**5. Structural Analysis**

The pXRD pattern obtained from exfoliated AgCrP2S<sup>6</sup> crystals, as shown in Figure 5a, was indexed in the space group *P*2/*a* (No. 13), in agreement with the literature [19]. No additional reflection were observed demonstrating the intrinsic phase purity of our crystals.

**Figure 5.** (**a**) pXRD pattern from powdered AgCrP2S<sup>6</sup> crystals compared to the calculated pattern based on the refined crystal structure model. (**b**) Zoomed-in view on the low angle 2*θ* regime (10–40◦ ). The marked reflections are expected to be systematically absent assuming a crystal structure in the space group of *C*2/*m* instead of *P*2/*a*.

The *C*2/*m* space group, which is typically observed for compounds of the *M*2P2S<sup>6</sup> family [23,27], including *M*2+*M*02+P2S<sup>6</sup> compounds of isovalent substitution series (e.g., MnFeP2S<sup>6</sup> [13], MnNiP2S<sup>6</sup> [14] and FeNiP2S<sup>6</sup> [16]), can be ruled out. Assuming a monoclinic unit cell, several observed reflections correspond to Laue indices that are systematically absent for *C* centering, as they violate the reflection condition *hkl*: *h* + *k* = 2*n*. Examples are the reflections at 2*θ* = 22.94◦ corresponding to 120 and at 2*θ* = 31.92◦ corresponding to 211, as shown in Figure 5b.

This implies that Ag and Cr indeed arrange as zig-zag stripes in AgCrP2S<sup>6</sup> and do not just randomly occupy the corners of the structural honeycomb network, as it is the case for isovalent substitutions. While the former scenario breaks the mirror symmetry of the *C*2/*m* space group of the Fe2P2S<sup>6</sup> aristotype [28], which results in a *P*2/*a* space group, the latter scenario would not. Furthermore, a *C*2/*c* space group, as reported, e.g., for CuCrP2S<sup>6</sup> [17] with a triangular arrangement of the two transition element cations, can be ruled out based on the same considerations.

Starting from the crystal structure model proposed by Colombet et al. [19], a refined crystal structure model is obtained using the Rietveld method which is sufficient to describe our experimental pattern with good agreement, as shown in Figure 5a. The obtained lattice parameter and reliability factors are summarized in Table 2 (top) and the refined structural model is given in the same table on the bottom and is illustrated in Figure 6. The strongest disagreement between model and experiment is observed for the high intensity 001 reflection at 2*θ* = 13.67◦ . As this reflection corresponds to the stacking of layers, it is most prominently affected by any kind of disorder or defects influencing the stacking. Due to the weak structural interaction between layers, which are only based on weak van der Waals forces, the *M*2P2S<sup>6</sup> compounds are prone to stacking faults and twinning between layers. In the presence of such defects, the shape of the corresponding 001 reflection is altered, which may be a reason for the observed deviation between the experiment and the model without defects.


**Table 2.** Top : Summary of experimental parameters of the pXRD experiment on AgCrP2S6, extracted lattice parameters and reliability factors of the structural model obtained by the Rietveld method. Bottom: Refined crystal structure model of AgCrP2S<sup>6</sup> and isotropic displacement parameters with standard deviations given in parentheses. All sites were treated as fully occupied.

Additionally, the experimental pattern exhibits significantly altered reflection intensities compared to an initial model, which are attributed to a strongly preferred orientation of the crystallites in the investigated sample. Due to the layered structure with only weak van der Waals interactions between layers, the powder particles obtained from grinding AgCrP2S<sup>6</sup> crystals are plate-like and tend to lie flat on the sample holder. Thus, reflections with a dominant *l* component (e.g., 001) exhibit higher intensities than expected for spherical crystallites in transmission geometry. To adjust for this effect in the model, the method proposed by March [29] and extended by Dollase [30] was used. However, the preferred orientation in AgCrP2S<sup>6</sup> is strongly pronounced, such that it might be beyond the limit of what the semi-empirical March-Dollase model is capable of describing accurately. This may furthermore contribute to the deviation between model and experiment around the 001 reflection.

**Figure 6.** Refined crystal structure model of AgCrP2S<sup>6</sup> after Rietveld refinement. View along *a* in (**a**), along *b* in (**b**) and along *c* ∗ in (**c**). The CrS<sup>6</sup> and AgS<sup>6</sup> coordination environments are shown in the color of the respective central atom.

The refined crystal structure model for AgCrP2S<sup>6</sup> shows that the Ag–S bonds are notably longer than the Cr–S bonds, as expected based on the difference between the size of the transition element cations (e.g., ionic radii for octahedral coordination: *r*(Ag1+) = 1.15 Å and *r*(Cr3+) = 0.62 Å [31]). These different bond lengths result in a distortion of the structure compared to the aristotype Fe2P2S6, which can be clearly observed, e.g., in Figure 6a. In detail, the CrS<sup>6</sup> coordination environment remains antiprismatic (i.e., close to octahedral with a slight trigonal elongation along *c* ∗ ) with the faces above and below the shared plane of the transition elements being parallel to each other. However, the AgS<sup>6</sup> coordination environment as well as for the P2S<sup>6</sup> environment are distorted in such a way that the faces above and below the transition element plane are not parallel to each other. In the view along the *c* ∗ direction in Figure 6c, this distortion manifests in Ag and P<sup>2</sup> being shifted off-center in their respective sulfur coordination environments away from the closest Cr positions. Meanwhile, Cr is located exactly in the center of the CrS<sup>6</sup> unit. The observation that the CrS<sup>6</sup> unit is closer to an ideal octahedral coordination environment than the AgS<sup>6</sup> unit can be understood considering the local charge density (i.e., ionic size and charge). Cr3<sup>+</sup> is small and highly charged and, thus, interacts with the surrounding S atoms stronger than the comparable large and less charged Ag1+. Another notable structural aspect is the strong distortion of the [P2S6] <sup>4</sup><sup>−</sup> units that demonstrates how flexible this covalent complex anion is. This complex anion is a common and characteristic building unit in the *M*2P2S<sup>6</sup> family and its flexibility may indicate that several more compounds of the general formula *M*1+*M*03+P2S<sup>6</sup> are stable but have not been synthesized yet.
