Longitudinal zero thermal expansion in Re-Fe (R = Tb, Er) eutectic alloys with high fracture resistance

INTRODUCTION

Zero thermal expansion (ZTE) alloys are vital for high-precision fabrications due to their unique size-invariance property under temperature fluctuations^[1-7]. Critical applications exist that call for ZTE in one direction but normal positive thermal expansion (PTE) in other directions, i.e., longitudinal ZTE (LZTE). For example, optic support systems of a space telescope should have an extremely small CTE (coefficient of thermal expansion, α_l < 1 × 10^-6 K^-1) in the supporting direction to ensure its focus accuracy, but have positive CTEs (α_l ≈ 10 × 10^-6 K^-1) in the radial planes, allowing for compliant mounting of optical elements^[8-12]. However, most commercial ZTE alloys are based on a high-symmetric face-centered-cubic (fcc) structure (e.g., the Fe-Ni Invar) with isotropic performances^[13-20]. In recent years, several LZTE systems with hexagonal or tetragonal symmetries have been developed, such as Ho₂Fe₁₇, Er-Fe-V-Mo, ZrFe₂, etc.^[20-28]. However, these alloys are generally ordered intermetallic phases that are highly brittle due to their insufficient deformation mechanism and exhibit catastrophic failure under stress. New alloy systems with superior mechanical properties are desirable for developing LZTE devices.

On the R-Fe (R = rare earth) diphasic diagram, R₂Fe₁₇ can form a eutectic system with Fe^[29] (see Figure 1). Hence, the α-Fe phase and the R₂Fe₁₇ phase will coexist to form the natural dual-phase alloy by hypo-eutectic or hyper-eutectic reactions. Interestingly, Fe is a common and low-cost element and among its phases, α-Fe, which has both features of plasticity and isotropic PTE. Meanwhile, R₂Fe₁₇ is a representative anisotropic negative thermal expansion (NTE) intermetallic compound with high strength and low plasticity. This provides a possibility to obtain a toughened LZTE alloy if the phase fractions and crystallographic orientation of R₂Fe₁₇ and α-Fe phases could be controlled suitably in the dual-phase alloy. As shown in Figure 1, the former property can be reached by adjusting the composition of R_xFe_1-x samples through hypo-eutectic or hyper-eutectic reactions, while the latter one can be realized by controlled axial cooling and crystallizing using the electric arc furnace^[22].

Figure 1. (A) The Tb-Fe phase diagram and design thinking of LZTE alloys with comprehensive properties. (B) Schematic of controlled axial cooling and crystallizing for a dual-phase alloy using the electric arc furnace.

In this work, the thermal expansion performance was successfully tailored from moderate PTE to desired ZTE and then to NTE in the Tb-Fe and Er-Fe systems. Encouragingly, the LZTE dual-phase alloys with nominal compositions of Tb_0.05Fe_0.95 and Er_0.04Fe_0.96 were designed and synthesized. The alloys have high thermal circulation stability over a wide temperature range covering room temperature, a moderate combination of strength and plasticity, and machinability. The hard R₂Fe₁₇ phases are the matrix of the dual-phase alloy, preserving their high strength within it. The plastic α-Fe phase impedes the propagation of microcracks in the R₂Fe₁₇ matrix under compression, enhancing the plasticity of the dual-phase alloy. These alloys hold application prospects as LZTE materials in high-precision technology.

MATERIALS AND METHODS

RESULTS AND DISCUSSION

XRD analysis revealed the crystal structure of targeted samples. It is found that all 2.5Tb, 5Tb and 7.5Tb alloys are dual-phase, composed of α-Fe (labeled as α) and Tb₂Fe₁₇ phases (expressed as H) without other detective impurities, while for 2Er, 4Er, 7Er and 9Er alloys, all the peaks belong to the α-Fe or Er₂Fe₁₇ phase, agreeing well with the R-Fe phase diagram (see Figure 2A and B). With rising rare earth content, the intensity of peaks corresponding to crystal plane 302(H) gradually increases, while that corresponding to crystal plane 110(α) gradually decreases. It means that the content of the H phase augments, and that of the α phase declines (see Figure 2C). In addition, the Rietveld refinement of XRD results for samples verifies an approximately linear evolution with Tb/Er mole fractions in these dual-phase alloys (see Figure 2D, the full-profile fitting patterns for 2.5Tb, 5Tb and 7.5Tb alloys, see Supplementary Figure 1 and 2Er, 4Er, 7Er and 9Er alloys, see Supplementary Figure 2. The crystal structures of the H and α phases refined by XRD data are shown in Figure 2E. In the structure of the hexagonal phase, the Tb/Er atom and the Fe atom occupy sites 2b (0,0,1/4), 2d (1/3,2/3,3/4), 2c (1/3,2/3,1/4) and sites 4f (1/3,2/3,z), 6g (1/2,0,0), 12j (x,y,1/4), 12k (x,2x,z), respectively. The H phase adopts a Th₂Ni₁₇-type structure (space group: P6₃/mmc) with cell parameters of a = 8.4583 ± 0.01 Å,c = 8.3005 ± 0.01 Å, V = 514.28 ± 0.03 ų while the α phase adopts a body-centered-cubic phase (space group: Im-3m) with cell parameters a = 2.8387 ± 0.01 Å, V = 22.87 ± 0.02 ų and the Fe atom occupy site 2a (0,0,0). The XRD results indicate that the design idea of regulating the two-phase ratio of the alloys by controlling the chemical ratio of the samples was successfully realized.

Figure 2. Phase and crystal structure. (A-C) X-ray diffraction for 2.5Tb, 5Tb, 7.5Tb and 2Er, 4Er, 7Er, 9Er alloys, respectively. (D) The ratio of H and α phases in samples obtained by Rietveld refinement. (E) Crystal structures of H and α phases.

To explore the morphology and phase distribution of the dual-phase alloys, SEM and EBSD measurements were carried out. Due to the similarity of these alloys, we systematically studied only the microstructure of the 5Tb alloy, as shown in Figure 3A-F. As to the microstructure of the 4Er alloy, refer to Supplementary Figure 3. The SEM images and element mapping inside the TD (transverse direction)-ND (normal direction) planes show that the dendritic lamellar α phase (in dark, 10-100 μm) is homogeneously dispersed in the continuous H phase matrix (in gray, 50-100 μm, see Figure 3A-D), which is mutually confirmed with the XRD results. Above all, the EBSD inverse pole figure (IPF) of 5Tb indicates that the crystal orientations of H and α phases are highly consistent along the longitudinal direction (LD) (the EBSD pole figures of 5Tb alloy, see Supplementary Figure 4). It suggests the existence of crystallographic texture along the LD for both the H and α phases ([001]H//[111]α//LD), as seen in Figure 3E and F. This phenomenon results from the huge temperature gradient from the melt to the copper cooling wall during the crystallization of bulk materials^[20]. (The Pictures in Supplementary Figure 5 show a huge temperature gradient). It provides a basis for manipulating the uniaxial ZTE due to the anisotropic nature of the H phase.

Figure 3. Microstructure of the 5Tb alloy. (A) The morphology of the 5Tb alloy was measured by scanning electron microscope (SEM) in the TD (transverse direction) - ND (normal direction) plane. (B) The enlarged region in (A) is marked by a dotted rectangle. (C and D) Element mappings of Fe (C) and Tb (D) corresponding to the region shown in (B). (E) Electron backscattered diffraction (EBSD) inverse pole figures of crystal orientation for the 5Tb alloy in the TD-ND plane. (F) EBSD phase figure for the 5Tb alloy. (G and H) Temperature-dependent synchrotron X-ray diffraction for 5Tb. (I) Lattice thermal expansions of H in the a and c axes, α in the a axis. L(a) and L(c) represent the average “lattice length” of the two phases in the LD and TD-ND plane, respectively.

The existence of crystallographic texture of the H phase manifests that the uniaxial ZTE could be reached if the NTE of H along the c axis compensates for the PTE of α along the a axis. Thus, temperature-dependent SXRD for 5Tb was performed to reveal the lattice thermal expansion behaviors (see Figure 3G-I). Obviously, the 110(α) peak gradually shifts to lower angles as the temperature increases. This shows a broadening in the spacing of the 110(α) crystal planes and an expansion in the lattice constant for the α phase. Likewise, the 302(H) and 220(H) peaks gradually move to lower angles with the temperature elevation, which corresponds to the expansion of interplanar spacing inside the basal a-b plane for the H phase. More importantly, the 004(H) peak obviously shifts to higher angles with temperatures over 105-430 K, suggesting the contraction of the c axis. This peak moves back to lower angles when the temperature is further increased above 430 K (the magnetic Curie temperature, see Supplementary Figure 6A). As shown in Figure 3I, the lattice thermal expansions are α_a = 3.3 × 10^-6 K^-1 and α_c= -10.5 × 10^-6 K^-1 for the H phase and α_a = 11.1 × 10^-6 K^-1 for the α phase (110-430 K) (The lattice constants are refined from the full-profile fitting patterns for 5Tb at different temperatures using SXRD data, see Supplementary Table 1 and Supplementary Figure 7).

The hexagonal H phase shows NTE in the LD and the body cubic center α phase shows PTE, so tuning the phase contents in the samples could control the CTEs of dual-phase alloys. Therefore, the macroscopic thermal expansion curves (ΔL/L0) of these dual-phase alloys were measured using a dilatometer, as shown in Figure 4. The CTE along the LD can be tuned from positive (α₁ = 6.0 × 10^-6 K^-1 for 2.5Tb alloy and α₁ = 4.0 × 10^-6 K^-1 for 2Er alloy) to negative (α₁ = -4.9 × 10^-6 K^-1 for 7.5Tb alloy and α₁ = -15.7 × 10^-6 K^-1 for 9Er alloy) with gradually increasing Tb/Er content in dual-phase alloys (see Figure 4A and B). Among these alloys, both 5Tb and 4Er alloys exhibit axial ZTE along LD over a temperature range involving room temperature (α₁ = 0.029 × 10^-6 K^-1, 110 to 425 K for 5Tb alloy, α₁ = -0.33 × 10^-6 K^-1, 110 to 330 K for 4Er alloy). The temperature ranges of ZTE for 5Tb and 4Er alloys are consistent with the changes of their macroscopic magnetic properties (see Supplementary Figure 6). Meanwhile, the linear thermal expansion curves of 5Tb and 4Er along the TD-ND plane confirmed normal PTE in other directions (see Figure 4C). Both 5Tb and 4Er alloys show normal PTE in the TD-ND plane (α₁ = 6.72 × 10^-6 K^-1, 110 to 425 K for 5Tb alloy, α₁ = 6.56 × 10^-6 K^-1, 110 to 330 K for 4Er alloy), i.e., exhibiting the LZTE behavior. This finding is consistent with the result of variable temperature SXRD shown in Figure 3I: α_c = -1.7 × 10^-6 K^-1, and α_a = 6.4 × 10^-6 K^-1, 110-430 K. (Because the EBSD IPF verifies the existence of crystallographic texture along the LD for both the H and α phases ([001]_H//[111]_α//LD), the average “lattice” thermal expansion of 5Tb in the LD and TD-ND plane can be calculated by L(a) = a(α) × mol. α % + a(H) × mol. H % and L(c) = c(α) × mol. α %+c(H) × mol. H %).

Figure 4. Dilatometric thermal expansion behaviors and TEM images of the 5Tb alloy. (A) The thermal expansion curves of 2.5Tb, 5Tb, and 7.5Tb alloys and pure iron along the LD. (B) The thermal expansion curves of 2Er, 4Er, 7Er, and 9Er alloys and pure iron along the LD. (C) The thermal expansion curves along LD, TD- ND plane for 5Tb alloy and 4Er alloy. (D) The thermal expansion curves of 5Tb alloy and 4Er alloy along the LD under the thermal cycling between 77 and 373 K. (E and F) The transmission electron microscope (TEM) (E) and high-resolution transmission electron microscope (HRTEM). (F) of the interface structure between the H and α phases.

In order to verify the thermal circulation stability of 5Tb and 4Er alloys with LZTE performance, a thermal cycling test was carried out by switching between 77 and 373 K (see Figure 4D). The CTE variations of both alloys are negligible after hundreds of thermal cycling (Δα₁ = -0.16 × 10^-6 K^-1 for 5Tb alloy and Δα₁ = -0.69 × 10^-6 K^-1 for 4Er alloy after 100 times of thermal cycling, Δα₁ = -0.31 × 10^-6 K^-1 for 5Tb alloy and Δα₁ = -0.81 × 10^-6 K^-1 for 4Er alloy after 200 times of thermal cycling). As shown in the TEM and HRTEM images (see Figure 4E and F), such excellent thermal circulation stability of 5Tb and 4Er alloys is a benefit from the formation of a firm and natural phase boundary between the αand H phases due to the hypo-eutectic reaction process. It gives rise to a natural dual-phase structure that maintains perfect integrity under thermal cycling that greatly elevates the application potential under intense temperature changes^[20].

The mechanical property is critical for LZTE alloys because most LZTE alloys suffer from severe brightness. Figure 5 demonstrates the engineering stress-strain curves along the LD of the 5Tb and 4Er alloys under compressive conditions. They manifest that the ultimate compressive stress (δ_US) reaches 0.80 GPa with a strain of 3.9% for the 5Tb alloy and 0.73 GPa with a strain of 13.8% for the 4Er alloy. Figure 5C proves that the mechanical and thermal expansion properties of the two alloys exceed most known LZTE alloys^{[20,28,30-36]} and that moderate plasticity and strength make the LZTE alloys easily machined. The SEM images of the fractured surface of the 5Tb alloy are shown in Figure 5D and E. It is seen that the fractured α phase is dispersed in the cracked matrix of the H phase, suggesting that the plastic α phase hinders the enlargement of cracks in the H phase during compressing test^[20,37,38]. On the other hand, because the H phase is the matrix of a dual-phase alloy, the high strength of this phase is retained in the LZTE alloy (see Figure 3A). Hence, 5Tb and 4Er alloys - two novel LZTE dual-phase alloys with a desired combination of plasticity and strength were obtained, which satisfied the design principle shown in Figure 1. Moreover, moderate plasticity and strength make the LZTE alloys easily machined (see Figure 5E), and the high Fe contents of LZTE alloys make them low-cost.

Figure 5. Mechanical properties. (A and B) Engineer compressive stress-strain curves of 5Tb alloy (A) and 4Er alloy (B) with the inset ingots, respectively, along the LD during loading. (C) The Ashby-type plot for the typical LZTE alloys: ultimate strain, strength, and temperature window, and the mechanically machined components of 5Tb and 4Er alloys are on the right side. (D) SEM image of the fractured 5Tb ingot surface. (E) The enlarged region in (D) is signed with a red rectangle.

CONCLUSION

In summary, it was shown that a phase fraction tuning design of optimizing the compositions of alloys and hypo-eutectic reactions yields two types of novel LZTE dual-phase alloys, Tb_0.05Fe_0.95 and Er_0.04Fe_0.96. Both alloys are characterized by high mechanical properties, thermal circulation stability, machinability, and LZTE effect over a wide temperature range including room temperature. The crystallographic texture of H and α phases in the LD and the appropriate phase ratios result in the LZTE of the Tb_0.05Fe_0.95 and Er_0.04Fe_0.96 alloys. The plastic α phase dispersed in the H phase improves the plasticity of the dual-phase alloy by hindering the crack propagation inside the H phase under compression. Besides, the dual-phase alloys retain high strength because the H phase is the matrix of the dual-phase alloys. Such comprehensive properties of Tb_0.05Fe_0.95 and Er_0.04Fe_0.96 alloys are scarce in LZTE alloys, which could have a broad application foreground.