## 3 Results
### Core-Shell Features and High-Defect Low-Density KDP Component  
#### 3.2.1 Pore Shell Evolution during CSP  
The existence of a transient, high-defect, possibly amorphous, low-density, dissolved and re-precipitated, solid phase at grain boundaries during CSP is becoming better established [12; 25]. Here, improved fits to the data were obtained by assuming this to be a low-density shell at the pore/grain interface. Given the hydrogenous nature of the morphology during CSP, it has been assumed that this shell has an X-ray scattering-length (form-factor) density half-way between water (in the pores) and fully dense KDP. Additionally, the shell thickness was constrained to be the same for both the macroscale and nanoscale pore populations. These assumptions maximize the information that can be extracted here from the microstructural model fitting to the USAXS/SAXS data, but it is recognized that they represent a likely over-simplification of the true situation. Figure 9 presents the variation of the fitted shell thickness with CSP sintering time. Note that, whereas the shell thickness values (<20 nm) are negligible compared to the macroscale median pore diameters, they are clearly very significant compared to the nanoscale pore mean diameters. There is more scatter in these shell thickness results than indicated by the expected fitting standard uncertainties, probably associated with some stochastics as CSP progresses, even for the custom-designed stage used. Nevertheless, the shell thickness clearly decreases during CSP. However, only in the case of CSP for p = 150 MPa at 60 \({}^{\circ}\)C does the shell thickness decrease to near zero. The volume of low-density hydrogenous KDP material in the pore shell layers adjacent to the solid KDP grains was also deduced versus cold sintering time. The total surface area per unit sample volume of any lognormal distribution is given by a standard analytical result [23], and this can be calculated either for pores including the shell layer or excluding the shell layer (core volume only). In this case, the latter can simply be multiplied by the shell thickness to obtain the volume fraction of shell material in the sample. Figure 10 presents the variation in low-density KDP shell phase versus cold sintering time for each of the in situ CSP studies. The initial volume fraction of the shell phase is \(\approx\)1.5%, significantly greater than the nanoscale porosity of \(\approx\)0.3% (Figure 6). The larger value for the shell arises due to including the shell volume associated with the much larger population of macroscale pores. The transient nature of this phase is clearly revealed by the significant decrease in its volume fraction during CSP. However, note that some residual pore shell volume fraction persists after CSP at 100 MPa  
Figure 8: SEM micrographs of KDP samples after fracture during late-stage CSP for **(a,b)** p = 50 MPa at 60 \({}^{\circ}\)C; **(c,d)** p = 150 MPa at 60 \({}^{\circ}\)C. (a,c) show intact outer surfaces of the samples after CSP; **(b,d)** show the fracture surfaces.  
at any of the 3 temperatures used, and the shell volume fraction goes to near zero only for the case of CSP with p = 150 MPa at 60 \({}^{\circ}\)C.