Quantitative X-ray diffraction analysis (QXDA)

QXDA of a mixture of phases is based on the fact that the intensity of a particular reflection (area under a peak) is proportional to the volume fraction of the phase producing it. The proportionality constant is determined by the crystal structure of the phase, the sample and equipment geometry, and the level of X-ray absorption occurring in the mixture. A weighed proportion of an internal standard is interground with the sample to eliminate the ‘practical factors’ associated with specimen preparation and exposure to x-radiation in the diffractometer. Ratios of the intensities of the selected reflection from each component of the clinker (or cement) to a chosen reflection for the internal standard are determined and calibration curves, prepared with synthetic reference samples of each of the clinker minerals, are used to convert intensity ratios for the unknowns into mass fractions. The internal standard chosen should provide a reflection close to those of the clinker minerals but not

overlapping them. Rutile (TiO2) or silicon are frequently chosen and the

reflection used for rutile is indicated in Fig. 4.3.

Cooperative inter-laboratory exercises have revealed the limitations of this conventional single-peak method in QXDA of clinker and cement,

although it can give acceptable results for C3A for which the peak at

33.25º 2 is used. Aldridge (1982) reported results obtained using

chemical (Bogue), microscopic and single peak QXDA for the phase analysis of six commercial clinkers and the corresponding cements in eleven laboratories. Between-laboratory standard deviations found for alite contents, ranging from 45 to 75% in the six clinker samples, and the cements (values in brackets) were: Bogue 3.6 (2.2); microscopy 3.4;

QXDA 8.9 (7.2). For C₃A contents (range 5–10%) in the same clinkers

and cements these methods gave: 0.8 (0.4); 2.0; and 2.1 (2.1), respectively. Within-laboratory standard deviations were mostly from 0.4 to 0.8 times between-laboratory values. The only between-laboratory standard deviations considered acceptable were those for chemical analysis (Bogue). The higher standard deviations observed for clinkers than for cements were attributed to greater sampling errors.

The principal sources of error in conventional QXDA (other than equipment and sampling) are considered to be:

(a) reference clinker phase used in the preparation of a calibration curve does not have the same composition/structure as that in the sample being analysed and also there may be more than one polymorph present in the sample being analysed;

(b) difficulty in locating the base line in peak area measurement;

(c) the use of a weak peak for a phase such asC₂S because its strong

peaks overlap with those of other phases;

(d) poorly standardised and over-grinding which can affect clinker constituents and internal standard differently;

(e) preferred orientation of crystallites;

(f) phase segregation during sample preparation.

Attempts to overcome the first three problems have involved a change from single to multi-peak (whole pattern) methods. They require accurate qualitative identification of the phases present in the unknown. A computer is used to create and match by a least-squares procedure weighted data for the reference phases identified and the digitally recorded diffraction pattern from the sample being analysed. Refinements can be introduced to allow for line broadening effects, such as crystallite

size, and for background radiation as a function of 2. Gutteridge (1984)

created a database of diffraction patterns recorded over the range 24–39º

2 for 10 alite, 6 dicalcium silicate, 4 C₃A and 10 ferrite compositions,

together with a further 19 patterns for minor phases which can be present. Most of these have been incorporated into the JCPDS files (Joint Committee on Powder Diffraction Standards).

A second method uses published basic crystallographic data, for the phases identified in a sample of clinker or cement, to calculate the proportions of each which give the best fit of calculated and observed

diffraction patterns over a wide range of 2 values. The method of

breaking down (deconvoluting) composite peaks was originally devised by Rietveld (1969) for neutron diffraction and adapted subsequently for QXDA. Its wider use has been made possible by the increasing application of computers since about 1990. The essential feature of the method is the simultaneous, interactive calculation of a least-squares fit and diffraction pattern refinement (Young, 1993). Programmes available permit the introduction of line broadening effects and the variation in background intensity. To obtain meaningful results by this technique requires high quality equipment and a high level of theoretical and experimental technique.

Taylor and Aldridge (1993) obtained root mean square deviations between Rietveld and optical microscopy in the quantitative analysis of six cements as: 2.1% for alite, 3.1% for belite, 1.7% for the aluminate, and 1.3% for ferrite. Neubauer et al. (1997) reported acceptable

correlations between the contents of alite, belite, free lime and C3A +

ferrite determined by Rietveld analysis, and those obtained by microscopy for twelve samples of commercial clinker taken from a single production line. However, poorer correlations were obtained for five samples from a second plant using waste oil and sewage as partial coal replacements. Since computers are capable of making the calculation within two or three minutes, the potential of the method is being examined for quality and possibly process control in cement plants (Mo¨ller, 1998).

4.5 Electron microscopy

Transmission electron microscopy (TEM) is regarded as a research method of value in the investigation of composition and defect structure of clinker particles at the highest levels of resolution and electron diffraction can be used to confirm phase identity. In the examination of microstructure, extremely thin specimens are required and they are produced by ion beam thinning of sections prepared in the usual way (Groves, 1981). TEM has been used to examine defects in alite crystals (Hudson and Groves, 1982) and twinning in belite (Groves, 1982). It has also been of considerable value in the examination of hardened cement pastes (Section 8.2) although the sample must be liquid nitrogen cooled at the ion beam milling stage and extreme care is required in minimising exposure to the electron beam in the microscope to avoid damage (Richardson and Groves, 1994). Scrivener (1997) pointed out that it is vital that samples examined by TEM are characterised by other methods to ensure that the small amount of material which can be examined is representative.

The initial application of scanning electron microscopy (SEM) in the 1960s and 1970s to cement-containing materials made use of the secondary electrons emitted from the surface 10 nm of a sample when it is exposed to an electron beam. In the most modern instruments, resolution is of the order of nm compared with angstroms in TEM. A particularly wide range of magnifications (from 20 up to 200 000) is available, making possible the examination of the topography of fracture surfaces of hardened cement pastes, mortars and concretes at several levels (Fig. 8.1). Where the extreme drying conditions of very high vacuum are undesirable, an environmental cell or an environmental microscope (ESEM) can be used. An example described by Donald (1998) employs the differential pumping principle. While the electron gun

is maintained at 10 7 _{torr, the other sections of the microscope are}

maintained at progressively higher pressures with the specimen held at around 10–20 torr.