As to multifunctional titanium alloys with high strength and low elastic modulus,thermal training is crucial to tune their thermal expansion from positive to negative,resulting in a novel linear expan-sion which is stable in a wide temperature range.Aided by the high-order Hooke's law of elastic solids,a reversible atomic rearrangement mechanism was proposed to explain the novel findings which are unexpected from typical shape memory alloys.To confirm this continuous mechanism,a Ti-Nb based alloy,which possesses a nanoscale spongy microstructure consisting of the interpenetrated Nb-rich and Nb-lean domains produced by spinodal decomposition,was used to trace the crystal structure change by in-situ high energy synchrotron X-ray diffraction analyses.By increasing exposure time,the over-lapped diffraction peaks can be separated accurately.The calculated results demonstrate that,in the nanoscale Nb-lean domains,the crystal structure parameters vary linearly with changing temperature along the atomic pathway of the bcc-hcp transition.This linear relationship in a wide temperature range is unusual for first-order martensitic shape memory alloys but is common for Invar alloys with high-order spin transitions.Furthermore,the alloy exhibits smooth DSC curves free of transformation-induced heat peaks observed in shape memory alloys,which is consistent with the proposed mechanism that the reversible transition is of high-order.