[en] The lattice parameters, a, of the f.c.c. β-phase of the rare-earth dihydrides RH_2+x (R = Y, Gd, Tb, Dy) have been determined by X-ray diffractometry in the temperature range between 90 and 295 K, for various values of the excess H-concentration on octahedral sites, x. The generally linear contraction of a with x up to the β-phase limit is confirmed at room temperature; the contraction coefficients β = (1/a)Δa/Δx are for YH_2+x: -0.50 x 10^-2, for GdH_2+x: -0.65 x 10^-2, for TbH_2+x: -0.85 x 10^-2, for DyH_2+x: -0.57 x 10^-2 per atom H. At 90 K, the contraction is generally stronger than at 295 K, and deviates from linearity for higher values of x indicating an interaction between the octahedral H-atoms leading to eventual ordering. This ordering is seen on the thermal expansion a(T)-curves as an x-dependent anomaly, its temperature increasing with growing x. The β-phase limit, x^max_β, has been deduced for YH_2+x: x^max_β = 0.100(5), and for DyH_2+x: x^max_β = 0.23(1). (orig.)