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InAlN lattice-matched to GaN was grown by molecular beam epitaxy (MBE) using ammonia as the nitrogen source. The alloy composition, growth conditions, and strain coherence of the InAlN were verified by high resolution x-ray diffraction ω-2θ scans and reciprocal space maps. Scanning transmission electron microscopy and energy-dispersive x-ray spectroscopy of the InAlN revealed the absence of lateral composition modulation that was observed in the films grown by plasma-assisted MBE. InAlN/AlN/GaN high electron mobility transistors with smooth surfaces were fabricated with electron mobilities exceeding 1600 cm2/Vs and sheet resistances below 244 Ω/sq.