Nd2Fe14B and Nd2 − xDyxFe14B magnetic particle preparation process is quite simple and final product was conveniently obtained in a few steps. Chemical reactions and mechanisms during co-precipitation and R-D processes are explained in the supporting information. R-D reaction follows the mechanism proposed by the Haider et al.27 XRD patterns for Nd2Fe14B and Nd2 − xDyxFe14B particles are similar due to the almost same crystal structure (Fig. 1(a)). They have the Nd2Fe14B (JCPSD #36-1296) as main phase with additional peaks corresponding to the extra Nd phase. Nd substitution with Dy makes the peaks position be shifted to the right side (Fig. 1(a)).
This is due to the different crystal lattice parameters of Nd2 − xDyxFe14B and to the smaller ionic radii of Dy (178 pm) as compared to the Nd (181 pm). Both “a “and “c” dimensions of the crystal lattice were decreased after the Dy substitution in the Nd2Fe14B crystal lattice (Fig. 1 (b)). The decreased values of these Nd1.5RE0.5Fe14B crystal parameters are also evidence of Dy substitution in Nd2Fe14B crystal. In order to calculate the lattice parameters (“a” and “c”), at first d-spacing values were calculated from the XRD patterns (Fig. 1). h,k and l values were determined from Nd2Fe14B JCPSD #36-1296. Finally, “c” and “a” value were calculated by the following equation as the same method reported by Rahimi et. al .17
SEM-BSE images in Fig. 1 (c,d,e) revealed that the particles were in irregular shape and the size distribution is in the range of 0.3–10 µm. The Nd2Fe14B had the largest average particle size as 3.5 µm while Nd1.5Dy0.5Fe14B had the least average particle size as 0.8 µm. Nd1.75Dy0.25Fe14B had the average particle size of 1.7 µm. SEM-EDS confirmed that Nd and Dy are homogeneously distributed with Fe in the particles (Figure S5,6). The microstructure, elemental composition and distribution of Nd1.5Dy0.5Fe14B particles were evaluated with STEM as shown in Fig. 2. The elemental distribution of Nd, Dy, Fe, and O was investigated by using STEM-EDS, which confirmed that the Dy was substituted for Nd in the crystal structure and it was distributed inside the grain. Figure 2 (b) is the line EDS taken from the blue circle of LAADF-STEM image of Nd1.5Dy0.5Fe14B. Figure 2 (c) shows the EDS line profile of interface between two fused Nd1.5Dy0.5Fe14B particles, as marked with the blue circle in Fig. 1 (b). No oxygen was detected in EDS mapping because boundaries of the particles were not exposed to the water during washing process.
To evaluate the crystallinity of the specimen, SAED patterns (Fig. 3 (b)) of the marked area with red circle in the TEM image (Fig. 3 (a)) were obtained. It was confirmed that the particles produced were single crystalline. It was deduced by SADP of strong diffraction maxima that each grain was completely single crystalline. Figure 3 (d) shows the high resolution BF-STEM image of the Nd1.5Dy0.5Fe14B observed at the [-101] zone axis and Fig. 3 (e) represents the corresponding atomic arrangement simulated by JEMS software (P. Stadelmann, www.jems-saas.ch.).
Both the BF-STEM image and simulated atomic arrangement showed the series of trigonal prism units. Figure 3 (c) illustrates the arrangement of the atoms in the prism. Boron atom occupies the center of trigonal prisms surrounded with three nearest Fe atoms on top and the three Fe atoms at bottom. The triangular prism facets participate to form the complete tetragonal Nd2Fe14B lattice.
To know the accurate site of the RE in the crystal lattice, HAADF-STEM image was taken at the [100] zone axis as shown in Fig. 4. At [100] zone axis, columns having “4f” site and “4g” site of Nd/Dy can be clearly distinguished. In addition, there is no Fe atom overlapping at each Nd position because of different locations of Fe and RE at [100] zone axis. Peak intensity of the histogram increases with the average atomic number, the HAADF-STEM image can be used to distinguish the Dy and Nd, and their positions ( “f” or “g” site). Figure 4 (b) is HAADF-STEM image, which confirms the same arrangement of atoms as the standard Nd2Fe14B [100] zone axis (Fig. 3(a)). Intensity histogram for red dotted panel in Fig. 4 (b) was acquired. It is observed that the intensity of atoms (Dy) at “4f” column is higher than that of the atom (Nd) at “4g” column. Higher peak intensity confirms that the substitution site of Dy is “4f” site because the atomic number of Dy (66) is larger than that of Nd (60), which leads to the higher intensity as compared to the Nd. The ‘a’ value of Nd1.5Dy0.5Fe14B crystal lattice is 8.78 Å (Fig. 3-c), which is well consistent with the standard Nd1.5Dy0.5Fe14B value.
Standard Nd2Fe14B have ‘a’ and ‘b’ values of lattice parameters as 8.80 Å.28 Standard distance of atomic column between “4f” site and “4g” site of Nd2Fe14B is 1.1 Å. In this study, the obtained distance is 1.09 Å as shown in histogram Fig. 4 (c). This is well matched with theoretical value. A slight error is due to a noise induced by the fine drift of the sample or the poisson noise in the STEM. Hence, site preference for the Dy in Nd2Fe14B is proved to be “4f” as the previously theoretically reported by Liu et al. 21 It was found that 100% “g” sites are occupied by the Nd (Fig. 5) and Dy was substituted only at “f” site.
Fe is ferromagnetic with electronic configuration of [Ar] 3d6 4s2. This electronic configuration shows that it has 8 valance electrons. Arrangement of the electrons in the relevant orbitals is shown in the rigid band model as Fig. 6 (c). Density of the electrons was taken on X-axis and energy was taken on Y-axis. Ef indicates the Fermi level of the rigid band. Energy level of 3-d electrons is similar to the 4s electrons, hence, there is no movement of electrons between the 4s and 3d orbital. Four unpaired electrons will be in the spin up configuration. Presence of the unpaired electrons makes the Fe ferromagnetic.
Being completely filled, 5d orbitals in Nd or Dy do not play any role to determine the magnetic properties of Nd or Dy. However, Nd and Dy have unpaired electrons in the 4f orbitals, those impart the ferromagnetic character. Orbital magnetic moment (L) direction of the unpaired valance electrons in Dy is opposite to the Nd because 4f electrons in Dy are in spin down state. Nd has the unpaired electrons in the spin up direction, hence, they are ferromagnetic with the Fe.
Simultaneously Dy with the spin down configuration couples anti-ferromagnetically with Fe and Nd (Fig. 6 (c)). 3d band in Fe may hybridize with the 5d orbital of the neighboring Nd and/or Dy. Schematic illustration of the exchange coupling and hybridization in the Nd2Fe14B and Nd2 − XDyXFe14B is shown in Fig. 6 (c).
Magnetic moment of Nd2 − xDyxFe14B have been strongly affected by Dy owing to its anti-ferromagnetic coupling with Fe and Nd. Individual values of magnetic moments of Nd2Fe14B, Nd1.75Dy0.25Fe14B and Nd1.5Dy0.50Fe14B, were determined as 25.50, 23.48, and 21.03 µB, respectively. Mganetic moments were determined by the the Ms values from M-H curves (Fig. 6(a)). Complete M-H curves with applied magnetic field range of -9.5 to 9.5 Tesla are provided in supporting information as Figure S-7. These experimentally determined values of magnetic moment are lower than the values by theoretical calculation because the theoretical parameter conditions are not fixed as the experimental ones. 21 For example, the theoretical calculation was based on the temperature at 5 K and all particles are single domain and un-oxidized. Dy coupled anti-ferromagnetically to Fe in the crystal lattice, resulting in the lower magnetic moment of Nd2 − xDyxFe14B. The change of magnetic moment critically affected the coercivity. From the Fig. 6 the coercivity (Hc) values of Nd2Fe14B, Nd1.75Dy0.25Fe14B and Nd1.5Dy0.50Fe14B were determined as 4.58, 5.84 and 9.55 kOe, respectively. Nd2 − xDyxFe14B showed the higher Hc due to stronger anisotropy energy and reduced magnetic moment. Additionally, Dy substituted particles have a smaller grain size as shown in SEM results. It is well known that coercivity increases as particle size gets smaller and approaches to the single domain size. The increasing order of coercivity as Nd2Fe14B < Nd1.75Dy0.25Fe14B < Nd1.5Dy0.5Fe14B and the decreasing order of magnetic moment as Nd2Fe14B > Nd1.75Dy0.25Fe14B > Nd1.5Dy0.5Fe14B were obtained from M-H curves.
Energy density or energy product is the amount of energy stored in the anisotropic Nd2Fe14B (or Nd2 − xDyxFe14B) lattice because of arrangement of the atoms in the crystal. It is confirmed that the Dy substitutions results in the higher energy density. Energy densities for Nd2Fe14B, Nd1.75Dy0.25Fe14B and Nd1.5Dy0.50Fe14B were recorded as 39.71, 50.29 and 53.71 KJ/m3, respectively. Mr (emu/g), Ms (emu/g), squareness ratio (Sq), magnetic moment (µB), coercivity (Hc), and energy density values for the all Nd2Fe14B and Nd2 − xDyxFe14B particles are shown in Fig. 6 (b), comparatively.
Nd2Fe14B and Nd2 − xDyxFe14B are expected to be anisotropic, hence, magnetic moment and energy density are angular dependent magnetic properties. Closely packed particles of Nd2Fe14B and Nd2 − xDyxFe14B were aligned at 5 T with easy direction of magnetization, then magnetic field was reduced to the 200 Oe. Thereafter, sample was rotated in the angle range of 0–1800. Figure 7 (a) explains the preparation of the sample for the measurement of magnetic anisotropy. During the measurement at MPMS, the magnetic particles were closely packed, which stopped the rotation of the particles at low applied magnetic field (200 Oe). All processes were performed at room temperature so that the effect of thermal energy was neglected.
Figure 7 (b) shows the anisotropic character of the Nd2Fe14B and Nd2 − xDyxFe14B. When magnetic particles were rotated in the range of 0 to 180o at constant applied magnetic field of 200 Oe, magnetic moment of the particles was changed significantly. Nd2Fe14B and Nd2 − xDyxFe14B have maximum magnetic moment along “c” crystal direction, with parallel/anti-parallel orientation to the applied field of (θ = 0, 180o). This is because of the “c” crystal dimension is easy direction for magnetization. On the contrary, along “a and b” crystal direction magnetic moment approached to zero.
Maximum magnetic moment value (24.13 µB) of Nd2Fe14B obtained during rotation was lower than the magnetic moment values obtained from M-H curves (25.50 µB). Reduced value of magnetic moment was observed because of weak applied magnetic field (200 Oe) during the rotation of the magnetic particles. However, the trend of magnetic moment variation for both the Nd2Fe14B and Nd2 − xDyxFe14B was same. Conclusively, substitution of Dy for Nd does not affect the anisotropic patterns of the crystal, however, value of the energy density can be changed. Figure S-8 explains the interaction of the applied magnetic field and the electron spin density of Nd2Fe14B during the rotation.
Magnetic moments of Nd2Fe14B, Nd2 − xDyxFe14B and Nd were calculated theoretically by full potential linearized augmented plane wave method, as implemented in the Wien2k code. Individual magnetic moments of Nd and Dy atoms at different sites were also calculated theoretically by this method. Theoretically calculated magnetic moment values for Nd2Fe14B, Nd (f) and Nd (g) were 30.20, 3.32 3.30 µB, respectively. Experimentally determined values for the Nd2Fe14B, Nd (f) Nd (g) were 24.3, 2.69, 2.67 µB, respectively. Details of experimental and theoretical calculations are provided in the supporting information.
Theoretically Nd always occupies the “g” site in Nd2Fe14B, Nd1.75Dy0.25Fe14B and Nd1.5Dy0.50Fe14B. 19–21 This is also confirmed in this work (Fig. 4). Hence in case of Nd1.75Dy0.25Fe14B and Nd1.5Dy0.50Fe14B there is negligible change in the magnetic moment on the “g” site after substitution. In Nd2Fe14B formula unit, Nd is distributed equally among 50 % “f” and 50 % “g” sites. Magnetic moment on “f” and “g” sites of in Nd2Fe14B is determined as 2.69 and 2.67 µB, respectively.
In Nd1.75Dy0.25Fe14B and Nd1.5Dy0.50Fe14B, Nd occupies 75% and 50% “f” sites, simultaneously Dy occupies leftover 25% and 50% “f” sites respectively. Hence magnetic moment on one “f” sites in Nd1.75Dy0.25Fe14B and Nd1.5Dy0.50Fe14B was determined as 0.82 and − 1.05 µB, respectively. Dy, which has almost double magnetic moment (5.34 µB) as compared to the Nd (2.45 µB), reduces the magnetic moment very effectively after the substitution. Reduction of magnetic moment of in the Nd2 − xDyxFe14B formula unit is actually the reduction of the magnetic moment of the “f” site.
After obtaining the experimental values of the magnetic moments of the Nd2Fe14B, Nd (f) Nd (g) anisotropic behavior of “f” and “g” sites was studied. Figure 7. (a) explains the sample preparation for the measurement of magnetic anisotropy. Nd2Fe14B, and Nd1.75Dy0.25Fe14B particles were compressed in the plastic discs and then attached to the rotating plate with the resin. Wires and springs used in the apparatus are made of Cu, which is non-magnetic. When these samples were kept in the MPMS they were rotated by application of force on the spring. Magnetic moment values of the “f” and “g” sites in Nd2Fe14B and Nd2 − xDyxFe14B at various angles of rotation are given in the Table 1. Figure 7 (b) graphically illustrates that the magnetic moment of Nd2Fe14B and Nd2 − xDyxFe14B as the function of rotating angle in the constant magnetic field. Figure 7 (c-e) shows the variation of individual magnetic moments of “f” and “g” sites as the function of rotating angle.
Table 1
Magnetic moment values of Nd2Fe14B and Nd2 − xDyxFe14B at “f” and “g” sites at rotating angle of 0 and 1800.
Substitution
sites
|
Magnetic Moment (µB)
|
Nd2Fe14B
|
Nd1.75Dy.25Fe14B
|
Nd1.50Dy.50Fe14B
|
f sites (00)
|
2.69
|
0.82
|
-1.05
|
f sites (1800)
|
-2.71
|
-0.85
|
1.06
|
g sites (00)
|
2.67
|
2.67
|
2.67
|
g sites (1800)
|
-2.71
|
-2.71
|
-2.71
|