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Bidwell and Speiser 1964

publicité
THE
RELATIVE THERMODYNAMIC
SOLID NICKEL-PALLADIUM
L.
R.
PROPERTIES
ALLOYS*
OF
and R. SPEISER$
BIDWELL?
The relative thermodynamic properties of solid nickel-palladium alloys were determined in the
temperature range 700-1200°C using a galvanic cell with a solid electrolyte. Within experimental error,
the relative partial molar free energies of nickel were linear functions of the temperature, signifying
that AC, above 700°C is essentially zero and that the specific heats at elevated temperatures can be
approximated by the Kopp-Neumann
rule. Nickel-rich solutions were found to exhijit endothermic
enthalpies of mixing and positive deviations from Raoult’s law for the activity of the solvent and
negative deviations for the activity of the solute. palladium-rich solutions, on the other hand, exhibit
exothermic enthalpies of mixing and negative deviations from Raoult’s law for the activity of the solvent
and solute alike. The excess entropies of mixing are positive for all compositions. This is considered to be
primarily a result of the ferromagnetic properties of the alloys. From a consideration of magnetic,
electronic, vibrational, and lattice distortional factors it has been concluded that nickel-palladium
alloys, particularly those rich in palladium, exhibit significant short-range order.
PROPRIETES
THER~~ODYNAMIQUES
DES
ALLIAGES
NICKELPALLADIUM
Les auteurs ont Btudie les propriirtcs thermodynamiques relatives des atliages nickel-paladin
B,
l’etat so&de, dans le domaine de temperature de 700 B. 12OO”C, en utilisant une cellule Zt electrolyte
solide. Dans les limites des erreurs experimentales, ils ont observe que les energies libres molaires partie&s du nickel etaient des fonctions lineaires de la temperature, ce qui implique que AC, est essentiellament nul au-dessus de 7OO”C, et qu’on peut obtenir, de man&e approchee, les chaleurs specifiques aux
temperatures Blevees en utilisant la regle de Kopp-Neumann.
Les autcurs ont observe que les solutions
riches en nickel montraient des enthalpies de melanges endothermiques, des deviations positives de la loi
de Raoult pour l’activitb du solvant et des deviations negatives pour l’activite du solute. D’autre part,
les solutions riches en palladium montrent des enthalpies de melange exothermiques et des deviations
negatives de la loi de Raoult aussi bien pour la solvant que pour lc solute. L’exces de l’entropie de
Ces proprietes semblent &re au premier chef une
melange est positif pour toutes les compositions.
consequence des proprietes ferromagnetiques des alliages. En prenant en consideration les facteurs
magnetiques, electroniques, vibratoires, et la distorsion du reseau, les auteurs concluent que les alliages
nickel-palladium, et particulierement ceux riches en palladium, possedent un ordre rl petite distance
significatif.
DIE
RELATIVEN
THERMODYNAMISCH~~
EIGENSCHAFTEN
PALLADIUM-LEGIERUNGEN
FESTER
NICKEL-
Die relativen thermodynamischen Eigenschaften fester Nickel-Palladium-Legierungen
wurden im
Temperaturbereich
700-1200°C mit Hilfe einer galvanischen Zelle mit festem Elektrolyt bestimmt.
Innerhalb der Fehlergrenzen warm die relativen partiellen molaren freien Energien von Nickel linearo
Funktionen der Temperatur. Dies bedeutet, d& AC, oberhalb 700°C im wesentlichen Null ist und daB
die spezifischen Warmen bei hohen Temperaturen durch die Kopp-Neumann-Regel
approximiert
werden k&men. Nickelreiche Legierungen zeigten endotherme ~~hungsenthalpien,
positive Abweichungen vom Raoult’schen Gesetz fdr die Aktivitat des Lijsungsmittels und negative Abweichungen fur
die Aktivitiit
dss gel&ten Stoffes.
Palladiumreiche
Legierungen zeigten andererseits exotherme
Mischungsenthalpien und negative Abweichungen vom Raoultschen Gesetz fur die Aktivitat sowohl
des Losungsmittels als such des geliisten Stoffes. Die Uberschuflmisohungsentropien
sind fur alla
Zusammensetzungen positiv. Dies wird in erster Linie auf die ferromagnetischen Eigenschaften der
Legierungen zurtickgefiihrt.
Es wird auf Grund &nor Betrachtung dsr magnet&hen,
elektronischen,
Schwingungs- und Gitter-Ve~rrun~fak~~n
geschlossen, de0 in Nickel-Pall~i~-Legierungen,
insbesondere in den pall~iu~eichen,
starke Nahordnung auftritt.
INTRODUCTION
THE nickel-palladium
system, unlike the closely
related Fe-I’d, Fe-P& Co-Pt, and Ni-Pt systems,
has generally been regarded as a complete series of
solid solutions in which no superlattices are formed.(l)
The most prominent
evid,enoe
for the absence
of
ordering in the system is the careful X-ray diffraction
work of Hulgtren and Zapffe.f2) Using a series of
* Received May 4, 1964; revised June 22, 1964.
This paper is based in part on a dissertation submitted
by L. R. Bidwell to the Ohio State University in partial
fulfillment of the requirements for the Ph.D. degree.
t Aerosuace Research Laboratories. Office of Aerosnace
Rekearch,-Wright-Patterson
Air Force ‘Base, Ohio.
*
$ Department
of Met.a~~gieal
Engineering,
The Ohio
State University, Columbus, Ohio.
ACTA METALLURGICA,
VOL.
13, FEBRUARY
1965
well homogenized alloys that had been annealed for
periods up to 2 weeks at 600°C and 3 weeks at 4OO”C,
they found that the cell Dimensions followed a
smooth curve as a function of composition with a
considerable positive deviation from Vegard’s law.8
They could not 6nd any evidence for the existence of
ordering or for a miscibility gap that had been
suggested earlier by Fraenkel and Stern.t4) In recent
years, however, several Russian investigate
have
noted anomalous electrical and magnetic behavior at
the stoichiometric composition NiPd, which they
conclude is due to the existence of a superstructure
at that composition. Among the effects observed are
5 X-ray studies by the authors confirm this observation.(3’
61
62
ACTA
METALLURGICA,
a satellite peak in the variation of the thermoelectrio
force as a function of longitudinal and transverse
magnetic field strength ;(S) a small but sharp variation
in the Curie temperature and a maximum in the
temperature coefficient of the longitudinal galvanomagnetic effect;@*‘) a sharp change in the magnitude
of the odd Nernst-Ettingshausen effect;(s)* and a
sharp change in magnetostriction in both longitudinal
and transverse magnetic [email protected]) Although it is
questionable whether or not these observations are
related to the presence of a superlattice, particularly
in view of the negative but more direct X-ray results,
they do suggest that a tendency toward ordering,
perhaps in the form of increased short-range order,
may exist in palladium-rich alloys. This possibility
becomes especially attractive when the nickelpalladium system is compared with the iron-palladium system. While iron has a larger number of
positive holes in the d-band than nickel, there are
many obvious similarities between the two systems,
e.g., their small difference in atomic size, the conformation of their phase diagrams,“) and their deviations
from Vegard’s law. t2) The iron-palladium system
shows strong ordering effects, with superlattices
stable to SOO-900°C being formed at compositions
roughly corresponding to FePd and FePd,. It was
expected that a knowledge of the solution properties
of solid nickel-palladium alloys would contribute
substantially to a better understanding of their
alloying behavior and might also provide further
insight into the question of ordering in the system.
EXPERIMENTAL
PROCEDURE
The relative thermodynamic properties of solid
nickel-palladium alloys were derived from measurements of the reversible potential of the solid galvanic
cell
Pt 1Ni, NiO
10.85Zr0, * 0.15CaO 1Ni-Pd, NiO 1Pt
as a function of composition and temperature. Solid
galvanic cells employing calcia stabilized ziroonia as
the electrolyte have been used with considerable
success by Kiukkola and Wagner(lO~ll) in determining
the standard free energies of formation of several
oxides at elevated temperatures and by Rapp and
Maak(12) in an investigation of the thermodynamic
properties of solid copper-nickel alloys. It can be
shownds) that under conditions of pure anionic
conductivity of the electrolyte, the activity (aNi) and
relative partial molar free energy (Apx,) of nickel in
the nickel-palladium alloy can be obtained directly
* Reference 8 refers to Ni,Pd, however, the experimental
data clearly indicate that Ni Pd, is intended.
VOL.
13,
1965
from the open circuit potential of the cell using the
relation
E=
-Elna,
2F
= _A’Ni
21r”
(1)
where E is in volts, T is the absolute temperature, R
is the gas constant, and F is the Faraday oonstant.
The standard state for this case is solid nickel saturated
with oxygen. However, since the solubility of oxygen
in nickel is less than 0.08 at.% in the 700-1200°C
temperature range covered,(i) this is essentially
equivalent to a standard state corresponding to pure
solid nickel. The nearly pure anionic conductivity
of the electrolyte in this temperature range and in
the range of oxygen partial pressures imposed by the
electrodes (Ni-NiO equilibria for 0.04 < aNi < 1.0)
has been well established by Kingery et uZ.(13) and by
Schmalzried.04) According to the relative values of
the standard free energies of formation of ZrO,,
NiO, and Pd0,d5) mixed potentials arising from
displacement reactions involving the cell components
would not be expected.
The cell apparatus consists of a cell holder and an
impervious mullite reaction tube that serves as a
gas-tight furnace enclosure for maintaining the cell
in an inert environment, The reaction tube is graded
to Pyrex joints at each end and.is encased in electrically grounded platinum foil in order to shield the
measuring circuits from induced a.c. potentials. The
essential features of the cell holder, which is a
modification of the configuration employed by
Schmalzried,06) are shown in Fig. 1. The tapered
brass fixture serves as the seal for one end of the mullite
reaction tube and as an exit for the electrical leads.
In addition, it aligns the two small concentric mullite
tubes which clamp the galvanic cell. A portion of
the outer tube, which is held to the brass fixture
under spring tension, is cut away to facilitate placement of the cell and to provide a seat for the alundum
thrust block. The inner tube, which acts as a pushrod,
is positioned via a compression spring by a hollow
threaded screw located in the brass fixture. The
hross
Towed
Ground
Alignment
Fixture
Mullitr
Tuber
to fit Pyrex
Gloss Joint
FIG. 1. Schematic diagram of galvanic cell holder.
BIDWELL
AND
SPEISER:
THERMODYNAMICS
tablets and platinum electrodes which make up the
cell are held against the alundum thrust block by
applying a moderate pressure with the pushrod.
The cell, which consists of a stabilized zirconia
electrolyte tablet sandwiched between metal plus
nickel oxide electrodes backed with platinum contacts,
is roughly 4 mm long by 8 mm dia., thus minimizing
the effects of thermal gradients. The cell assembly
was heated by a tubular resistance furnace which was
held to within f 1.5”C by a proportional band
controller. Cell temperatures were measured by means
of a Pt-13% Rh thermocouple placed in the alunclum
thrust block, l-2 mm from the alloy electrode. The
thermocouple used for this purpose was calibrated
against the melting points of pure zinc and gold.
Cell potentials were measured with a Leeds and
Northrup K-3 potentiometer and a high sensitivity
galvanometer using a three wire circuit in which the
platinum leg of the thermocouple acted as the positive
lead to the galvanic cell. The negative lead to the
cell was grounded through a 0.01 ,uF capacitor as a
further precaution against the introduction of induced
potentials.
The alloys were prepared at nominal 10 at.%
intervals from high purity carbonyl nickel and
commercial high purity palladium sponge by induction
melting in vacua. The alloy ingots were cold forged
and then homogenized in vacua beginning with 5 hr
at 1075”C, followed by successively higher temperatures, and ending with a 1 hr treatment within 100°C
of the solidus. Chemical analyses of the alloys
indicated that they contained less than 200 ppm
impurities, exclusive of oxygen.
The electrode
tablets were prepared from reagent grade NiO and
from metal powder ground from the homogenized
ingots with a tungsten carbide dental drill. Prio;
to use, the NiO was heated in purified helium several
hours at 1000°C in order to free it of excess oxygen.
Tablets 6 mm dia. by 2 mm thick were cold-pressed
at 5000 psi in a hardened steel die. It was f0und
from experience that metal to oxide ratios of 5 : 1 to
10: 1 were preferable to lower ratios because of the
improved sensitivity in the measurements made
possible by the lower circuit resistance.
The electrolyte tablets were prepared from high
purity Wah Chang (99.98%) zirconia and reagent
grade calcium carbonate. The appropriate mixtures
of zirconia and calcium carbonate were compacted
by cola-pressing ad calcinecl at 1300°C for 12 hr.
The calcined material was ground in a boron carbide
mortar, cold-pressed into tablets 1-2 mm thick by
9 mm dia., and then sinterecl in air at 1750°C for
36 hr.
OF
Ni-Pd
ALLOYS
63
In starting an experiment, the mull&e reaction
tube was alternately evacuated with a mechanical
pump and purged with purifiecl helium several times
in order to obtain a clean system. The helium was
purified by passing it over anhydrous magnesium
perchlorate, ascarite, hydrogen-reduced copper catalyst at 15O”C, oxidized copper catalyst at 15O”C,
again over anhydrous magnesium perchlorate and
ascarite, and finally through a liquid-nitrogen cold
trap. In a few of the earlier experiments the cell was
heated to 700°C and data recorded with increasing
temperature. In all subsequent ones however, the
initial equilibration of the cell was hastened by
making the first measurements at 1100°C. The cells
were usually allowed to equilibrate 8-12 hr (overnight)
at this temperature. After the initial equilibration
period, the cdl potential was measured to the nearest
0.01 mV every 10-20 min over a period of several
hours. When the voltage had attained a constant
value the furnace temperature was lowered and the
cell allowed to equilibrate at the new temperature.
Data on the nominal 20, 40, 60 and 80 at.% compositions were recorded both on cooling and heating.
The data on the nominal 10, 30, 50, 70 and 90 at.%
compositions were checked with measurements on a
duplicate cell. The time required for the cells to
reach equilibrium, for all but the initial equilibration,
varied from 1 to 2 hr at the higher temperatures to
4 to 8 hr at the lower temperatures.
EXPERIMENTAL RESULTS AND DISCUSSION
Within experimental error, the cell potentials were
linear functions of the temperature. Values taken
from the smoothed experimental data at even 100°C
intervals are shown in Table 1. The overall reproducibility of the experimental measurements was
exceptionally good. In the earlier experiment,s, where
only normal precautions were observed in the preparation and manipulation of the cell components and
in the assembly of the cell, the scatter in the data was
generally less than &2.5%.
In later experiments,
where improved techniques were employed, the scatter
was in all cases considerably less than f 1 Oh.
In general, the observed cell voltages were very
stable over’ long periods of time. For example, the
pot.ential of a cell containing a 47.4 at. y. Pa electrode
equilibrated at 12OO”C, changed by only 0.04 mV
in over 28 hr. However, cells involving 77.7 and
86.5 at.% Pd electrodes were exceptions to this rule
at temperatures of 1000°C and above. After one of
these cells appeared to reach equilibrium, the voltage
drifted downward, continuously, at the rate of several
hundredths of a millivolt per hour. In all cases the
64
ACTA
METALLURGICA,
VOL.
13,
1965
TABLE 1. Cell potentials for nickel-palladium alloys
Cell potential (mV)
NPd
700°C
800°C
900°C
1ooo”c
llOO°C
1200°C
0.107
0.191
0.287
3.51
6.25
10.45
4.09
7.32
12.30
4.64
8.39
14.15
6.27
9.47
15.98
6.86
10.55
17.83
6.45
11.63
19.68
0.382
0.474
0.564
17.43
26.75
41.40
20.13
30.40
46.40
22.76
34.00
51.40
25.41
37.66
56.35
28.03
41.30
61.35
30.69
44.90
66.35
0.681
0.777
0.866
66.30
93.40
132.85
73.05
102.15
144.05
79.80
110.86
155.10
86.50
119.55
166.25
93.30
128.20
177.26
100.05
136.90
188.35
NiO content at the electrolyte interface appeared to
decrease on the alloy side and to increase on the
nickel side. This behavior was attributed to concentration polarization of the electrodes due to the small
but finite electron conduction in the electrolyte. By
allowing these cells to remain at 1000°C and above
only long enough to achieve practical equilibrium,
the drop in potential attributable to polarization
could be held well within the limits of reproducibility
dictated by the other experimental errors.
Although there is no direct experimental criterion
for cell reversibility, reproducibility is generally
accepted as a strong indication of it. Cells were
checked for thermal reversibility by recording
potential measurements with increasing as well as
decreasing temperature. They were also checked for
electrical reversibility by momentarily unbalancing
the potentiometer, causing a small current of several
microamps to flow according to the direction of
unbalance.
When the cells were displaced from
equilibrium in this manner, they rapidly returned to
their initial voltage, usually within a matter of
minutes.
The activities (aNi) and relative partial molar free
energies (ApNi) of nickel, taken relative to solid
nickel saturated with oxygen, were calculated from
equation (1). The corresponding quantities for
palladium were evaluated from a graphical integration
of the Gibbs-Duhem equation in the form :
Nm
1% yPd
=
@NilNNiNPd
-
s
aNi
dNPd,
(2)
other but have been spread out somewhat in order to
show the number of measurements. Figures 3 and 4
illustrate the manner in which the activities and
relative molar free energies change with temperature
from 700 to 12OOW.
From a consideration of the phase diagram, i.e.,
the absence of miscibility gaps, compounds, or superlattices, and the similarities in the atomic size and
electronic structure of nickel and palladium, the small
deviations of the activities from ideal solution
behavior seen in Fig. 3 are not surprising. However,
the details of the observed deviations are noteworthy,
particularly in the case of nickel, which exhibits both
positive and negative departures from Raoult’s law.
Although this type of behavior is unusual, it is not
without precedent in systems involving transition
metals with nearly or completely filled d-shells.
Similar behavior has been observed by Weibke and
Matthea
in Cu-Pt alloys, Schmahl(ls) in Au-Pd
alloys, Orianios) in Co-Pt alloys, and by Aukrust and
Muant20)in Fe-Pd alloys.
The relative partial molar entropies of nickel
(A&) were calculated from the slopes of potentialtemperature curves using the relation
=2p
p.Npd
aE
[ 6'T P,Npd' (3'
I
The values for palladium were determined in a similar
manner from the slopes of APpd-temperature curves
(Fig. 5). The relative partial molar enthalpies were
evaluated from equations of the form :
1
where the Ni are the appropriate mole fractions,
ypd is the activity coefficient of palladium (apd/Npd),
and aNi E log yNi/NPd2 (see Tables 2 and 3). The
activities of nickel and palladium calculated from
the smoothed data at 900°C are shown in Fig. 2.
Also included in this figure are the values for a,,
calculated directly from the experimental data. In
most cases these values fall nearly on top of each
A& = AFi + TA&
(4)
Like the activities, the enthalpies of mixing exhibit
rather unusual behavior (Fig. 6) in that they are
endothermic for nickel-rich solutions and exothermic
for palladium-rich solutions. It is worthy of note,
although no explanation can be offered, that the
partial enthalpies of mixing of nickel and palladium
pass through maximum positive and negative values,
BIDWELL
SPEISER:
AND
THERMODYNAMICS
TABLE 2. Activities
-_
in nickel-palladium
oPd
!PC
0.107
0.191
0.287
0.382
0.474
0.564
0.681
0.777
0.865
700
0.920
0.862
0.779
0.660
0.528
0.373
0.206
0.108
0.042
0.072
0.105
0.145
0.201
0.272
0.372
0.530
0.680
0.824
1000
0.908
0.841
0.749
0.629
0.503
0.358
0.207
0.113
0.048
0.068
0.106
0.154
0.217
0.292
0.400
0.556
0.701
0.833
0.107
0.191
0.287
0.382
0.474
0.564
0.681
0.777
0.865
800
0.915
0.854
0.766
0.647
0.518
0.367
0.206
0.110
0.044
0.070
0.104
0.148
0.206
0.278
0.381
0.540
0.687
0.827
1100
0.906
0.837
0.740
0.623
0.498
0.355
0.207
0.115
0.050
0.067
0.106
0.157
0.221
0.298
0.408
0.565
0.705
0.835
0.107
0.191
0.287
0.382
0.474
0.564
0.681
0.777
0.865
900
0.912
0.847
0.756
0.638
0.510
0.362
0.206
0.112
0.047
0.068
0.105
0.151
0.211
0.284
0.390
0.548
0.694
0.830
1200
0.903
0.833
0.733
0.617
0.493
0.352
0.207
0.116
0.051
0.066
0.106
0.160
0.225
0.303
0.413
0.570
0.709
0.836
_
-214
-387
-653
-1050
- 1569
-2372
-3682
-5112
-7156
-
A Fm
-6255
-5255
-4407
-3626
-2930
-2194
-1405
-851
-435
aNi
molar quantities for nickel-palladium
aPd
alloys at 900°C
cal/deg-mole
AFJf
-860
-1317
-1731
-2034
-2214
-2271
-2132
-1801
-1342
Ai&
Ai&
0.271
0.497
0.852
1.222
1.678
2.302
3.110
4.614
5.131
5.652
4.406
3.220
2.522
1.902
1.315
0.825
0.516
0.336
Cal/mole
AS”
AHNI
0.847
1.243
1.531
1.719
1.784
1.746
1.554
1.296
0.983
104
195
346
384
399
329
-34
-403
-1138
0.4
in nickel-palladium
alloys at 900°C.
65
alloys
aNi
AFm
Fm. 2. Activities
ALLOYS
T”C
Cal/mole
0.107
0.191
0.287
0.382
0.474
0.564
0.681
0.777
0.865
Ni-Pd
NPd
TABLE 3. Relative
h’d
OF
AHpd
AH=
375
-87
-630
-668
-699
-652
-437
-246
-39
133
141
66
-18
-121
-225
-309
-281
-189
0.6
0.0
FIG 3. Temperature variation of the activities in nickelpalladium alloys.
ACTA
METALLURGICA,
VOL.
13,
1965
---- Idea1Solution
NPd
FIG. 4. Tempemture variation of the relative integrtal
molar free energy of nickel-palladium alloys.
FIG.
5.
Relative molar entropies of nicked-palladium
alloys in the range XK-1200°C.
FICX.6. Rebtive molar enthalpiss of nickel-palladium
aIloys in the range ?oO-1200°C.
BIDWELL
AND
SPEISER:
THERMODYNAMICS
respectively, at about 45 at.% Pd, which corresponds
to the Gom~osition of the ~nimum
in the phase
diagram.
The relative molar entropies and enthalpies are
listed in Table 3. Since the oell potentials at constant
composition were, within experimental error, linear
factions
of the ~mperature, the relative molar
entropies and enthalpies listed can be regarded as
constant over the entire 700-1200°C temperature
range. It follows therefore, that AC, g 0 and within
this temperature range the specific heat of the alloys
can be approxima~
by the ~opp-Neumann rule.
Although electroche~oal
methods are generally
considered to be inferior to calorimetric methods in
obtaining enthalpy data, the excellent reproducibility
of the potintial measurements and the minimization
of side-reactions made possible by the use of a solid
rather than a liquid electrolyte, permitted an accuracy
which is considered to be comparable with that
obtainable by calorimetry. On the basis of the scatter
in the data, the limits of error are estimated to be less
than: 10.005 for the activities; f20 Cal/mole for
+ 100 Cal/mole for AH= ; and fO.1 calfdegf
AF=;
mole for AL?.
GENERAL
DISCUSSION
The characteristic features of the thermod~amic
functions obtained for nickel-pa~di~
alloys are
best described by referring to the appropriate excess properties (Fig. 7) obtained by subtracting
the properties for an ideal solution from the observed
properties. Thus, the excess entropies of mixing
(ASExs) are small and positive and the heats of
mixing are small and change from positive to negative
with increasing palladium content.
The positive ASEX’ indicates the important role
of non-configurational factors in determining thermodynamic properties that has been stressed in recent
years by a number of investigators, particularly
[email protected]
Any deviation from ideal (random)
mixing such as clustering or ordering leads necessarily
to a negative contribution to the excess entropy of
mixing. In order to assess the con~ational
aspects
of the mixing process in the nickel-palladium system,
non-configurational factors such as the magnetic,
electronic, and lattice vibrational contributions to the
thermodynamic properties must be taken into account.
Although specific heat data for the system are not
available, the order of magnitude of these contributions
can be crudely estimated from other considerations.
One would expect a magnetic contribution to
ASExs due to the ferromagnetic properties of nickelpalladium alloys at lower temperatures. Saturation
OF
Ni-Pd
ALLOYS
67
FIG. 7. Relative
integral molar excess properties of
nickel-palladium alloys at 900°C.
magnetization measurements(a2-M) on these alloys
have shown that the average magnetic moment per
atom is larger than can be accounted for by nickel
alone. This means that in the ferromagnetic state
a greater degree of electron spin ordering is present
in the alloys than in the corresponding amounts of
pure nickel and pa~~ium.
Con~quently, at 700°C
and above, where both the alloys and pure nickel are
in the paramagnetic state, the alloys will have a
positive magnetic entropy of mixing due to their
larger relative magnetic entropy of disordering.
According to Gugge~e~,(~)
the statistical mechanical value for the molar magnetic entropy in changing
from the ferromagnetic to the paramagnetic state is
given by
S (magnetic) = R In (2s + I),
(5)
where s is the resultant spin quantum number of the
unpaired electrons and (2s + 1) is the multiplicity of
states. In applying this relationship to nickelpalladium alloys a question arises as to whether one
should consider the d-electrons collectively or as
bound to specific atoms. On the basis of the former
one concludes from magnetic measurements that
niokel and palladium both contain approximately
0.6 electrons in the s-band and an equal number of
positive holes in the d-band. In the case of nickel, the
68
ACTA
d-band is completely
holes
are present
has suggested
number
polarized,
in one
that
and only
the relative
and
nickel-palladium
Equally
attractive,
however,
the d-electrons
regarded
the electrical
is the
of
generalized
by Van Vleck.(2s)
a band
In this
but are
Nickel is considered
to be
0.6 moles of magnetic
with
moment
a magnetic
In addition
of
one
to yielding
for nickel in remarkably
atoms, each
Bohr
magneton
a magnetic
entropy
close agreement with experi-
ment,@a) this model does not require the use of nonhalf-integral
spin numbers
by the authors.
model
is assumed
(5) that
palladium
and is therefore
If the number
to
entropy
alloy can be obtained
S (magnetic)
=
alloy, both taken at 0°K.
from the expression
expressions
of nickel
magnetization
The product
represents the mole fraction
By combining
(6)
magnetization
and 5, is the relative saturation
3ds state.
as
for a nickel-
cO,uBRIn 2,
where pB is the saturation
equation
in this
on alloying,
for the band model, it follows
the magnetic
of the
<ohs in this
of atoms in the
(6) with the corresponding
for the pure components
shown that the magnetic
entropy
it can readily be
of mixing
is given
by the relation
ASM
saturation
remarkably
result
data
accounts
well.
from
N,i)
In 2.
(7)
(7)
using
from
of
Sadron(22)
to 0°K are compared
ASEXS in Fig. 8.*
(magnetic)
-
calculated
(magnetic)
experimental
netic)
= ,@(10
magnetization
WentJ2s) extrapolated
ASM
ASEXS (nonmagnetic),
Fig. 8.
the
same
(Fig.
The negative
the
loss
values of ASM (magof
ferromagnetism
at
Although
the differences
between
97 at.%
Pd.
ASExs and ASM (magnetic) may be trivial in view
of the uncertainties
in each, they represent values of
* If one ignores the requirement for half-integral spin
numbers and somewhat arbitrarily
uses the expression
(pB + 1) for the multiplicity of states as has been done in
some instances,‘sl-ss’ we obtain the relation AS”(magnetic)
=
R[ln (&,1ug+ 1) - NNi In (,u~ + l)]. This leads to values of
AS”(magnetic)
that are slightly larger (less than 10 per cent
in all cases) than those shown in Fig. 8.
as the
for nickel
curve
enthalpy
since the magnetic
at temperatures
for
AHM
rich solutions
rich solutions.
may only be coincidental
unexpected
curve in
that this curve exhibits
features
for palladium
similarity
and
Although
this
it is not totally
contribution
to the
well above the Curie point
is essentially zero(34) and AHM (nonmagnetic) s Apv.
The contribution to ASEx’ and AHM arising from
changes
in the
electronic
and
vibrational
heat on mixing cannot be satisfactorily
absence
of low-temperature
specific
from
Stoner’s
ferromagnetic
ya =
of the former
relation
heat coefficient
[y = C,
Jf!L[(l
for the electronic
pure
While
ferromagnetic,
the assumption
approximate,(36)
50 )1’s] 9
(8)
for the alloy and
component
respectively.
of a parabolic
this equation
of a
band shape?)
+ 50)1’s + (1 -
where ya and y. are the coefficients
the
Howcan be
(electronic)/T]
alloy with a parabolic
2113
specific
evaluated in the
specific heat data.
ever, the order of magnitude
and
ASEx’
general
7), i.e. positive
negative
with the
It can be seen that
for the observed
shown as the dotted
It is worth noting
estimated
ASM (magnetic)
The
NPd
FIG. 8. Comparison of calculated relative magnetic entropies with experimental relative excess entropies of
nickel-palladium
alloys well above the Curie temperature.
preferred
of s-electrons
be constant
suggested by Wohlfarth
from
-0.2 -
of 3ds and 3d1° states such that one mole
of atoms contains
(s = +).
holes
coefficients(28)
do not form
as quasi bound.
a mixture
the
alloys.
Heisenberg model introduced
model
Hall
0.6
This model has
to explain
ordinary
1965
constant
of positive
is changed.
been used quite successfully
resistivities(27)
remains
distribution
13,
Wohlfarth(26)
and palladium,
in the s-band
in the two half d-bands
VOL.
i.e. all of the positive
half-band.
on alloying
of electrons
METALLURGICA,
band
predicts
is only
a reasonable
value of y for pure palladium(35) and might therefore
be expected to approximate the value of y for alloys.
Using the 5, determined from the data of Sadron’22)
and Went(23) the values
predicted
change
specific
in the electronic
for Ay, i.e., the
heat coefficient
mixing, are positive and less than 2.5
mole for nickel-rich
solutions
for
solutions.
palladium-rich
x
on
10-a cal/deg2/
and 10H4 cal/deg2/mole
If
by
is
assumed
HIDWELL
independent
butions
of temperature,
to AS”s”
THERMODYNAMICS
ANI) SPEISER:
contri-
deviations
are less
are many
the corresponding
(900°C)
and AHM (900°C)
OF Ni-Pd
of the activities
times
from ideal solution behavior
larger
and
at least
solutions
palladium
alloys.
long-range
order is the most
0.1 cal/deg/mole
mole for palladium-rich
Although
solutions.
a suitable
method
vibrational
contributions
properties
is not available,
that
a positive
low
temperatures-and
enthalpy
at
for estimating
to
the
lattice
to expect
to the specific
hence
the
heat
lower
therefore
temperature,
seems
stable
the
and
The above
result
from
evaluation
the nickel-palladium
use of various
theoretical
made
system.
It must
be recognized,
palladium.
An idea of the magnitude
evidence
cannot
be
distortional
energy, often termed the misfit energy,(21)
can be shown that
of the lattice
at the composition
It
and tempera-
The current
suspicion
permit
models
regarded
present
only qualitative
at best.
free
palladium
the solid.
If it is assumed
does not change greatly
able assumption
that the entropy
on melting,
and solidus curves
suggest
difference
solid,
in the
A(AH’f)
misfit energy
coordination
heat
=
number
and the lattice
roughly
AH”
AH”(‘),
and
reflects
the
different
heat
the ASEXS and
and asymmetric
with
maximum
0.3 cal/deg/mole
to be
and
toward
negative
800 Cal/mole
aspects
by X-ray
temperature
AND
indicates
nickel
Raoult’s
law.
The
magnitude
those
obtained
remaining
ASESS
leave
the
and AHM even more negative,
If
these quantities are interpreted
statistical
and nearest-neighbor
theories,
alloys,
it might be concluded
particularly
short-range
possibly
atures.
energy
order
in terms of the usual
chemical interaction
that nickel-palladium
palladium-rich
at
even long-range
elevated
would
solutions,
temperatures
possess
and
order at much lower temper-
A comparison of the activity and excess free
data with those for solid and liquid iron-
palladium
possibility
alloys(20) casts some doubt on the latter
however.
In the iron-palladium
system,
the course of t,he activity
and excess free energy curves
is strikingly similar to those shown in Figs. 2 and 7.
However.
even
for liquid
alloys,
the negative
iron-palladium
(iii) The
small
and
Palladium-rich
alike.
diagram,
the
exhibit
solutions,
data
Aukrust
which
deviations
negative
deviations
activity
by
in
the activities
solutions
solvent
solute
evaluated,
phase
exhibit
negative
of solid
by an electrochemical
the
Nickel-rich
for the
for the solute.
properties
determined
solid solubility,
and palladium
measurements.
a solid electrolyte.
with
complete
deviations
were
range 700-1200°C
that employed
of the
such as might
CONCLUSIONS
alloys
(ii) Consistent
helium
analysis
of the alloys,
thermodynamic
nickel-palladium
minimum,
a
liquid
diffuse scattering
SUMMARY
(i) The relative
A more
above the ferromagnetic
and an experimental
hand, exhibit
be
as
configurational
be obtained
this
of the nickel-
from
to temperatures
The deletion
of vibrational
contrirespectively.
butions, which are assumed to be positive but whose
cannot
require,
transformation
factors
which is presumed
would
measurements
temperatures
method
and electronic
are negative
solutions
than
liquid
of the solid and liquid.
with composition,
remaining
less
of the
and the slightly
misfit’ energy,
palladium-rich
values
-
of magnetic
parabolic
in the atomic
system
specific
in the liquid and solid,
AHM(s) _ AHMU). The
of mixing
of the lattice
In the absence
in the liquidus
similarities
AHcM’)
of mixing
which is a reason-
since the flat minima
and electronic configurations
then AF.=SYS _ AFE=U) i
for
that
reservation.
of refinement,
AFEXS(‘) = 612 Cal/mole, i.e. the excess
energy
indirect
are not above
state
conclusions
of
by the
order in the
however,
of alloy solutions
and in their
behavior
without
definite analysis of the alloying behavior
than
length
provides
AFEXS(“) -
is 612 Cal/mole more negative
if
at
temperature
of short-range
ture ofthe minimum in the phase diagram,
of the liquid
that
possible
models,
for the existence
due to Wagner.t3*)
likely
configuration
of the alloying
system,
evidence
by methods
energy
for nickel-
critical
the lattice distortions(37) caused by the 10% mean
difference
in the atomic diameters
of nickel and
can be obtained
free
than
of time.
at
entropy
temperatures-will
some
It
excess
negative
may be too low for it to occur in a reasonable
thermodynamic
it is reasonable
contribution
higher
and 70 cal/
more
the
than 0.3 cal/deg/ mole and 170 Cal/mole for nickel-rich
and less than
five times
69
ALLOYS
positive
deviations
on the other
for the solvent
are very
and
of
from
similar
Muant20)
for
and
to
the
system.
relative
partial
molar
nickel are, within experimental
of the temperature,
signifying
free
energies
of
error, linear functions
that AC, above
760°C
is essentially
zero and that the specific heats of alloys
at elevated
temperatures
the Kopp-Neumann
(iv) The heats
thermic
can be approximated
of mixing
for nickel-rich
negative
i.e.
coincident
diagram.
values,
with
are small and are endo-
solutions
palladium-rich
solutions.
of nickel and palladium
and
by
rule.
and exothermic
respectively,
the
for
The partial heats of mixing
attain maximum
positive
minimum
at
45 at.%
in
the
Pd,
phase
70
ACTA
METALLURGICA,
(v) The excess entropies of mixing are small and
positive and pass through a maximum also coincident
with the composition of the phase diagram minimum.
The positive sign of the ASEXS is considered to be
primarily a result of the ferromagnetic behavior of the
alloys.
(vi) The experimental activity measurements were
very reproducible and permitted the heats of mixing
to be determined with an accuracy comparable to
that obtainable by calorimetric methods.
(vii) Based on a qualitative consideration of
magnetic, electronic, vibrational, and lattice distortional factors, it has been concluded that nickelpalladium alloys, particularily palladium-rich solutions, exhibit significant short-range order.
ACKNOWLEDGMENTS
The authors would like to thank Dr. R. A. Rapp,
for his helpful discussions of the experimental method,
and the Battelle Memorial Institute for performing
the chemical analyses. They would also like to
express their appreciation to the International
Nickel Company, especially Mr. R. Vines, for providing the pure nickel and palladium used in this
investigation.
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