Research Progress on Zero Thermal Expansion Metallic Materials

doi:10.11900/0412.1961.2024.00264

Acta Metall Sin

2025, Vol. 61

Issue (6): 809-825 DOI: 10.11900/0412.1961.2024.00264

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Research Progress on Zero Thermal Expansion Metallic Materials

SONG Yuzhu¹(

), ZHANG Jimin¹, ZHOU Chang², SHI Naike¹, CHEN Jun¹(

)

1 Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, China
2 State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China

Cite this article:

SONG Yuzhu, ZHANG Jimin, ZHOU Chang, SHI Naike, CHEN Jun. Research Progress on Zero Thermal Expansion Metallic Materials. Acta Metall Sin, 2025, 61(6): 809-825.

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Abstract

With the advancement of technology, the exploration of space, oceans, and underground resources continues to deepen. An ever-increasing demand for devices that operate under extreme conditions propels the need for the precise control of the thermal expansion properties of the materials used. Zero thermal expansion metals exhibit constant dimensions despite temperature variations, a unique feature that imparts these metals a significant application value in high-precision and high-stability devices. This article summarizes the research progress on zero thermal expansion metals since the discovery of Invar alloy over a century ago. It provides an overview of the definition, classification, and historical development of zero thermal expansion metals. Furthermore, this article introduces several main mechanisms inducing zero thermal expansion in metals and highlights several categories of metals with excellent zero thermal expansion properties and high application value. Moreover, it discusses the crystal structures, zero thermal expansion properties, and methods for controlling the thermal expansion properties of different types of metals. The coupling relationship between the magnetism, phase transitions, and thermal expansion properties is explored. Finally, the article provides a perspective on future trends in the development of zero thermal expansion metals.

Key words: zero thermal expansion low thermal expansion alloy functional metallic material thermal expansion control

Received: 31 July 2024

ZTFLH:

O482.2

Fund: National Key Research and Development Program of China(2022YFE0109100);National Natural Science Foundation of China(22275014);National Natural Science Foundation of China(12104038);Beijing Outstanding Young Scientist Program(JWZQ20240101015)

Corresponding Authors: SONG Yuzhu, associate professor, Tel: (010)62332265, E-mail: yuzhusong@ustb.edu.cn;
CHEN Jun, professor, Tel: (010)62332265, E-mail: junchen@ustb.edu.cn

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	SONG Yuzhu
	ZHANG Jimin
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https://www.ams.org.cn/EN/10.11900/0412.1961.2024.00264 OR https://www.ams.org.cn/EN/Y2025/V61/I6/809

Fig.1 Zero thermal expansion (ZTE) of metallic materials, originates from the mutual cancellation between the positive contribution to volume (ΔV₂) from lattice vibrations and the negative contributions to volume (ΔV₁) from magnetovolume efect, martensitic phase transitions, or valence state changes (T_C—Curie temperature)

Fig.2 Volume (showed by numbers) decreases of the Invar alloy as the ferromagnetic ordered magnetic structure transitions to a disordered paramagnetic structure^[9]

Table 1 Thermal expansion data of zero thermal expansion metallic materials^[14-46]

Fig.3 Comparison of zero expansion temperature zone of different materials (Dashed line represents room temperature)

Fig.4 Calculated spin configurations at Fe (orange) and Ni (blue) atoms in fully ordered ferromagnetic states (0 K), ambient states, and paramagnetic states (The size of the arrow is proportional to the calculated magnetic moment)^[48] (a), the relationship between the magnetization of Invar alloy and the pressure (P)^[48] (b), comparison of linear expansion of Invar alloy, Fe, Cu and Al (Δl / l₀—relative length variation) (c), change of phonon entropy and magnetic entropy of Invar alloy with pressure (S_ph—phonon entropy; ΔS_mag—magnetic entropy change)^[48] (d), and change of the sum of phonon entropy and magnetic entropy (ΔS_ph—phonon entropy change)^[48] (e)

Fig.5 Zero thermal expansion properties of AFe₂ (A = Zr, Nb, Hf, Ta, Sc, and Ti) systems^{[18,19,21,22,24,26]}
(a) comparison of macroscopic linear expansion of Zr_0.8Nb_0.2Fe₂, Fe_0.64Ni_0.36, and Fe^[18]
(b) temperature dependence of cell parameters for neutron diffraction and synchrotron radiation analysis of (Zr_0.65Nb_0.35)_0.95Fe_0.05Fe₂ (ZNFF)^[19] (SXRD—synchrotron X-ray diffraction, NPD—neutron powder diffraction, a—cell parameter, α_a —thermal expansion coefficient of crystal in a-axis direction)
(c) variation of cell parameters of Zr_0.7Ta_0.3Fe₂ with temperature (Δa—change of a,ZTE—zero thermal expansion, FM—ferromagnetic, AFM—antiferromagnetic)^[21]
(d) relative cell volume of (Sc, Ti)Fe₂ varies with temperature when x = 0 (PTE—positive thermal expansion), x = 0.45 (ZTE), and x = 0.6 (NTE—negative thermal expansion)^[22] (ΔV / V—relative cell volume variation; CMVE—traditional magnetic volume effect; UMVE—unconventional magnetic volume effect)
(e) temperature dependence of unit cell volumes for HfFe_{2 +}_δ (δ = 0.3, 0.5, and 0.6)^[24] (LTE—low thermal expansion)
(f) dilatometer thermal expansion of TiFe₂ and Hf_0.6Ti_0.4Fe_{2 +}_x (x = 0, 0.5, and 1.3)^[26]

Fig.6 Magnetic structure, crystal structure, and thermal expansion regulation of RCo₂ (R = Tb, Gd, and Dy) systems^[28,29]
(a) crystal and magnetic structures of Tb(Co_1.9Fe_0.1) intermetallic compound at 10 K^[28]
(b) Tb(Co_{1 -}_x Fe _x)₂ macroscopic linear expansion curves^[28]
(c) comparison of intrinsic volume expansion and macroscopic linear expansion^[28]
(d) crystal structure of Gd_0.25Dy_0.75Co_1.93Fe_0.07 (GDCF)^[29]
(e) linear thermal expansion of Gd _x Dy_{1 -}_x Co₂ and GDCF (Inset shows Δl / l₀ of GdCo₂ (x = 1) in the high temperature region)^[29]

Fig.7 Thermal expansion properties and macroscopic magnetic properties of La(Fe, M)₁₃ (M = Si, Al) type metal materials^[31,32]
(a, b) thermal expansions of LaFe_{13 -}_x Si _x (x = 1.5, 2.0, 2.4) (a) and LaFe_{13 -}_x Si _x hydrides (x = 1.5, 2.0, 2.4) (b)^[31] (Δa / a_{300 K}—rate of change of cell parameter relative to 300 K, ΔT—temperature difference)
(c, d) macroscopic magnetisms of LaFe_{13 -}_x Si _x (c) and LaFe_{13 -}_x Si _x hydrides (d)^[31] (Inset in Fig.7d shows the T_C curves for original and hydrogenated LaFe_{13 -}_x Si _x sample)
(e) thermal expansion of LaFe_{13 -}_x Al _x (x = 2.5, 2.7)^[32] (SS304—304 stainless steel, ΔL / L_{(300 K)}—linear thermal expansion reative to 300 K)
(f) macroscopic magnetism of LaFe_{13 -}_x Al _x (x = 1.8, 1.9, 2.1, 2.3, 2.5, 2.7)^[32] (PM—paramagnetic)

Fig.8 Thermal expansion properties of Ho₂(Fe, Co)₁₇ and its regulation mechanism^[34]
(a) volumetric thermal expansion of Ho₂(Fe, Co)₁₇ (ΔV—relative volume variation, SIV—super Invar)
(b) stability of zero expansion of Ho₂Fe₁₆Co (ΔT₁—100-208 K, ΔT₂—208-377 K, ΔT₃—377-416 K) (c, d) magnetic ordered densities of state (DOS) of Ho₂Fe₁₇ (c) and Ho₂Fe₁₅Co₂ (d) (E—electronic energy level, FIM—ferrimagnetic, DLM—disordered local moment) (e) changes of Fe magnetic moment and cell volume (V) of Ho₂Fe₁₆Co at 6g (M_Fe/Co—magnetic moment of Fe/Co atoms, T—temperature, μ_B—Bohr magnetron) (f) contribution of the magnetic moment (M_Fe) and magnetic order of the Fe sublattice to the cell volume (V_M) (V_M(T)—contribution of magnetic ordering to the unit cell volume, |Σ M_Fe|—magnetic moment of Fe sublattice. Inset in Fig.8f shows the |Σ M_Fe| as a function of Co content)

Fig.9 Anisotropic thermal expansion and cyclic properties of titanium-based shape memory alloys^[40-42]
(a) evolution of macroscopic strain with temperature of rolled 60% (thickness reduction rate) Ti_50.6Ni_49.4 alloy sheet along RD, 22.5°, 33.5°, 45°, 67.5°, and TD after annealing for 60 min at 523 K^[40] (RD—rolling direction, TD—transverse direction)
(b) Ni_50.8Ti_49.2 alloy through three steps rolling (CroR-15%-10%-5%: the thickness of the first rolling direction is reduced by 15%-the thickness in the vertical direction from the first rolling direction is reduced by 10%-thickness is reduced by 5% along the first rolling direction) to a thickness of 30% of the total thickness after the internal macroscopic thermal expansion change^[41] (CroR—cross rolling, TE—thermal expansion)
(c) Ti22Nb CR (cold-rolled) plate along the rolling direction in eight cycles (cycle 01 T_max (maximum temperature) = 350 ^oC, thermomechanical analyzer measurements were performed in cycle 02-08 at T_max = 300 ^oC)^[42] (Inset shows the transmission Kikuchi diffraction (TKD) band contrast (BC) + inverse pole figure (IPF) map inside a primary martensite lath in the sample heating to 350 ^oC)

Fig.10 Multi-component reinforcement designs and thermal expansion performances of xLFCS/Cu metal matrix composites
(a, b) enhanced metal matrix composites (MMC) with a single NTE material (a) and a multi-component NTE material (b)
(c, d) linear thermal expansions of LaFe_10.5Co_1.0Si_1.5 (c), and six compositions of LaFe_{11.5 -}_x Co _x Si_1.5 (dashed line) and xLFCS (solid line) (d)
(e, f) MMC reinforced with a single NTE material (e) and a multi-component NTE material (f)

Fig.11 Thermal expansion control of different biphase alloy systems^{[14-16,45,94]}
(a) zero thermal expansion dual-phase alloy obtained by synergistic combination of negative thermal expansion L phase (La(Fe, Co, Si)₁₃) and positive thermal expansion α phase (α-(Fe, Co, Si)) (α_Calc.—calculated S-3 ZTE (empty circle point line) is derived from L-phase and α phase thermal expansions)^[14]
(b) thermal expansion behavior of LaFe_0.939_x Co_0.061_x Si_0.0583_x (x = 37.5, 47.5, 57.5, and 67.5, designated as S-1, S-2, S-3, and S-4, respectively)^[14]
(c) macroscopic linear expansion of samples labeled S-3 (x = 0.03) to S-9 (x = 0.09) in Ho _x Fe_{1 -}_x with x = 0.03, 0.04, 0.05, 0.07, and 0.09^[15]
(d) linear thermal expansion curves of samples in (LaFe_10.8CoSi_1.2)_{100 -}_y -Cu _y alloys where y = 0, 15, 25, 35, and 45^[94]
(e) thermal expansion of Er₂Fe_{14 +}_x B_{1 + 0.07}_x alloy compared to pure iron^[16]
(f) cyclic thermal expansion properties of Fe_2.85Mn_0.15PtB_0.25^[45]

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[1]	SONG Xiaoyan SUN Zhonghua. REVIEW IN ANTIPEROVSKITE MANGANESE NITRIDES WITH NEGATIVE THERMAL EXPANSION PROPERTIES[J]. 金属学报, 2011, 47(11): 1362-1371.

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