[en] We study the phase diagram and magnetic properties of a transverse spin-1 Ising model with random longitudinal crystal field interactions within an expansion technique for cluster identities of spin-1 localized spin systems. The partially ordered phases appear for a particular two valued distribution P(D_i) = 1/2[δ(D_i-(1+α)D)+δ(D_i-(1-α)D)], and for sufficiently small transverse field Ω. The longitudinal and transverse magnetizations, the quadrupolar moments are calculated. General formulae applicable to structures with arbitrary coordination number, are given. (author). 19 refs, 3 figs