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Zero Thermal Expansion in Magnetic and Metallic Tb(Co,Fe)2 Intermetallic Compounds Yuzhu Song, Jun Chen, Xinzhi Liu, Chinwei Wang, Ji Zhang, Hui Liu, He Zhu, Lei Hu, Kun Lin, Shantao Zhang, and Xianran Xing J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b12235 • Publication Date (Web): 02 Jan 2018 Downloaded from http://pubs.acs.org on January 2, 2018

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Journal of the American Chemical Society

Zero Thermal Expansion in Magnetic and Metallic Tb(Co,Fe)2 Intermetallic Compounds Yuzhu Song,† Jun Chen,*,† Xinzhi Liu,‡ Chinwei Wang,§ Ji Zhang,ǁ Hui Liu,† He Zhu,† Lei Hu,† Kun Lin,† Shantao Zhang,ǁ Xianran Xing† †

Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, China

‡

Helmholtz-Zentrum-Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany

§

Neutron Group, National Synchrotron Radiation Research Center, Hsinchu 30077, Taiwan

ǁ

National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, College of Engineering and Applied Science & Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

Supporting Information Placeholder ABSTRACT: Due to the advantage of invariable length with temperatures, zero thermal expansion (ZTE) materials are intriguing but very rare especially for the metals based compounds. Here, we report a ZTE in the magnetic intermetallic compounds of Tb(Co,Fe)2 over a wide temperature range (123 ~ 307 K). A negligible coefficient of thermal expansion (αl = -6 -1 0.48 × 10 K ) has been found in Tb(Co1.9Fe0.1). Tb(Co,Fe)2 exhibits ferrimagnetic structure, in which the moments of Tb and Co/Fe are antiparallel alignment along the c axis. The intriguing ZTE property of Tb(Co,Fe)2 is formed due to the balance between the negative contribution from the Tb magnetic moment induced spontaneous magnetostriction and the positive role from the normal lattice expansion. The present ZTE intermetallic compounds are also featured by the advantages of wide temperature range, high electrical conductivity, and relatively high thermal conductivity.

of ZTE in metals or alloys remains challenging. If ZTE can be achieved in alloys and intermetallic compounds, the unique advantages of alloys and intermetallic compounds can be taken. A good example is the discovery of the ZTE Invar alloys of Fe0.65Ni0.35, which brings fundamental studies and wide applications over the last century.5 Here, we report an intriguing wide temperature ZTE in the magnetic and metallic intermetallic compounds of Tb(Co,Fe)2. A negligible thermal expansion has been found in TbCo1.9Fe0.1, which is almost two order smaller than that of the common alloys. The ZTE mechanism of Tb(Co,Fe)2 is correlated to magnetovolume effect (MVE), which has been revealed by a combined analysis of temperature dependent synchrotron X-ray diffraction (SXRD), neutron powder diffraction (NPD), and macroscopic magnetic measurements. The direct link between the ZTE behavior and the magnetic structure has been embodied.

It is well known that interatomic distance increases on heating, due to anharmonic lattice vibration, which results in positive thermal expansion (PTE) for most solids. Generally, solids with strong bonds exhibit relatively low thermal ex1 pansion, while weak bonds to have a strong PTE. In order to reduce coefficient of thermal expansion (CTE) of metals, 2 metal matrix composites (MMCs) are often fabricated, such 3 4 as Al/SiC, and Cu/ZrW2O8 composites. Zero thermal expansion (ZTE) materials exhibit neither expansion nor contraction with respect to various temperatures, which are de5 manded but very rare. After the discovery of negative thermal expansion (NTE) 6 in ZrW2O8 in 1996, the remarkable achievements have been 7,8,9,10,11,12,13,14,15,16,17 made in control of thermal expansion. So far, some interesting ZTE materials have been found in Zr1−xSnxMo2O8,10 Tetramethylammonium Copper(I) Zinc(II) Cyanide,11 β-eucryptite,12 ReO3-based fluorides,13 , Fe[Co(CN)6],14 Mn-based anti-perovskites,15 16 Fe0.65Ni0.3517 and etc., which are most inorganic compounds. However, owing to the nature of weak metallic bonds, the achievement

Figure 1. Crystal and magnetic structure of the Tb(Co1.9Fe0.1) intermetallic compounds at 10 K. The magnetic and crystal structure of Tb(Co1.9Fe0.1) intermetallic compounds has been determined by temperature dependence of NPD from 10 K to 400 K. Tb(Co1.9Fe0.1) inter-

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metallic compound exhibits ferrimagnetic structure (space group: R3m) below its TC (Figure 1), in which Tb, Co/Fe1 and Co/Fe2 atoms occupy Wyckoff sites 6c (0, 0, z), 3b (0, 0, 0.5), and 9e (0.5, 0, 0), respectively. The moments of Tb and Co/Fe are antiparallel alignment along the c axis with the moment magnitude of MTb = 9.18 μB, MCo/Fe(3b) = -0.90 μB and MCo/Fe(9e) = -0.65 μB at 10 K. At the magnetic phase transition temperature (TC = 307 K), the ferrimagnetic rhombohedral structure (R3m) is transformed to the paramagnetic cubic one (3). The magnetic structure of Tb(Co2-xFex) is similar to that of TbCo2.18

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on TbCo2 and Tb(Co1.9Fe0.1) during the investigations of , magnetism and magnetocaloric effect.18 19

Figure 3. Temperature dependences of zero-field-cooling (ZFC) and field-cooling (FC) magnetization (M) at a magnetic field of 500 Oe for the Tb(Co2-xFex).

Figure 2. (a) Temperature dependence of linear thermal expansion (Δl/l0) of Tb(Co2-xFex) determined by a thermodilatometer. (b) Zero thermal expansion in the Tb(Co1.9Fe0.1) measured by both dilatometer and SXRD. Intriguingly, the Tb(Co1.9Fe0.1) intermetallic compounds exhibit a ZTE property over a wide temperature range (123 ~ 307 K, Figure 2b). The average linear CTE of Tb(Co1.9Fe0.1) -6 -1 determined by thermo-dilatometer is αl = 0.48 × 10 K . The reliability of ZTE can also be confirmed by the temperature dependence of unit cell volume, which was determined by both SXRD and NPD (Figure S5). The almost agreement on both macroscopic dilatometer measurement and intrinsic unit cell volume reveals the nature of ZTE in the present Tb(Co1.9Fe0.1). Figure S5 also shows the thermal expansion property of Tb(Co1.9Fe0.1) and TbCo2 at even lower temperatures. It needs to note that the present Tb(Co1.9Fe0.1) compounds not only exhibit ZTE but also have a wide temperature range, which is an exceptional in intermetallic compounds or alloys. As a comparison, the CTE value of the present Tb(Co1.9Fe0.1) is even two orders of magnitude smaller -6 than those of common metals such as Al (αl = 23.1 × 10 /K) -6 and Cu (αl = 17.7 × 10 /K). It is also smaller than the CTE of -6 -1 ZTE Invar alloys of Fe0.65Ni0.35 (αl = 1.5 × 10 K , 193 ~ 373 K).17 Furthermore, by adjusting the chemical composition of Fe in Tb(Co2-xFex), NTE and PTE can be obtained (Figure 2a). We notice that the temperature dependence of lattice parameters of Tb(Co,Fe)2 was reported in the previous studies

The macroscopic ferrimagnetic behavior of Tb(Co2-xFex) is determined by the measurements of zero-field-cooling (ZFC) and field-cooling (FC) upon heating at a magnetic field of 500 Oe (Figure 3). From the derivative curves of FC-ZFC, the TC can be determined to be 230 K, and 307 K for x = 0, and 0.1, respectively. The magnetic transition temperatures coincide with the disappearing temperatures of ZTE or NTE (Figure 2a, and Figure 3), indicating that the abnormal thermal expansion phenomenon is entangled with the magnetic behavior. To reveal the role which determines the ZTE property of the present Tb(Co1.9Fe0.1), the temperature dependence of NPD and SXRD has been carried out for both ZTE Tb(Co1.9Fe0.1) and NTE TbCo2. The NTE TbCo2 is studied as a reference. Figure S6 shows temperature dependence of lattice parameters for both x = 0 and x = 0.1. With increasing temperature, a(b) axis shows normal PTE; However, c axis contracts in the rhombohedral ferrimagnetic phase, which brings abnormal thermal expansion of unit cell volume. It is believed that the hidden role which determines the shrinkage of c axis should be the nature for ZTE. Figure 4a shows the temperature dependence of magnetic moment of Tb and Co/Fe in the ZTE TbCo1.9Fe0.1. It is found that the magnetic moment of Tb is much larger than that of Co/Fe, such as MTb = 9.18 μB, MCo/Fe(3b) = -0.90 μB and MCo/Fe(9e) = -0.65 μB at T = 10 K, which should be ascribed to the fact that the orbital magnetic moment of 3d transition elements are quenched, and Co/Fe atoms magnetism only 20 comes from the contribution of spin moments. As a result, the Tb magnetic moment plays a dominating role in the ferrimagnetism of TbCo1.9Fe0.1. With increasing temperature, the moments of Tb, and Co/Fe nonlinearly decrease to zero at the TC (307 K). To study the correlation between ZTE and magnetic structure, we utilize the spontaneous volume magneto-


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striction (ωs) to quantitatively describes the contribution of magnetovolume effect (MVE) to the abnormal change in the

Figure 4. (a) Temperature dependence of magnetic moment of Tb and Co(Fe) in the ZTE Tb(Co1.9Fe0.1). (b) Thermal expansion properties of TbCo1.9Fe0.1. ωexp is the experimental relative unit cell volume obtained by NPD, ωnm is the nominal one contributed from the nonmagnetic state, and ωs is the contribution of spontaneous volume magnetostriction from magnetic ordering. Temperature dependence of (c) the 2 square of Tb moment (MTb ) and (d) ωs in Tb(Co2-xFex). 21,22

thermal expansion. As shown in Figure 4b, the value of ωs is calculated by ωs = ωexp - ωnm, in which ωexp is the experimental unit cell volume obtained by NPD, ωnm is the nominal one of a nonmagnetic reference, which is calculated accord23,24 ing to the Debye-Grüneisen relationship. Here, the temperature dependence of both Tb moment and ωs is performed for the detailed analysis of ZTE mechanism. As shown in Figure 4c and 4d, it is interesting to reveal a strong 2 correlation between MTb and ωs, which can be quantitatively ascribed by the equation of 1

where k and C are the compressibility and the magnetovolume coupling constant, and M(T) is the amplitudes of local 25,26 magnetic moment. It means that the MVE is determined by the local magnetic moment, and thus thermal expansion can be tuned. In other words, the magnitude of magnetic 27 moment represents the degree of spin ordering. In the present study, with increasing temperature the reduction of Tb magnetic moment brings negative contribution to volume expansion. To directly reveal the relation between lattice and magnetic ordering, the lattice parameter c of ferrimagnetic Tb(Co2-xFex) (x = 0 and 0.1) as function of the Tb moment (MTb) is shown in Figure S7. Obviously, the lattice parameter c decreases almost linearly with respect to the Tb moment. That is why the rapid decrease in the Tb magnetic moment produces NTE, while the relatively slow decrease in the Tb magnetic moment produces ZTE. Another important feature of the ZTE property in the present intermetallic compounds of Tb(Co1.9Fe0.1) is that ZTE occurs over a wide temperature range (123 ~ 307 K). Such advantage of wide ZTE temperature is benefited from the enhanced magnetic moment, in which the magnitude of

magnetic moment determines the magnetic phase transition temperature and simultaneously controls the temperature range of ZTE. As shown in Figure 5, a good correlation can be

Figure 5. TC of Tb(Co2-xFex) as function of the square of Tb 2 moment (MTb ) at 10 K. well established between TC and the square of Tb moment at 2 10 K (MTb ), following with Landau theory: /3 2 28

where Mloc is the value of local magnetic moment. As a result, it is not difficult to understand that ZTE occurs over a wide temperature range, since its TC is promoted by the increased magnetic moment of Tb. In the Tb(Co2-xFex), the substitution of Fe can enhance the Tb magnetic exchange interaction, and thus increase the Tb magnetic moment. Furthermore, the present ZTE intermetallic compounds of Tb(Co,Fe)2 can be benefited from the advantages of high electrical and thermal conductivities due to the nature of metallic chemical bonds. As shown in Figure S8, the present ZTE Tb(Co1.9Fe0.1) exhibits metallic property. At room temperature the electrical resistivity of the ZTE Tb(Co1.9Fe0.1) is -6 2.4 × 10 Ω·m. With increasing temperature, the electrical conductivity is linearly reduced in the ferrimagnetic phase, which reveals the nature of metallic conductivity. Furthermore, the thermal conductivity of Tb(Co1.9Fe0.1) is 6.3 −1 W·(m·K) at room temperature, which is higher than most inorganic solids, such as the prototype NTE oxide of ZrW2O8 −1 29 (0.5 W·(m·K) ). In summary, ZTE has been found in the magnetic intermetallic compounds of Tb(Co1.9Fe0.1), which exhibits a negligible thermal expansion over a wide temperature range. Tb(Co1.9Fe0.1) exhibits ferrimagnetic structure with the c axis aligned antiparallel moments of Tb and Co/Fe. The magnetic moment of Tb dominates the magnetism of Tb(Co2-xFex). Direct experimental evidence reveals the detailed relationship between magnetism and ZTE behavior. The decrease of Tb magnetic moment determines the spontaneous magnetostriction (ωs), which neutralizes the normal lattice expansion (ωnm) and thus produces ZTE. Furthermore, the Tb magnetic moment is enhanced by the substitution of Fe, which increases the magnetic transition temperature and thus gives rise to the wide ZTE temperature range.



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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the 9

ACS Publications website. Sample preparation, experiment methods, and structure analysis.

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AUTHOR INFORMATION

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Corresponding Author

11

∗[email protected].

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Phillips, A. E.; Halder, G. J.; Chapman, K. W.; Goodwin, A. L.;

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The authors declare no competing financial interests.

13

ACKNOWLEDGMENTS

Deng, J. X.; Yu, R. B.; Xing, X. R. J. Am. Chem. Soc. 2014, 136,

This work was supported by the National Natural Science Foundation of China (grant nos. 21590793, and 21231001), the Changjiang Young Scholars Award, and the Fundamental Research Funds for the Central Universities, China (FRF-TP17-001B). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DEAC02-06CH11357. Variable temperature neutron powder diffraction (NPD) data was collected at the high-intensity diffractometer Wombat of the Australian Nuclear Science and Technology Organisation (ANSTO).

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Figure 1. Crystal and magnetic structure of the Tb(Co1.9Fe0.1) intermetallic compounds at 10 K. 63x73mm (300 x 300 DPI)


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Figure 2. (a) Temperature dependence of linear thermal expansion (∆l/l0) of Tb(Co2-xFex) determined by a thermo-dilatometer. (b) Zero thermal expansion in the Tb(Co1.9Fe0.1) measured by both dilatometer and SXRD. 83x111mm (300 x 300 DPI)



Figure 3. Temperature dependences of zero-field-cooling (ZFC) and field-cooling (FC) magnetization (M) at a magnet-ic field of 500 Oe for the Tb(Co2-xFex). 83x69mm (300 x 300 DPI)


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Figure 4. (a) Temperature dependence of magnetic moment of Tb and Co(Fe) in the ZTE Tb(Co1.9Fe0.1). (b) Thermal ex-pansion properties of TbCo1.9Fe0.1. ωexp is the experimental relative unit cell volume obtained by NPD, ωnm is the nominal one contributed from the nonmagnetic state, and ωs is the contribution of spontaneous volume magnetostriction from magnetic ordering. Temperature dependence of (c) the square of Tb moment (MTb2) and (d) ωs in Tb(Co2-xFex). 83x61mm (300 x 300 DPI)



Figure 5. TC of Tb(Co2-xFex) as function of the square of Tb moment (MTb2) at 10 K. 76x58mm (300 x 300 DPI)


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