- Email: [email protected]
Studies of solution ideality in the Praseodymium-Neodymium system
STUDIES
OF SOLUTION C.
E.
IDEALITY
LUNDIN,?
A.
IN THE PRASEODYMIUM-NEODYMIUM S. YAMAMOTOt
and
J.
F.
SYSTEM*
NACHMAN$
Solutions of the praseodymium-neod~ium alloy system were studied both in the liquid and solid state. The thermodynamic activities at 1525’, 1500” and 1475°C an,d densities at 1240°C were determined for the liquid alloy solutions, and the latt,ice pa,rs+metersand densities were obtained for the roomtemperature solid solutions. The resulting activities and atomic volumes were plotted against alloy composition in mole fraction, and, within experimental error, they exhibit a linear relationship. Therefore, it is concluded that praseodymium-neodymium alloy solutions behave essentially as ideal solutions both in the liquid and solid states. ETUDE
Dir SYSTEME
PRASEODYMIUM-NEODYMIUM
Les auteurs ont 6tudiB des solutions du systbme praseodymium-neodymium aux Btats liquide et solide. Pour lee solutions liquides, ils ont d&termin6les activitds B 1525, 1500 et 1475°C et les densitis B 1240°C. Pour les solutions aolides, ils ont determine & la temperature ambiante les param&res r&iculaires et Ins dens%&. 11 existe une relation lin&re entre les activitBs et les volumes atomiques d’une part et la composition de l’aliiage exprim&e en fraction molaire, d’antre part, Les auteurs en concluent que les solutions d’alliage pr~~ymium-neod~ium se compcrtent essentiellement comme des solutions idbales 8, la fois B 1’8tat aolida et & l’Btat liquide. UNTERSUCHUNG
DER
LdSUNGSIDEALITdT NEODYMIUM
IM SYSTEM
PRASEODYMIUM-
L6sungen des Legierungssystems Praseodymium-Neodymium wurden im f%issigen und im fester1 &stand untersucht. Fiir die fliissigen Le~erungsl6sungen wurden die therm~~mischen Aktivitliten bei 1625”, 1500’ und 1475” und die Diohte bei 1240°, fiir die festen Liisungen bei ~um~mperatur der Gitterparameter und die Dichte bestimmt. Die sich ergebenden Aktivit&en und Atomvolumina warden gegen die Legierungszusammensetzung in Molenbriichen aufgetragen, und innerhalb der Fehlergrenzen ergab sich ein linearer Zusammenhang. Es wird da&r gefolgert, daI3 sich Praseodymium~NeodymiumLegierungen im fliissigen und im festen Zustand im wesentlichen wie ideale LBsungen verhalten.
1. INTRODUCTION
objective of this research is to establish an understanding of the principles of alloy formation using the rare-earth metals. The praseodymiumneodymium system was selected as the first of a continuing series of binary systems to be studied using the ideality of solution as the criterion of analyzing alloy behavior.(l) The parameters normally considered to affect alloy behavior are atomic diameter, crystal structure, electrone~ti~ty, and electronic structure, The pr~eod~ium-neodymium system was chosen first because these parameters are essentially invariant between the two components. Praseodymium and neodymium are similar in every respect, with the exception of the” one electron difference in the 4f electronic shell. This difference is not expected to affect the alloying behavior. Earlier work by the author@) has established the phase diagram of the system. The solid state is characterized by a lowtemperature h.c.p. phase and a high-temperature The
* Received June 1, 1964; revised August 24, 1964.
DJn$nve;orz;osearch $ A&&s
Institute,
University
of
International, Canoga Park, California.
ACTA METALLURGICA,
VOL. 13, MARCH 1965
Denver,
b.c.c. phase. The components are completely miscible in each of these two solid-state allotropes and also in the liquid state. Thus, one would predict that alloys of this system would behava as ideal solutions. The research described herein was designed to establish the solution ideality. 2. EXPERIMENTAL The Knudsen effusion apparatus was designed and constructed for the determination of activity measurements for this study. Briefly, the apparatus consists of a high-vacuum source, a bell jar in which is contained a .vacuum balance, and a furnace chamber where the effusion is conducted from an appropriately heat-shielded Knudsen effusion cell. A platinum target is suspended above the effusion cell from the hanger pan of the vacuum balance to collect the vapor condensate. The sensitivity of this vacuum balance is 0.1 mg. The vacuum observed at experimental tomperatures is in the order of 1 to 4 x lo-’ mm Hg. The effusion cell consists of an all-~n~lurn chamber. The orifice in the lid is a knife-edge opening whose diameter varies from 0.0797 to 0.1773 cm. Heating of the effusion cell is accomplished by using a tungstenresistance heating coil. Temperature measurements 149
ACTA
150
METALLURGICA,
are made exclusively with a tungsten/tungsten-25% rhenium thermocouple of 0.005 in. dia. inserted into a thermocouple well in the bottom of the effusion cell. At first, difficulty was experienced in forming a sound, ductile bead with a thermocouple, of this type. To avoid brittle failure et the bead, a 0.005 in. tantalum wire is used as a brazing metal. The bead is formed by arc-discharge technique in an inert atmosphere. Integrity of the thermocouple is checked after each vapor-pressure determination by observing the thermal arrests or inflections of the specimen recorded on the controller chart. Calibration of the tungsten/ tungsten-25y0 rhenium thermocouple with the tantalum-brazed bead is carried out in the apparatus against a standard platinum/platinum-13a/o rhodium thermocouple, which is checked, in turn, against the ‘The melting points of selected pure metals. estimated accuracy of the tungsten/tungsten-25% rhenium thermocouple is less than ,t3”C over t’he calibrated temperature range from 700” to 1500°C. Distilled praseodymium and neodymium of special high-purity grade were purchased from the Ames Laboratory, Iowa State University, Ames, Iowa, with the chemical analyses as tabulated below: Impurity $ 0 F Fe La ck Pr Nd Sm C& Si Mg Tl%
Pr
Nd
65 p.p.m. 50 p.p.m. 27 p.p.m. <0.005~! ~0.01% ~0.06°/o
62 p.p.m. 39 p.p.m.
<0.02% <0.025%
200 p.p.m. 0.1% ~O.os~o
Immediately prior to weighing, the roughly cut pieces of the two metals were filed to remove the oxidized surface layer. The weighing was conducted as rapidly as possible, and the alloy charge was weighed to the nearest 0.1 mg. Each charge was then placed in a standard non-consumable-electrode arc furnace, evacuated to prevent further oxidation, and melted in a purified atmosphere of argon. Each ingot was inverted four times and remelted to assure homogeneity. Accurate analyses of the alloys, as well a,s the precise determinations of the relative amounts of each component in their vapor phase, were imperative for obtaining accurate thermodynamic activities. X-ray spectrographic analysis was employed in this study. A 100 kV NORELCO spectrograph was
VOL.
13,
1905
equipped with a tungsten-target, X-ray tube, LL lithium-fluoride analytical crystal, a scintillationcounter detector, and associated electronic circuits. Standard solutions of both praseodymium and neodymium were prepared by dissolving the known amount (0.5 g) of each in nitric acid, evaporating to dryness, and diluting to a known volume (10 ml) with dilute nitric acid. The fixed-angle positions of praseodymium and neodymium “L” spectrum lines for line-intensity measurements were two-theta angle values of 68.23 and 65.06”, respectively. The X-ray tube was operated at 50 kV and 25 mA with intensity measurements for fixed-time intervals of 10 set each at the aforementioned two-theta angle values. All concentration values for praseodymium and neodymium were determined from the average X-ray spectrographic intensity of triplicate sample mounts rather than from a single sample mount. These values were used to prepare the standard reference calibration curves. An average of 0.6% mean deviation was indicated for the overall precision of instrumental measurements and sample replication. The procedure for analyzing the unknown was as follows: Either the arc-melted elloy or its vapor condensate was dissolved in dilute nitric acid. The solution was evaporated to dryness, the residue dissolved in dilute nitric acid and made up to a known volume, usually 10 ml. An appropriate portion of the 10 ml was then evaporated on an X-ray spectrographic mount, so that the total mass of material on the mount was 10 or 15 mg. The composition of these samples as determined by X-ray spectrographic analysis was accepted as the composition of the alloy vapor or liquid at the temperature of the determination. X-ray diffraction analyses of powders of the alloys were conducted with a back-reflection film camera. The camera was calibrated using both high-purity potassium chloride and silicon. The lattice parameters obtained were in excellent agreement with the literature values. The -325 mesh powders were prepared in an inert atmosphere dry box, wrapped in tantalum foil, sealed in evacuated quartz capsules, and stress relieved at 35O’C for 24 hr. The powder patterns were produced using copper radiation and were measured and analyzed employing a leastsquares program on the Burroughs 205 digital computer. The technique followed that of Cohen in which the error is represented by 4 tan 4. In spite of careful preparation and handling of the X-ray specimens, a trace of oxide was observed in the patterns. Determinations of room-temperature densities of
LUNDIN
et al.:
IDEALITY
OF
SOLUTIONS
praseodymium, neodymium, and their binary alloys were made using the displacement method. The medium was monobromobenzene, which was calibrated against variations in the room temperature. The weighing was done on an analytical balance having an accuracy of kO.2 mg. Liquid densities of the praseodymium-neodymium alloys were measured in the Knudsen effusion apparatus by the displacement method. A tantalum crucible was used, and a tantalum bob of known weight and volume was used for the immersion in the liquid alloy. This bob was suspended by a 0.003 in. tantalum wire from the pan of the vacuum balance. A temperature of 1240’ C was used for all liquid density measurements. Since this technique was not calibrated by determining the known densities of some liquid metals in the experimental range, the liquid density values obtained are relative. 3. RESULTS
AND
DISCUSSION
The vapor pressures of the pure elements, praseodymium and neodymium, were determined and reported previously. t3) For praseodymium, the vapor pressure in the temperature range, 17241874’K, was determined to be :
logI0P (mmHg) =
-18,450
f
425
T
+ 8.34 f
0.24
and that of neodymium in the range, 163%1791”K, was determined to be:
log,
P
(mm J&x)=
-18,375 T
f
480
+ 9.57f 0.28
Eight alloys were prepared by appropriate increments throughout the alloy system. The activities of these alloys in the liquid state were then studied by the Knudsen effusion technique.@) The activity of each component in the liquid alloy can be determined by obtaining the analysis of the participating components in the condensed vapor ‘phase. The activity of each component, in turn, can be calculated from a modified Gibbs-Duhem relation. If it is assumed that the vapor of the alloy behaves as an ideal gas, the activity of component “i” is obtained from the following expression :
where the superscripts 1, v and o refer to the liquid, the vapor and the pure component, respectively, and j and P represent the fugacity and the pressure, respectively. The modified Gibbs-Duhem relation
IN
THE
Pr-nTd
emplo.yed is : _ _ p1 In ail = ln = PI0
161
SYSTEM
N1”=NIV N
s NIV=1
I
LdlnN,”
N,”
where the subscripts 1 and 2 represent the components, and N expresses the mole fractions of each component either in the liquid or vapor phase. Each alloy was vaporized for specified times at the selected temperatures, 1475’, 1500”, and 1525°C. The vapor condensate was collected on a cold target, and the condensate was analyzed by an X-ray spectrographic technique. From these data, plots were made of N,dl/N,dv vs. In NPrV and Nprr/Np,” vs. In NNdZI. Figure 1 is a representative plot of the 1500°C data, but is typical also for the other temperatures. Values of apzz and aNdr were obtained from these plots by graphical integration in conjunction with the Gibbs-Duhem equation. Figure 2 is a plot of aprz and aNdz vs. NPlr at 15OO”C, also similar for the other two temperatures. Table 1 presents a tabulation of the composition of the alloys, the compositions of the vapors, and the resulting activities at three different temperature levels, 1475’, 1500”, and 1525“C. The linear. relationship observed in the plots of activity vs. mole fraction demonstrates that the solutions are essentially ideal in character, since they conform to Raoult’s law wherein the activity is equal to the mole fraction. This approach to ideality in the liquid state is also supported by considering liquid density measurements as determined by the displacement technique. The atomic volume of the alloy can be calculated by using the experimentally observed alloy density, p, using an average atomic weight for the alloy according to the relationship,
where N, = mole fraction of component 1 Ml,2 = atomic weight of components 1 and 2 Y = atomic volume of alloy Thus, from the criterion that an ideal solution exhibits no volume change on mixing, a linear plot of atomic volume vs. mole fradtion will confirm that ideahty. Figure 3 shows the plot for the liquid solution at a temperature of 1240°C. The plot is essentially linear within experimental error. The observed liquid density data are also presented in Table 2. The solid solution at room temperature also conforms to the criterion for ideality that there is no volume change on mixing. The densities as determined by either the X-ray diffraction analysis or the displacement technique (densities were independently
ACTA
162
METALLURGICA,
VOL.
13,
1966
1.0 Ts 1773.
K
0.6 -
Gi Y %ki
0.4 -
0.2 -
-05.0
I -4.0
I -3.0
I -2.0 In
I -1.0
Nk
FIa. 1. Plot of NNdz/NNaYvs. In NPrvfor liquid alloys at 150°C. ,22.60
l-
$ 20.m 3 u
20.60
B
20.50 20.40
0.6 -
a’
0.4 36ec )2.,6X >oa o-
5.66C,?‘65t I-
)
Fro. 2. Activities of Nd and Pr in the Pr-Nd system at 1500°C.
,--0-
1
3.w >-
Flu. 3. Plots of lattice parameters (26%) wd liquid (1240°C) and solid (25°C) densities vs. mole fraction of Pr for the Pr-Nd system.
LUNDIN
et aZ.:
IDEALITY
OF
SOLUTIONS
Alloys nominal at.% Pr
Temperature, “C
0.995
0.895
90
0.800
80
0.604
60
0.412
40
0.308
30
0.206
20
0.111
10
Analyzed Pr, at.%
100 80.0 50.0 20.6 -
0 (Pure Nd)
SYSTEM
153
NrrV
a,,’
1475
0.041
0.959
0.005
0.996
1500
0.031
0.969
0.003
0.994
1525
0.043
0.957
0.005
0.995
1475
0.469
0.531
0.099
0.904
1500
0.484
0.516
0.100
0.886
1525
0.490
0.510
0.095
0.898
1475
0.684
0.316
0.216
0.793
1500
0.649
0.351
0.183
0.800
1525
0.658
0.342
0.1176
0.809
1475
0.834
0.166
0.336
0.616
1500
0.836
0.164
0.390
0.590
1525
0.867
0.133
0.462
0.548
1475
0.912
0.088
0.584
0.432
1500
0.912
0.088
0.565
0.409
1525
0.920
0.080
0.614
0.405
1475
0.947
0.053
0.734
0.302
1500
0.953
0.047
0.693
0.265
1525
0.943
0.057
0.712
0.321
1475
0.962
0.038
0.798
0.232
1500
0.969
0.031
0.800
0.190
1525
0.965
0.035
0.816
0.217
1475
0.981
0.019
0.889
0.126
1500
0.984
0.016
0.891
0.109
1525
0.984
0.018
0.923
0.121
Alloys
80 50 20
Pr-Nd
N NdV
TABLE 2. Liquid density data for the praseodymiumneodymium system
Nominal Pr, at. o/o
THE
1. Composition and activity data for praseodymium and neodymium alloys
TABLE
99.5
IN
Density, g/cm’
Atomic volume, cm*/g-atom
6.27
22.47
6.31 6.37 6.42
22.44 22.38 22.36
6.46
22.33
determined by both methods and are essentially the same) were converted into atomic volumes. Table 3 presents the lattice parameters, X-ray densities, experimental densities, and calculated atomic volumes for the solid solution. The linearity of these data vs. mole fraction can be seen in Fig. 3. The X-ray lattice parameters of the room-temperature phase are also presented in this same figure. Thus, the prediction of essentially ideal behavior in both the solid and liquid solutions of the praseodymium-neodymium alloy system based on their
TABLE 3. Solid solution data for the praseodymium-neodymium system Alloys
Density, g/cm* (25°C)
Analyzed Pr, at.%
Observed
X-ray
Atomic volume, cm8
100 90
89.5
6.772 6.793
6.774 -
20.80 -
80
80.0
6.816
6.819
20.76
70 60
70.5 60.4
6.840 6.858
6.844 -
20.73 -
50 40
50.0 41.2
6.887 6.908
6.889 -
20.70 -
3.6646 f -
30 20
30.8 20.6
6.931 6.958
6.935 -
20.65 -
3.6620 f -
10
11.1
6.981
6.986
20.60
3.6587
-
7.005
7.012
20.67
3.6566 f 0.0005
Nominal Pr, at. o!
0 (pure Nd)
Lattice parameters a,, A 3.6715 f -
%,A
c/a
11.8354 f -
0.0027
3.224 -
3.6690 & 0.0008
11.8270 i
0.0029
3.223
3.6670 f 0.0004 -
11.8247 f -
0.0017
3.225 -
0.0005
11.8181 f -
0.0019
3.225 -
0.0004
11.8106 f -
0.0019
3.225 -
0.0007
-
11.8030
-
11.7983 & 0.0026
3.226 3.226
164
ACTA
METALLURGICA,
similar atomic diameters, crystal structures, electronic structures, and electronegativities was experimentally verified.
VOL.
13,
1965
to Mr. Merlyn Salmon, Fluo-X-Spec Analytical Laboratory, Denver, Colorado, for developing the X-ray spectrographic techniques.
4. ACKNOWLEDGMENT
This research was supported under Contract PJo. AF 33(616)-6787 under the technical cognizance of Dr. Lawrence Bidwell of the Metallurgy and Ceramics Research Laboratory of the Aeronautical Research Laboratories. The authors appreciate the counsel of Dr. Rudolph Speiser, Ohio State University and Dr. M. J. Pool, University of Denver. Thanks are due to Mr. R. J. McManis for his assistance with the experimental work and Mr. Maurice Salmon for the X-ray diffraction analyses. Special appreciation is also due
REFERENCES J. F. NACHYAN, C. E. LUNDIN and A. S. YAMAMOTO,Final Report, January 1903, Contract AF 33(616)-6787, ARL 63-15, University of Denver, Denver Research Institute. C. E. LUNDIN, J. F. NACHMANand A. S. YAUOTO, Proceedings of the Third Conference on Rare Earth Research, April 1963, Cleammter, Florida, to be published, sponsored by Purdue University. J. F. NACHMAN, C. E. LUNDIN and A. S. YAMAMOTO,Proceedings of the Second Conferenceon Rare Earth Research, September 24-27, 1961, Gordon and Breach Science Publishers. 4. R. SPEISER, A. J. JACOBSand J. W. SPRETNAK, Trane. Met. Sot. AZME 215, 185 (1959).
OF SOLUTION C.
E.
IDEALITY
LUNDIN,?
A.
IN THE PRASEODYMIUM-NEODYMIUM S. YAMAMOTOt
and
J.
F.
SYSTEM*
NACHMAN$
Solutions of the praseodymium-neod~ium alloy system were studied both in the liquid and solid state. The thermodynamic activities at 1525’, 1500” and 1475°C an,d densities at 1240°C were determined for the liquid alloy solutions, and the latt,ice pa,rs+metersand densities were obtained for the roomtemperature solid solutions. The resulting activities and atomic volumes were plotted against alloy composition in mole fraction, and, within experimental error, they exhibit a linear relationship. Therefore, it is concluded that praseodymium-neodymium alloy solutions behave essentially as ideal solutions both in the liquid and solid states. ETUDE
Dir SYSTEME
PRASEODYMIUM-NEODYMIUM
Les auteurs ont 6tudiB des solutions du systbme praseodymium-neodymium aux Btats liquide et solide. Pour lee solutions liquides, ils ont d&termin6les activitds B 1525, 1500 et 1475°C et les densitis B 1240°C. Pour les solutions aolides, ils ont determine & la temperature ambiante les param&res r&iculaires et Ins dens%&. 11 existe une relation lin&re entre les activitBs et les volumes atomiques d’une part et la composition de l’aliiage exprim&e en fraction molaire, d’antre part, Les auteurs en concluent que les solutions d’alliage pr~~ymium-neod~ium se compcrtent essentiellement comme des solutions idbales 8, la fois B 1’8tat aolida et & l’Btat liquide. UNTERSUCHUNG
DER
LdSUNGSIDEALITdT NEODYMIUM
IM SYSTEM
PRASEODYMIUM-
L6sungen des Legierungssystems Praseodymium-Neodymium wurden im f%issigen und im fester1 &stand untersucht. Fiir die fliissigen Le~erungsl6sungen wurden die therm~~mischen Aktivitliten bei 1625”, 1500’ und 1475” und die Diohte bei 1240°, fiir die festen Liisungen bei ~um~mperatur der Gitterparameter und die Dichte bestimmt. Die sich ergebenden Aktivit&en und Atomvolumina warden gegen die Legierungszusammensetzung in Molenbriichen aufgetragen, und innerhalb der Fehlergrenzen ergab sich ein linearer Zusammenhang. Es wird da&r gefolgert, daI3 sich Praseodymium~NeodymiumLegierungen im fliissigen und im festen Zustand im wesentlichen wie ideale LBsungen verhalten.
1. INTRODUCTION
objective of this research is to establish an understanding of the principles of alloy formation using the rare-earth metals. The praseodymiumneodymium system was selected as the first of a continuing series of binary systems to be studied using the ideality of solution as the criterion of analyzing alloy behavior.(l) The parameters normally considered to affect alloy behavior are atomic diameter, crystal structure, electrone~ti~ty, and electronic structure, The pr~eod~ium-neodymium system was chosen first because these parameters are essentially invariant between the two components. Praseodymium and neodymium are similar in every respect, with the exception of the” one electron difference in the 4f electronic shell. This difference is not expected to affect the alloying behavior. Earlier work by the author@) has established the phase diagram of the system. The solid state is characterized by a lowtemperature h.c.p. phase and a high-temperature The
* Received June 1, 1964; revised August 24, 1964.
DJn$nve;orz;osearch $ A&&s
Institute,
University
of
International, Canoga Park, California.
ACTA METALLURGICA,
VOL. 13, MARCH 1965
Denver,
b.c.c. phase. The components are completely miscible in each of these two solid-state allotropes and also in the liquid state. Thus, one would predict that alloys of this system would behava as ideal solutions. The research described herein was designed to establish the solution ideality. 2. EXPERIMENTAL The Knudsen effusion apparatus was designed and constructed for the determination of activity measurements for this study. Briefly, the apparatus consists of a high-vacuum source, a bell jar in which is contained a .vacuum balance, and a furnace chamber where the effusion is conducted from an appropriately heat-shielded Knudsen effusion cell. A platinum target is suspended above the effusion cell from the hanger pan of the vacuum balance to collect the vapor condensate. The sensitivity of this vacuum balance is 0.1 mg. The vacuum observed at experimental tomperatures is in the order of 1 to 4 x lo-’ mm Hg. The effusion cell consists of an all-~n~lurn chamber. The orifice in the lid is a knife-edge opening whose diameter varies from 0.0797 to 0.1773 cm. Heating of the effusion cell is accomplished by using a tungstenresistance heating coil. Temperature measurements 149
ACTA
150
METALLURGICA,
are made exclusively with a tungsten/tungsten-25% rhenium thermocouple of 0.005 in. dia. inserted into a thermocouple well in the bottom of the effusion cell. At first, difficulty was experienced in forming a sound, ductile bead with a thermocouple, of this type. To avoid brittle failure et the bead, a 0.005 in. tantalum wire is used as a brazing metal. The bead is formed by arc-discharge technique in an inert atmosphere. Integrity of the thermocouple is checked after each vapor-pressure determination by observing the thermal arrests or inflections of the specimen recorded on the controller chart. Calibration of the tungsten/ tungsten-25y0 rhenium thermocouple with the tantalum-brazed bead is carried out in the apparatus against a standard platinum/platinum-13a/o rhodium thermocouple, which is checked, in turn, against the ‘The melting points of selected pure metals. estimated accuracy of the tungsten/tungsten-25% rhenium thermocouple is less than ,t3”C over t’he calibrated temperature range from 700” to 1500°C. Distilled praseodymium and neodymium of special high-purity grade were purchased from the Ames Laboratory, Iowa State University, Ames, Iowa, with the chemical analyses as tabulated below: Impurity $ 0 F Fe La ck Pr Nd Sm C& Si Mg Tl%
Pr
Nd
65 p.p.m. 50 p.p.m. 27 p.p.m. <0.005~! ~0.01% ~0.06°/o
62 p.p.m. 39 p.p.m.
<0.02% <0.025%
200 p.p.m. 0.1% ~O.os~o
Immediately prior to weighing, the roughly cut pieces of the two metals were filed to remove the oxidized surface layer. The weighing was conducted as rapidly as possible, and the alloy charge was weighed to the nearest 0.1 mg. Each charge was then placed in a standard non-consumable-electrode arc furnace, evacuated to prevent further oxidation, and melted in a purified atmosphere of argon. Each ingot was inverted four times and remelted to assure homogeneity. Accurate analyses of the alloys, as well a,s the precise determinations of the relative amounts of each component in their vapor phase, were imperative for obtaining accurate thermodynamic activities. X-ray spectrographic analysis was employed in this study. A 100 kV NORELCO spectrograph was
VOL.
13,
1905
equipped with a tungsten-target, X-ray tube, LL lithium-fluoride analytical crystal, a scintillationcounter detector, and associated electronic circuits. Standard solutions of both praseodymium and neodymium were prepared by dissolving the known amount (0.5 g) of each in nitric acid, evaporating to dryness, and diluting to a known volume (10 ml) with dilute nitric acid. The fixed-angle positions of praseodymium and neodymium “L” spectrum lines for line-intensity measurements were two-theta angle values of 68.23 and 65.06”, respectively. The X-ray tube was operated at 50 kV and 25 mA with intensity measurements for fixed-time intervals of 10 set each at the aforementioned two-theta angle values. All concentration values for praseodymium and neodymium were determined from the average X-ray spectrographic intensity of triplicate sample mounts rather than from a single sample mount. These values were used to prepare the standard reference calibration curves. An average of 0.6% mean deviation was indicated for the overall precision of instrumental measurements and sample replication. The procedure for analyzing the unknown was as follows: Either the arc-melted elloy or its vapor condensate was dissolved in dilute nitric acid. The solution was evaporated to dryness, the residue dissolved in dilute nitric acid and made up to a known volume, usually 10 ml. An appropriate portion of the 10 ml was then evaporated on an X-ray spectrographic mount, so that the total mass of material on the mount was 10 or 15 mg. The composition of these samples as determined by X-ray spectrographic analysis was accepted as the composition of the alloy vapor or liquid at the temperature of the determination. X-ray diffraction analyses of powders of the alloys were conducted with a back-reflection film camera. The camera was calibrated using both high-purity potassium chloride and silicon. The lattice parameters obtained were in excellent agreement with the literature values. The -325 mesh powders were prepared in an inert atmosphere dry box, wrapped in tantalum foil, sealed in evacuated quartz capsules, and stress relieved at 35O’C for 24 hr. The powder patterns were produced using copper radiation and were measured and analyzed employing a leastsquares program on the Burroughs 205 digital computer. The technique followed that of Cohen in which the error is represented by 4 tan 4. In spite of careful preparation and handling of the X-ray specimens, a trace of oxide was observed in the patterns. Determinations of room-temperature densities of
LUNDIN
et al.:
IDEALITY
OF
SOLUTIONS
praseodymium, neodymium, and their binary alloys were made using the displacement method. The medium was monobromobenzene, which was calibrated against variations in the room temperature. The weighing was done on an analytical balance having an accuracy of kO.2 mg. Liquid densities of the praseodymium-neodymium alloys were measured in the Knudsen effusion apparatus by the displacement method. A tantalum crucible was used, and a tantalum bob of known weight and volume was used for the immersion in the liquid alloy. This bob was suspended by a 0.003 in. tantalum wire from the pan of the vacuum balance. A temperature of 1240’ C was used for all liquid density measurements. Since this technique was not calibrated by determining the known densities of some liquid metals in the experimental range, the liquid density values obtained are relative. 3. RESULTS
AND
DISCUSSION
The vapor pressures of the pure elements, praseodymium and neodymium, were determined and reported previously. t3) For praseodymium, the vapor pressure in the temperature range, 17241874’K, was determined to be :
logI0P (mmHg) =
-18,450
f
425
T
+ 8.34 f
0.24
and that of neodymium in the range, 163%1791”K, was determined to be:
log,
P
(mm J&x)=
-18,375 T
f
480
+ 9.57f 0.28
Eight alloys were prepared by appropriate increments throughout the alloy system. The activities of these alloys in the liquid state were then studied by the Knudsen effusion technique.@) The activity of each component in the liquid alloy can be determined by obtaining the analysis of the participating components in the condensed vapor ‘phase. The activity of each component, in turn, can be calculated from a modified Gibbs-Duhem relation. If it is assumed that the vapor of the alloy behaves as an ideal gas, the activity of component “i” is obtained from the following expression :
where the superscripts 1, v and o refer to the liquid, the vapor and the pure component, respectively, and j and P represent the fugacity and the pressure, respectively. The modified Gibbs-Duhem relation
IN
THE
Pr-nTd
emplo.yed is : _ _ p1 In ail = ln = PI0
161
SYSTEM
N1”=NIV N
s NIV=1
I
LdlnN,”
N,”
where the subscripts 1 and 2 represent the components, and N expresses the mole fractions of each component either in the liquid or vapor phase. Each alloy was vaporized for specified times at the selected temperatures, 1475’, 1500”, and 1525°C. The vapor condensate was collected on a cold target, and the condensate was analyzed by an X-ray spectrographic technique. From these data, plots were made of N,dl/N,dv vs. In NPrV and Nprr/Np,” vs. In NNdZI. Figure 1 is a representative plot of the 1500°C data, but is typical also for the other temperatures. Values of apzz and aNdr were obtained from these plots by graphical integration in conjunction with the Gibbs-Duhem equation. Figure 2 is a plot of aprz and aNdz vs. NPlr at 15OO”C, also similar for the other two temperatures. Table 1 presents a tabulation of the composition of the alloys, the compositions of the vapors, and the resulting activities at three different temperature levels, 1475’, 1500”, and 1525“C. The linear. relationship observed in the plots of activity vs. mole fraction demonstrates that the solutions are essentially ideal in character, since they conform to Raoult’s law wherein the activity is equal to the mole fraction. This approach to ideality in the liquid state is also supported by considering liquid density measurements as determined by the displacement technique. The atomic volume of the alloy can be calculated by using the experimentally observed alloy density, p, using an average atomic weight for the alloy according to the relationship,
where N, = mole fraction of component 1 Ml,2 = atomic weight of components 1 and 2 Y = atomic volume of alloy Thus, from the criterion that an ideal solution exhibits no volume change on mixing, a linear plot of atomic volume vs. mole fradtion will confirm that ideahty. Figure 3 shows the plot for the liquid solution at a temperature of 1240°C. The plot is essentially linear within experimental error. The observed liquid density data are also presented in Table 2. The solid solution at room temperature also conforms to the criterion for ideality that there is no volume change on mixing. The densities as determined by either the X-ray diffraction analysis or the displacement technique (densities were independently
ACTA
162
METALLURGICA,
VOL.
13,
1966
1.0 Ts 1773.
K
0.6 -
Gi Y %ki
0.4 -
0.2 -
-05.0
I -4.0
I -3.0
I -2.0 In
I -1.0
Nk
FIa. 1. Plot of NNdz/NNaYvs. In NPrvfor liquid alloys at 150°C. ,22.60
l-
$ 20.m 3 u
20.60
B
20.50 20.40
0.6 -
a’
0.4 36ec )2.,6X >oa o-
5.66C,?‘65t I-
)
Fro. 2. Activities of Nd and Pr in the Pr-Nd system at 1500°C.
,--0-
1
3.w >-
Flu. 3. Plots of lattice parameters (26%) wd liquid (1240°C) and solid (25°C) densities vs. mole fraction of Pr for the Pr-Nd system.
LUNDIN
et aZ.:
IDEALITY
OF
SOLUTIONS
Alloys nominal at.% Pr
Temperature, “C
0.995
0.895
90
0.800
80
0.604
60
0.412
40
0.308
30
0.206
20
0.111
10
Analyzed Pr, at.%
100 80.0 50.0 20.6 -
0 (Pure Nd)
SYSTEM
153
NrrV
a,,’
1475
0.041
0.959
0.005
0.996
1500
0.031
0.969
0.003
0.994
1525
0.043
0.957
0.005
0.995
1475
0.469
0.531
0.099
0.904
1500
0.484
0.516
0.100
0.886
1525
0.490
0.510
0.095
0.898
1475
0.684
0.316
0.216
0.793
1500
0.649
0.351
0.183
0.800
1525
0.658
0.342
0.1176
0.809
1475
0.834
0.166
0.336
0.616
1500
0.836
0.164
0.390
0.590
1525
0.867
0.133
0.462
0.548
1475
0.912
0.088
0.584
0.432
1500
0.912
0.088
0.565
0.409
1525
0.920
0.080
0.614
0.405
1475
0.947
0.053
0.734
0.302
1500
0.953
0.047
0.693
0.265
1525
0.943
0.057
0.712
0.321
1475
0.962
0.038
0.798
0.232
1500
0.969
0.031
0.800
0.190
1525
0.965
0.035
0.816
0.217
1475
0.981
0.019
0.889
0.126
1500
0.984
0.016
0.891
0.109
1525
0.984
0.018
0.923
0.121
Alloys
80 50 20
Pr-Nd
N NdV
TABLE 2. Liquid density data for the praseodymiumneodymium system
Nominal Pr, at. o/o
THE
1. Composition and activity data for praseodymium and neodymium alloys
TABLE
99.5
IN
Density, g/cm’
Atomic volume, cm*/g-atom
6.27
22.47
6.31 6.37 6.42
22.44 22.38 22.36
6.46
22.33
determined by both methods and are essentially the same) were converted into atomic volumes. Table 3 presents the lattice parameters, X-ray densities, experimental densities, and calculated atomic volumes for the solid solution. The linearity of these data vs. mole fraction can be seen in Fig. 3. The X-ray lattice parameters of the room-temperature phase are also presented in this same figure. Thus, the prediction of essentially ideal behavior in both the solid and liquid solutions of the praseodymium-neodymium alloy system based on their
TABLE 3. Solid solution data for the praseodymium-neodymium system Alloys
Density, g/cm* (25°C)
Analyzed Pr, at.%
Observed
X-ray
Atomic volume, cm8
100 90
89.5
6.772 6.793
6.774 -
20.80 -
80
80.0
6.816
6.819
20.76
70 60
70.5 60.4
6.840 6.858
6.844 -
20.73 -
50 40
50.0 41.2
6.887 6.908
6.889 -
20.70 -
3.6646 f -
30 20
30.8 20.6
6.931 6.958
6.935 -
20.65 -
3.6620 f -
10
11.1
6.981
6.986
20.60
3.6587
-
7.005
7.012
20.67
3.6566 f 0.0005
Nominal Pr, at. o!
0 (pure Nd)
Lattice parameters a,, A 3.6715 f -
%,A
c/a
11.8354 f -
0.0027
3.224 -
3.6690 & 0.0008
11.8270 i
0.0029
3.223
3.6670 f 0.0004 -
11.8247 f -
0.0017
3.225 -
0.0005
11.8181 f -
0.0019
3.225 -
0.0004
11.8106 f -
0.0019
3.225 -
0.0007
-
11.8030
-
11.7983 & 0.0026
3.226 3.226
164
ACTA
METALLURGICA,
similar atomic diameters, crystal structures, electronic structures, and electronegativities was experimentally verified.
VOL.
13,
1965
to Mr. Merlyn Salmon, Fluo-X-Spec Analytical Laboratory, Denver, Colorado, for developing the X-ray spectrographic techniques.
4. ACKNOWLEDGMENT
This research was supported under Contract PJo. AF 33(616)-6787 under the technical cognizance of Dr. Lawrence Bidwell of the Metallurgy and Ceramics Research Laboratory of the Aeronautical Research Laboratories. The authors appreciate the counsel of Dr. Rudolph Speiser, Ohio State University and Dr. M. J. Pool, University of Denver. Thanks are due to Mr. R. J. McManis for his assistance with the experimental work and Mr. Maurice Salmon for the X-ray diffraction analyses. Special appreciation is also due
REFERENCES J. F. NACHYAN, C. E. LUNDIN and A. S. YAMAMOTO,Final Report, January 1903, Contract AF 33(616)-6787, ARL 63-15, University of Denver, Denver Research Institute. C. E. LUNDIN, J. F. NACHMANand A. S. YAUOTO, Proceedings of the Third Conference on Rare Earth Research, April 1963, Cleammter, Florida, to be published, sponsored by Purdue University. J. F. NACHMAN, C. E. LUNDIN and A. S. YAMAMOTO,Proceedings of the Second Conferenceon Rare Earth Research, September 24-27, 1961, Gordon and Breach Science Publishers. 4. R. SPEISER, A. J. JACOBSand J. W. SPRETNAK, Trane. Met. Sot. AZME 215, 185 (1959).