Investigation of short-range structural order in Zr_69.5Cu₁₂Ni₁₁Al_7.5 and Zr_41.5Ti_41.5Ni₁₇ glasses, using X-ray absorption spectroscopy and ab initio molecular dynamics simulations

Short-range order has been investigated in Zr_69.5Cu₁₂Ni₁₁Al_7.5 and Zr_41.5Ti_41.5Ni₁₇ metallic glasses using X-ray absorption spectroscopy and ab initio molecular dynamics simulations. While both of these alloys are good glass formers, there is a difference in their glass-forming abilities (Zr_41.5Ti_41.5Ni₁₇ > Zr_69.5Cu₁₂Ni₁₁Al_7.5). This difference is explained by inciting the relative importance of strong chemical order, icosahedral content, cluster symmetry and configuration diversity.

1. Introduction

Growing interest in glass-forming alloys is inspired by their great technological promise (e.g. armour-penetrator, bio­medical implants, magnetic storage material, etc.) resulting from enhanced anti-corrosive and mechanical properties (Greer & Mathur, 2005; Greer, 1995; Ball, 2003). Since these enhanced properties hinge on amorphous/glassy structure, understanding the structure and its role in the glass-forming ability (GFA) of these alloys is important for their success (Yavari, 2006; Madden, 2005; Biazzo et al., 2009; Cozzini & Ronchetti, 1996; He & Ma, 2001; Miracle, 2004; Sheng et al., 2006a,b, 2008; Kelton et al., 2003; Ma et al., 2007, 2009; Mattern, 2009; Liu et al., 2008; Saida et al., 2000, 2007, 2008; Luo et al., 2004; Zalewski et al., 2009; Yang et al., 2005, 2012; Saksl et al., 2003; Long et al., 2009; Herlach, 1994; Cahn, 1986; Inoue et al., 1990; Inoue, 2000; Cheng et al., 2008; Shi & Falk, 2006; Tanaka, 2005; Peng et al., 2010; Li et al., 2009; Takeuchi et al., 2009; Greer, 1993).

Close-packed icosahedra, incompatible with translational symmetry, are the most widely recognized structural units of metallic glasses. As the number (n) of atomic components (X_n) of the alloy increases (e.g. multi-component alloy), the system becomes confused and disfavours any preferential structural order, a phenomenon called the `confusion principle' (Greer, 1993); instead, the structural configuration assumes distribution. Thus, multi-component systems, owing to their inherent disorder, are more inclined to be amorphous in character which promotes their GFA. Further composition-dependent modulations by chemical order, packing efficiency, etc. are the factors which determine the final structure of the system (Cheng et al., 2009; Fujita et al., 2009; Köster et al., 1996; Lee et al., 2008).

In this work we critically assess the role of short-range order (SRO), particularly the relative importance of chemical ordering, icosahedral content, cluster shape symmetry and configuration diversity, on relative GFA of two multi-component glasses, viz. Zr_69.5Cu₁₂Ni₁₁Al_7.5 (n = 4) and Zr_41.5Ti_41.5Ni₁₇ (n = 3) (Köster et al., 1996; Lee et al., 2008). While both these alloys are good glass formers and yield quasi-crystalline daughter phases, their GFA differ on a relative scale: GFA = Zr_41.5Ti_41.5Ni₁₇ ≈ Zr_69.5Cu₁₂Ni₁₁Al_7.5; δ(GFA) ≥ 25%. For each alloy we derived site-resolved SRO for glassy and daughter phases of both the alloys, by employing X-ray absorption spectroscopy (XAS) (Prins & Koningsberger, 1987) and supporting with ab initio molecular dynamics (AIMD) simulations. To comprehend the extent of chemical ordering in these alloys we employed XANES (X-ray absorption near-edge structure). [XANES is the portion of XAS spectra within 30 eV of the absorption edge and sensitive to oxidation state, coordination chemistry, orbital hybridization, etc. (Prins & Koningsberger, 1987).]

The X-ray absorption spectrum μ(E) of matter is modulated from the atomic absorption coefficient μ₀(E) by post-edge (E₀) oscillatory fine features, known as `X-ray absorption fine structure' (XAFS). A photoelectron ejected from the excited atom (BE = E₀) is backscattered from the neighbouring atoms within radial distance (R = 8–10 Å). The interference, between backscattered and original photoelectron waves, gives rise to an oscillatory final-state vector in the absorption matrix. This is the origin of XAFS oscillations. The principle of XAFS is not based on long-range order, which makes it a unique probe for amorphous systems. Detailed structural information [viz. near-neighbour species (Z), their coordination (N), bond lengths (R) and mean square displacement (σ²)] is derived from the Fourier transformation (FT) of XAFS oscillations. In the case of these multi-component alloys, several correlated XAFS variables could result in non-unique structural models. To select the final model unambiguously, we generated structural models from AIMD simulations independently and verified the consistency with XAFS results.

2. Experimental details

Zr_41.5Ti_41.5Ni₁₇ and Zr_69.5Cu₁₂Ni₁₁Al_7.5 alloys were prepared from pure Zr, Ti, Al, Cu and Ni by vacuum arc melting. The melt-spun ribbons (thickness = 20–30 µm; width = 5 mm) were produced by rapid solidification of the melted alloy and amorphous character confirmed by X-ray diffraction (XRD) (Fig. 1a). Details of the synthesis method are provided elsewhere (Budhani et al., 1982). From differential scanning calorimetry measurements (Fig. 2) we derived the relevant temperature points for calculating GFA, viz. (T_g, T_x, T_m) corresponding to glass transition, crystallization and melting, respectively (Table S1 of the supporting information¹). Different GFA parameterizations unanimously yield GFA: Zr_41.5Ti_41.5Ni₁₇ ≈ 1.3 × (Zr_69.5Cu₁₂Ni₁₁Al_7.5) [δ(GFA) ≥ 25%]. Some of these as-cast ribbons were annealed (T > T_m) for 1 h and quasi-crystalline daughter phases obtained (Fig. 1b). [In order to compare their GFA through casting diameter, both the alloys were suction casted into a 3 mm-diameter copper mould. Fig. S1(a) (see supporting information) shows the cylindrical rods of the as-cast Zr-based metallic glasses. To confirm the structure of the phases present in as-cast alloys, the samples were characterized by XRD. The XRD pattern of Zr_41.5Ti_41.5Ni₁₇ in Fig. S1(b) exhibits broad peaks, characteristic of amorphous structure. The XRD pattern of Zr_69.5Cu₁₂Ni₁₁Al_7.5 in Fig. S1(c) shows the presence of the diffraction peaks, characteristic of crystalline phases present in the sample. The presence of amorphous and crystalline phases in Zr_41.5Ti_41.5Ni₁₇ and Zr_69.5Cu₁₂Ni₁₁Al_7.5, respectively, confirms that the former has better GFA.]

Figure 1 XRD of the (a) glassy and (b) annealed phases of Zr41.5Ti41.5Ni17 and Zr69.5Cu12Ni11Al7.5.

Figure 2 Differential scanning calorimetry results at low heating rate. Glass transition (Tg) and crystallization (Tx) temperatures are shown. Differential scanning calorimetry, at high heating rate, is shown in the inset. The melting temperature (Tm) is indicated.

XAFS spectra (viz. Cu, Ni and Zr K-edges on as-cast and annealed ribbon samples of each alloy) were recorded in transmission mode at BAMline, BESSY.² A Si (111) monochromator in conjunction with a harmonic rejection mirror was used to filter out the required wavelengths. Argon- and krypton-filled ionization chambers were used to monitor the incident and transmitted X-ray intensities, respectively. The data were processed using the ATHENA code³ and the resultant χ curves are shown in Fig. 3. The fast decay of XAFS oscillations beyond 10 Å⁻¹ is typical of amorphous materials. The data were fitted for the Fourier transform (FT) range (Δk = 2.5–10 Å⁻¹; k^{w = 1–3}) and R-range (ΔR ≈ 1.5–3.0 Å⁻¹), using the FEFF8 and FEFFIT codes (Newville et al., 1995). A good fit quality (R-factor < 0.01) was obtained in all cases (Newville et al., 1995; Newville, 2001; Ravel & Newville, 2005).⁴

Figure 3 (a) Cu K-, (b) Ni K-, (c) Zr K-edges for Zr69.5Cu12Ni11Al7.5; (d) Ni K- and (e) Zr K-edges for Zr41.5Ti41.5Ni17.

AIMD simulations were carried out using the finite-temperature local density functional theory, as implemented in the Vienna ab initio simulation package (VASP) (Kresse & Hafner, 1994; Kresse & Furthmüller, 1996; Fang et al., 2009; Hui et al., 2009). These calculations employ projector augmented wave (PAW) potentials along with a plane wave basis set. To obtain good convergence we used a plane wave energy cut-off of 450 eV. Brillouin zone integrations were carried out using the Γ point. The simulations were performed on a 200-atom cubic supercell with periodic boundary conditions. The initial configurations were prepared by randomly placing the constituent atoms inside the cubic box at known experimental densities of 6.08 and 6.76 g cm⁻³ for ternary and quaternary systems, respectively. The simulations were carried out in a canonical ensemble (NVT) with a Nosé thermostat for temperature control and the equations of motion were solved with a time step of 3 fs. First the systems were melted at 2500 K, followed by a 6 ps equilibration period. Then these systems were quenched to 300 K at a rate of ∼12 × 10¹³ K s⁻¹ (typical of ab initio simulations) (Hui et al., 2009; Oji et al., 2009), followed by a 6 ps equilibration period. It may be noted that the cooling rate in simulations is too fast compared with that during experimental quenching. While this may have influence on the development of medium-range order, short-range order is expected to be accurate (Oji et al., 2009).

3. Results and discussion

3.1. Structure of the glassy phase

For each alloy, Fourier-transformed (FT) XAFS spectra of glassy and daughter (annealed) phases are shown in Fig. 4. The similarity between the spectra of glassy and respective daughter phases is consistent with a gradual crystallization process (discussed later).

Figure 4 XAFS data for the glasses before and after annealing.

It may be noted that the peaks at distances of less than 1.5 Å are not real but result from the slight oscillatory character of the background fit polynomial. The background oscillation arises due to the limited k-range available (2.5–10 Å⁻¹). Following several background-fitting strategies (e.g. different k ranges, k weights, R ranges), the optimal background yields the observed peaks at low R. It may be clarified that the low-R limit (∼1.5 Å), for fitting the peak of interest (∼1.5–3.0 Å), is set such that the leakage from the background peak is negligible. Hence, the derived XAFS fit parameters are expected to be free of background-related artifacts.

3.1.1. Zr_69.5Cu₁₂Ni₁₁Al_7.5

AIMD simulations yielded partial distribution functions g_ik(R) (i, k = Ni, Zr, Al, Cu) [Figs. 5(a) and 5(b)].⁵ The bond lengths (peak positions)⁶ are consistent with the literature (Kaban et al., 2013; Takeuchi et al., 2005). Out of these, R_NiZr (2.67 Å) and R_NiAl (2.47 Å) are significantly (∼10%) shortened from their sum-of-atomic radii distances, viz. R_Ni+Zr (2.96 Å) and R_Ni+Al (2.76 Å), respectively. [Atomic radii were directly obtained from the respective homo-nuclear bond distances: R_Cu (1.25 Å) → R_Al (1.37 Å) → R_Ni ( 1.39 Å) → R_Zr ( 1.57 Å)]. This indicates the existence of Ni–Al and Ni–Zr chemical interactions (Pilarczyk, 2013) in the system (discussed later).

Table 1
XAFS fit results

Bond type	Phase	Bond length (Å)	XAFS coordination number (N^EXAFS)†	DWF (Å^2)
Zr69.5Ni11Cu12Al7.5
Ni—(Ni+Cu)	Glassy	2.61 (8)	0.36 ± 0.05	0.006 ± 0.002
	Annealed	2.72 (6)	0.68 ± 0.08	0.005 ± 0.002
Ni—Zr	Glassy	2.61 (1)	2.61 ± 0.08	0.011 ± 0.001
	Annealed	2.72 (1)	2.91 ± 0.2	0.007 ± 0.001
Cu—Zr	Glassy	2.72 (1)	2.39 ± 0.2	0.010 ± 0.001
	Annealed	2.81 (1)	3.22 ± 0.19	0.004 ± 0.001
Zr—Zr	Glassy	3.07 (1)	6.51 ± 0.58	0.023 ± 0.002
	Annealed	3.16 (1)	6.51 ± 0.37	0.012 ± 0.002
Zr41.5Ti41.5Ni17
Ni—Ti	Glassy	2.59 (1)	2.64 ± 0.17	0.018 ± 0.002
	Annealed	2.54 (4)	2.30 ± 0.24	0.015 ± 0.002
Ni—Zr	Glassy	3.11 (2)	1.11 ± 0.24	0.007 ± 0.003
	Annealed	3.07 (5)	0.71 ± 0.35	0.004 ± 0.006
Zr—Ti	Glassy	3.06 (1)	5.96 ± 0.33	0.013 ± 0.001
	Annealed	3.02 (2)	3.94 ± 0.25	0.007 ± 0.001
Zr—Zr	Glassy	3.23 (1)	8.09 ± 0.84	0.028 ± 0.003
	Annealed	3.14 (2)	8.23 ± 0.98	0.027 ± 0.003

†S₀ ² = 0.8–0.9 from measurement of standards.

Figure 5 AIMD simulations for Zr69.5Cu12Ni11Al7.5 and Zr41.5Ti41.5Ni17 around the Zr and Ni centres.

The partial pair coordination (N_ik) and total coordination number (CN) around each site (N_i = ) are obtained from the region within the first minima (R_c ≃ 4 Å). The average CN around each site is thus obtained: N_Cu ≃ 10; N_Al ≃ 12; N_Ni ≃ 11; N_Zr ≃ 13. The shift in CN is consistent with the solute–solvent atomic size ratio (R^*) (Sheng et al., 2006a,b; Miracle et al., 2006). The ensemble-averaged CN = 12.5 (= , where is the stoichiometric fraction).

As mentioned, the above are only average results; in reality the ensemble consists of a distribution of cluster configurations and the nature of the distribution has important implications for GFA. In Fig. 6(a) we show the site-resolved CN distribution (N_j,f_j)_i for this glass [i = (Ni, Zr, Al, Cu); N_j = 8–16; f_j = frequency of clusters]; the main peak position (N_j)_i shifts in agreement with R_i^*. From Fig. 6(a) we generated , i.e. the distribution (N_j,F_j) of the entire ensemble, in Fig. 6(b). We observe that clusters with N = 12–14 are the most dominant ( = 75%; F_12,13,14 ∼ 25%) in the ensemble, comparable with reported multi-component glasses (Yang et al., 2013; Hui et al., 2009; Fang et al., 2009; Fujita et al., 2009; Cheng et al., 2009). [For each CN, clusters of slightly varying geometry exist.] With such a narrow CN distribution (N = 12–14) and small variation in cluster volume (first shell radius ≃ 2.6 Å) and geometry, the configuration primarily resembles `quasi-equivalent clusters', similar to that observed for good glass formers (Sheng et al., 2006a,b, 2008). A secondary cluster domain with N = 10 (F₁₀ = 12%) co-exists in the ensemble (around the smaller centres), adding non-uniformity to the configuration (discussed later).

Figure 6 Site-resolved population distribution (%) of the nearest-neighbour coordination for (a) Zr69.5Cu12Ni11Al7.5 and (c) Zr41.5Ti41.5Ni17. Ensemble-distribution for (b) Zr69.5Cu12Ni11Al7.5 and (d) Zr41.5Ti41.5Ni17.

Independent XAFS data fitting yielded nearest-neighbour bond lengths (Table 1) consistent with AIMD results. (Fits are compared with data in Fig. 7.) Despite multiple components, analysis was simplified by (i) ignoring the (negligible) contribution of Al due to its low stoichiometric fraction and backscattering factor, and (ii) treating Ni and Cu scattering paths equivalently owing to their indistinguishable backscattering factors and similar bond lengths (Fig. 5). [R_Ni–Ni = R_Ni–Cu = 2.6 Å validates this assumption at the Ni K-edge. |R_Zr–Cu − R_Zr–Ni| ≃ 0.05 Å is negligible; any attempt to separately fit these paths (Zr K-edge) was redundant and resulted in a large error bar. Thus, assumption (ii) is justified for the Zr K-edge as well.]

Figure 7 Comparison of fit with data for Zr69.5Cu12Ni11Al7.5 glass.

Following these assumptions, XAFS analysis is simplified to fitting two scattering paths (Ni, Zr) at each edge. To reduce further uncertainties in the (Ni, Zr) bond parameters, we simultaneously fitted the (Ni, Zr)-edge data with the common variable (R_Ni–Zr, ). From the XAFS fit results in Table 1, we observe that the total coordination around each site is lower than the AIMD results, e.g.

These results did not improve even with the inclusion of higher cumulants (Prins & Koningsberger, 1987; Fukuhara et al., 2010).⁷

To reconcile these independently derived XAFS and AIMD coordination results, e.g. N_Ni^XAFS () N_Ni^AIMD (= 11), we consider the respective interpretation of coordination and its relevance to such highly disordered systems. In AIMD, N_i^AIMD is R_c-dependent (Sheng et al., 2006a; Oji et al., 2009). The positions of the first minima (R_c) are different for XAFS and AIMD [viz. ] due to a larger dis­order in the AIMD configuration and significant peak broadening. Reducing R_c^AIMD = 4 3 Å indeed reduces N_Ni^AIMD  11 5 N_Ni^XAFS. On the other hand, N_Ni^XAFS should be interpreted in an `effective' sense (rather than absolute) for highly disordered systems (e.g. multi-site configuration). XAFS contributions from individual paths can be slightly out of phase with each other and reduce the net XAFS amplitude. This is reflected as reduced (N<sub>Ni</sub> 3) `effective' XAFS coordination (Meyerheim et al., 2012). Thus, N_Ni^XAFS 3 in our case could well be consistent with N_Ni^AIMD = 11.

To reconcile the XAFS and AIMD results more conclusively, we constructed a Ni K-edge XAFS spectrum using the AIMD-generated atomic configuration. Scattering paths for the atoms were generated using FEFF6. With these paths and the `NOFIT' option in the feffit.inp file, we simulated the normalized XAFS spectrum (with respect to the number of Ni atoms in the configuration). The simulated XAFS spectrum matches reasonably well with the experimental Ni K-edge XAFS spectrum (Fig. 8a). [The slight difference may be ignored considering that the AIMD-generated atomic configuration is highly disordered. This makes the theoretical XAFS spectrum highly sensitive to the exact atomic positions. The slight relative displacement of atoms (for test) resulted in reduction of the peak amplitude (de-phasing) or shift in the peak position.] By reproducing the experimental spectrum with N_Ni = 11 and large disorder, we could reconcile the AIMD and XAFS results and justify the low XAFS coordination (N_Ni = 11 3).

Figure 8 XAFS data compared with FEFF simulations generated from AIMD cluster configuration for Zr69.5Cu12Ni11Al7.5 around (a) Ni and (b) Zr. The AIMD-based fit is compared with XAFS data in the inset of (a).

To make our argument more conclusive, we actually fitted Ni K-edge XAFS using a theoretical AIMD distribution (Fig. 5b) as the basis for the fit and R_c^AIMD = 3.2 Å. [Since there is no XAFS feature beyond R = 3 Å we have defined the XAFS fit range over R = 1.5–3 Å. The contribution from the AIMD paths beyond 3.27 Å is negligible.] A detailed description of the fit method is included in the supporting information. We obtained a good quality fit (shown in the inset of Fig. 8a). Our fit result, R_NiZr = R₀ = 2.67 Å; AIMD-based XAFS fit coordination, viz. N_Ni^XAFS-AIMD = 4.5, is now closer to our earlier model-independent XAFS fit result N_Ni^XAFS = 3 (i.e. N_Ni^XAFS - N_Ni^AIMD-XAFS = −34%). This directly confirms our observation from AIMD: `R_c^AIMD = 4 3 Å reduces N_Ni^AIMD 11 5', and establishes an agreement between XAFS and AIMD coordination.

Additionally, we incite the sensitivity of the coordination to the degree of charge transfer between the central (Ni) and neighbour (Al, Ni/Cu, Zr) atoms. AIMD and XAFS both confirm Ni—Zr bond shortening (10%) from the sum-of-atomic-radii value, due to charge transfer (Ni—Al bond shortening is observed from AIMD). This suggests a change in the effective size of each ion (from its atomic size) which reduces the effective (centre: neighbour) atomic size ratio (R^*). Low N_Ni (as observed from XAFS) could be consistent with lower R^* (Miracle et al., 2006), reflecting these ionic effects. The difference (>40%) between the AIMD and XAFS coordination has been reported earlier for glasses with strong chemical interaction (Liu et al., 2012, 2014; Mansour et al., 1994, 2002; Saksl et al., 2005).

The conclusions for the Ni K-edge hold good for the Cu K-edge. However, the Zr K-edge results could not be validated unambiguously due to the larger disorder around the Zr sites. [Adding successive scattering paths progressively reduced the XAFS amplitude by de-phasing (Fig. 8b).]

3.1.2. Zr_41.5Ti_41.5Ni₁₇

AIMD simulations [Fig. 5(c) and 5(d)] yielded bond lengths consistent with the reported literature (Hennig et al., 2003; Sadoc et al., 2001, 2002; Mechler et al., 2010a). The existence of a strong Ni–Ti interaction is shown from the Ni—Ti bond shortening (∼10%) from its sum-of-atomic-radii value [i.e. R_NiTi (= 2.59 Å) < R_Ni+Ti (= 2.79 Å)]. The average CN around each site is consistent with R^*: N_Ti 12; N_Ni 11; N_Zr 14 and ensemble averaged CN: N = 13.1.

Site-resolved and ensemble-averaged CN distributions are shown in Figs. 6(c) and 6(d), respectively. The site-resolved distribution in Fig. 6(a) demonstrates the R_i^*-dependent shift in peak position. In Fig. 6(b), the ensemble-averaged CN distribution extends over [N = 11–15]; out of these, clusters with CN = [12–14] emerge as the most dominant configuration ( = 70%). With such a narrow and continuous CN distribution, the ensemble configuration is consistent with the model of `quasi-equivalent clusters'.

Independent XAFS fitting results, listed in Table 1, yield similar bond lengths as AIMD. The first coordination shell around Ni is significantly distorted: (i) (Ti, Zr) atoms displace in opposite directions (with respect to Ni), instead of converging at a common radial distance ( = R_NiZr − R_NiTi = 0.5 Å), signifying a strong Ni–Ti affinity and repulsive Ni–Zr interaction. (ii) (N_Ni^Zr:N_Ni^Ti) 0.4:1, instead of 1.67:1 (Mechler et al., 2010b; Wang et al., 2004). Reduced N_Ni^Zr indicates several broken Ni—Zr bonds. Thus, both bond length and coordination features suggest the weakening of the Ni–Zr interaction by a much stronger Ni–Ti interaction (Antonowicz et al., 2011).

3.1.3. Chemical order

To probe the extent of the chemical interaction in these glasses, we calculated the orbital projected density of states (PDOS) functions for each atomic species of the two alloys. From PDOS functions [Figs. 9(a) and 9(b)] it is obvious that both alloys are metallic as they have an appreciable amount of electronic density of states at the Fermi level. The main peaks of the Cu and Ni d-states lie a few electronvolts below the Fermi level. However, the d-states of Zr and Ti participate actively in the bonding as their main PDOS weight pass through the Fermi level. The p-states of Zr and Ti also contribute significantly to the bonding. The Ni d-states lie slightly deeper in Zr_69.5Cu₁₂Ni₁₁Al_7.5 but they show an appreciable overlap with different states of other atoms in both the systems [Figs. 9(a) and 9(b)]. From Fig. 9(b) the PDOS contribution of Ti clearly exceeds that of Zr by 50%, confirming the strong interaction of Ti. This is further supported by Ni K-edge XANES: comparison of the derivatives of the normalized spectra in Fig. 9(c) shows a significantly enhanced (×2) pre-edge feature (at 8332 eV) for Zr_41.5Ti_41.5Ni_17, compared with Zr_69.5Cu₁₂Ni₁₁Al_7.5 and Ni foil. X-ray absorption is dominated by the dipole transition rule = ±1), e.g. an transition, which contributes to the main peak of the XANES spectra. The pre-edge peak results from transitions to hybridized orbitals () and is an indicator of p–d hybridization/charge transfer (Yamamoto, 2008). A strong (×2) pre-edge feature for Zr_41.5Ti_41.5Ni₁₇ (with respect to a 0− charge state in Ni foil) confirms a strong charge transfer to Ni, most likely from Ti. In comparison, the pre-edge of Zr_69.5Cu₁₂Ni₁₁Al_7.5 is only (∼25%) developed relative to the Ni foil, suggesting a much lower charge transfer.

Figure 9 Atom projected electronic density of states PDOS (states eV^−1 atom^−1) of (a) Zr69.5Cu12Ni11Al7.5 and (b) Zr41.5Ti41.5Ni17 glasses. (c) Derivative of XANES spectra for these glasses compared with Ni foil.

3.2. Structure of the annealed phases

The structural changes, upon annealing, demonstrate gradual relaxation towards respective equilibrium phases and improved ordering. The degree of structural evolution is bond-dependent and varies between the two alloys.

3.2.1. Zr_69.5Cu₁₂Ni₁₁Al_7.5

(i) Bond-lengths expand towards their respective values in NiZr₂/CuZr₂, e.g. R_Ni–Zr = 2.61 Å 2.72 Å (R_Ni–Zr|_NiZr2 = 2.77 Å).⁸ (ii) Reduction of the Debye–Waller factor (DWF) ( = 30–60%) is consistent with the improved order in the annealed samples. (iii) Increased coordination ( = 0–35%) represents retrieval of broken bonds in the process of atomic re-arrangement during ordering.

3.2.2. Zr_41.5Ti_41.5Ni₁₇

In this system, all bond lengths contract ( 0.04–0.1 Å) towards their equilibrium (AIMD) values. Ordering, viz. , is negligible, considering error bars [except > 20%].

In both systems we consistently observe that the annealed structure is significantly far from the crystalline phases (e.g. NiZr₂)⁹, signifying the existence of a large crystallization barrier. It is likely that a strong chemical interaction (viz. Ni–Al, Ni–Zr, Ni–Ti) raises this barrier, restricts atomic mobility and arrests crystallization (Yang et al., 2010; Pilarczyk, 2013).

3.3. Structure and glass-forming ability

Compiling all these results, we list the relevant (with respect to GFA) SRO parameters of Zr_69.5Cu₁₂Ni₁₁Al_7.5 and Zr_41.5Ti_41.5Ni₁₇. Both of these alloys are good glass formers, as shown from their thermal parameters (Table S1), quasi-crystalline daughter phases (Fig. 1b) and large crystallization barrier (Fig. 4). Consistently, the SRO of the two alloys is broadly similar (±5%) and comparable with the SRO parameters of reported good glass formers, viz. (i) ISRO content (F₁₂ 25%), (ii) configuration model (= quasi-equivalent clusters), (iii) dominant cluster configuration (N = 12–14; F 70–75%), (iv) ensemble-averaged coordination (N 12) and (v) strong chemical interaction [(Ni–Al, Ni–Zr); (Ni–Ti)], resulting in bond shortening. SRO parameters promote GFA by enhancing the packing efficiency and amorphous template; in parallel, strong chemical interaction suppresses their crystallization by raising the crystallization barrier and restricting atomic mobility.

To understand their relative GFA difference, viz. Zr_41.5Ti_41.5Ni₁₇ > Zr_69.5Cu₁₂Ni₁₁Al_7.5 [δ(GFA) 25%], we incite the importance of cluster shape non-uniformity and strength of chemical interaction:

(i) On a relative scale, the CN distribution of Zr_69.5Cu₁₂Ni₁₁Al_7.5 demonstrates the tendency for increased cluster shape non-uniformity by the presence of two domains, viz. N = 12–14 (F 75%), N = 10 (F 12%). The latter forms around smaller centres (e.g. Cu, Al); non-uniformity is thus a consequence of the large variance in the constituent atomic sizes of this alloy. In contrast, the CN distribution of Zr_41.5Ti_41.5Ni₁₇ is smooth. The correlation between good GFA and regular shape symmetry has been established in earlier work (Guo et al., 2011; Xi et al., 2007; Sha et al., 2010). From this perspective, a smoother CN distribution of Zr_41.5Ti_41.5Ni₁₇ could have contributed towards its better GFA.

(ii) From our XANES results, it is clear that the chemical (Ni–Ti) interaction is significantly much stronger in Zr_41.5Ti_41.5Ni₁₇ involving a large degree of p–d hybridization: (100% versus 25%) in Zr_41.5Ti_41.5Ni₁₇ and Zr_69.5Cu₁₂Ni₁₁Al_7.5, respectively. Owing to this strong chemical interaction, atomic mobility is arrested and the crystallization barrier is significantly larger in Zr_41.5Ti_41.5Ni₁₇. This is shown from negligible (∼0%) structural evolution (post-annealing). In comparison, the relatively relaxed chemical interaction in Zr_69.5Cu₁₂Ni₁₁Al_7.5 allows for (30%) ordering.

4. Conclusion

With the help of XAFS measurements and AIMD simulations, we have attempted to obtain a structural understanding of the relative glass-forming-abilities of Zr_69.5Cu₁₂Ni₁₁Al_7.5 and Zr_41.5Ti_41.5Ni₁₇ (Zr_41.5Ti_41.5Ni₁₇ > Zr_69.5Cu₁₂Ni₁₁Al_7.5). While both are good glass formers and have broadly similar short-range order, noticeable differences in cluster shape uniformity and strength of chemical interaction exist between the two systems. We show that these two factors play crucial roles in determining their relative glass-forming abilities. Glass formation is more favoured for Zr_41.5Ti_41.5Ni₁₇ by smoother cluster distribution in the ensemble and a significantly stronger (Ni–Ti) chemical interaction; the former enhances amorphous packing efficiency and the latter increases the crystallization barrier. Thus, this work emphasizes the crucial role of these two factors on the glass-forming abilities of competitive and broadly similar systems.

Footnotes

¹Supporting information for this paper is available from the IUCr electronic archives (Reference: HF5264 ).

²https://www.helmholtz-berlin.de/pubbin/igama_output?modus=einzel&sprache=en&gid=1625&typoid=35512 .

³https://cars9.uchicago.edu/~ravel/software/doc/Athena/html/athena.pdf .

⁴https://cars.uchicago.edu/~newville/feffit/feffit.pdf .

⁵g_Al(r); g_Cu(r) are not shown.

⁶AIMD bond lengths concur with XAFS bond lengths in Table 1.

⁷The `thickness effect' may be ruled out since we measured samples with various degrees of polish (also splat-cooled) and thickness. The low coordination from Zr K-edge XAFS, despite the latter's insensitivity to the thickness problem (due to large absorption length), asserts that the observed low coordination is real.

⁸The same is true for the other bonds.

⁹NiZr₂: R_NiZr = 2.79 Å (N = 8); R_ZrZr = 2.82–3.17 Å (N = 3); R_ZrZr = 3.3–3.47 Å (N = 8).