  We study the structural and magnetic orders in electron-doped BaFe2-xNixAs2
by high-resolution synchrotron X-ray and neutron scatterings. Upon Ni-doping x,
the nearly simultaneous tetragonal-to-orthorhombic structural T_s and
antiferromagnetic (T_N) phase transitions in BaFe2As2 are gradually suppressed
and separated, resulting in T_s>T_N with increasing x as was previously
observed. However, the temperature separation between T_s and T_N decreases
with increasing x for x> 0.065$, tending towards a quantum bi-critical point
near optimal superconductivity at x=0.1. The zero-temperature transition is
preempted by the formation of a secondary incommensurate magnetic phase in the
region 0.088< x < 0.104, resulting in a finite value of T_N \approx T_c+10$ K
above the superconducting dome around $x\approx 0.1$. Our results imply an
avoided quantum critical point, which is expected to strongly influence the
properties of both the normal and superconducting states.
