## 3 Results and Discussion  
### Density and Microstructure  
First, the pure density of the raw materials, i.e., CSA cement and hollow glass microspheres (HGMSs), was measured using helium pycnometry. The pure densities of HGMSs and CSA cement were found to be 0.142 g\(\cdot\)cm\({}^{-3}\) and 2.87 g\(\cdot\)cm\({}^{-3}\), respectively. The Archimedes measurement was performed on three specimens for each composition reported in Table 2. Equation (1) was used to calculate the open porosity (\(\varepsilon\)) of each specimen using the dry mass (\(m_{\mathrm{dry}}\)), the buoyancy mass (\(m_{\mathrm{b}}\)), and the mass of the water-infiltrated specimen (\(m_{\mathrm{wet}}\)). \[\varepsilon=\frac{m_{\mathrm{wet}}-m_{\mathrm{dry}}}{m_{\mathrm{wet}}-m_{ \mathrm{b}}} \tag{1}\]Figure 2 illustrates the calculated open porosity for each plaster composition, starting with 100% cement at the left side. The open porosity, \(\varepsilon\), changed slightly with a changing composition. The specimens with 100% and 90% cement (samples 100C and 90C) had open porosities of around \(\varepsilon=25\%\). With an increasing HGMS content, the open porosity increased to \(\varepsilon=32.7\%\) with 60% cement (sample 60C) but decreased slightly to \(\varepsilon=30\%\)-31% with further addition of HGMSs (samples 50C to 30C). Because the addition of HGMSs mainly contributes to closed porosity, the open porosity is generally not expected to be affected much by addition of HGMSs. Moreover, an open porosity of 26% is the void fraction of the densest sphere packing of uniformly sized spheres with a volume fraction of 74 vol.%. The increase in the void fraction above 30% as a function of the rising HGMS fraction was probably caused by remnants of the increasing water amount used for the plaster's preparation (see Table 3). Excess water, which is not used during hydration, accumulates in the voids until the specimen has dried. The evaporating water leaves pore space behind, which then contributes to the overall open porosity. The open porosity values and pure densities of the HGMSs as well as the pure density of hydrated CSA cement (2.24 g\(\cdot\)cm\({}^{-3}\)) were used to determine the real volume fractions (\(\phi_{i}\)) of CSA cement and HGMSs with \(\phi_{\rm air}=\varepsilon\), respectively. Table 3 shows the volume fractions \(\phi_{i}\) for each specimen. The volume fraction of HGMSs reached 48.3% with an addition of only 10 wt.% of HGMSs (specimen 90C), and then increased to 67.6% in specimen 30C. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Specimen** & **100C** & **90C** & **80C** & **70C** & **60C** & **50C** & **40C** & **30C** \\ \hline \(\phi_{\rm air}\) (vol.\%) & 25.9 & 24.1 & 28.5 & 29.5 & 32.7 & 31.3 & 30.3 & 30.6 \\ \hline \(\phi_{\rm HGMS}\) (vol.\%) & 0 & 48.3 & 57.1 & 61.4 & 61.5 & 64.6 & 66.9 & 67.6 \\ \hline \(\phi_{\rm CSA}\) (vol.\%) & 74.1 & 27.6 & 14.4 & 9.1 & 5.8 & 4.1 & 2.8 & 1.8 \\ \hline Density (g\(\cdot\)cm\({}^{-3}\)) & \(1.63\pm 0.02\) & 0.82 \(\pm\) 0.01 & 0.44 \(\pm\) 0.01 & 0.26 \(\pm\) 0.02 & 0.23 \(\pm\) 0.01 & 0.19 \(\pm\) 0.02 & 0.16 \(\pm\) 0.01 & 0.13 \(\pm\) 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculated volume fractions, \(\phi_{i}\), of CSA cement, HGMSs, and air as well as the calculated density of the hydrated and dried specimens according to open porosity. Figure 2: Open porosity measured using the Archimedes method for each sample composition using three specimens each (\(N=3\)). The specimens were investigated after 14 days of hydration. The bulk densities were determined according to the Archimedes method using Equation (2). The bulk densities (\(\rho\)) of the specimen were calculated from the dry mass (\(m_{\text{dry}}\)), the buoyancy mass (\(m_{\text{b}}\)), and the mass of the infiltrated specimen (\(m_{\text{wet}}\)). Since the infiltration medium is deionized water at 20 \({}^{\circ}\)C, the density \(\rho_{\text{b}}\) is 0.9982 g\(\cdot\)cm\({}^{-3}\).