  We present x-ray powder diffraction (XRPD) and neutron diffraction
measurements on the slightly underdoped iron pnictide superconductor
Ba(1-x)K(x)Fe2As2, Tc = 32K. Below the magnetic transition temperature Tm =
70K, both techniques show an additional broadening of the nuclear Bragg peaks,
suggesting a weak structural phase transition. However, macroscopically the
system does not break its tetragonal symmetry down to 15 K. Instead, XRPD
patterns at low temperature reveal an increase of the anisotropic microstrain
proportionally in all directions. We associate this effect with the electronic
phase separation, previously observed in the same material, and with the effect
of lattice softening below the magnetic phase transition. We employ density
functional theory to evaluate the distribution of atomic positions in the
presence of dopant atoms both in the normal and magnetic states, and to
quantify the lattice softening, showing that it can account for a major part of
the observed increase of the microstrain.
