Submonolayer phase transitions of parahydrogen and orthodeuterium on graphite have been investigated with positronium annihilation. It is shown that in contrast with conventional specific-heat measurements, quantitative assessments of gas in the mixed commensurate solid plus gas phases are possible, which will lead to a redrawing of the phase diagrams.The study of physisorbed monolayers on smooth graphite surfaces is now a mature field. The adsorption of a range of gases, from hydrogen to xenon, has been well investigated with a variety of methods, including isotherms, specific heats, neutron scattering, low-energy electron diffraction, x-ray diffraction, and others. The nature of the twodimensional ͑2D͒ phase transitions and the role of the underlying carbon substrate have been especially interesting. 1 H 2 and D 2 monolayers on graphite allow one to study ordering phenomena and phase transitions in quantum systems. In both cases at low coverages, a commensurate ()ϫ)) R30°phase forms due to the corrugation of the carbon surface potential, and at coverages near monolayer completion an incommensurate triangular 2D solid phase is created. Specific-heat measurements on submonolayers have allowed phase diagrams to be drawn for H 2 ͑Refs. 2 and 3͒ and D 2 ͑Ref. 4͒ that describe the transitions from 2D gas to commensurate solid plus gas. These measurements, however, based on broad peaks, are not very informative. They do indicate differences between H 2 and D 2 , which have been attributed to differing zero point motions of the quantum particles, but they cannot give quantitative descriptions of the mixed gas/solid phases.In this paper we report on measurements with a new method employing positronium ͑Ps͒ formation, which offers the prospect of detailed examination of these phase transitions.Positronium offers a unique means of studying the behavior of two-dimensional systems. It is well known that positrons injected into metals quickly thermalize by electronic and phononic excitations and may then diffuse to a surface to cause the emission of Ps by capturing a surface electron. 5 In the special case of graphite, Sferlazzo et al. 6 with a positron beam experiment observed that under normal conditions at room temperature little emission occurs. However, their 2-␥ angular correlation study revealed that large amounts of Ps were emitted at high temperatures. The lack at low temperatures was attributed to the band structure of graphite, 7 which showed that parallel momentum conservation would forbid surface electrons at the top of filled bands participating in Ps formation, whereas at high temperatures the abundance could be explained with a mechanism in which momentum conservation was satisfied by the emission and absorption of phonons. 6 The basal plane of graphite offers an ideally smooth substrate for the thermodynamic study of condensed gas mono-layers: their creation and their phase transitions. 8 The exfoliated form of graphite, grafoil, is a leaflike structure ͑of typical dimension, 100 nm͒ 8 with basal plane surfa...