Intermetallic formation in Sn3Ag0.5Cu and Sn3Ag0.5Cu0.06Ni0.01Ge solder BGA packages with immersion Ag surface finish

The intermetallic compounds formed in Sn3Ag0.5Cu and Sn3Ag0.5Cu0.06Ni0.01Ge solder BGA packages with Ag/Cu pads are investigated. After reflow, scallop-shaped η-Cu₆Sn₅ and continuous planar η-(cu_0.9Ni_0.1)₆Sn₅ intermetallics appear at the interfaces of the Sn3Ag0.5Cu and Sn3Ag0.5Cu0.06Ni0.01Ge solder joints, respectively. In the case of the Sn3Ag0.5Cu specimens, an additional ε-Cu₃Sn intermetallic layer is formed at the interface between the η-Cu₆Sn₅ and Cu pads after aging at 150°C, while the same type of intermetallic formation is inhibited in the Sn3Ag0.5Cu0.06Ni0.01Ge packages. In addition, the coarsening of Ag₃Sn precipitates also abates in the solder matrix of the Sn3Ag0.5Cu0.06Ni0.01Ge packages, which results in a slightly higher ball shear strength for the specimens.     

Effects of Co Alloying and Size on Solidification and Interfacial Reactions in Sn-57 wt.%Bi-(Co)/Cu Couples

Solidification and interfacial reactions in Sn-57 wt.%Bi-(Co)/Cu couples are investigated. The addition of 0.05 wt.% Co and 0.5 wt.% Co and changes between 2 g and 20 mg solder sizes have no significant effects on the undercooling of Sn-57 wt.%Bi solders. Both η-Cu₆Sn₅ and ε-Cu₃Sn phases are formed in Sn-57 wt.%Bi/Cu couples reacted at 80°C, 100°C, and 100°C, whereas only η-Cu₆Sn₅ is formed at 160°C. The formation of ε-Cu₃Sn is suppressed and only η-Cu₆Sn₅ is found in the couple with 0.05 wt.% Co and 0.5 wt.% Co addition in Sn-57 wt.%Bi solder. Both the growth rate of η-Cu₆Sn₅ and the dissolution rate of the Cu substrate increase with Co addition. The morphology of η-Cu₆Sn₅ is also altered with Co addition, becoming a porous structure with solder trapped in the voids.     

Developing a lead-free solder alloy Sn-Bi-Ag-Cu by mechanical alloying

A new lead free alloy, Sn-6Bi-2Ag-0.5Cu, has been developed by mechanical alloying and has great potential as a lead-free solder system. Initial trials on the manufacture of solder joints with this alloy revealed that a high quality bond with copper could be formed. Its melting range of 193.87°C to 209.88°C is slightly higher than that of eutectic tin-lead solder. Examination of the microstructure of the as-soldered joints revealed that it mainly consists of small bismuth (1 μm to 2 μm) and Ag₃Sn (1 μm) particles finely dispersed in a nearly pure tin matrix with a small amount of η-Cu₆Sn₅ particles. The Cu-Sn intermetallic compound (IMC) layer formed at solder-copper interface is the η-Cu₆Sn₅ phase with grain size of 2 μm. The shear strength of the solder joint is higher than that of Sn-37Pb or Sn-3.5Ag. Under shear loading, fracture occurred at IMC layer-solder interface as well as in the bulk of solder.     

Interfacial microstructure between Sn-3Ag-xBi alloy and Cu substrate with or without electrolytic Ni plating

The microstructure of the interfacial phase of Sn-3Ag-xBi alloy on a Cu substrate with or without electrolytic Ni plating was evaluated. Bismuth additions into Sn-Ag alloys do not affect interfacial phase formations. Without plating, η-Cu₆Sn₅/ε-Cu₃Sn interfacial phases developed as reaction products in the as-soldered condition. The η-phase Cu₆Sn₅ with a hexagonal close-packed structure grows about 1-μm scallops. The ε-phase Cu₃Sn with an orthorhombic structure forms with small 100-nm grains between η-Cu₆Sn₅ and Cu. For Ni plating, a Ni₃Sn₄ layer of monoclinic structure formed as the primary reaction product, and a thin η-Ni₃Sn₂ layer of hexagonal close-packed structure forms between the Ni₃Sn₄ and Ni layer. In the Ni layer, Ni-Sn compound particles of nanosize distribute by Sn diffusion into Ni. On the total thickness of interfacial reaction layers, Sn-3Ag-6Bi joints are thicker by about 0.9 μm for the joint without Ni plating and 0.18 μm for the joint with Ni plating than Sn-3Ag joints, respectively. The thickening of interfacial reaction layers can affect the mechanical properties of strength and fatigue resistance.     

Effect of microelements addition on the interfacial reaction between Sn-Ag-Cu solders and the Cu substrate

Three kinds of Sn-Ag-based lead-free solders, Sn-3.5Ag-0.7Cu, Sn-3.5Ag-0.5Cu-0.07Ni-0.01Ge, and Sn-3.5Ag-0.07Ni (in wt.%), were selected to explore the effect of microelements (Ni and Ge) on the interfacial reaction between the solder and the Cu substrate. The thickness of the interfacial intermetallics formed with the Sn-3.5Ag-0.5Cu-0.07Ni-0.01Ge and Sn-3.5Ag-0.07Ni solders is several times that of the Sn-3.5Ag-0.7Cu solder. The added microelements converted the feature of interfacial intermetallics from pebble shape to worm shape. However, the results of x-ray diffraction (XRD) analysis suggest that the interfacial intermetallics formed with both solders have the same crystal structure. The results of energy dispersive spectroscopy (EDS) analysis show that the major interfacial intermetallic formed with the Sn-3.5Ag-0.7Cu solder is Cu₆Sn₅, while it is (Cu_x,Ni_1−x)₆Sn₅ with Sn-3.5Ag-0.5Cu-0.07Ni-0.01Ge. Ni influences the interfacial intermetallics and plays the influential role on the difference of interfacial reaction rate between liquid solder and solid Cu and the morphology of interfacial intermetallics. Additionally, the growth kinetics of the interfacial intermetallic compounds (IMCs) formed in the systems of Cu/Sn-3.5Ag-0.7Cu and Cu/Sn-3.5Ag-0.07Ni at high-temperature storage was also explored.     

Interfacial reactions in Ag-Sn/Cu couples

Interfacial reactions between Sn-3.5 wt.%Ag, Sn-25 wt.%Ag, and Sn-74 wt.%Ag alloys with Cu substrate at 240°C and 450°C have been studied here by examining the reaction couples. It is found that Sn is the fastest diffusion species among the three elements during the reaction, while Ag is the slowest. The reaction path is liquid/η/ɛ₁/Cu for the Sn-3.5 wt.%Ag/Cu couples reacted at 240°C. The paths are liquid/ɛ₁/δ/Cu, liquid/ɛ₁/δ/Cu, ɛ₂/ζ/ɛ₁/δ/Cu, for the Sn-3.5 wt.%Ag/Cu, Sn-25 wt.%Ag/Cu, and Sn-74 wt.%Ag/Cu couples at 450°C, respectively. These reaction paths are in agreement with the isothermal sections of the Ag-Sn-Cu ternary system at 240°C and 450°C. The isothermal sections are proposed based on the limited ternary phase equilibria data and the phase diagrams of its three constituent binary systems, Ag-Sn, Cu-Sn, and Ag-Cu.     

Intermetallic reactions in Sn-3.5Ag solder ball grid array packages with Ag/Cu and Au/Ni/Cu pads

During the reflow process of Sn-3.5Ag solder ball grid array (BGA) packages with Ag/Cu and Au/Ni/Cu pads, Ag and Au thin films dissolve rapidly into the liquid solder, and the Cu and Ni layers react with the Sn-3.5Ag solder to form Cu₆Sn₅ and Ni₃Sn₄ intermetallic compounds at the solder/pad interfaces, respectively. The Cu₆Sn₅ intermetallic compounds also appear as clusters in the solder matrix of Ag surface-finished packages accompanied by Ag₃Sn dispersions. In the solder matrix of Au/Ni surface-finished specimens, Ag₃Sn and AuSn₄ intermetallics can be observed, and their coarsening coincides progressively with the aging process. The interfacial Cu₆Sn₅ and Ni₃Sn₄ intermetallic layers grow by a diffusion-controlled mechanism after aging at 100 and 150°C. Ball shear strengths of the reflowed Sn-3.5Ag packages with both surface finishes are similar, displaying the same degradation tendencies as a result of the aging effect.     

Intermetallic reactions in Sn-8Zn-20In solder ball grid array packages with Au/Ni/Cu and Ag/Cu pads

During the reflow process of Sn-8Zn-20In solder joints in the ball grid array (BGA) packages with Au/Ni/Cu and Ag/Cu pads, the Au and Ag thin films react with liquid solder to form γ₃-AuZn₄/γ-Au₇Zn₁₈ and ε-AgZn₆ intermetallics, respectively. The γ₃/γ intermetallic layer is prone to floating away from the solder/Ni interface, and the appearance of any interfacial intermetallics cannot be observed in the Au/Ni surface finished Sn-8Zn-20In packages during further aging treatments at 75°C and 115°C. In contrast, ε-CuZn₅/γ-Cu₅Zn₈ intermetallics are formed at the aged Sn-8Zn-20In/Cu interface of the immersion Ag BGA packages. Bonding strengths of 3.8N and 4.0N are found in the reflowed Sn-8Zn-20In solder joints with Au/Ni/Cu and Ag/Cu pads, respectively. Aging at 75°C and 115°C gives slight increases of ball shear strength for both cases.     

Effects of solid-state annealing on the interfacial intermetallics between tin-lead solders and copper

The interfacial intermetallics between Cu and solder were studied for four Sn-Pb compositions at the annealing temperatures of 125°C, 150°C, and 175°C for up to 30 days. The η-phase (Cu₆Sn₅) layer formed during reflow continues to grow during annealing. An additional layer of ɛ-phase (Cu₃Sn) forms at the η/Cu interface after an incubation annealing time. The thickness results fit a power-law relationship against time with average exponents 0.69 and 0.44 for the η phase and the ɛ phase, respectively. On prolonged annealing, the proportions of the individual phases in the total layer reach a steady state.     

Intermetallics Evolution in Sn-3.5Ag Based Lead-Free Solder Matrix on an OSP Cu Finish

The 0.2Co + 0.1Ni dual additives were used to dope a Sn-3.5Ag solder matrix to modify the alloy microstructure and the solder joint on an organic solderability preservative (OSP) Cu pad. The refined microstructure of the Sn-3.5Ag-0.2Co-0.1Ni solder alloy or the reduced β-Sn size was attributed to the depressed undercooling achieved by the Co-Ni addition. After soldering on the OSP Cu pad, a large Ag₃Sn plate was formed at the Sn-3.5Ag/OSP solder joint, whereas it was absent at the Sn-3.5Ag-0.2Co-0.1Ni/OSP solder joints. With isothermal aging at 150°C, large Ag₃Sn plates formed at the Sn-3.5Ag/OSP solder joint were still observed. A coarsened and dispersed Ag₃Sn phase was found in the solder joints with Co-Ni additions as well. Compared to Cu₆Sn₅, the (Co,Ni)Sn₂ intermetallic compound showed much lower microhardness values. However, (Co,Ni)Sn₂ hardness was comparable to that of the Ag₃Sn phase. Pull strength testing of Sn-3.5Ag-0.2Co-0.1Ni/OSP revealed slightly lower values than for Sn-3.5Ag/OSP during aging. Such results are thought be due to the phase transformation of (Co,Ni)Sn₂ to (Cu,Co,Ni)₆Sn₅.     

Microstructural evolution of a lead-free solder alloy Sn-Bi-Ag-Cu prepared by mechanical alloying during thermal shock and aging

In a previous study, a lead-free solder, Sn-6Bi-2Ag-0.5Cu, was developed by mechanical alloying. The alloy shows great potential as a lead-free solder system. In the present work, the microstructural evolution during thermal shock and aging was examined. In the as-soldered joints small bismuth (1 μm to 2 μm) and Ag₃Sn (1 μm) particles were finely dispersed in a nearly pure tin matrix with a small amount of η-Cu₆Sn₅ phase in the bulk of solder. During thermal shock and aging microstructural evolution occurred with Cu-Sn intermetallic compound (IMC) layer growth at interface, bismuth phase coarsening and Ag₃Sn phase coarsening. The microstructure of the solder appeared to be stable at high temperature. The shear strength of the present solder joint is higher than that of Sn-37Pb and Sn-3.5Ag solders. Shear failure occurred Cu-Sn IMC layer-solder interface and in the bulk of solder.     

Interfacial Reactions of Sn-3.5Ag-<Emphasis Type="Italic">x</Emphasis>Zn Solders and Cu Substrate During Liquid-State Aging

The effects of Zn (1 wt.%, 3 wt.%, and 7 wt.%) additions to Sn-3.5Ag solder and various reaction times on the interfacial reactions between Sn-3.5Ag-xZn solders and Cu substrates a during liquid-state aging were investigated in this study. The composition and morphological evolution of interfacial intermetallic compounds (IMCs) changed significantly with the Zn concentration and reaction time. For the Sn-3.5Ag-1Zn/Cu couple, CuZn and Cu₆Sn₅ phases formed at the interface. With increasing aging time, the Cu₆Sn₅ IMC layer grew thicker, while the CuZn IMC layer drifted into the solder and decomposed gradually. Cu₅Zn₈ and Ag₅Zn₈ phases formed at the interfaces of Sn-3.5Ag-3Zn/Cu and Sn-3.5Ag-7Zn/Cu couples. With increasing reaction time, the Cu₅Zn₈ layer grew and Cu atoms diffused from the substrate to the solder, which transformed the Ag₅Zn₈ to (Cu,Ag)₅Zn₈. The Cu₆Sn₅ layer that formed between the Cu₅Zn₈ layer and Cu was much thinner at the Sn-3.5Ag-7Zn/Cu interface than at the Sn-3.5Ag-3Zn/Cu interface. Additionally, we measured the thickness of interfacial IMC layers and found that 3 wt.% Zn addition to the solder was the most effective for suppressing IMC growth at the interfaces.     

Influence of Cu addition to interface microstructure between Sn-Ag solder and Au/Ni-6P plating

The formation and growth of intermetallics at the interface between Sn-Ag-(Cu) alloy balls and Au/Ni-6P plating were experimentally examined as a function of soldering period. Joint strengths were also evaluated by a ball pull test. For the joint with Sn-3.5Ag, the primary reaction product of Ni₃Sn₄ exhibits growth and shrinkage in thickness repeatedly with a passage of reaction time up to 30 min, while the Ni₃SnP reaction layer monotonously increases its thickness without fluctuation. In the cases of the joints with Cu bearing solder, Sn-3Ag-0.5Cu and Sn-3.5Ag-0.8Cu, a single η-(Cu,Ni)₆Sn₅ interface layer grows by fast Cu segregation from liquid solder to the interface layer on soldering. For all the soldered joints, a P-rich layer appears at the surface region of a Ni-6P plating layer by Ni depletion to form those intermetallic compounds at interfaces. The growth rate of a P-rich layer for Sn-3.5Ag is faster by about 4–8 times than those of the Sn-Ag-Cu. The presence of Cu in solder enhances the formation of the Cu₆Sn₅ intermetallic layer at the interface resulting in prevention of Ni diffusion to liquid solder. For all the soldered joints, coarsened reaction interfaces decrease the joint strengths.     

Intermetallic reactions in reflowed and aged Sn-9Zn solder ball grid array packages with Au/Ni/Cu and Ag/Cu pads

During the reflowing of Sn-9Zn solder ball grid array (BGA) packages with Au/Ni/Cu and Ag/Cu pads, the surface-finished Au and Ag film dissolved rapidly and reacted with the Sn-9Zn solder to form a γ₃-AuZn₄/γ-Au₇Zn₁₈ intermetallic double layer and ε-AgZn₆ intermetallic scallops, respectively. The growth of γ₃-AuZn₄ is prompted by further aging at 100°C through the reaction of γ-Au₇Zn₁₈ with the Zn atoms dissolved from the Zn-rich precipitates embedded in the β-Sn matrix of Sn-9Zn solder BGA with Au/Ni/Cu pads. No intermetallic compounds can be observed at the solder/pad interface of the Sn-9Zn BGA specimens aged at 100°C. However, after aging at 150°C, a Ni₄Zn₂₁ intermetallic layer is formed at the interface between Sn-9Zn solder and Ni/Cu pads. Aging the immersion Ag packages at 100°C and 150°C caused a γ-Cu₅Zn₈ intermetallic layer to appear between ε-AgZn₆ intermetallics and the Cu pad. The scallop-shaped ε-AgZn₆ intermetallics were found to detach from the γ-Cu₅Zn₈ layer and float into the solder ball. Accompanied with the intermetallic reactions during the aging process of reflowed Sn-9Zn solder BGA packages with Au/Ni/Cu and Ag/Cu pads, their ball shear strengths degrade from 8.6 N and 4.8 N to about 7.2 N and 2.9 N, respectively.     

Intermetallic growth kinetics for Sn-Ag, Sn-Cu, and Sn-Ag-Cu lead-free solders on Cu, Ni, and Fe-42Ni substrates

Soldering with the lead-free tin-base alloys requires substantially higher temperatures (∼235–250°C) than those (213–223°C) required for the current tin-lead solders, and the rates for intermetallic compound (IMC) growth and substrate dissolution are known to be significantly greater for these alloys. In this study, the IMC growth kinetics for Sn-3.7Ag, Sn-0.7Cu, and Sn-3.8Ag-0.7Cu solders on Cu substrates and for Sn-3.8Ag-0.7Cu solder with three different substrates (Cu, Ni, and Fe-42Ni) are investigated. For all three solders on Cu, a thick scalloped layer of η phase (Cu₆Sn₅) and a thin layer of ε phase (Cu₃Sn) were observed to form, with the growth of the layers being fastest for the Sn-3.8Ag-0.7Cu alloy and slowest for the Sn-3.7Ag alloy. For the Sn-3.8Ag-0.7Cu solder on Ni, only a relatively uniform thick layer of η phase (Cu,Ni)₆Sn₅ growing faster than that on the Cu substrate was found to form. IMC growth in both cases appears to be controlled by grain-boundary diffusion through the IMC layer. For the Fe-42Ni substrate with the Sn-3.8Ag-0.7Cu, only a very thin layer of (Fe,Ni)Sn₂ was observed to develop.     

Morphology and growth kinetics of intermetallic compounds in solid-state interfacial reaction of electroless Ni-P with Sn-based lead-free solders

A comparative study of solid/solid interfacial reactions of electroless Ni-P (15 at.% P) with lead-free solders, Sn-0.7Cu, Sn-3.5Ag, Sn-3.8Ag-0.7Cu, and pure Sn, was carried out by performing thermal aging at 150°C up to 1000 h. For pure Sn and Sn-3.5Ag solder, three distinctive layers, Ni₃Sn₄, SnNiP, and Ni₃P, were observed in between the solder and electroless Ni-P; while for Sn-0.7Cu and Sn-3.8Ag-0.7Cu solders, two distinctive layers, (CuNi)₆Sn₅ and Ni₃P, were observed. The differences in morphology and growth kinetics of the intermetallic compounds (IMCs) at the interfaces between electroless Ni-P and lead-free solders were investigated, as well as the growth kinetics of the P-enriched layers underneath the interfacial IMC layers. With increasing aging time, the coarsening of interfacial Ni₃Sn₄ IMC grains for pure Sn and Sn-3.5Ag solder was significantly greater than that of the interfacial (CuNi)₆Sn₅ IMC grains for Sn-0.7Cu and Sn-3.8Ag-0.7Cu solders. Furthermore, the Ni content in interfacial (CuNi)₆Sn₅ phase slightly increased during aging. A small addition of Cu (0.7 wt.%) resulted in differences in the type, morphology, and growth kinetics of interfacial IMCs. By comparing the metallurgical aspects and growth kinetics of the interfacial IMCs and the underneath P-enriched layers, the role of initial Cu and Ag in lead-free solders is better understood.     

Phase identification and growth kinetics of the intermetallic compounds formed during in-49Sn/Cu soldering reactions

For the application of In-49Sn solder in bonding recycled-sputtering targets to Cu back plates, the intermetallic compounds formed at the In-49Sn/Cu interface are investigated. Scanning electron microscopy (SEM) observations show that the interfacial intermetallics consist of a planar layer preceded by an elongated scalloped structure. Electron-probe microanalyzer analyses indicate that the chemical compositions of the planar layer and the scalloped structure are Cu_74.8In_12.2Sn_13.0 and Cu_56.2In_20.1Sn_23.7, respectively, which correspond to the ε-Cu₃(In,Sn) and η-Cu₆(In,Sn)₅ phases. Kinetics analyses show that the growth of both intermetallic compounds is diffusion controlled. The activation energies for the growth of η- and ε-intermetallics are calculated to be 28.9 kJ/mol and 186.1 kJ/mol. Furthermore, the formation mechanism of intermetallic compounds during the In-49Sn/Cu soldering reaction is clarified by marking the original interface with a Ta-thin film. Wetting tests are also performed, which reveal that the contact angles of liquid In-49Sn drops on Cu substrates decline to an equilibrium value of 25°C.     

Creep deformation of Sn-3.5Ag-xCu and Sn-3.5Ag-xBi solder joints

Creep properties of lead-free Sn-3.5Ag-based alloys with varying amounts of Cu or Bi were studied by single lap-shear test. Solder balls with five different compositions of Cu (0 wt.%, 0.75 wt.%, 1.5 wt.%) and Bi (2.5 wt.%, 7.5 wt.%) were reflowed on Cu. The Cu-containing alloy had a lower creep rate than the Bi-containing alloy. The Sn-3.5Ag alloy showed the lowest creep rate on Cu, implying that the Cu element already dissolved in the Sn-3.5Ag alloy during reflow. The Cu-containing alloy was strengthened by dispersed small precipitates of Cu₆Sn₅. As the Cu content increased up to 1.5 wt.%, the Cu₆Sn₅ coarsened and platelike Ag₃Sn intermetallics were found, which deteriorated the creep resistance.     

Intermetallic compounds formed during the reflow and aging of Sn-3.8Ag-0.7Cu and Sn-20In-2Ag-0.5Cu solder ball grid array packages

After reflow of Sn-3.8Ag-0.7Cu and Sn-20In-2Ag-0.5Cu solder balls on Au/Ni surface finishes in ball grid array (BGA) packages, scallop-shaped intermetallic compounds (Cu_0.70Ni_0.28Au_0.02)₆Sn₅ (IM1a) and (Cu_0.76Ni_0.24)₆(Sn_0.86In_0.14)₅ (IM1b), respectively, appear at the interfaces. Aging at 100°C and 150°C for Sn-3.8Ag-0.7Cu results in the formation of a new intermetallic phase (Cu_0.70Ni_0.14Au_0.16)₆Sn₅ (IM2a) ahead of the former IM1a intermetallics. The growth of the newly appeared intermetallic compound, IM2a, is governed by a parabolic relation with an increase in aging time, with a slight diminution of the former IM1a intermetallics. After prolonged aging at 150°C, the IM2a intermetallics partially spall off and float into the solder matrix. Throughout the aging of Sn-20In-2Ag-.5Cu solder joints at 75°C and 115°C, partial spalling of the IM1b interfacial intermetallics induces a very slow increase in thickness. During aging at 115°C for 700 h through 1,000 h, the spalled IM1b intermetallics in the solder matrix migrate back to the interfaces and join with the IM1b interfacial intermetallics to react with the Ni layers of the Au/Ni surface finishes, resulting in the formation and rapid growth of a new (Ni_0.85Cu_0.15)(Sn_0.71In_0.29)₂ intermetallic layer (IM2b). From ball shear tests, the strengths of the Sn-3.8Ag-0.7Cu and Sn-20In-2Ag-0.5Cu solder joints after reflow are ascertained to be 10.4 N and 5.4 N, respectively, which drop to lower values after aging. An erratum to this article is available at .     

Mechanisms for the intermetallic formation during the Sn-20In-2.8Ag/Ni soldering reactions

The morphology and growth kinetics of intermetallic compounds formed during the interfacial reactions between liquid Sn-20In-2.8Ag solder and Ni substrates are investigated. Energy-dispersive x-ray (EDX) analysis identifies the composition of the interfacial intermetallics as Ni₃(In_0.99In_0.01)₄. The soldering reactions at lower temperatures (225–275°C) result in the predominant formation of a homogeneous intermetallic layer whose growth is diffusion controlled. At higher soldering temperatures (300–350°C), the interfacial intermetallics appear to be long needlelike crystals, and the grooves in between the intermetallics provide fast-diffusion paths for Ni atoms to react with Sn atoms at the intermetallic front, which leads to interface-controlled growth kinetics. The intermetallic needles turned out to be flat slablike after selective etching of the unreacted solder. Kinetics analysis showed that they not only lengthened in the longitudinal direction, but also coarsened transversely by the Ostwald ripening mechanism.