Formation of supersaturated solid solutions in the immiscible Ni–Ag
system by mechanical alloying
J. Xu,a) U. Herr, T. Klassen, and R. S. Averback
Department of Materials Science and Engineering, University of Illinois at Urbana–Champaign, Urbana,
Illinois 61801
~Received 8 November 1995; accepted for publication 8 January 1996!
The mechanical alloying process in the immiscible Ni–Ag system with a positive heat of mixing
was investigated by x-ray diffraction and differential scanning calorimetry. High energy ball milling
of mixed elemental powders, with nominal composition Nix Ag1002x (x 5 95, 90, 70, 50, and
30!, results in the formation of mixtures of supersaturated, nanocrystalline Ni-rich and Ag-rich solid
solutions. The solubilities and final grain sizes of these phases depend on the nominal composition
of the powder. The maximum solubilities were determined using Vegard’s law to be 4.3 at. % Ni in
Ag and 6.6 at. % Ag in Ni for samples milled at room temperature. The effect of milling temperature
on mechanical alloying was examined in the range 2195 to 250 °C. Lower temperature milling
leads to a larger solubility of Ni in the Ag-rich samples, up to 7.1 at. % for the Ni30Ag70
composition. Indications for the existence of a concentrated solid solution (Ni36Ag64-Ni44Ag56)
were also found. Milling at higher temperatures leads to lower solubilities. A study of the thermal
stability of supersaturated Ag-rich and Ni-rich phases shows that milling at high temperature can be
understood in terms of a competition between mechanical mixing and thermal decomposition. At
room temperature, nonequilibrium vacancies are responsible for decomposition. The results give
new insight into the general characteristics of the mechanical alloying process in thermodynamically
unstable systems. © 1996 American Institute of Physics. @S0021-8979~96!06708-X#
I. INTRODUCTION
Mechanical alloying ~MA! has become a widely used
technique to synthesize nonequilibrium materials, such as
amorphous alloys, nanocrystalline metals, compounds, and
supersaturated solid solution. During the past few years, the
formation of supersaturated solid solutions in normally immiscible alloy systems by high energy ball milling has received increased attention. A number of binary systems with
positive heats of mixing have now been investigated, including Ag–Cu,1,2 Ag–Fe,3 Fe–Cu,4 –9 Co–Cu,10–12 Cu–W,13
Cu–V,14 Cu–Ta,15,16 Ti–Mg,17,18 and Ce–Yb.19 In most of
these systems, a more or less complete range of solid solutions are formed despite miscibility gaps in their respective
equilibrium phase diagrams. Exceptions are Ag–Fe and Ti–
Mg, where only little mutual solubility has been observed.
There have been attempts to explain the formation of solid
solutions in these systems by thermodynamic arguments
based on local free energy increases in the milled materials
above the free energy of the solid solution.5,12,16 It has been
argued that the system would then somehow transform into
the lower free energy state, i.e., the solid solution. This argumentation resembles the usual explanation of nonequilibrium phase formation and phase transformations in metastable systems with negative heats of mixing.20 It must be
kept in mind, however, that the above mentioned systems
with positive heat of mixing are unstable with respect to
decomposition into their elemental constituents, which at
high enough concentrations may occur by spinodal decomposition and hence without nucleation. This process would
a!
Permanent address: Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, China.
J. Appl. Phys. 79 (8), 15 April 1996
lead to a lower free energy than the proposed transformations
into the solid solution.5,12,16 The validity of the free energy
arguments for the phase formation process in systems with
positive heat of mixing is therefore questionable.
Kinetics can also play an important role in metastable
phase formation. This was illustrated in a recent computer
simulation study in which a fcc binary solid solution, with
positive heat of mixing, was simultaneously subjected to
shear deformation and diffusion.21 It was observed that pure
shear deformation leads to the formation of homogeneous
solid solutions while diffusion opposes the mixing process.
The system reaches steady states which are characterized by
the ratio of shear events to diffusion events. The picture
emerging from this simulation study of ball milling is thus
similar to that describing irradiation processes where forced
atomic jumps induced by irradiation compete with thermally
activated jumps of point defects. Models of the irradiation
processes are, of course, far more developed than those for
ball milling.22
In the present work, we have chosen the immiscible system Ni–Ag for a thorough investigation of phase formation
under ball milling. In the equilibrium phase diagram, Ni and
Ag are immiscible in both the solid and liquid states. The
maximum equilibrium solid solubility is about 0.2 at. % Ni
in Ag near 960 °C and about 1 at. % Ag in Ni near the monotectic temperature 1435 °C.23 The heat of mixing of the equiatomic solution has been estimated to be DH mix 5 115
kJ/mol.24 The thermochemical properties of the Ni–Ag system thus resemble those of the Ag–Fe system, which does
not form a solid solution under ball milling.3 DH mix is somewhat smaller in Ni–Ag, however, making mechanical alloying more likely. In this respect, previous studies indicated
that solid solutions of Ni and Ag can be realized using other
0021-8979/96/79(8)/3935/11/$10.00
© 1996 American Institute of Physics
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means of nonequilibrium processing. Ricci-Bitti et al.25 reported that a Ag-14 at. % Ni solid solution could be formed
in thin films by condensation of Ag–Ni vapor onto a substrate at room temperature. Formation of homogeneous solid
solutions over an even larger range of concentrations was
observed during vapor condensation onto a substrate held at
liquid nitrogen temperature.26 More recently, it was found
that concentrated Ni12x Agx films could be condensed onto
substrates at room temperature if laser ablation techniques
were employed.27 Tsaur et al.28 reported that supersaturated
solid solutions of Ag–Ni could also be obtained by ion beam
mixing of multilayer, thin-film specimens. Solubilities of 4.5
at. % Ni dissolved in Ag and 16 at. % Ag dissolved in Ni
were observed. Finally, Froes et al.29 indicated that the terminal solid solubilities in Ni–Ag could be extended to 3.8
at. % Ni in Ag and 9.0 at. % Ag in Ni by mechanical alloying, but no details were provided in this report. These studies
show, therefore, that the means of processing Ni–Ag plays
an important role in determining the alloy solubility, and
hence Ni–Ag is a potentially useful system for elucidating
the mechanisms of alloy formation in driven immiscible systems.
In the present work, a systematic study of mechanical
alloying in the Ni–Ag was undertaken, examining the effects
of powder composition and milling temperature on phase
formation. The variation of the milling temperature is of obvious importance to this investigation, for as it will be seen,
milling temperature strongly influences the balance between
mixing and decomposition. The average powder composition, on the other hand, might not be thought to be important
for alloy formation. In principle, it should only control the
relative fractions of the terminal phases, but we will show
that it, in fact, affects the terminal solubilities. The paper
proceeds as follows. In Sec. II, experimental details are described, Sec. III reviews the results of the various experiments, it is divided into ~A! effects of the composition of the
powder mixture, ~B! thermal stability of Ag–Ni solid solutions and ~C! effects of milling temperature. In Sec. 4 the
results are discussed using the picture of the simultaneously
occurring forced and thermally activated transport processes.
A complete picture of the ball milling process begins to
emerge if the effects of nonequilibrium vacancies generated
in the course of the deformation process are included. These
effects were found to dominate the behavior at room temperature in Ni–Ag, which is generally the standard milling
condition.
II. EXPERIMENT
Elemental powders of Ag and Ni with 99.9% purity and
a particle size smaller than 150 mm were blended to give
average compositions of Nix Ag1002x in the concentration
range x 5 30 to x 5 95. To avoid contamination from the atmosphere, the powder handling and the milling process were
carried out in a glove box under argon using a gas purification system ~oxygen and water contents in the atmosphere
were typically below 1 ppm!. The ball milling was performed in a SPEX 8000 shaker mill using hardened steel
balls and a tungsten-carbide vial. The ball-to-powder weight
ratio was 5:1. Milling at high temperature was realized by
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J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
heating the vial using a flexible heating tape. The temperature was measured and controlled using a thermocouple attached to the vial. The milling at low temperature was performed outside the glove box, but the handling of the
powders was carried out in it. The vial in this case was
sealed using indium wire, and it was cooled by dripping
liquid nitrogen directly onto it. The temperature was measured within seconds of stopping the mill. After different
times, the milling process was interrupted and a small
amount of the milled powder was removed for analysis.
The powders were characterized by x-ray diffraction
~XRD! using a Rigaku D-max diffractometer with Cu K a
radiation ~l50.1542 nm! and a secondary graphite monochromator. The contamination of iron due to abrasion of the
milling tools was determined using energy-dispersive x-ray
analysis ~EDX! in a scanning electron microscope. Significant iron contamination was found after extended milling,
especially in the Ni rich powders, but only samples with iron
contents less than 1 at. % were used for the present study.
Thermal analysis of the samples was performed using a differential scanning calorimeter ~Perkin–Elmer DSC 4! under
flow of purified argon. The samples were measured at a heating rate of 10 °C/min in a temperature range from 100 to
550 °C. For each sample, a second run was recorded as a
reference under identical conditions as the first. The difference between the two runs represents the energy released
during irreversible transformations in the powder samples.
III. RESULTS
A. Effects of powder composition
The phase formation in the ball milled powders was followed by x-ray diffraction. Diffraction patterns obtained
from Ni95Ag5 and Ni50Ag50 powders after different milling
times are shown in Figs. 1~a! and 1~b! as typical examples.
Due to the overlap of Ni~111! with Ag~200! and Ni~220! with
Ag~311!, only the Ag~111!, Ag~220!, Ag~222!, Ni~200!, and
Ni~311! peaks can be observed separately. For Ni95Ag5 the
Ag peaks completely disappear after 5 h of milling, leaving
only the Ni peaks @Fig. 1~a!#. This observation demonstrates
that 5 at. % Ag can be dissolved in the Ni to form a homogeneous Ni-rich solution. In the case of Ni50Ag50 , the microstructures formed in the milled powders consisted of twophase mixtures of Ni-rich and Ag-rich fcc phases, even after
extended milling @Fig. 1~b!#. With increasing milling time,
diffraction peaks of both Ni and Ag broaden significantly,
indicating the refinement of grain size and the introduction of
internal strain. Similar changes of structure were found in the
samples Ni90Ag10 , Ni70Ag30 , and Ni30Ag70 . Figure 2
shows x-ray diffraction patterns of the powders with different compositions after milling for 25 h. ~The Ni95Ag5 was
milled only for 10 h to avoid Fe contamination.! For the
Ni90Ag10 sample a residual Ag~111! peak is still observed
indicating that not all of the Ag had dissolved in the Ni.
The structural evolution in the course of mechanical alloying can be further characterized by the changes in the
lattice parameters and grain sizes of the Ni-rich and Ag-rich
phases with milling time. Figures 3~a! and 3~b! show
changes in lattice parameters as a function of milling time
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FIG. 1. X-ray diffraction patterns for powder blends with the nominal compositions ~a! Ni95Ag5 and ~b! Ni50Ag50 after different milling times.
for powders with different compositions. The lattice parameters were calculated according to Cohen’s method30 using
only the separated Ag or Ni reflections. The peak positions in
the XRD patterns were determined by a least-squares profile
fitting program. It can be seen in Fig. 3~a! that between 1 and
5 h, the lattice parameters in all of the Ni samples increase
rapidly and approach an asymptotic value after approximately 5 h of milling, indicating that the alloy approaches
steady state by about this time. The steady state value of the
lattice parameter of Ni is seen to depend on the composition
of the milled powders, i.e., on the relative Ag content. Notice
that the Ni lattice parameter does not continue to increase
FIG. 2. X-ray diffraction patterns for the steady states obtained after milling
of Nix Ag1002x powder blends.
J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
FIG. 3. Lattice parameters of ~a! Ni and ~b! Ag phases in Nix Ag1002x powders as a function of milling time.
with increasing Ag content in the powder beyond 10%, as it
should if the Ag concentration in the Ni rich phase were to
increase. Rather, it begins to decrease with increasing
amounts of Ag. This means that the Ag supersaturation in the
Ni phase decreases with increasing Ag. The lattice parameters of the terminal Ag phase show no significant change
FIG. 4. Variation of lattice parameters for the Ni and Ag phases as a function of nominal composition of the milled powder blends.
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FIG. 6. Dependence of grain sizes of the Ni and Ag phases on the nominal
composition of Nix Ag1002x powder blends after milling to steady state.
phase decreases monotonously with increasing Ni content to
about 8 nm for the Ni70Ag30 sample. The Ni grain sizes
follow a similar trend, decreasing from 28 nm for Ni95Ag5 to
about 8 nm for the Ni50Ag50 and Ni70Ag30 compositions.
B. Thermal stability of supersaturated solutions
FIG. 5. Grain sizes of ~a! Ni and ~b! Ag phases as a function of milling time
for Nix Ag1002x powders.
during milling in the cases of Ni50Ag50 and Ni30Ag70 compositions, as seen in Fig. 3~b!. A reduction in the Ag lattice
parameters was observed in the samples, Ni70Ag30 and
Ni90Ag10 , however, indicating the formation of dilute, Agrich, solid solutions in these samples. The compositions of
the solid solutions can be estimated using Vegard’s law, assuming an ideal solution model. The steady state lattice parameters are plotted in Fig. 4 as a function of overall powder
composition. For comparison a linear interpolation between
the lattice parameters of Ag and Ni is included. For the
samples milled at room temperature, maximum solubilities
of 4.3 at. % Ni in Ag and 6.6 at. % Ag in Ni can be estimated
from these data. These results show that the solubilities in
the terminal phases depend on the composition of the powder
and that significant solubilities occur only for the powders
where the Ag concentrations are 30 at. % or lower.
The average grain sizes of the Ni and Ag phases were
calculated from the full width at half maximum ~FWHM!
measurements, using the Hall–Williamson method. Figures
5~a! and 5~b! show the variation of the grain sizes of the Ni
and Ag phases with increasing milling time for the different
powder mixtures. In the early stages of milling, the grain
sizes decrease rapidly to less than 20 nm and then reach their
final values after 10 h of milling. It is interesting that the
grain sizes of the resulting products depend upon the overall
compositions of the powder mixtures, which is similar to the
behavior of the terminal solubilities. This is illustrated in Fig.
6 and Table I. It is seen that the grain size of the Ag-rich
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J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
The phase formation was examined in more detail by
performing differential scanning calorimetry ~DSC! measurements on the milled powders. The DSC traces for
Ni50Ag50 samples milled for different times are shown in Fig.
7~a!. Again, the final state is attained after 5 h of milling. The
maximum heat flow is detected at about 340 °C ~using a
10 °C/min heating rate!. In Fig. 7~b!, the total enthalpy
evolved from samples milled for different times is shown. A
value of about 3.5 kJ/mole is found after 5 h. In Fig. 8, DSC
traces for samples with different compositions and milled to
steady state conditions are shown. It is observed that the
maximum in the heat flow shifts from more than 400 °C for
the Ni-rich samples to about 340 °C for the Ni30Ag70 powder
composition, indicating a lower thermal stability of the Agrich samples. The total stored enthalpy versus concentration
is shown in Fig. 9. For the samples milled at room temperature 4.5 kJ/mole were released from the Ni90Ag10 samples
whereas only 2 kJ/mole were evolved from the Ni30Ag70
sample. A systematic decrease of stored enthalpy with decreasing Ni content is found for samples with 10 at. % Ag or
more. This is reasonable since the supersaturation in the Nirich phase exceeds that in the Ag-rich phase, and, as pointed
out above, the supersaturations decrease with decreasing Ni
content.
To better understand the origin of the heat release,
samples which had been heated in the DSC to different temperatures were reexamined by x-ray diffraction. Results for a
Ni50Ag50 sample milled at room temperature are shown in
Fig. 10. With increasing temperature, a narrowing of the reflections is observed as expected from both grain growth and
strain relief. Figure 11 shows just the changes in grain sizes
of the Ag and the Ni-rich phases for the samples with
Ni50Ag50 and Ni70Ag30 composition. Significant increases in
the grain sizes are found for annealing temperatures above
250 °C. Figure 12 shows the lattice parameters of the AgXu et al.
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TABLE I. Data summary of Nix Ag1002x powders after milling at room temperature to steady state.
Data
Ni95Ag5
Ni90Ag10
Ni70Ag30
Ni50Ag50
Ni30Ag70
Milling time ~h!
a 0Ag (nm) a
a 0Ni (nm) b
D Ag (nm) c
D Ni (nm) d
10
•••
0.3560
•••
28.2
25
0.4064
0.3561
•••
12.3
25
0.4065
0.3545
8.1
7.2
25
0.4085
0.3539
13.4
8.1
25
0.4082
•••
30.8
•••
e
^ e 2 & 1/2
Hg (%)
2 1/2
f
^ e & Ni (%)
•••
•••
1.0
0.21
0.54
0.42
3.8
3.7
3.7
0.29
3.4
2.7
•••
DH(kJ/mole!g
S Ag in Ni ~at %) h
S Ni in Ag ~at %) i
0.95
2.7
•••
•••
0.80
4.4
6.6
4.3
•••
2.0
•••
•••
a
a 0Ag: lattice parameter of Ag phase.
a 0Ni: lattice parameter of Ni phase.
c
D Ag: grain size of Ag phase.
d
D Ni: grain size of Ni phase.
e
^ e 2 & 1/2
Ag : internal strain of Ag phase.
1/2
f
: internal strain of Ni phase.
^ e 2 & Ni
g
DH: stored enthalpy.
h
S Ag in Ni: solid solubility of Ag in Ni.
i
S Ni in Ag: solid solubility of Ni in Ag.
b
and the Ni-rich phases for these samples. A significant decrease of the lattice parameters in the Ni-rich phases is found
for both samples on heating above 250 °C. For the
Ni70Ag30 sample, an increase in the Ag lattice parameter is
found on heating to 250 °C, but with no additional change at
higher temperatures.
FIG. 7. DSC results of Ni50Ag50 powder blends milled for different times.
~a! DSC scan and ~b! total stored enthalpy.
J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
C. Effect of milling temperatures on phase formation
The phase formation during ball milling at different temperatures has been studied by heating or cooling the milling
vial during mechanical alloying. A temperature range between 2195 and 250 °C was studied. In Fig. 13, x-ray diffraction patterns from Ni50Ag50 powder mixtures milled at
2195, 20, 150, 200, and 250 °C are shown. The powders in
each case had reached steady state. It can be observed that
the widths of the reflections decrease with increasing temperature, indicating larger grains at higher temperatures. This
is explicitly shown in Fig. 14 where the grain sizes of both
phases are plotted as a function of milling temperature. The
lattice parameters of the thermal solid solutions are shown in
Fig. 15 as a function of milling temperature. These data illustrate that the solubilities at the lowest milling temperature
are largest. At room temperature and above, no significant
deviation of the Ag lattice parameter from the pure Ag value
is found for this Ni50Ag50 powder. The Ni lattice parameter,
on the other hand, decreases more or less continuously on
FIG. 8. DSC scans of steady states obtained by milling Nix Ag1002x powder
blends.
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FIG. 9. Compositional dependence of the total stored enthalpy for
Nix Ag1002x powder blends after milling to steady states at room temperature
and 2195 °C.
raising the milling temperature up to '200 °C, although between room temperature and 150 °C, the lattice parameter is
nearly constant. It is noteworthy that the grain sizes and the
lattice parameters follow the same dependence on milling
temperature, possibly indicating a coupling between the
grain size at steady state and the solute content in the Ni- or
Ag-rich phases, respectively.
Results of DSC measurements of the Ni50Ag50 samples
milled at different vial temperatures are shown in Fig. 16~a!.
The general observation is that the heat release during the
DSC runs occurs at higher temperatures for the samples
milled at higher temperatures. The total stored enthalpies for
the Ni50Ag50 samples milled at different temperatures are
shown in Fig. 16~b!. A large difference of 2 kJ/mole is found
between the samples milled at 2195 °C and RT, while only
little change occurs between RT and 150 °C. A further decrease in the heat release is found for the samples milled at
200 and 250 °C. The stored enthalpy thus follows the same
trend with the milling temperature as the lattice parameters
~Fig. 15!and grain sizes ~Fig. 14!.
The powder mixtures with compositions Ni30Ag70 ,
Ni70Ag30 , and Ni90Ag10 were also milled at 2195 °C, and
the x-ray diffraction patterns obtained from these samples are
shown in Fig. 17. A significant intensity between the Ag~111!
FIG. 10. X-ray diffraction patterns for a Ni50Ag50 powder blend, which was
milled for 25 h at room temperature and subsequently annealed to different
temperatures.
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J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
and Ni~111!/Ag~200! reflections is observed in the samples
with Ni70Ag30 and Ni50Ag50 composition. Detailed analysis
of the diffraction patterns using a least-squares fitting program with Lorentzian peak profiles indicates a weak additional peak at about 41.5 and 42 deg in 2U, which is consistent with a small fraction of a Nix Ag1002x solid solution in
the concentration range x536 to 44. An exact determination
of the concentration and the molar fraction of this phase is
difficult since this peak overlaps with the adjacent, stronger
Ag and Ni reflections. The stored enthalpies measured for the
different sample compositions milled at low temperature are
included in Fig. 9. A large difference of about 2 kJ/mole
between the samples milled at room temperature and low
temperature is found for the Ni70Ag30 and Ni50Ag50 compositions. The lattice parameters of the terminal solid solutions
milled at low temperature, which have been incorporated in
Fig. 4, also indicate significant concentrations of both Ag in
the Ni-rich phase and Ni in Ag-rich phase for these same
samples.
The thermal stability of the concentrated Nix Ag1002x alloy phase and the supersaturated terminal solutions formed at
low temperature was further examined. The powder with
composition, Ni50Ag50 , was reexamined after being stored
for 3 weeks at room temperature. No changes in the XRD
patterns, Fig. 18, or the heat release were observed relative to
the first examinations immediately ~ca. 2 h! after the ball
milling. This indicates that no diffusion takes place at room
temperature in the absence of ball milling. In a second experiment, a Ni50Ag50 powder milled at low temperature was
remilled at room temperature for 5 h. The lattice parameters
of the Ni-rich and Ag-rich phases both changed as indicated
in Fig. 18. For the Ni-rich solution, it became identical to
that obtained after milling only at room temperature, while
for the Ag-rich solution it increased to 0.4079 nm which lies
between the values after low-temperature milling ~0.4072
nm! and room-temperature milling ~0.4085 nm!.
Finally, we note that the presence of stacking faults in
ball milled powders may influence the determinations of
grain size.31 Whether stacking faults influence the present
FIG. 11. Grain sizes for the Ni50Ag50 and Ni70Ag30 powder blend, which
was milled for 25 h at room temperature and subsequently annealed to
different temperatures.
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FIG. 12. Dependence of the lattice parameters of the Ni and Ag phases on
annealing temperature following milling at room temperature for 25 h.
Nominal compositions are Ni50Ag50 and Ni70Ag30 .
results can, in principle, be determined by checking for systematic deviations of the diffraction peak positions from their
values in defect free material for the systematic deviations of
the peak broadening at different reflections.32 Unfortunately,
the evaluation of the stacking fault density using these methods is difficult here, owing to the overlap between the Ag
and Ni peaks. For the Ni90Ag10 sample, however, where
there is nearly no contribution from the Ag-rich phase, the
distance (2 u 200 – 2 u 111), which is a good indicator of stacking faults, shows little evidence of their presence. An upper
limit on the stacking fault density can be set from these experiments at 0.003 ~1 fault per 300 lattice planes!; hence,
stacking faults should have no measurable influence on our
values of the lattice parameter.
FIG. 13. X-ray diffraction patterns for a Ni50Ag50 powder blend after milling to steady state at different temperature.
~ii!
~iii!
~iv!
IV. DISCUSSION
The experimental investigation reported here on the effect of temperature and powder composition on phase formation in ball-milled Ni–Ag, and the thermal stability of these
phases, was performed to elucidate the mechanisms of mechanical alloying in driven, immiscible systems. Models of
phase formation in driven systems have already been developed for irradiation processes,22 and recently they have been
applied to the ball milling process.21 In Ref. 21, which was
mentioned in the introduction, alloy formation of an AB alloy on a coherent lattice, undergoing simultaneous shear deformation and thermal diffusion, was studied by computer
simulation. It was demonstrated that the steady state phase
was determined by a competition between mechanically
driven alloying and diffusion controlled decomposition. Two
regimes were identified as the relative rates of shearing
events and diffusion jumps were varied. A random solid solution was found if the shearing rate dominated and a decomposed state if the diffusion rates did. For the latter, the solubilities of the decomposed states increased with increasing
shearing. In the following, we will discuss the experimental
results in terms of the relative rates of shearing and diffusion,
First, however, we recall the following principal experimental findings of this work:
~i!
Solubilities in the two terminal phases decrease with
increasing milling temperature.
J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
~v!
Milling at liquid nitrogen temperature increases the
terminal solubilities and appears to create a small
amount of a highly enriched solution containing
'35%– 45% Ni. A possibly important experimental
detail concerning this result is that the milled powders
were always warmed to room temperature prior to
analysis.
Maximum solubilities depend on the composition of
the powder mixture, increasing with increased Ni content.
Decomposition of the two solid solution phases occurs at higher temperatures during thermal annealing
than during milling. Milling at room temperature, after first milling at low temperature leads to partial
decomposition, whereas thermal decomposition of the
same low-temperature milled powder only begins at
temperatures greater than 150 °C.
Grain growth becomes significant during thermal annealing at approximately the same temperature as did
phase decomposition.
The first result, that solubilities are increasingly enhanced with decreasing temperature, fits intuitively well with
FIG. 14. Grain sizes for Ni50Ag50 powders after milling to steady state at
different temperature.
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FIG. 15. Dependence of the lattice parameters of the Ni and Ag phases in
Ni50Ag50 powder blends on milling temperature.
the concept of competition between mechanically driven
mixing and thermally activated decomposition. The rate of
thermal diffusion should increase with temperature while the
rate of mechanical mixing is expected to be insensitive to
temperature. In terms of the kinetic model discussed above,
the alloying process shifts further to the diffusion dominated
regime with increasing temperature. The result can also be
understood by the concept of an ‘‘effective temperature,’’22
which was formulated for the case of irradiation processes in
systems that exhibit ordering or decomposition reactions under equilibrium conditions. According to this concept, the
state that the system assumes under a competition between
FIG. 16. DSC scan ~a! and stored enthalpies ~b! of Ni50 Ag50 powder blends
after milling to steady states for different temperatures.
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J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
FIG. 17. X-ray diffraction patterns for Nix Ag1002x powder blends after milling to the steady states at 2195 °C.
irradiation and diffusion corresponds to an equilibrium state
at a temperature higher than the actual sample temperature.
In the special case of immiscible solids, the corresponding
state, which is the region of the phase diagram at higher
temperature, will in general exhibit larger solubility. The
maximum terminal solubilities for solid Ni–Ag, however,
are still far lower than those observed in the milling experiments, and it must be assumed for the present study that the
corresponding state is a liquid where the solubilities of the
terminal solutions can be much larger.
The above discussion a priori assumes that diffusion increases with increasing temperature. If the decomposition
were mediated by vacancies in thermal equilibrium, this assumption would indeed be valid, but extrapolation of diffusion data measured on dilute Ni–Ag solid solutions at high
temperature back to room temperature, yields extremely low
diffusivities, D 5 2 3 10248 m2 /s for Ag in Ni ~Ref. 33! and
D 5 2 3 10244 m2 /s for Ni in Ag ~Ref. 34!. The diffusion
processes at room temperature, therefore, cannot be controlled by equilibrium vacancies, but must involve vacancies
produced by a nonequilibrium process, which in this case is
ball milling. Fast diffusion along dislocations or grain
boundaries would not explain the results since the milled
samples are stable at room temperature in absence of milling.
This conclusion is not surprising since it is well known that
nonequilibrium concentrations of vacancies can be generated
FIG. 18. X-ray diffraction patterns for a Ni50Ag50 powder blend after milling at 2195 °C and subsequent annealing or milling at RT.
Xu et al.
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not only by particle irradiation but also by mechanical deformation. Moreover, it has been established that these vacancies can lead to significant recovery of deformation or
radiation-induced defects in Ag below or close to room
temperature.35
Unlike the case for thermally induced decomposition,
the temperature dependence of decomposition from millinginduced vacancies is not obvious and in fact depends on the
driving conditions. If we assume here that the vacancies produced by ball milling all migrate to sinks, such as nearby
grain boundaries or dislocations, then the appropriate rate
equation for the excess vacancy concentration is
dc v
5K 0 2 a D v c v c s ,
dt
~1!
where K 0 is the generation rate of vacancies, D v is the vacancy diffusivity, a is a constant, and c v and c s are the concentrations of excess vacancies and sinks. At steady state, the
atomic diffusion coefficient, D, becomes
D5D v ~ c v 1c 0 ! 5
K0
1D v c 0 ,
acs
~2!
where c 0 is the equilibrium concentration of vacancies.
Equations ~1! and ~2! indicate that there should be different
temperature regimes for phase formation. At low temperatures, vacancies are immobile and complete solid solutions
should evolve. @Equation ~2! does not apply to this case since
it assumes some vacancy mobility.# At higher temperatures,
just below room temperature for Ag and just above for Ni,
vacancies become mobile, but their equilibrium concentrations are negligible. In this regime, D is independent of temperature. Phase formation should thus also be independent of
temperature except, possibly, for variations in the sink concentration, the generation rate of vacancies, or the intermixing rate. Finally, at even higher temperatures, the equilibrium
concentration of vacancies dominates and the decomposition
rate should increase with increasing temperature. There are
not sufficient data to clearly delineate these regimes, but they
are compatible with this picture, particularly the nearly temperature independent regime shown in Fig. 13, between
room temperature and 150 °C. This is just the regime where
vacancies are mobile and other diffusion processes are suppressed. A similar conclusion was noted by Pochet et al.36
and Klassen et al.37
Our results for low-temperature milling of the Ni50Ag50
sample provide additional evidence that nonequilibrium vacancies are important to phase formation. As mentioned
above, the XRD pattern from the low-temperature milled
sample was unchanged after being stored at room temperature for 3 weeks, but it changed significantly during a subsequent ball milling treatment at room temperature. The final
state, in fact, was almost the same as after ball milling at
room temperature, alone. The need for milling for decomposition to occur at room temperature provides strong evidence
that nonequilibrium vacancies caused the decomposition of
the low-temperature milled specimen. Also, the observation
that the steady state phase is independent of the sample’s
previous history shows that the steady state is fixed by the
relative shearing and decomposition rates. This conclusion
J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
was also found in the computer simulations.21 Along this
same line of reasoning, the generation of nonequilibrium vacancies during the mechanical alloying process might explain the difficulties of forming Ag-rich solid solutions at
room temperature. We need only suppose that the ratio of
diffusion to mechanically alloying is higher in the Ag-rich
than Ni-rich solutions. This is reasonable since vacancy motion in Ni is very sluggish at room temperature, but not in
Ag.38 We point out that in a recent study of mechanical
grinding of the intermetallic phase, FeAl, it was argued that
the generation of vacancies during the milling process plays
an important role in establishing the steady state degree of
order.36 These results, therefore, provide a consistent picture
for the role of milling induced vacancies in phase formation,
both in order–disorder and immiscible systems.
An important question is why the specimens milled at
low temperatures did not form a single homogeneous solid
solution, as would be predicted by the computer simulation
model since vacancy motion is suppressed at low temperatures. Unfortunately, we do not know whether a single concentrated phase formed, or not, since the specimen could
only be examined by x-ray diffraction after warming to room
temperature. These diffraction patterns, however, do provide
some evidence for such a phase. The x-ray diffraction pattern
indicates a small amount of a nearly equiatomic solid solution and the stored enthalpies in these samples were '2 kJ/
mole larger than in samples milled at room temperature. We
suggest that the coexistence of two supersaturated terminal
phases and a small amount of a concentrated phase in the
specimen warmed to room temperature is consistent with a
two-part decomposition process, one involving nonequilibrium vacancies below room temperature and one involving
thermal vacancies above room temperature.
The vacancies generated during low-temperature milling
are initially frozen in the sample. On warming to room temperature, they become mobile and migrate to sinks. During
their migration, they can mediate the atomic diffusion required for decomposition. Since the supply of these vacancies is limited to their quenched-in concentrations, only incomplete decomposition is possible. Final decomposition
would be delayed to higher temperatures, '250 °C, when
other diffusion processes take place. It is noteworthy that
grain growth becomes significant just as this second phase of
decomposition takes place, which further indicates a second
diffusion process coming into play. We suggest that grain
boundary diffusion is this second process since bulk diffusion at 250 °C is still small in Ni.
This picture is consistent with the results noted above
concerning Ni–Ag films produced by cosputtering at liquid
nitrogen temperatures26 and laser quenching films at room
temperature.27 A change in the diffraction patterns of
Ni0.44Ag0.56 samples was observed on heating the cosputtered
films from 2195 °C to room temperature, indicating the partial decomposition. The laser quenched Ni–Ag specimens,
presumably having already undergone partial decomposition
at room temperature, consisted of a concentrated Ni–Ag solution and nearly pure Ni and Ag phases. The concentrated
phase underwent final decomposition at '175 °C, which is
about the same temperature as observed here for ball-milled
Xu et al.
3943
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Ni–Ag. These results thus suggest that partial decomposition
of the concentrated Ni–Ag phases occurs near room temperature by the motion of quenched in vacancies and that
final decomposition occurs by other thermally activated diffusion processes near 200 °C. We believe, therefore, that a
homogeneous solid solution might form during milling at
2195 °C but that it would partially decompose upon heating
to room temperature. Within the computer simulation model,
this must be the case, but the atomistic details of mechanical
alloying are not well known nor are they included in the
computer simulations. It may be that Ni and Ag simply cannot be fully intermixed by mechanical alloying, regardless of
temperature. We are currently investigating this possibility.
Another striking result is the asymmetry of phase formation with respect to the concentration of elemental components. In the Ag-rich powders, no significant solubility of Ni
in Ag is found whereas on the Ni-rich side, solubility of Ni in
Ag is observed and the solubility of Ag in Ni is measured.
These observations clearly illustrate the kinetic aspects of the
milling process since the thermodynamics are invariant to
the relative fractions of the two phases. It must be concluded
that increasing the relative fraction of the Ag-rich phase increases diffusional processes relative to the mechanically alloying processes. Only a detailed understanding of the interfacial shearing process would make it possible to rigorously
explain our observations, but it can be argued that the results
are at least plausible. It is known that milling mixtures of
soft and hard materials leads to the coating of the hard particles with the softer one.39 We therefore suspect that when
the Ag concentration becomes too large, the Ni particles become coated with a thick layer of Ag. As a consequence,
when the particles are sheared against each other, too much
of the energy is absorbed in the Ag layers to allow for interfacial shearing of the soft Ag and hard Ni particles. At the
same time, vacancies will be generated in the Ag by shearing
of the Ag layers, still providing for decomposition. It should
be mentioned that increasing the Ag concentration also reduces the amount of Ni–Ag interface, per particle, and with
it the amount of intermixing. This latter explanation, however, cannot be complete, since the solubility of the Ni-rich
phase also decreases with increasing Ag in the powder mixture.
Finally, we note the coincidence of the change in Ni
lattice parameter with the maximum in the heat flow for the
samples alloyed at room temperature. It indicates that the
main contribution to the heat release in the samples milled at
room temperature is the decomposition of the Ni-rich solid
solution, and grain growth. An estimate of the heat of mixing
stored in the Ni-rich solid solutions can be made using the
above mentioned 15 kJ/mole value from Miedema’s model
and the regular solution approximation. This gives a value of
2.9 kJ/mole for a Ni95Ag5 solid solution which is close to the
stored enthalpy measured for that powder composition. Little
energy is stored in the grain boundaries, since in this sample,
the grain size is 28 nm. Larger amounts of stored energy are
observed in the more Ag-rich powders, and these increases
can not be explained by the heat of solution, alone. Recall
that the amount of Ag dissolved in the Ni is actually lower
for the Ag-rich samples and the fraction of the Ni-rich solid
3944
J. Appl. Phys., Vol. 79, No. 8, 15 April 1996
solution decreases with increasing Ag in the powder. It is
therefore necessary to assume an additional contribution
from grain growth and strain release. The contribution from
the grain boundaries of nanocrystalline Ni with a grain size
of 8 nm can be estimated to be '3 kJ/mole if one assumes an
average grain boundary energy of 1J/m2 . The contribution
from Ag grain boundaries should be somewhat lower, for the
same grain size, due to its lower cohesive energy. Our estimate of energy stored in the grain boundaries lies well in the
range of the observations.
V. CONCLUSION
The results of the investigation of the phase formation in
Nix Ag1002x powder mixtures show that partial solid solutions up to 4.3 at. % Ni in Ag and 6.6 at. % Ag in Ni are
formed. The solubility found in materials milled at room
temperature depends on the overall composition of the powders with only small solubility for the Ag-rich compositions.
Milling at higher vial temperature leads to further reduction
of the solubility whereas cooling the vial with liquid nitrogen
leads to enhanced solubility for the Ag-rich compositions.
Indications for the formation of a more concentrated
Nix Ag1002x alloy with x 5 36– 45 are found in the samples
milled at low temperature. The results are interpreted in
terms of a competition between mechanically driven alloying
and decomposition of the thermodynamically unstable alloy.
The diffusion processes at room temperature are mediated by
nonequilibrium vacancies generated during the mechanical
deformation process. The influence of the powder composition on the solubility may be explained by the difference of
the diffusional properties of Ag and Ni resulting in a lower
thermal stability of the Ag-rich phase at room temperature.
The increase of the introduction rate of Ni into Ag by shear
deformation explains the existence of a Ag-rich solid solution for higher nominal Ni concentrations. Analysis of the
thermal stability of the solid solutions formed at room temperature shows that the final states formed under milling at
elevated temperatures are comparable to those after room
temperature milling and annealing at higher temperature. The
milling results at high temperature therefore seem to be
dominated by diffusion of thermally generated vacancies in
contrast to the phase formation at room temperature.
ACKNOWLEDGMENTS
The authors gratefully acknowledge contributions of Dr.
P. Bellon in applying his kinetic model to this work. This
research was supported by the U.S. Department of Energy,
Basic Energy Sciences, under Grant No. DEFG 02-91 ER
45439.
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