Following the border of antiferromagnetism (AF) to zero temperature is a promising route to unconventional metallic and superconducting phases. Many interesting examples of antiferromagnetic quantum phase transitions can only be reached by pressure tuning. The range of quantitative experimental probes, which can be realised in a high-pressure environment is limited. However, advances have recently been made in neutron scattering, where elliptically shaped neutron guides now increase the beam intensity directed to mm size sample for high pressure studies. This has been demonstrated on the simple antiferromagnet NiS₂. Neutron scattering also allows highly accurate measurements of the lattice constant via the Larmor diffraction technique, which proved extremely useful in studying the high-pressure phase diagram of the itinerant helimagnet MnSi. We now combined Larmor diffraction with conventional diffraction measurements to investigate the pressure-temperature phase diagram of URu₂ Si₂ up to 20 kbar. URu₂ Si₂ offers a further spectacular example for the presence of unconventional phases in the vicinity of antiferromagnetism. In this compound, antiferromagnetism is replaced below approximately 5 kbar by the mysterious "hidden order" (HO) and unconventional superconductivity. Our measurements allow the observation of magnetic order and changes in the a- and c-axis lattice constants across the phase transitions in the same experiment. The results contain clear indications of a first-order transition and strong differences between the AF phase and the HO phase in the coupling to the lattice.