Fig. 2: Synthesis kinetics, microstructure and thermal expansion property of the invar alloy fabricated from oxides.

a, Minimum melting energy cost as a function of the melting point for common species. The estimation is conducted by adding the enthalpy change of heating up a certain substance from ambient temperature to its melting point and the enthalpy of fusion, that is, \({\Delta E}_{\min }={\int }_{{25}^{^\circ }{\rm{C}}}^{{T}_{{\rm{m}}}}{c}_{{\rm{p}}}\,{\rm{d}}T+{\Delta H}_{{\rm{f}}}\). Only the enthalpy of fusion is considered for ice. Thermophysical parameters for these estimations are acquired from the literature⁴¹. b, Predicted Ellingham–Richardson diagram for the oxides of Fe (Fe₂O₃, Fe₃O₄ and FeO) and Ni (NiO) under 1 atm (SGTE database⁴² and refs. ^2,41). c, Secondary electron micrograph of the Fe₂O₃ + NiO powder mixture and the corresponding EDS maps. d, Two-dimensional SXRD diffractograms of the as-compacted oxide pellet (left) and the synthesized invar alloy (right). e, Macroscopic morphological evolution at different conversion rates. f, TGA curve showing the reduction kinetics. Inset: the instantaneous mass loss as a function of time. g, IPF map of the as-synthesized alloy (Σ3 annealing twin boundaries are excluded). h, The corresponding phase map. i, EDS mapping of Fe and Ni. j, Bulk thermal expansion (top, measured using dilatometer) and lattice thermal expansion (bottom, measured using in situ SXRD) results. The bulk and the lattice thermal expansion data for the invar alloys fabricated using different methods are reproduced from the literature^25,26,29,30. k, Examples of microstructure tunability. Details of the microstructure after pressure-free sintering are provided in Extended Data Fig. 2. i, Vickers hardness and bulk mass density comparison among the green invar alloys synthesized from oxides and the one fabricated using the conventional melting–casting–recrystallization (REX) method. The recrystallization conditions for the invar alloy processed through melting–casting were also chosen as 900 °C, 0.5 h (around 70% cold-rolling thickness reduction), whose grain size is about 50 μm. a.u., arbitrary units; CTE, coefficient of thermal expansion. Scale bars, 1 μm (c, top and bottom, i); 5 mm (e); 2 μm (g,h); 5 μm (k).