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 determinations. 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 equation 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; therefore, for small wl,rlwl may be neglected yields in comparison with rzwz. The following 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 concentration 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. -4 better fit for 2~20.2 Similarly azis small compared with unity could be obtained by taking K = 0.68 1 and, for small w2,the term u2wz may be f= in this region of concentration. I neglected in comparison with ulzcl: 1 f 1.26 3 The weight fraction of anatase in an the equation obtained is 14 anatase-rutile mixture may be deter-

VOL. 29, NO. 5, MAY 1957 * 761 mined by calculatingffrom the observed of 3 to 4%. Two experimental deter- LITERATURE CITED minations of known mixtures led, how- x-ray intensities and hv referrineI to (1) Alexander, L., KI~~,H. P., ANAL. Figire 3. ever, to errom of only 0.9 and 0.2%. CHEM.20, 886 (1948). The most imnortant contribution to (2) Bum, C. W., J. Sa. Znstr. 18, 70 (1941). the experimental error in f arises from (3) Xlug, H. P., ANAL,CmM. 25, 704 the lack of reproducibility of scattering ACKNOWLEDGMENT ,~”-”,.1105?\ intensities recorded by the diffractom- (4) Xlug, H. P., Alexander, L., “X-Ray eter. Optimum precision can be The authors are indebted to A. G. Diffraction Procedures,” Wiley, New York, 1954. obtained by the use of slow scanning Hastings and R. L. Grantham, Hughes (5) Klug, H. P., Alexander, L., Kum- speed, and by averaging several values Research Laboratories, for analyses of mer, E., ANAL. CHEM. 20, 607 of I~/ln,where the ratio contains two the two materials discussed in this (1948). intensity values from the same run. paper. (6) Legrand, C., Chimie et Industrie 68 Electron micrographs of anatase and 360 (1952). It was found from 18 determinations (7) Rahm, J. A,, ANAL.CHEM. 24, 1832 that the standard error in f due to lack rutile particles were made with the (1952). of instrument reproducibility is about collaboration of D. C. Pease. Anatomv 2%; the inclusion of other experimental Department, University of ’ California R~~~~~~ for review September 17, errors suggests a standard error for f at Los Angeles. 1956. Accepted December 31, 1956.

Steroid X-Ray Diffraction Powder Data

JONATHAN PARSONS, WILLIAM T. BEHER, and GIZELLA D. BAKER The Edsel B. Ford Institute for Medical Research, Henry Ford Hospital, Detroit 2, Mich.

t X-ray diffraction .powder data and powder pattern photographs are presented for 32 steroids.

o CONTINUE. . the studies on the T.identification of steroids by x-ray powder diffraction, 32 additional com- pounds were investigated. Their inter- spacing data and powder pattern photographs are here reported. The earlier papers (I-3) in this series gave powder data for 106 steroids. The x-ray patterns were obtained in 5 hours, using nickel-filtered copper x-radiation produced at a potential of 35 kv. and a current of 20 ma. (f,f?). The methods of recrystallization used were the same as those discussed and used in the last paper of this series (3). The majority of the steroids were recrystallized from ethyl alcohol, the exceptions being noted in Table I.

Figure 1. X-ray diffraction powder patterns of steroids Key found Table I

762 ANALYTICAL CHEMISTRY