Quantitative Analysis of Anatase-Rutile Mixtures with an X-Ray Diffractometer ROBERT A. SPURR and HOWARD MYERS Hughes Research laboratories, Culver City, Calif. ,An analytical procedure based on average: 98.68. The values for the the value of IA/IRfor sample 11 would x-ray diffraction intensities is presented weight fractions of anatase in anatase- be infinite; and if R were pure rutile, for the determination of the relative rutile mixtures determined by the the value of this ratio for sample 1 amounts of anatase and rutile in their method described are insensitive to would be zero. It is not difficult, how- mixtures. several per cent variations in the total ever, to estimate the impurities in A and titanium dioxide content. R to a sufficient degree of accuracy to Particle diameters smaller than 5 mi- establish an analytical method for ana- ITAXIUM DIOXIDE may be incorpo- crons are desirable to ensure adequate tase and rutile. Trated into a plastics molding com- reproducibility of diffraction intensity pound to adjust the dielectric constant measurements (4). Electron micro- to a desired value. Either anatase or graphs taken at a magnification of a zo rutile may be used; these allotropic 36,000 diameters indicate that particle forms differ in dielectric behavior. diameters are 0.04 to 0.6 micron for o ie Xeither is available commercially in a anatase and 0.08 to 0.5 micron for pure state; a preparation consisting rutile. The particle sizes are, there- 0 16 largely of one form is apt to contain, in fore, sufficiently small for reproduci- addition to other impurities, an admix- bility of intensity measurements. 0 14 ture of the other. In order to permit proper formulation of filled resins, RESULTS AND METHOD OF CALCULATION 0 I2 therefore, it is desirable to establish a method for determining the relative For a given sample, the ratio (IAIIR) II 4 010 amounts of anatase and rutile in mix- of the intensity of the strongest anatase tures. The application of photometry reflection to the intensity of the strong- to this problem has been discussed est rutile reflection is independent 008 (2,6). This paper develops a method of fluctuations in diffractometer char- using the more precise technique of acteristics. This ratio therefore pro- OW diffractometry. vides a useful index of sample composi- tion. The first three columns of Table 004 I show the weights of A and R in the APPARATUS AND MATERIALS samples; the average values of IA/IR 002 The instrument used vias a Xorelco were found from a total of 53 deter- minations. Geiger-counter x-ray diff ractometer 0 002 004 006 008 OK) ole equipped with voltage and current The intensity data show that the A dabilizers, counters, and a strip-chart material contains a small amount of UI'W2 recorder; it was operated at a voltage rutile and the R material a small amount Figure 1. Intensity ratio as a function of 35 kv. with a filament current of 25 of anatase. If A were pure anatase, of weight ratio for small w1 ma. Scanning speed was 0.25" per minute; the width of the receiving slit was 0.003". For rapidity and con- venience, most of the intensity data were obtained from the strip chart Table I. Compositions and X-Ray Intensity Data for Anatase-Rutile Mixtures and showed a satisfactory agreement 1 with the results obtained by direct f= IR "$7 1 + 1.266 counting. The accuracy and repro- ZCI, ZCZ, IAIIR Weight ducibility of this type of instrument Sample IT-eight ITeight Intensity Fraction Intensity have been discussed by Klug and co- so. of A, G. of R. G. Ratio of Anataee Function workers (3, 6). The strongest reflec- 1 0 1.997 0.0165 0.0112 0.0115 tions for anatase and rutile are con- 13 0.0099 0,9898 0.0312 0.0205 0.0240 veniently located for CuKo radiation 16 0.0399 0.8002 0,0869 0.0564 0,0573 at the Bragg angles 12.68" and 13.73", 14 0.0501 0.9500 0.0920 0,0588 0,0677 respectively. 2 0.202 1.749 0.183 0.110 0.126 3 0.451 1,335 0.431 0.252 0.253 The materials studied are two com- 4 0.626 I.121 0.680 0.350 0.349 5 0.822 1.022 0.941 0.438 0.426 mercial products, one of which is largely 6 0.996 0.918 1.21 0.510 0.489 anatase (A) and the other largely rutile 7 1.290 0.622 2.31 0.658 0.645 (R). When total titanium dioxide was 8 1.502 0.518 3.28 0.724 0.722 determined by the method of Rahm (7), 9 1.726 0.355 5.31 0.807 0.809 10 2.856 0.268 9.54 0.889 0.883 the percentages found in three deter- 15 0.9501 0,0496 13.51 0,919 0.915 minations were A. 98.00, 97.68, 98.08; 11 2.050 0 55.9 0.972 0.978 average: 97.92. R. 98.70, 98.73, 98.62; 760 ANALYTICAL CHEMISTRY The first three columns of Table I titanium dioxide in A and R as deter- '2 = K2 + KZ3 3 (for small wp) give the weight of A (97.9% TiOn, IA ai a1 w1 mined by chemical analysis. largely anatase), the weight of R (98.7% (7) Ti02, largely rutile), and the ratio of a2 - 0.0165 the intensity of the strongest anatase where K2 is the value of K in the K,T, - reflection to that of the strongest rutile region where w2is small compared with wl. Figure 2 is a graph of IR/IAus. - 1.425 reflection for the various sample mix- K, rT - tures. The last two columns give the w2/zc1 in this region. The straight line weight fraction of anatase and a func- drawn may be represented by the equa- tion Kt? = 0.0230 (9) tion of the intensity ratio that approxi- a1 mates the weight fraction of anatase. = 0.0230 + 0.820 = 0.820 For a given sample, the relation be- IA5 2 Kz 2 tween the weight ratio and the intensity a1 ratio for anatase and rutile is given by There are nom six unknown quantities- a1 + rl = 0.9T9 the expression alJ rl, a2,rtJ K1, and K2--which may be uz rz = 0.987 related by the following six equations. + The first four are obtained by comparing Solution of these simultaneous equations coefficients in Equations 5 through 8; yields where WA and WR are the weights of the last tITo give the total amounts of anatase and rutile, respectively, in the = 0.952 sample. It is known that, for mixtures r1 = 0.027 of allotropes, intensity of scattering for Q50 each component is substantially pro- dz = 0.011 (10) portional to its weight fraction (I). r2 = 0.976 It may be expected, therefore, that K will be approximately constant over 0.40 K1 = 0.68 narrow ranges of concentration. K2 = 0.80 The weight of pure anatase in the sample is given by the equation It is seen that the A material contains 0.W 95.2% anatase and 2.7% rutile and that w.4 = UlWl + UZW? (2) the R material contains 97.6% rutile and where wl is the weight of A, w2 is the 1.1% anatase. It is non- possible to cal- weight of R, ul is the weight fraction of culate the weight fraction of anatase in anatase in A, and a2 is the weight frac- 0.20 the titanium dioxide for each sample; tion of anatase in R. A similar expres- these values, given in the fourth col- sion gives the weight of pure rutile in umn of Table I, may be considered the sample: reliable to within about 0.01 unit. 0 10 For the analysis of anatase-rutile WR = rlwl + rzwl (3) mixtures, it is convenient to devise a function of the intensities that is where rl and r2 are the weight fractions approximately equal to the weight frac- of rutile in A and R, respectively. tion XI of anatase present. This Substitution of Equations 2 and 3 in 1 0 010 020 030 ow OH) 0.60 weight fraction is given by gives VI '9 UlWl UzW2 = K + (4) Figure 2. Intensity ratio as a function rlwl + TZWZ ZR of weight ratio for small w2 The combining of Equations 11 and 1 r1 is small compared with unity; there- fore, for small wl,rlwl may be neglected yields in comparison with rzwz. The follow- ing approximate equation can thus be derived : If the variation of K with concentration is now neglected and if K is taken as (5) 0.79, or 1/K as 1.26, an approximation Here Iil denotes the value of K in the to XI is obtained that may be designated region where w1is small compared with as f: w2. Figure 1 is a graph of IA/IRus. 1 w1/w2. The fact that the points lie s= 1 + 1.26 I-IR (13) near a straight line is an indication that ", K1is approximately constant in this con- centration range. The equation for This quantity f is tabulated in the the line is f, INTENSITY FUNClWN last column of Table I and a graph of xA us. f is shown in Figure 3. It can be = 0.0165 + 1.425 2 Figure 3. Weight fraction x.& as f ZR seen that is, in fact, approximately function of equal to 2.4.