# In-situ monitoring the structural pathway of a Ti-based alloy from metallic liquid to metallic glass

Konstantinos Georgarakis, Martin Stiehler, Louis Hennet, Yaofeng Guo, Jerzy Antonowicz, Dmitri Louzguine-Luzgin, Mark Jolly, Jérôme Andrieux, Gavin B.M. Vaughan, A. Lindsay Greer

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## ► To cite this version:

Konstantinos Georgarakis, Martin Stiehler, Louis Hennet, Yaofeng Guo, Jerzy Antonowicz, et al. In-situ monitoring the structural pathway of a Ti-based alloy from metallic liquid to metallic glass. Journal of Alloys and Compounds, 2025, 1025, pp.180214. 10.1016/j.jallcom.2025.180214. hal-05031547

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# In-situ monitoring the structural pathway of a Ti-based alloy from metallic liquid to metallic glass

Konstantinos Georgarakis<sup>a, *,</sup>, Martin E. Stiehler<sup>a, *</sup>, Louis Hennet<sup>b</sup>, Yaofeng Guo<sup>c</sup>, Jerzy Antonowicz<sup>d</sup>, Dmitri V. Louzguine-Luzgin<sup>e,f</sup>, Mark R. Jolly<sup>a</sup>, Jérôme Andrieux<sup>g</sup>, Gavin B.M. Vaughan<sup>h</sup>, A. Lindsay Greer<sup>i</sup>

## ARTICLE INFO

### Keywords:

- Metallic glasses

- Vitrification

- Atomic structure

- Levitation

- Synchrotron radiation

- Structure formation

## ABSTRACT

A metallic glass is formed when a molten metallic alloy is cooled rapidly enough that crystallisation is avoided. However, the way the atomic structure of the liquid converts to that of the glass is generally unknown. The main challenge is the sufficiently fast experimental acquisition of structural data in the undercooled liquid regime necessitated by the high cooling rates needed to avoid crystallisation. In the present study, using aerodynamic levitation, the Ni-free Ti-based alloy Ti₄₀Zr₁₀Cu₃₄Pd₁₄Sn₂ was vitrified in-situ in a high-energy synchrotron X-ray beam while diffraction data were acquired during cooling from above the liquidus temperature Tᵢᵢᵣ to well below the glass-transition temperature T₉. The structure in the undercooled liquid regime shows an accelerated evolution. Both the local order in the short (SRO) and medium range (MRO) increases rapidly as the undercooled liquid approaches T₉, below which the amorphous structure “freezes”. Nevertheless, distinct differences between the evolution of SRO and MRO were observed. The structural rearrangements in the undercooled liquid are found to be correlated with a rapid increase in viscosity of the metallic liquid upon cooling. The new findings shed light on the evolution of the atomic structure of metallic liquids during vitrification and the structural origins of the sluggish kinetics that suppress nucleation and growth of crystalline phases.

## 1. Introduction

Understanding the remarkable kinetic arrest in glass-forming liquids and the dramatic change in viscosity by more than 12 orders of magnitude between liquidus temperature Tᵢᵢᵣ and glass-transition temperature T₉ is one of the most intriguing unresolved issues in materials research. Although the underlying microscopic origins remain unclear, recent studies indicate a relation with the evolution of the atomic structure of the glass-forming liquids [1–5]. Depending on the evolution of viscosity as a function of temperature, liquids can be categorised into strong and fragile [6]. Strong liquids exhibit Arrhenius-type behaviour

which implies a simple thermally activated behaviour for viscosity η(T) = η₀ exp(Eₐ/kₐT) where T is the temperature, η₀ a pre-exponential factor related to the viscosity at infinite temperature, kₐ the Boltzmann constant and Eₐ an effective activation energy for viscous flow. The viscosity of a fragile liquid, however, markedly departs from this function and exhibits non-Arrhenius behaviour. The bigger the deviation from Arrhenius behaviour the more fragile the liquid is, with viscosity increasing rapidly as T₉ is approached [7]. The fragility of metallic liquids is usually high. Due to their relatively simple structure, as compared to polymers and oxides, investigation of metallic undercooled liquids offers unique opportunities for improving our understanding of glass

<footnote><sup>a</sup> Faculty of Engineering and Applied Sciences, Cranfield University, MK43 0AL, UK</footnote>

<footnote><sup>b</sup> ICMN – UMR 7374 CNRS et Université d'Orléans, Orléans 45071, France</footnote>

<footnote><sup>c</sup> Protochips, Inc., Morrisville, NC 27560, USA</footnote>

<footnote><sup>d</sup> Faculty of Physics, Warsaw University of Technology, Warsaw, Poland</footnote>

<footnote><sup>e</sup> Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai 980-8577, Japan</footnote>

<footnote><sup>f</sup> MathAM-OIL, National Institute of Advanced Industrial Science and Technology (AIST), Sendai 980-8577, Japan</footnote>

<footnote><sup>g</sup> Université Claude Bernard Lyon 1, CNRS, LMI UMR 5615, Villeurbanne 69100, France</footnote>

<footnote><sup>h</sup> European Synchrotron Radiation Facility, Grenoble 38042, France</footnote>

<footnote><sup>i</sup> Department of Materials Science & Metallurgy, University of Cambridge, CB3 0FS, UK</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: k.georgarakis@cranfield.ac.uk (K. Georgarakis), martin.stiehler@cranfield.ac.uk (M.E. Stiehler).</footnote>
formation and glass transition. Recent advances in containerless solidification methods such as electrostatic and aerodynamic levitation provide new possibilities to study the structure of undercooled metallic liquids using synchrotron and neutron scattering techniques [8,9]. Nevertheless, the acquisition of structural information in the whole temperature range from the liquid to the glassy state for metallic liquids remains challenging since avoiding crystallisation during quenching requires cooling rates that are not easily achievable in in-situ diffraction experiments. Related results not only contribute considerably to the basic understanding of these materials but also of their application-related aspects. Metallic glasses offer an attractive combination of engineering properties such as high mechanical strength, high elastic strain, good corrosion resistance and excellent soft magnetic properties [10–13]. Furthermore, compared to their crystalline counterparts, metallic glasses exhibit lower Young's, bulk and shear moduli reduced by about 10%, 6% and 30%, respectively [11]. These characteristics make them attractive for a variety of applications including biomedical body implants, potentially diminishing the stress shielding effect that is often associated with conventional metallic implants [14]. However, many of the bulk-glass-forming alloys contain toxic elements such as Be, Ni, V or Al [14,15]. In this respect, Ti-based metallic glasses, free of toxic elements, are a particularly interesting class of alloys with high specific strength and good biocompatibility [13,14,16,17–19]. Among the Ni-free Ti-based metallic glasses, Ti₄₀Zr₁₀Cu₄Pd₁₄Sn₂ possesses the highest glass-forming ability (GFA) with a critical diameter d_c bigger than 10 mm [20]. Recent in-situ high-energy synchrotron diffraction experiments yielded results on the structural evolution of Ti₄₀Zr₁₀Cu₄Pd₁₄Sn₂ metallic glass upon heating from room-temperature towards crystallisation including signs of a possible metallic glacial glass phase [21–24]. Revealing the structural evolution during vitrification may offer new insights into the glass formation in Ti-based alloys supporting the design of biocompatible alloys with high bulk GFA and high functionality.

In the present work, aerodynamic levitation was used for in-situ probing the structure of the Ti₄₀Zr₁₀Cu₄Pd₁₄Sn₂ bulk-glass-forming alloy continuously along its pathway from equilibrium to undercooled liquid and through vitrification in a high-energy, high-flux synchrotron beam. The results indicate an accelerated structural evolution of the short (SRO) and medium range order (MRO) in the undercooled liquid towards $T_g$.

## 2. Materials and methods

Spherical ingots, about 2 mm in diameter, of a quinary alloy with the nominal composition Ti₄₀Zr₁₀Cu₄Pd₁₄Sn₂ (in at%) were prepared by arc melting from high-purity raw materials (Ti: 99.9%, Zr: 99.8%, Cu: 99%, Pd: 99%, Sn: 99.8%) under Ar atmosphere. Remelting five times ensured chemical homogeneity. A sphere of the alloy was then levitated by high-purity Ar flow through an Al nozzle [8] and melted using two CO₂-laser beams. During the subsequent free cooling the alloy's structure was investigated in-situ by high-energy X-ray diffraction in transmission mode carried out at beamline ID15 of the European Synchrotron Radiation Facility (ESRF) in the temperature range between 1473 K (well above $T_{liq}$ = 1176 K (Table 1)) and 487 K (well below the

<caption>**Table 1**</caption>

Thermophysical parameters of Ti₄₀Zr₁₀Cu₄Pd₁₄Sn₂ acquired by calorimetric methods taken from literature (the undercooled-liquid range $\Delta T_X = T_X - T_g$, the reduced glass-transition temperature $T_{rg} = T_g / T_{liq}$ as well as all average values were calculated here).

<table><thead><tr><th>T<sub>g</sub> [K]</th><th>T<sub>X</sub> [K]</th><th>T<sub>m</sub> [K]</th><th>T<sub>liq</sub> [K]</th><th>ΔT<sub>X</sub> [K]</th><th>T<sub>rg</sub></th><th>Ref.</th></tr></thead><tbody><tr><td>689</td><td>739</td><td>1126</td><td>1187</td><td>50</td><td>0.58</td><td>[20]</td></tr><tr><td>682</td><td>740</td><td>—</td><td>1164</td><td>58</td><td>0.59</td><td>[25]</td></tr><tr><td>695</td><td>743</td><td>—</td><td>—</td><td>48</td><td>—</td><td>[21]</td></tr><tr><td>688</td><td>730</td><td>—</td><td>—</td><td>42</td><td>—</td><td>[26]</td></tr><tr><td>689</td><td>738</td><td>1126</td><td>1176</td><td>50</td><td>0.59</td><td>average</td></tr></tbody></table>

calorimetric glass transition temperature $T_g = 689$ K (Table 1)). The wavelength of the incident monochromatic beam was $\lambda_i = 0.1245$ Å ($E_i = 100$ keV). X-ray diffraction patterns were continuously recorded by a Perkin-Elmer two-dimensional flat-panel detector with a time resolution of 100 ms as function of the scattering vector $\vec{Q}$ (with modulus $Q = |\vec{Q}|$ up to $25$ Å⁻¹), where $Q = 4\pi \sin\theta / \lambda$ and $2\theta$ the diffraction angle. Two optical pyrometers working at 1.625 µm (623 K - 2073 K) and 0.9 µm (1173 K - 3573 K), respectively, were used to measure the temperature $T$. Values below 623 K were calculated assuming a continued exponential temperature drop (Fig. 1). The average cooling rate during vitrification was of the order of 80 K/s with an initial cooling rate of the order of 150 K/s. The temperature calibration was verified using $T_m$ and the crystallisation temperature $T_X$ of the alloy (Table 1). The accuracy of the temperature values was estimated to be around ± 12 K above 900 K and better than ± 7 K below 900 K. The high cooling rates that can be achieved in our setup sets the experiment apart from similar studies using other containerless levitation techniques like electromagnetic [27] or electrostatic levitation [9]. This allows for the in-situ vitrification of metallic melts, like Ti₄₀Zr₁₀Cu₄Pd₁₄Sn₂, that have a comparatively low GFA. Minor non-amorphous features of unknown origin have been observed in a limited number of patterns below $T \approx 950$ K which were exempted from further analysis.

For each temperature $T$ the diffraction images were azimuthally integrated after corrections for polarisation and dark currents using the FIT2D software [28] yielding the integrated diffraction intensities $I(Q, T)$. After corrections for sample absorption, fluorescence, Compton scattering, Laue diffuse scattering, background contribution and normalisation to the atomic X-ray form factor the total structure factors $S(Q, T)$ were obtained with the help of the PDFgetX3 software package [29]. For structural analysis in real space PDFgetX3 furthermore performs the Fourier transformation [30] of $S(Q, T)$ yielding the reduced pair distribution function

$$G(r, T) = \frac{2}{\pi} \int_{0}^{Q_{\max}} Q[S(Q, T) - 1] \sin(Qr) dQ, \quad (1)$$

with an upper integration limit of $Q_{\max} = 15$ Å⁻¹ in the present case.

## 3. Results

Fig. 1 shows the temperature-time dependence $T(t)$ of the Ti₄₀Zr₁₀Cu₄Pd₁₄Sn₂ sample during cooling. The absence of recalescence indicates that crystallisation was avoided during solidification leading to the formation of a metallic glass.

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Temperature-time dependence $T(t)$ of the Ti₄₀Zr₁₀Cu₄Pd₁₄Sn₂ sample during free cooling in the aerodynamic levitation setup while in the synchrotron beam (the temperatures below 620 K (dashed) were calculated assuming exponential behaviour).</figcaption></figure>
Fig. 2 shows a set of X-ray diffraction results in the form of the structure factor $S(Q, T)$ recorded along the complete pathway. The observed change of the $S(Q, T)$ with decreasing temperature indicates structural evolution that leads to a more ordered structure during cooling. In particular, the shift of the maximum $Q_1(T)$ of the first peak, corresponding to the first diffuse diffraction halo, to higher Q with decreasing temperature T is consistent with the macroscopic volume contraction during cooling [31]. In addition, the increase of $S(Q_1(T), T)$ and the splitting of the second peak, corresponding to second diffuse diffraction halo, centred at around $5.2 \AA^{-1}$ observed during cooling clearly indicate an increasingly ordered structure at lower temperatures. This splitting is a frequent observation in metallic glasses and was discussed in relation to characteristic distances of the SRO [32]. It is interesting to note that it is mainly the low-Q feature of the second halo that is changing during cooling while the shoulder at the high-Q side remains almost unchanged over the complete measured T-range indicating that the responsible structure is already present at high T in the equilibrium liquid (Fig. 2). For a better visualisation of the structural changes in reciprocal space the reader is referred to Movie 1 of the Supplementary Material.

Supplementary material related to this article can be found online at doi:10.1016/j.jallcom.2025.180214.

In order to follow the structural evolution during cooling, several structural metrics derived from the first peak in $S(Q, T)$ over the complete T-range studied were analysed (Fig. 3). Fig. 3a shows the position $Q_{1,cent}(T)$ of the centroid of the peak (black circles). Centroids are also used for the analysis of other peaks throughout this study since they are comparatively less noisy as their calculation involves an integration over a complete peak which provides the opportunity to treat split peaks as well as non-split peaks in the same way without the need for background subtraction or assumption of a specific fit function. Furthermore, the height $S(Q_1(T), T)$ (Fig. 3b) and the full width at half maximum (FWHM) $\Delta Q_1(T)$ (Fig. 3c) are shown. The quantities are directly derived from the experimental data (grey shaded area in the inset of Fig. 3a) without any fitting [3,33]. Especially $Q_{1,cent}(T)$ and $S(Q_1(T), T)$ show non-linear behaviour. This indicates an accelerated structural ordering similar to what has been previously observed for $Zr_{60}Cu_{30}Al_{10}$ [3] and $Zr_{55}Cu_{30}$. $Ni_5Al_{10}$ [2]. Also similar to $Zr_{60}Cu_{30}Al_{10}$, a clear kink occurs near the calorimetric glass-transition temperature $T_g$ for almost all structural metrics presented (vertical dashed line in Fig. 3). Below, the metrics show linear behaviour (Fig. 3).

Supplementary material related to this article can be found online at doi:10.1016/j.jallcom.2025.180214.

<figure><img src="image_5.png" /><figcaption>Fig. 2. The evolution of the structure factor $S(Q, T)$ of $Ti_{40}Zr_{10}Cu_{34}Pd_{14}Sn_2$ during free cooling from 1473 K to 487 K; the inset shows a three-dimensional representation of the same data. See also Supplementary Movie 1.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. Structural metrics of $Ti_{40}Zr_{10}Cu_{34}Pd_{14}Sn_2$ in reciprocal space during free cooling derived from the first peak (relevant portion shaded in grey in the inset) of the structure factor $S(Q, T)$. a) position of the centroid $Q_{1,cent}(T)$ (black circles) as well as the viscosity $\eta(T)$ of $Ti_{40}Zr_{10}Cu_{30}Pd_{20}$ ($T_g = 687$ K [16]), $T_{liq} = 1279$ K [34] replotted from Mauro et al. [4]) (blue stars), b) the height $S(Q_1(T), T)$ and c) the FWHM $\Delta Q_1(T)$. The vertical dashed line indicates the temperature where an abrupt change in the behaviour of the metrics occurs. All other lines are guides for the eye. The arrows in a) indicate the average values of the thermophysically obtained $T_g$ and $T_{liq}$ of $Ti_{40}Zr_{10}Cu_{34}Pd_{14}Sn_2$ given in Table 1.</figcaption></figure>

The reduced pair distribution function $G(r, T)$ (Fig. 4a and Supplementary Movie 2) evolves noticeably with decreasing T, reflecting the changes towards vitrification as well. The first peak of $G(r, T)$, corresponding to the first nearest-neighbour shell, changes only very slightly in position, but increases in intensity and decreases in width indicating a narrower distribution of interatomic distances as well as a gradual increase in the number of atoms in the first shell. For the remainder of this paper, as adopted from [33], the term shell is used for regions with $G(r, T) > 0$ (hatched in green in inset of Fig. 4). The shells are numbered consecutively ($n = 1, 2, 3, ...$) with increasing distance from the central atom at $r = 0 \AA$. The regions with $G(r, T) < 0$ are denoted as anti-shells (cross-hatched in orange in inset of Fig. 4) [33].

The second shell also evolves and a shoulder gradually develops on the high-$r$ side ($r_{2h} \approx 5.4 \AA$) resulting in a partial splitting of the peak at lower temperatures. A split second shell is considered a characteristic
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** a) The evolution of the reduced pair distribution function $G(r, T)$ during cooling from 1473 K to 487 K (cf. also Supplementary Movie 2); the inset shows a three-dimensional representation of the same data. b) $\Delta G(r, T) = G(r, T) - G(r, 1473\,\text{K})$ functions showing the increasing difference between $G(r, T)$ at various temperatures during cooling and the one at 1473 K. Inset: $G(r, 478\,\text{K})$ to recall the shell/anti-shell concept [33] (see text).</figcaption></figure>

difference between the glassy and the liquid state attributed to the enhancement of chemical and topological MRO [35]. The shells with $n \ge 3$ shift to smaller interatomic distances $r$ and increase in height during cooling. The presence of clearly distinguishable shells in $G(r, T)$ extends up to about $r \approx 18\,\text{Å}$ at higher temperatures (liquid state), whereas at lower temperatures (glassy state) shells can clearly be observed up to $r \approx 25\,\text{Å}$ (cf. three-dimensional representation in Fig. 4a), indicating an extension of the MRO along the pathway from the liquid to the glassy state. This is consistent with an increasing coherence length $2\pi/\Delta Q_1(T)$ (c.f. decreasing FWHM $\Delta Q_1(T)$ during cooling in Fig. 3c). It is important to note that, in addition to the increasing height of $G(r, T)$ at the shells, the local minima of $G(r, T)$ (anti-shells) become more pronounced as well during cooling, indicating a migration of atoms from anti-shells to shells. This migration has been linked to the cluster evolution during glass formation leading to a distinct increase of the local ordering [3].

The visibility of the evolution of $G(r, T)$ can be enhanced by calculating $\Delta G(r, T) = G(r, T) - G(r, 1473\,\text{K})$ highlighting the changes in $G(r, T)$ compared to that of the highest measured temperature (Fig. 4b). The local maxima of $\Delta G(r, T)$ correspond to the increase of atomic population in the shells, whereas negative $\Delta G(r, T)$ correspond to the decrease of the number of atoms in the anti-shells. Especially the visibility of the increasingly split second shell in $G(r, T)$ (Fig. 4a) that develops during cooling is underlined by the two maxima at $r \approx 4.5\,\text{Å}$ and $r \approx 5.5\,\text{Å}$ in $\Delta G(r, T)$ (Fig. 4b). Furthermore, $\Delta G(r, T)$ emphasises that the evolution of $G(r, T)$ with decreasing $T$ extends up to high $r$, indicating a significant

enhancement of SRO as well as MRO along the alloy's pathway to vitrification. Integrating $\Delta G(r, T)$ for $\Delta G(r, T) > 0$ (purple region in inset of Fig. 5d) yields the same value for each $T$ (purple dots in Fig. 5d) as the absolute values of the integral of $\Delta G(r, T)$ for $\Delta G(r, T) < 0$ (green region in inset of Fig. 5d and green dots in Fig. 5d). This not only corroborates the mentioned migration but also indicates the continuous acceleration of this effect during cooling, supporting the observations in reciprocal

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Structural metrics of Ti₄₀Zr₁₀Cu₃₄Pd₁₄Sn₂ in real space during free cooling derived from the first peak (first shell, $n = 1$, relevant portion shaded in grey in the inset in b)) of the reduced pair distribution $G(r, T)$. a) position of the maximum $r_1(T)$ (green triangles) and the centroid $r_{1,cent}(T)$ (black circles), b) the peak height $G(r_1(T), T)$, c) its full width at half maximum (FWHM) and d) the integrated area of $\Delta G(r, T)$ below and above the baseline $\Delta G(r, T) = 0$. Arrows and lines as in Fig. 3.</figcaption></figure>
space (Fig. 3). Changes below $T_g$ can be attributed to the Debye-Waller factor.

Fig. 5a,b,c shows metrics derived for the first shell obtained by analogy with the first halo in reciprocal space. Additionally to the position of the centroid $r_{1,cent}(T)$ (black circles in Fig. 5a), as in reciprocal space, also the positions $r_1(T)$ of its maximum (green triangles) to characterise the shell distances are shown. Both $r_{1,cent}(T)$ and $r_1(T)$ show an apparent negative thermal expansion in the liquid and undercooled liquid regions which will be discussed below. Below $T_g$, as expected, a positive thermal expansion can be observed. The height $G(r_1(T), T)$ and the FWHM $\Delta r_1(T)$ show a quasi-linear behaviour over the complete T-range. The metrics for the first shell in real space presented in Fig. 5a-c do not reflect the changes in behaviour during cooling (accelerated ordering) as clearly as in reciprocal space. This may partially be attributable to the bigger scatter of the data. On the other hand, the values for the integrated areas of $\Delta G(r, T)$ (Fig. 5d), representing combined effect of all shells of a wide range of distances, reflect the accelerated ordering below $T_{liq}$ very well, which resembles the behaviour known from $Zr_{60}Cu_{30}Al_{10}$ [3].

## 4. Discussion

Various models have been proposed to describe the structure of metallic glasses since the 1960s, including Bernal's dense random packing model of hard spheres [36], Gaskell's stereochemically designed local structure units [37] as well as the efficient space filling scheme of solute-centred clusters by Miracle [38]. The influence of global interactions between the valence electrons and atoms of an alloy has also been shown to have an influence on structure formation in metallic glasses [39–42]. It is now widely accepted that the structure of metallic glasses is based on atomic clusters that give rise to SRO and MRO, while the long-range order of crystalline materials is absent. For many glassy alloys, specific local structural motifs have been identified by simulations and experiments [43–45], including the direct observation of interconnected atomic polyhedra by nano-beam electron diffraction [46]. The local atomic packing order as well as topological arrangements of clusters are important features that enable not only the description of the structure of metallic glasses but also provide insights about structure-property relationships. The formation of various local atomic clusters is controlled by both atomic size ratios and chemical bonding. It is also widely accepted that local icosahedral and icosahedral-like order prevails in many metallic-glass forming alloys [46–48]. On the other hand, the local order in metallic liquids is less pronounced than in the glassy state as shown in Fig. 2 and Fig. 4. Although the prevailing type of polyhedra in the local atomic structure of Ti-based BMGs has not been unambiguously established yet, the formation of quasicrystals with icosahedral symmetry has been reported for some Ti-based alloys [15,32,49]. According to the hard-sphere packing model, an atomic size ratio $R_{A/B} = r_A / r_B = 0.902$ ($r_A$ and $r_B$ being the radii of centre and first-neighbour-shell atoms, respectively) is required to form an ideal icosahedral cluster around a central atom [50]. In the case of $Ti_{40}Zr_{10}Cu_{34}Pd_{14}Sn_2$ $R_{Ti/Cu}$ and $R_{Cu/Ti}$ are 1.127 and 0.887, respectively [51]. Thus, around Ti or Cu, which are the most abundant elements in this quinary alloy, icosahedral packing might not be favourable. However, especially the atomic size ratio $R_{Ti/Zr}$ (0.899) and to a lesser extent $R_{Ti/Sn}$ (0.916) [51] are closer to the ideal value of 0.902 and therefore the additional elements Zr and Sn may facilitate the formation of local icosahedral-like symmetry in the cooling liquid. This could also be the reason underlying the high GFA of Ti-Zr-Cu-Pd-Sn-alloys as compared to other Ti-based alloys [15,32,49]. However, further exploration is necessary to verify the developing local symmetry during cooling. The increase of the atomic populations in the shells with decreasing temperature as inferred from Fig. 4a and b could be the result of i) the rearrangement of atoms previously located in anti-shell regions (local minima in Fig. 4a) into atomic clusters with local symmetry as the temperature decreases, ii) the reorganisation of

atomic clusters existing at higher temperatures into clusters with higher packing density at lower temperatures or iii) a combination of both mechanisms. Recent results from molecular-dynamics simulations in Zr-based metallic-glass forming alloys support the idea that the population of atomic clusters with icosahedral local symmetry increases faster than other clusters as the liquid metal is cooled towards $T_g$ [2,3,47].

With the exception of Cu-Sn (and Ti-Zr) all atomic pairs of $Ti_{40}Zr_{10}Cu_{34}Pd_{14}Sn_2$ have negative heats of mixing (Table 2) which supports good GFA according to one of the main (empirical) criteria suggested by Inoue [10].

In a simplistic approach, glass formation can be described as the rapid cooling of the amorphous structure of a liquid down to the glass transition temperature $T_g$ below which it “freezes” to become an amorphous solid. However, below $T_{liq}$, crystalline phases are thermodynamically favoured and a remarkable slowdown of the kinetics in the undercooled liquid is necessary to suppress crystal nucleation and growth during solidification. This kinetic arrest is manifested by a significant increase of viscosity in the undercooled liquid whose origins remain only poorly understood [7,56].

To relate the evolution of the atomic structure to the evolution of the viscosity, Fig. 3a shows literature data [4] for $\eta(T)$ of the very similar Ti-based alloy $Ti_{40}Zr_{10}Cu_{30}Pd_{20}$ ($T_g = 687$ K [16] and $T_{liq} = 1279$ K [34]) as such data for $Ti_{40}Zr_{10}Cu_{34}Pd_{14}Sn_2$ itself were not available. The curved behaviour of e.g. $Q_{1,cent}(T)$ and $S(Q_1(T), T)$ is reflected, even though much more pronounced, by $\eta(T)$ which increases by $\approx 1.5$ orders of magnitude in the small T-range for which data are available. This observation strongly supports the idea that the sharp increase of the viscosity, the kinetic arrest as well as the structural changes in the undercooled liquids may have the same origin [1–4]. The increasing slope observed in the structural metrics as function of T points to an acceleration of the atomic rearrangements during undercooling towards $T_g$ (Fig. 3a). For Pd- and Zr-based BMG-forming alloys, direct structural signatures of the viscosity increase and, hence, fragility of the undercooled liquid could be identified [1,2]. In these materials, the peak in $G(r)$ representing the first shell can be decomposed into two sub-peaks by fitting Gaussian functions. The evolution of the ratio of the areas under these two functions during undercooling between $T_{liq}$ and $T_g$ strongly resembles the evolution of the viscosity in this temperature range. The change of this ratio has been associated with the change in activation energy during undercooling, providing a structural measure for fragility [1,2,57]. In the present case, the first peak of $G(r)$ cannot be unambiguously deconvolved into subpeaks. However, applied to the second shell, a similar behaviour can be observed (Fig. S3 in the Supplementary Material). Following the analysis used for $Pd_{40}Cu_{30}Ni_{10}Pd_{20}$ and $Zr_{55}Cu_{30}Ni_{5}Al_{10}$ [1,2,57], $Ti_{40}Zr_{10}Cu_{34}Pd_{14}Sn_2$ is found to be a

<caption>**Table 2**</caption>

Heats of mixing $\Delta H_{mix}$ (according to Miedema's model) [52], interatomic distances $d_{at}$ [51], Faber-Ziman weights $W_{ij}$ [53] and probabilities for random contact $P_{ij}$ [54,55] for all atomic pairs $i-j$ occurring in $Ti_{40}Zr_{10}Cu_{34}Pd_{14}Sn_2$.

<table><thead><tr><th>pair i-j</th><th>ΔH<sub>mix</sub> [kJ/mol]</th><th>d<sub>at</sub> [Å]</th><th>W<sub>ij</sub></th><th>P<sub>ij</sub></th></tr></thead><tbody><tr><td>Ti-Ti</td><td>0</td><td>2.84</td><td>0.085</td><td>0.160</td></tr><tr><td>Cu-Ti</td><td>-9</td><td>2.68</td><td>0.192</td><td>0.272</td></tr><tr><td>Cu-Cu</td><td>0</td><td>2.52</td><td>0.107</td><td>0.116</td></tr><tr><td>Pd-Ti</td><td>-65</td><td>2.84</td><td>0.125</td><td>0.112</td></tr><tr><td>Pd-Cu</td><td>-14</td><td>2.68</td><td>0.14</td><td>0.095</td></tr><tr><td>Pd-Pd</td><td>0</td><td>2.84</td><td>0.046</td><td>0.020</td></tr><tr><td>Zr-Ti</td><td>0</td><td>3</td><td>0.078</td><td>0.080</td></tr><tr><td>Zr-Cu</td><td>-23</td><td>2.84</td><td>0.087</td><td>0.068</td></tr><tr><td>Zr-Pd</td><td>-91</td><td>3</td><td>0.057</td><td>0.028</td></tr><tr><td>Zr-Zr</td><td>0</td><td>3.16</td><td>0.018</td><td>0.010</td></tr><tr><td>Sn-Ti</td><td>-21</td><td>2.97</td><td>0.019</td><td>0.016</td></tr><tr><td>Sn-Cu</td><td>7</td><td>2.81</td><td>0.022</td><td>0.014</td></tr><tr><td>Sn-Pd</td><td>-34</td><td>2.97</td><td>0.014</td><td>0.006</td></tr><tr><td>Sn-Zr</td><td>-43</td><td>3.13</td><td>0.009</td><td>0.004</td></tr><tr><td>Sn-Sn</td><td>0</td><td>3.1</td><td>0.001</td><td>0.001</td></tr></tbody></table>
comparatively strong liquid, in accord with viscosity measurements [4]
(Section S3 of the Supplementary Material).

Upon further cooling, the kink occurring near the calorimetric glass
transition temperature $T_g$ indicates the “freezing” of the amorphous
structure, i.e. structural changes have ceased to dominate and the linear
change of $Q_{1,cent}(T)$ below $T_g$ can mainly be attributed to usual thermal
expansion only (Fig. 3a). The linear increase of $S(Q_1(T), T)$, with a much
smaller slope, together with the almost constant $\Delta Q_1(T)$ below $T_g$ indi-
cate that the behaviour is now dominated by the Debye-Waller factor
(Fig. 3b,c).

As mentioned above, an apparent negative thermal expansion can be
observed for the first shell ($n = 1$) above $T_g$. This phenomenon has been
reported before, and different possible explanations have been put for-
ward [58–61]. Fig. 6 shows the positions of the centroids up to the
eighth shell ($n = 8$) normalised to the respective value at 487 K. The use
of centroids provides the possibility to obtain a measure for the distance
also for shells with high $n$ where a proper fit is hampered by termination
ripples. The different behaviour of the first shell in comparison with all
other shells can clearly be seen. Interestingly, for $n = 2$ and $n = 3$ the
shell distances behave very similarly to each other, but show a much
stronger thermal expansion than for $n > 3$. Except for $n = 7$ all other
shells behave virtually alike within the experimental uncertainty. Hints
for the existence of two structural regions with a demarcation between
$n = 3$ and $n = 4$ were recently reported for glassy $Zr_{60}Cu_{20}(Cu,Ni,Co)_{10}Al_{10}$ alloys where a possible explanation was given in terms of the
influence of the electronic structure [33]. The availability of T-depen-
dent measurements in the present case enables a more detailed study of
this behaviour. Also shown in Fig. 6 are $2\pi/Q_1(T)$ (solid red line on
yellow background) and $2\pi/Q_{1,cent}(T)$ (dash-dotted red line on yellow
background), respectively. A good agreement for $n \ge 4$ (again with the
exception of $n = 7$) is obvious. These observations corroborate the early
conjecture by Cargill [62] that the first maximum in $S(Q)$ represents the
MRO (but not SRO) from a certain distance onwards [62,63]. The
peculiar behaviour of shells 2 and 3, that seemingly can neither be
assigned to SRO or MRO, needs further attention in the future. As for the
different behaviour for $n = 7$ it is currently not clear whether this is a
structural feature or merely an experimental artefact.

Since according to Yavari et al., the macroscopic thermal expansion
is correlated with $Q_1(T)$ [31], the present results indicate that above $T_g$
only the behaviour for relatively high distances of the MRO, but not that
for smaller distances, especially not that for the SRO ($n = 1$), can be used
to evaluate thermal expansion in real space. A similar behaviour was
described for glassy $Cu_{65}Zr_{35}$ [64] and liquid and glassy

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Positions of the centroids of the first 8 shells normalised to their respective values at T = 487 K. Additionally, again normalised to their respective values at T = 487 K, $2\pi/Q_1(T)$ (solid red line on yellow background) and $2\pi/Q_{1,cent}(T)$ (dash-dotted red line on yellow background) are plotted for comparison. Arrows and vertical line as in Fig. 3.</figcaption></figure>

$Pd_{40}Cu_{30}Ni_{10}P_{20}$ where T-dependent changes of the distances of the
individual shells were compared to the macroscopic thermal expansion
obtained by dilatometry [65]. Together with the present results, this
suggests that the link between macroscopic thermal expansion and
$Q_1(T)$, as stated by Yavari et al. [31], also holds for the undercooled
liquid range. Below $T_g$ no structural changes take place anymore and all
shells behave roughly in the same way showing mainly the effects of
thermal expansion (Fig. 6) corroborating the findings in reciprocal space
discussed above. In general, it can be assumed that SRO and MRO are
affected differently during undercooling towards vitrification. Struc-
tural changes beyond a usual linear thermal expansion manifest them-
selves mainly in the first three shells, highlighting again that this region
should not be used to describe thermal expansion.

If the correlation between $Q_1(T)$ and the high-$r$ part of $G(r)$ holds,
changes in slope observed for the first halo in reciprocal space should
also be visible in real space for the shell distances for higher $n$.
Furthermore, due to the possibility of different effects on different length
scales, changes in behaviour may occur at different characteristic tem-
peratures for different shells. However, the scatter of the present data
prevents a more detailed analysis.

It is interesting to note that the positions of the maxima $r_n(T)$ as well
as those of their centroids $r_{n,cent}(T)$ for the peaks in $G(r, T)$ coincide with
each other for $n \ge 4$ (Fig. S2 in the Supplementary Material), which
indicates a transition of prevalence from local to global mechanisms of
structure formation of the real space structure between $n = 3$ and $n = 4$:
the influence of the individual local properties of the elemental species
(i.e. mainly their radii) has ceased to dominate and is more and more
replaced by a global statistical distribution (particle density oscillations
[66,67]) irrespective of the particular element, underlining the above-
mentioned reason for the demarcation put forward previously [33].
Indeed, $Q_1$ is also connected to a description of the structure of metallic
glasses in terms of global interactions between atomic and electronic
structure neglecting the differences between the individual species [40,
41]. In this model the energetically optimal state for an alloy is reached
when the “resonance condition” $Q_1 = 2k_F$ is fulfilled, i.e. the pseudo
Brillouin-zone (diameter $Q_1$) coincides with the Fermi sphere (diameter
$2k_F$) [39,40,68]. In this case a sequence of distances, known as spherical
periodic order (SPO), for the consecutive shells from the central atom
according to $r_n = (1/4 + n) \cdot 2\pi/Q_1$ is expected [40]. This relation would
suggest a parallel behaviour of all shells depending only on $Q_1$, which, at
least in the present case, is clearly contradicted by the results presented
in Fig. 6. The global description, therefore, seems to be valid for the
higher distances within the MRO only ($n \ge 4$) where the influence of
local effects between the atoms is negligible as discussed above. In this
respect a description of the real-space structure of metallic glasses based
on global electronic interactions, especially by invoking the SPO, has to
be reconsidered for small distances ($n \le 3$). It is worth noting that a
mean valence $Z \approx 1.5$ (electrons per atom), which has been discussed for
other metallic glasses as well [41,69,70], seems to be an appropriate
value to obtain a Fermi-sphere diameter $2k_F$ to be compatible with $Q_1$ or
$Q_{1,cent}$, respectively, observed in the present case (cf. Supplementary
Material for details of the related calculations).

In a sense, the measurement of the temperature-dependent shell
distances $r_n(T)$, especially in the undercooled liquid region, acts as a
powerful tool to probe the correlations between the different regions in
real (SRO and MRO, respectively) and reciprocal space (halo 1) and
helps to clarify the role of global effects in metallic glasses: shells for
$n \le 3$ seem to be strongly influenced by local effects which are also
responsible for the apparent negative thermal expansion, whereas for
$n \ge 4$ shells reflect global effects and are compatible with an expected
positive (macroscopic) thermal expansion. Above $T_g$ global electronic
effects can influence the nature of the atomic arrangement in the MRO
during undercooling. Below $T_g$, i.e. after structure formation has largely
ceased, changes in shell distances take place foremost due to thermal
expansion affecting all length scales almost identically. The different
influence of global electronic effects on different length scales cannot be
discerned easily anymore, potentially leading to the false impression
that they are equally as important in the SRO as well.

5. Conclusions

The evolution of the structure of Ti₄₀Zr₁₀Cu₃₄Pd₁₄Sn₂ metallic liquid during vitrification has been observed in-situ using high-energy synchrotron radiation and aerodynamic levitation. X-ray diffraction data have been recorded over a wide temperature range starting from above the liquidus temperature T<sub>liq</sub> down to well below the glass-transition temperature T<sub>g</sub>. The structural evolution has been analysed in terms of the temperature-dependent structure factor S(Q, T) and reduced pair distribution function G(r, T). Below T<sub>liq</sub> rapid structural changes occur by atoms migrating from anti-shell to shell regions leading to a strong enhancement of the short and medium range order as T<sub>g</sub> is approached. The structural rearrangements in the undercooled liquid of Ti₄₀Zr₁₀Cu₃₄Pd₁₄Sn₂ are found to be correlated with a rapid increase in viscosity and fragility. The structural rearrangements also cause an apparent negative thermal expansion of the first-nearest-neighbour shell in the undercooled liquid while in the glassy state a usual positive expansion occurs. Shells 2 and 3 cannot be clearly associated with either short or medium range order. The validity of a global description of the structure of metallic glasses, at least in the present alloy, is restricted to distances beyond the third shell. The results on the evolution of the atomic structure of metallic liquids during vitrification shed some more light on glass formation and on the structural origins of the sluggish long-range order kinetics that suppresses nucleation and growth of crystalline phases.

CRediT authorship contribution statement

Konstantinos Georgarakis: Conceptualisation, Methodology, Formal analysis, Validation, Writing - Original Draft, Visualisation, Project administration, Supervision, Funding acquisition. Martin E. Stiehler: Writing - Original Draft, Data Curation, Validation, Formal analysis, Methodology, Software, Visualisation. Louis Hennet: Methodology, Resources, Writing - Review & Editing, Validation, Data Curation. Yaofeng Guo: Formal analysis, Data Curation, Visualisation, Writing - Review & Editing. Jerzy Antonowicz: Conceptualisation, Methodology, Validation, Writing - Review & Editing. Dmitri V. Louzguine-Luzgin: Conceptualisation, Methodology, Validation, Writing - Review & Editing. Mark R. Jolly: Supervision, Writing - Review & Editing, Funding acquisition. Jérôme Andrieux: Methodology, Resources, Data Curation, Validation, Writing - Review & Editing. Gavin B.M. Vaughan: Methodology, Resources, Data Curation, Writing - Review & Editing. A. Lindsay Greer: Formal analysis, Validation, Writing - Review & Editing.

Declaration of Competing Interest

The authors declare the following financial interests/personal re-
lationships which may be considered as potential competing interests:
Martin E Stiehler reports financial support was provided by Engineering
and Physical Sciences Research Council. Konstantinos Georgarakis re-
ports financial support was provided by Engineering and Physical Sci-
ences Research Council. Konstantinos Georgarakis reports financial
support was provided by Japan Society for the Promotion of Science
London. Konstantinos Georgarakis reports financial support was pro-
vided by European Commission Seventh Framework Programme for
Research and Technological Development People. Yaofeng Guo reports
financial support was provided by European Commission Seventh
Framework Programme for Research and Technological Development
People. If there are other authors, they declare that they have no known
competing financial interests or personal relationships that could have
appeared to influence the work reported in this paper

**Acknowledgements**

This work is dedicated to the memory of Professor AR Yavari. The
authors extend gratitude to the ID15 beamline staff at the European
Synchrotron Radiation Facility (ESRF) for their untired experimental
support. Financial support by the “BioTiNet” EU Initial Training
Network (ITN) (Grant agreement ID: 264635), the JSPS KAKENHI
(Grant Number: 15K18201) as well as the EPSRC-DTP studentship “Bulk
Metallic Glasses: Revealing the Structural Pathway of Liquid Metals to
Vitrification” (project reference 2043971) within the framework of the
EPSRC Doctoral Training Partnership with Cranfield University (EP/
N509450/1) is gratefully acknowledged. MES thankfully acknowledges
the support by a Cranfield University 75th Anniversary Research
Fellowship.

**Appendix A. Supporting information**

Supplementary data associated with this article can be found in the
online version at doi:10.1016/j.jallcom.2025.180214.

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