Submicrostructure and Characteristics of the Short-Range Atomic Order in an Amorphous Ti–Ni–Ta–Zr-Based Surface Alloy Formed on a TiNi Substrate by the Electron-Beam Method

Abstract

This study presents the results of studying the microstructure and topological short-range atomic order in an amorphous Ti−Ni−Тa−Zr-based surface alloy formed by the additive method through pulsed electron-beam liquid-phase mixing of the “Ti₇₀Ta₃₀ film (50 nm)/Zr film (100 nm)/TiNi substrate” system. It is shown that an amorphous structure with a thickness of 2 μm is formed in the cross-section of the surface alloy and is characterized by the gradient chemical composition. It is found that the transition sublayer adjacent to the TiNi substrate has a nanocomposite crystalline structure based on the Ti₂Ni intermetallic compound. By means of the atomic radial distribution function method, using electron nanobeam diffraction data, a study of the topological short-range atomic order in the amorphous layer is performed. It is shown that the atomic structure in the amorphous surface Ti−Ni−Тa−Zr alloy has a cluster structure which can be described by the superposition of coordination polyhedra interconnected with each other by common faces corresponding to the different crystalline devitrification phases.

INTRODUCTION

At present, researchers have a particular interest in a relatively new class of materials which are known as bulk metallic glasses (BMGs) due to their unique combination of physical, mechanical, chemical, and other properties which are useful in practice [1–3]. These materials are produced on the basis of multicomponent metallic systems whose alloys are capable of being easily amorphized by quenching from the liquid state at relatively low cooling rates. Therefore, the search for metallic systems whose alloys possess a high glass-forming ability is one of the main problems in the area of BMG development.

Another important problem related to the development of BMGs is investigation of the atomic structure of the amorphous phase—the structure of short-range atomic order implemented in the amorphous matrix. The analysis of numerous scientific studies (for example, [4–8]) shows that the structure of short-range atomic order is determined by the conditions of production and chemical composition of amorphous alloys. The structure of short-range atomic order is analyzed by means of X-ray and electron-beam diffraction methods which comprise information about the nearest atom arrangement to be obtained with the help of atomic radial distribution functions (ARDFs). Despite the fact the ARDF provides only average statistical results on the relative position of atoms within a few coordination shells, the analysis of short-range atomic order by means of the ARDF is non-routine and may be useful in predicting the composition of alloys with a good glass-forming ability. The difficulty the difficulty is the fact that the fact that when analyzing nanoscale structures with translation-symmetry violation, it is necessary to carry out local structural analysis in the range of 1.5−2.0 nm. At present, this analysis can be made by high-resolution transmission electron microscopy (TEM) methods, in particular, by the electron nanodiffraction method [9]. There are few studies published elsewhere which are related to the use of this method for analyzing the atomic structure of amorphous alloys.

Nowadays, NiTi-based alloys are widely used as medical shape-memory materials for producing miniature implants and endoscopic instruments [1] used under cyclic loading conditions in such highly-corrosive media as biological fluids. Therefore, the problem of the surface modification of miniature constructions made of TiNi alloys, related to the formation of barrier layers with special properties, namely, preventing the nickel release from the implant material to biological tissues and, at the same time, enhancing the parameters of cyclic fatigue endurance of these materials, is relevant for alloys of this type. A promising way to form barrier layers with special properties, for example, to reduce the nickel concentration in the surface layers of TiNi alloys, enhance the corrosion resistance, biocompatibility, plastic-elastic and mechanical properties is the electron-beam method for the synthesis of surface alloys on the TiNi surface. This method was approved and described in [10, 11] by the example of obtaining thin (with a thickness of 3–5 μm) surface layers based on the Ti–Ta–Ni system with an amorphous nanocomposite structure and a high concentration of the alloying element, tantalum, on the surface of the TiNi-alloy substrates. Strong adhesion of the coatings to the substrate is a necessary requirement in problems related to the development of coatings and thin films on the surfaces of bulk materials. The absence of interlayers between the film and the substrate using the synthesis method of surface alloys removes the problem of adhesion between them. It was shown [12] that the use of the electron-beam method leads to an efficient increase in the radiopacity of a TiNi-alloy wire with a diameter of 150 μm, high biocompatibility, and corrosion resistivity of Ti−Ta−Ni surface layers, which is related in many respects to their amorphous nanocomposite structure.

The suitability of the synthesis of amorphous films and coatings on the surface of functional materials has been repeatedly noted in scientific publications (see, for example, [13–15]). The results of investigations [16, 17] prove that the use of thin amorphous nanocomposite films is efficient in improving the fatigue characteristics of materials. Evaluation of the mechanical and thermal stability of such films is related, above all, to investigation of their phase composition and internal atomic structure, including short-range atomic order of the amorphous phase.

The aim of this study is to reveal the characteristics of the submicrostructure and topological short-range atomic order of Ti–Ni–Ta–Zr-based amorphous surface alloy formed by the additive method by means of the pulsed electron-beam liquid-phase mixing of the “Ti₇₀Ta₃₀ film (50 nm)/Zr film (100 nm)/TiNi substrate” systems.

MATERIALS AND METHODS OF INVESTIGATIONS

Synthesis of the Ti–Ni–Ta–Zr surface alloy on the TiNi substrate was carried out using the RITM-SP automatic setup (Microsplav, Russia) [18]. The synthesis method is described in detail in [10] and schematically illustrated in Fig. 1a. In this study, for surface alloying, Zr and Ti–Ta (Ti₇₀Ta₃₀ at %) films were deposited by the magnetron method (Zr, Ti, and Ta targets with a purity of 99.95%, Girmet, Russia) onto a TiNi substrate. Control of the composition and thickness of the initial films was performed on test samples with TiNi substrates. Films with given thicknesses (Zr, 100 nm) and (Ti₇₀Ta₃₀, 1 μm) were obtained under the same deposition conditions (described below), however, without electron-beam treatment. Figure 1b shows the bright-field transmission electron microscope (TEM) image of the (Ti₇₀Ta₃₀, 1.0 μm)/(Zr, 100 nm)/TiNi layer composite; Fig. 1c shows the corresponding microdiffraction.

Fig. 1.

(а) Scheme illustrating the additive method for the synthesis of a surface alloy by means of the liquid-phase mixing of Zr and Ti₇₀Ta₃₀ films with a TiNi substrate; (b) bright-field image of the structure in the cross section for the system {(Ti₇₀Ta₃₀, 1 µm) coating/(Zr, 100 nm) film/TiNi substrate}; (c) microdiffraction pattern from the region inside the circle shown in Fig. 1b.

Synthesis of the surface alloy consisted of three stages. Stage 1 included preliminary treatment of the TiNi substrate by a low-energy high-current electron beam (LEHCEB) in the following mode: energy density E_S = 3.4 ± 0.7 J/cm², pulse duration τ = 2.0–2.5 μs, number of pulses n = 32. At stage 2, the TiNi substrate was arranged by means of a manipulator along the magnetron-module axis to deposit a Zr film with a thickness of 100 nm. For pulsed melting of the “Zr(100 nm)/TiNi” system, the samples were arranged along the electron-beam axis and treated by the LEHCEB in the following mode: energy density E_S= 2.0 ± 0.2 J/cm², number of pulses n = 5. Stage 3 included the alternating deposition of a Ti₇₀Ta₃₀ film with a thickness of 50 nm and its co-melting with the TiNi substrate surface-alloyed by Zr, using the same LEHCEB regime as that used in stage 2. The number of cycles of synthesis of the “Ti₇₀Ta₃₀(50 nm)/Zr/TiNi” system was N = 20, so that the total thickness of the melted Zr and (Ti, Ta) films was 1.1 μm. For uniform liquid-phase mixing of the film and substrate components, the total diffusion length of film atoms, $\ell {{}_{D}}$, in the substrate melt must considerably exceed the thickness of the initial film in each separate cycle. When choosing the modes of LEHCEB treatment and the film thicknesses, we were guided by the data obtained in [10]. According to the data of [10], we can conclude that for one cycle, $\ell {{}_{D}}$ ~ 5 × 100 = 500 nm ⪢ d_Zr = 100 nm and ⪢ d_TiTa = 50 nm, i.e., diffusion of the film components into the melt and their mixing in the melt took place. Let us designate the Ti–Ni–Ta–Zr surface alloy formed on the TiNi substrate as TNTZ alloy.

Investigations of the microstructure of the TNTZ surface alloy were performed by using equipment of the “Nanotech” center of collective use of the Institute of Strength Physics and Materials Sciences, Siberian Branch, Russian Academy of Sciences (Tomsk). To investigate the surface morphology, an Axiovert 200MAT optical microscope (Zeiss, Germany) was used. Electron-microscopic investigations by the bright- and dark-field methods, as well as the micro- and nanodiffraction analysis methods were performed using a JEM-2100 transmission electron microscope (TEM) (JEOL, Japan) at an accelerating voltage of 200 kV and an EVO 50 scanning electron microscope (SEM) (Zeiss, Germany). Energy-dispersion analysis of the element composition of the matrix was carried out using the methods described in detail in [19, 20], as well as in our papers [10, 21, 22], on INCA Energy energy-dispersive spectrometers (EDSs) (Oxford Instruments, Great Britain) installed at SEMs and TEMs. To obtain SEM/EDS data averaged over the analysis regions, surface areas were chosen with a magnification of ×1000 mainly to verify the Ni/Ti ratio in the sample (we investigated at least ten areas of analysis for each sample) and estimated the limits of detection of light elements (С, О). The parameters of the SEM/TEM analysis were as follows: accelerating voltage is 10 kV, standardization is the Ni/Ti standardization at 10 kV with the use of the results obtained at 20 kV, working distance is 8.5 mm. The diameter of the analyzed region for light (C, O) elements and and intermediate transition (Ti, Ni, Ta, Zr) metals was ~4 and ~1 μm, respectively. Element-composition analysis was performed along a cross-section to the irradiated surface. The parameters of the SEM/EDS analysis were as follows: the accelerating voltage is 200 kV; diameter of the electron probe is ∼12 nm; the analysis regions are rectangular areas with dimensions of ~400 × 100 nm. When estimating the concentration of light elements (carbon, oxygen), we considered the possibility of increasing their concentration not only as a result of electron-beam treatment, but also due to gas separation from the inner walls of the working chamber of the electron microscope and the surfaces of the equipment inside it. For this purpose, we used standard samples made of the same alloy without electron-beam treatment. Before the measurements, the surfaces of these samples were thoroughly cleaned in a HPT-100 (Henniker Plasma, USA) plasma cleaning system. Under the above-indicated conditions, the measurement errors were as follows: ±2 at % (Ti, Ni, Zr), ±1 at % (Ta), ±4 at % (О), and ±5 at % (С).

Foils for TEM were prepared using the EM 09100IS (JEOL, Japan) ion etching setup in the “cross-section” geometry.

Using the method proposed by Cockayne [23, 24], from the nanodiffraction data obtained from different local areas of the analyzed amorphous alloy, the analytical form of the ARDF G(r) was determined as follows:

$$G(r) = 4\int\limits_0^ \propto {\varphi {\text{(}}q{\text{)sin(}}qr{\text{)}}dq = 4\pi r[g(r) - {{\rho }_{0}}],} $$

(1)

where r is the radius vector, λ is the wavelength of electrons, q = 4π sin(θ)/λ is the scattering vector, φ(q) is the structural factor, and ρ₀ is the average density of the substance.

The RADF was constructed by using the standard procedure that considers corrections associated with high-frequency oscillation of the structural factor φ(q) at values of q > 8 nm^–1 by means of introducing the damping multiplier ~exp(−bq²) [23]:

$$\varphi (q) = \left[ {\frac{{I{{{(q)}}_{{\exp }}} - {{\sum }_{i}}{{N}_{i}}\left\langle {f_{i}^{2}(q)} \right\rangle }}{{{{\sum }_{i}}{{N}_{i}}{{{\left\langle {{{f}_{i}}(q)} \right\rangle }}^{2}}}}} \right]q\exp ( - b{{q}^{2}}),$$

(2)

where f_i (q), N_i are the atomic scattering factor of the ith atom and the number of scattering atoms of the ith kind, respectively; b is the damping factor.

The element composition of the amorphous phase corresponding to the depth of the layer from which nanodiffractions were obtained were determined from the SEM/EDS experimental data. The atomic scattering factors f_i(q) were taken from [25]. The approximation parameters N and С, responsible for the number of scattering centers and the intensity of the dark current, respectively, were chosen according to the conditions under which the structural factor represented the following function oscillating around the zero-position [26]:

$$\left\{ \begin{gathered} {{\sum\limits_i {{{w}_{i}}\left( {I{{{({{q}_{i}})}}_{{\exp }}} - N\sum\limits_j {{{p}_{j}}\left\langle {f_{j}^{2}({{q}_{i}})} \right\rangle - C} } \right)} }^{2}}{\kern 1pt} {\kern 1pt} = {\text{minimum}}{\text{,}} \hfill \\ I{{({{q}_{k}})}_{{\exp }}} - N\sum\limits_j {{{p}_{j}}\left\langle {f_{j}^{2}({{q}_{k}})} \right\rangle - C = 0,} \hfill \\ \end{gathered} \right.$$

(3)

where w_i is the statistical weight; p_j is the part of atoms of the jth kind in the analyzed region (in at %), i.e., the concentration of these atoms.

In this experiment, the foil thicknesses were larger than 50 nm, the range of electron scattering vectors in the reciprocal space was restricted by 10 nm^–1. The coordination numbers were not determined because of the contributions of inelastic and multiple electron scattering to the intensity I(q)_exp. The radii of the first, second, and third coordination shells were determined from the results of the analysis of three nanodiffractions at a probe-beam size of 10 nm. To obtain the azimuthally averaged intensity, the nanodiffractions were subjected to computer processing based on GatanMicroscopySuiteSoftware (DigitalMicrograph, PASAD) [27]. The accuracy in determining the radii of the first and second coordination shell were no worse than ±0.002 nm.

MEASUREMENT RESULTS AND THEIR DISCUSSION

Structure and Element Composition of the Ti−Ni−Ta−Zr Surface Alloy

Figure 2 shows optical images of the surfaces of TNTZ alloys. One can see the characteristic features of the surface microrelief related to multiple pulsed treatment of LEHCEB: the surface has a smoothed wavy microrelief with some microcraters (Figs. 2a and 2b). As was shown in [21], these effects are related in many respects to the radial melt flow of the alloy due to surface tension forces—Marangoni thermal- and concentration-capillary convection [28]. Another possible reason for the formation of a observed microrelief on the surface of TNTZ alloys is material evaporation from the free surface. The effect of the selective evaporation of nickel from the surface was observed in [29–31] in experiments on the irradiation of TiNi alloys by means of LEHCEB at energy densities (E_S = 3.0–3.4 J/cm²) close to those used in our study. In the process of the alloy being under the irradiation of a low-energy (up to 30 keV) electron flux, the value of the surface erosion coefficient can reach 10³ atom/electron [32], which leads (according to the estimations made in [31]) to the evaporation of a thin TiNi layer with a thickness of 17 nm for the period of pulse duration (E_S = 3 J/cm², τ = 1.5 μs). It is important to note that the modified surface does not contain micropores or cracks; the characteristic martensite relief, which indicates the presence of oriented elastic stress fields in the surface layer [21, 29], is absent.

Fig. 2.

Optical images of the TNTZ-alloy surface.

Figure 3 shows the results of the SEM/EDS and TEM/EDS analyses of the chemical-element distribution along the normal to the surface of the TNTZ alloy. According to the SEM/EDS data, the carbon concentration in the TNTZ surface alloy is below the detection limit (DL), while according to the TEM/EDS data, the carbon concentration is ~10 at % and does not change along the line of scanning (i.e., with depth from the treated surface). Similar carbon concentrations were observed in the control sample. Therefore, we can conclude that the reason for the determination of carbon in the analyzed regions is the residual atmosphere of the microscope working chamber. The oxygen concentration in the surface layer of the irradiated sample was found to be ∼10 at %, according to the data of both SEM/EDS and TEM/EDS analysis. In the layer with a thickness of ∼4 μm (SEM/EDS), the oxygen content dropped to a level of ∼4 at %, which is close to its values in the volume of the standard sample (∼3 at %) (Fig. 3b, inset). Based on the results obtained in this study, we have come to the conclusion that the presence of light elements in TNTZ surface alloy is minimal and is not related to the method of obtaining this alloy; therefore, it was not considered in further investigations.

The distribution profiles for the concentration of the main components along the normal to the surface of TNTZ alloy obtained by the SEM/EDS and TEM/EDS methods (Fig. 3a) qualitatively agree with each other. According to the TEM/EDS data, the element composition of the TNTZ alloy in the surface layer to a depth of ∼1 μm is nearly constant; while at a depth from ∼1 to ∼2.5 μm, gradient changes in the Ni, Ta, and Zr concentrations were observed, except for the Ti concentration. The following result confirmed by both analysis methods is important: zirconium is reliably fixed in the surface layer to a depth of ∼2.5 μm (Figs. 3a, 3c, 3d) at the DL level (≤2 at %) and is quasi-homogeneously distributed within this layer. At a depth of ≥2.5 μm, there are no alloying elements in the TiNi matrix; the Ti : Ni ratio is close to equiatomic. It follows from the above-mentioned findings, that by using the additive synthesis method, we have succeeded in forming a Ti–Ni–Ta–Zr 4-component surface alloy with a smooth gradient transition and nearly homogeneous component distribution over its depth. The element composition at the upper (a depth of 0.1 μm) and lower (a depth of 1.8 μm) boundaries of the surface alloy (Fig. 3a) corresponds to the Ti₅₂Ni₃₃Ta₁₃Zr₂ and Ti₅₁Ni₄₀Ta₇Zr₂ (at %) formulas, respectively.

Investigation of the TNTZ-alloy structure in the “cross-section” geometry has shown that the surface layer with a thickness of up to 3.5 μm has a gradient structure and consists of the following sublayers: an external amorphous layer (Figs. 4a–4d) with a thickness of 2 μm; a nanocrystalline sublayer consisting of nano-grains of the Ti₂Ni phase with a size of 20–50 nm (Figs. 4a, 4c, and 4e); a sublayer with a eutectic structure consisting of a matrix phase of equiatomic composition of TiNi (with an atom-ordered B2-type body-centered cubic (bcc) structure) and the phase of Ti₃Ni₄ with a rhombohedral structure (the R3 structural type) (Fig. 5). A nonmelted layer of the TiNi substrate is located at a depth below 3.5 μm and is characterized by a single-phase (based on the В2 phase) structural state similar to the initial state.

Fig. 3.

SEM/EDS (dotted lines) and TEM/EDS (solid lines) concentration profiles of the distribution of components of the TNTZ surface alloy over the depth from the surface (а); SEM image of the cross-section and the region of the SEM/EDS element analysis (b), on the inset: SEM/EDS concentration profiles of the oxygen change in the surface layer of the standard (TiNi) and investigated (TNTZ) alloys; SEM/EDS (c), TEM/EDS (d) spectra obtained at the same depth of ∼1 µm from the irradiated surface, on the insets: images of the cross-sections with the lines along which the EDS analysis was performed.

Fig. 4.

TEM images: (a) structure of the cross section of the surface layer of the TiNi sample with TNTZ alloy at its surface; (b) amorphous structure and microdiffraction pattern (inset) near the treated surface; (c) diffusion nanocrystalline sublayer; (d) nanopore and HAADF-STEM-image of this nanopore (inset); (e) microdiffraction from the diffusion sublayer.

Fig. 5.

Bright-field TEM image of the submicrostructure of the layer located in the heat-affected zone (HAZ) at a depth of 3 µm from the surface of the TNTZ alloy (a); nanodiffraction patterns from the particles of the Ti₃Ni₄ phase (b, c).

The presence of the amorphous structure in TNTZ alloy is confirmed by both the microdiffraction patterns (Fig. 4b, inset), which contain an amorphous halo, and the bright-field images (Figs. 4a, 4b, and 4d), in which there is a characteristic “salt-pepper”-type contrast. In the cross section inside the amorphous fields, one can observe spherical “inclusions”—nanopores (Figs. 4a and 4d) with a diameter from 20 to 100 nm, which can be observed practically over the entire thickness of the layer with the amorphous structure. The identification of such spherical “inclusions” and experimental evidence of nanopores existence were made by high-resolution TEM methods. At first, diffraction analysis of the regions inside the nanopore performed by the nanodiffraction method (diameter of the electron probe is ∼5 nm) did not reveal diffraction-point reflections from crystalline inclusions. Secondly, according to the TEM/EDS-analysis data, a “drop” in the intensities of the characteristic radiation from chemical elements of the analyzed material was observed. Thirdly, when performing TEM analysis of the regions with nanopores, we used the HAADF-STEM mode. In this case, the image contrast depends on the foil thickness and atomic numbers of the components and increases with decreasing foil thickness. It follows from analysis of the HAADF-STEM image (Fig. 4d, inset) of the region with the supposed nanopore in the amorphous matrix, that the regions projected inwards the circle have a significantly lower thickness than those in its vicinity. This is possible only in the case, if a spherical nanopore was formed in this region. Finally, earlier, in the studies [10, 33] devoted to investigating the structure of Ti–Ni–Ta surface alloys obtained in synthesis modes similar to those used in our study and containing an amorphous phase, the presence of nanopores in the amorphous matrix was experimentally proven. The experimental features which make it possible to reliably distinguish nanopores from solid-phase inclusions were determined. The results obtained in this study fully agree with the data of [10, 33].

It is important to emphasize the following. At first, according to the TEM data, the surface layer of the TNTZ alloy is fully amorphized up to a depth of ∼2 μm. This layer does not contain nanophase crystalline precipitates. In our opinion, this result is not only the consequence of high quenching rates which reach (according to the calculations of temperature fields [10]) values of about 4 × 10⁸ K/s. It can be caused by the simultaneous alloying of the surface layer of TiNi alloy by two elements—tantalum and zirconium. The results we obtained in [10, 11] confirm this supposition. In these studies, the Ti−Ni−Ta ternary-composition surface alloys obtained by the same electron-beam method and with the same irradiation parameters were investigated. However, as compared with fully amorphous TNTZ alloy, the Ti−Ni−Ta surface alloys had a mixed amorphous-nanocomposite structure. A question arises about the role of zirconium in the processes of amorphization of the surface layers of TiNi alloys by the electron-beam method; this question requires further investigations.

Secondly, in the case of using the synthesis modes (with an energy density of E_S = 2 J/cm²), the thickness of the surface-layer melt did not exceed 1 μm [10], which is half of the thickness of the external surface layer in the TNTZ surface alloy. Therefore, during the last cycles of surface-alloy formation, its lower boundary (at a depth of 1–2 μm) was located in the heat-affected zone (HAZ) and, correspondingly, underwent short thermal annealing. According to the calculations performed in [10], the temperatures in the HAZ reach 800–900°C. Despite this fact, crystallization of the amorphous structure did not occur. In our opinion, a high nickel concentration in the surface layer, which significantly increases the glass-forming ability of Ti–Ni–Ta–Zr-system alloys, as well as the presence of a small amount of zirconium (up to 2 at %) are the main factors that contribute to the formation of a relatively stable amorphous structure. The effect of increasing the glass-forming ability of metallic alloys by means of microalloying is often observed in systems of transition metals [4, 5, 34] and is supposedly due to the presence of topological and chemical atomic ordering in the medium-range atomic-order scale, i.e., at distances of up to 1.5 nm. The influence of the alloy composition on the parameters of the short-range order in the Ti–Ni–Ta–Zr surface alloy will be discussed in detail below.

Analysis of the positions of diffusion scattering regions on the electron microdiffraction patterns has shown that the center of gravity in the scattering intensity distribution for the first diffusion halo corresponding to the intensity maximum along the cross section of this ring shifts from d_halo = 2.32 Å to d_halo = 2.27 Å as the depth of the analyzed region increases from the surface into the deeper amorphous layer. The positions of the maxima of the diffusion scattering intensity determine the radius of the first coordination shell (R₁), which can be estimated by the Ehrenfest equation:

$${{R}_{{{\kern 1pt} 1}}} = \frac{{1.23\lambda }}{{2\sin (\vartheta )}} = \frac{{1.23 \times 2\pi }}{{{{{\mathbf{q}}}_{1}}}},$$

(4)

where q₁= 4π sin(ϑ)/λ is the scattering vector corresponding to the first diffusion maximum. Therefore, the calculated values of the radius of the first coordination shell decrease from R₁ = 2.85 Å to R₁ = 2.79 Å when the distance from the surface into the amorphous layer increases. Overall, the obtained results show that the atomic orders at the first coordination shell inside the amorphous layer, near its surface and over its depth (near the crystalline substrate) are different. This may be due to a change in the chemical composition in the short-range atomic arrangement in the surface-alloy structure. “The center of gravity” of the first halo coincides with the coordinates of the diffraction maxima of the {110}_β-(Ti,Ta) and {111}_α"(Ti,Ta) planes of phases based on the Ti–Ta solid solution. On the equilibrium diagrams of the Ti–Ni–(Ta, Zr) state, the average compositions of the amorphous phase indicated in Fig. 3a are in the region of the three-phase equilibrium TiNi + (Ti, Zr)₂Ni + Ti(Ta, Zr) [35, 36]. Hence, we can expect that the short-range atomic order in the amorphous phase would be “inherited” by these crystalline phases in the crystallization process, for example, in the heating process.

At a depth of 2 μm, one can observe a distinct transition sublayer between the outer amorphous layer of the TNTZ alloy and the TiNi substrate (Figs. 4a and 4c). This transition layer with a thickness of ~300 nm is nanocrystalline. The positions of the ring on the microdiffraction pattern (Fig. 4e) correspond to structural reflections from the intermetallic phase of Ti₂Ni. The nanocrystalline grains (according to the EDS/TEM data) are titanium-enriched and have the Ti₅₁Ni₄₃Ta₅Zr₁ average composition, at which the formation of (Ti, Ta)₂Ni or (Ti, Zr)₂Ni intermetallic compounds is possible. A similar result was observed by the authors of [37] when studying the structure of Ti–Ni–Hf films obtained by the magnetron-deposition method in the form of the (Ti, Hf)₂Ni intermetallic phase (the Fe₄W₂C, Fd$\bar {3}$m structural type [38]) in their structure. One can suppose that the formation of the nanostructure under the amorphous layer in the process of surface-alloy synthesis is associated with nanocrystallization of the amorphous phase according to the heterogeneous mechanism in a narrow concentration region, in which overcooling for this alloy reaches the lowest values. In fact, as is known, the size of the nucleus of crystallization is determined by the matrix overcooling value [39], while the critical rate of cooling depends on the tendency of the alloy to vitrification [40]. In this case, the multiple nucleation of small crystals will occur most probably at structural appropriate regions in which the average interatomic distances in the amorphous matrix determined from the ARDF are close to those in their crystalline counterparts.

The structure of the sublayer corresponding to the HAZ and located at a depth of 3 μm is shown in Fig. 5a. The structure is of the eutectic type that contains second-phase precipitates. According to the analysis of nanodiffraction patterns obtained from regions with moiré fringes, along with the main B2 phase in this sublayer, there are particles of the Ti₃Ni₄ phase (Figs. 5b and 5c) which satisfy the known orientation relations ${{(\bar {1}10)}_{{{\text{B}}2}}}||{{(3\overline {21} )}_{{{\text{T}}{{{\text{i}}}_{3}}{\text{N}}{{{\text{i}}}_{4}}}}}$ (Fig. 5b) [41]. An increase in the contrast in the bright field in those regions of the foil, where the second phase is present, is related to strong absorption due to the presence of the atoms with a higher atomic number that that of titanium (Ni, Zr, Ta) in the B2 matrix phase. This agrees with the SEM/EDS data which show the presence of alloying elements (Zr, Ta) along the sample cross section at a depth of more than 3 μm from the treated surface (Fig. 3a) and is evidence of the inhomogeneous chemical composition in this sublayer. At a depth of more than 3.5 μm, the microstructure of the material corresponds to the initial high-temperature B2 phase.

Structure of the Topological Short-Range Atomic Order in Ti−Ni−Ta−Zr Amorphous Surface Alloy Investigated by the Electron Nanodiffraction Method

Analysis of the structure of short-range atomic order in the amorphous layer was performed by using the nanodiffraction patterns obtained in regions ①, ②, ③ at a depth of 100 nm and in regions ④, ⑤, ⑥ at a depth of 1800 nm from the surface (Fig. 4a). Based on the TEM/EDS data on the element distribution along the cross section of the TNTZ surface alloy (Fig. 3a), it was considered that the average element composition at depths of 100 and 1800 nm from the surface corresponds to the chemical formulas Ti₅₂Ni₃₃Ta₁₃Zr₂ and Ti₅₁Ni₄₀Ta₇Zr₂. The RDF G(r) was calculated by using the above-mentioned compositions for the scattering vectors q within the range q = 0.7−10 nm^–1, at which the relative value of the “noise” on the diffraction patterns did not exceed 40%. The form of the G(r) profiles, including estimation of its asymmetry, and the positions of the maxima were analyzed by means of Gaussian functions.

Figure 6a shows the ARDFs G(r) calculated from the experiment. As is seen, all curves G(r) are oscillating functions whose number of maxima is more than two that damp within the range from 0 to >1 nm (10 Å). This means that, at first, the amorphous phase has a cluster structure; second, it can be described by clusters of the short-range arrangement with dimensions of individual clusters of 5−10 Å (short-range atomic order) and the cluster conglomerates with dimensions of larger than 10 Å (medium-range atomic order). It should be noted that the presence of cluster conglomerates in the amorphous structure is experimentally demonstrated by the authors of [8, 9, 42]. Therefore, it follows from the analysis of curves G(r) that the TNTZ amorphous surface alloy can be represented in the form of a clustered structure in the scale of medium-range atomic order consisting of structural motifs that comprise 2−3 clusters of different configurations (with different coordination numbers and shapes of clusters) inter-connected in their common faces, vertices, and edges.

Fig. 6.

(a) ARDFs G(r) constructed on the basis of nanodiffractions (b) obtained from the TNTZ surface alloy at a depth of 100 nm (①, ②, ③) and 1800 nm (④, ⑤, ⑥) from the surface (Fig. 4a); (b) magnified areas of the ARDF G(r) ② and ④ near the second asymmetrical maximum and approximating Gaussian functions corresponding to them (1–3) and (4−6).

The principal maximum of the ARDF G(r) located at about r = 2.5 Å (Fig. 6a) and characterizing the atom distribution at the first coordination shell is well described by a single Gaussian function (Fig. 6b, curves 1 and 4) with a high determination coefficient (R² > 0.98). As is seen from Fig. 6a, this feature is common for all curves G(r) and displays the fact that in the Ti-enriched amorphous matrix, there are correlations between all pairs of atoms that comprise the composition of the amorphous surface alloy.

Table 1 presents the values obtained from the curve G(r) for the radii of the first (R₁), second (R_2-1 and R_2-2 are the radii corresponding to the maxima of the Gaussian function approximating the second maximum on the experimental curve G(r)), and third (R₃) coordination shells that describe the structure of the amorphous matrix at depths of 100 and 1800 nm. As is seen from Table 1, with increasing nickel concentration (and decreasing tantalum concentration), one can observe the regular decrease in the average interatomic distances at the first coordination shell from R₁ = 2.87−2.90 Å to R₁ = 2.78−2.80 Å. A similar result was earlier obtained in works studying the short-range order structure in Zr−Cu and Zr−Cu−(Al, Ag) amorphous alloys [4, 6, 7], in which enrichment of the amorphous phase with an element with the lowest atomic radius (in our case, nickel) led to a decrease in the interatomic distance at the first coordination shell.

Table 1.   Parameters of the topological short-range order of the TNTZ surface alloy obtained from analysis of the experimental ARDFs

Another common feature of the ARDF G(r) for the TNTZ surface alloy is weak asymmetry of the second maximum of G(r) (Fig. 6a), whose profile is well approximated by the superposition of two Gaussian functions (Fig. 6b, curves 2, 3 and 5, 6). According to [46], this result is one more sign of the medium-range atomic order formed in the amorphous structure, which characterizes this structure in the form of conglomerates of clusters based on nearest-neighbors. According to [4, 6, 7, 47], this structure provides the most dense atomic packing inside the amorphous phase.

As is seen from Table 1, the values of the radii of the coordination shell near the surface (the Ti₅₂Ni₃₃Ta₁₃Zr₂ composition) exceed analogous values for the amorphous matrix at a larger depth (the Ti₅₁Ni₄₀Ta₇Zr₂ composition). Taking into account the gradient character of the change in the concentration of the TNTZ-alloy components over the depth of the amorphous layer, this result can be caused by the presence of the composition (chemical) short-range atomic order and, respectively, a significant concentration dependence of interatomic distances in the scale of the short-range atomic arrangement in the amorphous phase.

Comparison of the values of R₁ with the sum of the atomic $\left( {R_{A}^{{{\text{at}}}} + R_{B}^{{{\text{at}}}}} \right)$ and covalent radii characterizing the length of interatomic bonds for pairs of atoms of different types (Table 1) near the surface (Ti₅₂Ni₃₃Ta₁₃Zr₂) and at the boundary with the crystalline sublayer (Ti₅₁Ni₄₀Ta₇Zr₂) shows the following. Near the surface (at a depth of 100 nm), the experimental values R₁ = 2.87−2.90 Å are close to the interatomic distances calculated from the atomic radii only for pairs of atoms of the [Ti−Ta] and [Ni−Zr] types and to those calculated from the covalent radii for pairs of the [Ti−Zr] and [Ti−Ta] types. Therefore, in the amorphous structure, near the surface, the nearest-neighbor atomic arrangement may be described predominantly by atomic pairs of the [Ti−Zr], [Ni−Zr], and [Ti−Ta] types.

For the amorphous matrix at a depth of 1800 nm (the Ti₅₁Ni₄₀Ta₇Zr₂ composition), the experimental values R₁ = 2.78−2.80 Å are close to the interatomic distances calculated from atomic radii only for the [Ti−Ni], [Ta−Ni], and [Ni−Zr] pairs and to those calculated from the covalent radii for the [Ti−Ta] pairs. Hence, in the amorphous structure at a depth of 1800 nm, the nearest-neighbor atomic arrangement may be described predominantly by atomic pairs of the [Ti−Ni], [Ta−Ni], [Ni−Zr], and [Ti−Ta] types.

Table 1 shows the values of the mixing enthalpies ∆H_mix calculated using Miedema’s model [45] for binary systems from the composition {Ti, Ni, Ta, Zr}. It should be noted that the strongly negative values of the mixing enthalpy ∆H_mix are indirect evidence of the covalent nature of the binding forces between the atoms of a pair; while the positive and close to zero values of ∆H_mix are evidence of the predominantly metallic type of the interatomic bond. In addition, the formation of covalent bonds between atoms at the first coordination shell leads to significant “bond shortening”, as was established in [48]. We also observed this effect for the atomic pairs [Ti−Ta], [Ti−Zr], [Ni−Zr], and [Ta−Zr], for which the sums of the Goldschmidt atomic radii exceeded the experimental values determined according to the ARDF. Therefore, in the amorphous structure of the TNTZ alloy a mixed (covalent and metallic) type of chemical bond is implemented over the entire depth. However, according to analysis, an interatomic bond of the metallic type is implemented predominantly near the surface, while that of the covalent type is implemented at large depths.

The provided data characterizing the state of the atomic structure of TNTZ amorphous alloy at a level of short-range atomic order as the preferred types of pair bonds and interatomic distances that we obtained from the experimental ARDFs make it possible to present a supposed variant of the amorphous structure, for example, by means of the approach used in [5, 49, 50].

In fact, as was mentioned above, the multi-peak profile of the experimental ARDFs is evidence that the structure of the amorphous matrix has a cluster nature. Then, as primary clusters describing the short-range arrangement in the amorphous matrix, one can consider coordination polyhedra (CPs) of the crystalline phase with the high glass-forming ability; i.e., devitrification phases. As is known [47, 51], those can be phases with a large number of atoms in the unit cell (for example, Ti₂Ni), complex equilibrium phases (for example, the TiNiZr Laves phase), etc. Table 2 shows the crystallographic parameters of the devitrification phases for a Ti–Ni–Ta–Zr-based amorphous alloy chosen on the basis of analysis of the phase diagrams of binary and ternary systems and the phenomenological criteria for obtaining alloys favorable for easy amorphization.

Table 2.   Crystallographic data on the atomic structure of the most probable devitrification phases for the Ti−Ni−Ta−Zr system

As was shown above, in two regions of the TNTZ amorphous layer analyzed by the nanodiffraction method, the short-range atomic order cannot be described only by one type of atoms. Therefore, we can assume that the topological atomic order formed in the amorphous phase quenched from the melt is a superposition of CPs interconnected between each other by common faces corresponding to different crystalline devitrification phases. In this case, the structural motif consisting of several (as a rule, two or three) clusters, can be determined relatively easily, with consideration for the atomic ordering inside a cluster at the first coordination shell only. Table 3 shows the types of CPs of the crystalline devitrification phases in the Ti–Ni–Ta–Zr systems and their crystallographic parameters describing them—the coordination-shell radii (R_i), the ratios of the central-atom radius (r₀) to the average-weighted atom radius (r₁) at the first coordination shell in the hard sphere model. In addition, it would be interesting to compare the parameters of the topological short-range atomic order implemented in amorphous pure materials (Table 3) which, being in the crystalline state, are characterized by crystalline lattices (face-centered cubic (fcc) for Ni and body-centered cubic (bcc) for Fe) [5], with the experimental results of this study. Figure 7a shows line diagrams of the positions of the radii of the first and other coordination shells for different types of coordination polyhedra chosen for the analysis.

Table 3.   Types of coordination polyhedra of devitrification crystalline phases in the Ti−Ni–Ta−Zr system and crystallographic parameters that determine them: radii of coordination shells (R_i), ratio of the central-atom radius (r₀) to the weighted-mean atom radius (r₁) at the first coordination shell

Fig. 7.

Diagram of the “topological” short-range order (a) illustrating the affinity of the topological short-range order in the amorphous structure and the structure of devitrification crystalline phases. The clusters by means of which one can describe the structure of the medium-range atomic order in Ti−Ni−Ta−Zr surface alloy (b−h).

It follows from comparison of the data (Tables 2 and 3 and Fig. 7a) that the short-range atomic order in the amorphous structure of TNTZ alloy (Ti₅₂Ni₃₃Ta₁₃Zr₂) at a depth of 100 nm can be represented as the superposition of several CPs based on Ti−[Ti₄Ta₈] (the CP for the α"(Ti,Ta)-martensite structure), Ti−[Ti₆Ta₈] (the CP for the β(Ti,Ta)-austenite structure), Zr−[Ni₆Ti₆] (the CP for the Ti₂Ni structure), Zr−[Zr₄Ni₉Ti₃] (the CP for the TiNiZr structure) and, what is interesting, is similar to the short-range atomic order in the bcc lattice (for the TiNi structure). In local regions at a depth of 1800 nm in the amorphous phase of the Ti₅₁Ni₄₀Ta₇Zr₂ composition, one can most likely observe structural motifs consisting of Zr−[Zr₁₄Ti₆]-ordered CPs (the CP for the Ti₂Zr structure) and, as near the surface, the Ti−[Ti₆Ta₈] and bcc lattices. Figs. 7b–7h show all the types of above-mentioned clusters constructed with the help of the VESTA program [58] using the tabular values of the interatomic distances for atomic pairs (Table 1).

There are several arguments in favor of the chosen types of clusters (or coordination polyhedra) to describe the atomic structure of TNTZ amorphous surface. At first, all chosen clusters provide the densest atomic packing in the amorphous phase, which is seen from comparison of the experimental values of r₀/r₁ and those theoretically calculated using the Miracle’s model of efficient cluster packing [59] (Table 3). Second, the presence of Ti₂Ni-ordered Zr−[Ni₆Ti₆] clusters implies that Ti₂Ni, as a devitrification phase, must be observed in crystalline sublayers adjacent to the amorphous layer. Indeed, as was noted (Figs. 4c and 4e), the Ti₂Ni phase was experimentally found in samples of the TNTZ amorphous alloy in the nanocrystalline sublayer located directly under the amorphous layer. Third, the presence of clusters with a short-range atomic order structure for the bcc crystalline lattice (TiNi, β-Ti, β-Ta) is confirmed by the fact that the position of the principal diffusion maximum on the microdiffraction patterns coincides with the position of the principal diffusion maximum in the bcc structures of Ti or Ta.

CONCLUSIONS

In this study, using the method of the pulsed li-quid-phase electron-beam mixing of the “Ti₇₀Ta₃₀(50 nm)/Zr/TiNi” system, Ti−Ni−Ta−Zr amorphous surface alloy with a graded diffusion transition to the TiNi substrate was formed. Using the results of our investigations, the following conclusions can be made.

(1) It is established that the Ti−Ni−Ta−Zr surface alloy formed as a result of superfast quenching from the surface layer of a sample with a thickness of ~2 µm melted by means of an electron beam has an amorphous structure with a chemical composition gradient.

(2) Under the surface amorphous layer, a diffusion transition nanocrystalline sublayer of Ti₂Ni and a subjacent sublayer with a eutectic structure based on the В2(TiNi) + Ti₃Ni₄ phases are formed.

(3) From analysis of the atomic radial distribution functions obtained by using the electron nanodiffraction method, quantitative data on the radii of the coordination shells and their changes as functions of the surface alloy composition are obtained.

(4) The variants of the coordination polyhedra corresponding to the devitrification crystalline phases for an amorphous structure based on the Ti−Ni−Ta−Zr system are constructed using radii experimentally obtained for the first, second, and third coordination shells as equivalents of the interatomic distances for the corresponding atomic pairs.

(5) It is shown that the atomic structure in the Ti−Ni−Ta−Zr amorphous surface alloy has a cluster nature whose structural motif can be described as a superposition of the coordination polyhedra interconnected with each other by common faces corresponding to different crystalline devitrification phases.

In conclusion, we should emphasize the following important methodological aspect. The diffraction patterns, being a Fourier image of the electron scattering intensity in reciprocal space, can be obtained in situ by the majority of modern transmission electron microscopes by means of the fast Fourier transform (FFT). Such patterns (of micro- and nanodiffractions) can be processed with the purpose of obtaining ARDFs with the help of the software package developed on the basis of GATAN [27, 60]. The identification of phases formed after annealing in amorphous alloys of transition metals with different compositions can be predicted by calculating the radii of the coordination spheres on the ARDFs only. As is seen, the search for connections between the amorphous and crystalline structures found inside the synthesized amorphous-nanocomposite layer seems to be a routine task when using diffraction-analysis methods in a TEM which do not require complicated time-consuming experiments to be conducted. The method described in this study for analysis of the short-range atomic order structure in the amorphous phase with application of the electron nanodiffraction method can be used to determine the phase composition of nanocomposites formed from the amorphous phase in the process of its crystallization.