1.3 minutes. Input and output time, including calculation of check peaks and conversion of roots to percentages, is from 1 to 1.5 minutes.
The calibration matrix stored in memory is in terms of pattern coefficients, permitting easy correction of individual coefficients. The number and selection of equations to be solved for each sample are under the control of the mass spectrometrist. Residual peaks are computed for all equations in the original matrix to provide a check on both the accuracy of the algebra and the analysis of the sample. Input data are punched one peak per card and may be loaded in any order. Output data are punched one
component per card in a format suitable for use as a final report. Only peaks required for the analysis or for delta peak checks need to be included in the input data. The accuracy of the analysis is the same as mould.be obtained by inversion of the matrix for each sample, but computing time is much less. ACKNOWLEDGMENT
The author wishes to express his gratitude and appreciation to 1%’.JV. Leutert, hI. E. Le Prohn, J.W. Leonard, L. Penn, and Paul Work for their invaluable assistance in the preparation of this program.
LITERATURE CITED
(1) Berrv. C. E.. Wilcox. D. E.. Rock. ~,-I
S. M.:’ Washb;rn, H.‘ W., J: A p p l : Phys. 17, 262-72 (1946). (2) Burke, 0. W., Starr, C. E., Tuemmler, S. D., “Light Hydrocarbon Analysis,” p. 73, Reinhold, New York, 1929. (3) Dennis, L. M., Nichols, M. L., ‘(Gas Analysis,” p. 98, Macmillan, New York, 1951. (4) Householder, A. S., “Principles of Numerical Analysis,” p. 48, McGrawHill, New York, 1953. (5) Ibid., pp. 73-8. (6) Sweeney, D. W., “IBM Library Routines for the 650,” No. 5.2001, Matrix Inversion Routine.
RECEIVEDfor review March 3, 1959. Accepted RIay 14, 1959. ASTM Symposium on Mass Spectrometry, Los Angelea, Calif., May 1959.
Quantitative Determination of the Four Maior Phases of Portland Cement by Combined X-Ray and Chemical Analysis 1. E. COPELAND, STEPHEN BRUNAUER, D. 1. KANTRO, EDITH G. SCHULZ, and C. H. WEISE P orfland Cement Association Research and Development laboratories, Skokie, 111. ,A method was developed for evaluating the quantities of the four major compounds or phases (tricalcium silicate or alite, /3-dicalcium silicate or belite, tricalcium aluminate, and the ferrite phase) in portland cements by a combination of x-ray quantitative analysis and chemical analysis. Twenty portland cements of widely differing compositions, including all five types, were analyzed. The average composition of the ferrite phase was close to that of tetracalcium aluminoferrite (or brownmillerite). The cements investigated contained practically no glassi.e., material amorphous to x-rays. The material called glass or glassy phase by cement chemists was found to b e microcrystalline to x-rays. The systematic difference between Bogue’s potential compound values and the values given in this paper is negligible for tricalcium silicate and the ferrite, but Bogue’s method underestimates dicalcium silicate and overestimates tricalcium aluminate. The potential values are reasonably good, except for tricalcium aluminate. Microscopical analysis gives good values for tricalcium aluminate, but underestimates the three other phases.
of the composition. of portland cements has al\va\-Lq been a problem basic to the needs of KNOWLEDGE
the cement cheniist. The complexity of the cement system is such that, in spite of the long history of cement chemistry, until now no method has been devised for direct and accurate determination of the four principal compounds or phases in portland cement: tricalcium silicate, p-diealcium silicate, tricalcium aluminate, and calcium aluminoferrite. Prior to the present investigations, two methods had been developed for estimating portland cement compositions: the method of Bogue (2) (with its modifications) and microscopical analysis. The first is indirect; the composition is not measured, but is calculated on the basis of the amounts of calcium oxide, silicon dioxide, aluminum oxide, and ferric oxide obtained by chemical analyses. The Bogue method employs three assuniptionsnamely, the cement clinker attains complete crystalline equilibrium in the kiln, the ferrite phase is brovvnmillerite or tetracalcium aluminoferrite, 4Ca0&03 Fez03, and all aluminum not in the ferrite phase occurs as tricalcium aluminate, 3 C a 0 .A1203. A consequence of the last assumption is that the two silicate phases are taken to be pure tricalcium silicate, 3 C a 0 . SOz, and pure 6-dicalcium silicate, 2 C a 0 . Si02. The Bogue method, or the “potential” compound calculation, has proved very useful through the years. Important
modifications ha\ e been proposed by Lea and Parker (9, 10) and Dahl ( 7 ) , bared on assumptions of particular conditions for clinkering and cooling. Investigations by Yamauchi ($1) and Swayze (20) have shown that the ferrite phase is not necessarily tetracalcium aluminoferrite, but a member of a solid solution series ranging in composition from 2Ca0 Fez03 to 6Ca0 2A1203.FezOs. Recently, hIidgley ( 1 4 , 16) reported the determination of the composition of the ferrite phase in portland cement by a n x-ray method similar to one of those ured in the present investigations; he came to the conclusion that portland cements contain ferrites of differing conipoeitions. If the composition of the ferrite phase is other than 4Ca0 A1203 Fe205, as the experiments of the above investigators indicate, the Bogue method can *till be applied with appropriate modifications, as was shown by Dahl (20). The only means available until now for the direct determination of the principal compounds in portland cement was quantitative microscopical analysis. I n a n exhaustive study of 21 portland cement clinkers, Brown (3) found that the ratio of the microscopical value to the potential value ranged from 0.85 to 1.24 for tricalcium silicate, from 0.34 t o 1.21 for dicalciuni silicate, from 0.20 to 0.89 for tricaleium aluminate, and from 0 25 to 1.20 for the ferrite phase VOL. 31, NO. 9 , SEPTEMBER 1959
0
1521
(reported as 4Ca0. A1203. Fez03), The errors in the microscopical analysis were discussed in detail by Brown; the greatest error came from inability to measure the smallest particles accurately with a light microscope. The x-ray method described overcomes this difficulty, in that reflected x-ray intensity is measured, which is independent of particle size. It determines not only the amount but also the composition of the ferrite phase. I n a basic investigation of the chemistry of the hydration of portland cements, it is important to know the composition of the cement as accurately as possible. The present investigations have been aimed to achieve this goal by combining the data of chemical analysis with the method of quantitative x-ray analysis developed by Copeland and Bragg ( 5 ) . PORTLAND CEMENTS
The investigations were carried out on 20 portland cements. Twelve of these \yere chosen from the group of 21 “long-time study” (LTS) cements. Of the remaining eight cements, four were “special basic research” (SBR) cements, two were special Belgian (B) clinkers, furnished by W. L. DeKeyser and A. van Bemst of the University of Brussels, and two were Lone Star Cement Co. (LS) cements furnished by M. A. Swayze of that company. These last two cements were specially designed to contain no tricalcium aluminate. The history and scope of the longtime study project have been described by McMillan and Tyler (IS), and the manufacture of the test cements by McMillan and Hansen ( I d ) . The chemical analyses of these cements have been published by Lerch and Ford ( I I ) , whose data were used in the present investigations. The SBR cements were some of a group used by Powers and Brownyard (18) in investigations of the physical properties of hardened portland cement paste. The chemical analyses of the Lone Star and Belgian cements were furnished with the cements. OUTLINE OF METHOD
To obtain calibration data, tricalcium aluminate, four different compositions of the ferrite solid solution, and 11 alite-belite mixtures were prepared. Alite and belite are tricalcium silicate and pdicalcium silicate, each containing a small amount of alumina and magnesia. The compositions of the ferrite phase were 2Ca0 Fe203, 6Ca0 A1203 2Fe203,4Ca0 Fe203, and 6Ca0 281208.Fe&. The alitebelite mixtures ranged in composition from almost 100% alite to almost 100% belite.
1522
ANALYTICAL CHEMISTRY
The calibration data for the determination of the amount of tricalcium aluminate, the amount of ferrite, and the composition of the ferrite were obtained by using artificial portland cements of known compositions. In each cement, a.known amount of the 1 to 1 alite-belite mixture was used, to which known amounts of tricalciuni aluminate and one of the ferrites were added. Three different proportions of tricalcium aluminate to ferrite \$ere employed. Sixteen artificial cements were prepared, and to each a known amount of silicon was added to serve as an internal standard. The determinations were made by means of the strongest x-ray diffraction lines of tricalcium aluminate and of the ferrite phase, a t 2.71 and a t about 2.65 A,, respectively, using the 3.14-A. line of silicon as an internal standard. Suitable equations were set up to express the relationships between line intensities and percentages of the components, and the constants of the equations were evaluated from the data obtained for the artificial cements. Knowing the constants, the unknown percentages of the two components and the unknown composition of the ferrite phase in actual portland cements were obtained from the x-ray diffraction line intensity data combined with the ferric oxide content, known from chemical analysis. I n an alternative method, the position (d-spacing) of the strongest ferrite line and the ferric oxide content of the portland cement were used for determining the composition and amount of the ferrite phase. In the determination of the silicates, a somewhat different method was followed. Every line of tricalcium silicate or alite sufficiently intense for x-ray quantitative analysis overlaps a 6dicalcium silicate or belite line; consequently, only lines containing both alite and belite contributions could be used. The lines a t 2.20 and 1.77 A. were selected, and again the 3.14-A. silicon line was used as the internal standard. A suitabIe calibration equation was set up to relate the ratio of the intensities of the above alite-belite lines to the fraction of alite in a silicate mixture, and the constants of the equation were evaluated from the data obtained for the 11alite-belite mixtures. Knowing the constants, the unknown alite-belite ratio in a portland cement could be determined from the x-ray data. This ratio, combined with the calcium oxide content of the two silicates, gave the alite and belite ccntents of the portland cements. The available calcium oxide was obtained by subtracting from the total calcium oxide the calcium oxide in tricalcium aluminate, the ferrite phase, calcium sulfate, and free lime. In an alternative method, the alite and belite contents were ob-
tained by combining the ratio with the available silicon dioxide content, which n-as taken to be the total silica in the cement minus the insoluble residue. PREPARATION OF MATERIALS
All compounds were prepared from the purest available reagents, C.P. or certified reagent grade. The reaction mixtures were heated repeatedly a t the proper temperatures in platinum dishes in a Lindberg G-10 furnace. After each burn, the material was ground to pass a U. S. Standard No. 400 sieve. The preparation was considered complete when x-ray diffraction and microscopical examination showed little or no unreacted oxide or intermediate compound. Even then, if the diffraction lines of the product r e r e not sharp, another burn vas made. The final patterns consisted of sharp diffraction lines, indicating products having well developed crystals. The methods of preparation of tricalcium aluminate and the ferrite phase, in general, followed the directions of the various investigators whose work has been summarized by Bogue (1). The tricalcium aluminate and tetracalcium aluminoferrite were obtained from the Portland Cement Association Fellowship a t the National Bureau of Standards. Three other ferrites were prepared: 2CaO. Fez03, 6Ca0 A1203 2FeaO3, and 6Ca0. 2AlaO8.Fe2O3. The first required two, the others three burns, 1 hour each; the temperatures were in the vicinity of 1375” C. The preparations were sintered hard but not fused; 6Ca0 2A1203 FezOs may have fused very slightly. The tricalcium silicate and dicalcium silicate phases of portland cement each contain small amounts of impurities. These impurities stabilize the tricalcium silicate phase in a form known as alite, having a structure slightly different from that of pure tricalcium silicate. The impurities also stabilize the dicalcium silicate phase in its 8modification. This phase is often called belite. Jeffery (8) investigated the crystal structure of alite having the composition 54Ca0. 16Si02.A12Oa. MgO, which corresponds to the substitution of one alumina and one magnesia molecule for two of every 18 silica molecules. In the first phase of the present investigations, alite and several alite-belite mixtures were prepared from calcium carbonate and ground quartz to which amounts of alumina and magnesia were added to correspond to the composition found by Jeffery, and some boric oxide was added to stabilize the belite phase. In all preparations but that highest in belite, some tricalcium aluminate was also formed in the reaction, which did not diminish with subsequent burns. The fact that less tricalcium aluminate was present in preparations n-ith high belite contents indicated that
some of the alumina, and probably some magnesia as well, was going into the belite phase. Nurse (17) pointed out that neither alumina nor magnesia is able to stabilize p-dicalcium silicate. These conclusions have been confirmed experimentally by the present authors. HOKerer, Nurse did not consider stabilization by alumina and magnesia combined. This combination is a n excellent stabilizer, and this may be the way in which the dicalcium silicate phase in portland cement is stabilized in its p-modification. As a result of the observations on the first set of alite-belite preparations, a second set was prepared, having the same range of compositions, but no added boric oxide. Instead, enough alumina and magnesia JTere added to correspond to a replacement of two of every 54 silica molecules in both alite and belite. The dicalcium silicate phase was completely stabilized in the p-form in every case. The silicate mixtures, like the ferrites, were made from their component oxides, and not by separate preparation of alite and belite and subsequent mixing. Because no really pure alite and belite could be prepared, the composition of each had to be determined. If alite and belite had simply been mixed, the error in their compositions would have entered as a systematic error into the compositions of all mixtures. Separate preparation and determination of the compositions of the mixtures ensured randomizing of errors. The starting materials were subjected to a preliminary heating a t 1050" C. for 1 hour to drive off carbon dioxide. The reaction mixtures were ground and pressed into pellets inch in diameter and l/z inch long. This was repeated after each burn. Each burn was 1 hour long, a t 1450' to 1500" C. Alite, belite, and nine silicate mixtures, having alitebelite ratios of approximately 25: 1, l O : l , 6:1, 3:1, 2:1, 1:1, 1:2, 1:2, and 1:6 were prepared. The alite, 25:1, l O : l , and 1:6 mixtures each required four burns; the others required three burns. APPARATUS
The diffraction patterns were obtained with a North American Philips Geiger counter dzractometer, or, for the determination of some of the ferrite dspacings, with a North American Philips step scanner. The radiation was CuKa, obtained from a tube operated a t 40 kv. and 20 ma. The optical system contained a 2' divergence slit and 0.006 inch receiving slit. Each chart was scanned over the range 43'28 to 26'20, a t a scanning speed of 1lSQ20 per minute; thus, the scanning time required for each chart was 2 hours 16 minutes. All diffraction patterns were recorded on Brown chart paper No. 6279SR, having full scale width of 10 inches. The chart paper speed was l/* inch per minute, so the diffraction pattern was,
recorded at a scale of 1'20 per inch. Under these conditions, the diffraction peaks as drawn were neither too small nor too cumbersome for convenient planimetric integration. The areas under the peaks were measured with an Ott planimeter. PREPARATION OF SAMPLES FOR X-RAY MEASUREMENT
The silicon used as an internal standard was Fisher's technical grade, fused, assaying 97 to 98% Si. The lumps were ground to pass a U. S. Standard No. 200 sieve. All samples used for x-ray analysis were mixed in a 10 to 1 ratio with silicon, except in the case of the calibration of tricalcium aluminate for measurement of small amounts occurring in the alite-belite preparations. For this purpose, tricalcium aluminate-silicon mixtures were prepared having weight ratios 4:1, 2: 1, and 1:1. All mixtures were prepared by the vibratory ball-milling procedure described by Copeland and Bragg (6). I n the ferrite-silicon mixtures, the silicon served as an internal standard for d-spacing as well as intensity measurement. The 3.138-A. silicon line was used as an intensity standard and both this line and the 1.920-A. silicon line were used as d-spacing standards. The correction to the measured ferrite d-spacing was interpolated from the values necessary to correct the measured d-spacings of the standard lines. I n some preliminary work, potassium bromide was used as an internal standard for intensity measurements. The diffraction line used was that a t 3.30 A. Because only one half as much potassium bromide as silicon is required to give a line of about the same height as the 3.14-A. silicon line, 20 to 1 weight ratio mixtures of sample to potassium bromide had to be used. I n addition, the 3.30-A. potassium bromide line is narrower than the 3.14-A. silicon line, and hence the integrated intensity of the potassium bromide line is lower. Although the over-all results obtained with potassium bromide were not much different from those obtained with silicon, the internal precision was sufficiently poor to warrant selection of a more suitable internal standard. However, potassium bromide was as satisfactory as silicon as a standard for d-spacing measurements. For this purpose, the lines a t 3.300 and 2.333 A. were used, and the corrected ferrite d-spacings were obtained as described for the silicon standard case. CALIBRATION PROCEDURE A N D DETERMINATION OF TRlCALClUM ALUMINATE A N D CALCIUM ALUMINOFERRITE
The tricalcium aluminate contained 0.25% uncombined calcium oxide, determined by a modification of Franke's method (19). Three of the ferrites contained no observable amounts of impurities; 6Ca0 2A1203 Fez03 contained a very small amount of calcium
aluminate, which was deemed negligible in the calculations. The ratio of the intensity of an x-ray diffraction line of one component of a mixture to the intensity of a diffraction line of another component of the mixture is proportional to the weight ratio of those components (5),or
La!!! lo WQ
(1)
where Z refers to an intensity and u: to the weight fraction (or percentage) of a component of the mixture, and a IS a proportionality constant. The intensity ratio, Il/Io, is equal to the ratio of the areas under the respective diffraction peaks. A (2) lo Ao Let the subscript 0 refer to the internal standard and the subscript 1 to the substance to be measured. When the area ratio is determined for mistures of known composition, the value of a can be calculated by Equation 1. In some preliminary investigations, values of a were determined for tricalcium aluminate and each of the four ferrites from measurements on binary mixtures of each substance with potassium bromide. The 2.71-A. line for tricalcium aluminate, the main peak of the doublet a t about 2.65 A. for the ferrite, and the 3.30-A. line for potassium bromide ryere used. The tricalcium aluminate and ferrite contents in several cements were then determined, using potassium bromide as internal standard. The tricalcium aluminate values nere determined by a simple application of Equation 1. The determination of the ferrite content n a s complicated by the fact that the coniposition of the ferrite phase was unknown. A method of successive approximations was developed which gal e values for both composition and content. It was assumed that all the ferric oxide in the cement was in the ferrite phase, and that all ferrites had compositions of the form 2(m n)CaO mA1203 nFez03. Utilizing these assumptions and a curve showing the variation of a with AI2O3/FezO3ratio, a unique set of values could be obtained for any cement. A careful consideration of the values obtained by this method led to the conclusion that there was a systematic overestimation of tricalcium aluminate, a systematic underestimation of ferrite, and, because of the assumptions used, an underestimation of the A1203/Fe203 ratio in the ferrite. The cause for thwe inaccuracies is the variable amount of overlapping of the ferrite and tricalcium aluminate lines, discussed by Brownmiller ( 4 ) . The x-ray d i f h c tion patterns of the four ferrite prepamtions are shown in Figure 1. The
+
VOL. 31, NO. 9, SEPTEMBER 1959
1523
Figure 1. X-ray diffraction patterns calcium aluminoferrites
of
strongest line is a doublet, and the positions of both peaks of the doublet depend upon the composition of the ferrite phase, I n Figure 1, the location of the diffraction maximum for tricalcium aluminate is also indicated. As can be seen, the smaller component of the ferrite doublet can be to the right, superimposed upon, or to the left of the tricalcium aluminate peak, depending upon the composition of the ferrite. To prepare the diffraction charts for planimetric integration, the total area due to both tricalcium aluminate and ferrite was divided into two parts, as shown in Figure 2. One part was the area under a nearly symmetrical line whose breadth and height lvere, n-herever possible, determined by the peak appearing a t 2.71 A. When no definite peak appeared, a line was constructed having its maximum a t 2.71 A. The height of the maximum !vas taken as the height of the trace a t 2.71 A. after the contribution of the adjacent alite-belite line had been deducted. The breadth of the line u-as based on that of well defined tricalcium aluminate lines appearing in portland cement patterns. The area under the 2 . 7 1 4 . line, the dashed peak in Figure 2, contained the entire tricalcium aluminate contribution, and in addition, some from the ferrite. The remainder of the total area, that enclosed by the dotted line, was due entirely to ferrite. The amount of area to be subtracted from the first part, to leave only the tricalcium aluminate contribution, depended on the composition of the ferrite phase and the amounts of the ferrite and tricalcium aluminate phases present. I n view of these considerations, Equation 1, vhen applied to the determination of tricalcium aluminate, was written in the form PA
=
POP[RA - f(v)RFl
(3)
u here Pa and POare the weight fractions (or percentages) of tricalcium aluminate and internal standard, respectively; p is the value of l / a for tricalcium aluminate; RA and RF are the uncorrected intensity (or area) ratios of the lines a t 2.71 and at about 2.65 A. to the 3.14A. line of the silicon internal standard, respectively; and f(v) is a factor which depends on Y, the molar A1203/Fe203 ratio in the ferrite. The term f(v)RFis the amount that must be subtracted from RA to leave only the amount that represents the tricalcium aluminate. The true functional dependence of f ( v ) on Y is not known; therefore, a suitable empirical relationship was assumed. The relationship selected was a quadratic 1524
ANALYTICAL CHEMISTRY
I _ a _ . r-- 2- -
28
30
BRAGG
Figure 2.
32
ANGLE, 2
34
-
e
Construction of tricalcium aluminate and ferrite phase areas
expression in V . reprecenting actually the first three terms in a n infinite power series, the higher order terms of which mere deemed negligible. On this basis, Equation 3 becomes PA =
pop
[RA-
(TO
f
TIV
f r z u 2 ) R ~(4) ]
\\ here T ~ T, ~ and , T~ are the coefficients In the quadratic expression. The determination of ferrites reqnires a further modification of the form of Equation 1. The factor a is not a constant, but a variable depending on V. The equation for ferrite determination is of the form
P F = poBl(V)
IRF
+
g2(J’)RAl
(5)
here P p and Po are the weight fractions (or percentages) of ferrite and internal standard, respectirely; RF and R A have the same meanings as in Equations 3 and 4; and gl(v) and gz(v) are the A1203/Fe203 ratio-dependent factors. g l ( v ) replaces a in Equation 1. @ ( V ) R A 1s the correction to be added to the ferrite intensity ratio, R F . It is positive bec u s e some of tEe area belonging to fwrite is in the tricalcium aluminate region. As in the case of f(v) in Equation 3, quadratic expressions \\-ere used for SI(.) and g 2 ( v ) , so that Equation 5 became
IT
f’F
PO(U0
+
[RPf
UIY
(PO
f
U2V2)
+
f PIV
P2V2)RA4]
(6)
To evaluate the parameters of Equations 4 and 6, i t is necessary t o have calibration mixtures, the diffraction charts of which show the same kind of overlapping as is found in cement charts. This mas accomplished with mixtures containing known amounts of all four of the major cement compounds. Each mixture consisted of a quantity of the 1 to 1 alite-belite preparation t,o which had been added amounts of tricalcium aluminate, one of the four ferrite preparations, and the internal standard, silicon. Sixteen such mixtures were made (Table I, columns 2 to 5 ) . The molar A1203/Fe203ratio, Y, for the ferrite in each mixture is given in column 6, and the average values of the uncorrected tricalcium aluminate and ferrite ratios. RA and R F , are given in columns 7 and 8, respectively. The numbers in parentheses beside the intensity ratio values give the number of charts used to obtain the average value in each instance. The parameters in Equations 4 and 6 were evaluated from the data in Table I, columns 4 to 8, by the method of least squares. The values for the parameters of the tricalcium aluminate and ferrite equations are the first two groups of values given in Table 11. The calculation of these parameters and most of the calculations described subsequently were greatly facilitated by
Table 1.
Compositions and Average Relative Intensities of Ferrite-Tricalcium Aluminate Calibration Mixtures
hIixture DesigBelite, nation Awe, yo yo 41.5 41.5 B-42 42.0 42.0 B-37 41.0 41.0 B-46 41.5 41.5 B-41 B-49 43.5 43.5 42.0 42.0 B-39 39.0 39.0 B-51 41.0 41.0 B-47 41.5 41.5 B-40 43.5 43.5 B-48 42.0 42.0 B-36 39.0 39.0 B-50 41.0 41.0 B-44 41.5 41.5 B-43 42.0 42.0 B-38 41.0 B-47 41.0
Alumi- Ferrite, nate, To Yo 5.0 12.0 10.0 6.0 3.0 15.0 5.0 12.0 10.0 3.0 10.0 6.0 12.0 10.0 15.0 3.0 5.0 12.0 10.0 3.0 10.0 6.0 10.0 12.0 15.0 3.0 12.0 5.0 6.0 10.0 15.0 3.0
the use of a small electronic digital computer. The value of v in a portland cement was obtained from the ferrite data. After v was obtained, its value was substituted in Equation 4, which was then solved for PA, the tricalcium aluminate content. Calculation of the amount of ferrite presents a problem. If v is known, Equation 6 may be solved for PF. If v is not known, then because there are two unknowns, a second equation must be obtained which can be solved simultaneously with Equation 6 to obtain values for both Pp and Y. However, Equation 6 is a 4th degree equation in Y, and consequently not readily solved. Because of this, a n approximation was made to reduce Equation 6 to a simpler form, amenable t o solution. Inasmuch as preliminary work showed that the value of v usually did not deviate very far in either direction from unity a Taylor expansion of Equation 6 about a v value of unity was made. All series terms higher than 2nd order in v were neglected. The resulting approximation of Equation 6 is
Pi+’= PO[(UL
+
UiV
(Pi
f U;V2)RF
+d V +
+
PP;Y2)RAl
(7)
The values of the parameters in this equation are in the third group of numbers given in Table 11. The value of v can be obtained in two ways. The first is from the position of the stronger component of the ferrite doublet, the (200) line. For the compounds 2 C a 0 . Fe203, 6Ca0 A1203 .2Fe203, 4 C a 0 . A1203 Fe203, and 6Ca0 .2A1203 Fe203, the d-spacings obtained were 2.680, 2.656, 2.645, and 2.632 A., respectively. Newkirk and Thwaite (16), on samples of the same compounds prepared by themselves, obtained the values 2.680, 2.654, 2.644, and 2.631 A., respectively. If the molar ratio A1203/ (A1208 Fe203)in the ferrite is plotted against d-spacing, a straight line is
+
0 0 0
RA 1,061(3) 0.691(5) 0.756(3) 0.996(5) 0.481(31
1.0 1.0 1.0 1.0
0.374(3) 0.884(4) 0.417(3) 0.559(7 ) 0.932(5)
Y
0.5 0.5 0.5 0.5 0.5
1.0
2.0 2.0
2.0
Table II.
0.531(4) 0.374(3)
RF 0.105(3) 0.314(5) 0.453(3) 0.269(5) 0.426(3) 0 476(3) 0,417(5) 0.555(3) 0.341(4) 0.566(3) 0.485(7 ) 0.499(5) 0 751(5) 0 222(3) 0.472(4) 0.555(3)
Parameters for the X-Ray Analysis Equations
Tricalcium Approximate Aluminate Equation Ferrite Equation (Eq. 4) (Es. 7 ) ParamParameter eter symbol Value symbol Value P 1.459 UO’ 2 920 1.143 UI; -2.111 TO 71 -1.327 US, 0.978 0.444 0.152 72 0,024 0.072 P2/ Alite-Belite Ferrite Equation Equations (Eqs. 18 and 19) 0%.6) ParamParameter eter symbol Value symbol Value uo 2.920 A -0.0464 Ul -2.111 B 0.1850 u2 0.978 C -0 0298 ‘p0 0.043 a 0.1462 ‘p1 0.093 p 0 1368
2
‘p2
-0.078
obtained, fitting both sets of data very well, A1203/(A1203 Fe203)= 36.884 13.76 d (7a)
+
where d is the d-spacing in A. For a n y cement, the d-spacing of the (200) line, therefore, gives a value of V, designated v d . Midgley (14) published curves for the d-spacings of the (200) and (202) reflections as functions of the ferrite composition. The agreement between his values for the (200) line and the values given above is not good. The uncertainty in the determination of V d becomes significant when there is insufficient ferrite in the cement to produce a distinct diffraction peak, or, as pointed out by Midgley, when the ferrite phase is not homogeneous Consequently, an alternative method for the determination of v has also been used. The same assumptions are emVOL. 31, NO. 9, SEPTEMBER 1959
* 1525
Table 111. Mixture Designation B-28 B-69 B-70 B-63 B-64 B-61 B-58 B-63 B-63a B-59 B-60
Sominal Description
Compositions of Silicate Mixtures
Alite,
Tricalcium Free Aluminate, Magnesium Calcium Belite, 70 70 Oxide, 70 Oxide, yo
73.9 65.5 49.6 32.9 32.8 14.2 0.6
3: 1
2: 1 1:l 1:2 1:2
1:6 Belite
25.2
33.4 49.0 66.4 65.9 84.7 98.6
0.4 0 6
1 .o
0.4
0.8 0.6 0.5
0.1
0.4
0.1
0.4
0.2 0 1 0.1
0.1
0.1
ployed as in the original potassium bromide experiments-namely, that all the ferric oxide in the cement is in the ferrite phase, and that a n y ferrite may be represented by the general formula 2(m n)CaO . rnAl2o3.nFe203. I n this case, the following relationship is obtained
0.3
0.2
0.3 0.3 0.2
x-ray quantitative analysis. Calibration for the latter analysis was obtained with binary mixtures of tricalcium aluminate and silicon. The value of a in Equation 1, obtained from the binary mixtures, was exactly the same as the value of l / p in Equation 3, obtained from mixtures containing ferrite, alite, and belite in addition. PF = [kiY k21W.7 (8) I n the calculation of the composition where k, and kz are the molecular weight of alite, belite, and each of the silicate ratios 2Ca0 Fez03/Fez03 and 2Ca0 .mixtures, i t was assumed on the basis .41&,/Fez03, respectively, and W F is of Jeffery's work (8) that one molecule of aluminum oxide and one molecule of the weight fraction (or percentage) of Fez03 in the cement, obtained by chemmagnesium oxide together replaced two molecules of silicon dioxide. The aluical analysis. Equation 8 may be mina in the silicates was the difference derived as follows. By definition between the total alumina used in the preparation and the alumina in the nA y = tricalcium aluminate. The magnesia nF in the silicates was taken as the molar equivalent of the alumina in the siliwhere nAand nFare the number of moles cates, The total magnesia used in the of and Fe203, or of 2Ca0.A1203 preparation minus the magnesia in the and 2Ca0 Fe203, per gram of cement, silicates mas assumed to be uncombined respectively. Furthermore magnesium oxide. The compositions = WF/MF (8b) of the silicate preparations are given in Table 111. where is the molecular weight of The simultaneous determination of Fe203; and from Equation 8a alite and belite in portland cement is TLA = vnF = P W F / M F ( 8 ~ ) complicated by the fact that every alite line sufficiently intense for x-ray quantiThe amount of ferrite per gram of cetative analysis overlaps a neighboring ment is belite line, and vice versa. The general PF = ~ A M C A 7lFfifcF (8d) theory of x-ray quantitative analysis presented by Copeland and Bragg where 414cA and M c p are the molecular (6) includes the treatment of overlapweights of 2 C a 0 . A1203 and 2 C a 0 . Fe203, ping lines as a special case. respectively. Substituting, we obtain I n the alite-belite system, the diffraction lines selected were those at 1.77 and 2.20 A. The former, in the case which is Equation 8. of alite, is a strong line, while in the Equations 7 and 8 may be solved case of belite, the line is weak; hence the simultaneously to give values of Y total diffraction intensity per gram of and P F . The v value thus obtained is total silicates varies strongly with the designated ul. relative amounts of alite and belite. The tricalcium aluminate may be calBoth alite and belite show an equally culated by means of Equation 4 using strong line at 2.20 A.; as a result, the either v d or vi. total diffraction intensity per gram of total silicates is not very sensitive to CALIBRATION PROCEDURE AND the relative amounts of alite and belite. DETERMINATION OF ALITE A N D BELITE The two equations which relate the intensities of composition are Alite, belite, and the silicate mixtures were analyzed for uncombined calcium Ri = O ~ I X I 012x2 (9) oxide by the modified Franke method (19), and for tricalcium aluminate by Rz = Pixi PZXZ (10)
where R1 and R2 are the intensities of the 1.ii- and 2.20-A. lines, relative to the 3.14-A. silicon line, respectively, 01, QIZ, P I , and 62 are proportionality constants, similar to a in Equation 1, and xl and x2 are the weight ratios of alite and belite to silicon, respectively. The quantity R2 is not sensitive to the relative amounts of alite and belite, but the quantity R1/R2,or R3, which is the ratio of the intensity of the 1.77-8. line to that of the 2.20-A. line, varies with the alite-belite ratio strongly. Consequently, Equation 10 was replaced by
The weight fractions of alite and belite in the total silicates are given by
+
w1
+ +
1526
ANALYTICAL CHEMISTRY
21 22
21
+
and
+
+
=
22
w2
=
2,2
respectively. Since the sum of w1 and u 2is unity, substitution of Equations 12 and 13 in Equations 9 and 11 leads to Ri -= 21
+
(a1 22
-
adw1
+
a2
and
Using Equations 14 and 15, the four parameters of the system were evaluated by the method of least squares. However, when the values of Rl/(zl Q) were plotted against wl, the points ciid not fall on a straight line, as Equation 14 would predict it, nor did a plot of R3us. w1give a good fit. To obtain a better fit lvith the experimental data, Equation 9 was replaced by
+
+
+
Ri = ~ ( 1~ I W I ) X I
+
~ ( l W W Z ) X Z (16)
where y1 and y2 are constants. Equation 10 was retained for R2. Combining Equation 16 with Equation 10 gives for
RdRz,
Dividing Equation 16, as xell as the numerator and denominator on the XZ, right side of Equation 17, by x1 and substituting Equations 12 and 13, one obtains
+
-R1 21
+
22
-
ad1
+
YIW1)WI
+4 1+ y2w2)w2 (164
(17a)
It can be seen from Equations 12
The quantity, PA', is the difference between the total alumina in the portland cement and the alumina in the tricalcium aluminate and the ferrite phases. I n deriving Equation 24, all of PA' was considered a part of alite. Thus, it was assumed that alite consists of 3CaO. s i o z plus 6Ca0. A1203 MgO, and belite consists of 2 C a 0 . SiO,. The amount of alite per gram of cement is Pa = Pat 0 2
0 ,
0,
01
0 4
Alitc
0 6
01
Fraction of Toto1 S i l i s o l e s ,
08
09
ID
u,
Figure 3. Dependence of ratio of intensities of 51 ' 2 8 line to 41 '28 line on relative amounts of alite and belite in silicate calibration mixtures
Pg and 13 that wI = 1 - wz; consequently Equations 16a and 17a can be rearranged to give quadratic equations in w2,
+ ? - +- +- R1 = 0 + 201lYl)U' + z2 (16b) + + - + 201l-n + R,@2 + BiRa = 0 (17%)
-
(WYl
cY2YZ)wi
012
(011
011y1
011
21
[a,
cY?j.,W
-(01,-,1
PJlWZ
012
alYl
Aw;
+ ( B + C R ~ ) W- ~ + PRa Q
=
0 (19)
where now the system is described by five parameters. Parameters A , B , C, a , and p represent the quantities - (alyl cy2Y2), (cy1 - a2 2aIY14 (P? - P l ) , (a1 alyl),and PI, respectively. The five constants of Equations 18 and 19 were evaluated by the method of least squares, and their values are given as the last group of numbers in Table 11. Using these constants, a plot of R3 vs. w1 is shown in Figure 3 as the solid line, together with the experimental points. Although both Equations 18 and 19 are needed for suitable evaluations of the five parameters, only Equation 19 is needed for evaluation of the alite and belite contents in portland cements, when the chemical analysis is known. The solution of Equation 19 for w2 is
++
obtained as the difference between the total calcium oxide in the cement, from chemical analysis, and the amounts of calcium oxide in the tricalcium aluminate, calcium aluminoferrite, calcium sulfate, and free lime in the cement. The alite and belite contents are calculated from T , with the aid of the equations
a1
By redefining constants, these equations can be m i t t e n
+
(20) The ratio of alite to belite, r , can be obtained from to2
The alite and belite contents can be calculated from the value of T and the amount of calcium oxide or silicon dioxide in the alite and belite. The calcium oxide in the silicates is
(24a)
where Pal and Paifare the amounts of 3Ca0. SiOz and 6Ca0. A1203.MgO per gram of cement, respectively. The amount of belite, on the basis of Equation 23, is
0 0
+ Pall
=
(Pat
+ Pa")/?
(24b)
The amount of silica per gram of cement is
+
PS = pPa1 9Pg (240) Combining Equations 24b and 24c and solving for Pa!give
To obtain the total alite, Pa>! must be added, according to Equation 24a. (23) where Pa and Pp are the weight fractions (or percentages) of alite and belite, respectively, Pc is the amount of calcium oxide in the alite and belite, and c and d are the molecular weight ratios 3Ca0/3Ca0 Si02 and 2Ca0/ 2Ca0 SiO2, respectively. The lime content of alite is cP,,the lime content of belite is ~ P B .Therefore, Pg = Pa/r
Pc = cPa
+ dPp
(224
and Equation 22 is obtained by substituting Equation 23 in 22a. As indicated by the definitions of c and d, the compositions of alite and belite are taken to be 3 C a 0 . Si02 and 2Ca0 Si02, respectively, for the purpose of this calculation. Both alite and belite contain alumina and magnesia in portland cements. However, the approximation used in Equation 23 introduces a negligible error only. Instead of using the lime available for the two calcium silicates, as above, the available silica, which is the total silica in the portland cement minus the insoluble residue, may be used. The equation is
pa^^ can be obtained from the relation
PA' by
(2G) where s is the molecular weight ratio 6Ca0. A1203.MgO/A1203. Thus, Equation 24e becomes Pa'' =
SPA'
lvhich is identical with Equation 24, since b = ps. If one assigns all of PA' to belite, instead of alite, a derivation similar to the above leads to an equation formally identical with Equation 24, but b is replaced by a constant b', which is the molecular weight ratio (SiOJ (4Ca0 A1203.MgO)/ (A12O3)(2Ca0. Si02). The value of b is 1.236, and that of b' is 1.254. The average value of PA' is 1.0%; consequently, bPA' = 1.24 and b'P,' = 1.25%. Since Ps ranges from 20 to 25%, the values of Pa and Po obtained by the two methods differ only by a few hundredths of 1%.
(24) where Pa and r have the same meaning as in Equation 22, Ps is the total silica available for alite and belite, Pa' is the alumina in the alite and belite, and b, p, and p are the molecular weight ratios @io2) (6Ca0. A1203, MgO)/(AlZO3) ( 3 C a 0 . SiO,), Si02/3CaO. Si02, and Si02/2Ca0.Si02, respectively.
FERRITE COMPOSITIONS AND CONTENTS OF PORTLAND CEMENTS
The ferrite compositions and contents of 20 portland cements were calculated in the two ways described earlier (Table IV, columns 2 through 5). For two of the 20 cements (LTS-42 and SBR15754) the simultaneous solution of VOL. 31, NO. 9, SEPTEMBER 1959
1527
Equations 7 and 8 for v1 and P F resulted in a complex number for vl-that is, the discriminant in the quadratic solution had a negative value. For these two cements, no values are reported in Table IV, columns 3 and 5. The average value of the molar A1203/ Fe203ratio in the ferrite and the average value of the ferrite content for the 20 portland cements are given in Table V, columns 2 and 3, respectively. For each of the 18 cements for which solution of Equations 7 and 8 for v1 gave real values, the value of Y given is the average of v d and vi. For the other two cements, only the Y d value is reported. Similarly, for these tn-o ceinents, only the ferrite contents calculated from Y d are reported, while for the other 18 cements, the ferrite contents
Table
IV.
are taken as the averages of the values determined from Y d and vl. A comparison of the ferrite contents given in Table IV, columns 4 and 5, with the averages given in Table V, column 3, shows that only one of the values deviates from the mean by more than 0.6%. The average deviation from the mean is 0.4%. Brown's microscopical determinations (3) were made on LTS clinkers, whereas the x-ray determinations were made on portland cements; consequently Brown's values were corrected to make them comparable with the x-ray values. The corrected microscopical analvses for ferrite are shon-n in column 4 of Table V. The microscopical values for glass content are shown in column 5 , Glass is included hecause Brown stated
Ferrite AI2O3/Fe203 Ratios and Ferrite and Tricalcium Aluminate Contents in Portland Cements
Aluminate Content Ferrite Content ( P F ) ,yo (PA), % Cement vd PI From P d From V I From V d From v i LTS-11 0 73 1.36 8 5 6.4 7.6 9.2 LTS-I 2 1.00 1.03 7.4 7.3 7.6 7.7 1.15 LTS15 70 8 1 9 5 0 82 10.3 0.93 LTS- 17 0.76 8.5 9 1 7.2 79 1.44 LTS- 18 1.04 7 1 7 1 7.6 8.3 0.74 LTS-23 3 0 2.7 14.5 0 64 13 8 IATS-25 0.80 0.85 13.9 0.0 13.6 0 3 I;TS-?,I 1.17 0 99 6.9 6 4 7.6 7 3 1.25 LTS-33 0.92 7.3 7.0 8.4 7.8 LTS-41 0.86 0.94 14.3 14.8 0.0 0.5 TiTS-42 1.16 ... 8.8 ... 1.3 ... LTR-51 0.76 0.92 9.0 9.4 0.2 0.9 ... 8.0 ... 6.9 ... SBR-15754 1.44 SBR-15622 0.71 0.91 11.1 12.3 0.0b 0.0b SBR-15497 0.90 0.83 7.5 7.3 8.9 8.8 SBR-13669 1.22 0.99 6.4 5.8 1. 0 0.6 LS-1 0.30 0.46 10.9 12 0 0 Ob 0.0b 1,s-2 0 30 0 44 10 3 11 3 0 Ob 0 Ob B-H 0 83 13 8 0 66 12 6 6 9 59 B-L 1 07 0 82 9 1 8 1 9 8 8 6 a Solution of equation resulted in complex number. Kegative result, interpreted as zero. .41-01/Fe203 Ratio
Table
V.
Average Compositions and Contents of Calcium Aluminoferrites in Portland Cements
1 .os
LTS-11
2.7
5.7
8.4
7.3
LTS-25 0.83 13.8 14.1 1.08 6.6 1.8 LTS31 LTS-33 1 09 7.9 4.1 I>TS-41 0 90 14.6 15.4 2.4 LTS-42 1.16a 8.8b 9.3 LTS-51 0 84 6.2 SBR-I 5754 1.44" 8.0b SBR-15622 0 81 11.7 SBR-15497 0.86 7.4 1.11 SBR-15669 6.1 11.4 0 38 LS1 LS-2 10.8 0 37 13.2 0 75 R-H 0.94 13-L 8.6 Value from d-spacing determination only. Value based on Y d only.
0.2 3.0 0.0 2.9 3.0 3.0
14.3 4.8 4.1 18.3 5.4 9.2
14.9
1528
0
7.4
ANALYTICAL CHEMISTRY
6.4
7.6
15.2 8.2
10.0 6.7
12.8
7.9 5.8
...
14.9 8.8
that no means of sharp distinction heh e e n glass and the ferrite phase was devised. The sums of the microscopical ferrite and glass cclntents are s h o m in column 6. KO microscopical values are given for any hut the LTS cements, as no reliable values \\ere available for the others. A comparison of columiis 3 and 4 shows that the microscopical values are smaller than the x-ray values in 10 caces and greater in t x o cases. If the microscopical ferrite and glass value; are added together (column 6), comparison with column 3 shons that still onlg three of the 12 cements have values which exceed the x-ray values. Thus, the microscopical analysis underestimates the ferrite content. The average discrepancv betveen columns 3 and 6 is 2.57,. Because the quantity of the ferrite phase determined by x-ray analysis exceeds the quantity of ferrite plus glass determined hy microscopical analysis, the indication is that there is very little or no glass-!.e., truly amorphous material-in the portland cements investigated. Most of the material that appears as glass in the microscope is crystalline to x-rays, in agreement Ivith Bronxmiller's obqervations (4). The breadths of the tricalcium aluminate and calcium aluniinoferrite lilies indicate microcrvstallinity. The potential compound compositions given in this paper for the LTS cements are not identical n ith those published by Lerch and Ford (11). because, in the present work, the oxide analyses of these cements were corrected for niinor oxides. I n their work, conform:ng to industrial practice. only the calcium oxide analyses were corrected, the correction being for free calcium oxide. The oxide analyses of the SBR cements were likewise corrected for minor constituents, but the LS cements nere corrected only for free CaO and CaS04. and the B clinkers only for free CaO, since complete analyses for minor constituents were not availahle. The potential values are shonn in column 7 of Table V (except for the two LS cements). .4 modification of the potential calculation of Dah1 (20) gives two ferrites (4Ca0. =11203. Fen03 and 2 C a 0 . Fe&) and no tricalcium aluminate for these cements. Table 17, column 2 , shows that the Y values for the 20 cements as determined by x-rays range from 0.37 to 1.44 and have a median value of 0.92. Disregarding the two loir est values, for cements especially designed to have no tricalcium aluminate the range of the ratio is from 0.69 to 1.44, and the median value is 0.96. Because the median is so close to unity for the cements and clinkers reported here, it is to be expected that the results of the x-ray and potential calculations will be in reasonably good agreement. This
is actually so (Table T‘, columns 3 and 7). The largest difference between the x-ray and potential values is 2.270, and the average difference is 0.7%. For eight of the 18 cements the difference is 0.5% or less. For eight cements the Y value exceeds unity and the x-ray value exceeds the potential value; for the 10 other cements Y is less than 1,and the x-ray value is smaller than the potential value. Midgley (14) reported a range of molar A120a/FeL03ratios in the ferrite phase of 30 British portland cements and clinkers. The median value for his data is 0.72. RiIidgley’s calibration data did not agree with those obtained in the present work. However, if the same calibration curve were used for both the British and American portland cements, the median values for Y would be almost the same. TRlCALClUM ALUMINATE CONTENTS PORTLAND CEMENTS
Table VI.
Tricalcium Aluminate Contents of Portland Cements
X-Ray Value, 8.4
Cement LTS-11 LTS-12 LTS-15 LTS-17
7.6
9.9
7.6
LTS-42 LTS-51
LS-1 1,s-2 B-H B-L a Based on
0.6 6.9‘ 0.0
Microscopical Analysis, Dark 3Ca0. A1,0, prismatic 2.3 3.0 3.0 5.5 1.2 8.3 2.7 4.1 2.4 0 5 0 3 42 2 7 0.9 1.0
0 4 0 0 0.0
70
Total 5.3
8.5 9.5 6.8
6.1
2.6 1.7 7 3 9.8 1 9 0 9 1.0
Potential Value, 7 ’ 10.8 11.3 10.1 9.1 12.3 2 3 3 .9 9 7
8.8 0.8 0.0 0.0 6.4 8.9
~d
9 6 3 7
29 2.6 12.4 3.2 9.4 1.9
7.1 9.4
value.
OF
The tricalcium aluminate contents were calculated in two B-ays from Equation 4 (Table IV, columns 6 and 7). The average values for tricalcium aluminate content are shown in Table VI, column 2. For the two cements which gave complex numbers for V I , instead of the averages, the results based on the v d values are given. Only one of the values deviates from the mean by more than 0.5%, and the average of the absolute values of the deviations is 0.4%. I n his microscopical analyses, Brown ( 3 ) determined a tricalcium aluminate phase and a “dark prismatic” phase separately, but he considered the latter also tricalcium aluminate. The values for these two phases are shown in Table VI, columns 3 and 4, and their sums in column 5. Comparison of columns 2 and 5 shows that the microscopical values are larger than the x-ray values in six and smaller in six cases; thus, there is no systematic difference. The largest discrepancy is 3.1Y0, and the average difference is 1.1%. The potential values for tricalcium aluminate are shown in Table VI, column 6. The calculation assumes that all alumina not in the ferrite phase is in the tricalcium aluminate phase. Actually, some of the alumina is in the silicate phases. If, therefore, the potential calculation gives approximately correct values for the ferrite phase, which seems to be the case, i t is bound to overestimate the tricalcium aluminate. A comparison between columns 2 and 6 of Table VI shows that this is so; the potential value is larger than the x-ray value in all cases except one. The average discrepancy is 2.295, the largest discrepancy is 5.5%, and in six cases the discrepancy is greater than 370. It appears, therefore, that the potential calculation does not give
Table VII.
Cement LTSl1 LTS-12 LTS-15 LTS-17 LTS18 LTS-23 LTS-25 LTS-31 IJTS-33 LTS-41 LTS-42 LTS-51 SBR-15754 SBR-I 5622 SBR-15497 SBR-15669 LS-1 LS-2 B-H B-L
Silicate Contents of Portland Cements Belite Content, O/c Alite Content, Yo X-Ray Value fificroX-Ray Value MicroBased on scopical Potential Based on scopical Potential CaO Si02 value value CaO Si02 value value 56 7 58 6 56 1 54 8 18 9 19 4 12 4 18 0 54 1 56 8 47 3 48 9 21 6 22 6 22 2 24 5 647 622 562 724 127 122 6 0 3 3 56 2 57 0 50 0 55 5 19 6 19 9 22 0 19 5 47 9 48 3 58 5 47 8 27 7 27 8 16 4 25 0 54 6 .56 6 .53 7 .56 4 22 5 22 8 21 8 18 8 37 5 38 7 40 9 37 0 40 5 41 8 35 7 36 9 604 610 598 607 147 148 6 8 124 576 561 676 622 172 168 4 0 104 26 2 27 2 25 6 23 2 47 8 49 5 50 0 48 2 29 6 29 6 29 4 29 7 53 8 53 8 52 8 52 7 45.4 47.8 38.7 44.6 38 8 39.9 43.5 36.3 51.7 53.6 48.5 23.3 24.1 22.8 24 7 .e1 9 53 3 52 6 29 3 30 0 8 9 63 6 14 4 14 0 59 2 57 8 56 8 29 3 57 3 57 4 29 5 29 6 13 4 13 7 69 3 71 2 ... 11.6 11.7 69 2 70 3 23 5 52.0 21.8 22.6 54.8 56.9 55.2 56 0 55 0 27 0 27.3 25 2
satisfactory values for tricalcium aluminate. SILICATE CONTENTS OF PORTLAND CEMENTS
If one calculates the alumina content of tricalcium aluminate and the ferrite phase and compares it with the total alumina obtained by chemical analysis, the latter is greater than the former for each of the 20 cements. The difference ranges from 0.1 to leg%, with an average of 1.0%. This “missing” alumina is in the silicate phases. One set of values for the tricalcium silicate or alite contents and the dicalcium silicate or belite contents of the 20 portland cements is shown in Table VII, columns 2 and 6, respectively. These values were obtained by using Equations 22 and 23. I n the derivation of those equations, the compositions of the alite and belite phases Ivere assumed to be 3Ca0 Si02 and 2 C a 0 . SiOz. respectively. Xevertheless,
the alumina and magnesia in the silicates were implicitly considered, because P c was calculated as the total lime available for alite and belite, and not merely as the lime available for the silicate parts of alite and belite. I n Equation 22 constants c and d involve the molecular weights of alite and belite. Instead, however, the molecular n-eights of 3Ca0 SiOz anti 2 C a 0 . SiO2 nere used. This introduces a slight error, because in a part of the alite and belite 2Si02 is replaced by AI2O3 RlgO. The magnitude of the error is such that the approximation reduces the sum of the alite and belite contents by about 0.1% for each 1% “missing” alumina; therefore the error is negligible. A4second set of values for the alite and belite contents of the 20 cements (obtained by using Equations 24 and 23) is given in Table VII, columns 3 and 7 . Whereas Equation 22 takes
+
VOL. 31, NO. 9, SEPTEMBER 1959
1529
care of the alumina and magnesia in the silicates in an implicit manner, Equation 24 does i t explicitly. A comparison of columns 2 and 3, Table VII, shows that the alite values obtained by using Equation 24 exceed the alite values obtained on the basis of Equation 22 by 0.4%, on the average A comparison for belite (columns 6 and 7 ) leads to a similar conclusion, also with a difference of 0.4%. The agreement between the two sets of values is very good. If the alite values obtained by the two methods are averaged, the deviation from the average is greater than 1% for only two of the 20 cements. The deviation from the average belite values is less than 1%for all 20 cements. For 16 of the 20 cements (LTS and SBR cements), analytical data are available not only for the four major oxides-namely, CaO, Si02, A1203, and F e z o r b u t also for the minor oxidesnamely, SOa, MgO, NazO, K20, PzOa, TiOs, and hln203. Most of the magnesia constitutes a separate phase, periclase, though some of it is in the alite and belite. Besides A1203 and MgO, some silicates were reported to contain FeO, Fe203, MnO, and P205; alkalies were found in tricalcium aluminate and belite, Mn& in ferrite, etc. ( I , 8,9, I?‘). One can calculate the amounts of the minor oxides that are not in the four major phases, and thus arrive on the basis of the data of chemical analysis at a value for the sum of the major phases for each of the 16 portland cements. This can be compared with the sum of the values reported in this paper. The ferrite and tricalcium aluminate values are reported in Table V, column 3, and Table VI, column 2, respectively. If one uses the alite and belite values based on total available lime (Table VII, columns 2 and 6), the sum of the four major phases calculated from the oxide data of chemical analysis exceeds the sum of the values reported by 1.2%, on the average. If, however, one uses the alite and belite values based on total available silica plus missing alumina (Table VII, columns 3 and 7 ) , the sum of the oxides exceeds the values reported here only by 0.5%, on the average. Neither Equation 22 nor Equation 24 considers the contributions of the minor oxides, except magnesia, to alite and belite. It is clear, therefore, that even Equation 24 should underestimate the alite and belite contents; and i t does, However, the underestimation in this case is small. I n the following comparisons with the microscopical
1530
ANALYTICAL CHEMISTRY
and potential values, the alite and belite values based on Equation 24 are used. A comparison of columns 3 and 4 of Table VI1 shows that microscopical analysis tends to underestimate alite, in eight of the 12 cases the x-ray value being larger. Similarly, a comparison of columns 7 and 8 shows that microscopical analysis underestimates belite, the x-ray values being larger in nine of t,he 12 cases. Microscopical analysis underestimates the ferrite phase. These results are not too surprising, since the optical microscope may miss the smallest particles of each of these phases. Partly because of this, the agreement between the two methods is not very good for the silicates, the average difference being 4.6% for alite and 6.0% for belite. A comparison between columns 3 and 5 of Table VI1 shows t h a t the x-ray values for alite are larger than the potential values for 11 out of 18 portland cements. However, the systematic difference is negligible-less than 0.1%. A similar comparison between columns 7 and 9 shows that the x-ray values for belite are larger than the potential values for all but one portland cement. The systematic difference is 3.5%, on the average. The agreement between the x-ray and potential methods is not too bad; the mean of the absolute values of the differences is 3.6% for alite and 3.6% for belite. The average alite content of the 20 cements and clinkers investigated is 51.5%, as determined by x-rays (Table VII, column 3). The average discrepancy of 3.6% between the x-ray and potential values is 7y0 of the average alite content. The average belite content for the 20 cements is 28.0% (Table VII, column 7 ); thus, the discrepancy of 3.6% is 13% of the average belite content. The average ferrite content is 9.6% (Table V, column 3); the discrepancy of o.7yOis 7% of the average ferrite value. Finally, the average tricalcium aluminate content, not counting the two LS cements, is 5.1% (Table VI, column 2) ; the discrepancy of 2.2% is 43% of the average value. The conclusion is that the potential calculation gives, on the average, reasonably good values for the major phases, with the exception of tricalcium aluminate.
ments and suggestions, to L. S. Brown for microscopical examination of the materials used for calibration, to E. E . Pressler for free lime determinations, to Elaine Anderson and Tao-nan Chang for a part of the x-ray analysis, and to I. L. Tyler, T. C. Powers, W. L. D e Keyser, A. van Bemst, and M. A. Swayze for providing the portland cements and clinkers used in these investigations.
LITERATURE CITED
(1) Bogue, R. H., “Chemistry of Portland Cement,” 2nd ed., chap. 17, Reinhold, New York, 1955. (2) Bogue, R. H., IND.ENG. CHEM., ANAL.ED. 1, 192 (1929).
(3) Brown, L. S., J . Am. Concrete Znst. 19 (May 1948) ; Proc. 44,877 (1948). (4) Brownmiller, L. T., Am. J . Sci. 35, 241 (1938). (5) Copeland, L. E., Bragg, R. H., ANAL. CHEM.30, 196 (1958). (6) Copeland L. E., Bragg, R. H., ASTM Bull. 228 (hebruary 1958). (7) Dahl, L. A., Rock Products 41,48 (September), 46 (October), 42 (November), 44 (December 1938); 42, 68 (January), 47 (February), 50 (April 1939). (8) Jeffery, J. W., Proc. Third International Symposium on the Chemistry of Cement, London, 1952, p. 30, Cement and Concrete Association, London, 1954. (9) Lea, F. M., “Chemistry of Cement
and Concrete,” rev. ed., St. Martin’s Press, New York, 1956. (10) Lea, F. M., Parker, T. W., Budding Research Tech. Paper No. 16 (1935). (11) Lerch, W., Ford, C. L., J . Am. Concrete Inst. 19, 95 (1948); Proc.
44, 745 (1948). (12) McMillan, F. R., Hansen, W. C., J . Am. Concrete Inst. 19, 441 (March 1948); Proc. 44,553 (1948). (13) McMiUan, F. R., Tyler, I. L., J . Am. Concrete Znst. 19, 553-61 (February 1948); Proc. 44, 441 (1948). (14) Midgley, H. G., Mag. Concrete Research 10,No. 28, 13 (March 1958). (15) Midgley, H. G., Proc. Third Inter-
national Symposium on the Chemistry of Cement, London, 1952, p. 140, Cement and Concrete Association, London, 1954. (16) Newkirk T., Thwaite, R., J . Research Natl. Bur. ktandards 61,233 (1958). (17) Xurse, R. W., Proc. Third International Symposium on the Chemistry of Cement, London, 1952, p. 56, Cement and Concrete Association, London, 1954. (18) Powers T. C., Brownyard, T. L., J . Am. boncrete Znst.. Proc. 43. 306
ACKNOWLEDGMENT
The authors express their sincere appreciation t o M. A. Swayze, L. T. Brownmiller, Fred Ordway, Katharine Mather, T. C. Powers, and J. B. Alexander for their most helpful com-
RECEIVED for review February 11, 1959. Accepted May 25, 1959.
