**4. Crystal Morphology and Compositional Analysis**

The topographical SE image of a AgCrP2S<sup>6</sup> crystal in Figure 4a exhibits a flat crystal surface and sharp edges. The terrace close to the upper edge of the crystal is a typical feature of layered systems. Furthermore, on the upper edge of the crystal, some steps can be seen, which form 120◦ angles, indicative of a hexagonal crystal habitus. The SE image with BSE detector in in Figure 4b shows an overall homogeneous contrast over the surface of the crystal demonstrating that it is chemically homogeneous. At some small areas, a change in contrast is observed. In comparison with the SEM image in SE mode, these spots can be clearly attributed to impurity particles on top of the crystal and not to any region of intergrowth with a secondary phase.

**Figure 4.** SEM image of a AgCrP2S<sup>6</sup> crystal with topographical contrast (SE mode) in (**a**) and chemical contrast (BSE mode) in (**b**).

By EDX measurements on multiple spots on several crystals, the mean elemental composition of the crystals was obtained as Ag1.03(2)Cr1.06(2)P2.03(2)S5.88(1) . This composition is in ideal agreement with the expected composition of AgCrP2S<sup>6</sup> and the small standard deviations (given in parentheses) indicate a homogeneous elemental distribution and composition.
