There are many data points on Fig. In addition to the possibility of experimental errors, the most important explanations are:. The horizontal dotted-line arrow indicates the layer spacing of the C-S-H. The horizontal dashed-line arrow indicates the layer spacing of the C-S-H. They did however state that the method of synthesis and sample preparation might also be a factor, and Figs. Whilst these studies have provided valuable additional insight into the structure of C-S-H I phases, a significant drawback of the methodologies is that none of them attempted to refine the atom positions, essentially because of the lack of information in the diffraction data.
The refinements were therefore restricted to the lattice parameters, site occupancy, crystal size, preferred orientation and, in the case of Grangeon, Claret, Lerouge et al. Unfortunately, crystal-chemical problems will occur in the absence of atom-coordinate adjustment if the lattice parameters are changed by more than only a small amount. This is a particularly serious issue if the C-S-H I phase that is of interest has a layer spacing that is significantly larger or smaller than the starting model. An increase or decrease in the c parameter results in expansion or compression of the central Ca—O core of the structure and so it is important that this issue is addressed if crystal-chemically sensible distances and coordinations are to be retained in the model structure.
Tobermorites have layer structures that are classified by the interlayer distance. The structures in both families consist of layers of Ca—O polyhedra that have silicate chains clasped to each side that are kinked to produce a repeat of three tetrahedra, i.
Additional Ca ions and water molecules occur in an interlayer space. The BT of adjacent layers share an O atom and so the Dreierketten are linked, forming double chains that run parallel to b. Additional interlayer water molecules are present in the expanded interlayer. Formula 1 is a generalized structural—chemical formula for single-chain tobermorite or C-S-H I. Aluminium is the main substituent in those phases and so it is included together with charge-balancing ions; Al-substituted C-S-H is referred to as C-A-S-H.
There are four main-layer Ca atoms for every six tetrahedral sites. The formula for double-chain tobermorites or, indeed, for cross-linked C-A-S-H phases is. Formulae 1 and 2 can be combined to represent a mixture of single- and double-chain phases. In this formula, d represents the fraction of double-chain structure, i. These formulae and the equations that are given below are applicable to C-A-S-H phases in general.
Values for the variables in formulae 1 — 3 can be determined by experiment, although in practice problems can arise where samples contain more than one phase. These shifts are further influenced by the replacement of Si by Al.
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Double-chain tobermorites also have Q 3 0Al and Q 3 1Al sites. The assumption that Al cannot substitute for Si at paired sites is well supported by a number of experimental studies on single-chain structures Richardson, Brough et al. Schematic diagram that illustrates the nature of the linear aluminosilicate chains in C-S-H.
The unfilled triangles represent Si—O tetrahedra and the shaded triangle represents an Al—O tetrahedron. Al substitutes for Si only at bridging sites and paired sites cannot be vacant. The actual minimum and maximum values of f are dependent on the fraction v and distribution of vacant sites. The fraction of vacant tetrahedral sites that are present in double- or single-chain tobermorite or C-A-S-H can be calculated from 29 Si NMR data using equation 4.
In this equation — and those that follow — Q n m Al represents the relative intensity of a peak determined from the deconvolution of a 29 Si single-pulse MAS NMR spectrum assuming that the spectrum was collected using quantitative conditions. In the case of double chains, MCL corresponds to the average number of linked tetrahedra in sections of the chains along b that are separated by vacant sites, and thus includes paired Q 1 and Q 2 tetrahedra, and bridging Q 2 and Q 3 tetrahedra, the Q 3 being cross-linked with other bridging tetrahedra.
The MCL and the fraction of vacant tetrahedral sites, v , are related simply by. So for example, since one third of all tetrahedral sites are bridging sites, if all of the bridging sites were vacant, and ; i. If one half of the bridging sites were vacant, then and ; i. Whilst such short chains are not relevant to the crystalline tobermorite phases, they are relevant to the C-S-H I phases and also to tobermorite-based models for the C-S-H that forms in hardened cements. The fraction of vacant tetrahedral sites can therefore be calculated from the MCL using.
The fraction of tetrahedral sites that are occupied by Al can be calculated from 29 Si NMR data using. If Al ions are present at the bridging site as well as Si, then site occupancy factors for Si and Al are. Values for SOF BT can be calculated from NMR data by first calculating v and f using equations 4 and 8 and then substituting these into equations 10 — It can therefore be calculated easily from 29 Si NMR data by substituting for v.
C-S-H I preparations that are free of Al [ i. Data for preparations that have Q 3 tetrahedra or unreacted silica are not included and those that contain crystalline Ca OH 2 are represented using square symbols. The positions for silicate chains of finite length are indicated; i.
It is evident from Fig.
The area bounded on Fig. This is just an alternative way of representing the information in Fig. It is evident that the data for these synthetic C-S-H I preparations broadly follow the diagonal dotted line that is plotted on Fig. This line represents the equation.
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This situation is also represented by a dotted line on Fig. The data are from Chen et al. The dotted line in both parts of the figure represents equation The variation in the silicate anion structure that is represented by equation 15 is perhaps more easily envisaged if the equation is recast in terms of SOF BT. The data in Fig. Brunet et al. Any model or models for the structure of C-S-H I must therefore account for dimeric structure over most of the compositional range, i.
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The data are from: Chen et al. Square symbols indicate preparations that contain crystalline calcium hydroxide. The bold unfilled diamonds represent the model structures that are developed in this paper. The dotted line represents equation 16 , i. Any model for the structure of C-S-H I should be crystal-chemically plausible. Some general crystal-chemical principles can be established by inspection of the structures of related phases for which crystal structures have been reported.
It is evident that 2.
There are a small number of Ca atoms coordinated to eight oxygen atoms, but none to fewer than six, which is an important observation for atomistic modelling studies that are concerned with C-S-H. There are three sets of points for each value of connectivity: the middle set shows the average of the average distance present in the phases; the upper set represents the average of the maximum distance; and the lower set represents the average of the minimum distance. It is evident that the average Si—O distance in a silicate tetrahedron present in a calcium silicate hydrate decreases linearly with increasing connectivity of the tetrahedron.
The average value of the minimum distance decreases rather more rapidly than that of the average distance, whilst the average of the maximum distance is essentially constant, although there is much scatter in the data. These data indicate that the silicate tetrahedra in calcium silicate hydrates become increasingly distorted as the connectivity of the tetrahedra increases. Results from the analysis of the crystal structures of 35 crystalline calcium silicate hydrates and related phases the references are given in the caption to Fig. A good linear correlation also exists between the volume of the Ca—O polyhedra and the average Ca—O coordination number [Fig.
The details of the 16 model structures that are developed in this section are deposited 2 in a CIF file.
Datablock names from the CIF are referred to throughout the text and figure captions. The end-members of the dotted line on Fig. It is therefore necessary to first develop models for these two end-member structures. The faces of the interlayer Ca—O polyhedra are not shaded. Whilst the interlayer Ca atoms are coordinated to an appropriate number of O atoms, in both cases they are in distorted trigonal prism coordination — which is evident in Figs.
Dimeric structures can also be generated easily from an orthotobermorite that has silicate chains where the bridging tetrahedra are adjacent to one another instead of staggered, but they suffer from the same Ca-coordination issue. Two alternative hypothetical dimer structures derived from a staggered-chain orthotobermorite. In both cases, the space group is B 11 b No. The unit cell is indicated by black dotted lines. Just the silicate chains and interlayer Ca atoms are shown perpendicular to the b axis in b and e and along the c axis in c and f.
The Ca-coordination problem that is encountered with the orthotobermorite models derives from the fact that the silicate chains that are clasped to successive Ca—O main layers are directly adjacent to one another i. The problem is resolved by using clinotobermorite as the starting structure instead of an orthotobermorite. The structure of a hypothetical dimer that is derived from a clinotobermorite structure that has bridging tetrahedral sites that are adjacent to one another is shown in Fig.
In contrast to the orthotobermorite, in this case the chains that are on successive main layers are not directly adjacent to one another, as shown in Fig. This change in the position of the silicate chains results in the interlayer Ca atom being in octahedral coordination, which is evident in Fig.
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The c parameter for this structure is set at a compromise value for the Ca—O distance and polyhedral volume: the average Ca—O distance for the interlayer Ca atom is slightly longer than the ideal value for sixfold coordinated Ca 2. A hypothetical dimer derived from a clinotobermorite that had BT that were adjacent to one another. The relationship of the interlayer Ca with the silicate tetrahedra is illustrated in c and d. A model dimer can also be derived from a clinotobermorite structure that had staggered silicate chains, and as with the orthotobermorite models, there are two alternative positions for the interlayer Ca atom that seem plausible.