperature.The liquidus temperature was defined as the average of the holding temperatures either side of the transition from an endothermic peak to no endothermic peak.This gave an Ag 3 Sn liquidus in Sn-5Ag of 247±1 • C.This method is overviewed in more detail in the Supplementary Information.
To explore a much higher cooling rate, some Sn-3.5Ag/Cujoints were heated to 230 • C on a hot plate, held for 10 min and then quenched in water.

Optical and electron microscopy
Samples were mounted in Struers VersoCit acrylic cold mounting resin and then ground to 4000 grit with SiC paper followed by polishing with colloidal silica on a nap cloth for 6 min.
Polarised optical microscopy was used to reveal different orientations of Ag 3 Sn plates, taking advantage of the optical anisotropy of orthorhombic Ag 3 Sn.For scanning electron microscopy (SEM), a Zeiss Sigma field emission gun SEM fitted with Bruker e-FlashHR electron backscatter diffraction (EBSD) detector and XFlash 6130 energydispersive spectrometry (EDS) detector were used.Bruker Esprit 2.2 software, combined with the Orientation Imaging Microscopy (OIM™) Data Analysis software and MTEX 4.4 Toolbox within MATLAB™9.2(Mathworks, USA), were applied to analyse the growth habits of Ag 3 Sn single crystals, the orientation relationships in twinned crystals, and the orientation relationships between Ag 3 Sn and the Cu 6 Sn 5 reaction layer.
The crystal structures for Ag 3 Sn and Cu 6 Sn 5 assumed in this study are listed in Table 1.While the Cu 6 Sn 5 phase present at room temperature is likely to be superstructure ordered monoclinic η' and/or η'' [49][50][51], we use the high temperature parent hexagonal phase η-Cu 6 Sn 5 for indexing because this phase was present during solidification.Throughout this paper, all unit cell wireframes in Figures were plotted based on the Euler angles measured by EBSD.
To study the 3D morphology of Ag 3 Sn and the local geometrical features of the Cu 6 Sn 5 reaction layer, β-Sn was selectively etched in a solution with 5% NaOH and 3.5% orthonitrophenol at 80 • C for approximately 6 h.Extracted crystals were collected and placed on a stub for further study by analytical SEM.
To identify the main facets, electron transparent samples were milled from extracted Ag 3 Sn single crystal plates using a focused ion beam (FIB) of a TFS Helios 5 CX DualBeam FIB-SEM.The lamellae were used to determine the facet orientations using selected area electron diffraction (SAED) in a TFS Talos F200i transmission electron microscope (TEM).

Real time X-ray imaging
Sn-4Ag-0.5Cusolders were rolled down to ~100 µm foils before being punched into discs with a diameter of ~500 µm.The disc foils were then placed on a ~100 µm thick Cu-OSP printed circuit board (PCB) with flux and mounted between SiO 2 glass sheets that held the sample perpendicular to the X-ray beam.A first soldering process was carried out on a hot plate before synchrotron experiments to ensure proper joining.The synchrotron experiments were conducted at BL20XU in the Spring-8 synchrotron under 1 atm pressure of nitrogen gas using the same apparatus as in Ref. [54][55][56].An X-ray beam energy of 29 KeV was used.The imaging unit incorporated a phosphor screen and a CMOS camera, resulting in a field of view of 1038 µm x 1038 µm (2048 × 2048 pixels) with a resolution of 0.507 µm.The imaging exposure time was ~400 ms per frame recorded at 2 frames per second.A thermocouple was placed near the sample in the furnace to record the cooling curves and the temperatures were calibrated by the eutectic onset melting temperature.The peak temperature was 246 • C and the cooling rate was ~0.3 K/s prior to the nucleation of β-Sn.
After solidification, the synchrotron sample was soaked in acetone to remove the SiO 2 plates and the sample was then mounted in Struers VersoCit acrylic cold mounting resin, polished to an OPS finish, and studied by EBSD.The surface microstructure could then be correlated with the projected X-ray images from the in-situ image sequence.

Crystallography of Ag 3 Sn plates
Ag 3 Sn commonly grew as faceted single crystal plates.As an example, Fig. 1(a) is an extracted Ag 3 Sn plate from a Sn-5Ag solder ball cooled at 0.05 K/min where the nucleation undercooling for Ag 3 Sn was measured to be 13.1 • C. To identify the main facet of the plate, combined FIB-TEM analysis was performed.A foil was prepared by FIB milling of the extracted plate surface in the geometry and orientation shown in Fig. 1(a) and (b), followed by Pt-deposition of the foil sample into a TEM grid (Fig. 1(c)).The TEM-SAED pattern from the thin foil sample in Fig. 1(d) was indexed with 〈010〉 being the zone axis.Thus, the plate is orientated as indicated by the annotated coordinate system on Fig. 1(a), and (001) is the main facet.Note that Ag 3 Sn is orthorhombic where 〈100〉 ∕ = 〈010〉 ∕ = 〈001〉.Similar FIB-TEM analysis on multiple other Ag 3 Sn plates measured the same result with (001) as the main facet of the plate.
Ag 3 Sn has the D0 a structure type [52] which is a chemically-ordered derivative of the HCP structure with a small orthorhombic distortion [57] as shown in Fig. 1(f).The image in Fig. 1(e), which comes from the region of the SAED pattern, contains clear {100} planes which correspond to the close-packed {0001} plane in the pseudo-hexagonal structure.
SEM-based EBSD on Ag 3 Sn was prone to orientation misindexing due to the hexagonal pseudo-symmetry in Fig. 1(f).For example, using Hough transform-based auto-indexing, extracted Ag 3 Sn plates such as that in Fig. 1(a) auto-indexed as three orientations implying a facet of (001), (021) or (021).However, FIB-TEM showed that the main facet was always (001) which easily allowed the correct orientation to be selected from the three candidate orientations in EBSD.

Cyclic twinned Ag 3 Sn crystals
Another common growth morphology was cyclic twinned Ag 3 Sn plates.Fig. 2 shows a typical example in a Sn-5Ag solder ball cooled at 1.2 K/min with nucleation undercooling of 24.5 • C. Three interpenetrating plates span the entire solder ball.Fig. 2(a) is a polarised optical micrograph revealing three different colours of Ag 3 Sn where each plate has one colour (salmon, blue or brown), indicating that each plate corresponds to a different crystallographic orientation.Three Ag 3 Sn orientations were measured by EBSD mapping but, as shown in the IPF-X map in Fig. 2(b), there is strong orientation misindexing between the three orientations in the map.However, according to the FIB-TEM analysis in Section 3.1.1,the main facet of each Ag 3 Sn plate is {001} and therefore, the corresponding orientation of each plate could be assigned as plotted next to each plate in Fig. 2(b).This reveals that there is a cyclic twinning relationship between the three Ag 3 Sn plates involving multiple 60 • rotations about the common 〈100〉 direction, and the three twinned orthorhombic orientations form a combined pseudohexagonal symmetry, as shown in Fig. 2

(c) and (d).
Further insights can be gained by reanalysing the EBSD map using the pseudo-hexagonal unit cell as shown in Fig. 2(e).From this, we see that all three plates share the same pseudo-hexagonal orientation, and the facets of all plates correspond to the {1100} planes of the pseudohexagonal unit cell.A similar phenomenon was reported by Mueller et al. [45], from which they concluded that all the plates originated from a common centre.
The cyclic twin can be visualised by superimposing the atoms of the three orthorhombic Ag 3 Sn orientations onto a hexagonal close-packed structure, as in Fig. 2(f) forming a ring consistent with the measured orientations in Fig. 2(c).The near-perfect matching between the Ag 3 Sn and HCP atomic sites in Fig. 2(f) is due to Ag 3 Sn having a small orthorhombic distortion of only ~0.13 • from an HCP structure.The simple arrangement in Fig. 2(f) is intended to show the symmetry of the cyclic twin and does not indicate anything about the atomic structure of the common growth centre.Potential cyclic twin formation mechanisms are discussed in Section 3.1.5after presenting the dependence of cyclic twinning on the imposed cooling rate and the Ag 3 Sn nucleation undercooling in the next sections.single crystal plate at the smallest undercoolings (<20 • C).With deepening undercooling to ~25 • C, three plates formed each with a different single colour in polarised light imaging and all with the same pseudo− HCP orientation in EBSD mapping, with the three orthorhombic orientations related by multiple 60 • rotations around 〈100〉 similar to Fig. 2. Thus, the three plates grew from a common origin.Note that the examples in Fig. 3(b) and Fig. 2 are at a similar Ag 3 Sn undercooling and have a similar cyclic twinned Ag 3 Sn plate microstructure but the nucleation point is further from the cross-section in Fig. 3(b) than in Fig. 2, which will be the general case for a random cross-section.

Effect of Ag 3 Sn undercooling on growth morphology
When the undercooling exceeded ~40 • C, there were still three colours observed in polarised light imaging but the Ag 3 Sn plates also branched during growth and formed parallel plates.Such branching became more frequent at deeper undercooling.For example, there is one parallel plate in Fig. 3(c) and (d), and multiple parallel plates in Fig. 3 (e)-(g).
When examining Fig. 3, note that parallel plates always have the same single colour in polarised light imaging (and nonparallel plates always have a different colour), all plates are consistent with {001} facets, and all plates within one ball share the same pseudo-HCP orientation indicating a single Ag 3 Sn nucleation event per sample.Combining all parts of Fig. 3 we can see how the undercooling, which determines the growth velocity, affects crystal growth: (i) at the smallest undercoolings Ag 3 Sn grew as single crystal plates; (ii) as the undercooling deepened Ag 3 Sn grew as cyclic twinned plates where the twinning occurred only at the start of growth; (iii) at deeper undercooling, the cyclic twinned plates additionally branched during growth by twinmediated branching resulting in multiple parallel plates; and (iv) the extent of twin-mediated branching increased as the undercooling became deeper resulting in more complicated and irregular shapes.
At deeper undercoolings, the nucleation of β-Sn started to affect the growth of Ag 3 Sn, as shown in Fig. 3(e)-(g).For Fig. 3(e) and (g), there is a small temperature (and time) interval between the nucleation of Ag 3 Sn and β-Sn, allowing the Ag 3 Sn to retain its growth shape from rapid growth by being 'quenched' by rapid β-Sn growth.For example, from the cooling curve in Fig. 3 The Ag 3 Sn plate thickness was measured for the plates in Fig. 3(a)-(g) correcting the 2D measurements by accounting for the tilt angle between the (001) plate normal and the sectioning plane using the Euler angles obtained from EBSD.The Ag 3 Sn plate thickness is plotted versus undercooling in Fig. 4(a).The plate thickness decreases as the undercooling becomes deeper and there is also an effect of the temperature interval between the nucleation of Ag 3 Sn and β-Sn (as indicated in Fig. 3) which determines the growth time for Ag 3 Sn.In general, the plate thickness decreases with decreasing temperature interval and, comparing the primary Ag 3 Sn crystals with similar undercooling but significantly different growth time in Fig. 3(e) and (f), it is clear that Ag 3 Sn plates have the tendency to coarsen during growth.
The competition between β-Sn nucleation and primary Ag 3 Sn nucleation is overviewed in Fig. 4(b)-(c) as histograms of the measured nucleation onset temperature of Ag 3 Sn and β-Sn in Sn-5Ag and Sn-3.5Ag solder balls.The Sn-Ag binary phase diagram at the Sn-rich side from Thermo-Calc TCSLD4.1 is given in Fig. 4(d).For Sn-5Ag the measured nucleation temperatures for Ag 3 Sn and β-Sn both follow Gaussian distributions due to the stochastic nature of the nucleation event, and the two distributions have only a small fraction of their tails overlapping indicating that, in most Sn-5Ag solder balls, the chance of primary Ag 3 Sn nucleation being interrupted by β-Sn nucleation is fairly small.However, for Sn-3.5Ag as the Ag 3 Sn liquidus temperature decreases to 215 • C, the distribution for Ag 3 Sn shifts to lower temperature and starts to have a large fraction overlapping with β-Sn such that once a Sn-3.5Agball  In this study, the nucleation of primary Ag 3 Sn in freestanding solder balls was measured to be stochastic and relatively deep (Fig. 4), which indicates nucleation difficulties for primary Ag 3 Sn similar to those for β-Sn.This finding is significantly different to statements in the literature that the nucleation and ensuing growth of Ag 3 Sn occurs with minimal undercooling [11,12,34,37,38,41,[58][59][60].One reason for this discrepancy is the different sample mass used in past work.For example, in the DTA study of Moon et al. [35] their samples were much larger (2 g) than solder balls and their primary Ag 3 Sn exhibited undercooling ≤5 • C.

Effects of cooling rate on growth morphology
Fig. 5 is a summary of the relationship between cooling rate, nucleation undercooling and twinning frequency in Sn-5Ag.The mean nucleation temperature for Ag 3 Sn from 10 Sn-5Ag balls for each cooling rate is plotted in grey in Fig. 5(a).For each cooling rate, 10 samples with a range of undercooling were examined and the results are indicated by the red (single crystal) and blue (cyclic twinned) circles with respect to their Ag 3 Sn nucleation onset temperature.At the lowest cooling rate (0.05 K/min), all Ag 3 Sn were single crystals.With increasing cooling rate (0.2, 1.2 and 5 K/min), more Ag 3 Sn grew as twinned crystals which tended to form at lower temperature compared to the single crystals, i.e. the twinned crystals formed at deeper undercooling.At the highest cooling rate (20 K/min), all Ag 3 Sn formed as twinned crystals.In order to visualise the nucleation temperature data, Fig. 5(b) is a box plot for all the nucleation onset temperatures collected from the five cooling rates.We can see that, although for each cooling rate there is a wide range between the minimum and maximum value, the median and the mean value from each group give a clear trend that, with increasing cooling rate, the onset temperature for Ag 3 Sn nucleation decreases.The mean undercooling at different cooling rates was calculated from Fig. 5(b) with the liquidus temperature for Ag 3 Sn in Sn-5Ag measured as 247 • C with the cyclic DSC experiment.Fig. 5(c) quantifies the relationship between the twinning frequency and undercooling: the deeper the undercooling, the more likely that Ag 3 Sn grows as a twinned crystal.

Origins of cyclic twinning in Ag 3 Sn
From the previous sections, we see that cyclic twinning depends mostly on the undercooling at which Ag 3 Sn nucleates, with deeper undercoolings promoting cyclic twin formation.We next consider possible mechanisms leading to cyclic twinned Ag 3 Sn.
Cyclic twins in Ag 3 Sn are three interpenetrating plates that emanate from a common centre (Fig. 2).Thus, cyclic twinning is expected to originate during the nucleation process and/or the very early stages of growth in the undercooled melt.Indeed, towards the end of this paper, we present real-time synchrotron imaging of Ag 3 Sn cyclic twin growth in a solder joint on a copper substrate that directly proves that the cyclic twin grows from a common point from the earliest time that the crystal could be resolved.
From Fig. 1(f), we note that the atomic positions in the Ag 3 Sn crystal structure are almost identical to the HCP structure and that the lower symmetry orthorhombic structure arises mostly from chemical order in the crystal structure.Thus, one possibility is that cyclic twinning in Ag 3 Sn emerges from chemical disorder at the start of solidification.There are various ways that this might happen.One is that the nucleus structure may be chemically disordered or have imperfect chemical ordering, raising the symmetry to hexagonal.Another way is that disorder trapping may occur in the early stages of growth if the initial solidliquid interface velocity is sufficiently high that equilibrium chemicalordering is not achieved when atoms join the advancing interface at high undercooling [65,66].This too could result in initial growth with metastable hexagonal symmetry.It may not be necessary to have full disorder trapping, a high density of growth defects may be enough to give the first nanoscale solid hexagonal rather than orthorhombic symmetry.The subsequent growth of the equilibrium orthorhombic Ag 3 Sn structure from an HCP-like centre could occur in various ways.For example, the hexagonal structure could transform into orthorhombic Ag 3 Sn by a disorder-order type reaction, or orthorhombic Ag 3 Sn could nucleate on the HCP centre and grow off epitaxially.Both would result in the three orientations of Ag 3 Sn growing from a common centre, each one a variant of the following orientation relationship (OR) with respect to a single HCP orientation.To obtain evidence for or against these ideas, future research could study the local structure and chemical ordering at the centre of Ag 3 Sn cyclic twins with atomic resolution characterisation techniques.
A second possibility is that cyclic twinning may be related to growth twinning in the early stages of growth without chemical disorder at the start of solidification.Our results in Fig. 3(d-g) show that growth twinning occurred away from the nucleation point when the bulk undercooling reached ~50 • C, resulting in complex-shaped branched crystals.It is feasible that similar growth twinning could occur close to the nucleation point at smaller undercooling generating three orientations in the very early stages of solidification.The driving force for growth twinning seems to be related to the preferred growth directions of Ag 3 Sn.This orthorhombic phase is constrained by crystal symmetry to grow as a {001} plate (Fig. 1(a)-(e)) which produces quasi-2D growth.Multiple growth twinning in the very early stages of solidification would create another two orientations and allow the twinned crystal to grow more effectively in 3D when there is a high driving force (undercooling) for growth.Presumably, this is also the origin of twin-mediated branching during growth far from the nucleation point that leads to the complex branched growth shapes at deeper undercooling in Fig. 3 (e)-(g).
It is instructive to compare our findings with previous work on cyclic twinning in other phases.Ag 3 Sn has similarities to cyclic twinning in other low symmetry intermetallics with a close structural relationship to a higher symmetry crystal structure, and that form during solidification as a primary phase.In these cases, the cyclic twins usually contain all variants of the orientation relationship with the higher symmetry structure.For example, cyclic twins in monoclinic Al 13 Fe 4 contain ten orientations each rotated ~36 • around a common 〈010〉 and are the ten variants of the orientation relationship with a decagonal quasicrystal to which Al 13 Fe 4 is an approximant [67][68][69].In another example, cyclic twins in rhombohedral Al 8 Mn 5 contain four orientations each rotated ~90 • around the three common < 1102 > and are the four variants of the orientation relationship with a higher symmetry cubic gamma brass (Cu 5 Zn 8 ) [70].In Ag 3 Sn, the cyclic twin contains three orientations that are the three variants of the orientation relationship to the higher symmetry HCP structure.All could form by mechanisms similar to those outlined above although further work is required to explore if the detailed mechanisms are the same in all these cases.It is clear that cyclic twinning is a common feature of solidification when an intermetallic compound differs from a higher symmetry crystal structure only by a small distortion and different chemical ordering (e.g.Fig. 1(f) in the case of Ag 3 Sn).
Another important example for electronic soldering is the cyclic twinning of tetragonal β-Sn during solidification of ball grid array solder joints [71][72][73][74][75].This involves three orientations related by ~60 • rotations around a common 〈100〉 axis [74], giving the cyclic twin pseudo-hexagonal character.Similar to Ag 3 Sn, cyclic twinning in β-Sn is promoted by deeper nucleation undercooling [71].Lehman et al. [74] proposed that cyclic twinning in β-Sn starts at the nucleation stage and presented a pseudo/metastable hexagonal nucleus structure with a Cu or Ag atom at its centre.This nucleus structure is simpler and requires less atomic organisation than the stable β-Sn structure, which is analogous to a simpler chemically-disordered HCP nucleus for Ag 3 Sn.However, Ag 3 Sn is a simpler case since orthorhombic Ag 3 Sn differs from the higher symmetry HCP structure only by chemical ordering (Fig. 1(f)).

Ag 3 Sn in Sn-Ag-Cu alloys and joints on copper substrates
The effects of soldering to a Cu substrate are presented in Fig. 6 using Sn-5Ag/Cu, Sn-3.5Ag/Cu and Sn-3Ag-0.5Cu/Cujoints as examples.For each composition, a 2 × 2 array of joints was used, similar to the inset sketch in Fig. 6(a), and reflowed in the DSC by holding for 10 min at the peak temperature (280 • C for Sn-5Ag/Cu, and 230 • C for Sn-3.5Ag/Cu and Sn-3Ag-0.5Cu/Cu)before cooling at 5 K/min in the DSC.In each case four peaks associated with β-Sn nucleation and growth can be identified in the DSC traces while the four primary Ag 3 Sn peaks are smeared into one broad peak highlighted in the black boxes in the enlarged insets.Examination of the microstructures in Fig. 6 reveals that all Ag 3 Sn grew as simple plates similar to Fig. 1(a) and 3(a), and there were commonly multiple plates in the cross-section that all grew from the Cu 6 Sn 5 reaction layer, either the top or bottom layer or both.EBSD confirmed that all these plates are independent and correspond to different pseudo-HCP orientations, as shown in the unit cell wireframes plotted next to the plates, indicating multiple Ag 3 Sn nucleation events in these joints.From Fig. 6, we can conclude that soldering to a Cu substrate in a DSC caused multiple Ag 3 Sn nucleation events, simple Ag 3 Sn plates without twinning, and a much narrower range of Ag 3 Sn nucleation temperatures than in freestanding Sn-Ag balls in Fig. 3 and 4.
To understand how soldering to a Cu substrate catalyses Ag 3 Sn nucleation compared with freestanding Sn-Ag balls (Fig. 6 versus Figs. 3  and 4), the relative importance of Cu solute, primary Cu 6 Sn 5 crystals and the Cu 6 Sn 5 layer are considered next by comparing freestanding balls and joints of Sn-5Ag, Sn-3.5Ag,Sn-3Ag-0.5Cuand Sn-3Ag-1Cu (wt.%).Note that Sn-3Ag-1Cu is hypereutectic with respect to the Cu 6 Sn 5 liquidus and primary Cu 6 Sn 5 forms before the Ag 3 Sn liquidus temperature is reached.Fig. 7(a) summarises all the measured nucleation onset temperatures for freestanding balls (grey) and Cu-substrate joints (red), together with their corresponding liquidus temperatures (blue dashed lines) for primary Ag 3 Sn.
For freestanding balls in Fig. 7(a), Sn-5Ag had a deeper mean Ag 3 Sn undercooling than the other three compositions because there is less interruption from β-Sn nucleation as discussed in Section 3.1.3.Sn-3.5Ag and Sn-3Ag-0.5Cufreestanding balls had similar mean Ag 3 Sn nucleation undercooling (i.e. the temperature interval between the blue dashed line and the grey bar in Fig. 7(a)) and standard deviation, indicating that Cu solute in the liquid does not significantly affect the Ag 3 Sn nucleation undercooling.Similarly, Sn-3Ag-0.5Cuand Sn-3Ag-1Cu freestanding balls had similar mean nucleation undercooling and deviation range, indicating that the presence of Cu 6 Sn 5 primary crystals does not significantly affect the Ag 3 Sn nucleation undercooling.
For solder joints with Cu substrates, the Ag 3 Sn nucleation onset temperature is significantly higher than for the corresponding solder ball compositions with much narrower variation range and, similar to Fig. 6, all joints nucleated above their calculated Ag 3 Sn liquidus temperature.
Three specific examples are shown in Fig. 7(b) to further illustrate these points.The first two are freestanding balls of Sn-3Ag-0.5Cuand Sn-3Ag-1Cu where the Ag 3 Sn nucleated at similar undercooling and β-Sn nucleation occurred at 1~2 • C below.The Ag 3 Sn plates have different colours under polarised optical microscopy indicating multiple Ag 3 Sn (orthorhombic) orientations and EBSD showed these to have one pseudo-HCP orientation that is plotted as a wireframe, indicating a single Ag 3 Sn nucleation event in each ball.In Sn-3Ag-1Cu, primary Cu 6 Sn 5 is also present as labelled but it is located far from the Ag 3 Sn and no simple orientation relationship was measured between primary Cu 6 Sn 5 and Ag 3 Sn in this or any other sample investigated, further showing that primary Cu 6 Sn 5 did not significantly affect the nucleation of primary Ag 3 Sn.The third example shows a Sn-3Ag-0.5Cu/Cujoint with multiple (two) independent Ag 3 Sn plates and an Ag 3 Sn nucleation onset temperature that is significantly higher than in the freestanding solder balls.
From Fig. 7, it can be concluded that solder joints on Cu substrates resulted in multiple Ag 3 Sn nucleation events (Figs. 6 and 7(b)) and nucleation onset temperatures that were significantly higher than their corresponding solder balls and with much narrower variation range (Fig. 7(a)).This contrasts with Cu solute and the presence of primary To assess the Ag 3 Sn nucleation undercooling in joints, we need to consider the change in liquid composition due to copper substrate dissolution.The liquidus temperature for each composition was calculated using the Thermo-Calc TCSLD4.1 database assuming that Cu solute is fully saturated in the melt at the peak temperature during holding, which is reasonable as previous experiments and calculations confirmed that, for 500 µm solder balls, 10 min are enough for Cu to saturate into the melt from the substrate [76,77].Assuming uniform saturated melts, the calculated Ag 3 Sn liquidus temperature is plotted for all compositions as blue dashed lines in Figs. 6, 7(a) and 7(b).In all cases, the Ag 3 Sn nucleation onset temperature is above this Ag 3 Sn liquidus temperature, making the nucleation undercooling appear negative which is unphysical.This shows that the assumption of a uniform liquid composition is invalid and we need to also consider the variation in Ag content in the liquid due to the growth of Cu 6 Sn 5 layer.
In order to investigate the Ag solute field in the liquid before Ag 3 Sn nucleation, Sn-3.5Ag/Cu joints were heated to 230 • C, held for 10 min and then quenched in water.The cross section of such a solder joint is shown in Fig. 8(a) where no primary Ag 3 Sn plates formed.The enlarged BSE image in Fig. 8(b) highlights the small Ag 3 Sn eutectic particles in the bulk and between the scallops of the Cu 6 Sn 5 reaction layer.EDX elemental mapping of the same area in Fig. 8(c) reveals a highly heterogeneous Ag composition field caused by the liquid solidifying to produce a mixture of Ag 3 Sn particles containing ~73 wt.% Ag and β-Sn containing ~0.07 wt.% Ag (calculated with Ref [61].).Note in Fig. 8(c) that the EDX map implies that the top Ag 3 Sn particles are much larger than they are in Fig. 8(b); for more quantitative analysis EDX point analysis is required.
To quantify the original liquid solute field, averaging of more than 300 chemical analysis points near the bottom of the solder joint was performed.The individual data points are plotted in Fig. 8(d) as composition versus distance to the Cu substrate.The average thickness of the Cu 6 Sn 5 reaction layer was measured to be 3.56±1.75µm and is highlighted with the dashed lines.The data points between these lines correspond to points located in the gaps between the Cu 6 Sn 5 crystals/ scallops.The large scatter in the data is due to different amounts of Ag 3 Sn and β-Sn phases in the electron interaction volume at each measurement point and averaging is required to access the original liquid composition.All the data points were fitted with the thick dashed line which describes the distribution of Ag content with respect to the distance to the substrate.As can be seen, the Ag content decreases with increasing distance from the substrate and, for the area far from the substrate, the mean Ag content is close to 3.5 wt.% which is consistent with the bulk composition.The function of the fitted curve is written in Fig. 8(e), together with a contour plot of this change of Ag content and a sketch of the Cu 6 Sn 5 layer from the same region and scale of Fig. 8(b).From Fig. 8(e), we see how Ag solute was rejected into the liquid during Cu 6 Sn 5 layer growth and accumulated naturally in the gaps and valleys between Cu 6 Sn 5 scallops due to the scallop growth shape.This rejection of Ag is consistent with there being negligible solubility for Ag in the Cu 6 Sn 5 phase [35].
Combining the measured Ag profile in Fig. 8(d) and (e) with calculations of the Ag 3 Sn liquidus temperature for these compositions in Thermo-Calc TCSLD4.1, the relation between the Ag 3 Sn liquidus temperature and distance from the Cu substrate was obtained and is plotted in Fig. 8(f).The range of measured nucleation temperatures for Ag 3 Sn in Sn-3.5Ag/Cu joints in Fig. 7(a) is also plotted on Fig. 8(f) as a grey band.We see that the only locations where Ag 3 Sn could have nucleated in undercooled liquid are <~10 μm from the Cu substrate.Thus, thermodynamically, we can infer that Ag 3 Sn must have nucleated on or near the Cu 6 Sn 5 reaction layer in all joints on Cu substrates in Figs. 6 and 7(a) because their Ag 3 Sn nucleation temperatures are all above the liquidus temperature of the bulk (far field) liquid.This is a form of constitutional supercooling (up to ~12 • C in Fig. 8(f)) with respect to the Ag 3 Sn liquidus temperature due to the local accumulation of Ag solute in the liquid during diffusion ahead of the Cu 6 Sn 5 layer.Nucleation of Ag 3 Sn on the Cu 6 Sn 5 layer is also consistent with all Ag 3 Sn plates being in contact with the Cu 6 Sn 5 layer in the micrographs in Fig. 6.
Fig. 8(f) also shows that, when Ag 3 Sn nucleates on/near the Cu 6 Sn 5 layer in constitutionally supercooled liquid, the plate can only grow up to ~10 μm in supercooled liquid and further plate growth then depends on the rate of external heat extraction which is slow for DSC cooling at 5 K/min.This is consistent with Ag 3 Sn growing as single crystal plates (without growth twinning) in all joints on Cu in Fig. 6.
The relatively small solute-corrected nucleation undercooling for Ag 3 Sn of ~12 • C (Fig. 8(f)) with narrow variation range for Sn-3.5Ag/Cujoints (Fig. 7(a)) indicates that the nucleation site itself also has a relatively higher potency and possibly higher number density than in freestanding balls.Thus, orientation relationships (ORs) between the Cu 6 Sn 5 layer and Ag 3 Sn were explored.As revealed by Fig. 9(a), many small Ag 3 Sn particles were sometimes attached to the Cu 6 Sn 5 reaction layer surface in quenched samples, and direct EBSD on these particles revealed that many of them shared the same OR with the Cu 6 Sn 5 , as can be seen in Fig. 9(a)-(e).Fig. 9(a) is a 70 • tilted image of a faceted Cu 6 Sn 5 crystal in the reaction layer with multiple nanoscale Ag 3 Sn on the surface.The EBSD IPF-Z map in Fig. 9(b) shows that there are three pseudo-HCP orientations indexed for the 49 Ag 3 Sn particles: 43 Ag 3 Sn in red, 5 in pink and 1 in purple.In the pole figures in Fig. 9(c) the {0001} plane of Cu 6 Sn 5 is parallel to a {1120} plane of the red and pink pseudo-HCP Ag 3 Sn with two < 1100 > directions of Cu 6 Sn 5 parallel to one of the < 1100 > directions in each of the red and pink pseudo-HCP Ag 3 Sn respectively, as highlighted by black circles.This orientation relationship can be written as: The OR is also plotted with the unit cell wireframes in Fig. 9(e).Theoretically, there should be three Ag 3 Sn pseudo-HCP orientation variants corresponding to this OR.The missing one was calculated and is plotted in grey in Fig. 9(e) with its {1120} planes and < 1100 > directions also plotted as small grey circles in pole figures in Fig. 9

(d).
There is only one Ag 3 Sn particle (coloured in purple) at the bottom right of the surface that does not share this OR or any other simple OR with the Cu 6 Sn 5 crystal.
It is then natural to ask whether large Ag 3 Sn plates nucleate on the Cu 6 Sn 5 layer with the same OR.Note that the Ag 3 Sn plates are large and contact numerous different Cu 6 Sn 5 crystals in the Cu 6 Sn 5 reaction layer at the same time so we would not expect to find the nucleation OR between Ag 3 Sn plates and most of the Cu 6 Sn 5 scallops they contact on the reaction layer.Nevertheless, the OR was measured between some primary Ag 3 Sn plates and Cu 6 Sn 5 in the reaction layer.Fig. 9(f)-(k) gives an example.In Fig. 9(f), a large primary Ag 3 Sn plate has the OR with a contacting Cu 6 Sn 5 grain.Fig. 9(g)-(j) are the Kikuchi patterns taken from the red and green points in Fig. 9(f) with selected parallel planes and directions indexed.Since the (001) facet of Ag 3 Sn can be inferred from Fig. 9(f), the correct orthorhombic orientation can be deduced from the pseudo-HCP orientation as discussed with Figs. 1 and 2. The unit cell wireframes of the two orientations are plotted in Fig. 9(k) with the parallel planes and directions highlighted.The OR can be written in terms of orthorhombic Ag 3 Sn: To assess the reproducibility of this OR, Fig. 9(l) summarises this OR over 53 Ag 3 Sn crystals (both eutectic particles and primary plates) by projecting the parallel {1120} plane and < 1100 > direction of pseudo-HCP Ag 3 Sn into the standard pole figure of Cu 6 Sn 5 , with the deviation annotated for the parallel plane and direction.Furthermore, the superimposed crystal lattice of the two phases in Fig. 9(m) indicates a relatively low atomic mismatch with this orientation relationship, particularly along the parallel row 〈1100〉 Ag3Sn ‖〈1100〉 Cu6Sn5 which is the vertical direction in the upper part of Fig. 9(m).However, the match is less good along other directions and the overall match is significantly worse than potent nucleants in other systems such as PdSn 4 and α-CoSn 3 for β-Sn [78,79], TiB 2 for α-Al or Al 3 Ti [80,81], and Zr for α-Mg [82,83].Thus, it seems that Cu 6 Sn 5 is not a highly potent nucleant for Ag 3 Sn but is the lowest energy interface available for heterogeneous nucleation in the location where the liquid is constitutionally supercooled.
Previous work has shown that the Cu 6 Sn 5 layer also catalyses the nucleation of β-Sn in solder joints [84].It was shown by FIB-tomography that the triple points between Cu 6 Sn 5 scallops have a 3D shape similar to conical cavities which are known to be catalytic to nucleation [85].Thus, three factors probably combine to promote Ag 3 Sn nucleation on Cu 6 Sn 5 in the reaction layer: (i) constitutional supercooling which causes the maximum melt supercooling to exist between the scallops in the Cu 6 Sn 5 layer and enable Ag 3 Sn nucleation at a temperature higher than the liquidus temperature of the bulk liquid away from the layer; (ii) geometrical catalysis from the conical cavity-like shapes between Cu 6 Sn 5 scallops in the reaction layer; and (iii) a relatively good atomic match between Ag 3 Sn and Cu 6 Sn 5 for the nucleation OR.

Synchrotron study of Ag 3 Sn nucleation and growth
Fig. 10 overviews synchrotron radiography results of the nucleation and growth kinetics of primary IMCs in a Sn-4Ag-0.5Cu/Cujoint.Fig. 10 (a) is a snapshot at T = 211.1 • C when numerous primary Cu 6 Sn 5 have formed in the liquid as hollow rods (similar to Ref. [55]) and no Ag 3 Sn has yet nucleated.Note that Fig. 10(a) is a through-thickness averaged radiograph and the volume fraction of Cu 6 Sn 5 is much lower than it may appear from the projected image.Fig. 10(b) is a snapshot at lower temperature of T = 200.2• C when multiple Ag 3 Sn plates had nucleated and grown in the bulk and near the solder-substrate.There was no evidence of Ag 3 Sn nucleating on the primary Cu 6 Sn 5 , consistent with the results with bulk solder joints.
To visualise and quantify the growth kinetics of the Ag 3 Sn plates, in Fig. 10(c), pixels containing Ag 3 Sn have been coloured by the time at which they first became solid Ag 3 Sn.As we can see, most Ag 3 Sn are single crystals growing from a nucleation point (blue) into a faceted plate.A few Ag 3 Sn share a common growth centre, indicating cyclic twinning.For example, in the centre-right of Fig. 10(c), note the dark blue three-pointed star emanating from a common centre and growing into three plates of increasingly 'hot' colours.Thus, similar to bulk samples earlier in this paper, Ag 3 Sn grew as single crystal plates and as cyclic twinned plates in the synchrotron samples.However, there was additionally a significant difference: in bulk solder joints (e.g.Fig. 6) Ag 3 Sn nucleation occurred almost exclusively on the Cu 6 Sn 5 reaction layer whereas, in the thin synchrotron samples, Ag 3 Sn nucleation occurred both on the Cu 6 Sn 5 reaction layer and throughout the 'bulk'.We can infer that the Ag 3 Sn that appear to be in the bulk are actually attached to (and nucleated on) the cell walls since the Ag 3 Sn did not move under gravity despite being significantly denser than the liquid.Thus, the thin sample geometry affected the nucleation of Ag 3 Sn, with many Ag 3 Sn nucleation events forming on the walls of the cell.A further factor is that the ratio of the area of substrate to the volume of solder is much smaller in thin-sample synchrotron experiments than in solder joints, promoting Ag 3 Sn nucleation away from the Cu 6 Sn 5 layer.Fig. 10 (d) summarises the nucleation sequence of different types of Ag 3 Sn crystals.Most of the single crystal Ag 3 Sn plates growing from the reaction layer (triangles) tended to form at an earlier stage compared to the two cyclic twinned crystals (stars) observed forming in the bulk.The remaining single crystal plates nucleating on the cell walls (circles) nucleated throughout the whole time/temperature range.Fig. 11 plots the detailed growth process of one of the cyclic twinned Ag 3 Sn crystals by combined in-situ X-ray imaging and post-mortem EBSD.The in-situ radiography at different growth stages in Fig. 11(a) and (b) directly proves that the crystal comes from a common centre followed by growth into three large plates.Note that the greyscale depends on the thickness of Ag 3 Sn where thicker and overlapping Ag 3 Sn regions appear darker.The same three plates were identified on the surface of the specimen and EBSD was applied to measure their orientations.The measured orthorhombic unit cells from the three plates are plotted in Fig. 11(c).They are cyclic twinned with 60 • to each other along a common 〈100〉, and form a combined hexagonal symmetry similar to Fig. 2.
Combining information from the in-situ imaging in Fig. 11 Even with the significant differences in the synchrotron experiments related to the sample geometry and cooling conditions (e.g. the catalytic cell walls, different area to volume effects and local temperature gradient), the key findings are consistent with the solder joints in Figs. 6  and 7.The primary Cu 6 Sn 5 did not promote Ag 3 Sn nucleation, while the Cu 6 Sn 5 reaction layer was catalytic for Ag 3 Sn nucleation such that all Ag 3 Sn growing from the reaction layer were single crystal plates, while cyclic twinned crystals nucleated in the bulk at relatively deeper undercooling (Fig. 10(d)).The real-time X-ray imaging proves that cyclic twins grow from a common point, indicating that cyclic twinning of Ag 3 Sn occurred either in the process of nucleation or in the very early stages of growth as discussed in Section 3.1.5.

Conclusions
This work has revealed the following new insights into the nucleation and growth of primary Ag 3 Sn in 500μm solder balls and solder joints on copper substrates.
In freestanding Sn-Ag balls, the undercooling for Ag 3 Sn nucleation is more stochastic than reported/assumed in past work, spanning the range ~10-70 K.At the smallest undercoolings, Ag 3 Sn grew as single crystal plates with {001} as the main facet.Deepening of the undercooling promoted Ag 3 Sn cyclic twinning and, as the undercooling became deeper still, additional twin-mediated growth branching became increasingly common.
Cyclic twinned Ag 3 Sn crystals are three interpenetrating plates linked by 60 • rotations about a common 〈100〉 axis, forming a combined hexagonal symmetry related to the pseudo-HCP structure of Ag 3 Sn.The three plates emanate from a common centre in the undercooled melt.Possible formation mechanisms include (i) the development of chemical disorder in the process of nucleation or in the very early stages of growth, which would raise the crystal symmetry from orthorhombic to hexagonal, and/or (ii) multiple growth twinning in the early stages of growth to enable the Ag 3 Sn to grow in 3D in six directions rather than as a quasi-2D plate.
There is a competition between the nucleation of β-Sn and Ag 3 Sn.When β-Sn nucleates first, primary Ag 3 Sn is completely supressed.This can happen even for deep β-Sn undercoolings due to the stochastic nature of nucleation in both phases in freestanding balls.
Soldering to copper substrates significantly catalysed Ag 3 Sn nucleation, resulting in multiple independent Ag 3 Sn single crystal plates growing from the Cu 6 Sn 5 reaction layer with significantly higher nucleation onset temperature and narrower variation range compared to freestanding solder balls.Cu solute and primary Cu 6 Sn 5 appear to have no significant effect on the nucleation of Ag 3 Sn.Instead, it is the Cu 6 Sn 5 reaction layer that promotes Ag 3 Sn nucleation due to (i) constitutional supercooling generated by Ag solute rejection into the liquid between the scallops of the Cu 6 Sn 5 reaction layer, (ii) geometrical catalysis in the grooves between Cu 6 Sn 5 scallops and (iii) heterogeneous nucleation of Ag 3 Sn on Cu 6 Sn 5 with the reproducible orientation relationship (OR): {1120} Ag3Sn || {0001} Cu6Sn5 , with < 1100 > Ag3Sn || < 1100 > Cu6Sn5 .
The catalysis of Ag 3 Sn nucleation in solder joints results in more Ag 3 Sn growing as single crystal plates and fewer growing as cyclic twinned Ag 3 Sn crystals in joints compared with freestanding balls.

Declaration of Competing Interest
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.

Fig. 1 .
Fig. 1.(a) Ag 3 Sn single crystal plate extracted from Sn-5Ag cooled at 0.05 K/min where Ag 3 Sn nucleated at 13.1 • C undercooling.(b) Ag 3 Sn foil milled from Ag 3 Sn plate using FIB.(c) Ag 3 Sn foil attached to TEM grid, where a red box highlights the examined area in TEM.(d) Selected area electron diffraction pattern (SAED) along [010].(e) High resolution TEM image along [010].(f) Orthorhombic Ag 3 Sn structure compared with a hexagonal close-packed unit cell.

Fig. 3
overviews the role of undercooling on the growth of primary Ag 3 Sn in Sn-5Ag balls with a constant imposed cooling rate of 5 K/min.Results from seven balls are presented with Ag 3 Sn nucleation undercoolings ranging from ~17 -68 • C. The figure is arranged such that the Ag 3 Sn nucleation undercooling becomes deeper by ~10 • C in each row from Fig.3(a) to (g) (except Fig.3(f)).For each Sn-5Ag ball, the DSC cooling curve is plotted with the measured Ag 3 Sn liquidus temperature highlighted and the Ag 3 Sn undercooling marked.The SEM image, polarised optical microscope image and EBSD IPF-Z map of the primary Ag 3 Sn are also shown.The orthorhombic and pseudo-HCP unit cells from Fig.1(f) are plotted on the IPF-Z maps to show the relationship between the measured orientations.As can be seen, Ag 3 Sn grew as a

Fig. 2 .
Fig. 2. Cyclic twinned Ag 3 Sn in a Sn-5Ag ball with 24.5 • C undercooling cooled at 5 K/min.(a) Polarised optical microscope image of three interpenetrating Ag 3 Sn plates, each having a single colour.(b) EBSD IPF-X map superimposed on the optical image with unit cell wireframes plotted next to each plate.(c) The three Ag 3 Sn unit cell wireframes from (b) translated into a ring.Growth arrow colours correspond to the polarised image in (a); unit cell colours correspond to the IPF-X colouring in (b).(d) 〈100〉 and {001} pole figures of the three cyclic twinned orientations.(e) EBSD IPF-X map of the Ag 3 Sn indexed with hexagonal unit cell.(f) Hexagonal close-packed atoms (grey) superimposed with ordered Ag (blue) and Sn (orange) atoms from the three cyclic twinned Ag 3 Sn orientations.

Fig. 3 .
Fig. 3. Microstructures of Ag 3 Sn with different nucleation undercooling in Sn-5Ag cooled at 5 K/min.DSC cooling traces highlighting the Ag 3 Sn liquidus temperature (blue dashed line) and Ag 3 Sn undercooling.Polarised optical images showing Ag 3 Sn regions with the same orientation.EBSD IPF-Z maps plotted after indexing with an HCP structure.The hexagonal and orthorhombic unit cell wireframes are plotted from Euler angles with the hexagonal {1100} planes highlighted.
(e) the undercooling for primary Ag 3 Sn is 58.20 • C, and β-Sn formed soon (~3 • C) after Ag 3 Sn nucleation.In contrast, Fig. 3(f) shows a sample with similar Ag 3 Sn undercooling (60.50 • C) but different β-Sn nucleation temperature which is ~20 • C below Ag 3 Sn nucleation allowing more time for Ag 3 Sn growth and coarsening.

Fig. 4 .
Fig. 4. (a) Ag 3 Sn plate thickness versus undercooling measured from Fig. 3 using the orientation from EBSD to account for sectioning effects.(b)-(c) Histogram of nucleation onset temperature for Ag 3 Sn (red) and β-Sn (grey) in 82 Sn-5Ag (b) and 30 Sn-3.5Ag (c) solder balls with fitted normal distribution curves and mean Ag 3 Sn nucleation undercooling and standard deviations.Both compositions were cooled at 5 K/min.(d) Sn-Ag phase diagram at the Sn-rich side [61].
Y.Cui et al.   enters the overlapping region, the nucleation of β-Sn may happen first and prevent primary Ag 3 Sn from forming.This competition between the nucleation of Ag 3 Sn and β-Sn also changes the mean value of nucleation undercooling measured for primary Ag 3 Sn: for Sn-5Ag the measured undercooling for Ag 3 Sn is 34.3 ± 12.4 • C, and for Sn-3.5Ag it is almost halved: 17.7 ± 9.4 • C, indicating that it is more difficult to achieve deep Ag 3 Sn undercooling in Sn-3.5Ag due to the interruption by β-Sn nucleation.
(b) the range of Ag 3 Sn nucleation temperatures at each cooling rate indicates that the nucleation of Ag 3 Sn in each small (~500 μm diameter) ball is independent and stochastic, but the whole group of statistical data in Fig.5(b) reveals a clear trend between the nucleation undercooling and cooling rate: the higher the cooling rate, the deeper the undercooling that is reached in the melt.The relationship between the measured undercooling for Ag 3 Sn and cooling rate are plotted in Fig.5(d) and (e): the mean nucleation undercooling increases with cooling rate with a near-linear increase of ln(ΔT) with respect to ln (dT/dt), as shown with the logarithmic coordinates in Fig.5(e).A similar relationship has also been reported in other systems[62][63][64].

Fig. 5 .
Fig. 5. (a) Ag 3 Sn nucleation in Sn-5Ag at five cooling rates.Grey bars are mean temperature superimposed with the nucleation temperature of Ag 3 Sn from 10 individual samples in red (single crystal) and blue (twinned crystal) circles.(b) Box plot of the measured Ag 3 Sn nucleation onset temperature at different cooling rates.(c) Percentage of twinned Ag 3 Sn versus the mean undercooling from different cooling rates.(d)-(e) The relationship between mean undercooling for Ag 3 Sn nucleation and cooling rate.(a = 18.6, k = 0.17 for the fitting curve).

Fig. 6 .
Fig. 6.DSC cooling curves and microstructures of 2 × 2 solder joint arrays with Cu substrates: (a) Sn-5Ag, (b) Sn-3.5Ag and (c) Sn-3Ag-0.5Cu.The calculated Ag 3 Sn liquidus temperature is highlighted in blue dashed lines with nucleation onset temperature indicated by the extrapolation method.Orientations of the Ag 3 Sn plates were plotted using hexagonal unit cell wireframes measured by EBSD.

Fig. 8 .
Fig. 8. (a) The microstructure of a quenched Sn-3.5Ag/Cu joint.(b) Enlarged view of the white box area in (a).(c) The EDX Ag map of the same area as (b).(d) Ag content from multiple EDX point analysis versus measured distance to the Cu substrate.The Ag distribution is fitted with the black dashed line.The thickness of Cu 6 Sn 5 is plotted with vertical grey dotted lines.(e) A contour plot showing the change of Ag content near the Cu 6 Sn 5 reaction layer calculated from the black dashed line in (d).The function of the fitted line is also marked.(f) The change of Ag 3 Sn liquidus temperature with distance from the Cu substrate.The measured Ag 3 Sn nucleation temperature range from Fig. 7 is highlighted in grey and the constitutional supercooling is highlighted close to the Cu 6 Sn 5 reaction layer.

Fig. 9 .
Fig. 9. (a) 70 • tilt view of numerous Ag 3 Sn particles on a Cu 6 Sn 5 reaction layer surface after dissolving β-Sn from quenched Sn-3.5Ag/Cu joint.(b) EBSD IPF-Z map of the Cu 6 Sn 5 surface in (a) with both Ag 3 Sn and Cu 6 Sn 5 indexed using their corresponding hexagonal structure.(c)-(d) Pole figures for the Cu 6 Sn 5 and Ag 3 Sn in (b) with parallel planes and directions highlighted in black circles.The {1120} and < 1100 > for the grey unit cell in (e) was also plotted with grey circles.(e) The measured orientation relationship between Ag 3 Sn and Cu 6 Sn 5 .Three Ag 3 Sn orientation variants of the OR were plotted with two of them measured (red and pink) and one calculated (grey).(f) Primary Ag 3 Sn growing from Cu 6 Sn 5 reaction layer with the same orientation relationship.The two crystals are marked in red and green.(g)-(h) The Kikuchi patterns from the Ag 3 Sn and Cu 6 Sn 5 crystals in (f).In (i)-(j) selected parallel planes and directions are indexed on the Kikuchi patterns.(k) Unit cell wireframes of the two crystals with highlighted parallel planes and directions.(l) Summary of the OR by projecting the {1120} and < 1100 > of Ag 3 Sn orientations into pole figures with respect to the orientations of Cu 6 Sn 5 .(m) Atomic projection of Ag 3 Sn and Cu 6 Sn 5 on their parallel planes with unit cells highlighted.

Fig. 10 .
Fig. 10.Synchrotron radiography of Ag 3 Sn plate solidification in a Sn-4Ag-0.5Cu/Cujoint (a) A frame at 211 • C when only primary Cu 6 Sn 5 crystals are present.(b) A frame at 200 • C after the nucleation and growth of Ag 3 Sn crystals and prior to β-Sn nucleation.(c) A processed image where each Ag 3 Sn pixel is coloured by its Ag 3 Sn formation time in seconds.(d) Total number of Ag 3 Sn crystals versus time, with an inset comparing the nucleation temperatures of different Ag 3 Sn types.
(a) and (b) with the crystallographic orientations from EBSD in Fig.11(c), the {001} planes from the three unit cells are plotted in Fig.11(d) aligned along their common 〈100〉 twin axis with one of their 〈110〉 directions highlighted with black dashed lines emanating from a nucleation point.Note in Fig.11(d) that the plates match well with the plate shapes in Fig.11(a) and (b), that the three plates are rectangular (in 3D) with their edges parallel to the 〈100〉 and 〈010〉 directions consistent with Fig.1(a), and that each plate has a tendency of thickening along the 〈110〉 direction emanating from the common centre.Plate 1 and 2 stopped growing due to the interruption of the nearby Cu 6 Sn 5 rods while plate 3 stops growing as it impinged on the cell wall.

Fig. 11 .
Fig. 11.(a) Synchrotron X-ray image sequence of the nucleation and growth of twinned primary Ag 3 Sn in a Sn-4Ag-0.5Cu/Cujoint.(b) Images subtracted by a frame shortly before 106 s showing three plates grow from a common point.Ag 3 Sn plates appear dark.(c) Cyclic Ag 3 Sn unit cells showing three twinned orientations, as measured by post-mortem EBSD.(d) Three {001} Ag3Sn planes taken from the unit cells resemble the growth of actual Ag 3 Sn plates in (b).

Table 1
Crystal structures of Ag 3 Sn and Cu 6 Sn 5 assumed in this work.