## 3 Results and Discussion
### Density and Microstructure
\[\rho=\rho_{\text{b}}\cdot\frac{m_{\text{dry}}}{m_{\text{wet}}-m_{\text{b}}} \tag{2}\]  
Figure 3 shows the development of the bulk density as a function of the volume fraction of CSA cement, \(\phi_{\text{CSA}}\). The direction of the x-axis is inverted, so the pure cement appears on the left side at \(\phi=1\), and all mixtures with HGMSs follow into the right direction with increasing HGMS content. Since the open porosity did not vary significantly, the decrease in bulk density can be mostly attributed to the addition of HGMSs. The highest bulk density was 1.66 g\(\cdot\)cm\({}^{-3}\) for sample 100C, whereas the lowest value was 0.15 g\(\cdot\)cm\({}^{-3}\) for sample 30C (Table 3). The data points in the diagram show almost a linear behavior of density over volume fraction. Properties of composites containing two or more components are often described mathematically by a power law, here in the simplified form \(f(x)=a_{0}+a\cdot x^{v}\) with \(x=[0,1]\) for binary systems. The exponent, \(v\), can be determined by the slope of the curve in double logarithmic diagrams. A data fit performed for the measured bulk densities shows an exponent of \(v\approx 0.8\) if the composites are considered as a quasi-binary system and the contribution from air is neglected. The microstructure and the adhesion between HGMSs and CSA cement were investigated with SEM. Figure 4a shows the as-received HGMSs without addition of concrete. The diameter of the spheres varied between 10 and 90 \(\upmu\)m. Furthermore, very few spheres showed defects, such as being punctured or having completely destroyed shells. Since the HGMSs were not mixed or mechanically treated beforehand, these defects must originate from production, transport, or handling. Figure 3: Calculated bulk density of each specimen based on Archimedes measurement. Data fit to \(f(\phi)=a_{0}+a\cdot\phi^{v}\), with \(a_{0}=0.055\), \(a=2.184\), and \(v=0.81\). Figure 4b shows an SEM image of a fractured surface of a CSA prism containing no HGMSs (sample 100C) after the flexural bending test. The specimen was prepared with a _w/c_ ratio of 0.45 and hydrated for 14 days. The cracks that can be seen on the surface were most likely a result of the flexural bending test since no shrinkage was observed either after casting or after hydration. The sample showed a dense microstructure; needle-like crystals resulted from the formation of ettringite. Apart from ettringite crystals, clinker phases such as ye'elimite and anhydrite might still have been present due to an incomplete hydration reaction. Thus, XRD measurements were used to analyze the degree of hydration, which will be described in the last section. Figure 5 shows SEM images for mixtures with 50 wt.% HGMSs (sample 50C) at different magnifications. The volume fraction of the CSA cement was just 3.2%, yet the HGMSs were smoothly embedded in the cement matrix, which was forming an extended, needle-like network due to the hydration reaction. To a large extent, the HGMSs were intact, which is a prerequisite for achieving excellent insulating properties. The needle-like structures surrounding the HGMSs are characteristic for ettringite. This ettringite network provided a well-connected network and bonding between the cement phase and HGMSs. The ettringite matrix also contributed positively to the open  
Figure 4: (a) SEM image of HGMSs. The acceleration voltage was set to 3 kV, while a SE detector was used. (b) SEM image of the hydrated CSA cement (sample 100C) after storage for 14 days in a moist atmosphere. The acceleration voltage was set to 5 kV, and again a SE detector was used. Figure 5: SEM images of sample 50C, stored for 14 days in a moist atmosphere. The acceleration voltage was set to 5 kV, using a SE detector: (a) magnification 250\(\times\); (b) magnification 1500\(\times\). porosity and, hence, to a low thermal conductivity, but the addition of HGMSs probably lowered the mechanical properties in comparison with the pure CSA samples. Figure 6 shows SEM images of sample 30C, with 70 wt.% HGMSs.