Engineering medium-range order and polyamorphism in a nanostructured amorphous alloy

Like crystalline materials, the properties of amorphous materials can be tailored by tuning the local atomic-to-nanoscale structural configurations. Polyamorphism is evident by the coexistence of kinetically stabilized amorphous structures with tailorable short-to-medium-range orders, providing a viable means to engineer the degree of local order and heterogeneity. Here, we report experimental evidence of the coexistence of liquid-like and solid-like amorphous phases in a Ni82P18 amorphous alloy with enhanced thermal stability and plasticity prepared by pulsed electrodeposition. The two amorphous phases, of comparable volume fraction of ~50% each, have similar short-range order but are distinguished by packing at the medium-range length scale (>6 Å). Upon heating, a structure crossover at ~450 K was observed, where the liquid-like structure transforms to the solid-like structure, as evidenced by the enthalpy release and an anomalous contraction of atomic structure over the medium-range length scale, due to the metastable nature of the liquid-like structure. https://doi.org/10.1038/s42005-019-0222-9 OPEN

T he structure of amorphous materials is characterized by disorder on the long-range length scale but by local order at short-range to medium-range length scales [1][2][3][4] . This complexity has led to some ambiguities in describing these structures, particularly for evolving structures during phase transitions, e.g., glass transitions 1,5 . To modify the properties of amorphous materials, it is desirable to develop the ability to tailor the local order in disordered states 6,7 . However, the structure factor for glassy alloys prepared using conventional methods, i.e., rapid quenching techniques 8,9 , usually looks the same: beyond the first sharp diffraction peak, there are several peak maxima propagated at a limited momentum transfer, Q (5-20 Å −1 ) 10,11 . Moreover, there is often a right shoulder peak with lower intensity for the second peak maximum 12,13 , indicating the shortto-extended range structural order. Tailoring local order based on the temperature parameter in amorphous states is difficult due to the fast critical quenching rate for most metallic glass (MG) alloy systems 7,14 .
Before the first rapidly quenched glassy alloy was reported in 1960 15 , electrodeposition (ED) had already been employed as a powerful technique for preparing metastable alloys 16 . The ED amorphous alloys, e.g., the iron-group alloys 17 , which are similar to thermally synthesized alloys in structure, have been widely used in electronics applications, such as in computers, space technology, and energy storage devices, due to their attractive magnetic, mechanical, and chemical properties [16][17][18][19] . Pulsed ED has been successfully used to prepare Ni-P amorphous alloys 20,21 . The reported ED Ni-P amorphous alloys possessed similar diffraction patterns 22,23 as that of the MGs but showed nanoscale structure inhomogeneity. The different regions in the ED Ni-P are characterized by different chemical compositions or packing densities. Presumably, if one can obtain ED Ni-P amorphous alloys of dual phases with appropriate volume fractions by, for example, changing the parameters during deposition, it could be possible to tailor the packing scheme at medium-range order (MRO) in the amorphous state. Those changes in microstructure would be manifested in the structure factor, which can be determined using diffraction measurements.
Polyamorphous phase transitions (PPTs), including amorphous solid-to-solid (SS) [24][25][26][27] phase transition, and liquid-toliquid (LL) phase transition [28][29][30] , are still a debated issue. A PPT has been proposed in a Ni 82 P 18 glass upon heating 23,31,32 . In this regard, the observation of coexisting multiple amorphous states at the same time and space 33,34 would provide direct evidence for a PPT in amorphous alloys. That being the case, it would be possible to modify the local order in disordered materials by temperature or pressure-induced PPTs, which should lead to tailorable properties for amorphous materials, such as the thermal stability and mechanical properties 7 .
In this paper, we demonstrate that Ni 82 P 18 amorphous alloys, prepared using multi-phase pulsed ED within a specific pulse current range 20 , have a unique structure factor: for the second peak maximum, there are two sub-peaks with comparable diffraction intensities. The ED Ni 82 P 18 amorphous alloys consist of the following two kinds of amorphous structural components: nanometer-sized regions with solid-like structure (SLS, the atomic structure of melt-quenched MG-like Ni 82 P 18 ) and nanometer-sized regions with liquid-like structure (LLS, of loosepacking compared to a melt-quenched Ni-P ribbon sample). The structure of the ED Ni 82 P 18 amorphous alloy was determined using transmission electron microscopy (TEM) and high-energy synchrotron X-ray scattering. The composition distribution was characterized by atom probe tomography (APT). Real-space analysis, via pair distribution function (PDF), indicates that the loose-packing regions in ED Ni 82 P 18 alloys have larger atomic spacing over the medium-range length scale (~6 Å), which is consistent with the features of the difference between liquid and glassy states for two excellent glass-forming alloys, Zr 57 Nb 5 Al 10 -Cu 15.4 Ni 12.6 (Vit 106) and Pd 43 Cu 27 Ni 10 P 20 , respectively. Simultaneous small-angle/wide-angle X-ray scattering (SAXS/WAXS) reveal a 'solidification-like' structure transformation of the ED Ni 82 P 18 alloy upon heating. Finally, compared with the expansion behavior of MG Ni 82 P 18 alloys, an unusual thermal contraction at medium-range length scale for the LLS of the ED Ni 82 P 18 alloy is demonstrated by PDF analysis. The thermal mechanical analysis (TMA) measurements revealed an anomalous change in the coefficient of thermal expansion (CTE) for ED Ni 82 P 18 alloy upon heating, further confirming a PPT at~450 K. Furthermore, the as-prepared ED Ni 82 P 18 amorphous alloys show better thermal stability and even tensile ductility at the sub-micron scale.

Results
Thermal analysis and nanoscale heterogeneity. Figure 1a presents the differential scanning calorimetry (DSC) scans for the asprepared MG Ni 82 P 18 ribbons and ED Ni 82 P 18 amorphous alloys. The ED Ni 82 P 18 was prepared using the highest pulse current density (400 mA cm −2 ) to introduce a different structure. Supplementary Fig. 1 shows the S(Q) patterns for ED Ni 82 P 18 samples prepared at different pulse current densities. The crystallization temperature T X2 for the ED Ni 82 P 18 alloy is~633 K, which is~53 K higher than that of the MG Ni 82 P 18 alloy (T X1 580 K). Surprisingly, there is a thermal release phenomenon at T S ,~450 K, for the ED Ni 82 P 18 alloy, which is much lower than the nominal glass transition temperature (T g ),~570 K, for the MG Ni 82 P 18 sample 35 . The calorimetric studies suggest that there might be a structural change upon heating and the ED Ni 82 P 18 alloy has much better thermal stability than that of the MG Ni 82 P 18 alloy. The APT results in Fig. 1b illustrate the uniform distribution of the alloying elements (Ni and P) in the asdeposited ED Ni 82 P 18 alloy. Figure 1c is the high angle annular dark field (HAADF) image acquired in scanning transmission electron microscopy (STEM) mode for the ED Ni 82 P 18 alloy. It shows variations of mass/thickness contrast~10-20 nm, indicating that the microstructure of the ED Ni 82 P 18 alloy varies on a nanometer scale. The inset in Fig. 1c is the selective area electron diffraction (SAED) pattern, which illustrates that the sample is amorphous, with diffuse halos. Figure 1d, e display the HRTEM images for the dark and bright regions in Fig. 1c, showing typical maze-like amorphous structures. No distinct composition fluctuations were detected on the nanometer scale in the energydispersive X-ray spectroscopy (EDS) mapping, as shown in Fig. 1f. For comparison, Supplementary Fig. 2 illustrates the structural homogeneity using TEM observation for the MG Ni 82 P 18 sample with the same chemical composition. Figure 2a shows the SAXS profiles for the ED Ni 82 P 18 alloy and the MG Ni 82 P 18 ribbon. A hump at~0.02 Å −1 in the SAXS log-log plot of the ED Ni-P sample confirms the presence of nanoscale structures in the ED sample. The model fitting result was obtained based on a simple hard-sphere model. The inset in Fig. 2a shows the intensity variation of SAXS profile for ED Ni 82 P 18 , which is much higher than that of the MG Ni 82 P 18 ribbon sample, suggesting a much stronger scattering contrast for the scattering units in the ED sample. The SAXS profile of the MG alloy is nearly non-existent, suggesting a homogenous structure (see Supplementary Fig. 2). On the other hand, the SAXS profile of the ED alloy shows a hump at Q~0.02 Å −1 , indicating the presence of nanoscale heterogeneous structures. The SAXS data were analyzed by using the software package IRENA in Igor 36 . A spheroid model with polydispersity was employed to fit the scattering profile of the ED alloys. Figure 2b displays the calculated size distribution for the ED sample based The existence of LLSs. Figure 3a shows the S(Q) patterns of the ED and MG Ni 82 P 18 amorphous alloys. The second peak maximum (Q range: 4.5-7.0 Å −1 ) of the S(Q) of the ED amorphous alloy shows two sub-peaks instead of the peak plus a shoulder in the ordinary S(Q) pattern of MGs. As shown in Supplementary  Fig. 3, the Rietveld refinement results of the diffraction patterns for the ED and MG alloys after crystallization illustrate that there are two crystalline products, Ni (space group: Fmmm) and Ni 3 P (space group: I4), with almost the same weight percentage. Moreover, Supplementary Fig. 4 shows the S(Q) patterns of MG and ED alloys before and after crystallization. The peak positions for the crystalline products were superimposed. There are sharp diffraction peaks in S(Q) patterns of the samples after crystallization, which are different from the diffraction patterns of the amorphous alloys. Figure 3b illustrates the differential reduced PDF pattern, G(r), obtained by a fast Fourier transform (FFT) of the difference S(Q), which was obtained from ED Ni 82 P 18 alloy pattern after subtracting 50% of the MG Ni 82 P 18 ribbon pattern. The formation of ED Ni-P amorphous alloys is proposed to consist of nucleation and growth of the amorphous nanograins 20 . The structural model 37 of nanostructured amorphous alloys assumes amorphous nano-grains regions and the interface regions between the nano-grains. The atomic structure of the amorphous nano-grains is MG-like while the boundaries between those nano-grains exhibit a reduced packing density, i.e., higher free volume. Therefore, the change of the diffraction patterns with that of the deposition parameters in Supplementary Fig. 1 should originate from the increase of the interfacial regions between the amorphous nano-grains. The fitting to the SAXS profile of the ED Ni 82 P 18 alloy based on the Debye-Bueche (DB) random twophase model 38 illustrates that the volume fraction of the loosepacking regions is~53%. For comparison, the volume fraction of the MG-like phase in ED alloy used for calculating the difference S(Q) was estimated to be 50% based on the TEM observation and SAXS pattern fitting. For further details of the DB model fitting, the readers are referred to the Supplementary Note 1 and Supplementary Fig. 5. Furthermore, Supplementary Fig. 6 demonstrates that a fluctuation in volume fraction within ±10% would not affect the outcome of the differential G(r). Figure 3b shows that the PDF peaks for the MG-subtracted pattern shift to a higher value beyond r~6 Å (as indicated by an arrow), suggesting a MRO with larger atomic spacing. From the comparison of the peak positions of the calculated pattern with those of the MG sample, it can be seen that the first coordination shell changes little. However, the third coordination shell shifts bỹ 2.30%. It is noted that the position (6.5-6.7 Å) of the third coordination shell of the MG-subtracted pattern is similar to the position (~6.6 Å) of the third coordination shell of the Ni 81 P 19 metallic liquid 39 . To understand the significance of this increase, the peak positions for the third coordination shell of two representative metallic glass-forming liquids (MGFLs) and their glassy state counterparts: Zr 57 Nb 5 Al 10 Cu 15.4 Ni 12.6 (Vit 106) and Pd 43 Cu 27 Ni 10 P 20 were determined. For both alloys, the first coordination shell changes only slightly, but the higher coordination shells shift significantly. As shown in Supplementary Fig. 7, the calculated differences of the third coordination shells, between liquid and glassy states, are 2.33% and 2.26%, respectively, for Zr 57 Nb 5 Al 10 Cu 15.4 Ni 12.6 (i.e., Vit 106) and Pd 43 Cu 27 Ni 10 P 20 . The above results provided evidence for the existence of a LLS with a different MRO in the ED Ni-P alloy.
Polyamorphous phase transition upon heating. To further study the existence of the loosely packed LLSs and to probe the structural stability, we performed simultaneous SAXS/WAXS study during heating, summarized in Fig. 4. At temperatures above T x~6 33 K, crystallization occurs in the ED Ni 82 P 18 sample as evidenced by the abrupt appearance of Bragg peaks in the diffraction data, see inset of Fig. 4a. Meanwhile, the SAXS scattering intensity increases when heating above~633 K. No noticeable changes in the SAXS profiles were found before crystallization. However, an interference peak 40 in the ED Ni 82 P 18 sample appeared after crystallization, and its intensity continuously increases during heating. Figure 4b shows the plots for the SAXS integrated intensity at a Q range of 0.0049-0.1 Å −1 and the WAXS integrated intensity at a Q range of 5.0191-5.0253 Å −1 . The DSC scan of the ED Ni 82 P 18 alloy is superimposed, which recorded a heat release at T S~4 50 K. The SAXS intensity shows a decrease at temperatures above  Fig. 6 for FFT of the scaled difference S(Q) pattern. The red arrow shows that there is a peak position shift in the sequence of MG Ni 82 P 18 ribbon, ED Ni 82 P 18 , and the difference pattern ~T S and a sharp increase at T x . The decrease of the SAXS intensity is attributed to a reduction in the degree of the nanoscale heterogeneity above~T S . Conversely, the WAXS intensity shows an increase upon heating above~T S . Taken together, these results indicate an accelerated ordering with reduced heterogeneity at these temperatures, which is similar to the behavior of a solidification process of MGFLs upon cooling 41,42 . Supplementary Fig. 8 indicates that the WAXS intensity increases during a real solidification process for the Vit 106 MGFL. The DSC scan for the ED Ni 82 P 18 alloy is consistent with the 'solidification-like' scenario. However, as shown in Fig. 1a, there is no such heat release process for the MG Ni 82 P 18 at the temperature of~T S . All the data presented indicate that there is an accelerated local ordering upon heating due to the existence of abundant loosely packed LLSs. Furthermore, the WAXS patterns upon heating also rule out that crystallization occurs at~T S. Supplementary Fig. 9 shows the HRTEM results for ED Ni 82 P 18 when heating above 600 K (between T S and T x ), and present an additional confirmation of the amorphous nature of ED Ni-P alloys in this temperature range. These results indicate that the LLS is a metastable structure, which continues to settle during heating. Moreover, the TEM and diffraction results confirmed that the crystallization of MG Ni 82 P 18 sample (not shown here) starts already at~580 K, a much lower temperature, confirming the better thermal stability of the ED Ni 82 P 18 alloy compared to the MG Ni 82 P 18 alloy.
Real space structure analysis and negative thermal expansion. Figure 5 shows the structure evolution in real-space for ED Ni 82 P 18 and MG Ni 82 P 18 alloys upon heating. Figure 5a, b are G (r) profiles for ED and MG Ni 82 P 18 samples, respectively. Arrows indicate the first R 1 and third R 3 coordination shells. The differential G(r) profiles for both samples, as shown in Supplementary Fig. 10a, b, were obtained by subtracting the first pattern at room temperature. By tracking the position change of R 1 and R 3 for both samples, the structure evolution at short-range and medium-range length scales can be visualized. As shown in Fig. 5c, the peak position of R 1 increases, as expected from the results of thermal expansion measurements. However, the peak position of R 3 decreases, showing a contraction upon heating. As indicated by the arrow in Supplementary Fig. 10a, the behavior of the higher coordination shells beyond R 3 is similar to that of R 3 during heating. For comparison, the peak positions of R 1 and R 3 for MG Ni 82 P 18 samples were also plotted in Fig. 5d. Both are expanding during heating, as expected. Figure 6 presents the thermal expansion data for ED and MG Ni 82 P 18 alloys. The MG Ni 82 P 18 exhibits a linear expansion upon heating. However, the ED Ni 82 P 18 shows an anomalous expansion behavior at~T S during heating. The CTE of the ED Ni 82 P 18 decreases below T S and approaches the lowest value of~−3 × 10 −6 K −1 , before starting to increase. The valley in the CTE curve for the ED Ni 82 P 18 amorphous alloy is exactly at the temperature~T S . This anomalous thermal expansion behavior is an additional confirmation of the PPT at T S , consistent with the thermal contraction of the atomic structure at MRO for ED Ni 82 P 18 measured by synchrotron X-ray diffraction, as illustrated in Fig. 5c.

Discussion
One of the challenges in order to prove the existence of the PPT is whether kinetically stabilized polyamorphous structures can coexist. Ni 82 P 18 amorphous alloys with a nanometer-sized microstructure (called ED Ni 82 P 18 alloys), characterized by two subpeaks in the second maximum of structure factor, can be prepared by changing the pulse current density based on ED (Supplementary Fig. 1) 20,23,43 . The ED Ni 82 P 18 alloys were found to contain LLSs with abundant loosely packed regions of increased free volume. The main evidence is revealed by the differential PDF, as the higher-order coordination shells show larger distance between atomic pairs,~2.3% larger relative to the MG counterparts, which is similar to the situation of 'real' MGFLs as compared to their glass states. The volume fraction of LLSs in ED Ni 82 P 18 alloys was found to be~50% by SAXS measurements, consistent with TEM observations. As shown in Fig. 1, although EDS mapping and 3D APT mapping did not resolve noticeable compositional variations at the nanoscale, HAADF in STEM mode showed bright/dark regions, indicating the existence of phases with different densities. The phases with smaller density appear as dark regions in the HAADF images because of their lower density, potentially leading to faster polishing during the thinning process of TEM sample 44,45 . In summary, the experimental results confirm the coexistence of two amorphous phases with comparable volume fractions but different packing schemes at MRO in ED Ni 82 P 18 alloys. Due to the presence of LLSs, the ED Ni 82 P 18 alloys exhibit a 'solidification-like' accelerated local ordering upon heating. As shown by the SAXS/WAXS experimental data in Fig. 4, the structure change for the ED Ni 82 P 18 alloys at T S is similar to the one for the real metallic liquids at T*, a liquid-liquid phase transition (LLPT) temperature ( Supplementary Fig. 8), i.e., at medium-range length scale. The 'solidification-like' ordering process upon heating is likely due to the relaxation of the local structure by the fast dynamics in the LLS and the annihilation of excessive free volume. Hyperquenched MGs 46,47 and nanostructured Sc-Fe nanoglass 38 prepared by inert gas condensation (IGC) were reported to have an excess free volume. Glasses prepared by these two processing routes are characterized by an enthalpy release peak below the glass transition, which is similar to the anomalous heat release process at T S for the ED Ni 82 P 18 alloys upon heating. A structure transition temperature at~430 K has been proposed in Ni 81 P 19 glasses 32 , which varies by 20 K from the T S ,~450 K observed in the present study. The difference may be caused by the composition difference and/or the different sample production conditions, such as quenching temperature 31 . Recently, a cluster ordering process scenario has been proposed to explain the free volume annihilation process for hyperquenched MGs and Sc-Fe nanoglass prepared by IGC 38,46,47 . Thus, the structural change at~T S observed in the present study suggests that the anomalous thermal behavior of Ni 82 P 18 at T S is analogous to a transition from 'LLS-to-SLS' upon heating.   The anomalous thermal contraction of ED Ni 82 P 18 at higher coordination shells provided further evidence of the existence of a LLS at room temperature and suggested that the ED Ni 82 P 18 alloys have controllable MRO structure. The transition point during the thermal contraction is at~T S . The thermal contraction for the ED Ni 82 P 18 sample at the MRO is consistent with the structural features of the LLS as discussed earlier. The unusual change in the MRO structure in ED Ni 82 P 18 further indicates that there is a PPT from a less dense LLS to a denser SLS. The CTE measurements have often been used to identify 'first-order' phase transitions in condensed matter [48][49][50] . The anomalous change of CTE of the ED Ni 82 P 18 amorphous alloy by the TMA measurements confirmed the PPT at~T S , as shown in Fig. 6. The thermal expansion of the ED Ni 82 P 18 shows a transition point at T S , where the CTE of ED Ni 82 P 18 alloy is~zero. Upon heating to~T S , the SLS in ED Ni 82 P 18 alloy shows thermal expansion, while the LLS shows a contraction. The cancellation of the positive and negative thermal expansions by different phases could result in a~zero thermal expansion in ED Ni 82 P 18 amorphous alloys. By changing the volume fraction of the SLSs and LLSs with varied MRO, it is possible to design amorphous alloys with tailorable thermal expansion behavior.
The crystallization temperature (T X2 ) of the ED Ni 82 P 18 amorphous alloy is higher than that (T X1 ) of the MG Ni 82 P 18 amorphous alloy, suggesting higher stability of the ED amorphous alloys. Furthermore, it was also found by additional in situ diffraction studies (not shown here) that, at the same annealing temperature, the time to crystallization in the ED Ni 82 P 18 amorphous alloy is much longer than that in the MG Ni 82 P 18 alloy. As shown in Supplementary Fig. 11, although the final crystalline products are identical (Fig. S3) for both alloys, the structure of the ED Ni 82 P 18 alloy at medium-range scale (e.g., 5.57 Å) starts to relax before crystallization. However, there is no such relaxation process for the MG Ni 82 P 18 alloy. The relaxation of before crystallization also means that ED samples are more stable. Recently, a thermodynamic scenario for nanostructured glasses prepared by IGC has been proposed, where the free energy of the interfacial regions between the MG particles are described as a lower energy amorphous state compared to the MG state 51 . It has been shown that the MGs after the occurrence of LLPT often showed better stability 28,30,52 . These studies suggested that it is easier for the amorphous structure to approach the lowest energy state after relaxation [53][54][55] .
These structural differences can lead to a dramatic change in other macroscopic properties. Here we also would like to point out that the differences in structure and changes upon annealing also result in differences in the mechanical properties of these alloys, with ED Ni 82 P 18 alloys displaying improved ductility. As shown in Supplementary Fig. 12 and Supplementary Note 2, in situ TEM tensile tests for MG Ni 82 P 18 and ED Ni 82 P 18 alloys were conducted at room temperature. The MG Ni 82 P 18 is relatively brittle while the ED Ni 82 P 18 shows an improved tensile ductility. The structural origin of this difference could be attributed to the coexistence of LLSs and SLSs of comparable volume fractions in the ED alloy, which do not exist in the MG alloy. Therefore, the unique microstructure in the ED Ni 82 P 18 alloy may play an important role in the supercooled-liquid-like deformation behavior 56,57 observed in this material.
In conclusion, the coexistence of liquid-like and SLSs with comparable volume fractions but different packing schemes at medium-range length scale has been established in ED Ni 82 P 18 amorphous alloys, using calorimetry, electron microscopy, PDF analysis, and simultaneous SAXS/WAXS during heating. The ED Ni 82 P 18 alloy possesses a unique structure factor featuring two distinct maxima intensities in the region of the second diffraction peak, both of comparable diffraction intensity. The loosely packed LLS within these regions was characterized by a larger atomic spacing at medium-range length scale, as revealed by the differential PDF profile. The observed structure change at temperaturẽ T S provides evidence of an 'LLS-to-SLS' transition upon heating. The anomalous thermal expansion behavior, contracting at MRO and nearly zero CTE at T S , is consistent with the scenario of a polyamorphous phase transition at~T S , indicating that the ED Ni-P alloys have tailorable MRO. Moreover, the ED Ni-P amorphous alloys have better thermal stability against crystallization and exhibit improved tensile ductility. These results suggest strategies to tailor the macroscopic properties of amorphous alloys, via MRO structural engineering, through the use of ED techniques.

Methods
Sample preparation. ED Ni 82 P 18 alloys were prepared using a multi-phase pulsed ED method. The bath compositions contain 200 g L −1 NiSO 4 ·6H 2 O, 25 g L −1 NiCl 2 ·6H 2 O, and 15 g L −1 H 3 PO 3 . Boric acid (H 3 BO 3 ) was added as supporting electrolytes and pH buffer. The ED was carried out at 60°C and pH = 1.2. The applied voltage was varied during the ED process in the form of three steps. During the first step, a high current density of 400 mA cm −2 was applied for t on1 = 1 ms. The second step consisted of the application of a lower current density (50-400 mA cm −2 ) for t on2 = 19 ms. During the third and last step, the current was turned off for t off = 20 ms. This procedure was repeated for the total deposition time of 1-3 h. Supplementary Fig. 1 shows the structure factor patterns for different alloys prepared using different current densities. For additional details, we refer to Guo et al. 20 . MG Ni 82 P 18 ribbons with the same composition as ED Ni 82 P 18 alloys were prepared using melt-spinning with a wheel speed of~30 m s −1 under high-purity argon atmosphere, on to a single copper wheel at 4000 r.p.m.
Transmission electron microscopy. TEM foils are prepared using the twin-jet electropolishing method. The instrument for electropolishing is the automatic twin-jet electro-polisher (Fischione Model 110). The electrolyte using for electropolishing is 16% perchloric acid, 42% acetic acid, and 42% methanol. Polishing parameters are set as voltage~20 V, and current is~40 mA. The electropolishing was performed at~233 K. Details of the TEM sample preparation using electropolishing can also refer to refs. 44,45 . FEI TF 20 high-resolution TEM (high voltage 200 kV) was employed. Drift-correction mode during EDS mapping in HAADF/ STEM mode was used to eliminate the experimental error. The nano-probe with resolution~1 nm was used for EDS mapping.
Differential scanning calorimetry. The DSC curves during heating were measured using platinum crucibles with Netzsch DSC 404 F3 in a high-purity Ar atmosphere. The weight of the samples for DSC is~20 mg. The heating rate is 10 K min −1 .
PDF analysis. Synchrotron high-energy X-ray experiments for PDF analysis were conducted at beamline 11-ID-C at the Advanced Photon Source, Argonne National Laboratory. High energy X-rays with a beam size of 0.5 mm × 0.5 mm and wavelength of 0.10804 Å were used in transmission geometry for data collection. Twodimensional (2D) diffraction patterns were obtained using a Perkin Elmer amorphous silicon detector. The data acquisition time for each pattern is 1 s. In situ heating was performed using a Linkam TS 1500 stage purified by high-purity Argon flow. A graphite crucible was employed for X-ray diffraction measurements of high-temperature melts. To improve the statistics of the data, 100 patterns were acquired for data averaging. The static structure factor, S(Q) with Q max~3 0 Å −1 , was derived from the scattering data by masking bad pixels, integrating images, subtracting the appropriate background and correcting for oblique incidence, absorption, multiple scattering, fluorescence, Compton scattering, Laue correction using Fit2D and PDFgetX2.
Simultaneous SAXS/WAXS. Simultaneous SAXS/WAXS experiments were performed at the beamline1-ID-E at the Advanced Photon Source, Argonne National Laboratory. A conventional SAXS/WAXS detector array was used. High-energy Xrays with a beam size of 0.1 mm × 0.1 mm and wavelength of 0.17711 Å were used in transmission geometry for data collection. Two-dimensional (2D) diffraction patterns were obtained using four combination GE detectors. A 2D PIXRAD detector was used for SAXS measurements. In situ heating was performed using a Linkam TS1500 stage with purification by high purity Argon flow. The heating rate is~10 K min −1 . The data acquisition time for each pattern is 1 s. However, including the time for saving data, the total acquisition time is~5 s for each pattern. The static structure factor, S(Q) with Q range from 2 to 15.5 Å −1 , was derived from the scattering data by masking bad pixels, integrating images, subtracting the appropriate background and correcting for oblique incidence, absorption, multiple scattering, fluorescence, Compton scattering, Laue correction using Fit2D and PDFgetX2. SAXS profiles with Q range from 0.0049 to 0.1686 Å −1 were reduced with data corrected for empty cell scattering, transmission, and detector response using a beamline MATLAB script.
In situ TEM tensile tests. In situ TEM tensile test was conducted using the Hysitron PI 95 TEM Pico-Indenter. The T-shaped specimens were prepared from the ED and MG Ni 82 P 18 parent body by focused-ion-beam (FIB). The sample evolution during the tests was recorded in movies. The methods for details can refer to the Tian et al. 58 . A total of 10 specimens were tested to confirm the observed tensile plasticity of NG Ni 82 P 18 alloys.
Thermal expansion. Thermal expansion measurements were conducted in tensile mode using NETZSCH TMA 402F3. The sample is 15, 5, and 0.035 mm in length, in width, and in thickness, respectively. Before the experiment of the Ni-P samples, a standard sample, Al 2 O 3 , was employed for calibration of the instrument. Subsequently, a pre-set load force of 0.010 N was applied during the entire test with a nitrogen flow at a flow rate of 20 ml min −1 . The heating rate was 20 K min −1 , over a temperature range of 303-723 K.

Data availability
The data that support the findings of this study are available from the corresponding author upon request.