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 tetragonalto-orthorhombic structural (Ts) and antiferromagnetic (TN ) phase transitions in BaFe2As2 are gradually suppressed and separated, resulting in Ts > TN with increasing x as was previously observed. However, the temperature separation between Ts and TN decreases with increasing x for x ≥ 0.065, tending towards a quantum bi-critical point near optimal superconductivity at x ≈ 0.1. The zerotemperature 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 TN ≈ Tc + 10 K above the superconducting dome around x ≈ 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. A determination of the structural and magnetic phase diagram in correlated electron materials is important for understanding their underlying electronic excitations. In the iron pnictides, superconductivity arises at the border of both antiferromagnetic (AF) and structural orders [1][2][3][4][5]. This motivates the exploration of quantum critical points, where the transition temepratures for such orders are continuously suppressed to zero by a non-thermal control parameter. For the iron pnictide superconductors derived from electron or hole doping of their parent compounds, the most heavily studied materials are probably the electron-doped BaFe 2−x T x As 2 (where T = Co, Ni) because of the availability of high-quality single crystals [1, 6-15, 17, 18]. In the undoped state, BaFe 2 As 2 exhibits a tetragonal-to-orthorhombic structural transition at temperature T s and an AF phase transitions below nearly the same temperature T N ≈ T s ≈ 138 K [3, 4]. Upon electron-doping of BaFe 2 As 2 via partially replacing Fe by Co or Ni, various experiments, including transport [8,9], neutron [1,[11][12][13][14][15], and highresolution X-ray scattering [4,18] reveal that the structural (T s ) and magnetic (T N ) phase transition temperatures in BaFe 2−x T x As 2 gradually decrease and separate with increasing x, and have T s > T N for all doping levels. In the initial X-ray [10] and neutron [11] scattering work on BaFe 2−x Co x As 2 , it was suggested that the separated T s and T N smoothly extend into the superconducting dome, resulting in distinct structural and magnetic quantum critical points at different x. Subsequent X-ray [18] and neutron [12][13][14] scattering experiments on superconducting BaFe 2−x T x As 2 samples with coexisting AF order revealed that superconductivity actually competes with the static AF order and lattice orthorhombicity. As a consequence, the smoothly decreasing T s and T N are reported to bend back below T c , and the orthorhombic structure above T c for optimally doped sample evolves back to a tetragonal structure well below T c (termed the "re-entrant" tet...