RONALD C. GARVIE
1238
The Occurrence of Metastable Tetragonal Zirconia as a Crystallite Size Effect
by Ronald C. Garvie U . S . Department of the Interior, B u r e a u of M i n e s , College P a r k Metallurgy Rtsearch Center, College P a r k , Maryland (Received October 16, 1964)
Metastable tetragonal ZrOz was prepared in two ways: (I) precipitation from alkaline aqueous solution and (11) low temperature calcination of zirconyl nitrate. Both methods are standard techniques for preparing active powders with large surface area. This suggested that the excess surface energy (relative to a large single crystal) present in I and I1 stabilized the tetragonal form. The maximum specific surfaces in I and I1 were 194 and l j . 6 m.2/g., respectively, corresponding to crystallite sizes of 54 and 155 ,$. The excess energy of the active powders ranged as high as 6.7 kcal./mole. There appeared to be a critical crystallite size, about 300 A., above which the metastable tetragonal phase could not exist a t room temperature. Thermodynamic calculations showed that, if the surface upon passing from the tetragonal free energy of ZrOz increased from 770 to 1130 ergs/“ to the monoclinic structure a t 300”K., then the occurrence of the metastable tetragonal form could be accounted for as a crystallite size effect.
Introduction This research was undertaken to determine the reason for the occurrence of metastable tetragonal ZrOz. Normally, zirconia has a monoclinic structure a t room temperature which transforms to a tetragonal structure a t about 1100”. The enthalpy difference of the two structures a t 1205” is 1420 cal./mole.’ The high temperature form cannot be quenched, yet, surprisingly, it can exist a t room temperature if the zirconia is prepared either by precipitation from alkaline aqueous solution or by calcining a salt such as the chloride or nitrate a t low , Recently a “cubic” form of ZrOz, obtained by precipitation, has been r e p ~ r t e d . ~However, when this “cubic” phase is heated, certain broadened X-ray diffraction lines smoothly and gradually emerge as the characteristic tetragonal doublets. Thus, the “cubic” phase appears to be the tetragonal form with the doublets masked by line broadening. Although Ruff and Ebert first prepared the metastable tetragonal phase in 1929 by igniting zirconium salts, there has been only one attempt to account for this puzzling behavior of Zr02.4 Cypres, Wollast, and Raucq prepared the metastable phase by heating “Zr(OH)4.”5 These authors studied the problem with the aid of differential thermal analysis, thermogravimetry, electrical conductivity, infrared absorption, T h e Journal of Phyeical chemi8tTy
and X-ray diffraction. They concluded that small amounts (0.75 wt. %) of bound OH groups in solid solution stabilized the tetragonal form at room temperature. When the solid was heated in the region 600 to goo”, the OH groups were driven off as water, and simultaneously the formation of the monoclinic phase was noted. The present author holds that this view is untenable owing to the experimental results obtained by Clearfields3 He prepared an amorphous precipitate of hydrous ZrOz which was heated in distilled water under reflux. The following sequence of phases was observed in the precipitate: amorphous 4 tetragonal monoclinic + monoclinic. Under these conditions, bound OH groups could not be driven off, and therefore i t does not appear that OH groups have anything to do with the formation of the metastable tetragonal phase. Moreover, the results of the infrared studies made by Cypres and co-workers (which constitute their strongest
+
(1) J. P. Coughlin and E. G. King, J . Am. Chem. Soc., 72, 2262 (1950). (2) C. T. Lynch, F. W. Vahldiek, and L. B. Robinson, J . Am. Ceram. Soc., 44, 147 (1961). (3) A. Clearfield, Inorg. Chem., 3 , 146 (1964). (4) 0 . Ruff and F. Ebert, Z . anorg. allgem. Chem., 180, 19 (1929). (5) It. Cypres, R. Wollast. and J. Raucq, Ber. Deut. K e r a m . Ges.. 40, 527 (1963).
( . h X J R R E N C E O F lIETASTA4BLETETRAQONAL ZIRCONIA AS CRYSTALLITE SIZE
evidence for bound OH groups) are open to question. They prepared samples for infrared analysis by grinding them in isobutyl alcohol. Powders formed by precipitation have very large specific surfaces and therefore would tend to adsorb polar niolecules such as isobutyl alcohol. There is a possibility that the absorption peaks presented in their work arose from adsorbed alcohol. A preliminary examination of Debye-Scherrer Xray diffraction patterns of the metastable material prepared by this writer revealed the characteristic line broadening of a finely divided powder. Such powders are called active because they possess excess energy (relative to a large single crystal) and display unusual properties. For example, an increase in the heat of solution of samples of active MgO as high as 2 kcal./ mole over coarse-grained material has been reported.6 Again, one can obtain aluminum from alumina by heating the active oxide under vacuum at 500O.’ It is suggested that the reaction, monoclinic ZrOz tetragonal ZrOz, has been so affected by the extremely fine state of subdivision of the material that the tetragonal phase occurs at room temperature. Buerger earlier suggested a crystallite size effect to account for the appearance of high cristobalite in samples of opal a t room temperature.* In this work, the formation of the metastable tetragonal phase was correlated with those physical properties which are most important in describing active powders, namely, mean crystallite size, surface area, and excess energy. Experimental Procedure Zirconium dioxide was prepared in two ways: precipitation and calcination. In the former, a hot solution of zirconyl nitrate was added to a hot, stirred, 50 wt. yo solution of sodium hydroxide, and the zirconium dioxide was precipitated as the hydrous oxide. Details of the procedure were taken from a paper by Hathaway and Clearfield.9 I n the latter, the anhydrous nitrate was calcined a t 400” for 48 hr. The first preparation will be described hereafter as the precipitated oxide, and the second, as the calcined oxide. Samples of both types were heated in air a t various temperatures up to 1000° for a constant time of 24 hr. Standard X-rav diff ractometer techniques, using unfiltered iron radiation, were employed to determine the phases present and the mean crystallite Size of the air-quenched product. The specific surface of the samdes was measured by the B.E.T. method using- the continuous-flow technique of Nelsen and Eggertsen.10 Sample purity was checked by optical emission spect rography.
EFFECT
1239
The crystallite-size measurements will be described in greater detail because of the uncertainties and difficulties associated with this technique. According to the Scherrer formula, the crystallite size, D ,is inversely proportional to the true line broadening, 0,of the diffraction peak, occurring a t some angle, e. In this work the (111) line of both oxides was used for the size measurements. Instrumental broadening is measured by scanning diffraction pealis of a standard substance whose crystallite size is known to be greater than 10,OOO A. The material used in this work was a thin cleavage flake of mica which has been used effectively to align a diffractometer.” A mica flake is a single crystal oriented to produce a series of strong sharp reflections of the (001) type when mounted on a diffractometer sample holder. Values of p were obtained from the observed line broadening (defined as the line width a t half-peak intensity) and the instrumental broadening by means of calibration curves published by Klug and Alexander. l2 These curves, assumed to be valid for all diffractometers of the same design, were reproduced on an enlarged scale and used directly to obtain p. This method is claimed to give a precision of j = l O o j , in the region 100-lo00 8. for a related series of samples and an absolute accuracy of f25%. l9
Results and Discussion Spectrographic analyses of the precipitated and calcined oxides are given in Table I. The principal metallic impurity, other than halfnium, was sodium with a concentration of the order of 1%. This writer assumes that the level of impurities listed in Table I does not affect the experimental results. This assumption is supported by evidence obtained by Mazdiyasni, Lynch, and Smith, who observed the tetragonal phase a t room temperature in ultra high purity zirconia prepared by thermal decomposition (6) D . K. Thomas and T. W. Baker, Proc. Phys. SOC.(London), 9 2 , 673 (1959). (7) H . J. DeBoer, Ed., “Reactivity of Solids.” Elsevier Publishing Co., New York, N . Y., 1961, p. 525.
(8) M. J. Buerger, “Phase Transformations in Solids.” John Wiley and Sons, Inc., New York, N. Y., 1951, Chapter 6.
I
(9) A. J. Hathaway and A. Clearfield. “Preparation of Zirconia Solid Solutions by Coprecipitation,” Basic Science Division Meeting of t h e American Ceramic Society, Columbus. Ohio, o c t . 1962. (10) F. M.Nelsen and F. T. Eggertsen, Anal. Chem., 30, 1387 (1958). (11) D . K. Smith, ‘yorelco Reptr., 1 0 , 19 (1963). (12) A. P. Klug and L. E. Alexander, “X-Ray Diffraction Procedures,” John Wiley and Sons, Inc., New York, N . Y..1954, Chapter 9. (13) L. E. Alexander, >fellon Institute, Pittsburgh, P a . , private communication.
Volume 69,Number 4
April 13%
1240
RONALD C . GARVIE
Table I: 0pt)icnl Spectrographic Analyses of Zirconium Dioxide Elementu,*
A1
B cu Fe
Hf K Mg Mn Na Si Ti V
Precipitated
Calcined
0.003-0.03 0.001-0.01 0.00003-0.0003 0.3-0.03 0.3-3 0.003-0.03 0.003-0.03 0.0001-0.001 0.3-3 0,03-0.3 0,Ol-0.1 0.0003-0.003
n.d.c n.d. n.d. 0.0003-0.003 0.3-3 0.01-0.1 0.00001-0.0001 n.d. 0.3-3 n.d. 0.003-0.03 0.0003-0.003
zro2
ZrOn
where p = the density of the tetragonal phase. The small correction to account for the presence of the monoclinic phase in samples heated a t higher temperatures was neglected. The discrepancy between the curves is probably due to the development of an internal surface in the powder (unavailable for nitrogen adsorption) owing to partial sintering when the samples were heated. Allred and co-workers observed
Elements sought but not detected: Ag, As, Ba, Be, Bi, Ca, Cd, Ce, Co, Cr, Cs, Ge, Hg, Li, Mo, Nb, Ni, P, Pb, Rb, Sb, Weight per cent. Not deSn, Sr, Ta, Th, Ti, U, W, Zn. tected.
of zirconium a1k0xides.l~ They observed that the metastable phase persisted indefinitely a t room temperature and conversion to the monoclinic phase only occurred upon heating the oxide above 400". Figure 1 shows the phases detected in this work, a t room temperature, in samples of ZrOz heated to various temperatures. Initially, a t low temperatures, only the tetragonal phase is present. At intermediate temperatures, partial transformation occurs, and a two-phase region is observed. Finally, above approximately 800", complete transformation occurs, and only monoclinic %rOzis observed. This sequence of phases can be correlated with changes in the tetragonal mean crystallite size, the specific surface, and the excess energy of the active samples as shown in Figures 2, 3, and 4, respectively. I n Figure 2, the tetragonal mean crystallite size, determined on quenched samples, is given as a function of the firing temperature. The initial values of D were 54 and 155 A. for the precipitated and calcined oxides, respectively. When the samples were heated, the tetragonal crystallites grew to a maximum size of about 300 8. before complete conversion took place. Figure 3 shows the variation in specific surface as a function of crystallite size. The curve labeled SE is experimental. Initial values were 194 and 15.6 ni. "g. for the precipitated and calcined oxides, respectively. The ST curve is theoretical and was obtained from the following equation, valid both for cubes of edge D or spheres of diameter D.
I zw
O
4w
600
oao
800
TLMPLRATURE, * C
Figure 1. The phases present a t room temperature in active powders of ZrOI heated to various temperatures. 340
I
I
I
I
I
400
SI0
I
tt
i
-" 0
I
200
em
IEMPERYTURL. *C
Figure 2. Experimental values of the mean crystallite size of metastable tetragonal Zr02 as a function of temperatwe. (14) K. S. Maadiyasni, C. T. Lynch, and J. S. Smith, "Preparation f o Ultra-High Purity Submicron Refractory Oxides," 66th Annual Meeting, American Ceramic Society, Chicago, Ill., April 1964.
The Journal of Physical Chemistry
OCCURRENCE OF METASTABLE TETRAGONAL ZIRCOKIAAS CRYSTALLITE SIZEEFFECT
AB
CRYSTLLLITE SIZE. 4
Figwe 3. Comparison of theoretical and experimental values of the specific surface, S , as a function of crystallite size, D.
i " I 8
'
3:!
\
O
21
, 0
$00
I
I
I
IW
I50
NUMBER OF IONS I ZOO
I
,
300
400
CRYSTALLITE
PER
,
I
200
250
CUBE EDGE. n I
m
I
6~
300
I
1
700
eo0
51ZE 1 D ) . 4
Figiire 4. Comparison of theoretical and experimental values of the excess energy of active powders of ZrO:! as a function of crystallite size.
a sinlilar discreparlcy in a study of thorium dioxide powders. l5 In ICigure 4 , the excess energy (relative to a large single crystal) of active samples of the -precipitated oxide is plotted as a function of the crystallite size, D. The experimental values of AE (denoted by open circles) were obtained by heat of solution measuren,ents.~6 These data show that excess energy ranging as high as 6'7 kcal./mole is present in active Of precipitated ZrOz. The data were fitted to the theeretical expression
12N(n - 1)2d2Ky
n3
(2)
where AE = excess energy (kcal./niole); N = Avogadro's number; d = the diameter of the oxygen ion; K = a factor to corivert ergs to kilocalories; y = the surface energy (ergs/cm. z), Equatiori 2 was derived by using the same approach that Weissenbach employed for ?t/Ig0.17 The present author assumed that ZrOz had the ideal fluorite lattice and that the powder was composed of cubes with n oxygen ions/edge. The value selected for the surface energy was 770 ergs/cni. and was obtained from data given by Livey and Murray.'* In summary, tetragonal ZrOz a t room temperature appears in active powders of ZrOz characterized by small mean crystallite size, large specific surface, and appreciable excess energy. When the powders are heated, the crystallites grow so that the specific surface and excess energy diminish. Simultaneously, a phase transformation to the monoclinic structure occurs. These phenomena lead one to make the following postulate. The two phases are in equilibrium a t 300" when the crystallite size is about 300 A. The fact that a two-phase region is observed may be attributed to a crystallite size distribution which can be considerible, as shown by Quinn and Cherin.l9 If the two structures are in equilibrium a t the critical size of 300 A., then their free energies must be equal. This is expressed in the equation
G,
50
=
1241
+ ymAm
=
Gt
+ YtAt
(3)
where G = the molar free energy of ZrOz in the form of a large single crystal (cal./mole); y = the surface energy (cal./cm.2); A = the molar surface (cm.2/niole). The subscripts, ni and t, refer to the monoclinic and tetragonal phases, respectively. Equation 3 states that there is a difference in the surface free energies of monoclinic and tetragonal ZrO,; the surface energy of the former structure is greater than the latter. This difference in surface energy, when associated with a large value of the molar surface, causes the molar free energies of the two structures to be equal when D is about 300 A: a,nd, hence, the formation of the tetragonal phase a t room tempera-
I
(15) V. C . Allred, S. R. Buxton, and J. P. McBride. J . P h g s . Chem., 61, 117 (1957).
(16) Heat of solution measurements were made by R. Brtrnay and K . Kelley, U. S. Bureau of Mines Thermodynamics Laboratory. Berkeley, Calif. (17) B, Weissenbach, Radez Rund&au, 6,257 (1951). (18) D. T. Livey and P. Murray, J . A m . Ceram. SOC., 39,363 (1956). (19) H. F. Quinn and P. Cherin, Advan. X - R a y Anal., 5 , 94 (1962).
Volume 6.9, Number 4
April 1966
RONALD C. GARVIE
1242
ture. The situation is displayed graphically in Figure
I
5.
The results obtained by Clearfield also point to the possibility of some critical crystallite size which governs the formation of the metastable phase.3 He observed that the first crystalline product, obtained by heating amorphous, hydrous Zr02 in distilled water under reflux, was a mixture of tetragonal and monoclinic crystallites, whose size was about 20 to 25 A. After many hours of refluxing, the tetragonal phase disappeared, and only monoclinic crystallites, about 120 A. in diameter, were observed. These data indicate a critical size, less than 120 k.,which is considerably smaller than that observed in the present work. The reason for this discrepancy is unknown, although it may be related to the fact that in Clearfield's experiments the crystallites grew in an aqueous medium. It is of interest to calculate 7, from eq. 3. The molar surfaces may be calculated from eq. 1. The surface energy of the tetragonal phase, Tt, is known from the literature.18 There remains only to calculate the molar free energy difference a t 300"K., (Gt - Gm). An estimate of this quantity may be obtained from a knowledge of the heat of transition (1420 cal./mole) and the transition temperature (1478°K.). If the heat and entropy of transition are assumed to be temperature independent then (Gt - G,) amounts to 1130 cal./mole at 300°K. When all the numerical quantities are substituted in eq. 3, the value of Y~ is 1810 ergs/cm.2. Listed below are some values of the free surface energy in ergs/cm.2 (at 0°K.) for some refractory oxides. The relatively small change in these values produced by increasing the temperature to 300°K. would not affect the semiquantitative argument: hIg0,2" 1040; 1150; U02,21 1030. But the value of y,, obtained above, is far higher than that usually found in refractory oxides and therefore is not probable. The way out of this difficulty may lie in the nature of the high temperature monoclinic tetragonal transformation itself which has been studied in detail a t this research center.22 The inversion which occurred in single crystals or well-sintered powders is of the type described by Ubbelohde as c o n t i n u ~ u s . ~ The ~ outstanding feature of a continuous transformation is the coexistence of both structures in a hybrid single crystal during the inversion. During the heating cycle, domains of the tetragonal structure grow in a matrix of the monoclinic form. Strain a t the domain boundaries brings the reaction to a halt after a short time, and a consiant ratio of phases is observed at some temperature, T , in the transition region. To change the phase ratio, the temperature must be changed. The Journal of Physical Chemistry
I
I
I
1
I 1
'
I
-s
POWeer Of
"Q
e
Clys'OlI
cryilo
I
L' MOLAR
SURFACE
'e
meor 5 it
33OA
~-
~-
Crr2/wol
Figure 5 . Schematic free-energy diagram of monoclinic and tetragonal ZrOs.
This behavior is termed athernial kinetics. Consider a powdered monoclinic sample whose mean crystallite size is less than a domain. Coexistence of the two structures is impossible, and coexistence phenomena, such as athernial kinetics, should not be observed. Indeed, classical kinetics in which the amount of reactant (monoclinic phase) steadily diminished with time were noted for the inversion occurring in very fine-grained monoclinic powders. One can predict, on the basis of the above discussion, that the heat of transition of a well-sintered powder is not the same as the heat of transition of very finegrained powders whose mean crystallite size is less than a domain. The heat of transition of well-sintered powders would contain a contribution owing to the chemical difference of the two structures, as well as a contribution from the strain energy associated with the inversion. On the other hand, the heat of transition of a fine-grained powder would contain only the contribution arising from the chemical difference of the two forms. These ideas are expressed in the following equations. For well-sintered powders
For very fine-grained powders AHtrans
= AHchem
(5)
The difference in AHtranashown by eq. 4 and 5 (20) G . J a r a and C. Garland, J . A m . Chem. Soc., 74, GO33 (1952). (21) G. C. Benson, P. I. Freeman. and E. Dempsey, J . A m . Ceram. SOC.,46,43 (1963). (22) C. Grain and R. Garvie, U. S. Bureau of Mines Report of Investigations, in press. (23) A. R. Ubbelohde, Quart. Rev. (London), 11, 246 (1957).
OCCURRENCE OF METASTABLE TETRAGONAL ZIRCONIAAS CRYSTALLITE SIZEEFFECT
should be detectable in a differential thermal analysis (d.t.a.) of the transition using coarse-grained and finegrained powders. Accordingly, two samples of monoclinic ZrOz were prepared; one was heated for 24 hr. at 1500" (coarse-grained), and one a t 900" (finegrained). The mean crystallite size of the former material was 820 A., and the latter, 232 A. D.t.a. experiments were carried out on both powders a t a heating rate of lO"/niin. The results are shown in Figure 6 (a and b). The area under the peak of the coarsegrained sample is much larger than that for the finegrained sample, in good agreement with the prediction. The area under the d.t.a. peaks is proportional to the heat of transition. Therefore, AHtransfor the finegrained powder is obtained from the ratio of the small peak to the large peak when the latter is set equal to 1420 cal./mole. The results are given in Table 11.
1243
iz( 0 )
(b)
(C)
Figure 6. Comparison of the d.t.a. peaks of the monoclinic --c tetragonal transformation in coarse-grained and fine-grained ZrOp.
Table I1
Sample
Area under peak, in.l
Sample weight, g.
Coarse-grained Fine-grained
0.130 0,057
2.2823 2.2870
Molar heat Peak of transition, temp., O C . cal.
1179 1155
1420 620
When the fine-grained sample was recycled through the inversion temperature, the same peak area was obtained'(Figure 6c) as that observed for the coarsegrained sample. This observation agrees with the kinetic studies which established that classical kinetics are only observed during the first cycle. The reason that eq. 3 yielded an unreasonable value for 7, is now clear. The free energy of transition used in the calculation included a strain contribution. However, the metastable transformation is concerned with very fine-grained samples, and so the free energy of transition must be based on eq 5 . (G, - G,) for fine-grained samples is then reduced to 491 cal./ mole at, 300°K., and, when this value is substituted into eq. 3 , Y~ amounts to 1130 ergs/cm.2. This value of Y~ is about the same as that for thorium dioxide and uranium dioxide and is therefore acceptable. A good check on the hypothesis presented in this work would be to niemure the surface tension of ZrOz in the region 1000 to 1200" and observe if the predicted change in value of this parameter (1130 to 770 ergs/ cm.z) really occurs.
It is interesting to note that metastable tetragonal HfOz cannot be p r e ~ a r e d . ~ If ' the hydrous precipitate or the nitrate is heated, the sequence of phases observed is amorphous -c monoclinic. The fact implies that the free-energy curves of the two structures intersect at such a small value of D that there is no long-range order in the solid, and only an amorphous phase can be observed.
Conclusions Current explanations for the occurrence of metastable tetragonal ZrOz are based on contamination of the oxide by impurities, such as chemically bound OH groups. This interpretation is not convincing in the light of recent research on this phenomenon. A new explanation is offered in this work in which the stabilization of the high temperature phase is correlated with the intrinsic properties of active powders, namely, small mean crystallite size, large specific surface, and appreciable excess energy.
Acknowledgments. It is a pleasure to thank L. R. Furlong, supervisory research physicist, W. J. Campbell, supervisory research chemist, and E. E. Rlaust, Jr., chemical engineer, for their very helpful discussions and constructive criticisms. (24) C . Grain, Bureau of Mines Metallurgy Research Center, College
Park,Md., private communication.
Volume 60,Number 4
April 1966
