Segregation phenomena in Nd–Fe–B nanoparticles

Abstract

We report on the phase stability and phase formation of Nd–Fe–B nanoparticles from the gas phase in the size range from 10 to 25 nm. Particular attention is paid to the question, if the intermetallic $\hbox {Nd}_{2}\hbox {Fe}_{14}\hbox {B}$ phase also forms in free particles with a few nanometers in size that grow without contact to any solid or liquid matrix in a low pressure Ar atmosphere. The paper also addresses the possible influence of segregation phenomena that go along with the phase formation and the effect of (rapid) thermal annealing on the structure and phase stability of the particles. Aberration-corrected transmission electron microscopy in combination with spectroscopic methods was used to determine the local atomic structure and the chemical composition of the particles. Unheated particles are found to be mainly amorphous, while the rapidly optically annealed particles are crystalline. In both cases, we observe an enrichment of Nd in the shell of the particles and a Fe enrichment in the core. This segregation of Nd toward the particles' surface is more pronounced in heated particles, which form a clear core-shell structure with a Fe core surrounded by a $\hbox {Nd}_{2}\hbox {O}_{3}$ shell. This finding is attributed to the comparably small surface energy and the higher affinity of Nd to oxygen as compared to Fe. A simple model is introduced and used in order to estimate these surface energies. These estimations support the experimentally observed segregation phenomena. It is further found that B prefers the vicinity of Fe over that of Nd atoms, which as a consequence leads to a B enrichment in the Fe-rich parts of the particles. Magnetic measurements show a soft magnetic behavior for both, unheated and heated Nd–Fe–B nanoparticles.

Appendix

The surface energy is estimated by determining the change in energy per area upon breaking all bonds between the atoms within a given facet and those in the “disconnected” hemisphere. For this at first, the individual binding energy, $W_{{\rm at}-{\rm at}}$, is calculated from the (molar) heat of atomization, $\Delta _{{\rm at}}H$, per bond of a dedicated surface atom

$$\begin{aligned} \text{Heat of atomization per atom:}\; \Delta_{\rm{at}}{h}=\frac{\Delta_{\rm{at}}{H}}{N_A} \\ \text{Binding energy per bond:}\; W_{{\rm{at}}-{\rm at}}=\frac{\Delta _{\rm{at}}{h}}{\beta} \end{aligned}$$

Here, ${\Delta _\mathrm{at}H},\,{N_A}$, and ${\beta }$ are heat of atomization of the involved elements, which represents the binding energy per mole, the Avogadro number, and the coordination number, respectively. Based on this, the surface energy is calculated as the total change in energy, W, per area, A, i.e., ${\gamma =\frac{W}{A}}$, and it follows:

$$\begin{aligned} \gamma&=\frac{1}{2} \cdot \alpha \cdot N_{\mathrm{bb}} \cdot W_{\mathrm{at-at}}\; \text { with }\; \alpha =\frac{N_{\mathrm{at}}}{A} \\ \gamma&=\frac{1}{2} \cdot \frac{N_{\mathrm{at}} \cdot N_{\mathrm{bb}} \cdot W_{\mathrm{at-at}}}{A} \\ \gamma&=\frac{1}{2} \cdot \frac{N_{\mathrm{at}} \cdot N_{\mathrm{bb}} \cdot \frac{\Delta _{\mathrm{at}}H}{N_{\mathrm{A}} \cdot \beta }}{A} \end{aligned}$$

The (molar) heats of atomization are available in the literature, while the number of atoms, $N_\mathrm{at}$, within an area, $A$, of a given facet and the number of broken bonds, $N_\mathrm{bb}$, have to be determined from the crystal structure. An illustration of the lattice planes of interest and the broken bonds of the involved atoms is shown in Fig. 13.

The results of these estimations for the surface energy are summarized in Table 1. Although the absolute values differ from the results of empirical electron theory, the general trend and thus the relative preference of the various facets are in perfect agreement with the results of Fu et al. (2009).

Table 1 Summary of the calculation of surface energies of bcc Fe and hcp Nd