Structure and Properties of the Melt-Spun Zr–(Al)–Ni–Cr–Ag Alloys

Abstract

The structure, mechanical and electrical properties of Zr-based melt-spun Zr–(Al)–Ni–Cr–Ag alloys were investigated as a function of elemental composition. X-ray diffraction reveals the structural evolution from fully amorphous to nanocrystalline states, with the latter containing Zr₂Ni “big-cube” (space group Fd3̄m, cF96), fcc-Zr₂Ni, and β-Zr phases depending on the alloying ratio: Cr-rich compositions (≥15 at.%) stabilize β-Zr within the amorphous matrix, whereas Ag-enriched alloys promote “big-cube” phase formation. Ag atoms can replace both Zr and Ni sites in the “big-cube” lattice, yielding a (Zr,Ag)₂(Ni,Ag) solid solution and highlighting its role as a structural bridge between the amorphous and crystalline states. Nanoindentation measurements show that hardness increases from 6.5 GPa in fully amorphous ribbons to 10.12 GPa in three-phase nanocrystalline composites, with an H/E ratio of ~0.08 indicating predominantly covalent bonding, and the fracture strength of the amorphous alloys is ~2 GPa, exceeding literature values for related Zr-based systems. Electrical resistivity measurements over the 4–298 K range show that most alloys deviate from Matthiessen’s rule, exhibiting a negative temperature coefficient of resistivity consistent with the Mooij correlation; the presence of the icosahedrally ordered “big-cube” phase further increases resistivity relative to fully amorphous alloys.

1. Introduction

Zirconium-based alloys with transition metals have a wide range of applications, from nuclear fuel cladding (Zr(Nb) with Zr content ≥ 98 at. %) to surgical implants (Zr–Cu–Co), structural materials for the chemical industry (high-temperature corrosion-resistant Zr–Cr–Al coatings [1]), and materials used in sporting goods [2]. Scientific interest in zirconium alloys has grown significantly after the discovery of a large, supercooled liquid region (SLR) in Zr–Al–(Ni, Cu) systems [3,4] and the production of bulk amorphous alloys within broad compositional ranges in Zr–Al–Ni-based metallic systems [5,6,7].

Although the fundamental characteristics of Zr-based amorphous alloys were discovered several decades ago, research activity in this area has remained high in recent years [8,9,10,11,12,13,14]. In particular, modern studies are focused on enhancing the mechanical properties and corrosion resistance of these alloys through the formation of amorphous–nanocrystalline composites and alloying with additional elements [10,11,12,13]. In multicomponent metallic systems, for instance, improved strength has been achieved by forming icosahedral phases and β- or ω-Zr phases within an amorphous matrix [15,16].

Of particular interest are the so-called “big-cube” phases—crystalline formations with a Ti₂Ni-type structure (space group Fd3̄m, cF96). Traditionally, they are viewed as common products of partial crystallization in Zr-based amorphous alloys. Recently, however, interest in these phases has grown significantly due to the discovery of “ZIP-phases” (zigzag intermetallic compounds). These A₃CB₂ ternary compounds exhibit dual atomic ordering and exist in two structural variants: cubic (with the same Fd3̄m symmetry as “big-cube” phases) and hexagonal. This discovery has brought renewed attention to classical Ti₂Ni-type phases, highlighting their potential for investigating the interplay between local atomic structure, electronic properties, and the formation of nanocomposite or even two-dimensional derivative structures [17].

It is worth noting that despite numerous publications, there is still no unambiguous understanding of phase formation processes and their impact on the physical and mechanical properties of these systems depending on the specific chemical composition and ratio of additional elements. On the other hand, the development of biocompatible materials for long-term implant applications remains one of the most important engineering tasks [14]. Therefore, the present study aims to investigate Zr–Ni–Al alloys featuring a composition close to a deep eutectic and a wide SLR [4] by adding Cr and Ag, which can improve mechanical properties and corrosion resistance, as well as contribute to the biocompatibility of the alloys. Additionally, the introduction of Ag may promote the nucleation of crystallization centers and improve the stability of the resulting composites [18,19].

2. Materials and Methods

The initial alloys were obtained by melting ingots of elementary metals with purity greater than 99.9 mass % using a high-frequency induction furnace (Vienna University of Technology, Wien, Austria) under a purified argon atmosphere. To achieve better homogeneity, the initial alloys were re-melted five times. Ribbons approximately 5 mm wide and about 0.03 mm thick were produced using the melt-spinning technique at a cooling rate of about 10⁶ K/s. The circumferential speed was 18 m/s (and 25 m/s in one case), with the distance between the nozzle with the melt and the wheel surface being 0.7 mm.

The structure of the as-quenched ribbon specimens was examined by X-ray diffraction (XRD), using Cu-Kα radiation, in step-scan mode with a step width of 0.011°. The crystallite sizes were evaluated from the XRD using FullProf.2k software (Website: https://www.ill.eu/sites/fullprof/, Access date: 15 June 2026) Prior to nanoindentation and microscopy tests, the samples were polished with a diamond paste to a mirror-like appearance using down to 1 μm diamond particles.

The mechanical properties (hardness and reduced elastic modulus) of the ribbon and sheet samples were evaluated by nanoindentation at room temperature in the load control mode. Hardness was measured as a function of depth by nanoindentation using a CSIRO UMIS nanoindenter with a Berkovich tip (Christian Doppler Laboratory “Surface Engineering of high-performance Components”, Wien, Austria). Twenty-five indentations (5 × 5 array with 50 μm spacing between indents) up to a fixed maximum depth of 2 μm were made on each specimen.

The temperature-dependent electrical resistivity of the alloys was studied using a four-point probe technique and employing a Lakeshore 370 a.c. resistance bridge Vienna University of Technology, Wien, Austria) in the range from room temperature down to 4 K. Electrical contacts to the melt-spun ribbon pieces (~1 cm in length) were made using gold wires attached with conductive silver paste. The temperature coefficient of resistivity (TCR) α was evaluated from the temperature dependence using a standard linear approximation:

ρ = ρ₀ [1 + α (T − T₀)]

(1)

where ρ₀ is the residual resistivity at 0 K.

3. Results and Discussion

In the ternary Zr–Ni–Al system, a significant number of intermetallic compounds can form, including both binary (Zr₂Ni, ZrNi, Zr₇Ni₁₀, Zr₃Al, Zr₂Al, Zr₃Al₂, Zr₄Al₃, etc.) and ternary phases (ZrAlNi₂, Zr₆Al₂Ni, etc.) [20,21,22]. These crystalline phases exhibit notably negative enthalpies of formation, which promote their stability and formation [23,24]. However, the intense competition among a large number of energetically close phases complicates the process of equilibrium crystallization and leads to suppression of crystal growth during rapid cooling. This phenomenon contributes to the increased tendency of such multicomponent alloys to amorphization, forming a metastable glassy structure instead of equilibrium crystalline phases [25,26]. Alloying the base Zr–Ni–Al system with chromium and silver significantly influences the structural formation processes during quenching from the liquid state.

This study investigates phase formation in rapidly quenched quinary Zr–Al–Ni–Cr–Ag alloys, as well as quaternary Zr–Ni–Cr–Ag alloys, using XRD. The compositions of the alloys were chosen to be in regions near the most well-known SLR, aiming to obtain glassy or amorphous structures with nanostructured α-/β-/ω-Zr or quasicrystalline phases.

3.1. XRD Analysis of the Rapidly Quenched Alloys

XRD patterns of alloys containing 7.5–8.5 at. % of Al (Figure 1a) show that Cr-rich compositions (Zr₆₅Al_7.5Ni₁₀Cr_17.5 and Zr₆₅Al_7.5Ni₁₀Cr₁₅Ag_2.5) consist of two structural components: β-Zr (bcc) and an amorphous phase. A Cr content decrease accompanied by an increase in Ag content leads first to the formation of a fully amorphous structure and subsequently to the appearance of nanocrystalline Zr₂Ni embedded in an amorphous matrix.

Figure 1. XRD patterns of the melt-spun Zr-based alloys using circumferential rotation speed 18 m/s: (a) with 65 at. % of Zr, and (b) with 67-70 at. % of Zr (the Zr₇₀Ni₁₀Cr_7.5Ag_12.5 alloy obtained also at a rotation speed of 25 m/s).

The observed Zr₂Ni phase is metastable and corresponds to the so-called “big-cube” fcc Ti₂Ni-type structure reported in the literature [27]. This phase has been previously identified as a crystallization product in the binary Zr–Ni system [27] and has also been observed in multicomponent (Co, Ni, Cu, Al)–(Zr, Ti) alloys, where it forms within an amorphous matrix, with its formation promoted by oxygen contamination [28]. Furthermore, a curious cyclic transformation of the Zr₂Ni phase was observed during high-energy mechanical grinding. Initially, the alloy contained tetragonal Zr₂Ni, which transformed as follows: tetragonal Zr₂Ni → fcc Zr₂Ni → “big-cube” Zr₂Ni → amorphous → “big-cube” Zr₂Ni → fcc Zr₂Ni with increasing grinding duration [29].

In alloys with a lower Al content or in Al-free compositions, the big-cube phase in the amorphous matrix is usually found as the main one. Only for the Zr₆₇Al₃Ni₁₀Cr_12.5Ag_7.5 alloy does the β-Zr phase in the amorphous matrix predominate. Another feature of these alloys is the presence of the Zr₂Ni (fcc) phase in the Zr₆₈Al₂Ni₁₀Cr_12.5Ag_7.5 and Zr₇₀Ni₁₀Cr_12.5Ag_7.5 alloys (Figure 1b). Increasing the circumferential wheel speed to 25 m/s results in the formation of a fully amorphous structure in the Zr₇₀Ni₁₀Cr_7.5Ag_12.5 alloy, while rapid quenching at 18 m/s results in a nanocrystalline structure. This observation indicates that increased compositional complexity and Al addition enhance the glass-forming ability even at relatively low spinning rates compared to those typically used for similar systems (35–50 m/s) [16,18,19]. A noticeable broadening of the amorphous halo with increasing wheel speed was observed even within this range [30].

It should be notedthat a slight decrease in the Al content (in Zr₆₇Al₃Ni₁₀Cr_12.5Ag_7.5 and Zr₆₈Al₂Ni₁₀Cr_12.5Ag_7.5 alloys) leads to the β-Zr content decreasing while the “big-cube” phase content increases.

Analysis of XRD reference patterns for Ti₂Ni-type structures shows that the (333) reflection (often indexed as (511)) exhibits significantly higher intensity than other diffraction peaks. Therefore, the unusually high intensity of the (422) reflection (at ~35.5° 2Θ) observed in the Zr₆₈Al₂Ni₁₀Cr_12.5Ag_7.5 and Zr₇₀Ni₁₀Cr_12.5Ag_7.5 alloys can be attributed to the superposition of reflections from the Zr₂Ni (“big-cube”) and β-Zr (bcc) phases.

The obtained results evidence that not only a reduction in the Al content in the alloys, but also the replacement of chromium with silver, promotes the formation of the Zr₂Ni (“big-cube”) phase. To understand why this occurs, the system of known binary phases of the A₂B type and ternary phases of the A₃CB₂ type with the Ti₂Ni structural type was analyzed. They are collected in Table 1. Since some of the determining factors in the formation of a particular structure are the ratios of atomic sizes, the structure of the outer electron shells, and electronegativity, these parameters were compared for different phases.

Table 1. Characteristics of binary (A₂B) and ternary (A₃CB₂) phases with a Ti₂Ni-type cubic lattice.

Phase	Cell Parameters, nm	Atomic Radii, pm and Their Ratio					Electronegativity of Elements, A; B; C	Electron Configuration
		rA	rB	rC	rA/rB	rA/rC
Zr2Ni	1.227	160	124		1.290		1.33; 1.91	[Kr] 4d2 5s2 [Ar] 3d8 4s2
Ti2Ni	1.128	147	124		1.185		1.54; 1.91	[Ar] 3d2 4s2 [Ar] 3d8 4s2
Sc2Pd	1.242	162	137		1.182		1.36; 2.20	[Ar] 3d1 4s2 [Kr] 4d10
Mg2Pd	1.207	160	137		1.168		1.31; 2.20	[Ne] 3s2 [Kr] 4d10
Sc2Ni	1.212	162	124		1.306		1.36; 1.91	[Ar] 3d1 4s2 [Ar] 3d8 4s2
Hf2Fe	1.206	167	126		1.325		1.30; 1.83	[Xe] 4f14 5d2 6s2 [Ar] 3d6 4s2
Hf2Ir	1.232	167	136		1.228		1.30; 2.20	[Xe] 4f14 5d2 6s2 [Xe] 4f14 5d7 6s2
Hf2Pt	1.244	167	139		1.201		1.30; 2.28	[Xe] 4f14 5d2 6s2 [Xe] 4f14 5d9 6s1
Zr2Rh	1.254	160	134		1.194		1.33; 2.28	[Kr] 4d2 5s2 [Kr] 4d85s1
Ti2Fe	1.128	147	126		1.167		1.54; 1.83	[Ar] 3d2 4s2 [Ar] 3d6 4s2
Zr2Fe	1.215	160	126		1.270		1.33; 1.83	[Kr] 4d2 5s2 [Ar] 3d6 4s2
Nb3SiNi2	1.119	146	124	132	1.177	1.106	1.60; 1.91; 1.90	[Kr] 4d45s1 [Ne] 3s23p2 [Ar] 3d8 4s2
Mg3AlPt2	1.189	160	139	143	1.151	1.119	1.31; 2.28; 1.61	[Ne] 3s2 [Ne] 3s23p1 [Xe] 4f14 5d9 6s1
Ta3SiNi2	1.116	149	124	132	1.202	1.129	1.50; 1.91; 1.90	[Xe] 4f145d36s2 [Ne] 3s23p2 [Ar] 3d8 4s2
Zn3SiNi2	1.071	138	124	132	1.113	1.045	1.65; 1.91; 1.90	[Ar] 3d104s2 [Ne] 3s23p2 [Ar] 3d8 4s2
Mn3SiNi2	1.076	135	124	132	1.089	1.022	1.55; 1.91; 1.90	[Ar] 3d54s2 [Ne] 3s23p2 [Ar] 3d8 4s2
V3SiNi2	1.078	134	124	132	1.081	1.015	1.63; 1.91; 1.90	[Ar] 3d34s2 [Ne] 3s23p2 [Ar] 3d8 4s2

The atomic radius ratio r_A/r_B for all binary phases ranges from 1.16 to 1.33. Smaller atoms of the same group generally have higher electronegativity and, in most cases presented here, possess two electrons in their outer shells. In the Ti₂Ni lattice, Ni atoms occupy equivalent positions, while Ti atoms occupy two inequivalent positions, with a ratio of 3:1 between the two types [31]. This explains the stoichiometry of ternary A₃CB₂ Ti₂Ni-type phases, where the third element occupies positions of the less numerous type. One can see (Table 1) that elements substituting Ti are also smaller and more electronegative. In ternary phases, atomic size differences are less pronounced than in binary phases, as smaller atoms occupying Ti sites allow larger atoms to occupy Ni sites.

Based on these considerations, the possible substitution of Cr and Ag atoms in the Zr₂Ni “big-cube” lattice was analyzed. Cr atoms are similar in size to Ni (130 pm vs. 124 pm) but have lower electronegativity, making substitution for Ni unlikely.

Substitution of Zr by Cr is also improbable due to the significant size mismatch (Cr 130 pm vs. Zr 160 pm). Consequently, Cr presence favors the formation of only an additional β-Zr (bcc) phase, as Cr is a stabilizer for β-Zr.

Ag atoms are larger than Ni (144 pm vs. 124 pm) but have similar electronegativity. Moreover, substituting Zr atoms with Ag, similar to ternary phases, can compensate for lattice distortion caused by Ni substitution. The sum of atomic radii Zr + Ni (284 pm) is close to 2×Ag (288 pm), suggesting that Ag can occupy both Zr and Ni sites, forming a solid solution of the type (Zr,Ag)₂(Ni,Ag). This specific Ag addition effectively increases the “Ni content” in the lattice, reducing the Zr/Ni ratio and favoring the formation of the (Zr,Ag)₂(Ni,Ag) (“big-cube”) phase during crystallization.

Detailed structural analysis reveals a hierarchical arrangement of atomic clusters within the Zr₂Ni (“big-cube”) lattice. Three distinct types of clusters can be identified (32e Ni, 16c Zr, and 48f Zr), differing in both the central atom and coordination geometry (Figure 2).

Figure 2. The structure of atomic clusters in the Zr₂Ni (“big-cube”) phase: (a) Ni centered distorted icosahedron, (b) Zr centered distorted icodahedron, (c) Zr centered fourteen-vertex polyhedron.

The first type of cluster is centered by Ni atoms and forms a distorted icosahedron (Figure 2a). The icosahedral coordination, characterized by twelve nearest neighbors, is an energetically favorable configuration for dense packing of atoms with varying atomic radii [32,33]. The other two types of clusters are centered by Zr atoms. One of them also has the geometry of a distorted icosahedron (Figure 2b), while the second forms a fourteen-vertex polyhedron with a more complex coordination environment topology (Figure 2c).

The substitution of Ni atoms with Ag is expected to induce strong local lattice distortions, resulting in compressive stresses. Conversely, replacing the Zr atoms with Ag ones at the centers of both clusters leads to tensile stresses. The results presented in Table 1 suggest that Ag atoms can probably substitute for Zr atoms at the 16c sites (cluster shown in Figure 2b). This conclusion is supported by the existence of the Mg₃AlPt₂ phase, where atomic radii closely match those of Zr and Ag. Thus, it can be inferred that Ag atoms can occupy both Ni (32e) and Zr sites (16c). In this process, Ag-Ag atomic pairs must form to minimize the lattice distortion energy. Based on this, one can estimate the limiting Ag content in the “big-cube” phase by assuming that Ag atoms fully occupy all 16c Zr positions. In this case, half of the 32e Ni positions would be occupied by Ag, resulting in a phase stoichiometry of Zr₃Ag₂Ni.

The metastable Zr₂Ni (“big-cube”) phase exhibits structural features reminiscent of icosahedral quasicrystals. Its diffraction pattern shows characteristic peak arrangements similar to quasicrystalline structures. In particular, the interplanar spacing ratio for the most intense reflections (d₄₂₂/d₅₁₁ ≈ 1.06) closely matches the analogous ratio for icosahedral quasicrystals (d_(18,29)/d_(20,32) ≈ 1.05) [34]. This correspondence indicates a deep relationship between the local atomic ordering in Zr₂Ni (“big-cube”) and the principles of quasicrystal organization, despite the fundamental differences in long-range periodicity.

The presence of icosahedral structural units in the Zr₂Ni (“big-cube”) phase is of particular interest in the context of amorphous state theory. It is known that the formation of atomic clusters with icosahedral symmetry is a characteristic feature of amorphous metallic alloys [32,33,35]. Icosahedral local ordering provides high packing density and energy stabilization of the disordered structure, thus preventing crystallization. Therefore, the presence of icosahedral clusters in the metastable Zr₂Ni (“big-cube”) crystal phase can be seen as a structural “bridge” between the amorphous, quasicrystalline, and crystalline states.

3.2. Mechanical Properties from Nanoindentation Measurement

Amorphous alloys exhibit high bending plasticity: the ribbons can be bent up to 180° without fracture and return to their original shape. Alloys containing additionally crystallized phases show reduced plasticity. Young’s modulus and hardness values were extracted from nanoindentation load–depth curves following Oliver and Pharr [36], assuming a Poisson’s ratio of 0.37. Single-phase amorphous alloys exhibit the lowest hardness values (Table 2). Alloys containing a higher fraction of nanocrystalline phases, as identified by XRD analysis, demonstrate the highest hardness (up to 10.2 GPa for the Zr₇₀Ni₁₀Cr_12.5Ag_7.5 alloy, which contains both Zr₂Ni “big-cube” and fcc phases). This trend is consistent with previous literature data [37], which reported an increase in the mechanical properties, particularly hardness and Young’s modulus, after partial crystallization of the alloys.

Table 2. Mechanical properties and phase content of the rapidly solidified ribbons (H—hardness, Y—Young’s modulus, A—amorphous phase).

No *	Alloy Composition	Phase Content	H, GPa	Y, GPa	H/Y
1	Zr70Ni10Cr12.5Ag7.5	(Zr,Ag)2(Ni,Ag) cc Zr2Ni β-Zr A	10.20 (0.47)	123.13 (8.90)	0.0828
2	Zr70Ni10Cr7.5Ag12.5	(Zr,Ag)2(Ni,Ag) A	8.12 (0.51)	102.44 (4.58)	0.0793
		A **	6.2 (0.35)
3	Zr67Al3Ni10Cr12.5Ag7.5	A β-Zr (Zr,Ag)2(Ni,Ag)	7.28 (0.31)	93.91 (2.01)	0.0775
4	Zr65Al7.5Ni10Cr17.5	β-Zr A	9.20 (0.46)	125.8 (3.68)	0.0731
5	Zr65Al7.5Ni10Cr12.5Ag5	A	6.51 (0.23)	87.74 (2.40)	0.0742
6	Zr65Al8.5Ni10Cr10Ag6.5	A	7.31 (0.48)	97.66 (3.25)	0.0749
7	Zr65Al7.5Ni10Cr10Ag7.5	A	7.00 (0.37)	82.38 (3.02)	0.0850
8	Zr65Al7.5Ni10Cr7.5Ag10	A (Zr,Ag)2(Ni,Ag)	6.48 (0.33)	87.04 (3.34)	0.0744

* The alloys numbers correspond to those in Figure 3. Data for the Zr₆₈Al₂Ni₁₀Cr_12.5Ag_7.5 and Zr₆₅Al_7.5Ni₁₀Cr₁₅Ag_2.5 alloys are not present because their hardness showed a strong load dependence and could not be measured precisely. ** A–Zr₇₀Ni₁₀Cr_7.5Ag_12.5 alloy obtained in amorphous state after quenching at 25 m/s wheel rotation speed.

The obtained Young’s modulus values are close to those reported for bulk Zr-based alloys (103–117 GPa) [37]. The experimental data points (Figure 3) follow the characteristic H/E ≈ 0.08 trend, indicating a high elastic strain limit. The H/E ratio can be related to the type of atomic bonding. The values were close to 1:10, indicating predominantly covalent bonding. For comparison, metallic alloys with an fcc lattice typically show an H/E ratio of ~1:500 [38]. The values are in good agreement with the results of structural studies. The Zr₂Ni “big-cube” and amorphous phases, built from similar clusters in which atoms are bonded by covalent bonds, are the main components in the alloy composition. The lowest ratio value (0.0731) is observed in the alloy with the composition Zr₆₅Al_7.5Ni₁₀Cr_17.5, where the contribution of metallic-type bonding is the most pronounced (due to the high β-Zr content) compared to the others.

Figure 3. Correlation between nanoindentation hardness (H) and Young’s modulus (E) for Zr-based melt-spun alloys. Experimental data points are color- and shape-coded by structural state: crystalline alloys—blue squares, fully amorphous—red circles, partially crystalline—cherry hexagons.

To estimate the fracture strength σ_f, the empirical equation H ≈ 3σ_f [39] was applied. The evaluated σ_f for amorphous alloys was approximately 2 GPa, which is markedly higher than previously reported values for amorphous and partially crystallized alloys of other Zr-based multicomponent systems. For example, the fracture strength of the Zr–Al–Ni–Ag [15] and Zr–Al–Ni–Cu–Ag [16] alloys doesnot exceed 1.5 GPa.

This improvement in the mechanical properties may be attributed to the Cr presence instead of Cu, which is usually used in Zr-based amorphous alloys. On the other side, a further increase in hardness was attributed to the Zr₂Ni (“big-cube”) phase. Being nanocrystalline and having a complex lattice, this phase can effectively hinder dislocation motion during plastic deformation, thereby enhancing the overall mechanical performance of the alloys.

3.3. Low-Temperature Electrical Resistivity Investigation

The study of the electrical resistivity temperature dependence in the melt-spun alloys provides valuable insights into structural changes that are often difficult to study by other methods. Low-temperature electrical resistivity measurements provide specific information on the structure of the rapidly quenched ribbons, while higher-temperature measurements reflect the occurrence of relaxation processes. Therefore, the electrical resistivity of the Zr–Al–Ni–Cr–Ag and Zr–Ni–Cr–Ag alloy systems was investigated in the temperature range 4–298 K (Figure 4). It was observed that increasing the temperature leads to a slight decrease in the electrical resistivity for most of the alloys. Furthermore, all alloys except Zr₆₇Al₃Ni₁₀Cr_12.5Ag_7.5 do not follow Matthiessen’s rule:

ρ(T) = ρ₀ + ρ^h(T),

(2)

where ρ^h(T) is the phonon contribution.

Figure 4. Temperature dependences of the electrical resistivity of the melt-spun Zr-based Zr-(Al)-Ni-Cr-Ag alloys with 65 at. % Zr (a) and 67-70 at. % of Zr (b).

The negative TCR observed in amorphous alloys results from the complex interplay between structural disorder, the electronic structure, and the electron scattering mechanisms, which differ significantly from those in crystalline metals [40,41].

It is worth noting that the obtained resistivity valuesare close to the values for Zr-based alloys. For example, the resistivity of binary amorphous Zr₇₀Ni₃₀ alloy is 180 μΩ·cm at room temperature [42]. The residual resistivity values, obtained from linear approximation, range from 92.80 μΩ·cm for Zr₆₅Al_7.5Ni₁₀Cr₁₅Ag_2.5 to 220.80 μΩ·cm for the Zr₇₀Ni₁₀Cr_7.5Ag_12.5 alloy, with a maximum change of 20 μΩ·cm as the temperature increases to room temperature. The highest TCR is observed for the Zr₇₀Ni₁₀Cr_7.5Ag_12.5 alloy, which has a value of −3.699(2) × 10⁻⁴ 1/K. In contrast, Zr₇₀Ni₁₀Cr_12.5Ag_7.5 shows a slight positive TCR of 0.7632(7) × 10⁻⁴ 1/K, in contrast to the negative values for the other alloys.

Analysis of the curves shown in Figure 4 reveals that, in some cases, the electrical resistivity of ribbons containing the Zr₂Ni “big-cube” phase exceeded the resistivity of fully amorphous ribbons. This phenomenon can be attributed to the atomic clusters present in the Zr₂Ni “big-cube” phase, which is known to resemble the structures found in icosahedral quasicrystals. It is well-established that the resistivity of metallic alloys with identical chemical compositions in a quasicrystalline state is much higher than that in an amorphous state [43]. However, since the “big-cube” phase has a periodic crystal structure, rather than a quasicrystalline one—yet shares a similar local atomic arrangement with the amorphous matrix—the temperature-dependent behavior of electrical resistivity shows negligible differences between the fully amorphous alloys and amorphous-crystalline composites.

Notably, a correlation between the absolute resistivity values and the TCR can be observed: as the resistivity increases, the slope of the resistivity vs. temperature curve decreases. In the limiting case, for the alloy with the lowest resistivity value (Zr₆₇Al₃Ni₁₀Cr_12.5Ag_7.5), the TCR becomes positive, which is characteristic of crystalline metallic alloys. The structural analysis reveals a clear size gradation: crystallite sizes in the range of 115–130 nm (alloys No.1–2) retain an amorphous-like structural contribution, whereas the coarse grains of the Zr₆₇Al₃Ni₁₀Cr_12.5Ag_7.5 (No.3) alloy (around 200 nm) drive the distinct metallic behavior, directly affecting the anomalous trend of the temperature coefficient of electrical resistivity. These experimental results align well with the Mooij correlation [43], which predicts the temperature dependence of resistivity on the absolute resistivity basis.

4. Conclusions

1. Based on X-ray diffraction analysis, a dependence of the formation of different structural states (amorphous; nanocrystalline with the Zr₂Ni “big-cube” phase; or with β -Zr) in the melt-spun Zr–Al–Ni–Cr–Ag and Zr–Ni–Cr–Ag alloys on the elemental composition ratio was established. Cr-rich alloys (≥15 at. %) contain two phases: β-Zr and an amorphous matrix. A decrease in Cr content accompanied by an increase in Ag content leads first to the formation of a fully amorphous structure and subsequently to the precipitation of a nanocrystalline metastable Zr₂Ni “big-cube” phase within the amorphous matrix. A reduction in Al content or its absence promotes the formation of the “big-cube” phase in the amorphous matrix. In alloys with a low Al content, the coexistence of “big-cube” Zr₂Ni, fcc Zr₂Ni, and β-Zr phases within an amorphous matrix was observed.

2. The specific role of Ag in the formation of the “big-cube” phase of Zr₂Ni is that Ag atoms can probably replace Zr and Ni atoms, leading to the formation of a solid solution of (Zr,Ag)₂(Ni,Ag). Phenomenologically, this can be explained by the fact that the sum of the atomic radii of Zr and Ni (284 pm) is close to the sum of the radii of two Ag atoms (288 pm), which minimizes the distortion of the crystal lattice and effectively increases the “effective” nickel content in the alloy, thereby promoting the formation of the (Zr,Ag)₂(Ni,Ag) phase.

3. The presence of icosahedral structural units in the crystalline Zr₂Ni “big-cube” phase is of fundamental importance for understanding its metastability and formation mechanisms. Since icosahedral local ordering is a characteristic feature of amorphous metallic alloys and provides high packing density and energetic stabilization of a disordered structure, the existence of such clusters in the metastable crystalline Zr₂Ni “big-cube” phase serves as a structural “bridge” between amorphous, quasicrystalline, and crystalline states, thereby explaining the facilitation of transitions between these states at different processing conditions.

4. It was established that the mechanical properties of the alloys are determined by their structural state: amorphous alloys are characterized by the lowest hardness (6.5–7.0 GPa) and high plasticity, while the presence of the nanocrystalline Zr₂Ni “big-cube” with fcc Zr₂Ni phases increases the hardness up to 10.2 GPa. The ratio H/E ≈ 0.08 (about 1:10) indicates a predominantly covalent nature of interatomic bonds in the alloys, in contrast to metallic fcc alloys (~1:500). The fracture strength (2.0 GPa) exceeds the known literature values for other Zr-containing amorphous systems.

5. Investigation of the electrical resistivity temperature dependence of the Zr–Al–Ni–Cr–Ag and Zr–Ni–Cr–Ag Zr-based alloys in the range of 4–298 K allowed us to establish that most alloys (except Zr₆₇Al₃Ni₁₀Cr_12.5Ag_7.5) do not follow Matthiessen’s rule, demonstrating a negative temperature coefficient of resistivity (TCR). A clear Mooij correlation was established: as the absolute value of electrical resistivity increases, the TCR systematically decreases, even undergoing a sign change. The presence of the nanocrystalline Zr₂Ni “big-cube” phase, containing icosahedral atomic clusters, increases the electrical resistivity of the alloys compared to their fully amorphous counterparts, despite its structural affinity with icosahedral quasicrystals.