is obtained by hydrothermal synthesis. All phases are found to be isostructural with ZnAlF5(Htaz) by powder X-ray diffraction. Weberite structures are prone to induce the magnetic frustration of antiferromagnetic interactions originating from the cationic topology of HTB layers. The (nD) magnetic properties of (0D) Co-Ga, (1D) Zn-Fe, (3D) Fe-Ga, Mn-Fe, Co-Fe and Co-V couples, are thus reported. Co 2+ or Fe 2+ magnetic anisotropy induces a negative magnetisation below N T and compensation temperatures for Mn-Fe and Co-Fe couples. All iron 3D magnetic phases exhibit high Néel temperatures, between 81 K and 102 K, and large N P T / ratii, signalling strong magnetic frustration. Their cation site occupancies and the deduced (de)protonation states of the amine are accurately determined by 57 Fe Mössbauer spectrometry. In addition, this spectroscopy evidences a subtle effect of the atmosphere that surrounds the samples: the magnetic ordering temperatures N T decrease significantly when the samples are cooled under vacuum with respect to samples that are cooled at ambient pressure. This novel phenomenon, that is highlighted for all studied (3D) triazole iron weberites, is reversible, and thus opens promising perspectives for understanding the underlying mechanism.