⇦Chinese Physics Letters, 2020, Vol. 37, No. 1, Article code 016501 Negative Thermal Expansion and Spontaneous Magnetostriction of Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ Compound * Li-Yu HAO (郝立宇)1, Tie Yang (杨铁)1**, Ming Tan (谭明)2** Affiliations 1School of Physics Science and Technology, Southwest University, Chongqing 400715 2College of Science, Henan Agricultural University, Zhengzhou 450002 Received 24 September 2019, online 23 December 2019 *Supported by the National Natural Science Foundation of China under Grant Nos 50871074 and 61474082, the Henan Agricultural University Start-up under Grant No 20190703Y00005.
**Corresponding author. Email: tanming912@163.com; yangtie@swu.edu.cn Citation Text: Hao L Y, Yang T and Tan M 2020 Chin. Phys. Lett. 37 016501    Abstract The structural, thermal expansion, and magnetic properties of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound are investigated by means of x-ray diffraction and magnetization measurements. The Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound has a rhombohedral Th$_{2}$Zn$_{17}$-type structure. There exists a small negative thermal expansion resulting from a spontaneous magnetostriction in the magnetic state of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound. The average thermal expansion coefficient is $-1.06\times 10^{-6}$/K in a temperature range 299–394 K. The spontaneous magnetostrictive deformation and the Curie temperature are discussed. DOI:10.1088/0256-307X/37/1/016501 PACS:65.60.+a, 75.80.+q, 75.30.Et, 75.60.Ej © 2020 Chinese Physics Society Article Text Materials with negative thermal expansion (NTE) coefficients and their composites with other materials are used in electric and optical devices as well as structural materials under high thermo-mechanical load to achieve a desired overall thermal expansion coefficient. Unfortunately, the only known materials with NTE coefficients are several oxide systems such as ZrW$_{2}$O$_{8}$ and HfW$_{2}$O$_{8}$, and a few Invar alloys.[1–5] Discovery of new materials with NTE coefficients and further understanding of the NTE mechanism may, therefore, play an important role in applications and theory. In the recent decades,[6–9] it was found that there was NTE in rare earth transition metal compounds with Th$_{2}$Ni$_{17}$-type structure or with Th$_{2}$Zn$_{17}$-type structure. It is very interesting to discovery the NTE of the Gd$_{2}$Fe$_{16}$Cr compound in a wide temperature range from 292 to about 572 K.[10] Another interesting result is the presence of near-zero expansion in the Nd$_{2}$AlFe$_{15}$Cr compound near room temperature.[11] This makes it necessary to further investigate the thermal expansion behaviors of other rare earth transition metal compounds with both the Th$_{2}$Ni$_{17}$-type structure and Th$_{2}$Zn$_{17}$-type structure. In this work, the thermal expansion behavior and its spontaneous magnetostrictions of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound are investigated by x-ray dilatometry and magnetization measurements. The raw materials of Nd, Fe, and Cr used in the experiment were at least 99.98% purity. The compound of Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ 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 vacuum tube, then annealed at 1050$^{\circ}\!$C for 5 days, after that, quenched in water. The ingot of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound was ground into powder. To decrease the stress, the powder of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound was sealed in a silicon vacuum tube, annealed at 300$^{\circ}\!$C 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 of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound. The Curie temperature $T_{\rm c}$ was derived from the temperature dependence of the magnetization curve measured by a vibrating sample magnetometer (VSM) in a field 40 kA/m. The thermal expansion of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound was measured by x-ray dilatometry. For the determination of the lattice parameters $a$ and $c$ of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound in the temperature range from 299 to 619 K, the powder sample was placed into an evacuated high-temperature chamber and step scanning (in steps of 0.01$^{\circ}$) x-ray diffraction patterns of the (113) and (303) 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 $\lambda_{\rm a}$, $\lambda_{\rm c}$, 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 and the Grüuneisen relation. The Debye temperature 400 K of $R_{2}$Fe$_{17}$ compound (where $R$ is rare earth elements) was used to extrapolate the temperature dependence of the lattice parameters of the sample, as it was carried out in the literature.[6–11] The XRD pattern of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ sample at room temperature is shown in Fig. 1. The indices of crystallographic plane ($h k l$) of reflections are marked on the peaks correspondingly. It is indicated that the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound is in a single phase with a rhombohedral Th$_{2}$Zn$_{17}$-type structure (space group, $R\bar{{3}}m)$. The lattice parameters $a$ and $c$ are 0.85754 nm and 1.24732 nm, respectively, and the unit-cell volume $v$ is 0.7944 nm$^{3}$.
cpl-37-1-016501-fig1.png
Fig. 1. The x-ray diffraction pattern of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound at room temperature (about 300 K).
cpl-37-1-016501-fig2.png
Fig. 2. Temperature dependence of the magnetization of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound in a field of 40 kA/m.
cpl-37-1-016501-fig3.png
Fig. 3. Temperature dependence of the unit cell volume $v$ of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound. The dashed line represents the values extrapolated from the paramagnetic range.
The temperature dependence of magnetization of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ sample is shown in Fig. 2. It is obvious that only one magnetic phase exists in the sample. This is different from the Nd$_{2}$Fe$_{14.5}$Cr$_{2.5}$ compound,[12] in which there are two magnetic phases. From Fig. 2, one can estimate the Curie temperature of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound to be about 375 K. This value is about 45 K higher than that of the mother compound Nd$_{2}$Fe$_{17}$.[13] Just as the Gd$_{2}$Fe$_{16}$Cr compound,[10] this may be attributed to the fact that Cr atoms prefer to occupy the $6c$ sites of the Th$_{2}$Zn$_{17}$-type structure. The x-ray diffraction of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ sample shows that the sample is still in a single phase with the rhombohedral Th$_{2}$Zn$_{17}$-type structure from 299 to 619 K. Figure 3 shows the temperature dependence of unit-cell volume $v$ of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ sample. It is obvious that there is a small negative volume thermal expansion of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ sample in the temperature 299–394 K. If the variation of the rate of $v$ is considered from 299 K to 619 K. One can obtain the average thermal expansion coefficients $\bar{\alpha }=\frac{\Delta v}{\Delta T\bar{v}}=-1.06\times 10^{-6}$/K in the temperature range 299–394 K, and $5.61\times 10^{-5}$/K in the temperature range 394–619 K, respectively. It is interesting that the absolute value of $\bar{\alpha }$ in the temperature range 299–394 K is very small to be near zero. This small thermal expansion coefficient was also found in the Nd$_{2}$AlFe$_{15}$Mn compound below 340 K.[11] Just as in the Nd$_{2}$AlFe$_{15}$Mn,[11] Tb$_{2}$Fe$_{16}$Cr[14] and Gd$_{2}$Fe$_{16}$Cr compounds,[10] this anomalous thermal expansion in the temperature range 299–394 K is ascribed to the existences of strong magneto-volume effect in the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound.
cpl-37-1-016501-fig4.png
Fig. 4. Temperature dependence of the lattice parameter $a$ of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound. The dashed line represents the values extrapolated from the paramagnetic range.
cpl-37-1-016501-fig5.png
Fig. 5. Temperature dependence of the lattice parameter $c$ of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound. The dashed line denotes the values extrapolated from the paramagnetic range.
The temperature dependences of lattice parameters $a$ and $c$ of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ sample are shown in Figs. 4 and 5. It is obvious that the negative volume thermal expansion of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ sample in the temperature range from 299 to 394 K is anisotropic, and the NTE occurs mainly along the $c$ axis.
cpl-37-1-016501-fig6.png
Fig. 6. Temperature dependences of the spontaneous volume magnetostrictive deformation $\omega_{\rm s}$ and the spontaneous linear magnetostrictive deformations $\lambda_{a}$ and $\lambda_{c}$ of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound.
The temperature dependences of the extrapolated values $v_{\rm p}$, $a_{\rm p}$, and $c_{\rm p}$ of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ sample are given in Figs. 3–5. As in Refs. [6–11,13–15] 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. Here m and p represent the magnetic state and the paramagnetic state, respectively. The temperature dependences of $\omega_{\rm s}$, $\lambda_{a}$ and $\lambda_{c}$ are shown in Fig. 6. It is indicated that the value of $\omega_{\rm s}$ decreases monotonically with temperature increasing from about $4.74\times 10^{-3}$/K at 299 K to $0.10\times 10^{-3}$/K at 394 K, and the value of $\lambda_{c}$ decreases monotonically from about $4.26\times 10^{-3}$/K at 299 K to $0.08\times 10^{-3}$/K at 394 K. This is similar to that of the Dy$_{2}$Fe$_{16}$Cr[15] and Gd$_{2}$Fe$_{16}$Cr compounds.[10] It is obvious that the value of $\lambda_{a}$ is much smaller than that of $\lambda_{c}$, and decreases slightly with temperature increasing below 370 K. This means that the spontaneous volume magnetostrictive deformation $\omega_{\rm s}$ is anisotropic, and mainly comes from the spontaneous linear deformation $\lambda_{c}$ along the $c$ axis. The Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound has a rhombohedral Th$_{2}$Zn$_{17}$-type structure. The Curie temperature of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound is higher than that of the Nd$_{2}$Fe$_{17}$ compound. There is a small negative thermal expansion coefficient of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound in a broad temperature range from 299 K to 394 K, and there exists anisotropic and spontaneous magnetostriction in the magnetic state of the Nd$_{2}$Fe$_{16.5}$Cr$_{0.5}$ compound. 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 alloys Fe 3 Ni -type chemical order in Fe 65 Ni 35 films grown by evaporation: Implications regarding the Invar problemThermal-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 compoundAnomalous thermal expansion and spontaneous magnetostriction of Gd2Fe16Cr compoundThermal expansion anomaly and magnetic properties of Nd 2 AlFe 16− x Mn x compoundsAtomistic study on the structure and Curie temperature for Nd2Fe17−xCrxNegative thermal expansion and spontaneous volume magnetostriction of Tb2Fe16Cr compoundNegative Thermal Expansion of the Dy 2 Fe 16 Cr Compound
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