⇦Chinese Physics Letters, 2019, Vol. 36, No. 6, Article code 066501 Negative Thermal Expansion of the Dy$_{2}$Fe$_{16}$Cr Compound * Li-Yu HAO (郝立宇)1, Tie YANG (杨铁)1**, Xiao-Tian WANG (王啸天)1, Ming TAN (谭明)2** Affiliations 1School of Physical Science and Technology, Southwest University, Chongqing 400715 2College of Science, Henan Agricultural University, Zhengzhou 450002 Received 12 April 2019, online 18 May 2019 *Supported by the National Natural Science Foundation of China under Grant Nos 50871074 and 61474082.
**Corresponding author. Email: yangtie@swu.edu.cn; tanming912@163.com Citation Text: Hao L Y, Yang T, Wang X T and Tan M 2019 Chin. Phys. Lett. 36 066501    Abstract Structural, thermal expansion, and magnetic properties of the Dy$_{2}$Fe$_{16}$Cr compound are investigated by means of x-ray diffraction and magnetization measurements. The Dy$_{2}$Fe$_{16}$Cr compound has a hexagonal Th$_{2}$Ni$_{17}$-type structure. There exists a negative thermal expansion resulting from a strong spontaneous magnetostriction in the magnetic state of the Dy$_{2}$Fe$_{16}$Cr compound. The average thermal expansion coefficient is $-0.794\times 10^{-5}$/K in the temperature range 292–407 K. The spontaneous magnetostrictive deformation and the Curie temperature are discussed. DOI:10.1088/0256-307X/36/6/066501 PACS:65.60.+a, 75.80.+q, 75.30.Et, 75.60.Ej © 2019 Chinese Physics Society Article Text Materials with negative thermal expansion (NTE) and their composites with other materials have been widely used in the fields of precision instruments, aerospace, and many other fields, thus a large number of theoretical and experimental studies have been carried out.[1–4] In recent decades,[5–8] it was found that there exists an NTE of rare-earth transition metal compounds of $R_{2}T_{17}$, where $R$ is rare-earth elements, and $T$ is transition metal elements. For example, in the Tb$_{2}$Fe$_{16}$Cr compound with hexagonal Th$_{2}$Ni$_{17}$-type structure,[9] the NTE occurs in the temperature range from 293 K to 550 K. Especially for the Gd$_{2}$Fe$_{16}$Cr compound with rhombohedral Th$_{2}$Zn$_{17}$-type structure,[10] the NTE was found in a broad temperature range from 292 to about 570 K. This makes the application of these compounds possible. Thus it is necessary to further study the thermal expansion property of the $R_{2}T_{17}$ compound. In a previous study,[11] it was found that the substitution of one Cr atom for one Fe atom can increase the Curie temperature of the Dy$_{2}$Fe$_{17}$ compound. To investigate the NTE in a broad temperature range, in this work, the thermal expansion behavior and its spontaneous magnetostrictions of the Dy$_{2} $Fe$_{16} $Cr compound from 292 K to 632 K are investigated by means of x-ray dilatometry and magnetization measurements. The raw materials of Dy, Fe, and Cr used in the experiment were of at least 99.98% purity. The compound of Dy$_{2}$Fe$_{16}$Cr was prepared by arc melting in an argon atmosphere of high purity. The ingot was re-melted four times to ensure its homogeneity and sealed in an evacuated silica glass tube, then annealed at 1373 K for five days. After that, it was quenched in water, then the ingot was ground into powder. To decrease the stress, the powder was sealed in a silicon vacuum tube, annealed at 573 K for 3 h, and slowly cooled to room temperature. The powder x-ray diffraction with Cu $K_{\alpha}$ radiation was used to examine the phase structure of the sample. The Curie temperature $T_{\rm c}$ was derived from the temperature dependence of the magnetization curve measured by a vibrating sample magnetometer in a field of 40 kA/m. The thermal expansion was measured by x-ray dilatometry. For the determination of the lattice parameters $a$ and $c$ of the Dy$_{2}$Fe$_{16}$Cr compound in the temperature range from 292 to 632 K, the powder sample was placed into an evacuated high-temperature chamber and step scanning (in steps of 0.001$^{\circ}$) x-ray diffraction patterns of the (112) and (302) reflections were recorded by the x-ray diffractometer with Cu $K_{\alpha}$ radiation monochromatized by a single-crystal graphite monochromator. The experimental error in the determination of $a$ and $c$ was 10$^{-4}$ nm. The magnetostrictive deformations $\lambda_{a}$, $\lambda_{c}$, and $\omega_{\rm s}$ were determined by the differences between the experimental values $a_{\rm m}$, $c_{\rm m}$, and $v_{\rm m}$ of the lattice parameters at a given temperature and the corresponding values $a_{\rm p}$, $c_{\rm p}$, and $v_{\rm p}$ extrapolated from the paramagnetic range according to the Debye theory, $C_{v}(T/T_{\rm D})=9R(\frac{T}{T_{\rm D}})^{3}\int_0^{T_{\rm D} /T} {\frac{\xi^{4}e^{\xi}}{(e^{\xi}-1)^{2}}d\xi}$, and the Grüneisen relation, $\alpha (T)=\frac{\gamma C_{v}}{{\rm K}_{0} V}$, with $C_{v}$ being the specific heat, $T$ the temperature, $T_{\rm D}$ the Debye temperature, $R$ the molar gas constant, $\alpha$ the thermal expansion coefficient, $\gamma$ the Grüneisen parameter, $K$ the modulus of elasticity, and $V$ the unit-cell volume. The Debye temperature 400 K of the $R_{2}$Fe$_{17}$ compound was used to extrapolate the temperature dependence of the lattice parameters of the sample; see Refs.  [8-10].
cpl-36-6-066501-fig1.png
Fig. 1. The x-ray diffraction pattern of the Dy$_{2}$Fe$_{16}$Cr sample at room temperature (about 300 K).
The x-ray diffraction pattern (at 0.02$^{\circ}$ intervals) of the Dy$_{2}$Fe$_{16}$Cr sample at room temperature is shown in Fig. 1. The indices of the crystallographic plane ($hkl$) of reflections are marked on the peaks correspondingly. It is obvious that the Dy$_{2}$Fe$_{16}$Cr compound is in a single phase with a hexagonal Th$_{2}$Ni$_{17}$-type structure (space group, $P6_{3}/mmmc$). The lattice parameters $a$ and $c$, and the unit-cell volume $v$ are 0.84500 nm, 0.83295 nm, and 0.51506 nm$^{3}$, respectively. Figure 2 shows the temperature dependence of magnetization of the Dy$_{2}$Fe$_{16}$Cr sample. It is indicated that only one magnetic phase exists in the sample. From Fig. 2, one can estimate the Curie temperature of the Dy$_{2}$Fe$_{16}$Cr compound to be about 438 K. This value is about 70 K higher than that of the mother compound Dy$_{2}$Fe$_{17}$.[11] As with the $Y_{2}$Fe$_{15}$Cr$_{2}$ compound,[12] this may be attributed to the Cr atom preferring to occupy the 4$f$ sites of the Th$_{2}$Ni$_{17}$-type structure.
cpl-36-6-066501-fig2.png
Fig. 2. Temperature dependence of the magnetization of the Dy$_{2}$Fe$_{16}$Cr sample in a field of 40 kA/m.
cpl-36-6-066501-fig3.png
Fig. 3. Temperature dependence of the unit-cell volume $v$ of the Dy$_{2}$Fe$_{16}$Cr compound. The dashed line represents the values extrapolated from the paramagnetic range according to the Debye theory and the Grüneisen relation.
The x-ray diffraction of Dy$_{2}$Fe$_{16}$Cr indicates that the sample is still in a single phase with hexagonal Th$_{2}$Ni$_{17}$-type structure from 292 K to 632 K. Figure 3 gives the temperature dependence of the unit-cell volume $v$ of the Dy$_{2}$Fe$_{16}$Cr sample. It is obvious that there is a negative volume thermal expansion of the Dy$_{2}$Fe$_{16}$Cr sample in the temperature range of 292–407 K. If the variation of the rate of $v$ is considered in the temperature range from 292 K to 632 K, we can obtain the average thermal expansion coefficients, $\bar{\alpha}=\frac{\Delta v}{\Delta T\bar{{v}}}=-0.794\times 10^{-5}$/K in the temperature range of 292–407 K, and $3.11\times 10^{-5}$/K in the temperature range of 407–632 K, respectively. Just as in the Tb$_{2}$Fe$_{16}$Cr and Gd$_{2}$Fe$_{16}$Cr compounds,[9,10] this NTE in the temperature range of 292–407 K is ascribed to the existence of a strong magneto-volume effect in the Dy$_{2}$Fe$_{16}$Cr compound. Figure 4 shows the temperature dependences of lattice parameters $a$ and $c$. It means that the negative volume thermal expansion of the sample in the temperature range from 292 to 407 K is anisotropic, and that the NTE occurs mainly along the $c$-axis.
cpl-36-6-066501-fig4.png
Fig. 4. Temperature dependences of the lattice parameters $a$ and $c$ of the Dy$_{2}$Fe$_{16}$Cr compound. The dashed line represents the values extrapolated from the paramagnetic range according to the Debye theory and the Grüneisen relation.
cpl-36-6-066501-fig5.png
Fig. 5. Temperature dependences of the spontaneous volume magnetostrictive deformation $\omega_{\rm S}$ and the spontaneous linear magnetostrictive deformations $\lambda_{a}$ and $\lambda_{c}$ of the Dy$_{2}$Fe$_{16}$Cr compound.
The temperature dependences of the extrapolated values $v_{\rm p}$, $a_{\rm p}$, and $c_{\rm p}$ are given in Figs. 3 and 4. As in Refs.  [8-10,13], one can derive the temperature dependence of the spontaneous volume magnetostrictive deformation $\omega_{\rm S}$ from the relationship $\omega_{\rm S}=(v_{\rm m}-v_{\rm p})/v_{\rm p}$, and the temperature dependences of the spontaneous linear magnetostrictive deformations $\lambda_{a}$ in the basal plane and $\lambda_{c}$ along the $c$-axis from the relationships: $\lambda_{a}=(a_{\rm m}-a_{\rm p})/a_{\rm p}$, and $\lambda_{c}=(c_{\rm m}-c_{\rm p})/c_{\rm p}$, respectively, where subscripts m and p represent the magnetic state and the paramagnetic state, respectively. Figure 5 shows the temperature dependences of $\lambda_{a}$, $\lambda_{c}$, and $\omega_{\rm s}$. It is indicated that the value of $\omega_{\rm s}$ decreases from about $5.76\times 10^{-3}$/K at 292 K to $0.97\times 10^{-3}$/K at 407 K, and the value of $\lambda_{c}$ decreases from about $4.31\times 10^{-3}$/K at 292 K to $0.25\times 10^{-3}$/K at 407 K. This is similar to that of the Gd$_{2}$Fe$_{16}$Cr compound.[10] Figure 5 also shows that the value of $\lambda_{a}$ is much smaller than that of $\lambda_{c}$, and decreases slightly with increasing the temperature below 407 K. This implies that the spontaneous volume magnetostrictive deformation $\omega_{\rm s}$ comes mainly from the spontaneous linear magnetostrictive deformation $\lambda_{c}$ along the $c$-axis. In summary, we can conclude that there exists an anisotropic and strong spontaneous magnetostrictive effect in the Dy$_{2}$Fe$_{16}$Cr compound. NTE behavior appears in the temperature range from 292 to 407 K. References Negative Thermal Expansion from 0.3 to 1050 Kelvin in ZrW2O8Anomalous behavior of thermal expansion of α-Fe impurities in the La(Fe,Co,Si)13- based alloys modified by Mn or selected lanthanides (Ce, Pr, Ho)Zero Thermal Expansion in Magnetic and Metallic Tb(Co,Fe) 2 Intermetallic CompoundsAn anomalous thermal expansion phenomenon induced by phase transition of Fe-Co-Ni alloysThermal-expansion anomaly and spontaneous magnetostriction of Nd2AlFe15Mn compoundAnomalous thermal expansion and magnetic properties of Tm2Fe17−xCrx compoundsStructural and Magnetic Properties of ${\hbox {Tm}}_{2}{\hbox {CrFe}}_{16-x}{\hbox {Si}}_{x}$ CompoundsNegative thermal expansion and spontaneous magnetostriction of Tb2Fe16.5Cr0.5 compoundNegative thermal expansion and spontaneous volume magnetostriction of Tb2Fe16Cr compoundAnomalous thermal expansion and spontaneous magnetostriction of Gd 2 Fe 16 Cr compoundMagnetic properties of Dy 2 Fe 17- x Cr x and Er 2 Fe 17- x Cr x ( x = 0-3) compoundsA high-resolution neutron study of at 77 K including magnetic propertiesThermal Expansion Anomaly and Spontaneous Magnetostriction of Y 2 Fe 14 Al 3 Compound
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