The peak shift for XRD of the 1T and 2H phases of $\ce{MoS2}$ differs by a few degrees (just below 10 degrees for 1T, 14 degrees for 2H).
In Rietveld Refinement, a standard CIF file can be used for peak fitting. A CIF for the 2H phase of $\ce{MoS2}$ is available from the COD database, but I can't seem to find the 1T phase CIF. Is this available from some other source (or am I just missing it on the COD website)?
(A shift of a peak by $\Delta2\theta \approx 4^\circ$ in PXRD may be considered as quite a bit.)
For multiple years, there is a website in common by CCDC about the public entries in the CSD file (organic/organometallic small molecule .cif) and ICSD database (inorganic .cif). It is not as comfortable as searching on their respective own interfaces (like WebCSD/conquest for CSD) or ICSD directly, though. It aims to help e.g., reviewing publications. Thus, CCDC blocks you (temporarily) if they associate your IP address with «too many attempts to download .cif/unit of time».* (Public entries refers to entries where authors of these data permit their data to be retrieved. There may be good reasons to deposit the data and e.g., await successful peer-review of the corresponding publication in a journal before such an «embargo» is lifted.)
However, you may search by compound name like molybdenum disulfide (example) to yield .cif one may download and a bibliographic reference to the original publication. Thus one finds models in $P 6_3/mmc$ ($a = b \approx \pu{3.16 Å}$, $c \approx \pu{12.3 Å}$, $\alpha = \beta = 90^\circ$, $\gamma = 120^\circ$ e.g., entry ICSD 49801) as well as two in $R3m$ ($a = b \approx \pu{3.16 Å}$, $c \approx \pu{18.4 Å}$, $\alpha = \beta = 90^\circ$, $\gamma = 120^\circ{}$ e.g., entry ICSD 196772).
*) If your school isn't yet subscriber to these databases (ask e.g., groups active in crystallography/inorganic chemistry/materials science/physics/organic chemistry), get in touch with research libraries. A single FTE becomes quite affordable (compared to other databases) if you join a local «consortium» of multiple interested groups where the library manages remote access and updates for you. Plus the benefit of the databases' infrastructure (e.g., tailored Python libraries for the CSD).
