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The crystalline structure of ∼ 5-20 μm water ice films grown at 165 and 172 K has been probed by measuring the fraction of positrons forming ortho-positronium (ortho-Ps) and decaying into three gamma photons. It has been established that films grown at slower rates (water vapour pressure ≥ 1 mPa) have lower concentrations of lattice defects and closed pores, which act as Ps traps, than those grown at higher rates (vapour pressure ∼100 mPa), evidenced by ortho-Ps diffusion lengths being approximately four times greater in the former. By varying the growth temperature between 162 and 182 K it was found that films become less disordered at temperatures above ∼172 K, with the ortho-Ps diffusion length rising by ∼60%, in this range. The sublimation energy for water ice films grown on copper has been measured to be 0.462(5) eV using the time dependence of positron annihilation parameters from 165 to 195 K, in agreement with earlier studies and with no measurable dependence on growth rate and thermal history.