Conversion of methanol and/or dimethyl ether (DME) on microporous acidic zeolites is of great interest for achieving sustainable production of fuels and chemicals based on carbon dioxide and green hydrogen. We have recently discovered that under low-pressure operating conditions, this reaction can exhibit pronounced kinetic oscillations during the initiation period - a phenomenon never before seen in zeolite materials during half a century of their intense investigations in both academia and industry. Here, we propose an in situ X-Ray diffraction experiment to monitor the temporal evolution of the zeolite unit cell parameters and electron density within the micro pores during the oscillations. Such data will help us in elucidating the underlying mechanisms involved in this phenomenon, which are presently unknown. For example, we will be able to test whether coherent framework deformations control the observed periodic release of hydrocarbon products form the zeolite.