CHARLES J. CARMAN AND WILLIAM J. KROENKE
2562 A more successful scheme than the regular solution theory was found to be the use of Lennard-Jones potential outlined in a previous paperas For this purpose it was necessary to make two more assumptions for the liquid mixtures. (a) The melting point of the mixture was assumed to be the compositional average of the melting points of the pure components in order that a reduced melting point can be obtained for the mixture in spite of the fact that a two-component liquid may have a melting range rather than a melting point. This assumption might appear to be questionable, but the use of either liquidus temperature or the average of liquidus and solidus temperatures does not affect the results greatly. (b) The hard core or the impenetrable spherical volume of the liquid was assumed to be the compositional average volume of the component molecules from which the impenetrable distance was computed. With only these new assumptions and following our previous procedure,s it was possible to calculate log K as a function of composition from a separate linear plot of log K vs. r 1 2 , where r is the distance between the solute molecule and
the impenetrable sphere of solvent molecules. The calculations give the values of log K , or AGO, at various compositions within a remarkably close range of about 2%. However, it is not our intention to claim that this procedure is applicable to solutions exhibiting unusual patterns in AG"" and AH"" of solution in the binary liquid systems. There is no molecular theory of solut i o n capable ~ ~ ~of accounting ~ ~ ~ ~for~ thermodynamic ~ properties of all solutions a t present. The success of our procedure is perhaps largely due to nearly regular behavior of N2H4-UDA!tH system. From a purely calculational point of view, it may be desirable to use the general formlj of eq 16 with additional terms 9x2 hxZ3 . . . , particularly if the experimental data are limited. Acknowledgments. The authors wish to express their appreciation for the assistance of C. D. Robison and T. R I . Poston of Aerospace Corporation.
+
+
(14) J. 5. Rowlinson, "Liquid and Liquid Mixtures," Butterworth and Co., Ltd., London, 1959. (15) For a similar equation see N. A . Gokcen, Rev. Met., 57, 261 (1960).
Electron Spin Resonance of or-Chromia-Alumina Solid Solutions by Charles J. Carman and William J. Kroenke The B. F . Goodrich Company, Research Center, Brecksville, Ohio 44241
(Received January 22, 1.968)
Electron spin resonance (esr) was used to characterize the electronic environment of Cr3+ ions in a series of polycrystalline a-chromia-alumina solid solutions. The solid solutions were formed a t 1350' and contained Esr resonances corresponding to electronically isolated Cr3+ ions, Cr3+ from 0.082 to 14.70 wt % CI'&. ions which are electronically coupled via weak exchange interactions, and Cr3+ions which are electronically coupled via strong exchange interactions were found. Isolated Cr3+ions predominate a t low Cr203 concentration. The relative concentration of isolated to coupled Cr3+ ions decreases with increasing Cr203concentration in a regular manner until all of the Cr3+ ions are strongly coupled. An explanation is proposed for the two resonances from coupled Cr3+ ions which occur a t intermediate Crz03concentrations. The results are compared to the esr studies of supported chromia-alumina catalysts which are reported in the literature.
Introduction Many investigators have reported electron spin resonance (esr) studies of chromia-alumina systems. Their results have been summarized by Poole and MacIver in a recent review of the physical-chemical properties of chromia-alumina catalysts.'" Nost of the esr studies have been made on catalysts consisting of mixtures of chromium oxides and y-alumina,lb or on single crystals of ruby, dilute solid solutions of chromia in a-alumina, but no one had reported a detailed investigation of the esr of polycrystalline a-chromiaT h e Journal of Physical Chemistrg
alumina solid solutions a t low to moderate chromia concentrations. O'Reilly and MacIver studied the esr at 77°K of impregnated chromia-alumina catalysts.* They studied both reduced and oxidized catalysts and reported three different "phases" of chromium ions: (1) 6 phase, (1) (a) C. P. Poole, Jr., and D. S. MacIver, Advan. Catalysis, 17, 223 (1967). (b) These mixtures will be designated as either impregnated or coprecipitated chromia-alumina. (2) D. E. O'Reilly and D. S. MaoIver, J. Phys. Chem., 66, 279 (1962).
ESROF a-CHROYIA-ALUMINA SOLIDSOLUTIOXS isolated Cr3+ions; ( 2 ) P phase, clusters of electronically coupled Crs+ ions; and (3) y phase, Cr5+ions. Poole, Kehl, and NacIver report esr measurements of coprecipitated chromia-alumina catalysts. They found the same three chromium ion phases reported by O'Reilly and MacIver, with one exception. At high chromia concentrations, 2 9 . 2 mol % chromia, they observed two 0-phase resonances, pw and PN, associated with electronically coupled Cr3+ions. An esr spectrum of polycrystalline ruby (-1% Cr203) was presented by O'Reilly and MacIver.la Poole, Kehl, and XacIver observed the ruby spectrum in 0.87 and 1.80 mol % a-Cr203-A41203solid solutions made at 1400°.2 They also obtained the esr of a solid solutions containing 5.3, 9.2, and 19.6 mol % Cr203. These spectra were characterized by a major resonance which was assigned to PN phase Cr3+ions. I n this paper we report the results of a study of the esr of polycrystalline a-Cr2O3-&03 solid solutions. The a-solid solutions, which were formed at 1350', contained from 0.1 to 15% chromia. We observed a resonance attributed to isolated Cr3+ ions and two resonances resulting from electronically coupled Cr3+ ions. A qualitative explanation is presented to explain our results. Experimental Part Two methods of preparing the a-Cr203-A1203solid solutions were used. One method consisted of impregnating Alcoa C-31 coarse hydrated alumina with reagent grade Cr(N03)a.9H20 dissolved in absolute ethanol. The resultant slurries were stirred continuously and heated to dryness over a steam bath. The dry, free-flowing impregnated aluminas mere calcined in air for 16 hr at 660". The resultant mixtures of chromium oxides and y-alumina were passed through an 80 mesh screen, and they were fired in air for 16 hr at 1350" in platinum-10% rhodium crucibles. The other preparative method was based on coprecipitating chromium-aluminum oxide gels. The hydrated gels were formed by rapidly injecting an aqueous stream of reagent grade chromium and aluminum nitrates into a vigorously agitated ammoniacal solution. They were recovered on a Buchner funnel and thoroughly washed with distilled water. After collapsing the gels by dehydrating them over a steam bath, they were fired in air for 8 hr at 1350" in platinum-10% rhodium crucibles. X-Ray diffraction analysis of all of the samples fired a t 1350' revealed that they were homogeneous solid solutions with the a-alumina, corundum, structure. No superlattice lines were observed, and although a quantitative evaluation was not made, the lattice parameters of the a-solid solutions appeared to increase regularly as the chromia content increased. X-Ray fluorescence spectrometry was used to determine the actual chromia concentrations to ==I 10 ppm.
2563 The esr spectra were obtained with a Varian E-3 esr spectrometer operating at 9.52 Gcps and 100 kcps modulation. The solid solutions were contained in 4-mm 0.d. quartz tubes. Although all of the solid solutions were analyzed at room temperature, the temperature dependence of selected solid solutions was determined between 77 and 553°K. The esr data discussed in this paper were obtained from the solid solutions prepared by the impregnation technique. Identical spectra were obtained from the solid solutions prepared using the sol-gel method. The particle sizes of the solid solutions used for esr analysis were between 53 and 63 p. Results The esr spectra of 15 a-Cr2O3-Al2O3solid solutions containing from 9.082 to 14.70% Cr203were obtained at room temperature. The chemical composition and esr data of these solid solutions are summarized in Tables I and 11. Table I: Electronic Phases of a-Cr203-Al203 Solid Solutions Prepared at 1350" Wt % CrnOs
0.082 0.47 0.94 1.48 2.71 3.79 4.78 5.80 6.81 7'73 8.42 9.75 11.71 14.70
Mole % Cr203
0.055 0.32 0.63 1.00 1.83 2.58 3.26 3.97 4.67 5.32 5.81 6.76 8.17 10.36
Cr3+ ion phases
8/6
+ Pia
Ruby Ruby Ruby; very weak P Ruby; PI; PN
1.000 1,000
6;
0.827 0.671 0.499 0.401 0 275 0.234 0.197 0.143 0.101
PI; P N
61;
PN
PI; P N
6;
PI;
6;
PN
PF
6; P X
6; P N PN
Very weak 6; E o 6; /9N
PN
...
...
0.000
Relative ratio of isolated to coupled Cr3+ions as defined in the text.
The solid solutions containing less than 1% Cr203 exhibited the characteristic esr spectrum of powdered. ruby. It results from electronically isolated Cr3+ ions (6 phase). Around 1.5% Cr203 two new resonances appear at g = 1.99 i 0.01. We attribute both of these resonances to Cr3+ ions electronically coupled with other Cr3+ ions. They apparently are related to the 0 phase resonances reported by other investigators.'-4 The two 0phase resonances, which we designated PI and (3) C. P.Poole, Jr., W. L.Kehl, and D. 5. MacIver, Jr., J . Catalysis, 1, 407 (1962). (4) C. P.Poole, Jr., and J. F. Itzel, Jr., J . Chem. Phya., 41, 87 (1964).
Volume 72,Number 7 J u l y 1068
CHARLES J. CARMAN AND WILLIAM J. KROENKE
2564
s
Table I1 : Esr Parameters of a-Crz03-Alz03Solid Solutions -.p
6 phase
mt %
(v/H)rn,x,a
CrzOs
Gcps/G
0.082 0.47 0.94 1.48 2.71 3.79 4.78 5.80 6.81 7.73 8.42 9.75 11.71 14.70
4.95 x 10-3 4.98 10-3 4.98 x 10-3 4.95 x 10-3 4.98 x 10-3 5 . 0 5 x 10-3 10-3 4.91 5.05 10-3 4.97 x 10-8 5.06 X 5.09 x 10-3 4.78 x 10-3 4.91 X
a
AH,*
*.
... ...
...
1.987 1.979 1.977 2.002 1.992 2.004 2.004 1.990 1.999 1I999
498' 476" 500 525 525 543 533 525 500 438
... ...
10-3 6
shown in Figure 1. We investigated the esr of solid solutions exhibiting both P I and PN resonances between 77 and 3OO"Ii. The observed temperature dependence indicates that the isolated Cr3+ ions and the Cr3+ ions responsiblc for both p phase resonances are paramagnetic. We suggest that the broad PI resonance results from Cr3+ ions intermediate to isolated Cr3+ ions and Cr3+ ions which are strongly coupled electronically (ON phase). It is interesting to note that the PI resonance was found only in the solid solutions containing between 2 and 6% Crz03. The significance of the two P phase resonances and their origin is discussed in detail in the Discussion section. As the Crz03content increases, the PN phase resonance increases in intensity. At approximately 4% Cr203the resonances of the coupled and isolated Cr3+ ions appear to be equal. As the Crz03 content continues to increase, the number of coupled Cr3+ ions increases while the resonance from the isolated Cr3+ ions broadens and decreases in intensity. Finally, at 15 wt % Cr203,we mere unable to detect any isolated Cr3+ ions. This can be seen in Figures 1 and 2. Figure 3 is a plot showing the change in relative concentration of isolated Cra+ ions (6 phase) to coupled Cr3+ ions (Ps phase) as a function of total Cr203concentration. This ratio of the concentrations of the two types of Cr3+ ions mas obtained by measuring the height from the base line to the maximum of the first derivative of the absorption for both the isolated Cr3+ resonance and the coupled Cr3+ resonance. The ratio is empirical. It does not provide an absolute measure of the number of spins contributing to the isolated Cr3+ resonance. The Journal of Physical Chemistry
I I I
I
R U B Y SPECTRUhil
I
phase resonance maximum.
Cannot be accurately measured.
PN are
I
0.01
' Separation between maximum and minimum of first derivative of absorption curve.
U
I
Av 1.993
=!= 0.08
Ratio of frequency to field of
3.79 WT. % C r z O J
G
I
x x
x
I
phase--Q
x
Av 4.97
I
1
1
1
1400
1
1
1
1900
1
2400
1
1
1
1
3400
2900
1
1
1
1
1
4400
3900
1
1
1
5400
4900
Figure 1. Appearance of coupled Cr3T ions ( p phase) with increasing CTpOg concentration in a-Cr~O3-Al~0~ solid solutions.
i\ /" I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
1400 1900 2400 2900 3400 3900 4400 4900 5400
Figure 2. Disappearance of isolated Cr3+ions ( p phase) with increasing CrzOa concentration in c ~ - C r ~ O ~ - Asolid l ~ 0solutions. ~
The plot in Figure 3 indicates that the relative concentration ratio of the two Cr3+ phases varies in a smooth, nonlinear manner. An accurate measure of this ratio cannot be made below 2% Cr2O3because of the low concentration of coupled Cr3+ions. Similarly, the point a t 11.71% Cr203was subject to error because of the inaccuracy involved in measuring such a low con-
ESROF ~-CHROMIA-ALUMINA SOLIDSOLUTIONS
2565
-
1.000
\+
Ogo0;
0800
\+
0700-
+
z
\
06003
n o w
5
u
+ 0500-
EE
5
0400-
z
0300-
0 200-
0 100-
OO
'
210
'
410
' ' 610
slo
!
'
I;.O
centration of isolated Cr3+ ions. Besides its obvious analytical significance, this plot graphically shows the dependence of the two major Cr3+ ion phases on the total Crz03 concentration. The esr data in Table I1 reveal that the peak to peak, full line width of the PN phase resonance essentially remains constant between 2.5 and 15% Cr203. This result is in contrast to the variation in line width with increasing chromia content that has been reported previously for a-CrzO3-Al2O3solid solution^.^^^ However, the other investigators have had to make a very large extrapolation since they only had two data points below 20 mole yo Crz03. Thus, we think that the constancy of the line width of the PN phase resonance which we established for eight different concentrations between 2.5 and 12% Crz03 is correct, and the slight decrease in line width of the 14.70% sample may be an indication of line narrowing with increasing Crz03 concentration. Additional data between 15 and 20% Crz03would be required to establish if we are observing line narrowing in the 14.70% sample.
Discussion The esr data in Table I1 show that the maximum of the derivative curve of the isolated Cr3+ions (6 phase) major resonance is independent of Cr203concentration. This means that in a-Crz03-A1203 solid solutions the origin of the 6 phase is unchanged and its identifying peaks correspond to the major resonances in powdered ruby. The well-resolved symmetrical 6 phase resonances in a-Crz03-Alz03 solid solutions contrast with the
very broad 6 phase resonance reported for impregnated and coprecipitated chromia-alumina c a t a l y s t ~ . ~ , 3 I n the a-solid solutions the isolated Cra+ ions are subjected to a strong axial crystal field in a highly ordered lattice. Consequently, in the dilute solid solutions the 6 phase resonances are narrow, symmetrical, and well defined. In contrast, the 6 phase resonance in impregnated and coprecipitated chromiaalumina catalysts is very broad. This is attributed to the imperfectly crystalline nature of the y-alumina host lattice.'& y-AlZO3solid solutions may not be necessary to produce the broad &phase resonance since a &phase resonance was found in some catalysts which did not contain a detectable y-Al203 solid solution phase.l& Cr3+ ions isolated on the surface also might produce a broad 6 phase resonance since they would not be subjected to a regular crystalline field. I n fact, it has been suggested that the isolated Cr3+ ions can exist either on the surface or in the bulk of the catalyst.'* Isolated Cr3+ions in an amorphous matrix also could produce a broad 6 phase resonance because of the absence of long-
alumina catalysts are highly a m o r p h o u ~ . ~ We have observed two P-phase resonances (PI and (IN) which we attribute to electronically coupled Cr3+ ions. We suggest that 01 results from Cr3+ions which are close enough to couple electronically but far enough apart to experience only a weak exchange interaction. On the other hand, we suggest that PN is a result of strong exchange interaction resulting from Cr3+-Cr3+ ion pairs. Our interpretation of the origin of the PI and px resonances is consistent with the results of esr measurements made on ruby single crystals. Statz, et al., verified that the strongest electronic interaction in ruby single crystals is between Cr3+ ion pairs occupying adjacent lattice sites along the c Furthermore, they identified esr lines resulting from Cr3+ion pairs. These would be centered at 3400 G at x-band frequencies. This result strengthens our assignment of the PN phase resonance which is centered about 3420 G. Statz, et al., also concluded that isotropic exchange interaction in Cr3+ion pairs in a-&O3 can be present out to the eleventh neighbor shell with a magnitude of about 0.5 (3m-I.' For the third, fifth, and sixth neighbor shells the exchange interaction is of the order of 1 cm-l. A sphere of radius 5.73 A encompassing the 11 neighbor shells will contain about 42 cation sites.' ( 5 ) R. J. Landry, J. T. Fournier, and C. G. Young, J . Chem. Phys., 46, 1285 (1967).
(6) H. Statz, L. Rimai, M. 3. Weber, and G. A . DeMMars, J . Appl. Phys., 32, 2189 (1961).
(7) L. Rimai, H. Statr, M. J. Weber, G. A. DeMars, and G. F. Koster, Phys. Rev. Letters, 4, 125 (1960). Volume 72,Number 7
July 1968
2566 The significance of this hypothetical sphere is that if it contained two or more Cr3+ions not forming nearestneighbor ion pairs they still would be electronically coupled by exchange interactions. We suggest the more distant Cr3+ ions are weakly coupled by such electronic exchange interactions and result in the PI phase resonance. In addition, in the cluster of ESR lines resulting from Cr3+ ion pairs the lines corresponding to the more distant neighbors are on the low-field side of the cluster.' 01also appears on the low-field side of the / 3 ~resonance and this is further evidence in support of our interpretation. We used the equations given by Poole and Itze14 to calculate a 9 to 1 ratio of unpaired to nearest-neighbor paired Cr3+ions for the 15% Crz03solid solution which showed only a single symmetrical PN resonance. Thus, in a statistical sense, the large increases in intensity we observed in the ON resonance of a-solid solutions a t higher Crz03 concentrations cannot be entirely accounted for in terms of simple nearest-neighbor ion pair formation. This is exactly what is expected based on the esr studies of ruby single crystals which showed that isotropic exchange interaction in Cr3+ ion pairs can be present out to the eleventh neighbor shell.7 I n other words, Cr3+ ion pairs other than nearest neighbors can contribute to the PS resonance. A narrow P phase resonance (also designated PN) was found in coprecipitated chromia-alumina catalysts.3 This antiferromagnetic PN resonance was attributed to the presence of clumps or small crystallites of a-Crz03.4 The PN phase resonance we observe in a-Cr203-Alz03 solid solutions corresponds in g value, line shape, and line width to the PN phase observed in coprecipitated chromia-alumina catalysts. However, there is one difference. We have found that the PN phase resonance in a-Cr203-A1203is paramagnetic up to about 10 mole % Crz03. This is in agreement with the report that the Keel points for a 9.2 and 19.6 mole % Crz03solid solutions were too poorly defined to be m e a ~ u r e d . ~ Another point to be considered is whether the PI phase resonance we have found in a-Cr203-A1203solid solutions is related to the PW phase resonance reported in coprecipitated supported catalyst^.^,^ It was reported that the p~ resonance was paramagnetic and suggested that it might be associated with Cr3+ions in solid solutions, Our identification of the paramagnetic pI resonance in a-Cr203-A1203solid solutions strength-
T h e Journal of Physical Cherntktry
CHARLES J. CARMAN AND WILLIAM J. KROENKE ens this suggestion, especially since PI and PW have very similar g values and line widths. However, it was reported that the PWresonance was independent of total Cr203 con~entration,~ and we have shown that PI is concentration dependent, apparently existing only between about 1.5 and 6.0% Cr203. This suggests that if solid solutions of Crz03and a-Alz03 are responsible for the PFVresonance found in the coprecipitated catalysts, they probably will contain about 1.5 to 6% Crz03. Since pw is apparently independent of concentration, perhaps the solubility limit of Cr203in 7-Al2o3,under the conditions of forming the coprecipitated catalysts, is within this range. Because of the poorly crystallized nature of the y-A1~03 in coprecipitated chromiaalumina catalysts, it would be difficult to detect the formation of dilute solid solutions.
Conclusions Three electronically different types of Cr3+ions exist at low chromia concentrations in polycrystalline aCrz03-A1203solid solutions. These are isolated Cr3+ ions, Cr3+ coupled by weak electronic exchange interactions, and Cr3+ ions coupled by strong electronic exchange interactions. The relative ratio of isolated to coupled Cr3+ions varies in a regular fashion. We suggest a simple physical picture to explain the esr of polycrystalline a-Cr203-A1203 solid solutions. At low Crz03concentrations (
