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# Microstructure and magnetic properties of the Cu-rich Nd(Fe,Mo)\_12 strip cast flakes

Sorana Luca, Johann Fischbacher, Camille Flament, Ryan Sedek, Patricia de Rango, Gabriel Gomez Eslava, Thomas Schrefl

► To cite this version:

Sorana Luca, Johann Fischbacher, Camille Flament, Ryan Sedek, Patricia de Rango, et al. Mi-crostructure and magnetic properties of the Cu-rich Nd(Fe,Mo)\_12 strip cast flakes. Journal of Alloys and Compounds, 2025, 1010, pp.178039. 10.1016/j.jallcom.2024.178039. cea-04850127

HAL Id: cea-04850127

https://cea.hal.science/cea-04850127v1

Submitted on 19 Dec 2024

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# Microstructure and magnetic properties of the Cu-rich Nd(Fe,Mo)₁₂ strip cast flakes

Sorana Luca<sup>a, *</sup>, Johann Fischbacher<sup>b</sup>, Camille Flament<sup>a</sup>, Ryan Sedek<sup>a,c</sup>, Patricia de Rango<sup>c</sup>, Gabriel Gomez Eslava<sup>a</sup>, Thomas Schrefl<sup>b</sup>

## ARTICLE INFO

### Keywords:

- Permanent magnets
- 1–12 compounds
- Microstructure
- Micromagnetics

## ABSTRACT

Nd(Fe,Mo)₁₂ compounds have been considered as promising candidates for next generation permanent magnet materials, thanks to their excellent intrinsic hard magnetic properties, comparable to those of the well-known NdFeB magnets, allowing a minimum usage of rare earth elements (RE). However, achieving high coercivity in an anisotropic microstructure has proven to be a significant challenge, which hinders their practical applications. In this work we present microstructural studies of the strip-cast Nd(Fe,Mo)₁₂-based alloy. Detailed microstructural characterization using high resolution transmission electron microscopy (TEM) reveals sub-micron sized 1–12 magnetic grains, indicating that the addition of Cu leads to grain boundaries segregated into RE and Cu. Micromagnetic simulations based on the observed microstructure emphasize the role of grain boundaries and of crystalline defects on the development of coercivity. This work provides evidence about relevant aspects of the microstructure of these compounds that is correlated to the coercivity development.

## 1. Introduction

The intensive use of rare earth elements (RE) is required in a vast spectrum of emerging key technologies like wind turbines or electric transportation, among others. As such, we experience a big pressure on the market of these critical elements that will only quickly increase in the upcoming years. This will affect the production of RE-based high performance permanent magnets, whose demand will rapidly grow within the next decade, in order to comply with the transport electrification and the wind energy deployment [1]. Thus, the replacement of Nd-Fe-B magnets by rare earth free [2], rare earth lean [3] or reducing the use of critical-rare-earth compounds [4] has become a matter of premier interest. Significant research activity has been devoted over the last decade to find alternative materials with similar, or even better, magnetic properties compared to the reference NdFeB magnets. The development of RE-free or RE-lean permanent magnets would be a great step-forward in terms of cost reduction and supply reliability [5].

Intermetallic RE-Fe₁₂ compounds, with tetragonal ThMn₁₂-type crystal structure, are known from more than 30 years [3] and are considered as the most promising candidates for the substitution of the

NdFeB permanent magnets, thanks to their relatively high Curie temperature (T_c), saturation magnetization (M_s) and magnetocrystalline anisotropy (MAE) [3]. The tetragonal ThMn₁₂-type structure of the 1–12 compounds without stabilizing elements was obtained only in thin-films with thicknesses up to 360 nm [6,7], whilst in its bulk form they can only be stabilized thanks to a partial substitution of Fe by other metallic elements, such as Ti, V, Cr, Mo, among others.

Different compositions of the REFe₁₂-xMₓ system have been studied, regarding different RE elements and the nonmagnetic stabilizing element (M) [8–19]. Most studies have focused on the Sm(Fe,M)₁₂ based compounds over the last decade, as it presents high uniaxial anisotropy at room temperature. A rather exhaustive investigation aiming to the development of the extrinsic magnetic properties of Sm-based 1–12 compounds (namely coercivity and remanence), resulted in significant progress in coercivity increase [11,12,20]. Nevertheless, the remanent magnetization remains low, if compared to NdFeB magnets. In addition, Sm-based 1–12 compounds have the advantage of holding high uniaxial anisotropy at room temperature, without the need for structural modifications through the insertion of light atoms. The investigation of the Nd-based 1–12 compounds as permanent magnets is of great interest, Nd

<footnote><sup>a</sup> Univ. Grenoble Alpes, CEA, Liten, DTNM, Grenoble 38000, France</footnote>

<footnote><sup>b</sup> Department for Integrated Sensor Systems, University for Continuing Education Krems, Viktor Kaplan Straße 2E, 2700 Wiener Neustadt, Austria</footnote>

<footnote><sup>c</sup> Univ. Grenoble Alpes, CNRS, Institut Neel, Grenoble 38000, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: sorana.luca@cea.fr (S. Luca).</footnote>
being more abundant in the Earth's crust compared to Sm. However, NdFe₁₂-xMₓ exhibits a weak uniaxial anisotropy at room temperature, dominated by the iron sub lattice [21], making it necessary to incorporate interstitial modifications by insertion of light elements, like H, B, C or N. As a consequence, not only the magnetocrystalline anisotropy is enhanced, but also the remanent magnetization and Curie temperature [22].

Nd(Fe,Mo)₁₂ is stable in a wide temperature range (from 600 to 1100 °C) [23], [24], and can be fabricated by different techniques like book mold, melt spinning or strip casting. Among the interstitial modified Nd(Fe,M)₁₂ alloys, nitrided Nd(Fe,Mo)₁₂-based compound have been considered as a promising material for permanent magnet applications, with a Curie temperature T_c ~ 320°C, high saturation magnetization M_s (up to 1 T) and large magnetocrystalline anisotropy H_a (up to 11 T) [10]. Despite these quite interesting intrinsic magnetic properties, coercivity is still low for permanent magnet applications [16, 25]. Understanding the formation of the 1-12 structure and the existence of competing phases, as well as of the nitrogenation process, is essential to obtain a high purity precursor, which is a prerequisite to increase the intrinsic magnetic properties. In addition to this, the relationship between microstructure and the extrinsic magnetic properties of the material is an important factor for the development of the performance of the final permanent magnet.

The coercivity mechanism in the 1–12 compounds is of nucleation-
type [19,26] similar to the benchmark NdFeB magnets. It is generally
influenced by the grain size and the magnetic decoupling of the grains
thanks to a non-magnetic grain boundary phase. For instance, in Sm(Fe,
M)₁₂ magnets, it was demonstrated that the optimization of the grain
boundary phase contributes to the enhancement of coercivity [11,12].
In the case of Nd-based nitrides the influence of grain boundary phases
has not yet been greatly investigated, mainly due to the fact that the
incorporation of nitrogen dramatically reduces the decomposition
temperature of the nitrided alloy, which is of 657°C for Nd(Fe,Mo)₁₂N
[27]. The typical coercive field (μ₀H_c) of NdFe₁₀.₅Mo₁.₅Nₓ powders ob-
tained from strip-cast alloys, is around 0.5 T [25], still far below the
feasible limits considering the Brown paradox (~ 30 % of H_a).

Though, maximum performances, i.e. maximum coercivity values,
are expected for dense materials, which cannot be produced by tradi-
tional sintering methods of nitrided Nd-based compounds. In addition,
the lack of suitable grain boundary phases, capable of magnetically
decoupling adjacent 1–12 grains, also contributes to the low coercivity
values registered up to now. In addition, the presence of macroscopic
and microscopic defects can also hinder the development of the coer-
civity. Thus, investigating the influence of grain boundary phases in Nd-
based 1-12 alloys (and their nitrides) together with crystalline defects,
offers the opportunity to identify an appropriate microstructure to
enhance μ₀Hc above the values reported so far.

In the present work, we investigate the particular microstructure of the Nd(Fe,Mo)12-based strip cast alloys. We chose a composition in the stability range of the 1–12 phase at temperatures between 600 and 1100°C, with the addition of Cu and an excess of Nd to allow the formation of a grain boundary phase insulating adjacent 1–12 grains. To understand the relationship between the microstructure and the magnetic properties, different length-scale analysis were conducted. The observed magnetic properties are compared to those obtained by micromagnetic simulations. The latter were performed based on our microstructural observations, for a more realistic modelling.

## 2. Experimental procedure

Alloys with nominal compositions (Nd<sub>0.75</sub>,Pr<sub>0.25</sub>)<sub>1.25</sub>Fe<sub>10.5</sub>Mo<sub>1.5</sub>Cu<sub>0.1</sub> (hereafter referred as Cu-rich Nd(Fe,Mo)<sub>12</sub>) were prepared by strip-casting (SC) technique, with wheel speed of 1.43 m/s under a controlled atmosphere of 300 mbar of Ar. As-cast alloy flakes, having a mean thickness of 287 ± 61 µm, were ball milled to coarse powder for X-ray diffraction (XRD). XRD patterns were acquired at room temperature

in a Bruker D8 Advance, with Cu Kα₁ radiation, at 2θ angles between 20 and 90°, with a step of 0.005° and counting time of 3 s/step.

Thermomagnetic measurements were carried out on a homemade
magnetic torque balance on non-oriented powders, sealed in a quartz
tube under inert gaz. Magnetization response as a function of the tem-
perature was measured upon heating from 30 to 850 °C.

Isothermal magnetization measurements were performed on magnetically aligned nitrogenated jet mill powders, embedded in epoxy resin and encapsulated in a Teflon mold, submitted to a magnetic field of 7 T for 12 h, during the solidification of the resin.

Nitrogenation experiments were conducted on fine monodisperse jet
milled powders (with a mean grain size D50 = 7.8 µm), at temperatures
between 300 and 500°C, under 100 kPa of nitrogen gas, using a Sievert-
type volumetric apparatus from HERA.

Microstructure observation was firstly performed by scanning elec-	ron microscopy (FEG-SEM, Zeiss Merlin) on resin-embedded flakes with
a polished surface to 0.04 µm colloidal silica. Submicron scale obser-
vations were performed by transmission electron microscopy (TEM),
using Bright Field (BF) and High Angle Annular Dark Field (HAADF)
detectors. Scanning transmission electron microscopy (STEM) in-
vestigations and high resolution TEM (HRTEM) observations were
conducted with a Thermo-Fisher Osiris Tecnai instrument, equipped
with an X-FEG source and operating at 200 kV. Energy dispersive X-ray
spectroscopy (EDX) was employed in STEM mode thanks to the Super-X
EDX system. EDX hyper-maps were acquired with Esprit 1.9 software
(Bruker). Crystal orientation was investigated thanks to the Automated
Crystallographic Orientation Mapping (ACOM) [28]). The software
Astar™ from Nanomegas was used to index the diffraction patterns and
to determine the orientation of the different phases. Diffraction patterns
were acquired without precession with a beam size of about 2 nm and
28 nm pixel. TEM sample was lifted out by focused ion beam (Zeiss
CB-550) and placed on a Mo grid.

Micromagnetic simulations were conducted to compute the demag-
netization curve of granular microstructures. The magnetic states along
the demagnetization curve are obtained by consecutive energy mini-
mization steps [29], starting from a positive external field in the range of
the anisotropy field of the given phase, in steps of –2 mT. The magnetic
material and an airbox surrounding the magnet were discretized with
tetrahedral finite elements. The resulting algebraic minimization prob-
lem was solved with a preconditioned conjugate gradient solver [30].
The airbox serves as a simple but effective method to treat the
open-boundary problem [31], when algebraic multigrid solvers are used
on graphical processors [32].

We created three variations of the granular structure of the magnet,
two with 20 grains and one with 60 grains within a 700x700x700
nm³ cube. The extensions of the model were chosen close to the limits of
the available hardware for these computations. We used the software
Neper with the grain-growth morphology option to define the shape of
the grains. This option allows for a wider grain size distribution and
higher grain sphericities compared to Voronoi tessellations [33,34]. The
average grain size was around 258 nm (min. 120 nm, max. 400 nm) for
the models with 20 grains and around 179 nm (min. 69 nm, max.
326 nm) for the model with 60 grains. Grain boundaries, defects and
twin planes were drawn with the software package Salome [35] and
then meshed within the SMESH module of Salome using MeshGems
[36]. The mesh size was chosen in the range of the Bloch parameter of
the hard magnetic main phase δ₀ = √A/K_u = 2.7 nm, which resulted in
finite element meshes with approximately 15 million to 16 million nodes
or 90 million to 100 million tetrahedrons. A is the exchange constant
and K_u the uniaxial anisotropy constant of the main phase. The thickness
of the grain boundary was 7 nm which adds up to a volume share in the
range of 4 % for the 20 grains model rising to 7 % for the model with 60
grains.

The uniaxial anisotropy constant K_u and saturation magnetization M_s
of the main phase Nd(Fe,Mo)12N were derived from the experimental
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** The images show the 10 scenarios a) to j) for one of the model geometries with 20 grains. The images in the second and fourth column show the 7 nm thick nonmagnetic grain boundary in grey. The grain boundary images and comparing simulation scenarios differing only in the presence of twinning defects, e.g. compare b) to c), may help to identify grain shapes and twinnig planes. Twinning planes are visible due to the color change within a grain, which denotes a change of the easy axis orientation within a grain. The color scale for the images in the first and third columns shows the misalignment of the easy axes with respect to the z-axis in degrees.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** XRD pattern and Rietveld refinement of Cu-rich Nd(FeMo)₁₂ powder. Bragg positions of the identified phases, from top to bottom, are tetragonal Nd(FeMo)₁₂ (> 99 %) with cell parameters *a* = 0.8598 nm and *c* = 0.4798 nm, and less than 1 % of dhcp-Nd with cell parameters *a* = 0.3665 nm and *c* = 1.1796 nm, cubic NdO with cell parameters *a* = 0.5065 nm and α-Fe.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Thermomagnetic measurements of jet milled powders of as-cast Cu-rich Nd(Fe,Mo)₁₂. The magnetizations are given in arbitrary units.</figcaption></figure>

results. $K_u$ was calculated from the anisotropy field. $K_u$ = 4.38 MJ/m³ and $\mu_0M_s$ = 1 T. The exchange constant $A$ = 32 pJ/m was taken from literature [10]. The intrinsic properties of α-Fe were set to $K_u$ = 0, $\mu_0M_s$ = 2.15 T and $A$ = 21 pJ/m. For nonmagnetic phases those three constants were set to zero.

We defined ten simulation scenarios, created three variants of the granular model geometries and applied the external field in three different directions, which gave a total of 90 simulations. Nine demagnetization curves per scenario were summarized in one averaged curve. The 30 simulations per geometry all used the same finite element mesh. The simulation scenarios were realized by changing the intrinsic properties of geometric features identified by tagged elements of the mesh. We kept the changes minimal to be able to compare the different scenarios.

The tessellation for 20 grains was used twice to create two granular models with the same grain shapes but different random orientations of the twin planes. The tessellation for 60 grains was used only once. The orientation of the twin planes defined the orientation of the easy axes. An isotropic distribution for the orientations of the easy axes was targeted. The angle between the easy axes of two variants of a grain with twin defect was given by 122° to match the experimentally measured twin angle of 58° (180°-122°). Each grain was split by a randomly oriented twin plane into two halves. For the random orientation of the twin planes we used sphere-point-picking [37]. To give the basic distribution

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** SEM-BSE image of the Cu-rich Nd(Fe,Mo)₁₂ flakes - polished section.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 4.** a) Thermomagnetic measurements of jet milled Cu-rich Nd(FeMo)₁₂N₁.₂₄₅ powders, nitrided at 350°C under 100 kPa of nitrogen gas. b) Room temperature M (H) curve of jet milled Cu-rich Nd(FeMo)₁₂N₁.₂₄₅ aligned powders.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 6. a) HAADF-STEM and b) BF-STEM images of the Cu-rich Nd(Fe,Mo)₁₂ flakes.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. Nd, Pr, Fe, Mo, O and Cu EDX maps of Cu-rich Nd(Fe,Mo)₁₂ flakes.</figcaption></figure>

of the easy axes, the two easy axis vectors per grain were then rotated + /- 61° out-of-plane to get an angle of 122° between the easy axes of the two variants of a grain with twin defect. For scenarios with grains without twin defects one of the two easy axes of the variants defined the easy axis for that grain.

Due to the small number of grains and hence poor statistics to model an isotropic magnet, we applied the external field along the x, y and z directions, respectively, to increase the number of simulations. By comparing the remanence magnetization of those simulations to the expected value of 0.5 M<sub>s</sub> we checked if the setup of the simulations was suitable. The external field was decreased from the positive anisotropy field μ<sub>0</sub>H<sub>a</sub> = 11 T in -2 mT steps. Nine computed demagnetization curves per simulation scenario (3 different geometries, times 3 different external field orientations) were summarized into one averaged curve.

The ten simulations scenarios were defined with the following
properties, mainly different in the nature of the grain boundary phase
and the presence of twin defects (see Fig. 1). Most of the scenarios except
for a) and h) come in pairs to identify the effects of twin defects. The
range in the volume shares and number of affected grains is a conse-
quence of the three model geometries.

a)Exchange-coupled grains.

b)Grains separated by a 7 nm thick nonmagnetic grain boundary.

c)Same as b) but grains with twinning defects.

d)Grains partially separated by a 7 nm thick nonmagnetic grain boundary. Only 30 % to 37 % of the grain boundary volume defined in b) is nonmagnetic.

e)Same as d) but grains with twinning defects.

f)Grains partially separated by a 7 nm thick nonmagnetic grain boundary. 63 % to 70 % of the grain boundary volume defined in b) is nonmagnetic.

g)Same as f) but including grains with twinning defects.

h)Mix of b) and c). Only grains larger than the average grain size of the model show twinning defects. In total, 6 out of 20 or 18 out of 60 grains are with twinning defects.

i)Same as b) but parts of the nonmagnetic grain boundary were replaced by α-Fe. α-Fe properties were assigned to 5 % to 7 % of the volume of the grain boundary in b) which corresponds to about 0.2 % to 0.5 % of the total volume of the model.

j)Same as i) but including grains with twinning defects.
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Analysis of a grain boundary phase. (a) HAADF STEM images on the Cu-rich Nd(Fe,Mo)₁₂ flakes. (b) and (c) Nd and O EDX maps. (d) HRTEM image of the same grain boundary. (e) Fourier Transform of the grain designated by a green square and oriented along [115] zone axis. (f) Fourier Transform of the grain designated by a blue square and oriented along [113] zone axis. (g) Fourier Transform of the phase at grain boundary.</figcaption></figure>

### 3. Results and discussions

#### 3.1. Structural analysis, intrinsic and extrinsic magnetic properties

Fig. 2 presents the graphical result of a Rietveld refinement of XRD pattern of the Cu-rich Nd(Fe,Mo)₁₂ powders. Three different phases were identified: 99 % of NdFe₁₀.₅Mo₁.₅, less than 1 % of cubic NdOₓ (space group Fm-3m) and metallic *dhcp* Nd (space group P 63/mmc). α-Fe was added to the Rietveld refinement in Fig. 2, however it was not detected, mainly due to superposition of its Bragg reflections to those of 1–12 phase, and to the tiny size of α-Fe crystallites (dendritic structure), contributing with very low intensity broad-peaks to the total diffraction pattern.

Magnetic measurements of non-nitrogenated powders (not shown here) reveal, as expected, low anisotropy field, μ₀Hₐ = 2 T (estimated from crossing point of M(H) curves measured parallel and perpendicular to the easy magnetization axis) and hence very low coercivity. The measured saturation magnetization is μ₀Mₛ = 1 T, consistent with previously reported values [10]. Thermomagnetic measurements on coarse powders exhibit one magnetic transitions at 155°C, corresponding to the 1–12 phase and a second one, only visible on heating, ranging from 550°C to around 770°C, corresponding to α-Fe (see Fig. 3). An amount of 11 wt% of α-Fe is estimated by comparison with the measurement of a piece of pure iron. Even though this phase is not detected with the XRD measurements, its presence is clearly evidenced with these measurements and was already identified in similar 1–12 compounds [38], and can be under the form of very small size crystallites and/or a poorly crystalized phase. The magnetic transition corresponding to the Curie temperature of α-Fe almost disappears upon cooling to room temperature, indicating that a recombination of α-Fe and free Nd take place between 550°C and 800°C. The estimated remaining amount of α-Fe is 0.4 wt%.

Following this result, as cast flakes were annealed at 850°C during 10 minutes and then jet milled to monodisperse powders of 7.8 µm mean grain size, prior to nitrogenation at 350°C and 100 kPa of N₂ gas, up to nitrogen uptake of 1.245 N atoms. Here we consider a nitrogen content of 1 corresponding to 1 N atom/unit formula of 1–12 phase, in the hypothetical case where the intergranular RE-rich phase does not absorb any nitrogen. The thermomagnetic measurements of jet milled nitrogenated powders show a single magnetic transition near 300°C on

heating, corresponding to the Curie temperature of the nitrogenated 1–12 phase (Fig. 4a), confirming a complete nitrogenation of the 1–12 phase. The magnetization curve shows a slight increase at around 600°C, indicating the decomposition of the nitrogenated powders with the subsequent formation of a soft ferromagnetic phase, certainly the α-(Fe-Mo) solid solution. This is corroborated by the fact that, upon cooling down to room temperature, only one magnetic transition is observed at nearly 700°C, meaning a complete decomposition of the 1–12 nitride. This was already reported in jet mill Nd(Fe,Mo)₁₂ nitrogenated powder [38].

Despite a large anisotropy field of μ₀Hₐ ~ 11 T of the nitrogenated powders (estimated from crossing point of M(H) curves measured parallel and perpendicular to the easy magnetization axis), coercivity values remains rather low (< 0.3 T) for permanent magnet applications (see insert of Fig. 4b).

In sum, fully nitrogenation of the 1–12 structure allows to greatly enhance both Curie temperature, from 155°C to 300°C and the anisotropy field from 2 T to 11 T. It also leads to the enhancement of the saturation magnetization from 1 T to 1.1 T, ascribed to the modification of the 3d band electronic structure of Fe [39].

#### 3.2. Microstructural analysis

The microstructures of the alloys have been firstly observed by SEM. Collected backscattered electrons are sensitive to atomic number, giving rise to chemical contrast to the images. The observed dark-grey phases (with grain size < 1 µm) may correspond to the 1–12 phase and light-gray ones to Nd-rich phases (metallic Nd and Nd-oxide) (Fig. 5). With the contrast achievable with the SEM, it can be noticed that the Nd-rich phase is not uniform within the flake, but rather concentrated in pockets. The desired grain boundary phase completely surrounding 1–12 grains is not detectable at this scale of analysis, either because of its small thickness or because of its non-uniform repartition around the grains. Black spots on the image represents closed porosity on the flakes.

To further characterize the microstructural features of the flakes and especially the distribution and composition of the intergranular phase, STEM-EDS have been employed. The observation of TEM sample in HAADF and STEM-BF mode (Fig. 6) reveals a microstructure constituted of fine grains, between 50 and 1000 nm. The presence of structural defects inside the grains are pointed out by arrows in Fig. 6b.
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** (a) Inverse Pole Figure, IPF-z (beam direction normal to the sample surface), showing the presence of twinned grains in Nd(Fe,Mo)₁₂ phase with the tetragonal ThMn12 - type crystal structure. (b) Misorientation angle profile across a twin boundary. (c) Diffraction patterns on either side of the twin boundary pointed out by black arrows and (d) the corresponding schematic representations of the crystal lattices.</figcaption></figure>

EDX Nd, Fe, Mo and Cu elemental maps of Cu-rich Nd(Fe,Mo)₁₂ grains, triple grain junctions and non-uniform grain boundaries are shown in Fig. 7. It confirms that Cu is not present in the Nd(Fe,Mo)₁₂ main phase, only in the grain boundary phase or the triple junctions, together with the excess of RE. On the other hand, Fe and Mo locate preferentially into the 1–12 grains. The exact composition of the grain boundary phase was not determined in this study, however relatively low Fe contents in the grain boundary have already been reported in Nd

(Fe,Mo)₁₂ melt spun ribbons [40], suggesting a paramagnetic feature of the grain boundary phase. Some of the thin grain boundary phases are Nd/Pr and Cu segregated however not all the grain boundaries present RE or RE-Cu enrichment. It is thus evidenced that magnetic 1–12 grains may be magnetically coupled, which in principle hinders the development of coercivity.

In Fig. 8a, b and c are shown HAADF-STEM images, associated with Nd and O EDX maps of a grain boundary which contains a Nd oxide. The
<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Chemical analysis of a twinned 1–12 grain. (a) HAADF-STEM image with its corresponding IPF-z map. (b) Nd, Pr, Cu, Fe, Mo and O EDX element maps. (c) chemical profile across the twin boundary as pointed out in the yellow rectangle in (a) (mean amount of Fe is 75 at%).</figcaption></figure>

Fourier Transform patterns of this same region are presented in Fig. 8.d, e, f and g. Both grains on either side of the grain boundary were indexed according to the tetragonal $ThMn_{12}$-type structure (space group I4/mm) with lattice parameters $a = 0.85917$ nm and $c = 0.47954$ nm, consistent with the values obtained from XRD analysis $a = 0.85982$ nm and $c = 0.47985$ nm. The Fourier Transform pattern of the grain boundary at point g revealed two planes with $d_{hkl1} = 0.319$ nm and $d_{hkl2} = 0.198$ nm and 36° between them. They can be indexed as (-1 1 1) and (-2 2 0) planes of the $NdO_2$ phase, which displays a face centered cubic structure with lattice parameters $a = 0.554$ nm, also comparable to XRD values ($a = 0.5065$ nm). This phase, paramagnetic at room temperature, is not harmful for the development of the coercivity. Small amount of it has proven to be even beneficial for coercivity and corrosion resistance improvement in NdFeB permanent magnets [41].

Fig. 9 shows an inverse pole figure (IPF) map evidencing grains with different crystal orientations. The IPF was indexed, thanks to ACOM-TEM, as Nd(Fe,Mo)₁₂ phase with a tetragonal $ThMn_{12}$ - type crystal structure. Misorientation indicating twin-like crystal defects are observed in some grains, pointed by arrows in Fig. 9a, also pointed out in Fig. 6b. These defects are observed in grains of different size order, starting from a few hundreds of nm up to micrometer size. The IPF along z axis (parallel to the electron beam) and the misorientation angle profile across the twin boundary show a misorientation angle of approximately 58° on either side of the twin boundary plane, corresponding to {011}-type plane. This value is consistent with previous reports showing the presence of twins in 1–12 intermetallics [42,43].

To highlight any element segregation at the twin boundary, fine EDX-TEM profiles have been performed across the twin boundaries of different grains. For that, the TEM specimen was oriented to observe the {011} twin plane quasi parallel to the electron beam in order to maximize the chance to detect a potential segregation at the twin boundary. As an example, in Fig. 10 we show the 2D compositional map of Nd, Pr, Cu, Fe, Mo and O of one twined grain (surface analyzed = 250 × 400 nm) with its corresponding HAADF-STEM image.

With the resolution of the analysis performed (beam size of about 1 nm and pixel size of 5 nm), no evidence of element segregation on the twin boundary was detected, contrary to what has already been observed by Atom Probe Analysis in other 1–12 systems [42,43]. We have analyzed several twined grains (not shown here) however no evidence of element segregation has been detected at the twin boundaries in any of them.

### 3.3. Micromagnetic simulations

In our simulations the sample size is much smaller than in experiment, causing an underestimation of the effects of demagnetizing fields. In fact, simulations with different micromagnetic models show that the coercive field decreases with increasing sample size [44]. Therefore, it is expected that critical fields obtained from simulations to be higher than values obtained from the actual experiment.

As a reminder, we defined ten simulation scenarios, created three granular model geometries and applied the external field in three different directions, which gave a total of 90 simulations. Nine demagnetization curves per scenario were summarized into one averaged curve labelled a) to j).

Fig. 11i shows the demagnetization curves for the scenarios without any twinning defects. The curves show the typical behavior of isotropic magnets with remanent magnetization $M_r$ close to 0.5 $M_s$. Reversible rotation of the magnetization occurs in a wide range of the applied external field. It can be noticed that an external field equal to the anisotropy field (11 T) is not enough to saturate the magnet but resulted in a magnetization of 0.92 $M_s$ which is close to the value computed by Stoner and Wohlfarth for randomly oriented non-interacting particles [45].

The critical field at which irreversible switching starts changes with defects and the nature of the grain boundary phases. In [46] the coercive field was defined as the field of maximum susceptibility in the demagnetization curve. We define the switching field $H_{sw}$ as the value of the
<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 11.** Averaged demagnetization curves for i) scenarios with grains without twin defect and ii) scenarios with grains with twin defect. Curves with the same color compare scenarios with the same grain boundary configuration and differences thus show the impact of twinning defects. The black round markers denote the switching fields $H_{sw}$ as defined above. The dashed and dotted vertical lines in both figures denote the switching field of scenario a) and the coercive field of scenario b), respectively, to ease comparison of the results.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. 12.** Comparison of absolute values of switching field and coercive field (green) and fullness factor (blue) for all scenarios. Hatched bars mark scenarios with grains presenting twin defects.</figcaption></figure>

external field where the difference quotient $dM_H/dH > 4$ for the first time along the averaged demagnetization curves. $M_H$ is the magnetization parallel to the applied external field $H$. This switching field represents the first irreversible switching of the magnetization of grains or parts of grains. The threshold value 4 was chosen to ignore outliers in any out of nine simulations forming an averaged demagnetization curve. $H_{sw}$ is shown in Fig. 11 as black markers. We define the coercive field $H_c$ as the value of the external field where $M_H \le 0$.

The best switching field is found for scenario b), where all grains are exchange decoupled by a non-magnetic grain boundary phase. For this “best-case” microstructure within the defined scenarios of these

micromagnetic simulations the switching field is $\mu_0H_{sw} = 4.07$ T, which is 37 % of the anisotropy field ($\mu_0H_a = 11$ T). The coercive field is $\mu_0H_c = 4.7$ T, which is 42.7 % of the anisotropy field. Demagnetizing fields and magnetostatic interactions reduce the coercive field compared to the 48 % of $H_a$ obtained from the Stoner-Wohlfarth model for non-interacting isotropic particles [45]. Exchange coupling between grains (scenario a) reduces the switching field by $\Delta\mu_0H_{sw} = 3.03$ T. This effect is caused by a partial domain wall formed at the grain boundary that acts as a defect easing the nucleation of a reversed domain [47]. The switching field for scenario a) is $\mu_0H_{sw} = 1.04$ T, which represents 9.5 % of the anisotropy field and the coercive field is $\mu_0H_c = 1.91$ T, which represents 17.4 % of the anisotropy field. Scenario a) defines the “worst-case” in terms of $H_{sw}$ and $H_c$ within this set of simulations shown in Fig. 11i. In scenarios d), f), and i) the grains are only partially exchange-decoupled by a non-magnetic grain boundary. The switching fields improve by 20 % to 108 % compared to scenario a) and the coercive fields improve by 13 % to 39 % compared to scenario a). In scenario i), 5 % to 7 % of the non-magnetic grain boundary volume (0.2 % to 0.5 % of the total volume) was replaced with $\alpha$-Fe, randomly distributed within the grain boundary phase (see Fig. 11i). Despite the small volume fraction of the soft magnetic phase this scenario conducts to a reduction of the switching field of about 50 % compared to scenario b). It can be attributed to exchange coupling of the grains through $\alpha$-Fe that conducts to switching field reduction owing to the presence of soft magnetic phase. The thickness of the soft magnetic phase is only 7 nm (same as grain boundary thickness) but it exceeds the critical dimension of soft phases as calculated by Kneller and Hawig [48].

Figure 11ii shows the demagnetization curves for the scenarios with twin defects. In a previous study, micromagnetic simulations were presented showing that the switching field of an isolated SmFe$_{11}$Ti grain with twin defect (similar twinning angle) was less than 0.4 $H_a$ considering various alignments with respect to the external field [42]. In [49], studying twin defects in MnAl-C, the switching field with respect to the orientation of the external field was plotted on the surface of a unit sphere. For an isolated spherical grain with twin defect (true coherent twin) the switching fields were below 0.5 $H_a$ for most external field orientations. In this work we investigate the impact of the presence of multiple twined grains in isotropic magnets. We observe that the first nonreversible switching event in any of the twinned-grains scenarios happens earlier or at similar external fields than for the “worst-case” scenario a) regardless of all the effort that is put into creating a nonmagnetic grain boundary. This is visible in Figure 11ii as all black round markers denoting the switching fields appear right of the dashed vertical line marking the switching field of scenario a). If all grains are exchange-decoupled by a nonmagnetic grain boundary (scenarios c) and h)) magnetization reversal starts at twin boundaries. This nucleation effect is similar to misoriented exchanged coupled grains, in which partial domain walls form at the interfaces. Introducing a non-magnetic grain boundary, that hinders the propagation of reversed domains, improves coercivity. While it also improves the switching field for scenarios without twin defect, in other scenarios exchange-coupled interfaces at the twin plane between the misaligned variants of a grain remain counteracting the positive effect of a nonmagnetic grain boundary with respect to the switching field.

To quantify the M-H loop squareness we introduce the fullness factor, defined as $(MH)_{max}/(H_c M_r)$ [50]. Fig. 12 summarizes the absolute values of the switching fields, coercive fields, and the fullness factors for all scenarios. Whenever twinning defects are present, the loop squareness is lower compared to the corresponding scenario with same grain boundary properties but without twinning defect. The lowest values of the fullness factor occur for the fully exchange-decoupled grains with twin defects (scenarios c and h). In all scenarios the remanent magnetization is almost the same, 0.5 $M_s$, but they differ in coercivity. $(\mu_0MH)_{max}$ is highest for scenario b) with 0.69 MJ/m$^3$ and lowest for scenario e) with 0.32 MJ/m$^3$. But scenario b) also has the highest coercive field with 4.7 T and consequently a low fullness factor of 0.36. On
<figure><img src="image_17.png" /><figcaption>**Fig. 13.** Sketch of the magnetic reversal process in scenarios b), c), i) and j). For each scenario three magnetization states along the demagnetization curve are shown and marked in the plot on the left hand side in red. Each state shows the magnetization component parallel to the applied external field $M_H$ and the parts of the magnet that reversed the magnetization identified by $m \cdot k < 0$, m - normalized magnetization vector, k - easy axis vector. The colorscale for the reversed domain shows $\theta_H$ which is the misalignment of the easy axis with respect to the external field, colored in six 15°-wide categories. The external field was applied parallel to the y-axis.</figcaption></figure>

the other hand, $\mu_0H_c = 1.7$ T for scenario e) is the lowest coercive field of all considered scenarios, but the fullness factor is relatively high with 0.46. We also computed the maximum energy density product, $(BH)_{max}$, assuming a demagnetizing factor of 1/3 for cube-shaped magnets. The energy density produced was approximately 50 kJ/m$^3$ for all scenarios, which is close to the theoretical maximum for $(BH)_{max}$, $\mu_0M_r^2/4 = 49.7$ kJ/m$^3$. $(BH)_{max}$ was limited by the low remanence of the isotropic magnets.

Fig. 13 shows images of the magnetic reversal process for scenarios b), c), i) and j) and Fig. 14 shows images for scenarios a), d), e) and h). The images show the results of one of the 9 simulations per scenario. The reversed domain is identified according to $m \cdot k < 0$, where m is the normalized magnetization vector and k is the easy axis vector (see Fig. 1 in [46]).

In scenarios b) and c) a nonmagnetic grain boundary hinders the propagation of a reversed domain and grains initially reverse independently. Grains or twin variants with a misalignment angle with respect to the external field in the range of 30° to 60° switch first in accordance with the Stoner-Wohlfarth model. In scenario c) the initial nucleus within grains forms at twin planes (barely recognisable above the reversed domain in the first image due to the small size of the nucleus with respect to the model size) before one variant of the grain reverses. In scenarios i) and j) $\alpha$-Fe is present and the initial nucleus forms there. Also better-aligned grains touching $\alpha$-Fe may reverse earlier in accordance with theoretical results for the angular dependence of grains with defects presented in [51]. In scenario j) nucleation at twin planes is noticeable as well.

In scenarios a) and d) without grain boundary or only partial nonmagnetic grain boundary nucleation starts at coupled grain

interfaces. In scenario e) additionally the nucleation at twin planes is observable. Strongly misaligned grains tend to reverse first followed by the expansion of the reversed domain. In scenario h) grains are separated by a nonmagnetic grain boundary and the initial nucleus again forms at the twin boundary. Most of grains showing twin defects reverse before any of the smaller regular grains. This agrees well with results presented in [42] that the switching field of isolated grains with twin defects in ThMn$_{12}$-type permanent magnets is below the lowest threshold of isolated Stoner-Wohlfarth grains.

## 4. Summary and conclusion

We have successfully prepared pure Cu-rich Nd(Fe,Mo)$_{12}$ based alloys by strip casting technique. Nitrogenation of the powders induce the increase of the Curie temperature and a huge increase of the anisotropy field. Detailed structural and microstructural characterizations of the Nd(Fe,Mo)$_{12}$ strip cast flakes reveal not only a non-uniform RE-Cu rich grain boundary distribution, but also the presence of twins, as already reported in the Nd(Fe,Ti)$_{12}$ [43] and Sm(Fe,Ti)$_{12}$ [42] systems. The misorientations angle across the twin boundary is approximately 58° and the twin boundary plane corresponds to a {0 1 1} family of the unit cell of Nd(Fe,Mo)$_{12}$. Down to the resolution of our TEM analysis, these twin boundaries are not segregated in elements, contrary to what has been revealed previously in Sm(Fe,Ti)$_{12}$ systems. As twin boundaries seems to appear in large grains (more than 400 nm), formation of twin boundaries can be attributed to the accumulation of internal stresses during solidification, where twin formation is favored over the formation of specific grain boundaries.

Micromagnetic simulations were carried out with a microstructure
<figure><img src="image_18.png" /><figcaption>Fig. 14. Sketch of the magnetic reversal process in scenarios a), d), e) and h). The external field was applied parallel to the z-axis.</figcaption></figure>

reproducing that of an ideal fully dense magnet, using the measured magnetic properties ($H_a$ and $M_s$) of our nitrogenated powders and the microstructural observations of as cast flakes. The results show that non-magnetic grain boundaries are the key feature to maximize the coercivity and one of the factors to improve the switching field values. On the contrary, completely exchange coupled grains conduct to a huge drop in the coercivity and the switching field values. Partially exchange-coupled grains improve the coercivity, but do not represent the “best-case”. This is the case highlighted by TEM analysis, and explains the low coercivity values measured on the powders, compared to the previously reported values [27].

The formation of twins does not significantly reduce the coercive field but for the same grain boundary configuration the switching fields are drastically reduced. The magnetization reversal starts at the twin plane interface between misoriented variants of the grains. The twin boundaries will act as nucleation sites due to partial domain walls forming. The low switching fields of grains with twinning defects will have a negative impact for high-performance permanent magnet applications. Formation of twin boundaries can be attributed to the accumulation of internal stresses during solidification, where twin formation is favored over the formation of specific grain boundaries. This is the case of large grains in our alloys, but still with sub-micrometric size. One pathway to overcome the formation of twins could be the grain size reduction to values below the limit of volume-to-surface energy ratio where there is no need to stress relief via twinning formation. This observation is supported by previous reported data, where twins were not evidenced in similar systems obtained by melt-spinning, that allow to reduce the grain size below 200 nm [16,27]. In addition, in the case of an isotropic configuration simulated here, the remanence is not affected by the presence of twinned grains, however to improve the energy density, the remanence should also be improved, in an anisotropic

configuration. In this case, twinning defect are harmful due to multiple easyaxes within a grain. It is therefore necessary to remove this crystallographic defects before the production of high performance Nd(Fe, Mo)₂ based permanent magnets.

In summary, we have demonstrated that the Cu-rich Nd(Fe,Mo)₁₂ system is a promising compound for permanent magnets, and identified areas for improvement to achieve the magnetic performance required for actual applications.

### CRediT authorship contribution statement

**Ryan Sedek:** Investigation, Formal analysis, Conceptualization.
**Patricia de Rango:** Validation, Supervision, Methodology, Funding acquisition, Conceptualization.
**Gabriel Gomez Eslava:** Writing – original draft, Investigation, Formal analysis.
**Thomas Schrefl:** Validation, Supervision, Methodology, Funding acquisition.
**Sorana Luca:** Writing – review & editing, Writing – original draft, Supervision, Project administration, Funding acquisition, Formal analysis, Conceptualization.
**Johann Fischbacher:** Writing – original draft, Methodology, Investigation, Conceptualization.
**Camille Flament:** Writing – original draft, Methodology, Formal analysis.

### Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

This work was supported by the Carnot Energies du Futur foundation
within the NAMASTE project. The financial support of the Austrian Federal Ministry of Labour and Economy, the National Foundation for Research, Technology and Development, Austria and the Christian Doppler Research Association, Austria is gratefully acknowledged.

## Data availability

No data was used for the research described in the article.

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