6837
J. Phys. Chem. 1989,93,6837-6843
l*O
tc
+
trations of these species, and C = C A CBis the total concentration of triplet state formed, which we shall assume constant in all cases. Defining X as the molar fraction of unprotonated triplet, CB = CX, and C A = C(l - X ) , we have
0
1
-D= DB
t ~ ( 1- 4 f X tB
t1 A and
1
3
5
7 P"
9
1
1
Figure 1. X = (D- DA)/(DB - DA)of phenazine versus pH.
spectroscopic and photolytic lamps.
Results and Discussion The optical density of phenazine corresponding to triplet-triplet transitions does not change for pH's above 4,according to our measurements. This seems to indicate that the unprotonated phenazine is already the predominant species present at pH = 4;then the phenazinium monovalent cation (HPhe') must be a rather strong acid. Since in most cases pKal < pK,", we may assume that the phenazinium divalent cation (H2Phe2+)is a very strong acid in the first triplet state and would exist only at extremely low pH's. So in the range that we have covered, from 1 to 12, the monoprotonated and unprotonated phenazine are only present according to the following equilibrium: HPhe+ e Phe
-
+ H+
Karl
Assuming that D is the optical density for a selected triplettriplet absorption (T, T,) at a given wavelength, measured when both HPhe' and Phe are present, and DB the optical density measured at a very high pH when only the unprotonated species is present, then3 D - eA(C - CB) + EBCB _ DB
4
with tA and tB the extinction coefficients of the acidic and basic forms, respectively; CA and CB are the corresponding concen-
where DA is the optical density at the PITSwhen only HPhe+ is present. Since the pK, for an acid dissociation corresponds to that value of the pH at which the concentration C Aof the protonated form equals that of the unprotonated CB,plotting the values of ( D DA)/(DB- DA), obtained experimentally from the microdensitometer data, versus the pH, we obtain the pK,"(T,) of HPhe+ in the first triplet state as the pH value where X = 0.5. Figure 1 shows the results obtained that yield a pK,(T,) = 1.9 f 0.2. The results obtained match very well the idea that only two species, HPhe+ and Phe, are predominant in our pH range. The pK,"(T,) obtained seems to indicate that the phenazine in the lowest triplet state does not follow the trend of most 1,4 polynuclear diazines and is not a much stronger base than in the ground state. Table I1 summarizes the results obtained for phenazine and compares our result with Grabowska's. The transient spontaneous Raman technique, used by Beck and Brus for studying the reaction dynamics of triplet quinoxaline in aqueous s o l ~ t i o n would ,~ be useful to clarify the behavior of phenazine. Acknowledgment. The support of the CAYCIT is appreciated. Registry No. Phenazonium, 22559-72-4. (9) Beck, S. M.; Brus, L. E. J . Chem. Phys. 1981, 75, 4934. (10) Bulska, H.; Chodkowska, A.; Grabowska, A.; Pakula, B.;Slanina, Z. J . Lumin. 1975, 10, 39.
Nonequlllbrlum (Ca,Mg)O Solid Solutions Produced by Chemical Decompositiont Giorgio Spinolo* and Umberto Anselmi-Tamburini CSTEICNR and Department of Physical Chemistry, University of Pavia, Male Taramelli, 16, I 27100 Pavia, Italy (Received: October 6, 1988; In Final Form: February 10, 1989)
In situ X-ray diffraction experiments on thermal decomposition of dolomite (CaMg(C03)2)at low temperatures and low pressures indicate that the first reaction product is a homogeneous, equicomposition,rock-salt-structured oxide solution, which unmixes into coupled Mg-rich [(Ca,Mg,,)O, c 0.11 and Ca-rich [(Mg,Ca14)0, 6 0.21 phases. This process is analyzed along the lines of the classical (linear) theory of spinodal decompositions. In a general way, the thermal decomposition of suitable precursors, such as double carbonates, gives a new method for preparing nonequilibrium oxide solutions. This paper discusses the thermodynamic, kinetic, and structural requirements for the feasibility of the method and outlines its applications to the synthesis of complex oxides.
-
-
Introduction This paper deals with two related subjects: mechanism of the thermal decomposition of dolomite ( c ~ M ~ ( c o ~ )and ~ ) spindal
decomposition in the (Ca,Mg)O binary system. Concerning the first subject, calcite-structured carbonates have been deeply investigated (see ref 1-9 and the references therein
Based on a thesis submitted by U. Anselmi-Tamburini in partial fulfillment of the requirements for a Ph.D at University of Pavia.
(1) Beruto, D.;Searcy, A. W. J . Chem. Soc., Faraday Trans. 1 1974, 70, 2145.
0022-3654/89/2093-6837$01.50/0 0 1989 American Chemical Society
6838 The Journal of Physical Chemistry, Vol. 93, No. 18, 1989
Spinolo and Anselmi-Tamburini
TQ
11
I
region
\
~
CaO Figure 2. Outline of the chemical decomposition (CD) method for preparing (Ca,Mg)O solutions from dolomite decomposition.
X
Figure 1. Outline of the temperature quenching (TQ) and composition variation (CV) methods for preparing spinodal solutions.
quoted) because they are convenient chemical models for the experimental study of endothermic decompositions and because their thermal decomposition easily produces specially reactive oxides1° when highly irreversible conditions are used. With slight distortions, the calcite crystal structure type also describes a number of ordered solid solutions, among which dolomite is the best known. The full decomposition" of dolomite is a close analogue of the thermal decomposition of simple carbonates and actually shows the same microstructural features. Its experimental investigation can therefore provide information on the mechanism of thermal decomposition for the whole set of calcite-structured carbonates. Concerning the second subject, it is wel1-knownl2that theoretical advances in the field of spinodal decompositions have been tested mostly with metallic or polymeric materials. Spinodal decomposition in crystalline ionic systems has not been so deeply investigated," because of the experimental difficulty of preparing solutions with composition inside the spinodal field with the usual method of quenching from the molten state. The aim of this paper is to show that also a chemical method for preparing spinodal solutions can be devised. It involves the thermal decomposition of a suitable precursor material and is particularly promising in the case of oxide systems, when the precursor can be chosen among Floquet, N.; Niepce, J. C. J. Mater. Sci. 1978, 13, 766. Powell, E. K.; Searcy, A. W. J. Am. Ceram. SOC.1978, 61, 216. Towe, K. N. Nature (London) 1978, 274, 239. Fubini, B.; Stone, F. S. J. Chem. SOC.,Faraday Tram. 1 1983,79,215. ( 6 ) Beruto, D.; Barco, L.; Searcy, A. W. J. Am. Ceram. Soc. 1984,67,512. (7) Spinolo, G.; Anselmi-Tamburini, U. Z . Naturforsch. 1984, 3 9 4 975, 981; High Temp.-High Pressures 1988, 20, 109. (8) Spinolo, G.; Anselmi-Tamburini, U. Solid State Ionics 1989, 32/33, (2) (3) (4) (5)
413. (9) For the more general problem of the kinetics and mechanism of gas-
solid reactions and, in particular, of endothermic decomposition reactions, reference is made to: Niepce, J. C.; Watelle, G. J. Phys. Colloq. 1977, C38, 365. Searcy, A. W.; Beruto, D. J. Phys. Chem. 1976.80.425; 1978.82, 163. Bertrand, G. Ibid. 1978,82, 2536. Searcy, A. W.; Beruto, D. Ibid. 1978,82, 2537. Bertrand, G.;Lallemant, M.; Watelle, G. J. Colloid Interface Sci. 1979,
a large class of double carbonates or similar compounds. In the first section, the various conditions required for applying this new method are discussed in a general way and for the particular system (Ca,Mg)O corresponding to dolomite thermal decomposition. The following sections present X-ray diffraction data in support of the feasibility of this approach, analyze these data along the lines of the linear theory of spinodal decompositions,1e16and discuss the role of a spinodal decomposition step in the overall mechanism of dolomite thermal decomposition. The importance of understanding the thermodynamic, kinetic, and microstructural features of the thermal decomposition of divalent carbonates, however, also relies on the fact that they are useful precursors of oxide reagents for many solid-state reactions. In particular, Longo et al.l7-I9 pointed out that the thermal decomposition of solid solution carbonates having the calcite structure is a convenient and promising method to synthesize mixed-metal oxides at significant lower temperatures and shorter times than are required by traditional ceramic techniques. The conclusions section compares the solid-state precursors technique of these authors with the results of the present work and discusses some practical aspects of this new method of producing nonequilibrium oxide solutions with particular reference to its potential application to the synthesis of complex oxide materials. Thermodynamic and Kinetic Background Binary systems with a solid-solid miscibility gap show several different phase diagram topologies. Without loss of generality, we can consider only the simplest topology, as outlined in the upper part of Figure 1. The lower part of the same figure recalls the meaning of binodal (equilibrium) and spinodal points and lines with reference to the underlying isothermal-isobaric thermodynamic potential (Gibbs free energy, g). An unmixing process driven by the time evolution of composition waves (spinodal decomposition) is possible for monophasic solutions corresponding to the composition-temperature region within the spinodal lines. These solutions are usually produced by quenching from high temperatures or, less frequently, by a continuous isothermal variation of composition. Both experimental procedures are outlined in Figure 1 by hatched arrows. Hereafter, they will be shortly referred to as the T Q (temperature quenching) and the CV (composition variation) methods. Now, let us consider the miscibility gap in the pseudobinary system of two simple oxides. Let us assume, for the sake of simplicity, that the cations (hereafter denoted by A and B) are divalent and that the end members ( A 0 and BO) belong to the same crystal structure type. Limited or negligible solubility arises
70, 223.
(10) Beruto, D.; Searcy, A. W. Nature (London) 1976, 263, 221. ( 1 1) The thermal decomposition of dolomite is not a unique reaction, since there is a possibility of either full decomposition leading to lime (CaO) and periclase (MgO) or halfdecomposition leading to calcite (CaC03) and periclase: here we are only concerned with full decomposition. A thermodynamic analysis of this problem has already been reported: Spinolo, G . ; Beruto, D. J. Chem. SOC.,Faraday Trans. I 1982, 78, 2631. (12) Hono, K.; Hirano, K.-I. Phase Transitions 1987, 10, 223. (13) See,e.&: Jantzen, C. M. F.; Herman, H. In Phase Diagrams. Materials Science and Technology; Alper, A. M.,Ed.; Academic Press: New York, 1978.
Cahn, J. W.; Hilliard, J. E. J. Chem. Phys. 1958, 28, 258. Cahn, J. W. J . Chem. Phys. 1965, 42, 93. Cook, H. E.; Hilliard, J. E. J. Appl. Phys. 1969, 40, 2191. Longo, J. M.; Horowitz, H. S . ; Clavenna, L. R. In Solid State Chemistry: a Contemporary Overuiew: American Chemical Society: Washington, DC, 1980; Adv. Chem. Ser. No. 186. (18) Longo, J. M.; Horowitz, H. S . In Preparation and Characterization of Materials, Proc. Indo-US Workshop; Honig, J . M., Rao, C. N. R., Eds.; Academic Press: New York, 1981. (19) Poeppelmeier, K. P.; Horowitz, H. S.; Longo, J. M. J. Less-Common Met. 1986, 116, 219. (14) (15) (16) (17)
The Journal of Physical Chemistry, Vol. 93, No. 18, 1989 6839
Nonequilibrium (Ca,Mg)O Solid Solutions in (A,B)O systems because of various structural factors (mainly a large discrepancy of ionic radii) which produce strong positive deviations of the integral molar free energy of the oxide structure from ideal behavior. The A/B solid solubility, however, can be greatly enhanced by replacing oxide with a polyatomic XO, anion, such as C03or SO4, since the larger anionic size better accounts for the cation misfit and possibly reduces short-range specific interactions. The empirical fact that an (A,B)XO, pseudobinary system (hereafter referred to as the compound system) generally shows wider solubility than the corresponding oxide systemZosuggests a third approach to the synthesis of (A,B)O solutions with composition inside the spinodal field. In plain words, this approach can be described as an isothermal jump into the spinodal region of the oxide system by starting from the corresponding ( x , T ) point of the compound system and replacing the complex XO, anion with the oxide anion without changing the A/B composition (x) or breaking the atomic-scale mixing of the cations. We may call it the chemical decomposition (CD) method, since it is essentially a chemical decomposition made under particular nonequilibrium conditions. The thermodynamics of the C D method is best discussed with reference (see Figure 2) to the ternary (or pseudoternary) system of three independent components: AO, BO, and XOW1(COz or SO3 in the previous examples). The oxide system is then one side of the composition triangle, whereas the compound system is the parallel segment connecting the midpoints of the other sides. Along the AO/XO,, or BO/XOWI sides, the phases corresponding to oxide and compound can be taken with sufficient accuracy as pure line compounds, Le., as phases with negligible homogeneity ranges and with stoichiometric compositions. Under isothermal conditions, the thermodynamic stability of the compound phase with respect to the oxide phase is controlled by a single external variable, the activity or partial pressure of the third component (XO,,). The compound system is not required to show complete solubility over the whole composition range. The CD method can be applied even when the end members of the compound system are not isostructural or when intermediate compounds exist: the important point is that, for a given ( x , T ) point lying within the spinodal field of the oxide system, the compound system should be able to provide a monophasic environment for the complete intermixing of the cations. For example, if we are interested in the 1:1 composition (x = 0.5) of a given (A,B) couple, we must look for a compound system showing a single phase around the midpoint. In the particular case of the CaO/MgO/C02 system, both lime (CaO) and periclase (MgO) belong to the rock salt (halite) structure, but their mutual solubility is very low (much less than 1 mol % at 1000 K). The C a C 0 3 (calcite)/MgC03 (magnesite) pseudobinary system shows a different topology. The solubility limits of the (isostructural) end phases do not enclose a single diphasic (calcite + magnesite) region because of the existence of a 1:l compound (dolomite), which shows a narrow homogeneity range and is separated from the monophasic regions of the calcite-structured phases by two diphasic fields (calcite dolomite and dolomite magnesite). Dolomite belongs to a slightly different crystal structure and is stabilized with respect to (calcite + magnesite) by its nature of ordered compound: this stability of the dolomite phase gives thermodynamic feasibility to the CD method of preparing (Ca,Mg)O halite-structured solutions with 1:l Ca:Mg ratio at temperatures much lower than those needed by the T Q method. Let us consider now the kinetic requirements of the CD method. Actually, the method involves a solid-state phase transformation of the type solid 1 solid 2 + gas
+
+
-
so that the previous thermodynamic discussion rules out reaction mechanisms involving either nucleation of a new crystal structure within its intrinsic stability limits or transport of structural ele(20) Davies, P. K.; Navrotsky, A. J . Solid State Chem. 1983, 46, 1.
ments through the old phase and across a phase boundary under the influence of chemical potential gradients. In particular, we require that the intimate mixture of two chemically different cations be preserved during the structural transformation: long-range diffusion is allowed only for the gaseous reaction product. Therefore, we must rule out the usual nucleation-andgrowth mechanism of heterogeneous reactions. It is now well-known that a number of endothermic decomposition reactions show distinctive features in good agreement with the above underlined requirements and that the thermal decompositions of calcite, magnesite, and dolomite are clear examples of this particular class of gas-solid reactions. According to several studiesl-*JO published in the past years on this subject, the calcite-structured carbonates decompose following a shear transformation mechanism: divalent cations and oxide anions do not undergo long-range diffusion but only local rearrangements to the sites of the new crystal structure and a concerted shrinkage, which is active on a scale of a few cell lengths and produces a particular microstructure made of small crystallites and pores with only minor changes of the external shape of the parent grains. In conclusion, the CaO/MgO/C02 system seemingly fulfills all the requirements of the CD method. We now give direct and indirect experimental evidence that (Ca,Mg)O solid solutions with rock salt structure and 1:l composition are actually produced during the thermal decomposition of dolomite. Experimental Section Different dolomite samples were investigated by monitoring the thermal decomposition with in situ powder X-ray diffraction (XRD). Several isothermal-isobaric runs were made using a standard diffractometer (Philips PW 1730 with copper radiation (wavelength 0.1 542 nm), scintillation counter, and graphite monochromator on the diffracted beam) and an environmental chambe? connected to a thermoregulator and to a vacuum diffusion pump. The XRD patterns were acquired in step scan mode with a personal computer and homemade software. More complete details on samples and experimental procedure have been described previ~usly.~ In a few cases, broadened overlapping peaks were analyzed by fitting the step scan data with linear background plus pseudo-Voigt functions Z(x) = Zo[rG(B,x)+ (1 - r)L(B,x)]
where G( ) and L( ) are normalized Gauss and Lorentz functions:
G(B,x) = (Go/a)-l/z exp(-G&; L(B,x) = (LfJa)-'/2[1
Go = 4 In 2 / B 2
+ Lox2l-1;
Lo = 4/BZ
B is the line width, r is the shape parameter, x = 2 9 - 200, 29 is the diffraction angle, and 2tJOis the exact Bragg location of the peak. Pseudo-Voigt functions were chosen because of their good performance in XRD profile fitting (see, e.g., ref 22). Each diffraction peak was modeled with a couple of functions, one for the aIand one for the az component line. Only four adjustable parameters (instead of eight) were allowed for each couple, since we assumed the same line width ( B ) and shape ( r ) parameters for both components and we fixed a priori the relative displacement and the intensity ratio Zo(al)/Zo(az) = 2. [2d0(a1)- 290(az)] Location [2Oo(a1)]and intensity [Zo(al)]parameters were given a structural meaning by assuming the stoichiometric model discussed below. The parameters were optimized with least squares using the MINUIT package.23 The investigated temperatures cover the range between 490 and 600 OC, the working pressures being between and lo4 Torr (i.e.. -lo-' and 1WZP a l These conditions corresmnd to reaction ;ate5 around mol cm-z s-l and have been selkcted as a compromise between conflicting requirements. Lower working tem(21) Spinolo, G.; Massarotti, V.;Campari, G. J . Phys. E 1979, 12, 1059. (22) Young, R. A,; Wiles, D. B. J . Appl. Crystnllogr. 1982, 15, 430. (23) James, F.; Ross, M. CERN Computer Centre Program Library, Program DS06,1974.
6840 The Journal of Physical Chemistry, Vol. 93, No. 18, 19'89
Spinolo and Anselmi-Tamburini
TABLE I: Lattice Constants of Anomalous Lime and Periclase Phases
h
5 m
decomposition conditions TIK PI Pa 873 10-2 853 10-1 850 lo-' 849 10-2 792 10-1 763 10-2
3
24
28
32
40
36
44
alnm
lime 0.4707 0.4684 0.476 1 0.4751 0.4758 0.4655
periclase 0.4240 0.4231 0.4230
48
undecomposed d o l o m i t e
r
n
,
I
24
28
32
1
I
36
40
44
48
Degree (279)
Figure 3. Typical XRD patterns of the solid materials produced by dolomite decomposition at about 850 K and -10-I Pa (upper pattern) or -IO-* Pa (lower pattern). The vertical bars show the expected positions of the XRD lines of pure lime and pure periclase.
peratures unavoidably require longer experimental times and produce more scattered results but decrease, on the other hand, the equilibrium pressure of the gaseous product and the kinetics of thermal decomposition. At the same time, the rate of removal of the gaseous product from reaction sites to sample surface is enhanced by low working pressures. These coupled low temperature-low pressure conditions were found very effective in hindering COz buildup inside the fine microstructure of the solid product and gas-phase-catalyzed recrystallization of the original crystallites and actually provide reliable quantitative data on the first step of the structural transformation. For a deeper discussion of the complex relationship between kinetics, thermodynamics, and microstructure, the reader is referred to recent investigations6** on the similar case of calcite decomposition.
Results Figure 3 reports the most interesting part of two typical XRD patterns. Generally speaking, these patterns show diffraction lines that can be indexed with reference to fcc oxides. Part of these lines can be assigned to a CaO-based phase (hereafter denoted as lime) and show large broadening and asymmetry, as well as displacement toward high diffraction angles (Le., low lattice spacings). These lines are usually well reproducible. During each decomposition run their intensity grows linearly with time, whereas location, shape, and width remain constant. A second group of lines can be assigned to an MgO-based phase (hereafter denoted as periclase). The periclase lines show a more complex and less reproducible behavior, analogous to that of lime (with opposite displacements) only in some runs. Table I reports the lattice constants of these anomalous lime and periclase phases, as inferred from the peak locations on the patterns: in this respect it is important to note that these lattice constants should be more correctly taken as limiting values (high limit for lime, low limit for periclase) because of more or less significant tails toward the corresponding lines of the other phase. However, other runs show sharp periclase lines very close to the expected positions for pure MgO, and, in most patterns, both kinds of lines are apparent. Then, the former lines show a smooth
c
0.
I I
I
1
I
30.
35.
40.
45.
diffraction angle Figure 4. Profile fit of an XRD pattern. The upper part compares the experimental data (dots) to the total scattered intensity (continuous line) and shows component peaks for (1 1 1)-Mg&al40, (1 1 l ) - C ~ . ~ M g 0 . ~ 0 ,
(200)-MgdCa,,0, (200)-Cao,5Mgo,,0,and (200)-Ca,Mgl-,0 as calculated with the best-fit parameters (see text). The lower part reports the difference plot: experimental-calculated intensity. time evolution, while the latter ones usually grow suddenly at the very beginning of the decomposition run. Except for this case, the XRD patterns also show that the crystallites of both phases are produced at a constant rate and their compositions and sizes are determined from the early decomposition stages and do not significantly change during reaction time. The large broadening of the peaks indicates a fine microstructure, which corresponds to mean crystallite sizes around 5 nm. Finally, some experimental runs show a large halo approximately midway between the positions of the (200) lines of pure lime and pure periclase, as can be seen in the lower part of Figure 3, while a few other runs do not show at all distinct periclase lines. For example, Figure 4 shows part of an XRD pattern recorded Pa). The large during decomposition at 863 K and lo4 Torr ( broadened (1 11) and (200)diffraction lines of the lime phase can be clearly seen, as well as the (104), (1 13), and (202)lines of some (yet unreacted) dolomite. Periclase lines are seemingly lacking, since the small effects around the (200) theoretical position accounts for only a few percent of the expected amount of this phase. However, a distinct tail of the lime (200) line must be explained. Part of this tail may well be due to a broadened periclase line around 42-43O, but significant diffraction intensity is also apparent around 40-41 O . We obtained a good fit of the whole XRD pattern between 30' and 46' (229) by assuming the simultaneous presence of four phases (dolomite, lime, periclase, and a 1:l oxide with halite structure and random mixing of the cations) according to the following stoichiometry: CaMg(C03), (dolomite) aCao,5Mgo,50(fcc) b(Ca,Mg,-,)O (fcc) + c(MgdCal-6)0(fcc)
-
+
In this model only three of the five parameters (a, b, c, 6, 6 ) are freely adjustable, because of the stoichiometric constraints. The best fit of the experimental pattern (see Figure 4) shows that 35% of the solid product of dolomite decomposition is in the equicomposition oxide ( a = 0.35 f 0.10), while the compositions of the nonequilibrium periclase and lime phases are 6 = 0.17 f 0.04
The Journal of Physical Chemistry, Vol. 93, No. 18, 1989 6841
Nonequilibrium (Ca,Mg)O Solid Solutions
TABLE 11: Elastic Data for CaO and MgO elastic constants, 10" dyn cm-2 material CaO
MgO
cI1 22.20 28.99
c12 8.20 8.57
CM
temperature derivatives, 103 ~
8.10 -0.353 15.49 -0.240
- 1
ce
ref
-0.720
26 27
c12
CII
-0.266 -0.110
-0.120
and c = 0.09 f 0.05. To our knowledge, this result, as well as the midway halo shown for example in the lower part of Figure 3, is presently the most direct experimental evidence that a 1:l oxide solid solution is formed as an intermediate step of the thermal decomposition of dolomite.
Discussion In spite of the seemingly complex experimental behavior described in the previous section, which cannot be satisfactorily explained in all its details, these data agree with our previous study on this subject7 and nicely add to other experimental evidence (e.g., time evolution of the microstructural parameters,6v7 topotactic relationships,z or TEM studies4) in favor of the shear transformation mechanism, since they are an independent (and more evident) proof that long-range cation diffusion does not play a significant role in the thermal decomposition of calcite-structured carbonates. As a first indication, the line shifts, or the anomalous lattice constants, show that the thermal decomposition of dolomite under vacuum yields a couple of halide-structured solid solutions, which are clearly nonequilibrium products, since their mutual solubilities at thermodynamic equilibrium and at the decomposition temperature correspond to XRD line positions indistinguishable from those of the pure oxides. This inference on the structural transformation is mainly based on the experimental results on the lime phase, but the poorly reproducible behavior of the other phase can be explained by assuming that, in spite of the mild reaction conditions, some diffusional recrystallization of the primary crystallites unavoidably takes place on the MgO side of the composition axis. It is convenient to discuss the present results by reference to the linear theory of spinodal decomposition (see, e.g., ref 18-20). According to this treatment, the coherent spinodal of the binary system can be calculated from the knowledge of the chemical and elastic contribution to the free energy of mixing by using the condition g"
+ 2qY = 0
where g"is the second derivative with respect to composition of the integral molar (chemical) free energy, Y i s the elastic coefficient of the solid solution and depends on the elastic moduli as well as on the crystallographic direction, and 7 is the composition coefficient of the lattice constant. Virkar and Plichtaz4later rederived the main equations of the classical theory by considering the electrochemical potential instead of the chemical potential. Their analysis shows that the electrostatic term does not give here a significant contribution, and so it has not been further taken into account. The chemical contribution to the free energy of mixing ( p ) of the (Ca,Mg)O binary has been evaluated7bby interpolating the available high-temperature solidsolid equilibrium dataz5with a subregular solution model
P'
R q x In ( x ) + (1 - x ) In (1
- x))+ x(l
- x)(A
+ B(l - 2x)) (1)
where x is the mole fraction of Caz+ cations and A I R T = -2.37 + 12800fT and BIR T = 0.87. Equation 1 can be used directly to evaluate the equilibrium (binodal) and the chemical spinodal (24) Virkar, A. V.; Plichta, M. R. J . Am. Ceram. SOC.1982, 66, 541. (25) Doman, R. C.; Barr, J. B.; McNally, R. N.; Alper, A. M. J . Am. Ceram. SOC.1963, 46, 313. (26) Bartels, R. A.; Vetter, V. H. J . Phys. Chem. Solids 1972, 33, 1991.
Figure 5. Equilibrium lines (continuous), chemical spinodal lines (dashed), and coherent spinodal lines (dotted) in the (Ca,Mg)O binary. The right part compares the calculated spinodal lines with the X-ray determinations of composition of the solid solutions produced by thermal decomposition. Points with error bars come from the profile fit of Figure 4.
lines of the (Ca,Mg)O binary, as well as the free energy displacement of the 1 : l oxide from the pure oxides. In evaluating the elastic term, it is important" to consider explicitly the temperature dependence of the pertinent parameters. We used the elastic moduli data summarized in Table 11. The temperature derivatives of the lattice constants were obtained from Krikorianz7 and from Liebfried and Ludwig.zs The left part of Figure 5 shows the binodal, chemical spinodal, and coherent spinodal lines calculated from this data set. In the right part of the figure, the last two lines are compared with the experimental (composition/temperature) data obtained from the location of the XRD lines assuming a linear relationship between composition and lattice constants (Table I). In the same figure, the points with error bars come from the profile fitting of the pattern which do not show periclase lines (Figure 4). Figure 5 clearly shows that the experimental data are far from the equilibrium binodal lines, which are here indistinguishable from the vertical x = 0 and x = 1 axes. On the contrary, the experimental data are somewhat midway between chemical and coherent spinodal lines and the agreement with the latter line is seemingly better for points on the CaO side of the composition axis and at lower temperatures. The important point here is that the decomposition does not proceed completely to thermodynamic equilibrium, so that the actual nature of the final products is indicative of the reaction path. Following the experimental results, we may argue that a spinodal decomposition step is active during the thermal decomposition of dolomite under low pressure-low temperature conditions, according to the following mechanism: (A) chemical decomposition, which produces an fcc solution (Ca,,sMg,,sO); (B) spinodal decomposition, which produces (different amounts of) periclase (Ca,Mg,,)O and lime (M&Ca14)0 (here 6 and 6 indicate the coherent spinodal points at the pertinent temperature); (C) formation of the equilibrium phases (practically pure lime and periclase) by uphill diffusion of Caz+ and Mgz+ across the phase boundary between the crystallites formed by the spinodal decomposition. According to the experimental data, the overall process in most cases ends near the coherent spincdal points. Due to the particular choice of the decomposition conditions, the further step required to approach the thermodynamic equilibrium is almost quenched, particularly a t lower temperatures and on the CaO side. Concerning the relationship between the spinodal and the chemical decomposition steps, it is worth recalling here that the chemical step of the process produces a particular microstructure of rod-shaped crystallites surrounded by similar pores. Crystallite (27) Krikorian, 0. H. UCRL Report No 6132; University of California, Berkelev. 1960. (28)-Liebfried, G.; Ludwig, W. Solid Stare Phys. 1961, 12, 275.
6842
The Journal of Physical Chemistry, Vol. 93, No. 18, 1989
0. 500. 1000.
T/K
Figure 6. Wavelength of the compositional fluctuation with maximum amplification factor for (Ca,Mg)O solutions.
and pore dimensions are on the order of magnitude of tens of nanometers. This microstructure masks many features of the following spinodal decomposition (and prevents us from obtaining experimental data on the kinetics of this process) but can be very effective in hindering long-range diffusion and crystallite growth in the final stages of the unmixing process. It is interesting to note here that crystallite size values around 5 nm are close to the , , ,A value (the wavelength of the compositional fluctuations corresponding to the highest amplification factor) obtained from theory of spinodal decomposition (see Figure 6 ) . A consequence of this agreement is that the particular microstructure produced by the chemical step markedly affects the time evolution of the spinodal step by dropping the contributions of the compositional fluctuations with wavelengths larger than. , ,A, We may argue that systems prepared with the CD method agree, better than those prepared by T Q and CV methods, with the limitations of the linear approximation and therefore can provide interesting models for testing the theory, in particular for what concerns the spinodal/nucleation competition (see, e.g., ref 1 and 29). Powell and Searcy3 studied dolomite thermal decomposition using combined torsion-effusionand torsion-Langmuir techniques. They noted a disagreement with the known thermodynamic functions of the relevant phases and explained the discrepancy by assuming that the equilibrium measured by the torsion-effusion data involves a metastable reaction product, having a molar free energy of formation g / R = 8800 - 4.4T (2) from the heterogeneous equimolar mixture of pure lime and pure periclase. They tentatively described this metastable phase as glasslike, since eq 2 agrees well with the free energy of formation of an ideal undercooled solution of the liquid oxides. We may now offer an alternative explanation of those effusion data by taking into account both the fine microstructure of the primary product and its displacement from equilibrium, as measured by the free energy of mixing (eq 1) at x = 0.5: g / R = 3200 - 1.29T (3) Specific surface areas near or above 100 m2 g-' are frequently obtained by thermal decomposition under vacuum of calcitestructured carbonates, and the surface energies of oxide materials are in the range 0.7-3 J m-2 (see, for example, ref 30). As a conclusion, by comparing eq 2 with eq 3, we may argue that the discrepancy of the torsion-effusion data from well-established thermodynamic data for decomposition to C02(g) and 0.5Ca0 + 0.5Mg0 in their standard states (regular halite structure without fine microstructure) can be ascribed in almost equal parts to a chemical contribution and to a surface energy contribution. Besides thermal decomposition experiments, the formation of a 1:1 halite-structured oxide solution has already been proposed31 on the basis of electron-induced decomposition experiments in a transmission electron microscope (TEM) and more recently discussed by Cater and B ~ s e using k ~ ~ the same technique. Ac(29) Goldburg, W. I. In Scattering Techniques Applied to Sopramolecular and Nonequilibrium Systems; Chen, S.-H., Chu, B., Mossal, R., Eds.; Plenum Press: New York, 1981. (30) Mackrodt, W. C.; Tasker, P. W. Chem. Br. 1985, 366. (31) Dai, T. T. LBL Report No 13602; LBL-University of California, Berkeley, 1981.
Spinolo and Anselmi-Tamburini
0 CaO
=
MgO
Figure 7. Microstructural scheme for solid-state synthesis using the conventional ceramic technique (top), the solid-state precursors technique with distinct oxide phases (middle), and the same technique with a single intermediate oxide (bottom). White, black, and gray polygons respectively indicate lime, periclase, and homogeneous (Ca,Mg)O solid solutions.
cording to the latter authors, the primary product of dolomite decomposition under the TEM beam is a 1:1 solid solution with the regular halite structure. After prolonged electron bombardment, this solution produces almost pure lime and periclase phases with particles sizes ranging between 1 and 10 nm. These authors also noted that, in some cases, an amorphous phase is formed just before the last step. TEM and XRD results are therefore in good agreement for what concerns both the primary formation of the equicomposition solution with regular crystallographic structure and the microstructure of this intermediate phase. The discrepancy about the nature of the final decomposition products, in our opinion, is directly related to the different experimental conditions. The relaxation time ( T ) of the spinodal process can be evaluated as the reciprocal of the largest amplification factor of the compositional fluctuations. An order-of-magnitude calculation shows that T = @ l o 2 s) at 800 K and T = 0(107 s) at 500 K. Note also that, according to Cater and B ~ s e k the , ~ ~energy of the electron beam is almost completely absorbed by the covalent bonds of the carbonate anions, without overheating of the sample. It seems therefore justified to infer that in the TEM experiments the spinodal decomposition process is completely frozen out, whereas in the XRD runs of the present work it occurs in a time comparable to that needed to acquire a single pattern. In this respect, the statement that the electron-induced decomposition is a low-temperature analogue of the thermal d e c o m p ~ s i t i o n ~ ~ should be somewhat amended, because the approach to the thermodynamic equilibrium of the intermediate unstable solution follows different paths in the different experiments. Conclusions The direct experimental data and their analysis according to the classic theory of spinodal decomposition strongly support the feasibility of the CD method, previously suggested on the basis of simple thermodynamic analogy. We may point out here that the CD method is significantly simpler than the T Q and CV methods, since it does not require very high temperatures or complex apparatuses, such as those for laser melting or ion implantation techniques. Even more important, the process leading to the spinodal solution here occurs under truly isothermal and (32) Cater, E. D.; Busek, P. R. Ultramicroscopy 1985, 18, 241.
Nonequilibrium (Ca,Mg)O Solid Solutions CO, CaCO,
CCaTiO, a
MgCO,
O
MgTiO, e MgO
A co2
TiO,
co2
A
cacP CaCO,
V
MgCO,
TiO,
CaO
CaTiO, CaTi(
MgTiO,
V TiO,
Figure 8. Reaction paths to mixed complex oxides.
isocomposition conditions and can be easily controlled by a completely independent external variable (the partial pressure of the third component, Le., the component forming the compound system). The previous section clearly indicates the experimental difficulties of using this chemical route to spinodal solutions, as well as its advantages for testing theoretical developments: we now discuss its applications to the synthesis of oxide materials. The schemes in the top and middle parts of Figure 7 compare the most remarkable microstructural features of two approaches to binary oxides: the conventional solid-state synthesis, starting from the pure components and using repeated high-temperature firing and regrinding, and the solid-state precursors technique due to Longo et al.17-'g In these schemes, white and black polygons stand for the crystallites of different oxide phases, whereas each cluster of polygons correspond to a single particle of the parent material. The orders of magnitude of the linear dimensions are a few nanometers (oxide crystallites) and several tens to several thousands of nanometers (parent particles). These schemes, here redrawn after,17 clearly illustrate the diffusional limitations of the conventional approach and the severity of reaction conditions necessary to overcome these limitations. Now, according to the present results, we can go one step farther by emphasizing the fact that the thermal decomDosition of the carbonate anion does not require by itself long-range migrations of the cations and
The Journal of Physical Chemistry, Vol. 93, No. 18, 1989 6843 therefore does not destroy the atomic-scale mixing of cations. In cases where the thermodynamic equilibrium of the oxide binary system corresponds to two distinct phases, the microstructure produced by the chemical decomposition step prevents, or at least slows down, the formation of crystallites with widely different compositions. Therefore, if the various requirements outlined in the previous sections are fulfilled, the product of the solid-state precursors technique is better described by the scheme of the bottom part of Figure 7, whereas the middle scheme is more precisely pertinent to cases where unmixing or recrystallization of the primary decomposition product takes place. In our opinion, the most recent advances in the understanding of the thermal decomposition mechanism of calcite-structured carbonates may be very important in planning solid-state synthesis and deserve careful attention. As a first tentative suggestion, we may here consider the synthesis of ternary oxides which are solid solutions of two complex oxides such as divalent titanates, zirconates, or so on. Figure 8 shows the different reaction paths of this synthesis when different techniques are used: the conventional ceramic technique (upper part), the solid-state precursors technique with distinct intermediate oxide phases (middle part), and the same technique with intermediate unstable oxide (lower part). It is apparent the advantage of the third path, which requires an interdiffusion process between two solid phases instead of three. This process is a potentially useful tool in the synthesis of oxide superconductors. As a final remark, we should remember that solid solutions having compositions within the spinodal range are in a particular state which is unstable from a strictly thermodynamic point of view.33 The actual possibility of obtaining nonequilibrium homogeneous oxide solutions, either as labile intermediate materials or as kinetically inert final products, is an entirely new fact with respect to mere reduction of the diffusion path lengths between intrinsically stable phases and widens the range of application of the solid-state precursors technique. Acknowledgment. The authors thank A. W. Searcy (Berkeley), who brought to their attention the relevance of the dolomite system for understanding the mechanism of endothermic decomposition reactions, and M. Sanesi and A. Magistris (Pavia) for their advice on the presentation of the subject of this paper. This work has been supported by the Department of Education of the Italian Government (MPI-40%). Registry No. CaMg(CO&, 16389-88-1; Ca0,5Mgo,50,104244-64-6; Cao,09Mgo,9,0, 121754-59-4; Mg0,,7Ca0.830,121754-60-7. (33) For a discussion of the meaning of spinodal within the framework of classical thermodvnamics. see: Reiss. H. Ber. Bunsen-Ges. Phvs. Chem. 1975. 79, 943.
