## 2 Materials and Methods
Due to the Bonse-Hart crystal diffraction optics underlying the USAXS measurement configuration, USAXS data are intrinsically slit-smeared. While the data can be de-smeared, the de-smearing step introduces noise artifacts into the data and it is preferable to slit-smear the SAXS data before merging with the USAXS data and fit a slit-smeared model to the combined slit-smeared data. Here, slit-smeared USAXS and sector-averaged SAXS data were reduced and absolute-intensi  
Figure 1: Photographic images of KDP samples at early and late stage CSP with **(a)** 50 MPa uniaxial compression at 60 \({}^{\circ}\)C; **(b)** 150 MPa at 60 \({}^{\circ}\)C. Additionally, plotted are piston displacements versus cold sintering time for each CSP condition (1 mm displacement \(\approx\) 500 piston steps). Figure 2: Schematic of CSP stage geometry for in situ USAXS/SAXS/WAXS measurements. Inset shows photograph of actual stage in operation. USAXS facility analysis software macro suite: _Indra_, _[PERSON]_ and _[PERSON]_, written in _[PERSON]_ (Wavemetrics Inc., Lake Oswego, OR, USA) [19,20]. Corresponding USAXS and SAXS datasets were merged to form a contiguous small-angle scattering dataset for absolute-intensity-calibrated I(q) versus q over the q range: 0.001 nm\({}^{-1}\) < q < 17 nm\({}^{-1}\). The practical maximum q for scattering was \(\approx\)3 nm\({}^{-1}\) for there to be significant SAXS signal above the scattering background. However, the first XRD peak (101) was also captured in the SAXS data at q = 12.37 nm\({}^{-1}\). WAXS data were reduced separately, also using the above USAXS facility software macro suite, to provide XRD data in the range 13 nm\({}^{-1}\) < q < 63 nm\({}^{-1}\). Figure 3a presents combined USAXS/SAXS I(q) versus q datasets for KDP CSP using p = 125 MPa at 60 \({}^{\circ}\)C, presented on a log-log plot. Figure 3b presents the corresponding WAXS data (combined with the high-q part of the SAXS datasets to capture the XRD 101 peak) on a linear-linear plot. As detailed below, the USAXS/SAXS data were subjected to microstructural model fitting to characterize the evolving pore morphology during CSP, while the XRD data were inspected to detect the presence of reprecipitated nanoscale material and/or the transient appearance of metastable phases during CSP. In situ USAXS/SAXS/WAXS CSP studies were carried out under the following conditions of uniaxial compression and temperature: p = 100 MPa at 40 \({}^{\circ}\)C, 50 \({}^{\circ}\)C and 60 \({}^{\circ}\)C; p = 125 MPa at 40 \({}^{\circ}\)C, 50 \({}^{\circ}\)C and 60 \({}^{\circ}\)C, and finally p = 150 MPa at 60 \({}^{\circ}\)C. A further comparison of the runs using all 3 compressions at 60 \({}^{\circ}\)C was also carried out. The small-angle scattering was assumed to arise primarily from the evolving pore morphology of the densifying sample and required a 3-component microstructure model to fit the data. The 3 components comprised (i) coarse voids (porosity) between the KDP powder grains; (ii) fine nanoscale pores where multiple grains meet, and where active dissolution and re-precipitation of KDP is most likely to occur; and (iii) semi-dense dissolved and re-precipitated solid KDP material at sintered junctions between grains, possibly containing a high concentration of vacancy defects. For (i) and (ii), it is assumed that the pore-space is filled with water due to the large water content in the system. Unlike what was found in the earlier studies, there was no obvious point during CSP where it could be assumed that all pore fluid had been removed. With each of (i) and (ii), it was assumed that the \"matrix\" external to the pores is fully dense KDP, but that a layer exists around each pore of low-density KDP, representing dissolved and re-precipitated, high-defect density material, possibly also with hydrogenous content. Here, it was assumed that the thickness of this shell layer was the same for all pores (all solid/pore interfaces) for both macropores and nanoscale pores but was allowed to vary with time during CSP.