The 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 scales1,2,3,4. This complexity has led to some ambiguities in describing these structures, particularly for evolving structures during phase transitions, e.g., glass transitions1,5. To modify the properties of amorphous materials, it is desirable to develop the ability to tailor the local order in disordered states6,7. However, the structure factor for glassy alloys prepared using conventional methods, i.e., rapid quenching techniques8,9, 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 maximum12,13, indicating the short-to-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 systems7,14.

Before the first rapidly quenched glassy alloy was reported in 196015, electrodeposition (ED) had already been employed as a powerful technique for preparing metastable alloys16. The ED amorphous alloys, e.g., the iron-group alloys17, 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 properties16,17,18,19. Pulsed ED has been successfully used to prepare Ni–P amorphous alloys20,21. The reported ED Ni–P amorphous alloys possessed similar diffraction patterns22,23 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-to-liquid (LL) phase transition28,29,30, are still a debated issue. A PPT has been proposed in a Ni82P18 glass upon heating23,31,32. In this regard, the observation of coexisting multiple amorphous states at the same time and space33,34 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 properties7.

In this paper, we demonstrate that Ni82P18 amorphous alloys, prepared using multi-phase pulsed ED within a specific pulse current range20, have a unique structure factor: for the second peak maximum, there are two sub-peaks with comparable diffraction intensities. The ED Ni82P18 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 Ni82P18) and nanometer-sized regions with liquid-like structure (LLS, of loose-packing compared to a melt-quenched Ni–P ribbon sample). The structure of the ED Ni82P18 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 Ni82P18 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, Zr57Nb5Al10Cu15.4Ni12.6 (Vit 106) and Pd43Cu27Ni10P20, respectively. Simultaneous small-angle/wide-angle X-ray scattering (SAXS/WAXS) reveal a ‘solidification-like’ structure transformation of the ED Ni82P18 alloy upon heating. Finally, compared with the expansion behavior of MG Ni82P18 alloys, an unusual thermal contraction at medium-range length scale for the LLS of the ED Ni82P18 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 Ni82P18 alloy upon heating, further confirming a PPT at ~450 K. Furthermore, the as-prepared ED Ni82P18 amorphous alloys show better thermal stability and even tensile ductility at the sub-micron scale.


Thermal analysis and nanoscale heterogeneity

Figure 1a presents the differential scanning calorimetry (DSC) scans for the as-prepared MG Ni82P18 ribbons and ED Ni82P18 amorphous alloys. The ED Ni82P18 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 Ni82P18 samples prepared at different pulse current densities. The crystallization temperature TX2 for the ED Ni82P18 alloy is ~633 K, which is ~53 K higher than that of the MG Ni82P18 alloy (TX1 ~ 580 K). Surprisingly, there is a thermal release phenomenon at TS, ~450 K, for the ED Ni82P18 alloy, which is much lower than the nominal glass transition temperature (Tg), ~570 K, for the MG Ni82P18 sample35. The calorimetric studies suggest that there might be a structural change upon heating and the ED Ni82P18 alloy has much better thermal stability than that of the MG Ni82P18 alloy. The APT results in Fig. 1b illustrate the uniform distribution of the alloying elements (Ni and P) in the as-deposited ED Ni82P18 alloy. Figure 1c is the high angle annular dark field (HAADF) image acquired in scanning transmission electron microscopy (STEM) mode for the ED Ni82P18 alloy. It shows variations of mass/thickness contrast ~10–20 nm, indicating that the microstructure of the ED Ni82P18 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 energy-dispersive 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 Ni82P18 sample with the same chemical composition.

Fig. 1
figure 1

Thermophysical behavior and structure inhomogeneity. a Calorimetric curves for metallic glass (MG) Ni82P18 ribbon (blue) and electrodeposition (ED) Ni82P18 alloy (red). b Composition mapping by 3D atomic probe, showing homogeneous Ni and P element distribution at nano-scale in ED Ni82P18 alloy; scale bar, 100 nm. c High angle annular dark field image (HAADF) of the ED Ni82P18 alloy, showing bright/dark contrast at 10–20 nm; scale bar, 50 nm. The inset is the selective area electron diffraction pattern (SAED) with diffused halos, illustrating the amorphous nature of the as-prepared ED Ni82P18 alloy; scale bar, 10 nm−1. High-resolution transmission electron microscopy (HRTEM) images with the typical maze-like amorphous structure for the dark region d and bright region e. HAADF image; scale bars, 2 nm. f Energy-dispersive X-ray spectroscopy (EDS) line mapping results for Ni element and P element, showing that there is no obvious composition fluctuation. The average composition is Ni~82 at.% and P~18 at.%. The mapping line is indicated by the red line as shown in c. Error bars are defined as the standard deviation

Figure 2a shows the SAXS profiles for the ED Ni82P18 alloy and the MG Ni82P18 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 Ni82P18, which is much higher than that of the MG Ni82P18 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 Igor36. 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 on the model fitting in Fig. 2a. It indicates that there are spheroidal granular-like structures with diameters distributed between 8 and 25 nm.

Fig. 2
figure 2

Determination of heterogeneous nanoscale structure. a Small-angle X-ray scattering (SAXS) profiles for the electrodeposition (ED) Ni82P18 alloy and the metallic glass (MG) Ni82P18 ribbon. The blue dotted line is the model fitting based on the spheroid model with polydispersity. Error bars are defined as the standard deviation of photon count. For the inset, red circles and blue dots are SAXS profiles for ED alloy, MG ribbon plotted as linear scale respectively. b Size distribution function for ED Ni82P18 sample calculated by model fitting in a, showing that there are various regions with diameter ~8–25 nm

The existence of LLSs

Figure 3a shows the S(Q) patterns of the ED and MG Ni82P18 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 Ni3P (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 Ni82P18 alloy pattern after subtracting 50% of the MG Ni82P18 ribbon pattern. The formation of ED Ni–P amorphous alloys is proposed to consist of nucleation and growth of the amorphous nano-grains20. The structural model37 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 Ni82P18 alloy based on the Debye–Bueche (DB) random two-phase model38 illustrates that the volume fraction of the loose-packing 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).

Fig. 3
figure 3

Determination of the liquid-like structures. a Structure factor, S(Q), for electrodeposition (ED) (red line) and metallic glass (MG) Ni82P18 (blue line) amorphous alloys. b Reduced pair distribution function (PDF), G(r), for ED alloy (red line) and MG ribbon (blue line). The turquoise line with solid circles is the pattern obtained by fast Fourier transform (FFT) of the scaled difference S(Q) between the ED alloy and ribbon. Details can be referred to the Supplementary 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 Ni82P18 ribbon, ED Ni82P18, and the difference pattern

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 by ~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 Ni81P19 metallic liquid39. 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: Zr57Nb5Al10Cu15.4Ni12.6 (Vit 106) and Pd43Cu27Ni10P20 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 Zr57Nb5Al10Cu15.4Ni12.6 (i.e., Vit 106) and Pd43Cu27Ni10P20. 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 Tx ~ 633 K, crystallization occurs in the ED Ni82P18 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 peak40 in the ED Ni82P18 sample appeared after crystallization, and its intensity continuously increases during heating.

Fig. 4
figure 4

‘Solidification-like’ behavior upon heating. a Synchrotron small-angle X-ray scattering (SAXS) profiles for the electrodeposition (ED) Ni82P18 alloy during heating. The inset shows the 3D plot of wide-angle X-ray scattering (WAXS) patterns acquired simultaneously during heating. A rapid development of SAXS intensity is observed above the crystallization temperature of Tx ~ 633 K. Error bars are defined as the standard deviation of photon count. b The turquoise circles are the normalized integrated intensity of WAXS patterns over Q range, 5.5007–5.5056 Å−1. The blue triangles are the normalized integrated intensity of SAXS patterns over Q range, 0.049–0.1 Å−1. The red line is the differential scanning calorimetry (DSC) scan of ED sample heating from room temperature to 700 K. The red dotted lines indicate the transition temperature TS and crystallization temperature Tx. The heating rate for the simultaneous SAXS/WAXS measurement and the DSC scan is 10 K min−1

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 Ni82P18 alloy is superimposed, which recorded a heat release at TS ~ 450 K. The SAXS intensity shows a decrease at temperatures above ~TS and a sharp increase at Tx. The decrease of the SAXS intensity is attributed to a reduction in the degree of the nano-scale heterogeneity above ~TS. Conversely, the WAXS intensity shows an increase upon heating above ~TS. 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 cooling41,42. 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 Ni82P18 alloy is consistent with the ‘solidification-like’ scenario. However, as shown in Fig. 1a, there is no such heat release process for the MG Ni82P18 at the temperature of ~TS. 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 ~TS. Supplementary Fig. 9 shows the HRTEM results for ED Ni82P18 when heating above 600 K (between TS and Tx), 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 Ni82P18 sample (not shown here) starts already at ~580 K, a much lower temperature, confirming the better thermal stability of the ED Ni82P18 alloy compared to the MG Ni82P18 alloy.

Real space structure analysis and negative thermal expansion

Figure 5 shows the structure evolution in real-space for ED Ni82P18 and MG Ni82P18 alloys upon heating. Figure 5a, b are G(r) profiles for ED and MG Ni82P18 samples, respectively. Arrows indicate the first R1 and third R3 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 R1 and R3 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 R1 increases, as expected from the results of thermal expansion measurements. However, the peak position of R3 decreases, showing a contraction upon heating. As indicated by the arrow in Supplementary Fig. 10a, the behavior of the higher coordination shells beyond R3 is similar to that of R3 during heating. For comparison, the peak positions of R1 and R3 for MG Ni82P18 samples were also plotted in Fig. 5d. Both are expanding during heating, as expected.

Fig. 5
figure 5

Real-space structure analysis. a Reduced pair distribution function (PDF), i.e., G(r) obtained by fast Fourier transform of the structure factor, profiles during the heating process for the electrodeposition (ED) Ni82P18 alloy. The arrows indicate the first coordination shell (R1) and the third coordination shell (R3). b The temperature-dependent reduced pair distribution function, G(r) of the metallic glass (MG) Ni82P18 alloy. c The peak positions of R1 and R3 as a function of temperature. The peak position of R1 shows normal expansion upon heating, but the R3 peak position shows an anomalous contraction upon heating and exhibits a crossover at TS. d The position of the first coordination shell, R1, and the third coordination shell, R3, as a function of the temperature of the MG Ni82P18 alloy

Figure 6 presents the thermal expansion data for ED and MG Ni82P18 alloys. The MG Ni82P18 exhibits a linear expansion upon heating. However, the ED Ni82P18 shows an anomalous expansion behavior at ~TS during heating. The CTE of the ED Ni82P18 decreases below TS and approaches the lowest value of ~−3 × 10−6 K−1, before starting to increase. The valley in the CTE curve for the ED Ni82P18 amorphous alloy is exactly at the temperature ~TS. This anomalous thermal expansion behavior is an additional confirmation of the PPT at TS, consistent with the thermal contraction of the atomic structure at MRO for ED Ni82P18 measured by synchrotron X-ray diffraction, as illustrated in Fig. 5c.

Fig. 6
figure 6

Anomalous thermal expansion behaviors. The blue curves are the relative displacements and the corresponding coefficients of thermal expansion for metallic glass (MG) Ni82P18 samples as a function of temperature, during tension using thermal mechanical analysis (TMA). The red dotted lines are the relative displacements and the corresponding coefficients of thermal expansion for electrodeposition (ED) Ni82P18 samples as a function of temperature, during tension using TMA. The MG sample exhibits a linear expansion upon heating, while the ED sample shows an anomaly. The coefficient of thermal expansion is almost zero, at temperature ~TS, as indicated by the star


One of the challenges in order to prove the existence of the PPT is whether kinetically stabilized polyamorphous structures can co-exist. Ni82P18 amorphous alloys with a nanometer-sized microstructure (called ED Ni82P18 alloys), characterized by two sub-peaks 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 Ni82P18 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 Ni82P18 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 sample44,45. In summary, the experimental results confirm the coexistence of two amorphous phases with comparable volume fractions but different packing schemes at MRO in ED Ni82P18 alloys.

Due to the presence of LLSs, the ED Ni82P18 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 Ni82P18 alloys at TS 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 MGs46,47 and nanostructured Sc–Fe nanoglass38 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 TS for the ED Ni82P18 alloys upon heating. A structure transition temperature at ~430 K has been proposed in Ni81P19 glasses32, which varies by 20 K from the TS, ~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 temperature31. 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 IGC38,46,47. Thus, the structural change at ~TS observed in the present study suggests that the anomalous thermal behavior of Ni82P18 at TS is analogous to a transition from ‘LLS-to-SLS’ upon heating.

The anomalous thermal contraction of ED Ni82P18 at higher coordination shells provided further evidence of the existence of a LLS at room temperature and suggested that the ED Ni82P18 alloys have controllable MRO structure. The transition point during the thermal contraction is at ~TS. The thermal contraction for the ED Ni82P18 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 Ni82P18 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 matter48,49,50. The anomalous change of CTE of the ED Ni82P18 amorphous alloy by the TMA measurements confirmed the PPT at ~TS, as shown in Fig. 6. The thermal expansion of the ED Ni82P18 shows a transition point at TS, where the CTE of ED Ni82P18 alloy is ~zero. Upon heating to ~TS, the SLS in ED Ni82P18 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 Ni82P18 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 (TX2) of the ED Ni82P18 amorphous alloy is higher than that (TX1) of the MG Ni82P18 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 Ni82P18 amorphous alloy is much longer than that in the MG Ni82P18 alloy. As shown in Supplementary Fig. 11, although the final crystalline products are identical (Fig. S3) for both alloys, the structure of the ED Ni82P18 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 Ni82P18 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 state51. It has been shown that the MGs after the occurrence of LLPT often showed better stability28,30,52. These studies suggested that it is easier for the amorphous structure to approach the lowest energy state after relaxation53,54,55.

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 Ni82P18 alloys displaying improved ductility. As shown in Supplementary Fig. 12 and Supplementary Note 2, in situ TEM tensile tests for MG Ni82P18 and ED Ni82P18 alloys were conducted at room temperature. The MG Ni82P18 is relatively brittle while the ED Ni82P18 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 Ni82P18 alloy may play an important role in the supercooled-liquid-like deformation behavior56,57 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 Ni82P18 amorphous alloys, using calorimetry, electron microscopy, PDF analysis, and simultaneous SAXS/WAXS during heating. The ED Ni82P18 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 temperature ~TS provides evidence of an ‘LLS-to-SLS’ transition upon heating. The anomalous thermal expansion behavior, contracting at MRO and nearly zero CTE at TS, is consistent with the scenario of a polyamorphous phase transition at ~TS, 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.


Sample preparation

ED Ni82P18 alloys were prepared using a multi-phase pulsed ED method. The bath compositions contain 200 g L−1 NiSO4·6H2O, 25 g L−1 NiCl2·6H2O, and 15 g L−1 H3PO3. Boric acid (H3BO3) 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 ton1 = 1 ms. The second step consisted of the application of a lower current density (50–400 mA cm−2) for ton2 = 19 ms. During the third and last step, the current was turned off for toff = 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 Ni82P18 ribbons with the same composition as ED Ni82P18 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 electro-polishing 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. Two-dimensional (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 Qmax ~ 30 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 X-rays 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 Ni82P18 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 Ni82P18 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, Al2O3, 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.