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The formation of particles from precursor vapors is an important source of atmospheric aerosol. Research at the Cosmics Leaving OUtdoor Droplets (CLOUD) facility at CERN tries to elucidate which vapors are responsible for this new-particle formation, and how in detail it proceeds. Initial measurement campaigns at the CLOUD stainless-steel aerosol chamber focused on investigating particle formation from ammonia (NH₃) and sulfuric acid (H₂SO₄). Experiments were conducted in the presence of water, ozone and sulfur dioxide. Contaminant trace gases were suppressed at the technological limit. For this study, we mapped out the compositions of small NH₃–H₂SO₄ clusters over a wide range of atmospherically relevant environmental conditions. We covered [NH₃] in the range from < 2 to 1400 pptv, [H₂SO₄] from 3.3 × 10⁶ to 1.4 × 10⁹ cm⁻³ (0.1 to 56 pptv), and a temperature range from −25 to +20 °C. Negatively and positively charged clusters were directly measured by an atmospheric pressure interface time-of-flight (APi-TOF) mass spectrometer, as they initially formed from gas-phase NH₃ and H₂SO₄, and then grew to larger clusters containing more than 50 molecules of NH₃ and H₂SO₄, corresponding to mobility-equivalent diameters greater than 2 nm. Water molecules evaporate from these clusters during sampling and are not observed. We found that the composition of the NH₃–H₂SO₄ clusters is primarily determined by the ratio of gas-phase concentrations [NH₃] / [H₂SO₄], as well as by temperature. Pure binary H₂O–H₂SO₄ clusters (observed as clusters of only H₂SO₄) only form at [NH₃] / [H₂SO₄] < 0.1 to 1. For larger values of [NH₃] / [H₂SO₄], the composition of NH₃–H₂SO₄ clusters was characterized by the number of NH₃ molecules <i>m</i> added for each added H₂SO₄ molecule n (&Delta;m/&Delta; n), where n is in the range 4–18 (negatively charged clusters) or 1–17 (positively charged clusters). For negatively charged clusters, &Delta; m/&Delta;n saturated between 1 and 1.4 for [NH₃] / [H₂SO₄] > 10. Positively charged clusters grew on average by &Delta;m/&Delta;n = 1.05 and were only observed at sufficiently high [NH₃] / [H₂SO₄]. The H₂SO₄ molecules of these clusters are partially neutralized by NH₃, in close resemblance to the acid–base bindings of ammonium bisulfate. Supported by model simulations, we substantiate previous evidence for acid–base reactions being the essential mechanism behind the formation of these clusters under atmospheric conditions and up to sizes of at least 2 nm. Our results also suggest that electrically neutral NH₃–H₂SO₄ clusters, unobservable in this study, have generally the same composition as ionic clusters for [NH₃] / [H₂SO₄] > 10. We expect that NH₃–H₂SO₄ clusters form and grow also mostly by &Delta;m/&Delta;n > 1 in the atmosphere's boundary layer, as [NH₃] / [H₂SO₄] is mostly larger than 10. We compared our results from CLOUD with APi-TOF measurements of NH₃–H₂SO₄ anion clusters during new-particle formation in the Finnish boreal forest. However, the exact role of NH₃–H₂SO₄ clusters in boundary layer particle formation remains to be resolved.