# Effect of C-S-H Nucleating Agent on Cement Hydration
## 2 Materials and Methods
### Methods
#### 2.4.3 Backscattered Electron Imaging Analysis (BSE)  
The technique of backscattered electron image analysis (BSE) helps to further understand the microstructure and hydration properties of cement slurry, which can make up for the shortages of other research methods [21]. In this work, the JEOL-JXA-840A scanning electron microscope was used to obtain the SEM and BSE images. The magnification of the BSE image is 250 times, and the acceleration voltage was 15 kV. When the shooting conditions of the BSE image are the same, the gray-scale characteristic value of the phase has repeatability in different images so that BSE can be used to quantitatively count the volume content of the phase-in cement [22]. In this work, the number of pictures taken in the quantitative calculation was six. Each BSE image was analyzed to estimate the capillary porosity and hydration degree of cement. A gray-level histogram was obtained for each image. This histogram indicates the number of pixels in the image having each possible brightness value (between 0 and 255). The gray level of a phase in a BSE image is related to its backscattering coefficient \(\eta\). The larger \(\eta\) is, the brighter phase is in the BSE image [23; 24]. For hydrated cement paste, capillary pores are darkest, calcium silicate hydrate (C-S-H) and other (aluminate) hydration products are dark gray, calcium hydroxide (CH) is light gray, and unhydrated cement is the brightest. The backscattering coefficient of a single phase can be calculated by the following formula [25]:  
\[\eta=\sum_{i}C_{i}\eta_{i} \tag{6}\]  
where \(C_{i}\) and \(\eta_{i}\) are the mass fraction and backscattering coefficient of atoms that make up the phase, respectively. The content of each component (such as pore and unhydrated cement) is the same as the one in the previous section. The concentration of the cement is \(\eta_{i}\), which is the ratio of the concentration of the cement to the concentration of the cement. The concentration of the cement is \(\eta_{i}\), which is the ratio of the concentration of the cement to the concentration of the cement.  
cement) in cement paste can be obtained by the threshold segmentation method [26], and the hydration degree of cement is estimated according to Equation (7).  
\[\alpha=\left[1-\frac{V_{cm}(t)}{V_{cm}(0)(1-V_{RS})}\right] \tag{7}\]  
where \(\alpha\) is the hydration degree of the cement, \(V_{cm}(t)\) is the volume (area) fraction of unhydrated cement at time \(t\), and \(V_{RS}\) the initial volume fraction of readily soluble phases in cement. In this work, \(V_{RS}\) = 8%. \(V_{cm}(0)\) is calculated based on the _w/c_ of the prepared paste, and the cement density is 3150 kg/m\({}^{3}\).  
In addition, based on the BSE images, the fractal dimension of cement hydration products can be calculated. Fractal characteristics can effectively quantify and compare the complexity of hydration products, which is related to the macron performance of concrete [27]. In this work, the box-counting dimension is used to evaluate the fractal characteristics of hydration products in the BSE image. For complex structures with autocorrelation, the box-counting dimension \(D^{b}\) can be expressed as:  
\[D^{b}=\log(N^{k})/\log(1/k) \tag{8}\]  
where \(N^{k}\) is the minimum number of grids that covering the surface of a complex structure with a square grid with side length \(k\). The box-counting dimension indicates that the number of square grids \(N^{k}\) increases with the decrease of side length \(k\), and the calculation algorithm of box-counting dimension on the BSE image is shown in Figure 2. Figure 2 is Calculation algorithm of box-counting dimension based on BSE image (a) and BSE image processing process. Original BSE image b)-1, BSE image after binarization b)-2, schematic diagram of meshing b)-3 and schematic diagram of fractal dimension fitting b)-4.  
Figure 2: Calculation algorithm of box-counting dimension based on BSE image (**a**) and BSE image processing process (**b**).