- Email: [email protected]
Lattice spacings and effective atomic diameters in the ternary system ThCeZr
JOURNAL
OF THE LESS-COMMON
METALS
LATTICE SPACINGS AND EFFECTIVE TERNARY SYSTEM Th-Ce-Zr
M. NORMAN, Department
Britain) (Received
I. R. HARRIS
of Physical October
4%
ATOMIC DIAMETERS
IN THE
AND G. V. RAYNOR
Metallurgy
and Science of Materials.
The University,
Birmingham
(Gt.
zznd, 1966)
SUMMARY
Analysis of lattice-spacing relationships in thorium-rich Th-Ce-Zr alloys with zirconium contents not exceeding 6 at.% shows that the large contraction for cerium atoms in dilute solution in thorium is increased by the substitution for thorium of the smaller zirconium atom. This supports the hypothesis that cerium atoms in solid solution adopt an apparent atomic diameter, by further ionisation of 4f electrons, which is strongly influenced by the magnitude of the compressive strain energy which would result from the solution in thorium of cerium in its y-form. This strain energy is enhanced in the ternary alloys by the substitution of zirconium for thorium. The apparent atomic diameter is also decreased by a decrease in temperature to an extent greater than that expected from normal thermal contraction of the alloy, suggesting that 4f -+conduction band transitions are encouraged by decrease in temperature. Such transitions occur at the expense of a small strain energy increase, and emphasise a tendency, previously noted, for cerium to change its effective valency towards that of the solvent in which it is dissolved.
INTROnUCTION
In recent communications from the authors’ laboratory, evidence relating to the apparent atomic diameter, and the associated electronic constitution, of cerium in solid solution has been discussed. It has been shown that, when cerium atoms in solution are in an environment which would correspond to severe compressive strain energy for the solution of y-cerium, a strong tendency exists for them to contract ; the compressive strain energy is thereby reduced. Although the atomic diameter of y-cerium exceeds that of thorium, the lattice spacing of the latter element is initially decreased at room temperature by the solution of cerium; the apparent atomic diameter of cerium in solid solution in thorium at room temperature is consistent with an effective valency of approximately 3.251-4, as opposed to the generally accepted value of approximately 3.1 for y-cerium 5. For zirconium-cerium alloys, in which the atomic diameter for zirconium is considerably smaller than those for either J. Less-Common
Metals, 12 (1967) 465-477
M. NORMAN,
466
I.R. HARRIS, G. V. RAYNOR
thorium or cerium, the higher degree of strain energy leads to a more severe contraction of the dissolved cerium atoms; the apparent atomic diameter is consistent with an effective valency of 4, achieved by transfer of the 4felectron entirely to the conduction band6. The change of valency is to, or towards, that of the solvent metal. Other experiments7 have suggested that cerium in solid solution in a trivalent solvent metal expands to an apparent atomic diameter consistent with an effective valency less than 3.1.Again the change is towards the solvent valency; in such cases the strain energy of solid solution tends to be smaller than in the thorium-cerium and zirconiumcerium systems. The atomic diameter of cerium in solid solution is thus sensitive to environmental factors, of which the magnitude of the compressive strain energy and the valency of the solvent are the most important. By examining a selection of binary systems, the effect of varying these factors may be studied, but the discrete values obtainable are limited by the properties of the solvent metals available. The study of ternary systems allows continuous variation of the strain energy and the effective electronic constitution of the solvent between the values characteristic of different solvent metals in a series of binary systems. The present paper reports the results of a study of the thorium-cerium-zirconium system, in which a solid solution alloy of composition C at.% Ce, x at.% Th and y at.% Zr may be regarded as a binary solid solution of C at. oh Ce in a composite solvent consisting of IOO x/x+y at.% Th and IOO y/x+y at.% Zr. By adjusting% andy, the effective atomic diameter of the composite solvent may be varied continuously; the effective valency of the composite solvent remains constant at 4. The effect of a gradually increasing compressive strain energy of alloy formation on the behaviour of cerium in solid solution may therefore be studied. PREVIOUS WORK
(a) Thorium-cerium system Face-centred cubic a-thorium and y cerium form a complete solid solution over a range of temperatures including room temperature. Up to a composition of approximately 26 at.% Ce the lattice is contractedrpz, and the lattice spacing/ composition curve exhibits a minimum at this composition. Both the rate of decrease and the composition of the minimum are temperature-dependents.4. This behaviour has been attributed to partial transfer of 4f electrons of cerium atoms into the conduction band, to avoid the large compressive strain energy which would correspond with the solution of y-cerium in thorium. (b) Zirconium-cerium system This system is of the simple eutectic types, with no intermediate phase+‘. Equilibrium relationships in the solid state have been examined by DIXON~~ and by HARRIS AND RAYNOR~. The solubility of cerium in c.p.h. or-zirconium is approximately 6 at.% at 900°C. The atomic volume/composition curve shows a large negative deviation from additivity; the cerium atoms are heavily contracted, suggesting that the compressive strain energy involved in the solution of cerium in zirconium is reduced as far as possible by the adoption of the smallest atomic diameter, and the highest valency (4) permitted by the electronic structure of cerium. J. Less-Common
Metals, IZ (1967) 465-477
LATTICE SPACINGSAND EFFECTIVEATOMIC
DIAMETERS
IN
Th-Ce-Zr
467
(c) Thorium-zirconium system The maximum solid-solubility of zirconium in f.c.c. thorium is 9.84 at.% at 92o”Cl3-14. At lower temperatures the solid solution is in equilibrium with the solid solution of thorium in p-zirconium, which decomposes eutectoidally at approximately 650°C forming the terminal solid solutions based on B-thorium and c.p.h. ol-zirconium. The lattice spacing/composition curve for the solid solution of zirconium in athoriuml2.13 is linear. (d) Thorium-cerium-zirconium system No information was available on the constitution of the ternary system, or on lattice spacing relations, prior to the work reported in this paper. MATERIALS
AND
EXPERIMENTALMETHODS
Roth the iodide thorium and hafnium-free zirconium were supplied by the Atomic Energy Research Establishment, Harwell, and typical analyses are given ip Table I. The cerium was obtained from Messrs. Johnson Matthey and Co. Ltd., aid contained less than IOOp.p.m. of other rare-earth metals and approximately 200 p.p.m. of base metals.
TABLE1 IODIDE
THORIUM
Impurity
(TYPICAL
AX~LYSIS)
Amount present
ZIRCONIUM
ImpLfYity
Amount present lat.%)
oxygen Silicon Iron Titanium Copper Hafnium
0.085 0.050
(wt.%)
Metallic Carbon Nitrogen Oxygen
0.10 0.02
0.01 0.10
0.20
0.10 0.006 0.01
Weighed quantities sufficient for specimens weighing 2.5 g were melted together in a non-consumable-electrode arc furnace using an atmosphere of purified argon at 15 cm Hg pressure. One series of alloys contained 20 at.% Ce with varying thorium and zirconium contents; the average weight loss for a 2.5 g specimen during preparation was 0.0025 g. If the whole of this weight loss is assumed to be due to volatilisation of cerium, the difference between the as-cast and nominal compositions is less than 0.2 at.% Ce; for this series nominal compositions were accepted. A second series was prepared in which the atomic ratio of thorium to zirconium remained at 24 : I while the cerium content varied. The weight lossesin this series varied from 0.0010 g for a thorium-rich 2.5 g specimen, to 0.010 g for a corresponding cerium-rich alloy. These losses were assumed to be entirely due to cerium loss, and the nominal compositions were appropriately corrected. All alloys were homogenised by annealing in a vacuum furnace (5 x 10-6 mm Hg), controlled to + 1°C at temperatures up to IOOO~C. J. Less-Common Metals, IZ (1967) 465-477
M. NORMAN, I. R. HARRIS, G. V. RAYNOR
468
Techniques used for the preparation and annealing of powder samples for X-ray investigation, and designed to minimise contamination of reactive materials, have been fully desaibed in a previous publicationi5. Annealing treatments for the relief of stress were terminated by rapid cooling; tests showed that lattice spacings measured at room temperature following treatments of various times at different temperatures agreed to within + 0.0002 kX. Powder specimens were exposed at room temperature in a Philips, Debye-Scherrer camera to CuKol radiation (1cui = I.537395 kX; hx~=1.541232 kX) and the resulting films were interpreted using the Nelson-Riley extrapolation function 16. The temperature fluctuations in the laboratory did not exceed _+ 2”C, which is equivalent to _+ 0.0002 kX; no correction for temperature variation during exposure was therefore made. the liquid-nitrogen-cooled camera For experiments at low lemperatures, described by WABER, HARRIS AND RAYNOR~ was used in conjunction with a Philips diffractometer. Copper radiation was again employed, and the results reported are the average lattice spacings deduced from the three diffraction peaks of highest Bragg angle. Magnetic susceptibilities were measured using a Sartorius, Vacuum Electra I microbalance, in which the load-induced torque is automatically compensated by an electrically-induced counter torque. Spherical specimens weighing 0.5 g were used, with platinum as a standard of comparison. EXPERIMENTAL
RESULTS
(a) Thor&n-cerium system In view of results obtained for certain alloys in the thorium-cerium-zirconium system, and to provide accurate comparisons, the lattice spacings of a series of binary thorium-cerium alloys were redetermined at room temperature. The results are given in Table II, and plotted against composition in Fig. 2 (open squares). These measureTABLE
II
LATTICE
SPACINGS
OF THORIUM-CERIUM
ALLOYS
AT ROOM TEMPERATURE
(Zf,‘c)
Filings rapidly cooled from 7oo’C Nominal composition (at.% Ce) 0
10.00 20.00 29.99 39.55 50.03
Lattice spacing (RX f 0.0002 kX) 5.0755 5.0729 5.0712 5.0730 5.0800 5.0846
Nominal composition (at.% Ce) 59.83 70.05 79.98 go.00 IO0
Lattice spacing (kX & o&d2 kX) 5.0931 5.1078 5.1224
5.1372 5.1508
ments are in good general agreement with earlier worki~2~8. There is evidence, however, for a lattice spacing/composition curve consisting of three linear portions, intersecting at the compositions 25.5 and 58.25 at.% Ce. The initial linear portion allows accurate extrapolation to IOO~/~ solute to obtain an apparent atomic diameter of 3.5718 kX for cerium in dilute solid solution in thorium, corresponding with an effective valency in J. Less-Common Metals,
12 (1967) 465-477
LATTICE
SPACINGS
AND
EFFECTIVE
ATOMIC
DIAMETERS IN
3.25, assuming
Th-Ce-Zr
the effective
469
solid solution
of approximately
GSCHNEIDNER
AND SMOLUCHOWSKI for y- and ol-cerium respectively5.
valencies
proposed
by
(b) Thorium-ccrium-zirconium system (i) Alloys with a constant cerium content of 20 at.%
The lattice spacings at room temperature for this series of alloys are given in Table III, and plotted in Fig. I, in which the lattice spacing/composition variation for TABLE
III
LATTICE
SPACINGS
TEMPERATURE
OF
THORIUM-CERIUM-ZIRCONIUM
ALLOYS
CONTAINING
20
AT.%
Ce,
AT
ROOM
(22Oc)
FiIings rapidly cooIed from 950% ___Lattice spacing Somixal compositions (at. O/J --(kX & O.QOOZkX) Ce zv Th ______ 20.01 X9.99
79.99 79.04 78.04 77.04
0.97 I.96 2.96 4.00 4.97 6.01
20.00
19.99 20.00
pi.00
75.02
20.00
73.99
20.00
5.0499 5.0654 5.0604 5.0555 5.0487 5.0420
5.0357
0 Th-Ct1207.l-Zr q
-.
Ih-Zr
v lh-Zr
1
2
3
4
5
6
7
8
9
I
x) 11 12
ATOMIC % ZIRCONIUM
Fig. I. Variation of lattice spacing with composition and Th-Zr systems. q , Th-Zrl*. v, Th-Zrl3.
0
10 20 30 40 50 60 70 ATOMIC % CERIUM
for alloys in the Th-Ce-Zr
Fig. 2. Variation of lattice spacing with cerium content in the system Th-Ce-Zr The lattice spacings in the system Th-Ce are included for comparison. Th-Ce, J. Less-Common
Metals,
80 90
100
(20 at.g/, Ce)
(Th: Zr = 24: 1). a; Th-Ce-Zr, (3. 12
(1967)
465-477
470
M.
NORMAN,I. R. HARRIS, G. v. RAYNOR
thorium-zirconium alloys has been included for comparison. The lattice spacings of the zirconium used were a=3.zzgo kX and c =5.1438 kX, as compared with values of a=3.2256 kX, c=5.1371 kX reported by TRECO~~, and a=32271 kX, c=5.1367 kX obtained by HARRIS AND RAYNOR~. The lattice spacing of the thorium used for this series of alloys was a=5.0749 kX, while that of the cerium employed was a= 5.1508 kX. The lattice spacing of the Th-zo at.% Ce alloy is decreased by the substitution of zirconium for thorium; initially the rate of decrease is identical with that produced by the solution of zirconium in thorium. At zirconium concentrations exceeding 3 at.%, however, the rate of decrease of lattice spacing in the ternary alloys, as thorium is replaced by zirconium, exceeds that in the binary alloys. The phase boundary between the thorium-cerium solid solution and zirconium, for a cerium content of 20 at.%, occurs at approximately 6.5 at.% Zr at 950°C. (ii) Alloys with a constant Th:Zr atomic ratio of 24:r This series of alloys was necessarily prepared from different samples of thorium and zirconium from those referred to in b(i) above. The lattice spacings recorded were as follows : Thorium,
a=5.0758
kX.
Zirconium,
a=3.zz7r
kX;
~‘5.1367
kX
The sample of cerium remained unchanged from that previously used. The lattice spacings obtained at room temperature for the ternary alloys are given in Table IV, and the lattice spacing/composition relationship is shown in Fig. 2, with the corresponding results for the thorium-cerium system. Both sets of results show three linear portions. The central portion for the ternary alloys (21.5-47 at.% Ce) is, however, more limited than the corresponding linear region for the thorium-cerium system. The effective lattice spacing for cerium in dilute solid solution in the thoriumzirconium alloy (Th : Zr = 24: I), obtained by extrapolation to 100% Ce of the initial linear portion of the curve is 5.0330 kX, and is appreciably smaller than the corresponding value (5.0513 kX) for the thorium-cerium system. TABLE IV LATTICE SPACINGS OFTHORIUM-CERIUM-ZIRCONIUM ALLOYS CONTAINING THORIUM AND ZIRCONIUM IN THE ATOMIC RATIO 24:1, AT ROOM TEMPERATURE (22'C) AND AT -6o”, -100' AND -186'C Filings
rapidly
cooled
Corrected compositions
from
(at.%)
700°C.
_ Lattice
spacing
(kX
& 0.0002 kX)
Th
Zr
Cc
22°C
-60°C
-IOO"C
-I86"C
96.00
4.00 3.80 3.59 3.21
-
5.0595 5.0587 5.0568
5.0538 5.0516 5.0508
29.83 40.00 50.00
5.0444 5.04’7 5.0408
5.0472 5.0430 5.0428 5.0322
2.80 2.40 2.01 1.61
5.0542 5.0572 5.0615 5.0691
5.0513 5.0485 5.0480 5.0401 5.0348 5.0301 5.0276 5.0362 5.0680
5.0255 5.0155 5.0030
91.20 86.53 76.91 67.36 57.60 47.99 38.45 29.32 lg.28 9.66 -
I.22 0.80 0.39 -
J. Less-Common
5.00 9.88 19.88
59.94 69.45 79.91 89.95 100.00
5.0857 5.1028 5.1192
5.0457 5.0635 5.0845 5.1082
5.1355 5.1508
5.1279 -
Metals, 12 (1967) 465-477
5.0930 5.1240 -
4.9911 4.9682 4.9315 4.8865 4.83
LATTICE
SPACINGS
AND EFFECTIVE ATOMIC DIAMETERSIN Th-Ce-Zr
471
The variation of lattice spacing with temperature over the approximate range 26” to - 186°C was investigated for the alloys listed in Table IV. The results for three typical alloys containing respectively, 5, 50 and 79.91 at.% Ce are shown graphically in Fig. 3. Curve A is typical of alloys containing 5, 9.88 and 19.88 at.% Ce, and is essentially linear. The alloys containing 29.83, 40, 50, and 59.94 at.% Ce show the type of behaviour illustrated by curve B; the spacing/temperature relationships for the remaining Ce-rich alloys are as in curve C
5.000
1
I.. 40
20
0
*. 20
. 60 80 100 120 140 160 180 xx) TEMPERATURE ‘C I
40
I,
8.
*,
0
Fig. 3. Variation of lattice spacing with temperature for alloys in the system Th-Ce-Zr (Th: Zr =
24:‘).
0, 5 at.% Ce (A); a, 50 at.% Ce (B); 8, 79.91 at.% Ce (C).
The lattice spacing/temperature curves determined for the individual alloys have been used to construct lattice spacing/composition curves for temperatures intermediate between room temperature and that of liquid nitrogen. Table IV and Fig. 4 summarise the values obtained at - 60” and - IOO’C. The minimum in the curve moves to higher cerium contents as the temperature decreases, and between -60” and -roo°C, moves from approximately 40 to 50 at.% Ce. Below - IOO’C, cerium-rich alloys begin to transform to a solid solution based on cx-cerium; the Y--W transformation temperature of cerium is raised by the addition of thorium. The diffraction peaks of the cerium-rich alloys broaden considerably at - 186°C owing to the large internal stresses involved in the transformation. The lattice spacings of the alloys, for which the Th : Zr atomic ratio is maintained at 24: I, at - 186°C are included in Table IV and plotted in Fig. 5, together with Extrapolation of the initial results for the thorium-cerium system at -ISOY?. thorium-rich section (o-35 at.% Ce) to IOO at.% Ce gives a value of 4.975 kX for the effective lattice spacing of cerium corresponding to solid solution in the thoriumzirconium alloy (Th:Zr =24: I) at -186°C; this compares with a value of 4.989 kX for the effective spacing of cerium in solid solution in thorium3 at a similar temperature. The lattice spacing/composition curve for the ternary alloys at - 186°C shows a large, positive deviation from the line joining the respective spacings of the thoriumzirconium alloy and of or-cerium. No experimental evidence was found in the present J. Less-Common
Metals, 12 (1967) 465-477
M. NORMAN, I. R. HARRIS, G. V. RAYNOR
472
I”“,
1.
‘.
5Jnol. *
* ’ * * J 10 20 xl 40 50 60 70 80 90 100
0
ATOMIC
% CERlUM
Fig. 4. Lattice spacing/composition -60°C (a), and -roo”C ( q).
relationships
Fig. 5. Lattice spacing/compos~~on relationships at -186”C, and Th-Ce (A) at -18o’C.
work for the existence and LX-Ce,respectively.
of any two-phase
I
*
4floo
x)
in the system
8.
1.
Th-Ce-Zr
in the systems Th-Ce-Zr
region between
.
.
.
20 30 40 50 60 70 ATOMIC % CERIUM
80 90
(Th: Zr -
(Th: Zr =
solid solutions
24: I) at
24: I) (Q)
based on ol-Th
~e~~e~~~ye ~~n~~~~ s~~cep~~~~~~t~es of Th_Ce-Zr allots (7%: Zr=24:1) The results obtained in the magnetic work are collected in Table V and the variation of magnetic susceptibility with composition at room temperature is shown in Fig. 6. The value obtained for the pure thorium used was 0.445 x IO-~ e.m.u./g, fc) Room
TABLE MASS
V OF Th-Ce-Zr
SUSCEPTIBILITIES
Corrected
(Th: Zr=24:
I) AT ROOMTEMPERATURE
Corrected composition
(wt.%)
Th
Zr
Ce
0.62 0.76 1.04
60.78 51.09 40.88
1.00 0.84 0.67
38.22 48.07 58.45 71.11 84.70
IO.74 13.55
*oo.oo
17.40
x
composition
ALLOYS
x
lo-6
e.m.zc./g
*
(wt.%) ____ Ce
I%
Th
Zr
98.39
-
92.14
x.61 I.56 x.50
85.29 77.90
1.40 1.27
13.31 20.83
1.66 2.53
28.42 15.06
0.47 0.24
69.66
1.14
29.20
3.43
-
-
95.29
J. Less-Commor
3.15 6.35
Met&,
IZ
(1967)
465-477
x x
4.81 6.51 8.48
10-e
(294
e.m.u./g
.* r%
LATTICE SPACINGSAND EFFECTIVE ATOMIC DIAMETERSIN Th-Ce-Zr
473
ATOMIC % CERIUM
I
..
N) WEIGHT
% CERIUM
L., . . . 0 10 20 XI LO 50 60 70 ATOMIC % CERIUM
. .’ 60 90
&
Fig . 6. Variation with cerium content of the mass susceptibility of Th-Ce-Zr alloys (Th: Zr = 24: I) at room temperature. Fig. 7. Deviations from ideal behaviour in Th-Ce-Zr alloys containing 0; I at.% Zr, 8; 2 at.% Zr, 0; 4 at.% Zr, v; 6 at.% Zr, El.
20
at.% Ce. o at.% Zr,
which may be compared with the value of 0.422 x 10-s e.m.u./g reported by LEACHES. The mass-susceptibility of zirconium was found to be 1.29 x 10-s e.m.u./g. DISCUSSION (a) Lattice spacing measurements In Fig. I the effect on the lattice spacings of replacing the thorium in a Th-20
at.% Ce alloy by zirconium is compared with the effect of zirconium on the spacing of thorium. In the binary system the lattice spacings decrease lineally as the zirconium content increases up to the solid-solubility limit, and the spacing/composition relationship approximates very closely to linear variation between the atomic volumes of the component+ as expected for components of equal valency. If the state of cerium in solid solution in the Th-2o at.% Ce alloy were unaffected by the replacement of thorium by zirconium, the curve of lattice spacing against zirconium content for the ternary series containing a constant cerium content of 20 at.% would lie parallel to the corresponding curve for the binary alloys. This behaviour is observed below 3 at. “/x Zr ; at higher zirconium contents the rate of decrease is greater in the ternary series than for the binary system. As the mean lattice spacing of the matrix is decreased by the substitution of thorium by zirconium, therefore the behaviour is consistent with further ionisation of the 4f electrons of the cerium atoms, which leads to contraction of the apparent atomic diameter, in order to prevent too large an increase in the compressive strain energy of solid solution, as previously suggestedi-3. The increase in slope of the curve for the ternary alloys in Fig. I at 3 at.% Zr suggests that a critical .I. Less-Common
Metals,
12
(1967)
465-477
474
M. NORMAN,
I. R. HARRIS,
G. V. RAYNOR
degree of additional strain energy may be necessary to induce further contraction of the cerium atoms which have already contracted considerably in forming the Th-2o at.% Ce alloy. For the series at 20 at.% Ce, an alloy containing x at.% Th and y at.% Zr can be regarded as a solution of 20 at.% Ce in a thorium-zirconium solvent of composition 5x/4 at.% Thand 5~14 at.% Zr and of constant valency(4). From Fig. I the effect of the solution of 20 at.% Ce on the lattice spacing of any composite solvent within the solid solution of zirconium in thorium may be derived, and Fig. 7 illustrates the results obtained for cerium dissolved in composite thorium-zirconium solvents containing o, I, 2, 4 and 6 at.% Zr. The straight lines indicate ideal behaviour in the sense of an additive relationship between the lattice spacings of the f.c.c. composite solvent and f.c.c. y-cerium. In all cases the strong negative deviation from additivity characteristic of the thorium-cerium alloys is maintained. The extrapolations to IOO at.% Ce represented by the broken lines in Fig. 7 again indicate that for zirconium contents in the composite solvent below about 3 at.%, the cerium atoms are essentially in the same electronic state as in the thorium-20 at.% Ce alloy. Further decrease of the mean lattice spacing of the composite solvent, however, leads to a further decrease of the apparent atomic diameter of cerium. The series of alloys for which the atomic ratio Th:Zr=24: I represents the solution of cerium in a composite binary solvent of composition thorium g6 at.% and zirconium 4 at.%. Extrapolation to IOO at.% Ce of the initial linear section of Fig. 2 gives the value 5.0330 kX for the apparent lattice spacing of cerium in the hypothetical face-centred cubic form corresponding to its electronic state in solid solution. Assuming the effective valencies suggested by GSCHNEIDNER AND SMOLUCHOWSKI~ for y- and or-cerium, and applying the Pauling relationship19 between atomic size and valency, the effective valency of cerium in solid solution in the composite solvent is assessed as approximately 3.3, as compared with the value 3.25 (effective lattice spacing=5.0513 kX) for the initial solution of cerium in thorium. These experiments emphasise the importance of strain energy factors, which depend upon the difference between the atomic diameters of the solvent and of cerium, in controlling the electronic constitution, and hence the atomic size of cerium in solid solution; the change of effective valency is, however, towards that of the solvent. Other evidence7 shows that a tendency exists for cerium in solid solution to change its effective valency towards that of the solvent, even at the expense of a small increase in strain energy. Both factors are probably operative in the present case; the two factors, for a 4-valent solvent of atomic diameter smaller than that of y-cerium, reinforce and the electronic constitution of cerium in solid solution at a given temperature represents the resultant effect. In thorium-rich alloys, it was found by HARRIS AND RAYNOR~ that the contraction of the cerium atom at a given composition was increased by a decrease in temperature and decreased with temperature increase, so that the slope daldt of the curve of lattice spacing against temperature for a thorium-rich alloy was greater than that for pure thorium. Curves of type A in Fig. 3 are similar to those previously obtained for thorium-cerium alloys, and indicate that there is no temperature-induced transformation in the ternary alloys containing less than 20 at.% Ce. Curves for alloys containing 30-60 at.% Ce (type B) are more complex and consist of three almost linear positions, suggesting that a continuous temperature-induced change occurs in these alloys, which is completed before the lowest temperature investigated is reached. J. Less-Commolz Metals, 12 (1967) 465-477
LATTICESPACINGS AND EFFECTIVEATOMICDIAMETERS IN Th-Ce-Zr
475
This behaviour may be discussed in terms of the electronic state of cerium in solid solution. At compositions below 21.5 at.% Ce in the ternary alloys, the evidence discussed above suggests that a sufficient proportion of 4f electrons per atom have been ionised to give rise to an effective valency of about 3.3. Above 21.5 at.% however the lattice spacing evidence suggests that the electronic state of cerium corresponds to a lower degree of ionisation. The number of 4f electrons per atom which can suffer transfer to the conduction band of the alloy on decrease of temperature is thus greater above 21.5 at.% than below this composition, and this may account for the increased value of daldt. The lattice spacing/temperature curves for alloys containing 69.45, 77.91 and 89.95 at.% Ce each show an abrupt decrease in lattice spacing at definite temperatures on cooling, owing to the transition from solutions based on y-cerium to those based on oc-cerium. The y-+a transformation temperatures for the 69.45, 77.91 and 89.95 at.% Ce alloys are - 115’, -140’ and - 145”C, which may be compared with the value - 157°C for pure cerium 20.The thorium-zirconium addition to cerium thus raises the y-ta transition temperature for cerium, in spite of the fact that a composite thorium-zirconium component has a more favourable atomic size factor with respect to y- than to cx-cerium. This suggests that the stabilising effect of the thorium-zirconium addition is connected with the greater similarity of the valency of this mixture (4) to that of cx-cerium (3.6)s than to that of y-cerium (3.1)s. Lattice spacing/composition curves for ternary alloys with an atomic ratio Th: Zr = 24: I and for temperatures intermediate between room temperature and -186”C, as deduced from the results of the present work, allow extrapolation to IOO at.% Ce to derive in each case an effective lattice spacing for cerium corresponding to its electronic state in dilute solution in the composite thorium-zirconium solvent. The effective atomic size so derived decreases continuously as the temperature is lowered, to an extent which is greater than would be expected from contraction to offset the effect of the decreased lattice spacings of the composite solvent. Thus, as the temperature is decreased, the effective valency of the cerium atoms in solid solution adjusts progressively closer to that of the composite solvent, in spite of the fact that the magnitude of the strain energy is slightly increased. This emphasises the importance of electronic factors in controlling the behaviour of cerium in solid solution. At - 186°C the apparent atomic diameter of cerium in dilute solid solution in the composite solvent with atomic ratio Th: Zr = 24: I (3.518 kX) is smaller than that of cerium in dilute solid solution in thorium (3.528 kX), as expected from the relative lattice spacings of the composite solvent and of thorium. The large deviation of the lattice spacing/composition curve from additivity of spacings between the solvent and of c*-cerium is of interest. The deviation is much larger than would be expected for components differing in valency by a small amount, and suggests that, as at room temperature, the apparent size of the cerium atom is dependent upon both strain energy and electronic factors. The form of the ternary alloy curve in Fig. z at cerium contents exceeding 47.5 at.% may be discussed in terms of the suggestion by EVANSAND RAYNOR~that the introduction into y-cerium of thorium results in local contractions which allow interactions to occur between the 4f and 5d electronic bands for cerium and facilitate promotion of 4f electrons to the conduction band. The local contractions around small zirconium atoms in the ternary case are more severe than around thorium atoms, so that a greater contraction of the cerium atoms than in the binary case is expected, J. Less-Common
Metals.
1% (1967)
465-477
476
M. NORMAN, 1. R. HARRIS, G. V. RAYNOR
and observed. The intermediate section of the lattice spacing/composition curve (21.5-47.5 at.% Ce) probably represents transition from this effect to the influences of compressive strain energy and the tendency towards the adoption of an effective valency more closely similar to that of the solvent on the effective atomic size of cerium in dilute solution. The lattice spacing measurements described in this paper suggest strongly, in conformity with previous work, that the apparent atomic diameter adopted by cerium in dilute solid solution in thorium-rich alloys is dependent upon both strain energy and electronic considerations. Increase in the compressive strain energy which would be caused by the solution of y-cerium, achieved by a decreased lattice spacing in thorium-zirconium alloys considered as solvents, leads to an increase in the contraction of the cerium atoms in solution. Other details of the results, however, such as the effect of temperature on the apparent atomic size of cerium in solution, indicate a tendency for cerium to adopt an effective valency closer in value to that of the solvent alloy. Both factors are therefore of importance, with the reduction of strain energy predominant in the system investigated. (b) Magnetic susceptibility measurements The results given in Table V enable calculation of the contribution per gram of cerium to the magnetic susceptibility of the alloy as a whole. If the mass susceptibilities of the alloy, of thorium and of zirconium are respectively XA, XTh and xzr and the weight percentages of the alloy components are Wrh, Wzr and Wee, then, assuming the mass susceptibilities of thorium and zirconium to remain unchanged on alloying, the susceptibility per gram of cerium is : Xce
=
[IOOXA
-X_ThWTh
-XZrWZr]
WC,
The values of xce are plotted against composition in Fig. 8. The curve shows three sections : (i) o-q.3 wt.% Ce (20 at.% Ce) (ii) 13.3-29.2 wt.% Ce (40 at.% Ce) and (iii) 29.2-100 wt.% Ce. The critical compositions correspond approximately to those at which changes of slope occur in the ternary alloy curve of Fig. 2. In the cerium-rich range, the susceptibility per gram of cerium is decreased by the thorium-zirconium addition; this decrease is consistent with a decrease in the number of 4f electrons of cerium as the concentration of composite alloy solvent increases, as suggested above in discussion of the lattice spacing results. In the range 40-20 at.% Ce the susceptibility per gram of cerium decreases less rapidly with decrease of cerium content than in the ceriumrich alloys: this is consistent with the lattice spacing results of Fig. 2. The susceptibility per gram of cerium in the composition range 0-20 at.% Ce is much less dependent on composition and considerably lower than that of y-cerium. This supports the conclusions drawn from the lattice spacing results, that the effective valency of cerium in dilute solid solution in the composite thorium-zirconium solvent corresponds with fewer 4f electrons per atom than in y-cerium and is essentially constant in the composition range corresponding to the initial linear contraction of the lattice J. Less-Common
Metals,
12 (1967)
465-477
LATTICE
SPACINGS AND EFFECTIVE
ATOMIC DIAMETERS
IN
Th-Ce-Zr
477
spacings of the solvent material. These results also justify the derivation of effective lattice spacings, corresponding to hypothetical forms of cerium having the same electronic constitution as the cerium in dilute solution, by extrapolation to IOO at.% Ce of the appropriate lattice spacing curves. ATOMIC % CERIUM la 20 30 LO 50 60 70 80
10 M
90
30 Lo 50 60 70 80 WEIGHT % CERIUM
0
90
Fig. 8. Susceptibility per gram of cerium in Th-Ce-Zr alloys (Th: Zr = q: I) plotted as a function of cerium content.
ACKNOWLEDGEMENTS
The work reported in this paper was carried out under the terms of a grant from the Science Research Council, to which grateful acknowledgement is made. The authors’ thanks are also due to the Atomic Energy Research Establishment for the loan of apparatus, and to the Royal Society, and Imperial Chemical Industries, Ltd., for support of the general programme of which this work forms a part. REFERENCES I R. T. WEINER, W. E. FREETH AND G. V. RAYNOR, J. Inst. Metals, 86 (1957-58) 185. 2 D. S. EVANS AND G. V. RAYNOR, J. Less-Common Metals, 4 (1962) 181. 3 J. T. WABER, I. R. HARRIS AND G. V. RAYNOR, Trans. AIME, 230 (1964) 148. 4 I. R. HARRIS AND G. V. RAYNOR, J. Less-Common Metak, 7 (1964) II. 5 K. A. GSCHNEIDNER AND R. SMOLUCHOWSKI, J. Less-Common Metals, 5 (1963) 374. 6 I. R. HARRIS AND G. V. RAYNOR, J. Less-Common Metals, 6 (1964) 70. 7 1. R. HARRIS AND G. V. RAYNOR, J. Less-Common Metals, 7 (1964) I. 8 J. H. N. VAN VUCHT, Philips Res. Reports, 12 (1957) 551. 9 IO II IZ 13 14 15 16 17 18 19 20
J. A. P. R. D. J. D. J. R. S. L. K.
M. BLACKLEDGE AND C. E. LUNDIX, unpublished work, 1959. H. DAANE AND F. H. SPEDDING, I.S.C. Rep. 530, 1954. R. DIXON, Ph.D. Dissertation, Univ. of Sheffield, 1957. H. JOHNSON AND R. W. K. HONEYCOMBE, J. NPLCZ.Mater., 4 (1961) 59. S. EVANS AND G. V. RAYNOR, J. Nucl. Mater., 4 (1961) 66. R. MURRAY, J. Less-Common Metals, 2 (1960) I. S. EVANS AND G. V. RAYNOR, J. Nucl. Mater., I (1959) 281. P. NELSON AND D. P. RILEY, Proc. Phys. Sot., 57 (1945) 160. M. TRECO, J. Metals, 5 (1953) 344. J’. LEACH, Thesis, Univ. of Nottingham, 1955. PAULING, J, Am. Chem. Sot., 69 (1947) 542. A. GSCHNEIDNER, JR., R. 0. ELLIOTT AND R. R. MCDONALD, J. Phys. Chem. Solids, 23 (1962)
555.
J. Less-Common
Metals, 12 (1967) 465-477
OF THE LESS-COMMON
METALS
LATTICE SPACINGS AND EFFECTIVE TERNARY SYSTEM Th-Ce-Zr
M. NORMAN, Department
Britain) (Received
I. R. HARRIS
of Physical October
4%
ATOMIC DIAMETERS
IN THE
AND G. V. RAYNOR
Metallurgy
and Science of Materials.
The University,
Birmingham
(Gt.
zznd, 1966)
SUMMARY
Analysis of lattice-spacing relationships in thorium-rich Th-Ce-Zr alloys with zirconium contents not exceeding 6 at.% shows that the large contraction for cerium atoms in dilute solution in thorium is increased by the substitution for thorium of the smaller zirconium atom. This supports the hypothesis that cerium atoms in solid solution adopt an apparent atomic diameter, by further ionisation of 4f electrons, which is strongly influenced by the magnitude of the compressive strain energy which would result from the solution in thorium of cerium in its y-form. This strain energy is enhanced in the ternary alloys by the substitution of zirconium for thorium. The apparent atomic diameter is also decreased by a decrease in temperature to an extent greater than that expected from normal thermal contraction of the alloy, suggesting that 4f -+conduction band transitions are encouraged by decrease in temperature. Such transitions occur at the expense of a small strain energy increase, and emphasise a tendency, previously noted, for cerium to change its effective valency towards that of the solvent in which it is dissolved.
INTROnUCTION
In recent communications from the authors’ laboratory, evidence relating to the apparent atomic diameter, and the associated electronic constitution, of cerium in solid solution has been discussed. It has been shown that, when cerium atoms in solution are in an environment which would correspond to severe compressive strain energy for the solution of y-cerium, a strong tendency exists for them to contract ; the compressive strain energy is thereby reduced. Although the atomic diameter of y-cerium exceeds that of thorium, the lattice spacing of the latter element is initially decreased at room temperature by the solution of cerium; the apparent atomic diameter of cerium in solid solution in thorium at room temperature is consistent with an effective valency of approximately 3.251-4, as opposed to the generally accepted value of approximately 3.1 for y-cerium 5. For zirconium-cerium alloys, in which the atomic diameter for zirconium is considerably smaller than those for either J. Less-Common
Metals, 12 (1967) 465-477
M. NORMAN,
466
I.R. HARRIS, G. V. RAYNOR
thorium or cerium, the higher degree of strain energy leads to a more severe contraction of the dissolved cerium atoms; the apparent atomic diameter is consistent with an effective valency of 4, achieved by transfer of the 4felectron entirely to the conduction band6. The change of valency is to, or towards, that of the solvent metal. Other experiments7 have suggested that cerium in solid solution in a trivalent solvent metal expands to an apparent atomic diameter consistent with an effective valency less than 3.1.Again the change is towards the solvent valency; in such cases the strain energy of solid solution tends to be smaller than in the thorium-cerium and zirconiumcerium systems. The atomic diameter of cerium in solid solution is thus sensitive to environmental factors, of which the magnitude of the compressive strain energy and the valency of the solvent are the most important. By examining a selection of binary systems, the effect of varying these factors may be studied, but the discrete values obtainable are limited by the properties of the solvent metals available. The study of ternary systems allows continuous variation of the strain energy and the effective electronic constitution of the solvent between the values characteristic of different solvent metals in a series of binary systems. The present paper reports the results of a study of the thorium-cerium-zirconium system, in which a solid solution alloy of composition C at.% Ce, x at.% Th and y at.% Zr may be regarded as a binary solid solution of C at. oh Ce in a composite solvent consisting of IOO x/x+y at.% Th and IOO y/x+y at.% Zr. By adjusting% andy, the effective atomic diameter of the composite solvent may be varied continuously; the effective valency of the composite solvent remains constant at 4. The effect of a gradually increasing compressive strain energy of alloy formation on the behaviour of cerium in solid solution may therefore be studied. PREVIOUS WORK
(a) Thorium-cerium system Face-centred cubic a-thorium and y cerium form a complete solid solution over a range of temperatures including room temperature. Up to a composition of approximately 26 at.% Ce the lattice is contractedrpz, and the lattice spacing/ composition curve exhibits a minimum at this composition. Both the rate of decrease and the composition of the minimum are temperature-dependents.4. This behaviour has been attributed to partial transfer of 4f electrons of cerium atoms into the conduction band, to avoid the large compressive strain energy which would correspond with the solution of y-cerium in thorium. (b) Zirconium-cerium system This system is of the simple eutectic types, with no intermediate phase+‘. Equilibrium relationships in the solid state have been examined by DIXON~~ and by HARRIS AND RAYNOR~. The solubility of cerium in c.p.h. or-zirconium is approximately 6 at.% at 900°C. The atomic volume/composition curve shows a large negative deviation from additivity; the cerium atoms are heavily contracted, suggesting that the compressive strain energy involved in the solution of cerium in zirconium is reduced as far as possible by the adoption of the smallest atomic diameter, and the highest valency (4) permitted by the electronic structure of cerium. J. Less-Common
Metals, IZ (1967) 465-477
LATTICE SPACINGSAND EFFECTIVEATOMIC
DIAMETERS
IN
Th-Ce-Zr
467
(c) Thorium-zirconium system The maximum solid-solubility of zirconium in f.c.c. thorium is 9.84 at.% at 92o”Cl3-14. At lower temperatures the solid solution is in equilibrium with the solid solution of thorium in p-zirconium, which decomposes eutectoidally at approximately 650°C forming the terminal solid solutions based on B-thorium and c.p.h. ol-zirconium. The lattice spacing/composition curve for the solid solution of zirconium in athoriuml2.13 is linear. (d) Thorium-cerium-zirconium system No information was available on the constitution of the ternary system, or on lattice spacing relations, prior to the work reported in this paper. MATERIALS
AND
EXPERIMENTALMETHODS
Roth the iodide thorium and hafnium-free zirconium were supplied by the Atomic Energy Research Establishment, Harwell, and typical analyses are given ip Table I. The cerium was obtained from Messrs. Johnson Matthey and Co. Ltd., aid contained less than IOOp.p.m. of other rare-earth metals and approximately 200 p.p.m. of base metals.
TABLE1 IODIDE
THORIUM
Impurity
(TYPICAL
AX~LYSIS)
Amount present
ZIRCONIUM
ImpLfYity
Amount present lat.%)
oxygen Silicon Iron Titanium Copper Hafnium
0.085 0.050
(wt.%)
Metallic Carbon Nitrogen Oxygen
0.10 0.02
0.01 0.10
0.20
0.10 0.006 0.01
Weighed quantities sufficient for specimens weighing 2.5 g were melted together in a non-consumable-electrode arc furnace using an atmosphere of purified argon at 15 cm Hg pressure. One series of alloys contained 20 at.% Ce with varying thorium and zirconium contents; the average weight loss for a 2.5 g specimen during preparation was 0.0025 g. If the whole of this weight loss is assumed to be due to volatilisation of cerium, the difference between the as-cast and nominal compositions is less than 0.2 at.% Ce; for this series nominal compositions were accepted. A second series was prepared in which the atomic ratio of thorium to zirconium remained at 24 : I while the cerium content varied. The weight lossesin this series varied from 0.0010 g for a thorium-rich 2.5 g specimen, to 0.010 g for a corresponding cerium-rich alloy. These losses were assumed to be entirely due to cerium loss, and the nominal compositions were appropriately corrected. All alloys were homogenised by annealing in a vacuum furnace (5 x 10-6 mm Hg), controlled to + 1°C at temperatures up to IOOO~C. J. Less-Common Metals, IZ (1967) 465-477
M. NORMAN, I. R. HARRIS, G. V. RAYNOR
468
Techniques used for the preparation and annealing of powder samples for X-ray investigation, and designed to minimise contamination of reactive materials, have been fully desaibed in a previous publicationi5. Annealing treatments for the relief of stress were terminated by rapid cooling; tests showed that lattice spacings measured at room temperature following treatments of various times at different temperatures agreed to within + 0.0002 kX. Powder specimens were exposed at room temperature in a Philips, Debye-Scherrer camera to CuKol radiation (1cui = I.537395 kX; hx~=1.541232 kX) and the resulting films were interpreted using the Nelson-Riley extrapolation function 16. The temperature fluctuations in the laboratory did not exceed _+ 2”C, which is equivalent to _+ 0.0002 kX; no correction for temperature variation during exposure was therefore made. the liquid-nitrogen-cooled camera For experiments at low lemperatures, described by WABER, HARRIS AND RAYNOR~ was used in conjunction with a Philips diffractometer. Copper radiation was again employed, and the results reported are the average lattice spacings deduced from the three diffraction peaks of highest Bragg angle. Magnetic susceptibilities were measured using a Sartorius, Vacuum Electra I microbalance, in which the load-induced torque is automatically compensated by an electrically-induced counter torque. Spherical specimens weighing 0.5 g were used, with platinum as a standard of comparison. EXPERIMENTAL
RESULTS
(a) Thor&n-cerium system In view of results obtained for certain alloys in the thorium-cerium-zirconium system, and to provide accurate comparisons, the lattice spacings of a series of binary thorium-cerium alloys were redetermined at room temperature. The results are given in Table II, and plotted against composition in Fig. 2 (open squares). These measureTABLE
II
LATTICE
SPACINGS
OF THORIUM-CERIUM
ALLOYS
AT ROOM TEMPERATURE
(Zf,‘c)
Filings rapidly cooled from 7oo’C Nominal composition (at.% Ce) 0
10.00 20.00 29.99 39.55 50.03
Lattice spacing (RX f 0.0002 kX) 5.0755 5.0729 5.0712 5.0730 5.0800 5.0846
Nominal composition (at.% Ce) 59.83 70.05 79.98 go.00 IO0
Lattice spacing (kX & o&d2 kX) 5.0931 5.1078 5.1224
5.1372 5.1508
ments are in good general agreement with earlier worki~2~8. There is evidence, however, for a lattice spacing/composition curve consisting of three linear portions, intersecting at the compositions 25.5 and 58.25 at.% Ce. The initial linear portion allows accurate extrapolation to IOO~/~ solute to obtain an apparent atomic diameter of 3.5718 kX for cerium in dilute solid solution in thorium, corresponding with an effective valency in J. Less-Common Metals,
12 (1967) 465-477
LATTICE
SPACINGS
AND
EFFECTIVE
ATOMIC
DIAMETERS IN
3.25, assuming
Th-Ce-Zr
the effective
469
solid solution
of approximately
GSCHNEIDNER
AND SMOLUCHOWSKI for y- and ol-cerium respectively5.
valencies
proposed
by
(b) Thorium-ccrium-zirconium system (i) Alloys with a constant cerium content of 20 at.%
The lattice spacings at room temperature for this series of alloys are given in Table III, and plotted in Fig. I, in which the lattice spacing/composition variation for TABLE
III
LATTICE
SPACINGS
TEMPERATURE
OF
THORIUM-CERIUM-ZIRCONIUM
ALLOYS
CONTAINING
20
AT.%
Ce,
AT
ROOM
(22Oc)
FiIings rapidly cooIed from 950% ___Lattice spacing Somixal compositions (at. O/J --(kX & O.QOOZkX) Ce zv Th ______ 20.01 X9.99
79.99 79.04 78.04 77.04
0.97 I.96 2.96 4.00 4.97 6.01
20.00
19.99 20.00
pi.00
75.02
20.00
73.99
20.00
5.0499 5.0654 5.0604 5.0555 5.0487 5.0420
5.0357
0 Th-Ct1207.l-Zr q
-.
Ih-Zr
v lh-Zr
1
2
3
4
5
6
7
8
9
I
x) 11 12
ATOMIC % ZIRCONIUM
Fig. I. Variation of lattice spacing with composition and Th-Zr systems. q , Th-Zrl*. v, Th-Zrl3.
0
10 20 30 40 50 60 70 ATOMIC % CERIUM
for alloys in the Th-Ce-Zr
Fig. 2. Variation of lattice spacing with cerium content in the system Th-Ce-Zr The lattice spacings in the system Th-Ce are included for comparison. Th-Ce, J. Less-Common
Metals,
80 90
100
(20 at.g/, Ce)
(Th: Zr = 24: 1). a; Th-Ce-Zr, (3. 12
(1967)
465-477
470
M.
NORMAN,I. R. HARRIS, G. v. RAYNOR
thorium-zirconium alloys has been included for comparison. The lattice spacings of the zirconium used were a=3.zzgo kX and c =5.1438 kX, as compared with values of a=3.2256 kX, c=5.1371 kX reported by TRECO~~, and a=32271 kX, c=5.1367 kX obtained by HARRIS AND RAYNOR~. The lattice spacing of the thorium used for this series of alloys was a=5.0749 kX, while that of the cerium employed was a= 5.1508 kX. The lattice spacing of the Th-zo at.% Ce alloy is decreased by the substitution of zirconium for thorium; initially the rate of decrease is identical with that produced by the solution of zirconium in thorium. At zirconium concentrations exceeding 3 at.%, however, the rate of decrease of lattice spacing in the ternary alloys, as thorium is replaced by zirconium, exceeds that in the binary alloys. The phase boundary between the thorium-cerium solid solution and zirconium, for a cerium content of 20 at.%, occurs at approximately 6.5 at.% Zr at 950°C. (ii) Alloys with a constant Th:Zr atomic ratio of 24:r This series of alloys was necessarily prepared from different samples of thorium and zirconium from those referred to in b(i) above. The lattice spacings recorded were as follows : Thorium,
a=5.0758
kX.
Zirconium,
a=3.zz7r
kX;
~‘5.1367
kX
The sample of cerium remained unchanged from that previously used. The lattice spacings obtained at room temperature for the ternary alloys are given in Table IV, and the lattice spacing/composition relationship is shown in Fig. 2, with the corresponding results for the thorium-cerium system. Both sets of results show three linear portions. The central portion for the ternary alloys (21.5-47 at.% Ce) is, however, more limited than the corresponding linear region for the thorium-cerium system. The effective lattice spacing for cerium in dilute solid solution in the thoriumzirconium alloy (Th : Zr = 24: I), obtained by extrapolation to 100% Ce of the initial linear portion of the curve is 5.0330 kX, and is appreciably smaller than the corresponding value (5.0513 kX) for the thorium-cerium system. TABLE IV LATTICE SPACINGS OFTHORIUM-CERIUM-ZIRCONIUM ALLOYS CONTAINING THORIUM AND ZIRCONIUM IN THE ATOMIC RATIO 24:1, AT ROOM TEMPERATURE (22'C) AND AT -6o”, -100' AND -186'C Filings
rapidly
cooled
Corrected compositions
from
(at.%)
700°C.
_ Lattice
spacing
(kX
& 0.0002 kX)
Th
Zr
Cc
22°C
-60°C
-IOO"C
-I86"C
96.00
4.00 3.80 3.59 3.21
-
5.0595 5.0587 5.0568
5.0538 5.0516 5.0508
29.83 40.00 50.00
5.0444 5.04’7 5.0408
5.0472 5.0430 5.0428 5.0322
2.80 2.40 2.01 1.61
5.0542 5.0572 5.0615 5.0691
5.0513 5.0485 5.0480 5.0401 5.0348 5.0301 5.0276 5.0362 5.0680
5.0255 5.0155 5.0030
91.20 86.53 76.91 67.36 57.60 47.99 38.45 29.32 lg.28 9.66 -
I.22 0.80 0.39 -
J. Less-Common
5.00 9.88 19.88
59.94 69.45 79.91 89.95 100.00
5.0857 5.1028 5.1192
5.0457 5.0635 5.0845 5.1082
5.1355 5.1508
5.1279 -
Metals, 12 (1967) 465-477
5.0930 5.1240 -
4.9911 4.9682 4.9315 4.8865 4.83
LATTICE
SPACINGS
AND EFFECTIVE ATOMIC DIAMETERSIN Th-Ce-Zr
471
The variation of lattice spacing with temperature over the approximate range 26” to - 186°C was investigated for the alloys listed in Table IV. The results for three typical alloys containing respectively, 5, 50 and 79.91 at.% Ce are shown graphically in Fig. 3. Curve A is typical of alloys containing 5, 9.88 and 19.88 at.% Ce, and is essentially linear. The alloys containing 29.83, 40, 50, and 59.94 at.% Ce show the type of behaviour illustrated by curve B; the spacing/temperature relationships for the remaining Ce-rich alloys are as in curve C
5.000
1
I.. 40
20
0
*. 20
. 60 80 100 120 140 160 180 xx) TEMPERATURE ‘C I
40
I,
8.
*,
0
Fig. 3. Variation of lattice spacing with temperature for alloys in the system Th-Ce-Zr (Th: Zr =
24:‘).
0, 5 at.% Ce (A); a, 50 at.% Ce (B); 8, 79.91 at.% Ce (C).
The lattice spacing/temperature curves determined for the individual alloys have been used to construct lattice spacing/composition curves for temperatures intermediate between room temperature and that of liquid nitrogen. Table IV and Fig. 4 summarise the values obtained at - 60” and - IOO’C. The minimum in the curve moves to higher cerium contents as the temperature decreases, and between -60” and -roo°C, moves from approximately 40 to 50 at.% Ce. Below - IOO’C, cerium-rich alloys begin to transform to a solid solution based on cx-cerium; the Y--W transformation temperature of cerium is raised by the addition of thorium. The diffraction peaks of the cerium-rich alloys broaden considerably at - 186°C owing to the large internal stresses involved in the transformation. The lattice spacings of the alloys, for which the Th : Zr atomic ratio is maintained at 24: I, at - 186°C are included in Table IV and plotted in Fig. 5, together with Extrapolation of the initial results for the thorium-cerium system at -ISOY?. thorium-rich section (o-35 at.% Ce) to IOO at.% Ce gives a value of 4.975 kX for the effective lattice spacing of cerium corresponding to solid solution in the thoriumzirconium alloy (Th:Zr =24: I) at -186°C; this compares with a value of 4.989 kX for the effective spacing of cerium in solid solution in thorium3 at a similar temperature. The lattice spacing/composition curve for the ternary alloys at - 186°C shows a large, positive deviation from the line joining the respective spacings of the thoriumzirconium alloy and of or-cerium. No experimental evidence was found in the present J. Less-Common
Metals, 12 (1967) 465-477
M. NORMAN, I. R. HARRIS, G. V. RAYNOR
472
I”“,
1.
‘.
5Jnol. *
* ’ * * J 10 20 xl 40 50 60 70 80 90 100
0
ATOMIC
% CERlUM
Fig. 4. Lattice spacing/composition -60°C (a), and -roo”C ( q).
relationships
Fig. 5. Lattice spacing/compos~~on relationships at -186”C, and Th-Ce (A) at -18o’C.
work for the existence and LX-Ce,respectively.
of any two-phase
I
*
4floo
x)
in the system
8.
1.
Th-Ce-Zr
in the systems Th-Ce-Zr
region between
.
.
.
20 30 40 50 60 70 ATOMIC % CERIUM
80 90
(Th: Zr -
(Th: Zr =
solid solutions
24: I) at
24: I) (Q)
based on ol-Th
~e~~e~~~ye ~~n~~~~ s~~cep~~~~~~t~es of Th_Ce-Zr allots (7%: Zr=24:1) The results obtained in the magnetic work are collected in Table V and the variation of magnetic susceptibility with composition at room temperature is shown in Fig. 6. The value obtained for the pure thorium used was 0.445 x IO-~ e.m.u./g, fc) Room
TABLE MASS
V OF Th-Ce-Zr
SUSCEPTIBILITIES
Corrected
(Th: Zr=24:
I) AT ROOMTEMPERATURE
Corrected composition
(wt.%)
Th
Zr
Ce
0.62 0.76 1.04
60.78 51.09 40.88
1.00 0.84 0.67
38.22 48.07 58.45 71.11 84.70
IO.74 13.55
*oo.oo
17.40
x
composition
ALLOYS
x
lo-6
e.m.zc./g
*
(wt.%) ____ Ce
I%
Th
Zr
98.39
-
92.14
x.61 I.56 x.50
85.29 77.90
1.40 1.27
13.31 20.83
1.66 2.53
28.42 15.06
0.47 0.24
69.66
1.14
29.20
3.43
-
-
95.29
J. Less-Commor
3.15 6.35
Met&,
IZ
(1967)
465-477
x x
4.81 6.51 8.48
10-e
(294
e.m.u./g
.* r%
LATTICE SPACINGSAND EFFECTIVE ATOMIC DIAMETERSIN Th-Ce-Zr
473
ATOMIC % CERIUM
I
..
N) WEIGHT
% CERIUM
L., . . . 0 10 20 XI LO 50 60 70 ATOMIC % CERIUM
. .’ 60 90
&
Fig . 6. Variation with cerium content of the mass susceptibility of Th-Ce-Zr alloys (Th: Zr = 24: I) at room temperature. Fig. 7. Deviations from ideal behaviour in Th-Ce-Zr alloys containing 0; I at.% Zr, 8; 2 at.% Zr, 0; 4 at.% Zr, v; 6 at.% Zr, El.
20
at.% Ce. o at.% Zr,
which may be compared with the value of 0.422 x 10-s e.m.u./g reported by LEACHES. The mass-susceptibility of zirconium was found to be 1.29 x 10-s e.m.u./g. DISCUSSION (a) Lattice spacing measurements In Fig. I the effect on the lattice spacings of replacing the thorium in a Th-20
at.% Ce alloy by zirconium is compared with the effect of zirconium on the spacing of thorium. In the binary system the lattice spacings decrease lineally as the zirconium content increases up to the solid-solubility limit, and the spacing/composition relationship approximates very closely to linear variation between the atomic volumes of the component+ as expected for components of equal valency. If the state of cerium in solid solution in the Th-2o at.% Ce alloy were unaffected by the replacement of thorium by zirconium, the curve of lattice spacing against zirconium content for the ternary series containing a constant cerium content of 20 at.% would lie parallel to the corresponding curve for the binary alloys. This behaviour is observed below 3 at. “/x Zr ; at higher zirconium contents the rate of decrease is greater in the ternary series than for the binary system. As the mean lattice spacing of the matrix is decreased by the substitution of thorium by zirconium, therefore the behaviour is consistent with further ionisation of the 4f electrons of the cerium atoms, which leads to contraction of the apparent atomic diameter, in order to prevent too large an increase in the compressive strain energy of solid solution, as previously suggestedi-3. The increase in slope of the curve for the ternary alloys in Fig. I at 3 at.% Zr suggests that a critical .I. Less-Common
Metals,
12
(1967)
465-477
474
M. NORMAN,
I. R. HARRIS,
G. V. RAYNOR
degree of additional strain energy may be necessary to induce further contraction of the cerium atoms which have already contracted considerably in forming the Th-2o at.% Ce alloy. For the series at 20 at.% Ce, an alloy containing x at.% Th and y at.% Zr can be regarded as a solution of 20 at.% Ce in a thorium-zirconium solvent of composition 5x/4 at.% Thand 5~14 at.% Zr and of constant valency(4). From Fig. I the effect of the solution of 20 at.% Ce on the lattice spacing of any composite solvent within the solid solution of zirconium in thorium may be derived, and Fig. 7 illustrates the results obtained for cerium dissolved in composite thorium-zirconium solvents containing o, I, 2, 4 and 6 at.% Zr. The straight lines indicate ideal behaviour in the sense of an additive relationship between the lattice spacings of the f.c.c. composite solvent and f.c.c. y-cerium. In all cases the strong negative deviation from additivity characteristic of the thorium-cerium alloys is maintained. The extrapolations to IOO at.% Ce represented by the broken lines in Fig. 7 again indicate that for zirconium contents in the composite solvent below about 3 at.%, the cerium atoms are essentially in the same electronic state as in the thorium-20 at.% Ce alloy. Further decrease of the mean lattice spacing of the composite solvent, however, leads to a further decrease of the apparent atomic diameter of cerium. The series of alloys for which the atomic ratio Th:Zr=24: I represents the solution of cerium in a composite binary solvent of composition thorium g6 at.% and zirconium 4 at.%. Extrapolation to IOO at.% Ce of the initial linear section of Fig. 2 gives the value 5.0330 kX for the apparent lattice spacing of cerium in the hypothetical face-centred cubic form corresponding to its electronic state in solid solution. Assuming the effective valencies suggested by GSCHNEIDNER AND SMOLUCHOWSKI~ for y- and or-cerium, and applying the Pauling relationship19 between atomic size and valency, the effective valency of cerium in solid solution in the composite solvent is assessed as approximately 3.3, as compared with the value 3.25 (effective lattice spacing=5.0513 kX) for the initial solution of cerium in thorium. These experiments emphasise the importance of strain energy factors, which depend upon the difference between the atomic diameters of the solvent and of cerium, in controlling the electronic constitution, and hence the atomic size of cerium in solid solution; the change of effective valency is, however, towards that of the solvent. Other evidence7 shows that a tendency exists for cerium in solid solution to change its effective valency towards that of the solvent, even at the expense of a small increase in strain energy. Both factors are probably operative in the present case; the two factors, for a 4-valent solvent of atomic diameter smaller than that of y-cerium, reinforce and the electronic constitution of cerium in solid solution at a given temperature represents the resultant effect. In thorium-rich alloys, it was found by HARRIS AND RAYNOR~ that the contraction of the cerium atom at a given composition was increased by a decrease in temperature and decreased with temperature increase, so that the slope daldt of the curve of lattice spacing against temperature for a thorium-rich alloy was greater than that for pure thorium. Curves of type A in Fig. 3 are similar to those previously obtained for thorium-cerium alloys, and indicate that there is no temperature-induced transformation in the ternary alloys containing less than 20 at.% Ce. Curves for alloys containing 30-60 at.% Ce (type B) are more complex and consist of three almost linear positions, suggesting that a continuous temperature-induced change occurs in these alloys, which is completed before the lowest temperature investigated is reached. J. Less-Commolz Metals, 12 (1967) 465-477
LATTICESPACINGS AND EFFECTIVEATOMICDIAMETERS IN Th-Ce-Zr
475
This behaviour may be discussed in terms of the electronic state of cerium in solid solution. At compositions below 21.5 at.% Ce in the ternary alloys, the evidence discussed above suggests that a sufficient proportion of 4f electrons per atom have been ionised to give rise to an effective valency of about 3.3. Above 21.5 at.% however the lattice spacing evidence suggests that the electronic state of cerium corresponds to a lower degree of ionisation. The number of 4f electrons per atom which can suffer transfer to the conduction band of the alloy on decrease of temperature is thus greater above 21.5 at.% than below this composition, and this may account for the increased value of daldt. The lattice spacing/temperature curves for alloys containing 69.45, 77.91 and 89.95 at.% Ce each show an abrupt decrease in lattice spacing at definite temperatures on cooling, owing to the transition from solutions based on y-cerium to those based on oc-cerium. The y-+a transformation temperatures for the 69.45, 77.91 and 89.95 at.% Ce alloys are - 115’, -140’ and - 145”C, which may be compared with the value - 157°C for pure cerium 20.The thorium-zirconium addition to cerium thus raises the y-ta transition temperature for cerium, in spite of the fact that a composite thorium-zirconium component has a more favourable atomic size factor with respect to y- than to cx-cerium. This suggests that the stabilising effect of the thorium-zirconium addition is connected with the greater similarity of the valency of this mixture (4) to that of cx-cerium (3.6)s than to that of y-cerium (3.1)s. Lattice spacing/composition curves for ternary alloys with an atomic ratio Th: Zr = 24: I and for temperatures intermediate between room temperature and -186”C, as deduced from the results of the present work, allow extrapolation to IOO at.% Ce to derive in each case an effective lattice spacing for cerium corresponding to its electronic state in dilute solution in the composite thorium-zirconium solvent. The effective atomic size so derived decreases continuously as the temperature is lowered, to an extent which is greater than would be expected from contraction to offset the effect of the decreased lattice spacings of the composite solvent. Thus, as the temperature is decreased, the effective valency of the cerium atoms in solid solution adjusts progressively closer to that of the composite solvent, in spite of the fact that the magnitude of the strain energy is slightly increased. This emphasises the importance of electronic factors in controlling the behaviour of cerium in solid solution. At - 186°C the apparent atomic diameter of cerium in dilute solid solution in the composite solvent with atomic ratio Th: Zr = 24: I (3.518 kX) is smaller than that of cerium in dilute solid solution in thorium (3.528 kX), as expected from the relative lattice spacings of the composite solvent and of thorium. The large deviation of the lattice spacing/composition curve from additivity of spacings between the solvent and of c*-cerium is of interest. The deviation is much larger than would be expected for components differing in valency by a small amount, and suggests that, as at room temperature, the apparent size of the cerium atom is dependent upon both strain energy and electronic factors. The form of the ternary alloy curve in Fig. z at cerium contents exceeding 47.5 at.% may be discussed in terms of the suggestion by EVANSAND RAYNOR~that the introduction into y-cerium of thorium results in local contractions which allow interactions to occur between the 4f and 5d electronic bands for cerium and facilitate promotion of 4f electrons to the conduction band. The local contractions around small zirconium atoms in the ternary case are more severe than around thorium atoms, so that a greater contraction of the cerium atoms than in the binary case is expected, J. Less-Common
Metals.
1% (1967)
465-477
476
M. NORMAN, 1. R. HARRIS, G. V. RAYNOR
and observed. The intermediate section of the lattice spacing/composition curve (21.5-47.5 at.% Ce) probably represents transition from this effect to the influences of compressive strain energy and the tendency towards the adoption of an effective valency more closely similar to that of the solvent on the effective atomic size of cerium in dilute solution. The lattice spacing measurements described in this paper suggest strongly, in conformity with previous work, that the apparent atomic diameter adopted by cerium in dilute solid solution in thorium-rich alloys is dependent upon both strain energy and electronic considerations. Increase in the compressive strain energy which would be caused by the solution of y-cerium, achieved by a decreased lattice spacing in thorium-zirconium alloys considered as solvents, leads to an increase in the contraction of the cerium atoms in solution. Other details of the results, however, such as the effect of temperature on the apparent atomic size of cerium in solution, indicate a tendency for cerium to adopt an effective valency closer in value to that of the solvent alloy. Both factors are therefore of importance, with the reduction of strain energy predominant in the system investigated. (b) Magnetic susceptibility measurements The results given in Table V enable calculation of the contribution per gram of cerium to the magnetic susceptibility of the alloy as a whole. If the mass susceptibilities of the alloy, of thorium and of zirconium are respectively XA, XTh and xzr and the weight percentages of the alloy components are Wrh, Wzr and Wee, then, assuming the mass susceptibilities of thorium and zirconium to remain unchanged on alloying, the susceptibility per gram of cerium is : Xce
=
[IOOXA
-X_ThWTh
-XZrWZr]
WC,
The values of xce are plotted against composition in Fig. 8. The curve shows three sections : (i) o-q.3 wt.% Ce (20 at.% Ce) (ii) 13.3-29.2 wt.% Ce (40 at.% Ce) and (iii) 29.2-100 wt.% Ce. The critical compositions correspond approximately to those at which changes of slope occur in the ternary alloy curve of Fig. 2. In the cerium-rich range, the susceptibility per gram of cerium is decreased by the thorium-zirconium addition; this decrease is consistent with a decrease in the number of 4f electrons of cerium as the concentration of composite alloy solvent increases, as suggested above in discussion of the lattice spacing results. In the range 40-20 at.% Ce the susceptibility per gram of cerium decreases less rapidly with decrease of cerium content than in the ceriumrich alloys: this is consistent with the lattice spacing results of Fig. 2. The susceptibility per gram of cerium in the composition range 0-20 at.% Ce is much less dependent on composition and considerably lower than that of y-cerium. This supports the conclusions drawn from the lattice spacing results, that the effective valency of cerium in dilute solid solution in the composite thorium-zirconium solvent corresponds with fewer 4f electrons per atom than in y-cerium and is essentially constant in the composition range corresponding to the initial linear contraction of the lattice J. Less-Common
Metals,
12 (1967)
465-477
LATTICE
SPACINGS AND EFFECTIVE
ATOMIC DIAMETERS
IN
Th-Ce-Zr
477
spacings of the solvent material. These results also justify the derivation of effective lattice spacings, corresponding to hypothetical forms of cerium having the same electronic constitution as the cerium in dilute solution, by extrapolation to IOO at.% Ce of the appropriate lattice spacing curves. ATOMIC % CERIUM la 20 30 LO 50 60 70 80
10 M
90
30 Lo 50 60 70 80 WEIGHT % CERIUM
0
90
Fig. 8. Susceptibility per gram of cerium in Th-Ce-Zr alloys (Th: Zr = q: I) plotted as a function of cerium content.
ACKNOWLEDGEMENTS
The work reported in this paper was carried out under the terms of a grant from the Science Research Council, to which grateful acknowledgement is made. The authors’ thanks are also due to the Atomic Energy Research Establishment for the loan of apparatus, and to the Royal Society, and Imperial Chemical Industries, Ltd., for support of the general programme of which this work forms a part. REFERENCES I R. T. WEINER, W. E. FREETH AND G. V. RAYNOR, J. Inst. Metals, 86 (1957-58) 185. 2 D. S. EVANS AND G. V. RAYNOR, J. Less-Common Metals, 4 (1962) 181. 3 J. T. WABER, I. R. HARRIS AND G. V. RAYNOR, Trans. AIME, 230 (1964) 148. 4 I. R. HARRIS AND G. V. RAYNOR, J. Less-Common Metak, 7 (1964) II. 5 K. A. GSCHNEIDNER AND R. SMOLUCHOWSKI, J. Less-Common Metals, 5 (1963) 374. 6 I. R. HARRIS AND G. V. RAYNOR, J. Less-Common Metals, 6 (1964) 70. 7 1. R. HARRIS AND G. V. RAYNOR, J. Less-Common Metals, 7 (1964) I. 8 J. H. N. VAN VUCHT, Philips Res. Reports, 12 (1957) 551. 9 IO II IZ 13 14 15 16 17 18 19 20
J. A. P. R. D. J. D. J. R. S. L. K.
M. BLACKLEDGE AND C. E. LUNDIX, unpublished work, 1959. H. DAANE AND F. H. SPEDDING, I.S.C. Rep. 530, 1954. R. DIXON, Ph.D. Dissertation, Univ. of Sheffield, 1957. H. JOHNSON AND R. W. K. HONEYCOMBE, J. NPLCZ.Mater., 4 (1961) 59. S. EVANS AND G. V. RAYNOR, J. Nucl. Mater., 4 (1961) 66. R. MURRAY, J. Less-Common Metals, 2 (1960) I. S. EVANS AND G. V. RAYNOR, J. Nucl. Mater., I (1959) 281. P. NELSON AND D. P. RILEY, Proc. Phys. Sot., 57 (1945) 160. M. TRECO, J. Metals, 5 (1953) 344. J’. LEACH, Thesis, Univ. of Nottingham, 1955. PAULING, J, Am. Chem. Sot., 69 (1947) 542. A. GSCHNEIDNER, JR., R. 0. ELLIOTT AND R. R. MCDONALD, J. Phys. Chem. Solids, 23 (1962)
555.
J. Less-Common
Metals, 12 (1967) 465-477