Quantitative analysis of mineralized white Portland clinkers: The structure of Fluorellestadite Isabel Pajares Instituto de Ciencias de la Construccio´n ‘‘Eduardo Torroja,’’ CSIC, C/Serrano Galvache s/n, 28033-Madrid, Spain A´ ngeles G. De la Torre Departamento de Quı´mica Inorga´nica, Cristalografı´a y Mineralogı´a, Universidad de Ma´laga, 29071-Ma´laga, Spain Sagrario Martı´nez-Ramı´rez, Francisca Puertas, and Marı´a-Teresa Blanco-Varela Instituto de Ciencias de la Construccio´n ‘‘Eduardo Torroja,’’ CSIC, C/Serrano Galvache s/n, 28033-Madrid, Spain Miguel A. G. Arandaa) Departamento de Quı´mica Inorga´nica, Cristalografı´a y Mineralogı´a, Universidad de Ma´laga, 29071-Ma´laga, Spain ͑Received 1 April 2002; accepted 15 July 2002͒

Fluorellestadite, Ca10(SiO4)3(SO4)3F2 , has been synthesized as single phase. This compound ϭ crystallizes in the type structure, s.g. P63 /m, with parameters a 9.4417(1) Å, c ϭ ϭ 3 6.9396(1) Å and V 535.76(1) Å . The refinement of its converged to RWP ϭ ϭ 12.33% and RF 4.58%. The atomic parameters have been used to analyze the phase content of mineralized white Portland clinkers. These clinkers contain Ca3SiO5 ,Ca2SiO4 ,Ca12Al14O32F2 and Ca10(SiO4)3(SO4)3F2 . The agreement between the elemental composition inferred from the Rietveld phase analysis and that measured by XRF is noteworthy. This comparison does not take into account the presence of amorphous phases and unmodeled elemental substitutions in crystalline phases. Similar Rietveld studies on commercial white Portland clinkers are also shown to be feasible. © 2002 International Centre for Diffraction Data. ͓DOI: 10.1154/1.1505045͔

INTRODUCTION below 1200 °C ͑Gime´nez and Blanco-Varela, 1995; Blanco- Varela et al., 1986͒. For the production of Portland clinkers, mineralizers It is of great importance to know the mineralogical com- and/or fluxes are often added to the raw mixes to accelerate positions of these clinkers in order to understand and predict reactions and enhance burnability. Traditional fluxes such as the mechanical strength of mortars or concrete elaborated Fe2O3 and Al2O3 have been partially substituted by the min- with these cements. So far, calculations with the method of eralizing pair CaF2 /CaSO4 to produce clinkers with low alu- Bogue ͑1929͒ are used to deduce the mineralogical compo- minate contents at temperatures between 1300 and 1400 °C sition by using the elemental content usually measured by ͑Gime´nez et al., 1991; Blanco-Varela et al., 1985, 1990; X-Ray Fluorescence ͑XRF͒. This method has well known Moir, 1982; Blanco-Varela et al., 1997; Wenxi et al., 1992͒. problems ͑Taylor, 1997͒ mainly due to the lack of thermody- The use of this mineralizing pair to partially replace alumi- namical equilibrium in the kiln. Hence, alternative analytical nates is particularly useful in manufacturing white clinkers, methods are being studied to measure the mineralogical because of the potential for energy conservation and seawa- compositions of clinkers and cements. Laboratory X-Ray ter resistance ͑Pajares et al., 2001͒. Powder Diffraction, LXRPD, is now widely used to carry out The phases that may be present in this type of mineral- quantitative phase analyses of crystalline mixtures ͑Hill and ized clinkers ͑Gime´nez and Blanco-Varela, 1995͒ are: alite, Howard, 1987; Bish and Howard, 1988; Madsen et al., 2001͒ ͓C3S, Ca3SiO5]; belite, ͓C2S, Ca2SiO4]; aluminate by using the Rietveld method ͑Rietveld, 1969; McCusker ͓C12A7 ,Ca12Al14O33] or a related compound ͓C11A7CaF2 , et al., 1999͒. The method compares the measured pattern and ͓ Ca12Al14O32F2]; and fluorellestadite 6CaO•3SiO2 that calculated with the crystal structures. This methodology ͑ •3CaSO4•CaF2 or Ca10(SiO4)3(SO4)3F2]. The alite rate for- has recently been applied to Portland clinkers De la Torre mation, in the presence of the mineralizing pair et al., 2001͒, aluminous cements ͑Guirado et al., 2000͒ and (CaF2 /CaSO4) is higher than that found for mixes mineral- calcium sulpho-aluminate cements ͑Schmidt and Po¨llmann, ͑ ͒ ized only with CaF2 Christensen and Johansen, 1980 . This 2000͒. The interest on the application of XRD to Portland ͑ faster rate for C3S is mainly due to the thermodynamic effect cements is recently increasing Goswami and Panda, 1999; of widening its stability range and the primary phase field of Taylor et al., 2000͒. crystallization. Additionally, ion mobility in the melt is en- On the other hand, in order to apply the Rietveld method hanced by CaSO4 and CaF2 as a new liquid phase appears to mineralized clinkers it is necessary to know the structure of fluorellestadite. Unfortunately, the crystal structure of this phase was not known although it can be prepared as a crys- a͒ Author to whom correspondence should be addressed: Departamento de Quı´mica Inorga´nica, Cristalografı´a y Mineralogı´a, Universidad de Ma´laga, talline single phase. Its powder pattern is present in the PDF ͑ ͒ 29071-Ma´laga, Spain, Phone: Intϩ34 952131874, Fax: Int Database JCPDS-ICDD with a hexagonal cell, s.g. P63 /m, ϩ ϭ ϭ ͑ 34 952132000, electronic mail: g–[email protected] of a 9.441 Å and c 6.939 Å Po¨llman and Neubauer,

281 Powder Diffraction 17 (4), December 2002 0885-7156/2002/17(4)/281/6/$18.00 © 2002 JCPDS-ICDD 281 TABLE I. Chemical analysis for the raw materials and mineralized clinker ͑%w/w͒.

Sample Sand Limestone Kaolin Gypsum Clinker-ECa Clinker-EAb Clinker-PAc

SiO2 89.43 3.79 57.72 - 1.68 23.04 22.25 26.2 Al2O3 5.11 0.75 27.94 - 0.00 2.61 2.70 1.05 Fe2O3 0.22 0.32 0.60 - 0.10 0.45 0.34 - CaO 1.46 53.76 1.12 - 37.86 67.73 69.06 69.3 MgO 0.42 0.35 0.98 - 0.07 0.53 0.88 -

SO3 0.00 0.00 0.00 - 40.05 2.75 2.98 2.50 K2O 0.93 0.11 0.23 - 0.05 0.32 nd - Na2O 0.11 0.22 0.11 - 0.08 0.29 nd - CaF2 - - - 99.9 - 2.28 nd 0.95 Lossd 2.30 40.70 11.29 - 20.11 - 0.48 - Ratioe 12.45 79.72 1.76 1.51 4.56 - - - a Expected composition for the mineralized clinker taking into account the raw materials ratio. b Elemental analysis of the mineralized clinker by XRF and expressed as oxide content. c Phase analysis of the mineralized clinker by the Rietveld method and expressed as oxide content. d Weight loss by heating at 1000 °C. e Raw materials ratio for the preparation of the mineralized clinker.

1993͒. The structure must be similar to that of apatite where White Portland clinker the phosphate groups are randomly replaced by silicate and A typical commercial white Portland clinker was sulphate tetrahedra and the hydroxyl groups are replaced by sampled from a factory and characterized by powder diffrac- ͓ the fluoride anions. In fact, a structure for ellestadite ap- tion. proximately Ca10(SiO4)3(SO4)3(OH)2] has been reported for a mineral from Cuba ͑Organova et al., 1994͒. This crystal was monoclinic but with the apatite framework and it con- LXRPD studies tained chloride anions and even a small amount of carbonate. The LXRPD pattern for FLELL was recorded on a The aim of this work is to determine the crystal structure Siemens D5000 ␪/2␪ diffractometer ͑flat reflection mode͒ by of fluorellestadite and use it for the quantitative analysis of ␣ ͑ ͒ using CuK 1,2 radiation 1.542 Å with a secondary curved the mineralized white Portland clinkers. graphite monochromator at 25 °C. The samples were loaded in an aluminum holder by sample-front pressing. The experi- mental details are given in Table II. The LXRPD data for a EXPERIMENT commercial white Portland clinker were collected as for the Fluorellestadite synthesis mineralized clinker but spinning the sample at 15 rpm to The raw materials used for fluorellestadite, FLELL, improve the particles statistics. (6CaO•3SiO2•3CaSO4•CaF2) synthesis were CaCO3 , CaSO4•2H2O, SiO2 and CaF2 with high purity grade in the stoichiometric ratio. The ground mixture was heated at RESULTS AND DISCUSSION 1000 °C for 2 h. Then, the sample was ground again in an The final goal of this work is the determination of the agate mortar and heated at 1000 °C for 32 h. To follow the mineralogical composition of mineralized white Portland synthetic procedure, free lime concentration was determined clinker by powder diffraction using the Rietveld methodol- by the ethylene-glycol method ͑UNE Standard 80-243-86, ogy. However, to do so, the structural information of all crys- 1986͒ giving 0.42% w/w of CaO. Routine LXRPD data in- talline phases is needed. As the crystal structure of FLELL dicated that the sample was a highly crystalline single phase. was not known, this structure was determined prior to the mineralogical quantification. Mineralized white Portland clinker preparation The chemical analysis of the raw materials used for the Crystal structure of Fluorellestadite preparation of the mineralized clinker is presented in Table I. FLELL crystallizes in an hexagonal cell, s.g. P63 /m, In order to get the required mineralizers content, the dosage PDF no. 45-0009, with edges very similar to those of the given at the bottom of Table I was selected. The resulting apatite type structure. Hence, the fluorapatite structure has silica modulus was 7.50 ͑% w/w͒. The raw materials were been used as starting model ͑Mackie and Young, 1973͒. The ground to particle size smaller than 45 ␮m except limestone powder pattern was analyzed by the Rietveld method with which was ground to particle size smaller than 125 ␮m. The the GSAS suite of programs ͑Larson and Von Dreele, 1994͒ mixes were hand homogenized, using ethanol as dispersive by using the pseudo-Voigt peak shape function ͑Thompson medium, taking great care to avoid any modifications of par- et al., 1987͒ corrected for axial divergency ͑Finger et al., ticle size and then dried. Cylindrical pellets of 2.5 cm diam- 1994͒. The background was fitted by linear interpolation eter and 1.5–2.0 cm length were prepared. The clinkering function. temperature was 1350 °C for1hinalaboratory furnace. The The P position in fluorapatite was substituted by Si and S 1 chemical composition of the clinker was determined accord- with 2 occupation factor for each type of atoms. Cell param- ing to UNE Standard 80-225-93 ͑1993͒. eters and the spatial atomic positions were refined. Finally,

282 Powder Diffr., Vol. 17, No. 4, December 2002 Pajares et al. 282 TABLE II. Data collection details and refined parameters for FLELL. better and so, the phase analysis gives more accurate results. First, the phases present in the synthetic clinker were identi- Soller slits 2 sets ͑ ͒ ͑ Divergence slit/mm 2 fied: C3S De la Torre et al., 2002 ,C2S Mumme et al., ͒ ͑ ͒ Antidivergence slit/mm 2 1995 ,C11A7CaF2 Williams, 1973 and fluorellestadite. The Receiving slit/mm 0.2 LXRPD multi-phase pattern was analyzed with the GSAS X-ray tube, V/kV and I/mA 40–30 suite of programs as above. Scale factors and unit cell pa- Step-size/°2␪ 0.03 ͑ ␪ rameters were refined for each phase and the positional and Angular range/°2 10–120 ͒ Sample spinner none thermal atomic parameters were NOT refined for any phase. Counting time/s/step 14 It is worthy to point out that the peak shape parameters for phases in low concentrations are unstable and usually hard to Chemical formula Ca10(SiO4)3(SO4)3F2 refine. In this case, a number of variables as low as possible a/Å 9.441 74͑9͒ c/Å 6.939 64͑8͒ should be used. Hence, only two parameters to describe the V/Å3 535.76͑1͒ pseudo-Voigt were used and only one parameter ͑LY͒ was M/g/mol 1003.25 refined for the phases in low concentrations. Alite presents Z 1 preferred orientation due to its large particle size. In this case ␣ No. reflections (K 1) 292 the effect was corrected using the spherical-harmonic correc- GW/0.01°2 5.8͑2͒ ͑ ͒ ͑ ͒ tion Von Dreele, 1997 . This method gives much better fits LX/0.01° 0.5 1 ͑ ͒ LY/0.01° 8.5͑3͒ for alite than the March–Dollase algorithm Dollase, 1986 . S/L 0.031 It used the cylindrical symmetry and the order of the spheri- H/L 0.016 cal harmonics was 10. The final texture index was 4.79 ͑1

RWP /% 12.33 texture index represents an ideal ‘‘random powder’’ and ϱ R P /% 8.85 stands for a single crystal͒. 4.58 RF /% The Rietveld plot for the mineralized white Portland clinker is given in Fig. 2. An enlarged view of the most informative part of the pattern is given in Fig. 3 ͑top͒ with the isotropic temperature factors were optimized. Preferred the peaks due to a given phase labeled. Details of the orientation was corrected by the March-Dollase algorithm ͑Dollase, 1986͒ along ͓001͔ direction and the refined param- Rietveld refinement of this pattern, including the phase eter was 0.978͑2͒. The pseudo-Voigt parameters were GW analysis, are given in Table IV. The phase content obtained ͑Gaussian part͒,LX(d*-independent Lorentzian part͒ and from the Rietveld analysis has been transformed to overall ͑ ͒ LY ( d*-dependent Lorentzian part͒. Some details of the elemental content expressed as oxides in Table I. However, FLELL refinement are given in Table II. one should exercise care when comparing these values with ϭ those expected from the dosage of the raw materials and The last refinement converged to RWP 12.3%, see Table II. The refined atomic positions and isotropic vibration those measured by XRF. In order to compare these numbers, temperature factors are given in Table III. The Rietveld plot the atomic substitution in the crystalline phases and the pres- is displayed in Fig. 1. The inset shows an enlarged view for ence of amorphous phases was neglected. This approxima- the fit in the high angle part of the pattern. Inter-atomic bond tion is coarse. However, under these constraints, the agree- distances range between 1.54 and 1.56 Å for Si/S–O bonds, ment in Table I is remarkably good. Some considerations can 2.39 and 2.85 for Ca–O bonds, and the Ca–F bond distance be drawn: ͑1͒ Overall CaO is always slightly overestimated is 2.30 Å. The angles for the tetrahedra (SiO4 or SO4) ranges in the Rietveld analysis as it includes the Ca/Mg substitution between 107.4 and 110.8° The structure of FLELL belongs which cannot be modeled. Consequently, MgO is not esti- ͑ ͒ to the well known apatite type structure, so no discussion mated. 2 Similarly, SiO2 is overestimated in the Rietveld will be reported. analysis as the Si/Al substitution cannot be taken into ac- ͑ ͒ count. Consequently, Al2O3 is underestimated. 3 The Phase analysis of the mineralized white Portland agreement for SO3 content is good and CaF2 is underesti- clinker mated in the Rietveld analysis probably due to the presence The sample was rotated during LXRPD data collection of amorphous fluorides which are the last crystallizing frac- as the particles statistic increases notably. The intensities are tion.

TABLE III. Refined atom parameters and thermal factors for Ca10(SiO4)3(SO4)3F2 .

2 Atom Wyck. pos. xyzUiso /Å O͑1͒ 6h 0.3234͑7͒ 0.4846͑6͒ 1/4 0.014͑2͒ O͑2͒ 6h 0.5865͑7͒ 0.4683͑8͒ 1/4 0.018͑2͒ O͑3͒ 12i 0.3385͑5͒ 0.2568͑5͒ 0.0709͑5͒ 0.022͑1͒ Sia 6h 0.3961͑3͒ 0.3684͑3͒ 1/4 0.012͑1͒ Sa 6h 0.3961͑–͒ 0.3684͑–͒ 1/4 0.012͑–͒ Ca͑1͒ 4 f 1/3 2/3 0.0016͑5͒ 0.031͑1͒ Ca͑2͒ 6h 0.2399͑3͒ 0.9920͑3͒ 1/4 0.022͑1͒ F 2a 0.0 0.0 1/4 0.026͑3͒

a The occupation factor is 0.5.

283 Powder Diffr., Vol. 17, No. 4, December 2002 Quantitative analysis of mineralized white Portland clinkers 283 Figure 1. Rietveld plot (10-120°/2␪) for fluorellestadite. The inset shows an enlarged view of the high angle part of the pattern.

Figure 2. Rietveld plot (20-70°/2␪) for the mineralized white Portland clinker.

284 Powder Diffr., Vol. 17, No. 4, December 2002 Pajares et al. 284 Figure 3. Selected region (28-35°/2␪) of the Rietveld plot for the mineralized white Portland clinker ͑top͒.Samese- lected region for a commercial white Portland clinker ͑bottom͒.

TABLE IV. Selected data for the LXRPD Rietveld refinement of the mineralized clinker.

Phase s.g. a/Å b/Å c/Å ␤/° V/Å3 GWa LY b w/w % ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ C3S Cm 33.058 4 7.0594 4 18.536 1 94.207 6 4314.1 7 12.8 9 16.7 6 72.3„3… ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ C2SP21 /n 5.509 2 6.756 2 9.313 2 94.41 2 345.6 1 5.0 – 39 4 15.1„7… ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ C11A7CaF2 I4¯ 3d 11.959 3 11.959 11.959 90.0 1710 1 5.0 – 25 8 2.1„3… ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ FLELL P63 /m 9.446 1 9.446 6.934 1 90.0 535.8 2 5.0 – 50 4 10.5„4… a S/Lϭ0.015 and H/Lϭ0.015 were used to describe the asymmetry due to axial divergence for all the phases. b GW is expressed in (0.01°)2 units. c LY is expressed in 0.01° units.

285 Powder Diffr., Vol. 17, No. 4, December 2002 Quantitative analysis of mineralized white Portland clinkers 285 Phase analysis of commercial white Portland clinker Gime´nez, S., Blanco-Varela, M. T., Palomo, A., and Puertas, F. ͑1991͒. The Rietveld analysis of a diffraction pattern for a com- ‘‘Production of low energy requirements cement. An industrial test,’’ Zement-Kalk-Gips 44, 12–15. mercial white Portland clinker manufactured without CaF2 Gime´nez, S. and Blanco-Varela, M. T. ͑1995͒. ‘‘Solid state phases relation- was carried out for the sake of comparison. This sample was ship in the CaO-SiO2-Al2O3-CaF2-CaSO4 system,’’ Cem. Concr. Res. simpler and it contained C3S, C2S and C3A. The phase 25, 778–782. analysis was carried out as described above and the most Goswami, G. and Panda, J. D. ͑1999͒. ‘‘Application of XRD in a rapid informative part of the Rietveld plot is given in Fig. 3 ͑bot- quality control system of cement,’’ Powder Diffr. 14, 114–117. tom͒. The results for white Portland clinkers, including the Guirado, F., Galı´, S., and Chincho´n, S. ͑2000͒. ‘‘Quantitative Rietveld analy- quantification of the non-diffracting part, will be reported sis of aluminous cement clinker phases,’’ Cem. Concr. Res. 30,1023– elsewhere. 1029. Hill, R. J. and Howard, C. J. ͑1987͒. ‘‘Quantitative phase analysis from neutron powder diffraction data using the Rietveld method,’’ J. Appl. Crystallogr. 20, 467–474. CONCLUSIONS Larson, A. R. and Von Dreele, R. B. ͑1994͒. ‘‘General Structural Analysis System,’’ Los Alamos National Lab. Rep. No. LA-UR-86-748. GSAS This paper reports the crystal structure of fluorellestadite program @ http://public.lanl.gov:80/gsas/. which belongs to the apatite type structure. This structure is Mackie, P. E. and Young, R. A. ͑1973͒. ‘‘Location of Nd dopant in fluora- used to quantify the mineralogical content of mineralized patite, Ca5(PO4)3F: Nd,’’ J. Appl. Crystallogr. 6, 26–31. white Portland clinkers. These clinkers contain C3S, C2S, Madsen, I. C., Scarlett, N. V. Y., Cranswick, L. M. D., and Lwin, T. ͑2001͒. C11A7CaF2 and fluorellestadite. Some guidelines for these ‘‘Outcomes of the International Union of Crystallography Commission type of Rietveld studies are presented. The agreement be- on powder diffraction round robin on quantitative phase analysis: tween the elemental composition inferred from the phase samples 1a to 1h,’’ J. Appl. Crystallogr. 34, 409–426. analysis and that measured by XRF is noteworthy taken into McCusker, L. B., Von Dreele, R. B., Cox, D. E., Loue¨r, D., and Scardi, P. ͑1999͒. ‘‘Rietveld refinements guidelines,’’ J. Appl. Crystallogr. 32,36– account the possible presence of amorphous phases. Similar 50. Rietveld studies on commercial white Portland clinkers are Moir,G.K.͑1982͒. ‘‘Mineraliser high alite cements,’’ World Cem. 374– also shown to be feasible. 382. Mumme, W. G., Hill, R. J., Bushnell-Wye, G., and Segnit, E. R. ͑1995͒. ‘‘Rietveld structure refinement, crystal chemistry and calculated powder diffraction data for the polymorphs of dicalcium silicate and related ACKNOWLEDGMENTS phases,’’ Neues Jahrb. Mineral., Abh. 169,35–68. This work has been supported by the FEDER 1FD97- Organova, N. I., Rastsvetaeva, R. K., Kuz’mina, O. V., Arapova, G. A., 0894 and PGC97-1144 research grants. S. Martı´nez-Ramı´rez Litsarev, M. A., and Fin’ko, V. I. ͑1994͒. ‘‘Crystal structure of low- thanks DGES ͑MEC͒ for the award of ‘‘Contrato de Incor- symmetry ellestadite in comparison with other apatitelike structures,’’ ´ Kristallografiya 39, 278–282. poracion de Doctores.’’ I. Pajares and A. G. De la Torre Pajares, I., Puertas, F., Blanco-Varela, M. T., Va´zquez, T., and Martı´nez- thank two studentships by MCYT and Junta de Andalucı´a, Ramı´rez, S. ͑2001͒. ‘‘Influencia del contenido de aluminatos en la apti- respectively. tud a la coccio´n, la hidratacio´n y el comportamiento meca´nico de ce-

mentos blancos mineralizados con CaF2 y CaSO4 ,’’ Cemento y Hormigo´n 825, 626–635. Bish, D. L. and Howard, S. A. ͑1988͒. ‘‘Quantitative phase analysis using Po¨llmann, H. and Neubauer, J. ͑1993͒. ICDD Grant-in-Aid. the Rietveld method,’’ J. Appl. Crystallogr. 21, 86–91. Rietveld, H. M. ͑1969͒. ‘‘A profile refinement method for nuclear and mag- ͑ ͒ Blanco-Varela, M. T., Va´zquez, T., and Palomo, A. 1985 . Spanish Patent netics structures,’’ J. Appl. Crystallogr. 2, 65–71. N° 54269. Schmidt, R. and Po¨llmann, H. ͑2000͒. ‘‘Quantification of calcium sulpho- ͑ ͒ Blanco-Varela, M. T., Va´zquez, T., and Palomo, A. 1986 . ‘‘A study of a aluminate cement by Rietveld analysis,’’ Mater. Sci. Forum 321–324, new liquid-phase to obtain low-energy cements,’’ Cem. Concr. Res. 16, 1022–1027. 97–104. Taylor,H.F.W.͑1997͒. Cement Chemistry, 2nd ed. ͑Thomas Telford, Lon- Blanco-Varela, M. T., Va´zquez, T., Palomo, A., Puertas, F., and Gime´nez, S. don͒. ͑1990͒. Spanish Patent N° 9001906. Taylor, J. C., Hinczak, I., and Matulis, C. E. ͑2000͒. ‘‘Rietveld full-profile Blanco-Varela, M. T., Palomo, A., Puertas, F., and Va´zquez, T. ͑1997͒. quantification of Portland cement clinker: the importance of including a ‘‘CaF and CaSO in white cement clinker production,’’ Adv. Cem. Res. 2 4 full crystallography of the major phase polymorphs,’’ Powder Diffr. 15, 9, 105–113. Bogue, R. H. ͑1929͒. Industrial Engineering Chemistry ͑Analytical Edition͒ 7–18. ͑ ͒ 1,192. Thompson, P., Cox, D. E., and Hasting, J. B. 1987 . ‘‘Rietveld refinement Christensen, N. H. and Johansen, V. ͑1980͒. ‘‘Mineralizers and fluxes in the of Debye-Scherrer synchrotron X-ray data from Al2O3 ,’’ J. Appl. Crys- clinkering process: Kinetics effects on alite formation,’’ 7th Inter. Cong. tallogr. 20, 79–83. Chem. Cement ͑Paris͒ II, I-1-I-16. UNE STANDARD 80-243-86. ͑1986͒. ‘‘Me´todos de ensayo de cementos. De la Torre, A. G., Cabeza, A., Calvente, A., Bruque, S., and Aranda, M. A. Determinacio´n del o´xido de calcio libre; me´todo del etilenglicol.’’ G. ͑2001͒. ‘‘Full phase analysis of Portland clinker by penetrating syn- UNE STANDARD 80-225-93. ͑1993͒. ‘‘Me´todos de ensayo de cementos. chrotron powder diffraction,’’ Anal. Chem. 73, 151–156. Ana´lisis quı´mico. Determinacio´n del dio´xido de silicio (SiO ) reactivo ͑ ͒ 2 De la Torre, A. G., Bruque, S., Campo, J., and Aranda, M. A. G. 2002 . en los cementos, en las puzolanas y en las cenizas volantes.’’ ‘‘The superstructure of C S from synchrotron and neutron powder dif- 3 Von Dreele, R. B. ͑1997͒. ‘‘Quantitative texture analysis by Rietveld refine- fraction and its role in quantitative phase analyses,’’ Cem. Concr. Res. ment,’’ J. Appl. Crystallogr. 30, 517–525. 32, 1347–1356. Wenxi, H., Guanglliant, X., and Zhongyuan, L. ͑1992͒. ‘‘The effect of Cal- Dollase, W. A. ͑1986͒. ‘‘Correction of intensities for preferred orientation in powder diffractometry: application of the March model,’’ J. Appl. Crys- cium Fluorsulpho-Silicate on Formation of Calcium Silicate,’’ 9th Inter. ͑ ͒ tallogr. 19, 267–272. Congr. Chem. Cem. New Delhi , 2, 379–385. ͑ ͒ Finger, L. W., Cox, D. E., and Jephcoat, A. P. ͑1994͒. ‘‘A correction for Williams, P. P. 1973 . ‘‘Refinement of the structure of powder diffraction peak asymmetry due to diaxial divergence,’’ J. Appl. (CaO)11(Al2O3)7CaF2 ,’’ Acta Crystallogr., Sect. B: Struct. Crystallogr. Crystallogr. 27, 892–900. Cryst. Chem. 29, 1550–1551.

286 Powder Diffr., Vol. 17, No. 4, December 2002 Pajares et al. 286