CHAPTER 1
PHYSICAL METALLURGY OF SOLDER SYSTEMS
J. F. Roeder, M. R. Notis and H. J. Frost
Introduction
Man's use of Pb and Sn spans well over a millennium [I]. These metals have
been exploited for their low melting points and are particularly useful for
soldering applications. Klein-Wassink [2] points out that the Romans used a PbSn alloy for solder joining of pipes. The usefulness of this alloy system has not
diminished in the following centuries; today Pb-Sn alloys are used extensively in
electronic solder joint applications [2-41. A number of other alloy systems find use
in electronic packaging; however, this chapter focuses primarily on the Pb-Sn
system and its ternary extensions.
This chapter provides a brief overview of the physical metallurgy of solder
systems relevant to the issues of mechanical properties and the actual solder
joint behavior described in the following chapters of this book. The present
discussion is limited to microstructural evolution resulting from solidification
and as a result of thermal treatments excluding the effects of stresses induced as
a result of thermal cycling. Chapters 3, 5 and 6 describe the significant effects of
stress induced by thermal cycling on the microstructure itself. Many of the
phenomena occurring in the Pb-Sn eutectic system are not peculiar to that
system, and the fundamental aspects may be extended to other eutectic systems
of interest. Solidification behavior of the Pb-In system, which contains two
peritectic reactions, is also described and contrasted to that of the Pb-Sn system.
To illustrate how a solder joint might undergo important thermal fluctuations,
consider as an example the hermetic sealing of electronic package lids [5]. A
hierarchy of solders with different melting points are employed to produce the
final product. A high melting point solder, such as 95Pb-5Sn (wt.%), might be
used in the component itself; a solder of lower melting point, such as 85Pb-15Sn,
might be used for hermetic sealing; and finally, a solder of even lower melting
point, such as eutectic Pb-Sn, might be used to joint the sealed package to the
printed circuit board. In this sequence, the joining cycles of the lower melting
point solders act as high-temperature heat treatments for the 95Pb-5Sn solder.
Service conditions can also involve significant thermal excursions of a cyclic
nature; for example, -55" to 125°C in aircraft 161 or involving long hold times
during power-on with temperatures reaching up to 80°C [7]. We emphasize that
most solder alloys are in high-temperature service from the moment of
fabrication to the end of useful life; even room temperature is 65% of the absolute
melting point for the eutectic Pb-Sn alloy. Thus, the microstructures of solder
alloys can undergo significant changes as they attempt to evolve toward
equilibrium in response to thermal conditions.
Now that some practical conditions causing microstructural evolution have been
identified, the remaining discussion first considers microstructures resulting
from solidification and then turns to the various precipitation phenomena that
can occur as these structures experience thermal fluctuations. Both continuous
(discrete) [8, 91 and discontinuous (cellular) [lo-191 reactions are examined. In
Solder Mechanics - A State of the Art Assessment
Edited by Darrel R. Frear, Wendell B. Jones
and Kenneth R. Kinsman
The Minerals, Metals & Materials Society, 1991
Solder Mechanics
2
each case, important effects of the microstructure on mechanical properties are
highlighted. Finally, the effect of ternary elements on soldification and precipitation are described.
Phase Equilibria and SolidifmationMicrostructures in Binary Solder Systems
Pb-Sn SYSTEM
The equilibrium Pb-Sn system [71 is characterized by a single eutectic reaction
that occurs a t 183OC as shown in Figure 1. Within this system, near equilibrium
microstructures resulting from solidification can be divided into three classes
based on their bulk composition: eutectic, hypoeutectic, and hypereutectic.
Hypoeutectic and hypereutectic alloys refer to those alloys with Sn contents below
that of the eutectic composition (61.9 wt.% Sn) and above the eutectic composition,
respectively. Binary Pb-Sn solder microstructures have been described recently by
Klein-Wassink [2] and by de Kluizenaar [20]. We first consider eutectic solidification, followed by the off eutectic alloys.
Weight Percent Tin
0
20
10
,
.....,I.
,
30
. ., -
40
,
50
, ,
,. . .. . ,
,
,
,
60
. I , . .
70
,
., ./ ., ..
90
80
I-.!
100
- ,
1327 502.C
3
0
- ,
0
...., .. ...
Ib
,
.. . , .....
20
0
, ,
., ,
$0
d0
Atomic Percent Tin
Pb
Figure 1
. . . , , . .i0
$0
80
90
100
Sn
Pb-Sn equilibrium phase diagram [71.
Equilibrium solidification of a Pb-Sn alloy with the eutectic composition follows
the eutectic reaction
Liquid
+ a-Pb + P-Sn
Chapter 1: Physical Metallurgy of Solder Systems
3
where the homogeneous liquid solution is stable above 183OC and separates into
two solid phases, a-Pb (FCC) and P-Sn (BCT), which are stable below 183OC. The
microstructure formed by this reaction consists of alternating lamellae of a-Pb
(light) and P-Sn (dark) as shown in the backscattered electron image in Figure 2.
Each region in which the lamellae are oriented in the same direction is tenned a
"colony" (an analogous term to "grain" that describes a region of uniform
crystallographic orientation in single-phase alloys). Individual lamellae grow by
rejection of solute (Sn for the a-Pb lamellae and Pb for the P-Sn lamellae) from the
liquid ahead of one lamella into the liquid ahead of its neighbor as the growth
front advances [21]. The interlamellar spacing varies with cooling rate due to a
balance of free energy contributions to the driving force for the eutectic reaction:
that of redistribution of solute a t the advancing front by diffusion and interfacial
energy between lamellae. In practice, slower cooling (where the reaction
proceeds more slowly) results in wider interlamellar spacing as shown by the
following relationship [21]:
where s is the interlamellar spacing and R is the velocity of the reaction front.
Colony size also varies with cooling rates due to the relationship of nucleation to
undercooling. Faster cooling enhances the number of colony nuclei formed, and
therefore colony size increases with slower cooling rates [22]. At sufficiently fast
cooling rates, the eutectic structure loses its lamellar character as shown in
Figure 3.
Figure 2
Backscattered electron
Figure 3
micrograph of slowly cooled
eutectic Pb-Sn alloy showing
a-Pb (light) and P-Sn (dark)
lamellae. After de Kluizenaar
[201; courtesy of Wela
Publications, Ltd.
Backscattered electron
micrograph of rapidly cooled
eutectic Pb-Sn alloy showing
a-Pb (light) and P-Sn (dark)
non-lamellar structure. After
de Kluizenaar [201; courtesy of
Wela Publications, Ltd.
Both colony size and interlamellar spacing are important factors in determining
mechanical properties of the eutectic alloy. It has recently been demonstrated
that isothermal fatigue life decreases with increasing colony size [22]. In
addition, the tensile strength of unidirectionally solidified eutectic alloys [23] and
tensile strength and ductility of randomly solidified eutectic alloys 1221 vary with
Solder Mechanics
4
interlamellar spacing. It is therefore important to understand these parameters
in the actual solder joint when applying the constitutive models discussed in
detail in this book.
An additional phase appears in the solidified microstructure of off eutectic alloys.
This phase is termed the proeutectic (meaning "before eutectic") phase because it
forms on cooling before the eutectic reaction temperature is reached. In
hypoeutectic alloys, the proeutectic phase is primarily a-Pb, as shown in Figure
4. Dendrites of the proeutectic phase begin to form when the liquidus line is
crossed for the bulk composition of the alloy of interest. The composition of the
first solid to form is given by the end of the tie-line opposite that defined by the
liquidus temperature for the bulk composition of the alloy [24]. As cooling
continues, the composition of the solid phase changes as defined by the solidus
end of the tie-line. At bulk compositions above the solubility limit of Sn in Pb (19.2
wt.%), a fraction of liquid remains in the melt when the eutectic temperature is
reached. This remaining liquid is then converted to solid phases through the
eutectic reaction. The resulting microstructure consists of proeutectic a-Pb
surrounded by the eutectic reaction product.
In hypereutectic alloys, solidification is directly analogous to hypoeutectic alloys
except that the proeutectic phase is P-Sn. Figure 5 shows a typical hypereutectic
alloy in the as-solidified condition.
Figure 4
Backscattered electron
micrograph of as-solidified
hypoeutectic Pb-Sn alloy
showing proeutectic a-Pb
dendrites (light). After de
Kluizenaar 1201; courtesy of
Wela Publications, Ltd.
Figure 5
Backscattered electron
micrograph of as-solidified
hypereutectic Pb-Sn alloy
showing proeutectic P-Sn
dendrites (dark). After de
Kluizenaar [201; courtesy of
Wela Publications, Ltd.
Pb-In SYSTEM
The equilibrium phase diagram for the Pb-In [25] system differs markedly from
that of the Pb-Sn system because it contains two peritectic reactions as shown in
Figure 6. Also, the solid solubility for In in Pb is very large (> 50 wt.%). Given the
wide range of solubility for In in Pb coupled with the peritectic reaction, Pb-rich
alloys generally consist solely of primary Pb dendrites. For more In-rich alloys,
such as 50Pb-50In, i t is possible to reach the peritectic reaction
Chapter 1: Physical Metallurgy of Solder Systems
Liquid + Pb + a
with sufficiently rapid cooling. A peritectic reaction product would normally
form a n envelope around the primary Pb dendrites. However, in the 50Pb-50In
alloy, the predominant constituent in the microstructure is the primary Pb
dendrites. In this case, the peritectic reaction product is contained in the pockets
of liquid remaining when the solidification process is complete.
M e ~ g h tP e r c e n t L e a d
0
350;
10
,
...,
In
Figure 6
30
20
1
,
40
, ,
,
50
,
,
60
-I1 --
70
80
gO
100
+
.
Atomic P e r c e n t Lead
Pb
Pb-In equilibrium phase diagram L251.
MicrostructuralEvolution in the Solid State
Discussion thus far has concentrated on as-solidified microstructures. The microstructure of such a n alloy may evolve further toward equilibrium 1261 under
service conditions involving elevated temperature holding time or even a t room
temperature, which, as pointed out earlier, is a significant fraction of the
melting point of the alloys under consideration. Solid-state diffusion a t these
temperatures leads to dramatic changes in microstructure.
COARSENING
The driving force for solid-state microstructural evolution stems from interfacial
surface energy. A given microstructure attempts to minimize its total interfacial
energy by reducing the interfacial area within it [271. In a single-phase alloy, this
leads to grain growth. In the case of a multiphase alloy, the feature sizes of the
as-solidified alloy increase and may change character in a process known as
Solder Mechanics
6
coarsening. While coarsening occurs in Pb-Sn alloys a t room temperature over
extended periods of time, the process is accelerated at elevated temperature due
to increased diffision. This is illustrated in Figure 7 reproduced from KleinWassink [2] where a 65Pb-35Sn alloy is shown in the as-cast condition and after
an isothermal heat treatment of 300 h a t 155OC. Coarsening also occurs in
association with fatigue crack propagation during thermal fatigue. Chapter 5
describes this effect.
Figure 7
Light optical micrographs showing coarsening in 65Pb-35Sn alloy: (A) as-cast, (B)
after 300 h a t 150°C. The a-Pb phase is dark, P-Sn phase is light. After KleinWassink [21; courtesy of Electrochemical Publications, Ltd.
PRECIPITATION
Precipitation reactions occur readily in the a-Pb phase in the Pb-Sn system due to
its large solubility for Sn at high temperatures. The equilibrium phase diagram
in Figure 1shows that the solubility of Sn and Pb is 19.2 wt.% at 183OC. With
decreasing temperature, the solubility limit for Sn drops considerably; at 20°C,
the solubility limit for Sn is -2 wt.%. Careful inspection of the proeutectic a-Pb
dendrites (dark) in the light optical micrograph shown in Figure 8 reveals 0-Sn
(light) precipitates dispersed throughout the phase. These precipitates develop
because the a-Pb formed during solidification has a composition rich in Sn
compared to that which is stable at low temperature.
Figure 8
Light optical micrograph of slowly solidified 65Pb-35Sn alloy. a-Pb phase is dark, PSn phase is light. After Klein-Wassink [21; courtesy of Electrochemical
Publications, Ltd.
Chapter 1: Physical Metallurgy of Solder Systems
Precipitation may also occur due to a classical solution treatment and aging
sequence [28]. For example, consider an alloy of 5 wt.% Sn. If this alloy is heated
above -lOO°C, it crosses the a-(Pb1a)-Pb+P-Snsolvus line and enters the single
phase a-Pb region where the alloy becomes single phase, given the required time
interval (solution treatment). Rapid cooling results in a supersaturated solid
solution a t temperatures below the solvus. During subsequent aging,
precipitation of P-Sn occurs to relieve the metastable state of supersaturation.
Continuous Precipitation
Both continuous (discrete) [8, 91 and discontinuous (cellular) precipitation [lo-191
of P-Sn has been observed in Pb-rich alloys. Frear et al. [9] recently showed that
the nature of the precipitation reaction in a 95Pb-5Sn alloy depends upon the
cooling rate from the solution treatment temperature. Discrete precipitation is
favored under rapid cooling while cellular precipitation was found to occur for
slower cooling rates. Discrete P-Sn precipitates are shown in the transmission
electron microscope (TEM) image in Figure 9. These precipitates were found t o
occupy a (111)type habit plane with the orientation relationship (1ll)pb N ( 0 1 0 ) ~ ~
and [Olllpb // [OO1lsn.
Figure 9
Transmission electron microscope bright field image of P-Sn continuous
precipitates in a 5Sn-95Pb alloy. Courtesy of Frear et al. [91.
The precipitates that often occur in the proeutectic phase upon cooling described
earlier (Figure 8) appear to be of the continuous type. This most likely occurs
because the Sn content in the dendrites is relatively high, and therefore the a(Pbla)-Pb+P-Sn solvus is crossed a t a correspondingly high temperature on
cooling. At higher temperatures, volume (lattice) diffusion is enhanced
Solder Mechanics
8
compared to grain boundary diffusion, and discontinuous precipitation occurs
via grain boundary diffusion (this is discussed later).
Discontinuous Precipitation
The precipitation reaction in low-Sn alloys usually proceeds as discontinuous
precipitation in which cells of lamellae of the Sn phase nucleate a t the grain
boundaries and grow into the matrix. This process, also known as cellular
precipitation, has been well studied in Pb-Sn alloys by Turnbull and Treaftis [ l l ,
121 and Tu and Turnbull [13-171. Other studies are summarized elsewhere [19,
29-33]. The process begins with nucleation of particles of the Sn phase along the
grain boundaries of the original solid solution matrix. These particles typically
have a particular crystallographic orientation with respect to one or the other of
the parent grains. Tu and Turnbull [I31 reported the same relationship as
observed by Frear et al. [9] for continuous precipitation: ( 1 l l ) p b N ( 0 1 0 ) and
~~
[ O l l l p b N [OO1]sn. The Sn particles then grow as a colony of lamellae in the
direction of the grain with which they did not have a special orientation
relationship, accompanied by the migration of the grain boundary. This behavior
evidently minimizes the energy of the Pb-Sn interfaces, and it allows the diffusion
required to gather the Sn to occur along the high-diffusivity path of the grain
boundary. The discontinuous precipitation process is generally favored over
continuous precipitation under conditions in which the availability of the highdiffusivity path is important. This is usually a t relatively low temperatures
(compared to the melting temperature) because the ratio of grain-boundary
diffusivity to lattice difisivity increases dramatically as the temperature is
lowered. The discontinuous precipitation reaction therefore becomes more
evident for lower Sn concentrations, because for a given slow cooling rate, the
precipitation occurs a t higher temperatures for higher Sn concentrations. For
the alloy of Pb-3.5 wt.% Sn the transformation a t room temperature produces an
interlamellar spacing that is easily observed optically, and a transformation rate
that is slow enough for convenient metallography. Figure 10 shows some cells of
Sn lamellae during the early stage of growth. For higher Sn concentrations, the
interlamellar spacing is finer, and can become difficult to resolve optically.
Figure 11 shows how the cells grow out from grain boundary facets to consume
the matrix for the Pb-5 wt.% Sn alloy.
Figure 10
Microstructure of Pb-3.5 wt.% Sn aged a t 23'C after solution annealing. The
individual Sn lamellae are visible growing out from the grain boundaries in cells.
Chapter I : Physical Metallurgy of Solder Systems
Figure 11
Micrographs of Pb-5 wt.% Sn alloy aged a t -16°C for various times after solution
annealing. At this magnification, the lamellae of the Sn phase are too small to
resolve. The series shows how the cells (which appear dark) nucleate a t the grain
boundary facets and grow out to consume the matrix. A) Aged 16 hrs, transformed
fraction = 5%, B) Aged 30 hrs., transformed fraction = 24%,C) Aged 72 hrs.,
transformed fraction = 58%, D)Aged 97 hrs., transformed fraction = 85%.
The progress of the precipitation transformation is usually described in terms of
the Avrami equation that gives the volume fraction transformed f as a function of
time t based on random nucleation followed by growth to impingement:
where the constant K depends on temperature, and n is an exponent that is
typically between 1 and 4 1281. Experimental measurements of K and n allow
quantitative calculations of the extent of the phase transformation. Care must be
taken, however, to understand how K and n depend on the microstructure and
conditions to avoid invalid extrapolations. The kinetic constant K depends on both
the cell boundary velocity and the nucleation rate or the density of nucleation
sites. The value of n depends on both the nucleation conditions and the growth
geometry or dimensionality. For continuous nucleation (at random locations, a t a
constant rate per unit of untransformed volume) of spherical regions (cells), with
a constant growth rate, we find that n = 4. For simultaneous nucleation (at t = 0,
a t random sites), with cell growth as spheres, we find that n = 3. For twodimensional models (growing circles), continuous nucleation gives n = 3, and
simultaneous nucleation gives n = 2: one-dimensional models give n = 2 and n =
1,respectively. Lutender [33,341 found n = 2 for alloys with 2.0 to 5.0 wt.% Sn.
Solder Mechanics
10
Turnbull and Treaftis [12] found n = 3 for alloys with 6.7 to 10.5 wt.% Sn. The
difference between these results is not well explained. It may be due to the
difference in composition, or perhaps to a difference in grain size and specimen
size. Lutender used bulk samples with a n initial grain size of 0.5 to 1.0 mm.
Turnbull and Treaftis used wires that were cast in small pyrex tubes with a n
inside diameter of about 0.5 mm. The value of n = 2 is consistent with a onedimensional model in which cells grow out from grain-boundary facets in such a
way that their volume increases (on average) only linearly with the distance the
cell boundary moves. In general, we must expect K to depend on the grain size
because i t should depend on the density of boundary nucleation sites. We may
also expect both K and n to depend on the ratio of grain size to sample size,
particularly if surface nucleation is important.
A quantitative evaluation of the transformation kinetics has been experimentally
achieved for a range of compositions. Figure 12 shows this in terms of a timetemperature-transformation curve. The temperature for the maximum
transformation rate increases with increasing Sn content. For 3 to 5 wt.% Sn, the
maximum rate is near room temperature; for 2 wt.% Sn, i t is a t a lower
temperature. For practical purposes, transformation in the 2 wt.% Sn alloy
requires many days, but in the 5 wt.% Sn alloy a t 20' to 40°C, i t is completed
within one day. A more fundamental treatment could be derived from
measurements of the cell boundary velocity as a function of composition and
temperature, coupled with a quantitative model of the nucleation behavior. A
series of papers [lo, 35-42] have attempted to construct theoretical models to
predict cell boundary velocity and the interlamellar spacing. Zener's early
treatment [35] of the eutectoid transformation (such as austenite to pearlite in
steels) first recognized that the available chemical-driving free energy must be
spent on both the creation of new interfaces between the lamellae of the new
phases, and on driving the diffusive fluxes to achieve the phase separation. On
this basis, he derived a n expression for the velocity of the transformation front v
as a function of the interlamellar spacing S of the form
v = (kinetic constants) - I---
( Sgin)
where S,;, is the minimum spacing that could be obtained if all the driving free
energy went into interface creation. The maximum velocity occurs for a
particular spacing (at S = 2 Sminin the equation shown), but there are other
combinations of velocity and spacing that are admissible solutions. Turnbull [lo]
adapted Zener's theory for the case in which the diffusion is limited to the grain
boundary or interphase interface, as is expected in dilute Pb-Sn alloys. In this
case, a n addition factor of (11s) must be included in the equation for velocity.
Cahn [36] pointed out that the relationship between velocity and spacing depends
on another kinetic parameter that describes the mobility of the boundary of the
reaction. The driving free energy must also supply the free energy that is
dissipated in the diffusive process of boundary migration, in addition to that
dissipated in diffusion along the boundary or stored in interlamellar interfaces.
Finally, there is a component of the driving free energy that is not dissipated by
the process, but is stored in the supersaturation that remains in the phases
produced by the precipitation. Hillert [38-401 has developed more detailed models
of the process based on the four components of free energy loss or storage. In his
Chapter 1 : Physical Metallurgy of Solder Systems
11
treatment, there remains a range of permissible velocity and spacing values. The
minimum spacing is given in Zener's treatment. Sundquist [41] showed that a
maximum spacing can be estimated by considering that if two neighboring
lamellae become too widely spaced, a new lamella can nucleate between them.
Solorzano and Purdy [421 propose that the optimal spacing is that for which the
rate of dissipation of free energy is a maximum. This is generally a different
spacing from that which produces the highest velocity, but should be related. As
a general conclusion here, we do not expect that any theoretical treatment will be
sufficiently simple and convenient to give cell boundary velocity as a function of
temperature and composition, and we must depend on experimental
observations.
50%TRANSFORMATION
TIME (HOURS)
Figure 12
Time required for a 50% transformation for the precipitation reaction in Pb-Sn
alloys of various compositions. The curves for 2 to 5 wt.% Sn are from
metallographic observations [341. Those for 6 and 9 wt.% Sn are taken from the
resistivity measurements of Borelius e t al. 1531.
Early studies of the cellular precipitate structure 111, 291 discovered that the
average spacing between Sn lamellae decreased with increasing Sn
concentration and decreasing precipitation temperature. This is certainly the
expected behavior for a diffusion-controlled phase transformation, and was
confirmed by Frost et al. [18,34,43]. Figure 13 shows the variation in
microstructure produced by different precipitation temperatures. Figure 14
shows that the reciprocal of interlamellar spacing decreases approximately
linearly with increasing temperature. The interlamellar spacing can be an
important element of the microstructural state because it can strongly affect the
flow stress of the alloy. The precipitation process removes Sn from the Pb matrix
and therefore reduces a strengthening component due to the solid solution.
Solder Mechanics
12
However, the precipitation adds a strengthening component, analogous to grain
size strengthening, which is probably proportional to the inverse square-root of
the interlamellar spacing. Speich [44] found that relationship for the hardness of
Fe-30 Ni-6 Ti, and Nakase and Bernstein [451 found i t for the yield strength of
various pearlitic steels. When the interlamellar spacing of Pb-Sn is smaller than
about 1 pm, the precipitate structure strengthening outweighs the loss of solid
solution strengthening and becomes significant [34].
Dissolution Behavior
When the temperature is raised above the solvus temperature, the precipitate
structure begins to dissolve. This process may be as complicated as the
precipitation. One possible mechanism is the direct diffusion of the Sn into the Pb
phase. Another mechanism is the retraction of the cell boundaries as a reversal
of the cellular precipitation process, as shown in Figure 15. The grain
boundaries here provide a fast diffusion path for the dispersal of the Sn into the
Pb phase. This process is dominant a t the relatively lower temperatures only
slightly above the solvus. Higher temperatures result in faster dissolution, both
because of the temperature dependence of the diffusion coefficients and because
the thermodynamic driving force for dissolution increases with temperature.
The apparent activation energy for the process is therefore not directly
comparable to the activation energy of the rate-limiting diffusion process.
Figure 13
Scanning electron micrographs of the Pb-5 wt.% Sn alloy showing the variation of
interlamellar spacing with the aging temperature at which the cellular precipitation
took place. Aged at: A) 40"C, B) 23'C, C) O'C and D)-20'C.
Chapter I : Physical Metallurgy of Solder Systems
TEMPERATURE
("C)
Figure 14
Reciprocals of interlamellar spacings a s a function of transformation temperature,
for various Sn concentrations. Data for 2.0, 3.0, 3.5 and 5.0 wt.% Sn are from
Lutender [331. Data for 4.1 wt.% are from Liu and Aaronson [291. Data for 6.7, 7.5,g.O
and 10.5 wt.% Sn are from Turnbull and Treaftis [Ill.
Figure 15
Scanning electron micrographs showing the progressive dissolution of the
precipitate structure in the Pb-3.5 Sn wt.% alloy a t various annealing times a t 90°C
[431. The precipitation was formed during aging a t 23°C. The regions containing Sn
precipitates appear light. Each micrograph shows nearly the same region, but a t a
slightly different depth because of the microtoming and etching needed for each
photograph. At later times, there is evidence of spheroidization. Aged at: A) 38 hr.
90"C, B) 89 hr. 90"C, C) 205 hr. 90°C and D) 370 hr. 90'C.
14
Solder Mechanics
Tu and Turnbull [16] observed that dissolution by cell boundary retraction would
occur even a t temperatures slightly below the solvus. (The effect extends to about
10°C below the solvus.) One driving force for this retraction is the surface energy
of the interfaces between the Pb and Sn phases. Frost et al. [431 have reported that
the rate of dissolution by cell boundary retraction increases with smaller
interlamellar spacings. This effect results both from shorter diffusion distances
required to disperse the Sn and from the additional driving force for retraction
provided by the interphase interfaces. The dissolution rate therefore depends on
the temperature a t which the precipitate structure initially formed.
The rate of cellular dissolution was described by Tu and Turnbull [16] in terms of
the velocity of the cellular interface v, which depends on the interlamellar
spacing S, and the grain boundary thickness and diffusion coefficient 6Db. A
related formulation is given by Gupta and Nakkalil [46,47], based on the
formulation for cellular precipitation of Peterman and Hornbogen [48]:
In this formula, k is the ratio of the solute concentration of the matrix obtained as
a result of the cellular dissolution to the solute concentration in the boundary (the
segregation ratio), and AGd is the driving force available for dissolution. R is the
gas constant and T is temperature. (The sign of AGd must be negative for the
dissolution velocity to be positive.) Part of the driving force is due to the chemical
free energy change AGdC when the depleted a phase and the P phase transform
into a more concentrated a phase. Another component of the driving force is due
to the release of the surface free energy of the alp interface released during
dissolution. The total driving force is then:
where y is the surface free energy and Vm is the molar volume. In this
formulation, we see that the total driving force AGd can be negative (implying
dissolution) even if the chemical driving force AGdC is positive, because of the
driving force for dissolution produced by the interfaces. This agrees with the
observation of Tu and Turnbull that dissolution by cell boundary retraction may
occur a t temperatures slightly below the solvus. We also see that the dependence
of velocity on interlamellar spacing is more complicated than just the inverse
spacing squared.
The chemical driving force available for dissolution may actually be a
complicated matter. Cellular precipitation cannot produce exactly the
equilibrium compositions for the given precipitation temperature, because exact
compositional equilibrium cannot be reached in a finite time. The Pb matrix is
supersaturated with Sn, the Sn is slightly supersaturated with Pb, and the
degree of supersaturation should depend on the precipitation temperature. The
dissolution therefore requires less diffusion than i t would for compositions that
were in equilibrium solvus a t the precipitation temperature. Such variations in
Chapter I : Physical Metallurgy of Solder Systems
15
composition should have pome effect on dissolution rates, but probably less effect
than variations in the interlamellar spacing.
During the process of dissolution by cell boundary retraction, there is also an
evolution in the structure of Sn lamellae within the cells. The Sn phase actually
occurs as blades with numerous rifts and holes instead of complete plates [13].
The lamellae are therefore subject to instabilities due to capillarity effects that Pb
to breakup of the lamellae and spheroidization. This spheroidization was
observed by optical metallography [33, 34,491, as shown in Figure 16. During the
spheroidization process, there is also some dissolution of the Sn phase by lattice
diffusion directly into the Pb matrix. For temperatures near the solvus a t low Sn
concentrations, the lattice diffusion is so slow that direct dissolution by lattice
diffusion is not completely accomplished before the cellular dissolution is nearly
complete. Cellular dissolution by cell boundary migration continues after the
spheroidization has become prominent, but the boundaries appear to slow down.
Spheroidization should reduce two components of the driving force for the cell
boundary migration. It reduces the area of lamella-matrix interface, and i t also
disperses some Sn into the Pb matrix, thereby reducing the chemical driving
force for cell boundary migration.
Figure 16
Microstructure of Pb-5 wt.% Sn after precipitation a t room temperature, followed by
annealing at 100°C for 64 h [491. Most of the precipitate structure has undergone
cellular dissolution; in those regions that have not, the lamellar Sn precipitates have
undergone spheroidization.
The cellular dissolution process can also be analyzed in terms of the Avrami
transformation equation (Equation 21, in which f is taken to be the fraction in
which the cellular precipitate has dissolved. Stone [49] found that for dissolution,
the exponent n was about 1. This is the same as Gupta [46] found for a Cu-In
alloy, and Sulonen [50] found for Cu-Cd alloys. It is distinctly less than the n = 2
observed for precipitation. The value n = 1is consistent with a model of onedimensional growth from a constant number of initial nuclei. In this context, the
Avrami transformation equation implies that the cell boundaries that moved to
allow the precipitation are evidently immediately available for reversed
16
Solder Mechanics
migration to produce dissolution, without any (random) waiting or incubation
time for particle nucleation or cell initiation.
Discontinuous Coarsening
Just as the precipitate microstructure is unstable to coarsening and
spheroidization during dissolution above the solvus, i t is also unstable below the
solvus. The initial cellular precipitation process cannot produce a
microstructure that is completely a t equilibrium. There must be some free
energy of the interfaces between the two phases, and the compositions of the two
phases will deviate from their equilibrium values. These factors provide a driving
force for evolution towards a coarser microstructure. If the Sn were distributed
in small spherical particles, then those particles should coarsen in the usual
manner. Frear et al. [9] report a decrease in hardness during aging, which is
directly attributable to such coarsening. If the Sn were distributed in planar
lamellae, without imperfections, then coarsening might occur in a
discontinuous fashion by the passage of interfaces that consumed the fine
lamellae and left behind coarse lamellae. Although the process of discontinuous
or cellular coarsening has long been recognized [48, 511, i t has not yet been
quantitatively studied in Pb-Sn alloys. Fournelle [52] has successfully modeled
the kinetics of the process, including both the chemical and the interfacial
driving forces. The velocity of the coarsening front depends on both the new
interlamellar spacing and the previous interlamellar spacing. It therefore must
depend upon the temperature of the initial precipitation process. If the
precipitation and coarsening temperatures are allowed to be different, the
general formulation becomes complicated. In any event, we expect that the
cellular coarsening process would be much slower than the cellular precipitation
(for a given temperature), and will therefore become important only for extended
dwell times a t intermediate temperatures below the solvus. It probably accounts
for the overaging (softening aRer several months) a t room temperature reported,
for example, by Frost et al. [34].
MICROSTRUCTURES FAR FROM EQUILIBRIUM
Superplastic behavior of the Pb-Sn eutectic has received sigriificant attention [54571. When the eutectic Pb-Sn alloy is in the superplastic state, it exhibits
unusually large ductilities: up to 4850% elongation in tensile testing [56].
Improved fatigue behavior might be expected with such a ductile alloy. Chapters
3 and 6 discuss this in detail.
Unfortunately, the Pb-Sn eutectic alloy must be heavily cold worked to induce the
recrystallization necessary to produce the required small grain size (< 1 pm)
[58] to obtain a superplastic condition. During discussion a t the workshop, i t was
further suggested that rapid cooling might be used to produce a small grain size.
-
Like superplasticity, rapid cooling of Pb-Sn alloys has received much attention
[59-621. It has been shown [61,621 that the eutectic behavior of the equilibrium
system gives way to a peritectic reaction involving a metastable Pb phase ( a l )
under rapid cooling. These investigations have generally involved the use of
small droplets of alloy that can be cooled from the melt a t rapid enough rates t o
induce sufficient undercooling to form the metastable a1 phase. The question as
to whether sufficiently small grain size of the eutectic alloy could be achieved by
Chapter 1: Physical Metallurgy of Solder Systems
rapid cooling, without cooling too fast and causing the formation of the
metastable a1 phase, remains open. It seems likely that such a cooling rate
would be difficult to apply to electronic packages due to the thermal shock it
would impart.
Ternary Element Additions
The effects of third element additions to binary solder systems, such as for Pb-Sn
solders, include
Reactions between binary solders and substrates (which provide the
third element) and which form intermetallic layers by reactiondiffusion. (These are described in Chapter 2).
Modification of melting-solidification temperatures and wetting
characteristics by third element addition, and which may therefore be
of significant importance to aid in manufacturing.
Formation of distributed third-phase intermetallics as a consequence of
third element additions, and which could affect a broad range of
mechanical properties, strength, creep behavior and fracture. In the
latter case, although significant ternary effects are expected, these
effects have not been clearly elucidated-no definitive work on the effect
of distributed intermetallic phases upon mechanical properties of
solders has been performed
The most studied Pb-Sn-X ternaries include Pb-Sn-Cu and Pb-Sn-Au because of
bonding of Pb-Sn solders to Cu printed circuit boards or to Au-plated Si devices:
Pb-Sn-Ag because of its use as a ternary solder alloy system and Pb-Sn-Bi because
of its low ternary eutectic melting temperature. A useful summary of
information on ternary Pb-Sn-X systems is given by Steen and Becker [63] and is
included in modified form in Table 1. It is convenient to categorize the various PbSn-X ternary systems according to the proximity of the ternary eutectic ET with
respect to the binary Pb-Sn eutectic (EB).
Table 1. Relationship of Ternary Pb-Sn-X to Binary Pb-Sn
ET near EB (wt.%)
ET distant from EB
No ET
The amount (volume fraction) and morphology of the third phase may be
estimated from a knowledge of phase equilibria and surface energies for each of
18
Solder Mechanics
the phases encountered. Thus, with reference to the schematic ternary diagram
shown in Figure 17, a t the eutectic liquid composition, and the three solid eutectic
phases in equilibrium with x, y, and z, then
Because x and y are closest to the A and B corners respectively, they may be
considered as the solid solution limits of the binary A-B (for example, Pb-Sn)
system, and z may be considered as the composition of the third component phase
(for example, AggSn and AuSnq). As the equilibrium liquid eutectic composition
moves closer to the A-B binary side of the diagram, or as the position of the third
component phase moves further away from the A-B binary ( the intermetallic
phase contains a lesser amount of A or B), then the % z will decrease.
Figure 17
Schematic demonstrating the equilibrium tie triangle for the four-phase eutectic
reaction X + Y + Z.
Many intermetallic phases tend to be faceted, elongated, and needle-like, platelike or blade-like in shape, because of the large directional anisotropy in their
surface energies and growth rates as related to their crystal structures [64]. In
addition, third element impurities commonly lead to segregation a t the liquidsolid interface during solidification which in turn can lead to cellular interfaces
and dendritic growth. Therefore, depending upon the specific system and
solidification conditions, the morphology of the intermetallic phases can range
from rounded-dendritic to faceted-elongated.
The effects of third element impurities on surface energies as related to wetting
behavior are discussed by Steen and Becker [63]. They propose that the wetting
force is lowered most strongly by (1)impurities which have eutectics very close to
Chapter 1: Physical Metallurgy of Solder Systems
the binary solder eutectic (for example, As, Fe, Ni) and which tend to form
intermetallics that are present in the liquid during soldering, and (2) impurities
that tend to enhance oxidation (for example, Al, In, Sn). At the same level of
addition, Cu, Ag and Au all have lesser effects on wetting force than those
mentioned above. Carol1 and Warwick [651 indicate that addition of Bi(0-4 wt.%)
or Sb(0-5 wt.%) reduce the surface tension of 60Sn-40Pb, while Cu(0-0.6 wt.%),
Ag(0-4 wt.%) and P(0-0.013 wt.%) increase surface tension. For the cases of Bi
and Sb versus Cu and Ag, this effect appears related to the difference in
segregation behavior of these elements a t the Sn-Pb solder interface.
A short summary of recent work related to phase equilibria and microstructure
for each of the ternary Pb-Sn-X systems follows. Table 2 also contains this
information.
(Pb-Sn) - Ag: A recent summary of this system, but without figures, has been
given by Petzow and Effenberg [66]. The liquidus surface is given in Hofmann
[67]. The ternary eutectic has been determined by Earle [68] to be a t 1.35 wt.% Ag,
62.5 wt.% Sn, and 36.15 wt.% Pb, and 178°C;the ternary eutectic phases are
AggSn, Pb and Sn. Tarby and Notis [691 have performed a thermodynamic
analysis to evaluate the lowering of the Pb-Sn eutectic temperature, which was
found to decrease by 3.3OC by the addition of 1wt.% Ag; this value was in good
agreement with experimental determinations.
Figure 18 shows the microstructure of a eutectic Pb-Sn solder with 2 wt.% Ag
addition. This alloy is slightly Ag-rich with respect to the ternary eutectic
composition, and primary-phase AgaSn is observed in the alloy. Surrounding the
AggSn primary-phase is a "halo-like" region (Figure 18B) which is depleted by
Ag. Due to non-equilibrium cooling and the presence of the primary AggSn, only
the Pb-rich and Sn-rich phases are nucleated by the pre-existing phase. The true
ternary eutectic solidification microstructure of three solid phases growing
cooperatively is observed only outside this "halo-like" region. Thwaites [70] has
used deep-etching studies to show that the AggSn phase can appear as thin
rectangular platelets; therefore the two-dimensional images shown in Figure 18
can be misleading concerning the true morphology of the third intermetallic
phase in a ternary microstructure.
Hoyt [71 indicates that a 2 wt.% Ag addition provides both increased solder
strength and refined eutectic structure, and more recently, Hwang and Vargas
[72] have noted superior creep resistance for Ag-containing solders.
(Pb-Sn) - Au: This system has been reviewed recently by Prince, Raynor and
Evans 1731. Of the Pb-Sn-X systems studied in the literature, this is by far the
most complex, and only the most pertinent reactions are listed here. There is a
ternary eutectic (Pb) + (Sn) + AuSnq (near the Pb-Sn binary eutectic) a t 177OC
with composition 3.0 wt.% Au, 32.5 wt.% Pb, and 64.5 wt.% Sn. There is a second
ternary eutectic (Pb) + AuSn + AuPbg at 211°C, very close to the Pb-AuPb3 binary
eutectic.
Because of the considerable importance of this ternary system for a number of
manufacturing processes, i t is of interest to understand the effect of changing the
Au concentration with respect to a eutectic Pb-Sn solder. The liquidus surface in
the Pb-Sn-Au system near the binary Pb-Sn eutectic, showing solidification paths
20
Solder Mechanics
for 60Sn-40Pb solder with 1wt.% and 5 wt.% Au is shown in Figure 19A. For 1
wt.% Au, the primary crystallization is Pb, followed by the Pb-Sn three-phase
reaction line, and ending a t the ternary Pb-Sn-AuSnq ternary eutectic. For 5
wt.% Au, the primary crystallization of Pb gives way to the Pb-AuSnq three-phase
reaction line, and ends a t the ternary eutectic. The AuSnq which is produced by
the three-phase reaction is much coarser than that produced in the ternary
eutectic reaction; this is shown in Figure 19B. The finer Pb-Sn-AuSnq ternary
eutectic microstructure appears towards the top of this figure.
Figure 18
Backscattered electron (A), wave length dispersive spectroscopy (WDS)-Ag X-ray
(B), WDS-Pb X-ray (C), and WDS-Sn X-ray (Dl images of a eutectic Pb-Sn alloy
with 2 wt.% Ag.
(Pb-In) - Au: SGTE (Scientific Group Thermodata Europe) has performed an
assessment of thermodynamic data for the condensed phases in the Au-In-Pb
ternary system. Experimental work on this system has recently been reviewed by
Prince, Raynor and Evans [73]. Most of the ternary field involving reactions with
the liquid is dominated by a liquid-liquid immiscibility region. There is a ternary
eutectic near the Pb corner, (Pb) + AuIn + AuPbg a t 207.5%.
(Pb-Sn) - Bi: The most recent evaluation of this system is given by Osamura [74].
The lowest temperature reaction involving the liquid is the ternary eutectic a t 50
wt.% Bi, 32.5 wt.% Pb, and 17.5 wt.% Sn a t 96'C. There are two ternary peritectic
reactions in the system; the one closest to the Pb-Sn binary eutectic is a t 32.6 wt.%
Bi, 40.8 wt.% Pb, 26.6 wt.% Sn at 137.q°C.
(Pb-Sn) - Cd: This is a simple system with a ternary eutectic a t 18 wt.% Cd, 32
wt.% Pb, and 50 wt.% Sn, and 145°C [75]. Savintsev et al. [76] have studied
interdiffusion reactions a t 160°C and give an isothermal section a t that
temperature. Major and Rutter [771 have performed directional solidification
studies of the ternary eutectic and have examined the crystallographic
Chapter 1: Physical Metallurgy of Solder Systems
21
orientation relations between the solid-phases, as well as the nature of the liquidsolid interface morphology. They noted, as have previous investigators, the
unusual morphology of this ternary eutectic (Figure 20) which has layers of Sn
(dark phase), and Pb-rich solid solution (white phase) on either side of essentially
pure Cd (grey phase), producing an ABCBA layering.
Figure 19A The Pb-Sn-Au liquidus
surface near the binary
Pb-Sn eutectic.
Figure 20
Figure l9B Backscattered scanning
electron micrograph of Pb-6OSn
Solder with 5 wt.% Au addition
showing primary Pb (lower
right), AuSn4 (dark blades)-Pb
three-phase reaction products
(middle) and Pb-Sn-AuSn4
ternary eutectic product (top).
Note the large difference in size
of the AuSn4 product formed in
the two different reactions.
Backscattered scanning electron micrograph of Pb-Sn-Cd aIloy a t the ternary
eutectic composition.
[Pb-Sn) - Cu: The system has been reviewed by Chang et al. [78]. As in the Pb-SnZn system, there is a miscibility gap in the Pb-Cu binary system which extends
significantly into the ternary system. Marcotte and Schroeder [79] report a
ternary eutectic, (Pb) + (Sn) + Cug Sng, to occur a t 182°C (1°C below the binary Pb-
22
Solder Mechanics
Sn eutectic) a t a calculated composition of 0.16 wt.% Cu, 38.08 wt.% Pb, and 61.76
wt.% Sn. Figure 21 shows the CugSng phase as dendrite inclusions in a Pb-Sn
solder used for joining the shaft and base of an ancient Roman bronze (Cu-Sn-Pb)
candelabrum.
Figure 21
Scanning electron micrographs of Cu6Sn5 dendrite inclusions in a Pb-Sn solder
used for joining parts in an ancient Roman bronze (Cu-Sn-Pb) candelabrum. (A)
secondary electron image (B) wave length dispersive x-ray dot map for Cu.
(Pb-Sn)- In: There is no ternary eutectic in this system [80]. The most recent
study in this system is that of Evans and Prince 1811. They indicate the presence
of two quasi-peritectic invariant reactions with that closest to the Pb-Sn binary
eutectic to occur a t 59.4 wt.% Sn, 35.3 wt.% Pb, 5.3 wt.% In and a t 171°C.
(Pb-Sn) - Pt: No phase diagram for the Pb-Sn-Pt is known to the authors, but
Meagher and Bader [82] have examined reaction-diffusion in this system. The
only intermetallic phase observed during solid-state diffusion studies was PtSn4.
(Pb-Sn) - Sb: This system has been reviewed by Osamura [83]. There is a quasiperitectic reaction which occurs near the Pb-Sn binary eutectic a t 36.5 wt.% Pb,
60.5 wt.% Sn, and 3 wt.% Sb, a t 191°C. There is also a ternary eutectic near the Pb
corner a t 85 wt.% Pb, 11.5 wt.% Sb, and 3.5 wt.% Sn, a t 240°C.
(Pb-Sn) - Zn: There is a miscibility gap in the Pb-Zn binary system which extends
significantly into the ternary system. There is a ternary eutectic a t 24 wt.% Pb, 71
wt.% Sn, and 5 wt.% Zn, a t 177OC [75].
Chapter I : Physical Metallurgy of Solder Systems
23
Table 2. Information on Ternary Systems Sn-Pb-X
Ternary
Element
Amount in
Ternary
Eutectic
(wt.%)
xE
Bi
In
Amount in
Peritectic
(wt.%)
Eutectic
(Peritectic
Temperature) OC
32.6
5.0
2.5
Cd
Zn
Au
Mg
22.0
5.0
3.0
1.5
137
171
189
145
177
177
170
Ag
Cu
Al
Ni
Fe
As
Te
1.35
0.3
0.08
-0.01
-0.01
-0.01
-0.005
-0.005
-0.001
-0.001
178
183X
183X
183X
183X
183X
183X
183X
183X
183X
Sb
Se
S
P
Solid
Solubility
Sn(150°C)
(wt.%)
Pb(150°C)
(wt.%)
10
10
4
1
0.4
0.3
0.02
0.05
0.006
<0.01
0.01
0.001
<0.01
<0.05
0.02
<0.0001
?
20
70
3.5
5
0.005
0.03
2.5
0.05
0.007
<0.01
0.01
0.0002
0.04
?
?
<0.0001
?
Ternary
Phase
SbSn
Cd
Zn
AuSnq
Mg2Sn
Ag3Sn
CugSng
A1
NigSnq
FeSn2
As3Sn4
TeSn
SeSn
SnS
Sn4P3
? denotes solid solubility not known exactly, but very low.
denotes ternary eutectic temperature not known exactly but probably negligibly
different from that of the binary Sn-Pb eutectic.
X
summary
The preceding discussion has shown that the behavior of the Pb-Sn system,
which a t first glance appears deceptively simple, is actually quite complex. For
example, i t was shown that a microstructure of alterhating a-Pb and P-Sn
lamellae can occur by very different processes (eutectic solidification versus
discontinuous precipitation). Significant advancements have been made in
understanding the physical metallurgy of this system as a result of many years
of research. However, there still exists opportunity for improved understanding
in many areas, including discontinuous phenomena and ternary element effects
in solidification and precipitation. In particular, the development of continuous
cooling curve diagrams would aid in designing joint dimensions from a
microstructural point of view. Finally, the microstructures of electronic
packaging solder joints should be incorporated in a meaningful way into lifetime
prediction models.
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Solder Mechanics
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