KINETICSTUDIESON REACTIONS OF PRASEODYMIUM OXIDESIN OXYGENATMOSPHERE
1667
Kinetic Studies on Reactions of Praseodymium Oxides in an
+
Oxygen Atmosphere: Pr01.83 0 , z Pro,
by B. G. Hyde, E. E. Garver, U. E. Kuntz, and L. Eyringl Chemistry Department, State University of Iowa, Iowa City, Iowa
(Received November $7, 196.4)
The present paper augments an earlier one on the kinetics of reduction of certain oxide phases of praseodymium and terbium.2 We now report rate studies of the following reactions: (1) the oxidation of to Proz by oxygen gas at atmospheric pressure (745 torr) in the temperature range 235 to 314” and (2) the vacuum reduction of Proz to Pr01.83 in the temperature range 242 to 347”. The kinetics of both processes are analyzed and, with some reservations, would appear to fit the equation for a “phase-boundary-controlled’’ mechanism quite accurately over most of the composition range involved. This interpretation is in accord with the known properties and phase relationships of the two oxides concerned.
I. Introduction. The Pr0,-02 System The system praseodymium oxideoxygen, a t temperatures up to 1050” and oxygen pressures up to 1 atm., exhibits nine stable solid phases in the composition range 1.5 5 2 5 2.0.a-5 The structural relations between these phases and the kinetics of their transformation are matters of current study. A striking property of these solids, especially those of high oxygen content, is the very facile transport of oxygen through the lattice even a t low temperatures. This, and the fact that the cation lattice appears to be immobile in the same temperature range, makes the elucidation of structures and the study of phase relations difficult. With melting points close to 2500”, the Tammann temperatures (above which we might expect a reasonable degree of ionic mobility) are above 1000”. Indeed, work on ternary rare earth oxides systems6 indicates that temperatures well above this value must be attained before cation mobility becomes appreciable. In contrast, rapid “equilibration” between oxygen gas and the solid oxides occurs a t a much lower temperature,’ e.g., in a matter of a few minutes at 400”. The presence of hysteresis between corresponding oxidation and reduction processes* suggests that true equilibrium is not as rapidly achieved-certainly when two of the solid phases coexist. This latter situation we may term a “diphasic” system .a
In the present work we are concerned with the oxides, Pro,, in the composition range 1.83 5 2 5 2.0. High pressure oxidation studiese indicate that hysteresis attends composition changes in most of this range, but this, in turn, suggests and tensimetric and X-ray diffraction studieslO confirm that the range is largely occupied by a diphasic region a t the temperatures a t which we have worked. The Pr01.83phase has a definite, though small, homogeneity range, as has the Proz phase, also. Between these compositions (probably 1.84 5 2 5 1.99, see below) there is a miscibility gap with a consolute temperature above that obtaining in any of the present experiments. (1) Chemistry Department, Arizona State University, Tempe, Ariz. (2) U. E. Kuntz and L. Eyring, “Kinetics of High-Temperature Processes,” W. D. Kingery, Ed., John Wiley and Sons, Inc., New York, N. Y . , 1959, p. 50. (3) B t G. Hyde, D. J. M. Bevan, and L. Eyring, presented a t the Third-Rare Earth Conference a t Clearwater, Fla., April 1963, in press. (4) L. Eyring and N. C. Baenziger, J . A p p l . Phys. Suppl., 33, 428 (1962). (5) L. Eyring and B. Holmberg, Advances in Chemistry Series, No. 39, American Chemical Society, Washington, D. C., 1963, p. 46. (6) Unpublished work, this laboratory. (7) R. E. Ferguson, E. D. Guth, and L. Eyring, J . Am. Chem. Soc., 76, 3890 (1954). (8) J. M. Honig, A. F. Clifford, and P. A. Faeth, I n o r g . Chem., 2, 791 (1963). (9) W. Simon and L. Eyring, J . Am. Chem. SOC.,76, 5872 (1954). (10) C. L. Sieglaff and L. Eyring, ibid., 79, 2034 (1957).
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B. G. HYDE,E. E. GARVER,U. E. KUNTZ,AND L. EYRING
The dioxide possesses the flyorite structure, with a lattice parameter a. = 5.393 A. Pr01.83, the product phase when any praseodymium oxide is heated and cooled in has a related structure. It has been thought to be face centered cubic, a. = 5.469 8., derived from the fluorite structure by the removal of one-twelfth of the anions (giving PrsOll or Pr01.833). It seems likely that the anion vacancies are ordered; otherwise, it is diacult to explain the extreme stability and narrow homogeneity range of the phase. The observation of a number of extra, very weak peaks in a room temperature X-ray diffractometer pattern of this phase4 (as compared with the fluorite pattern) would seem to support this hypothesis. Additional and very convincing support is provided by d.t.a. studies.12 When this phase is heated in oxygen pressures greater than 100 torr, an endothermic process is observed to occur without any change in composition a t about 400". (At lower oxygen pressures it decomposes into PrO1.80 a t temperatures below 400".) A corresponding exothermic process occurs at only slightly lower temperatures on cooling in oxygen. It is significani that the temperatures a t which these processes occur are independent of the oxygen pressure. (A phase change accompanied by a composition change occurs a t a temperature which depends on the oxygen pressure since the diphasic equilibrium oxygen pressure is a function of temperature.) These observations would seem to be most reasonably interpreted as showing the presence of an order-disorder transformation in Pr01,83at -400"; the high rate of exchange of oxygen between the gas and solid phases a t ulis temperature is most easily understood if the ordering involves the oxygen sublattice. Thus, both the phases involved in the present studies (temperatures being less than 400") would appear to be ordered phases, probably nonstoichiometric, and with closely related structures. 11. The Oxidation of PrOl.83to Pro2
Material. The original sample (99.9+% PrO1.83 from Michigan Chemical Co., St. Louis, Mich.) was dissolved in dilute nitric acid; the solution was filtered, and the praseodymium precipitated as the oxalate. The precipitttte was then ignited at 650" and cooled in air to give PrOl.83again. Commercial tank oxygen, used for the oxidation, was dried by passing it through a column of Linde Molecular Sieve. (The kinetics were unaffected, however, by further drying using a trap at - 80" or by omitting the molecular sieve.) Apparatus. The apparatus used was an automatic recording therm~balance'~ based on Mauer's design14 and operating a t atmospheric pressure. The 0.5-g. The Journal of Physical Chemistry
sample, in a small platinum bucket, was suspended by a h e platinum wire into a Vycor tube beneath the R h thermocouple located balance. A Pt-Pt-lO% close to the bucket was used to measure the sample temperature. The thermocouple e.m.f. and the sample weight were simultaneously recorded by a multipoint recorder. Sensitivities were j ~ 0 . 0 1mg. (equivalent to a composition change Ax N Zk0.0002) and 10.1". A slow stream of oxygen at 1 atm. bathed the sample during the kinetic run. The Vycor tube was surrounded by a Kanthal A, noninductively wound, alumina tube furnace (-45.7 X 5.08 cm. i.d.); a chromel-alumel thermocouple, inserted through the base of the furnace, was used to actuate a Minneapolis-Honeywell temperature controller. In this way, sample temperature variations were kept down to less than 0.2". Atmospheric pressure was measured by a Fortin-type barometer and was virtually constant at 745 ~k 5 mm. (uncorrected). Method. After loading the Pr01.83into the apparatus, the sample was heated in oxygen at about 330". A small weight loss occurred, presumably owing to the elimination of adsorbed water. The sample was then reduced in flowing hydrogen a t 630" to yield the standard weighing form, assumed to be PrOl.aooo. Using this weight, all subsequent weights could be converted to composition values (xin Pro,). After the hydrogen reduction, the sample was heated in oxygen again, the temperature being gradually reduced in small steps from 320" downward, until noticeable oxidation of the PreOll occurred. The temperature was held a t that value (314") and the first oxidation run carried out. Subsequently, when a run was completed, the oxygen stream was replaced by argon so that the dioxide reduced, and the sample temperature was adjusted to the new value required for the next run. When the system had attained thermal equilibrium, the argon was rapidly flushed out and replaced by oxygen ; instantaneous oxidation to Pr01.837 occurred,15 followed by slow oxidation to the dioxide. Depending on the temperature and the extent of reaction, the duration of a run varied between 11 hr. and 5 days-being usually about 2 days. Some of the runs were stopped before the reaction was complete; this was a regrettable mistake since the form of ~~
~
(11) H. A. Pagelland P. H. Brinton, J.Am. Chem. Soc., 51, 42 (1929). (12) E. D. Guth, J. R. Holden, N. C. Baenziger, and L. Eyring, ibid., 76, 5239 (1954). (13) A. G. Ostroff, Thesis, State University of Iowa, 1957. (14) F. Mauer, Rev. Sci. Instr., 25, 598 (1954). (15) It was constantly observed that the composition of the sample, reignited in oxygen, was close t o PrOi.sar rather than PrOi.8aa. The latter composition is that normally observed for air-ignited oxide; the former presumably reflects the higher ambient oxygen pressure.
KINETICSTUDIES ON REACTIONS OF PRASEODYMIUM OXIDESIN OXYGENATMOSPHERE
-/ t t t t . 0.10
1669
0.15
0 0
$..o
d-
e 0 0
0
0.05
i
1
2.00 1
0
1
I
5
l
1
I
l
I
10
1
I
I
1
l
1
l
I
I
20
15
I
l
l
I
25
I
l
I
1
I
30
I
I
I
I
35
Time.
Figure 1. Oxidation of PrsOll to Proz; composition zt us. time. Time scale, 1 unit = 100 min., except for run a t 234O, where 1 unit = 1000 min.
the kinetics toward the end of the reaction turns out to be especially interesting. All runs were a t T I 320°, Le., well below the temperature of the postulated order-disorder transformation. The data reported were all obtained with a single sample of oxide, cycled as described above. Two additional runs-of only incidental interest-were made. One of these, utilizing a fresh sample of oxide from the original preparation, established that the initial Hz reduction was quite unnecessary; the reaction proceeded in the same manner without the sample being thus “activated.” The second run utilized a small single crystal so that the effect of particle size could be observed. After 4 days at 305” the average composition of this sample had changed by Ax N 0.006; the run would have lasted 6-12 months, and so it had to be abandoned. Results and Dkussion. The relation between composition and time at a series of temperatures is shown in Figure 1. If the rates of nucleation and growth of the product phase are comparable (SO that the two processes are concurrent rather than consecutive), then the relative importance of the two factors must be evaluated experimentally by changes in conditions, e.g., temperature and particle size.16 A comprehensive classification of such reactions has been given by Jacobs
and Tompkins17 and will not be repeated here. Diffusion processes may also be rate ~ o n t r o l l i n gl9. ~ ~ ~ Finally, adsorption processes may be the limiting factorz0Vz1although this appears not to be the case in PrO,-O2 systems-nor would we expect that they would be.229 At first sight, the curves of Figure 1 appear to resemble closely those given by a process in which diffusion rates are high and surface nucleation is more or less rapid and complete, the growth of the product phase being rate determining. In such a case, the kinetics depend only on the rate of advance of the reactant-product phase boundary. This advance rate is often assumed to be constant throughout a reaction. For some reactions for which there is direct observational evidence this is true, a t least by the time the nuclei reach visible size.17v24 However, in some (16) S. Aronson, R. B. Roof, Jr., and J. Belle, J . Chem. Phys., 27, 137 (1957), and references therein. (17) P. W. M. Jacobs and F. C. Tompkms, “Chemistry of the Solid State,” Butterworth and Co. Ltd., London, 1955, p. 184. (18) W. Jost, “Diffusion in Solids, Liquids, Gases,” Academic Press, New York, N. Y., 1960, p. 46. (19) K. B. Alberman and J. S. Anderson, J . Chem. SOC.,S303 (1949). (20) P. W. M. Jacobs and A. R. T. Kureishy, “Reactivity of Solids,” Elsevier Publishing Co., Amsterdam, 1960, p. 353. (21) B. V. Erofeev, ibid., p. 273. (22) J. S. Anderson and K. J. Gallegher, ibid., p. 222. (23) J. S. Anderson and K. J. Gallagher, J . Chem. Soe., 52 (1963).
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B. G. HYDE,E. E. GARVER,U. E. KUNTZ, AND L. EYRING
1.85
0.5
1.90
2
0.4
h
H
i.I
I
1.95
8 H v
0.3
1.99
other reactions there is weighty, but necessarily indirect, evidence of an acceleration of the growth rate with time while the nuclei me still of submicroscopic s i ~ e . ~This ' ~ ~will ~ concern us later. Surface area measurements (B.E.T. method), Xray line broadening, and electron microscope examination of Pro, powders, prepared in the same way as were the present samples, all indicate that the particles are approximately 0.5 p in diameter.26 The last technique also shows the particles to be spherical. In common with most theoretical treatments of solidstate reactions, we therefore assume, as a model, a homogeneous collection of spherical particles. For such a system, rapid complete surface nucleation together with a constant (linear) rate of growth resultsn in the kinetic equation (1 - a) = (1
- Vt/a)3
(1)
where a is the extent of reaction, V is velocity of advancement of the reactant-product interface, a is particle radius, and tis time. The Jourrull of Physical Chemistry
If xt,xo, and x, denote the (average) composition of the sample at times t, 0, and m ,respectively, then (zt - xo)/(z.. - $0) which, together with (1) gives, after rearrangement, (z, - zt)1/8= kt c (2) where k = - V ( x , - xo)"8/a, and C = (zm- zO)'/'; k is a rate constant if x, - 5 0 is temperature independent. Thus, a graph of (2, - ~1~)''~ us. time will be linear. However, agreement with eq. 2 will be sensitive to error in the value of x,-particularly toward the end of the reaction where the composition scale is much expanded in a cube root plot. Since it is not feasible to measure z, experimentally for a reaction as slow as the present one, we have had Q
=
+
(24) P. J. Anderson and R. F. Horlock, Trans. Faraday SOC.,58, 1997 (1962). (25) P.Jacobs and A. R. T. Kureishy, ibid., 58, 551 (1962). (26) H.S. Schuldt, Thesis, State University of Iowa, 1960. (27) See, e.g., J. S. Anderson, L. E. J. Roberts, and E. A. Harper, J. Chem. Soc., 3946 (1955).
KINETICSTUDIESON REACTIONS OF PRASEODYMIUM OXIDESIN OXYGEN ATMOSPHERE
to select an optimum value by trial and error. The best agreement obtains for 1.990 5 z, 5 2.000 in all runs. In some, 2.000 is slightly better than 1.990, but in general it is not possible unambiguously to select x, to better than -=!=0.005. We have therefore utilized x, = 2.0000 in all cases, and the resulting cube root plots are shown in Figure 2. Agreement between the experimental data and eq. 2 is good, except a t the beginning and end of the reaction. We now consider possible causes of these deviations. As already mentioned, there is not a great deal of experimental in formation for the end of the reaction. In four of the runs the maximum x value attained was -1.92 to 1.95 only. Any explanation of the deviation a t high a-values must therefore be tentative. A plausible possibility is that the falloff in rate toward the end of the reaction is a consequence of the particles having a range of sizes.28 However, the temperature dependence of the observed effect (cf. runs a t 285 and 307”) suggests that this is not wholly responsible. It is also possible that the diffusion of oxygen through the product phase could become rate controlling when this phase becomes thick enough. (Surface area measurementsZ6indicate that the reactant and product are coherent.) We believe that this latter is the correct explanation of the deviations observed. While more precise data are needed for an unambiguous decision, the following considerations show that our observations are not inconsistent with the hypothesis. Figure 3 shows, schematically, the free energy of formation of the nonstoichiometric phases, PrBOll (I) and Pro2 (11), as a function of composition at two different temperatures. T1 is well below the equilibrium temperature for coexistence of I and I1 a t 1 atm. of oxygen; Tz (>T1) is only slightly below the equilibrium temperature. Providing the system is not too far from equilibrium, the chemical potential of oxygen a t the surface of the reacting solid (ie., phase 11) is that of the gas phase and is given by G (at both temperatures). Also, that part of phase I1 at the phase boundary (1-11) will similarly have an oxygen potentid close to the minimum value given by the “common tangent,” i e . , PI a t TIand PB at Tz. GPz is less than GP1; clearly G P decreases with increasing temperature, becoming zero at the equilibrium temperature. Now GP is the maximum potential difference available for diffusing oxygen through the product phase, from the particle surface to the 1-11 boundary. According to Fick’s first law, the rate of oxygen transport across unit area is given by dno,/dt = Ddpo,/dx DGP/d, where D is the diffusion coefficient of oxygen through 11, and d is the thickness of product phase 11.
0
0.647
1671
0.667
Atom fraction of oxygen.
Figure 3. Free energy of formation us. composition (schematic) for the phases PreOll (I) and Pr0~(11) at two temperatures, TI and TZ> TI. (See text.)
If, as the temperature is increased, GP falls faster than D rises, the maximum rate of oxygen transport through the shell of product will decrease. This will also be true even if conditions are far from equilibrium. Thus, as the temperature of the system approaches that for equilibrium between I and 11, the phaseboundary-controlled reaction could become throttled by slow diffusion of oxygen to the interface. This effect will be accentuated by increasing d, ie., increasing a and t, and by increasing temperature. This is consistent with the observed “tailing-off” of the reaction rate. An approximate theoretical treatment of this complex situation has been made. However, the data are not precise enough to allow any firm conclusions to be drawn. Finally, we consider the systematic deviations from linearity a t the beginning of the oxidation that are apparent in Figure 2. Consideration of Figure 3 shows that oxidation will, in general, consist of a t least four (28) Cf. K. J. Gallagher, 5th International Symposium on the Reactivity of Solids, Munich, 1964, to be published.
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B. G. HYDE,E. E. GARVER,U. E. KUNTZ, AND L. EYRING
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distinct processes : (i) monophasic oxidation of the reactant phase (I), x, + xb and possibly Zb + x,, (ii) nucleation, (iii) growth of the product phase 11, xb xd, and (iv) monophasic oxidation of the product phase to its equilibrium composition, x d + xe = x,. In the absence of a rate-limiting surface process (see above), stage (i) is necessarily diffusion controlled. Furthermore, it is likely to be faster than stage (iii), which is not diffusion controlled, at least initially. Such a fast initial stage is observed, and the data are consistent with the equation for diffusion into a sphere. m
a = 1 - (6/n2)
[nV2exp(--n2?r2Dt/a2)] (3) n=l
I n this context the behavior of the fresh (“uncycled”) powder sample is relevant. It was first exposed to 1 atm. of oxygen at 320”; oxidation proceeded to a limited extent only (zo = 1.837, x, = 1.851) and then ceased. The data give a linear plot of log (x, 2,) us. t with z, = 1.851. Similarly, the main sample at 321” oxidized only t o x, = 1.846, and again log ( 2 , - x,) is linear with t. Thus, these results are not inconsistent with eq. 3 although accuracy is again severely limited by the very small weight change involved (-0.3 mg.). It would appear that, at the beginning of the reaction, the rate is to be explained as follows. Rapid diffusion of oxygen into the Pr6OI1 particle causes the surface region to become supersaturated with oxygen (a + b + e, Figure 3). Then, if nucleation is accompanied by rapid spreading of the product phase over the surface of the particle, the growth rate increases with increasing CY.(Note acceleratory period just before the linear “cube root” relationship commences.) Alternatively, if the growth rate is constant, either the nucleation rate or the spreading of the nucleus over the surface is slower than instantaneous. During this period the production of the phase boundary occurs, and it is noteworthy that a t the commencement of linearity in Figure 2 (stage (iii) above) the j a l u e of CY indicates a product shell only about 140 A. thick. This is not unreasonable as a critical value below which “unmixing” of the supersaturated surface layer to give a phase boundary would be inhibited by the relatively high surface free energy of the boundary. The slopes of the linear portions of the curves in Figure 2 were used t o construct the Arrhenius plot shown in Figure 4. The rate of the phase boundary reaction has a maximum a t -302”. As the temperature approaches that for equilibrium between the two phases, I and 11, the driving force for the reaction (the height of c above bd in Figure 3) falls to zero. The The Journal of Physical C h a i s t r y
t r I
1.0’
I
1.70
I
I
I
1.80 108/T°K.
I
I
1.90
I
2.00
Figure 4. Oxidation of Pr6011to PrOz; Arrhenius plot for phase-boundary-controlled reaction. k is the pseudo rate constant (eq. 2) from Figure 2.
slope of the low temperature part of Figure 4 yields of 26.9 kcal./g.-atom of 0. an activation energy, M0,, 111. The Reduction of Proz to Pr01.,3 Material. Praseodymium oxide (99.9+%), containing
