SOLIDSOLUTION OF ALUMINUM OXIDEIN RUTILETITANIUM DIOXIDE
0 r
F=O H-0
- Qc=o
I
\O-H.*a
I1
It has previously been proposed that I represented picolinic acid in D20.4 Internal hydrogen bonding of this sort was also proposed for nicotinic and isonicotinic acids. It is difficult to see how an internal hydrogen
2157
bond can be formed in the latter two cases due to the separation of the hydrogen bonding atoms. As the data in this work show, the spectra can be explained in terms of the dipolar species existing in DzO. In summary, by assuming the dipolar form for the three acids as the principal species in aqueous solution, a variety of solution infrared results can be explained. Acknowledgment. The authors wish to thank the American Chemical Society for supporting this work through PRF Grant 2710-B.
Solid Solution of Aluminum Oxide in Rutile Titanium Dioxide1 by Richard A. Slepetys2and Philip A. Vaughan Department of Chemistry, Rutgers-The
State Uniuersitg, New Brunswick, New Jersey
(Received July $8, 1968)
The solubility of A1203in rutile Ti02 was determined in the temperature region of 1200-1426' from the change of the c unit-cell parameter. Solubility increased with equilibration temperature, ranging from 0.62% A1203 by weight at 1200' to 1.97% at 1426'. Corundum was the equilibrium solute phase below, and AlzTiOs above, 1240'. Solubility also increased with the addition of NblOS. The density of a rutile sample equilibrated at 1426' containing 1.6% by weight A1203was 4.199 g/cma, not significantly different from 4.202 g/cm3 measured for a corresponding pure rutile sample. These results are consistent with an interstitial solubility model in which AIS+ and 02in 1:2 proportion are placed on the respective rutile lattice sites, and the remaining A13+ occupies interstitial spaces. Treatment of the temperature dependence of the solubility data gave values for AH' of solution of 35 kcal/mol and 100 kcal/mol for A12Ti05 and AlzOs, respectively. The heat of formation of AlzTiOs computed from these results is -559 kcal/mol near the transition temperature. Introduction Several investigator^^-^ have studied the system AlzOa-TiOz. Their phase diagrams show one compound, A12TiO;, and eutectics with both component oxides. Lang, Fillmore, and XIaxwel16 also indicated a region of instability occurring in the range of about 750-1300' wherein aluminum titanate decomposed into the respective oxides. The solubility of aluminum oxide in rutile titanium dioxide had not been studied systematically. In her work on the preparation and structure determination of aluminum titanate, Hamelid noted that the solubility of aluminum oxide in rutile, if any, is very limited. F10rke7 reported an approximate value of 2 mol % at 1400". In the present investigation the extent of solid solubility of A1203 in rutile was measured in the region of the reported transition AbO3
+ Ti02
A12Ti05
The temperature of this transition was more firmly established, some thermochemical results were derived, and a solubility model was proposed.
Experimental Section A . Chemicals. The compounds used in this study were TiCL obtained from National Lead Co., Titanium Division, Baker Analyzed reagent AlCls 6H20, and Ciba anhydrous NbC16. E . Sample Preparation. Mixtures of oxides of titanium and aluminum were prepared by coprecipitation from a chloride solution. Measured amounts of analyzed stock solutions were mixed and diluted to contain about 0.07 g of Ti02/ml, the solution was heated to 55', neutralized with ammonium hydroxide to pH 6.5, filtered, washed, dried at 120', and ground in an agate +
(1) Based upon a dissertation submitted by R.A. Slepetys in partial fulfillment of the requirements for the Ph.D. degree in chemistry. (2) To whom correspondence should be addressed a t National Lead Company, Titanium Division, P.O. Box 58, South Amboy, N. J. (3) H. yon Wartenberg and H. J. Reusch, Z . Anorg. A&. Chem., 207, l(1932). (4) E. N. Bunting, J . Res. Nat. Bur. Stand., 11, 725 (1933). (6) S. M. Lang, C. L. Fillmore, and L. H. Maxwell, ibid., 48, 298 (1952). (6) M. Hamelin, BUZZ. SOC.Chim. Fr., 1421 (1957). (7) 0. W. Florke, Ber. Deut. Keram. Ges., 38, 133 (1961).
Volume 73, Number 7 July 1969
RICHARD A, BLEPETYS AND PHILIPA. VAUGEIAN
2158 mortar. Small samples were heated in platinum boats at 1344-1426" in a Lindbergh combustion furnace with a steady flow of oxygen at atmospheric pressure for 24 hr and quenched subsequently in water. Temperatures were measured with a platinum-platinum-rhodium (13%) thermocouple. We estimate that errors in the temperature measurements (arising mostly from fluctuations) are less than 5". Samples equilibrated at lower temperatures (1200-1312") were prepared from those heated at or above 1344" by reheating at the lower temperature for 48 hr and quenching in water. Samples containing niobium were also prepared in the same manner. C. X-Ray Procedures. Norelco X-ray equipment with Ni-filtered Cu K a radiation was used throughout this study. Powder photographs were obtained with 360/n mm camera of the Straumanis type on Kodak No-screen Medical X-ray film covered with a 0.5-mil Ni foil. Lattice parameters were calculated by the method of Vogel and Kempters with the Nelson-Riley9 extrapolation function. Diff ractometer measurements of powder lines were made by a stepwise counting technique with 0.02" (20) increments, 1" divergence and scatter slits, and 0.003-in. receiving slit. Centroid positions were calculated by Wilson'slo formula for truncated diffraction peaks, and lattice parameters were then obtained by Cohen's method with a (sin 8 cos2 8) extrapolation function, Errors associated with the determination of the c parameter on individual samples for the photographic method and were 4.8 X A for diffractometric. 11.6 X In some cases intensities of the line were obtained by numerical integration of data. The diffraction peaks were scanned in 0.02" (20) steps taking duplicate counts at every step with a scintillation counter. Flat samples were always used. D. Density Determinations. Density determinations were made according to the method of Baker and R'lartin'' with a modification that the immersion fluid was added to the powdered specimen in an evacuated chamber.
Results and Discussion A . Solubility of Al203 in Rutile. It was found experimentally that at a given temperature the c parameter of the tetragonal unit cell of rutile decreased linearly with increasing AlzOa addition until saturation was reached, while a was not affected. The c parameter as a function of A1203 addition is plotted in Figure 1, wherein the declining portion represmits true solid solution, the horizontal portion the presence of a solute phase, and the intersection of the two the limit of solubility at the given equilibration temperature. The position of this intersection was calculated by a least-squares procedure, and results are presented in Table I. These solubility values are in agreement with an approximate solubility of A1203in rutile of about 2 The Journal of Physical Chemistry
9Ok
90
"6
86
&
1Q6'
Figure 1. Rutile c axis as a function of mole fraction of AlOa/, (5)added: 0, photographic data; A, diffractometric data.
mol Yo at 1400" mentioned by Florke' as well as the "region of instability" of AlzTiOs below 1300"; i.e., corundum was the solute phase below, and AlsTi06 above, 1240". Table I : Solubility of AlzOain Rutile Std dev,
-Solubility-Temp, O C
wt %
Mole fraot of A1
AI208
1200
0 0098
0.62
1240
0.0158 0.0191 0.0228 0.0306
1.01
1312 1344 1426
I
1.22 1.46 1.97
wt
76 AI208
0.10 0 09 0.11 0.17 0.18 I
Solute phase
Corundum Corundum AI2TiO6 AliTiOs AlzTi06
B. Models of Solid Solution. Rutile TiOz has a tetragonal unit cell containing six atoms: two titaniums are located at O,O,O and l/~,l/z,l/z, and four oxygens a t u,u,o; -24,-u,o; '/z u,'/z - u,'/2; '/z - u, '/z u,
+
+
(8) R. E. Vogel and C. P. Kempter, "A Mathematical Technique for the Precision Determination of Lattice Constants," Report LA2317, Sept 3, 1959. (9) "International Tables for X-Ray Crystallography," Vol. 11, The Kynoch Press, Birmingham, England, 1959. (10) G. L. Clark, "Encyclopedia of X-Rays and Gamma Rays," Reinhold Publishing Corp., New York, N. Y.,1959. (11) I. Baker and G. Martin, Ind. Eng. Chem. Anal. Ed., 15, 279 (1943).
SOLIDSOLUTION OF ALUMINUM OXIDEIN RUTILETITANIUM DIOXIDE l/p. Two possibilities of accommodating ALO3 in the rutile lattice were considered: substitutional and interstitial. Because of similar crystal ionic radii (0.64 A for Ti4+and 0.57 A for AP+) aluminum can occupy regular cation positions giving a substitutional solid solution. I n the rutile lattice these aluminums are thus present as a defect with a single (defect) negative charge A I T i ’ . Some oxygen vacancies Vo” also result Depending on the solute phase in equilibrium with the solid solution, one can write the following expressions for the solubility and the equilibrium constants. I
+ vo’*+ 300”
A1203 _I 2A1~;’
K , = [ ~ ( A l ~ i ’ ) ] ~ ~ [u(OO’)]~ (vo‘’) A12Ti06)J2A1~i’ v{’ 500“ T i T i ”
+
+
(1)
K, = [ ~ ( A l ” ) ] ’ a ( ~ o ’ ’ ) ~ ([6(00”)]‘U(Ti~i”) o~~) (2) The activities of the charged solute species can be given by their concentrations ( M ) multiplied by the respective activity coefficients, and those of the uncharged solvent species are assumed to be given by the atom fractions on the corresponding sites ~ ( A h i ‘ )= C(AlTi‘)T(Ahi‘); C(A1Ti‘)
a(V0”)
=
C(Vo”)?(Vo’.); C(Vo‘.) a(Oo‘)
=
U(TiTi‘)
=
=
2C(AhO3)
C(A1203)
1 - 0.25~ =
1-X
where x is defined by the formula AlzTi~-z02-c,,~z, and C(A120s)is the total A1203concentration in solid solution. As an alternate possibility, aluminum and oxygen can be placed on the regular cation and anion sites, respectively, in 1:2 ratio as required by the stoichiometry of Ti02. The remaining aluminum would then occupy interstitial positions giving an Ali”‘ lattice defect. Alto3
+ l/zAli”‘ + 300” + 6/2Si’
3/2AlTi’
K i = [ a ( A li~’) ] ‘Iz [a(A1i” ‘) ] [a(S iz) 16/’
Jr ‘/zAhi’ + ‘/zAli”’ +
AlzTiOs
500’
Ki
=
+
’/&iz
(3)
-/- TiTi’
[~(Al~~‘)]”/”(Ali’’’)]”~ [a(Si”)]g’za(Ti~i5)(4)
a(A1Ti’) = C(AlTi’)T(AlTi’); C(AITi’)
=
‘/2C(AlzOa)
a(Ali“’) = C(Ali”*)y(Ali’**);C(Ali*“) = S/&’(A120a) a(Si”)
=
U(TiTi”) =
2 2
- 0.752 -0.5~
1-x 1 - 0.252
I n these equations Si” denotes an empty interstitial site. There are two types of such sites in the rutile
2159
lattice : octahedral and tetrahedral. Most investigat o r ~ ~ who ~ -have ~ ~ studied phenomena related to the interstitial defects in rutile consider the octahedral sites to be more favorable. The unit cell of rutile contains four such sites, related by symmetry and located at midpoints of a edges and centers of a-c faces. On the other hand, Huntington and Sullivan*e maintain that tetrahedral positions may be favored by interstitial cations because in the octahedral sites the two nearest oxygen neighbors are only 1.66 8 away and the other four oxygens 2.23 8 away, while the tetrahedral positions are surrounded by four equidistant oxygens 132 8 away. The latter value is closer toothe normal Ti-0 distances in rutile (1.944 and 1.988 A) than the octahedral distances. There are four such tetrahedral positions in the unit cell of rutile and they are displaced from the octahedral ones by 0 . 2 5 ~ . C. Addition of NbzOj. The two models of solubility equilibrium presented in the preceding section have different equilibrium constants as given in eq 1-4. They were tested by adding NbzOs, which can interact with one of the products in each solubility reaction. The crystal ionic radius of Xb5+ (0.70 A) is also similar to Ti4+; therefore] this ion can be accommodated in the rutile lattice. Two levels of niobium were added, giving Ti: Pib mole ratios of 1:0.02138 and 1: 0.04276. At each niobium level three concentrations of aluminum oxide were added in excess of the expected solubility, samples were equilibrated at 1426’, and the solubility was determined by the extrapolation of the intensity of two strong aluminum titanate lines. The extrapolation was based on the fact that under fixed conditions the intensity of a diffraction line is proportional to the weight per cent of the given phase in the powder sample. The intensity ratio R between the solute phase and rutile lines can be given by
where I1is the intensity of the solute phase line, I z is the intensity of the rutile line, K is the proportionality constant, and f l is the weight fraction of the solute phase in the sample, If Z1 is the weight fraction of AlzOsused in the preparation, and S is solubility expressed as a weight fraction (of the solid solution phase), then
z1 = flP + (1 - f1)X
(6)
where P is the weight fraction of A1203 in the solute phase. Eliminating f1 gives R(P 21) = KZi - KX (7)
-
(12) T.Hurlen, Acta Chem. Scand., 13, 365 (1959). (13) P.F. Chester, J . A p p l . Phys., 32 (Suppl), 2233 (1961). ‘(14)R. D.Carnahan and J. 0. Brittain, ibid., 34, 3095 (1963). (15) J. B. Waohtman, Jr., and L. R. Doyle, Phys. Rev., 135, A276 (1964). (16) H.B. Huntington and G. A. Sullivan, Phys. Rev. Lett., 14, 177 (1965).
Volume 73, Number 7 July lQ69
RICHARD A. SLEPETYS AND PHILIP A. VAUCHAN
2160
&5
c
1-x a(TiTiz) = 1 - 0.252
+ 1.25~
+ +
2 - 0.75~ 2.75~ a(Si2) = 2 - 0 . 5 ~ 2 . 5 ~
Once the equilibrium constants are known from the solubility measurements of AI208 in pure rutile, eq 9 and 10 may be used to determine the solubility of Alz08in rutile as a function of Nbz05 addition. These functions are plotted in Figure 3. To test the solubility either the predicted solubility values can be compared with the measured ones, or the equilibrium constants can be calculated from experimental data, and their constancy can be examined.
Weight Fraction
&Og,
ZA
Figure 2. Extrapolation of diffraction intensities in the presence of Nbz06: 0, 1 Ti:0,02138 Nb mole ratio; A, 1 Ti: 0.04276 Nb mole ratio.
A straight line with an intercept on the abscissa equal to S is obtained when R ( P - 21)is plotted against Z1 (Figure 2). This method of extrapolation of intensities of diffraction lines of the solute phase was also used in several instances to check the solubility of aluminum oxide in rutile TiOz when no Nbz05was added. The results were solubilities (weight per cent) of 1.04 at 1240" and 1.84 at 1426", which are in good agreement with the data of Table I. According to the substitutional model, Nb5+ occupies titanium sites, and the extra oxygen eliminates some of the vacancies. NbzOa VO"+ZNbTi' 500' (8) The equilibrium constant expression shown in eq 2 now must be modified to take into account the interaction between oxygen vacancies and niobium pentoxide, as well as the change in the fraction of sites occupied by oxygen and titanium
Ks = 4 [C(Alz03)l2 [C(AlzOS) C(Nbz05) 3 [Y (AL i ') 127(vo")U(Ti~ i") [U(Oo") l5 (9)
where x and y are defined by the formula Al,Nb,.5y. According to the interstitial model Ti1--202-0.5~+2 Nb2O6interacts with the Ali"' interstitials Nb206
Ki
+ '/2Ali"'
+
+
+
+
2 N b ~ i ' l/ZAl~i' 500" "/2Si" '/4[3C(A1203) C(Nbz06)]"/' X [C(A1203) - C(h'bzO~)]'/* X [Y(AITi')18/' [r(Ali'") ]'/'a(TiTizj[a(S?) ]'//" (10)
The Journal
+
of
Physical Chemistry
3 0 -6 0
I 0.2
I
I
I
I
0.4
0.6
0.8
1.0
Nb,O,,
I
1.2
I
1.4
I
1.6
Molse/LIt.r
Figure 3. Solubility of A1203 in rutile at 1426" as a function of Nb206 addition: 0 , experimental points; solid lines, theoretical curves.
The activity coefficients were estimated by the Debye-Huckel equation. Because rutile is anisotropic, a geometric mean dielectric constant of 81.4 was used, calculated from the data of von Hippel, Kalnajs, and Westphal" at 500". Similarly, a geometric mean distance of closest approach was used in the calculation of activity coefficients. I n the substitutional model it was 1.959 A for the six octahedral neighbors of an Ahi' defect, and in the interstitial model 2.578 A for the neighbors of an octahedrally located Ali"'. Activity coefficients and concentrations entering the equilibrium constants are listed in Table 11. Equilibrium constants for pure and Nbz05-containing rutile and solubilities predicted according to the two models on the basis of equilibrium constants established in the absence of NbzOj are compared in Table 111. (17) A. von Hippel, J. Kalnajs, and W. B. Weatphal, J. Phys, Chem. SoEids, 23, 779 (1962).
SOLIDSOLUTION OF ALUMINUM OXIDEIN RUTILETITANIUM DIOXIDE
2161
Table I1 : Concentrations and Activity Coefficients ?Substitutional-
--Interstitial---
0.00 1.07 2.07 1.63 1.80 2.45 0.815 0.365 0.182
0.00 1.22
...
...
0,969 0 946 0.915 0.992 0 997 0.998 I
I
...
...
...
0.914 0.917 0.912 0.697 0.707 0.691
...
" Concentration
...
..,
.(.
1.07 1.62 .
I
.
2.07 2.34 .
I
.
0.408 0.183 0.0908 0.977 0.946 0.915 I
,.
* I .
I .I
*
0.996 0.998 0.999 0.921 0.924 0.919 ..,
...
0.475 0.489 0.467
units are moles per liter. l
,
o&
0.50
1:O.OOOOO 1:0.02138 1:0.04276
Equilibrium --constants---. Interst Subst
0.50 0.51 0.59
1.18 0.66 0.56
--Solubilities, Measured Solub u
1.97 2.16 2.91
0.18 0.08 0.07
% AlzOs by wtPredioted Interst Subst
...
...
2.15 2.82
2.48 3.23
YMeasd0.0% -1.6% Al2Oa Dens.
Calod -SubEtitutionDens. Change
-1nteratitialDens. Change
4.250 4.213 -0.037
4.240 -0.010
7
AlzOeChange
4.202 4.199 -0.003
0.0%
AliOa
Calculations for the substitutional model indicate a substantial drop in density of the rutile phase upon dissolution of 1.601, A1203, while the interstitial shows only a very small change. The experimentally determined densities show practically no change, in agreement with the interstitial model. The experimental values were somewhat lower than the calculated ones because a perfect crystal was assumed in the calculations while the actual samples were quenched rapidly from 1426" and apparently contained some flaws which were not completely filled by the immersion liquid. That these differences are not explained by formation of vacancies is ruled out by the measurement of such vacancies by Straumanis, et aln18 E. Calculation of AH". Equilibrium constants were calculated according to eq 3 and 4 for the interstitial
l
I
1
o,64
,
,
0.66
1
0,6$
Figure 4. Temperature dependence of log K : 0 , experimental points and least-squares lines.
solubility model, and a plot of log K us. 1 / T is given in Figure 4. Numerical data are Temp, 'C Log K
Solubilities predicted by the interstitial model were in satisfactory agreement with the measured values, while the differences for the substitutional model were considerably larger. Similarly, the equilibrium constant calculated by the interstitial model remained relatively unchanged, while the substitutional model caused its value to decrease to about one-half of the original amount when Nb205 was added. D . Density Determination. Densities were determined for samples containing 0.0 and 1,6% by weight AIzOa,heated a t 1426". The results are
l 062
1000/1!
Table I11 : Equilibrium Constants and Predicted Solubilities Ti:Nb mole ratio
,
1426 -0.2972
1344 -0.5427
1312 -0.0891
1240 -0.8362
1200 -1.2290
Two straight lines were calculated by least squares corresponding to and A12Ti05solute phases. The intersection of these lines occurred slightly below 1240°, yet at this temperature corundum still was the solute phase. Therefore, 1240" was taken to be the transition temperature for the reaction t>1240°
+ TiOz' 1 AlzTiOs
A1203
t
