Systematic study of the dependence of magnetic and structural properties of Nd2Fe14B powders on the average particle size

Journal Pre-proof Systematic study of the dependence of magnetic and structural properties of Nd2Fe14B powders on the average particle size J.F. Durán Perdomo, G.A. Pérez Alcázar, H.D. Colorado, J.A. Tabares, L.E. Zamora, J.J.S. Garitaonandia PII:

S1002-0721(19)30371-0

DOI:

https://doi.org/10.1016/j.jre.2019.09.012

Reference:

JRE 613

To appear in:

Journal of Rare Earths

Received Date: 20 May 2019 Revised Date:

16 September 2019

Accepted Date: 23 September 2019

Please cite this article as: Perdomo JFD, Alcázar GAP, Colorado HD, Tabares JA, Zamora LE, Garitaonandia JJS, Systematic study of the dependence of magnetic and structural properties of Nd2Fe14B powders on the average particle size, Journal of Rare Earths, https://doi.org/10.1016/ j.jre.2019.09.012. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © [Copyright year] Published by Elsevier B.V. on behalf of Chinese Society of Rare Earths.

Systematic study of the dependence of magnetic and structural properties of Nd2Fe14B powders on the average particle size J.F. Durán Perdomo1, G.A. Pérez Alcázar1*, H.D. Colorado1, J.A. Tabares1, L.E. Zamora1, and J.J.S. Garitaonandia2 1 Department of Physics, University of Valle, A.A.25360 Cali, Colombia 2 Applied Physics II Department, Basque Country University, 48080 Bilbao, Spain.

Abstract: A systematic study of the magnetic and structural properties dependence on the particle size was realized. For this, commercial NdFeB powder was separated into five different mean particle sizes using sieves.Besides, fromthe original powder, eleven samples were also produced by mechanical milling assisted by surfactant, using variousmilling times. A total of sixteen samples were studied by scanning electron microscopy (SEM), X-ray diffraction (XRD), vibrating sample magnetometry (VSM), and Mössbauer spectrometry (MS). The particle sizes of the samples vary from the micrometer to the nanometer scale. The crystallite size decreases with decreasingparticle size.XRD resultindicates that the Nd2Fe14B phase is found in all the samples, and the presence of this phase is also corroborated by MS using six sextets for fitting their spectra, with an additional singlet corresponding to the Nd1.1Fe4B4phase. The mean hyperfine magnetic field increaseswith increasingparticle size because the magnetic dipolar interaction between the magnetic moment of the particles increases with particlesize. From the VSMmeasurements the magnetic energy density (BH)maxvalues were calculated for different particle sizes,and their maximum value of 34.45 MGOe is obtained for the sample with the particle size of 60 µm.

Keywords: hard magnetic material;XRD; Mössbauer spectrometry, magnetization; particle size; rare earths *Foundation item: Project supported by Colciencias, Colombian Agency,and Universidad del Valle (Contract No.110671250407) and the project 691235-INAPEM of the H2020 Program. *Corresponding author:[email protected], 57-3174329147

1. Introduction The development of permanent magnets (PMs)is motivated by the need to storelarge amounts of magnetic energy in small volumes.PMs havea wide variety of applications, such as in computers, office products, automotive and transportation industry, domestic electronic products, products for factory automation, medical industryand military applications [1]. Currently, PMs based on the nanostructured NdFeBcompounds have the best magnetic properties,leading to their increasing use. The magnets based on the Nd2Fe14B phase are obtained by different methods, includingmelt spinning [2, 3], magnetron sputtering [4, 5], sintering[6, 7],and mechanical alloying[8, 9]. To improve the magnetic properties of the nanostructured NdFeB magnets,they have beendoped with different elements such as Ru, Co, and Ni [10-12]. Other studies have reported on the effect of replacingNdby other rare earth(RE) elements such asDy, Ga and Pr[13]. Theoretical studieshavesuggested that the best magnetic properties (highremanence, coercivity, and (BH)max) can be obtainedwhen a hard system such as Nd2Fe14B is coupled by magnetic exchange with soft magnetic phasessuch asα-Fe or Fe-B to form nanocomposite PMs[14, 15].It was proposed by Balamuruganet et al. [16] that the hard material should beimmersed in a matrix formed by the magnetically soft material whose particle sizes should not be greater thantwice the thickness of the

domain walls of the hard phase, so that the particle size of the soft phase must be close to 10 nm. Additionally, to favor the exchange coupling, the magnetic inversion of the hard and soft phases must occur simultaneously in nanocomposites. If the dimensions of the soft phase are very large, the magnetic inversion begins in the soft phase (due its lower anisotropy), inducing the propagation of the domain walls and leading to a reduction in the coercivity and the remnant magnetization in the soft phase.Unfortunately, experimentallyobtained results have not yet been able to matchthe outstanding theoretically predicted values of the magnetic properties, becausemany variables must be controlled for the realization of theoretical predictions. The grain size of the hard and soft phases must be on the order of 10 nm, andboth phases must be distributed homogeneously to allow an effective exchange coupling between them.Other works have reported on the effect of particle and crystallite sizeson the magnetic properties of the NdFeB magnetpowders, subjected to mechanical milling assisted by surfactant [17, 18],and onthe effect of plastic deformation on the magnetic properties of nanocomposite PMs through increasing the alignment of the grains of the magnetically hard phases [19, 20]. Due to the high costs of REs, many researchers are now investigatingRE-free PMs. Alloys of different transition elements such asFePt, CoPt, MnAl and MnBi, that have a tetragonal structure [21], andcompounds of the REFe12 type, in which small amounts of RE are used[22], are currently the most intensely studied materials.Improving the magnetic properties of PMs based on Nd2Fe14B is still a scientific and commercialchallenge.One of the routes used to improve their magnetic properties is by changing its particle and/or crystallite size. Some papers had been published concerning this topic. Scott et al. [23] produced sintered NdFeB magnets in oxygen, from powders of average particle sizes of 2.5, 3.0, 3.5 and 4.2 µm, respectively. The coercivity and oxidation resistance is low for the magnets produced with small particle size and is bigger for that produced with powders of 4.2 µm. Jurczyk et al. [24] studied NdFeB alloy powders produced by high energy ball milling. They produced powders with mean particle size between 200 and 0.3–1 µm for milling times between 0 and 2700 min, respectively. They found that the coercivity increases and then decreases passing through a maximum of 493 kAm–1 for the powders with particle size of 0.5–4 µm or 90 min milling. Li et al. [25] reported the hard-magnetic properties of NdFeB magnets produced by a single-stage hot deformation of powders with different particle sizes. The best magnetic properties were achieved for the particle size range of 45–100 µm. Sun et al. [26] reported that the effective anisotropy and the coercivity of nanocrystalline Nd2Fe14B magnets decrease with reducing the average grain size, and this is more rapid for grain sizes < 15 nm. Duan et al. [27] reported the effect of particle size on the properties of injection molded bonded NdFeB magnet and found that the optimal particle size for this magnet was 80-100 µm, the particle size smaller or higher than this range resulted in a deterioration of properties. Li et al. [28] studied the effect of grain size in the coercive field of NdFeB sintered magnets and found that the highest coercivity was obtained for a mean grain size of 4.5 µm, below this size the coercivity drops.Rong et al. [29] working with Nd2Fe14Bparticles of 6, 20 and 300nm, showed that the spin-reorientation transition temperature (TST) depends strongly of the particle size. TSTof the 300 nm particles is smaller than that of the bulk raw material, and TST for 20 nm particles is significantly lower than that of the 300 nm particles. Huang et al. [30] produced magnets of Nd2Fe14B by spark plasma sintering, working with powders of particle sizes ranged between 200–400, 10–200, 45–100, and <45 µm. They reported that the magnets obtained with larger particle size presented better magnetic properties, including remnant magnetization and (BH)max.Su et al. [31] used surfactant-assisted ball milling technique to synthesize NdFeB nanoparticles. They found that the best coercivity was obtained for powders of 20 nmand that the spin-reorientation temperature decreases with reducing the particle size.

Most of the previous works reported the magnetic properties dependence of NdFeB magnets or powders on the particle size but centered in smallranges of microparticle or nanoparticle sizes. Other works reported this dependence on the grain size. No one study reported this dependence using particles sizes across both ranges.The aim of this work is to report a systematic investigation of the particle size effect on the magnetic and structural properties of commercial Nd2Fe14B samples with a particle size varying frommicro tonanoscale.Our study includesalso the dependence with the mean crystallite size because this parameter is also studied in current work. The reduction of the particle size was performed byboth: sieving the original powder and milling it in surfactantat11 different milling times. 2. Experimental The original commercial powder of Nd2Fe14B, withan average particle size of 85µm,was separated using sieves of 100, 200, 325 and 400mesh (149, 74, 44 and 37 µm, respectively), and five sieved samples were obtained, including that which passes through the 400-mesh sieve.Theoriginal commercial powderwas also mechanically milled assisted by a surfactant (MMAS) at 11 different times, using oleic acid, under controlled argon atmosphere.Mechanical millingwas carried out in a planetary ball mill at 280 rpm, with a ball to sample mass ratio of 20:1 for times of 20, 40, 60, 80 minand 2, 3, 4, 5, 10, 15 and 20 h.All samples were studied by scanning electron microscopy (SEM), X-ray diffraction (XRD) with Cu radiation, vibrating sample magnetometry (VSM),and Mössbauer spectroscopy (MS). Using the SEM pictures of the different samples and the program ImageJ, the particle size distribution and the mean particle size of each obtained powder were obtained. The refinement of the XRD patterns was performed with the Rietveld method as implemented in the GSAS [32, 33]and MAUD [34] programs, using powder of LaB6 as calibration sample.Mössbauer spectrometry was performed in the conventional transmission mode using a57Co(Rh) source of 25 mCi,and the spectra were fitted using the MOSFIT program [35], and an αFe foil as calibration sample.All the experimental measurements were performedat room temperature. 3. Results and discussion 3.1 Scanning electron microscopy Fig.1 shows sometypical SEM micrographs and their respective histogramsfor the particle sizes for three of the prepared samples. They correspond to the powderwith bigger particle size (a), collected in the 100-meshsieve; that milled during 20 min (c); and that milled during 20 h (e).In this case the value Φ in the histograms is the mean particle size. SEM micrographs of all the prepared samples were obtained, and from them, their corresponding histograms and Φvalues were calculated.

Fig. 1. Micrographs and their corresponding particle size distributions for the sample with largest particle size (a, b), sample milled during 20 min (c, d); and sample milled during 20 h (e, f).

Fig. 2 shows the mean particle size as a function of the milling time. For t = 0 (original sample), the average value of the particles was 85 ± 29 µm. It is observed from Fig. 2 that, as the milling time increases, the average particle size decreases, and a large drop is observedat the beginning of the mechanical milling. The particles change with an averagesize decreasing from 85 µm to 1156 nm after only 20 min of milling;such reduction in the particle size with the milling time was also reported in [17, 36].

Fig. 2.Average particle size as a function of the milling time.

3.2 X-ray diffraction

Fig. 3. Diffractograms of the samples withaverage particle size of 160 µm, 1056 nm, and 106 nm, respectively.

Fig.3 shows the refined X-ray diffraction patterns for the powders with average particle size of 160 µm, 1056 nm, and 106 nm, respectively. After the refinement of all the patterns, the tetragonal Nd2Fe14B hard phase, with space group P42/mnm, was the onlyidentified one in the samples. The broadening of the diffraction lines, with the decrease of the mean particle size, was observed, and this is due the decrease of the crystallite size and the increase of the microhardness, as shown in Tables 1 and 2, and Figs. 4 and 5. After the refinement of all the patterns the structural parameters were obtained. The mean particle size, with their respective standard deviations σ,the a and c lattice parameters,the average crystallite size α, and the root mean square (rms) value of the micro strain<ε2>,for the sieved samples are listed in Table 1. The same values for the milled samples for the different milling timest, are listed in Table 2.The average crystallite size Φof each sample was obtained in the GSAS program by considering the instrumental broadening which is calculated from the refinement of the calibration sample (LaB6). This average was obtained by using the Scherrer formula for each line and thenpondered it with the fractional integral area of each line respect to the total integral area of the lines.

Table 1.Size of the sieved particles(T is the size of the mesh and the particles are on top of the respective mesh, and m400 means that the particles pass through the 400-mesh sieve), lattice parameters, and mean crystallite sizes. Φ

a

σ

c

α (nm)±0 .3

T (mesh) (µm)

(nm) ±0.0001

100

160

32

0.8777

1.2116

28.9

200

99

28

0.8778

1.2124

28.3

325

60

16

0.8777

1.2125

27.2

400

41

13

0.8773

1.2119

27.7

m400

18

7

0.8777

1.2126

27.2

Table 2. Milling times, size of the milled particles, lattice parameters, crystallite sizes andmicrostrain. Φ t (h)

σ (nm)

1/3

1150

2/3

1056

1

904

a

c

α (nm)±0. 3

1.2119

24.0

(nm) ±0.0001 665

<ε2> (10–4) ±1.0 1.7

701

0.8777 0.8776

1.2119

24.2

1.5

417

0.8778

1.2117

20.9

1.1

5/3

884

402

0.8780

1.2123

20.7

0.8

2

840

322

0.8782

1.2120

19.5

1.0

3

767

337

0.8782

1.2124

16.7

0.2

4

566

267

0.8794

1.2133

16.0

0.7

5

495

182

0.8793

1.2134

15.9

0.3

10

225

122

0.8798

1.2139

13.1

7.6

15

189

92

0.8801

1.2155

11.6

9.8

20

106

51

0.8812

1.2171

11.3

24.0

Fig.4 shows the mean crystallite size and lattice parameters a and c,obtained from the refinement of the patterns, as a function of the average particle size for thesieved samples only.It is observed that the mean crystallite size increases with increasing average particle size, while the lattice parameters remain constant.These parameters remain constant because the samples are part of the same original one, and they were notsubmitted to any cold work.

Fig. 4. Mean crystallite size and lattice parameters vs. average particle size for the sieved samples.

Fig. 5 shows the values of the mean crystallite size and of the micro strain as a function of the average particle size for the milled samples. It is observed that, as the average particle size increases, the crystallite size increases, in similar manner as for the sieved samples [37, 38].It is well known that the mechanical milling is a competitive process between fracture and welding, in which for small milling times the predominant one is the fracture and for bigger milling times, depending of the material type, the equilibrium between both is obtained and the particle and crystallite sizes remains nearly constant.The micro strainremains stable for up to five hours of milling (or mean particle sizes between ∼1160 to 500 nm) and then increases significantly for longer milling times (or mean particle sizes below 500 nm) [30]. These results can be explained knowing that this hard phase is very fragile, and itsfracture is facile,without accumulate big micro strain values until five hours of milling. After this time, the mean particle size and mean crystallite size values remain nearly constant (see Figs. 5 and 6, respectively) and the material begins to accumulate micro strains without appreciable fracture. It is interesting to note, in accord with the results of the mean crystallite size vs mean particle size of Fig. 5, that the discussion of our results of the dependence of the properties of the samples respect the mean particle size, can be extended to the dependence of the properties respect the crystallite size.

Fig. 5. Crystallite size and micro strainvs. the average particle size for the milled samples.

Fig. 6 shows the lattice parameters as a function of the average particle size and a dilation of the crystal lattice is observed with decreasing average particle size, or alternatively with the increase in the milling time.This can be a result of the mechanical milling that leads to an increase in the

number of the defects of the crystalline lattice.Largemilling timesincreasethe number of defects, increasing the micro strain and the latticeparameters, as reported by other researchers[4042].Therefore, the increase in thelattice parameters is due to the increase in the disorder caused by the milling process. This effect was also reported in Ref. [39], in which a rapid decrease of the longrange order parameter Swas observed for the first ten hours of milling, and then Sapproachesto a small value for long times.

Fig. 6. Lattice parameters of the milled samples vs mean particle size.

3.3 Mössbauer spectroscopy

Fig. 7. MS for thesamples with the mean particle size of 160 µm, 1056 nm,and 106 nm.

Fig.7 shows the Mössbauer spectra (MS) of the sampleswith the particle size of 160 µm (larger particles), that with mean particle size of 1056 nm, and that of sample with mean particle size of106 nm (obtained after20 h of milling).For the Mössbauer adjustments of the five sieved samples and the first three milled ones, six sextets and a doublet were used. Thesextetscorrespondtothesix Fe nonequivalentcrystallographicsites (NECS) 16k1, 16k2, 8j1, 8j2, 4c and 4e of the Nd2Fe14B phase[43]. An additional doublet was required (blue in Fig.7) for a good fit, and according with its parameters it corresponds to the Nd1.1Fe4B4phase[44]. This paramagnetic sitewasonly beingidentifiedby MSbut was not clearly identified by XRD, because the content of this phase is very low.The MS can be described based on the six sextets model that corresponds to the six occupation states (k1, k2, j1, j2, e and c), of the iron atoms in the unit cell, and taking into account that the populations of these states

are, 16, 16, 8, 8, 4 and 4 (for a total of 56 Fe atoms in the unit cell), respectively. The corresponding sub spectrum will contribute to the spectral area as 4:4:2:2:1:1:1 [10, 45, 46].To distinguish between the sites with equivalent relative area, the value of the hyperfine field (HHF) was used, which is accepted to decrease in the orderHHF(8j2)>HHF(16k2)>HHF(4c)>HHF(16k1)>HHF(8j1)> HHF(4e) [10, 47].In the case of the sieved samples, the relative areas obey the previous relation very well, but when the MMAS starts, imperfections, defects and disorder appear due the mechanical milling and, therefore, the relative areas begin to change.The same procedure was usedfor fitting the spectra of only the first three milled samples (20, 40 and 60 min). For higher times it was necessary to use a hyperfine magnetic field distribution (HMFD). The use of HMFD is justified by the fact that new magnetic environments appear around the iron atoms in the unit cell of the majority Nd2Fe14B phase. These new environments appear due the disorder, the imperfectionsand the dilation experience the lattice.

Fig. 8. Probability as a function of the hyperfine magnetic field for the samples milled during 4, 10 and 20 hours.

Fig.8 shows the curves of probability of the HMFs as a function of the hyperfine magnetic fields for the sampleswitha mean particle size of 566 nm (milled during 4 h), 225 nm (milled during 10 h), and 106 nm (milled during 20 h).The other samples fitted with HMFD present similar curves. It can be noted in Fig.8 that when the particle size decreases (bigger milling times) the broad of the MHFD increases: it passes from the range 12–37 T for Φ = 566 nm up to the range 2–42 T for Φ = 106 nm. Table 3 shows the Mössbauer parameters (isomer shift IS, quadrupolar shift 2ε, quadrupolar splitting QS, hyperfine field HHF, and the percentage of spectral area A) obtained for the samples withthe particle sizes of 160 µm, 1150 nm and 106 nm. Table 3. Mössbauer parameters for threeof prepared samples. Φ (nm)

160000

site

IS (mm/s) ±0.05

2ε (mm/s) ±0.05

16k1

–0.12

0.17

26.8

29.09

16k2

–0.15

011

28.8

29.09

8j1

–0.13

0.10

24.9

12.64

8j2

–0.02

0.63

32.5

12.64

4c

–0.11

–0.02

23.4

7.18

HHF (T) ±0.01

A (%) ±0.01

1150

106

4e

–0.15

0.14

19.0

7.18

doublet

–0.09

0.69 (QS)

0.0

2.19

16k1

–0.09

0.17

27.0

27.54

16k2

–0.12

0.14

29.0

27.98

8j1

–0.08

0.08

24.8

17.84

8j2

0.05

0.51

32.7

11.72

4c

–0.14

–0.01

22.3

7.29

4e

–0.18

0.47

16.6

5.30

doublet

–0.08

0.69 (QS)

0.0

2.34

HMFD

0.13

–0.02

26.6

95.46

doublet

0.07

0.60 (QS)

0.0

4.54

Figs.9 and 10 show the hyperfine parameters, 2ε and HHF as a function of the particle size for the six sites. Overall, no appreciable variation of these parameters is observed with the change in the average particle size, except the 2ε value for the 4e sitewhich presents a small decrease.

Fig. 9.2εas a function on the average particle size.

The use of HMFD for the MSs after 80 min of MMAS, is justified by the fact that new magnetic environments appear around the iron atoms in the unit cell of the Nd2Fe14B majority phase. These new environments appear due the disorder, the imperfections and the dilation experienced by the latticeduring the milling. Therefore, the MS cannot be adjusted with six sextets,and many more must be used, in order to describe their widening.

Fig. 10. HHFof the different sitesas function on the average particle size.

Fig.11 shows the behavior of the mean hyperfine magnetic field, as a function of the average particle size.It is observed from this figurethat the average hyperfine magnetic field decreases withdecreasing the particle size (corresponding to the increase in the milling time).This tendency is a consequence of the dipolarmagnetic coupling between the magnetic moments of the particlesthat, is larger for large particles, thus increasing the mean magnetic field acting on each Fe atom within the particles.This behavior was also reported for Fe-Al [48] and Fe-Mn-Al [49] powders. The most likely values of the HMFD(see Fig. 8) are between 27.6 and 29.6 T, and these values are close to those obtained in this work for the 16K1 and 16k2 sites (26.8 and 28.8 T, respectively)that are used to adjust the MS of the six sextets associated with the NECS. As was pointed previously these sites present the biggest spectral areas in the ordered samples.

Fig. 11. asa function of the average particle size.

3.4 Vibrating sample magnetometry Fig.12 shows the hysteresis loops of the samples with the average particle sizes of 160µm, 1056 nm, and 106 nm, respectively.All the samples present similar loops in accord with thehard-magnetic behavior typical of NdFeB magnets [50]. These loops were used to calculate the coercive field Hci, the saturation andremanencemagnetizations (4πMs and 4πMr, respectively), and the maximum magnetic energy density (BH)max. The variation of these parameters with the mean particle size is shown in Fig.13.

Fig.12. Hysteresis loops for the samples with mean particle sizes of 160 µm, 1056 nm and 106 nm.

It can be observed from this Fig. that all the magnetic properties increase with the increase of the mean particle size, pass for maxima values around the particles with an average size of 60 µm (60000 nm), and then decrease. The calculated values for this mean particle size were 9.611 kOe for the coercive field and 34.45 MGOe for the maximum magnetic energy density. This result is remarkable because it shows that a particle size of nanometric order is not required to obtain the best magnetic properties of the NdFeB permanent magnets.Our optimal mean particle size of 60 µm is in accord with the range of mean particle sizes of 45–100 µm reported by Li et al. [25] which used this powder to produce magnet by hot deformation and also with the range reported by Duan et al. [27] of 80–100 µm used to produce injection-molded bonded magnet.Huang et al. [30] reported the best magnetic properties for powders with bigger sizes, 200–400 µm. For our case, when the mean particle size decrease from 60 µm, the magnetic properties decrease, as reported in other works [2528, 50]. This decrease is related with the increase of the total area of the powders when the particle or crystallite size decreases, the increase of the lattice parameters of the unitary cell, the increase of the microstrainsand thegrain boundaries. In the surface of the particles and the crystallitesand in the grain boundaries, the crystal lost its coherence and with this, the align of its spins.This effect was detected in the HMFDs of Fig. 8, in which small HFs appear in then when particle size decreases.Similarly, in our work, when particle sizesare bigger than 60 µm the magnetic properties decrease (see Fig. 13), and this resultis related to the increase of the number of magnetic domains and also to the increase of the dipolar magnetic interaction (see Fig. 11), which try to decrease the magnetization of the grains or particles.

Fig. 13. Magnetic properties dependence on the average particle size.From top to bottom, coercive field, saturation magnetization, remnantmagnetization, and maximum magnetic energy density.

4. Conclusions Different mean particle sizes of commercial powders of Nd2Fe14Bwere obtained by sieving and by mechanical milling assisted by surfactant.XRD analysis showsthat the crystallite size decreases with decreasing particle size. For milled samples, the decrease in the particle sizeisaccompanied by the increase inthe number of defects and micro strainthat increase the lattice parameter. The fit of MS shows the presence of the Nd2Fe14B and Nd1.1Fe4B4 phases. Due to its low amount, the latter phase was not clearly identified by XRD measurements.For the sieved samples, and those milled with times smaller than 80 min, their Mössbauer spectra were fitted with six sextets, corresponding to the six Fe NECS present in the unit cell of the Nd2Fe14B phasereported for bulk samples[10, 44-47]. A doublet was used to adjust the Nd1.1Fe4B4 paramagnetic phase.Forbiggermilling times, it was necessary to use an HMFD, keeping the doublet site in the adjustment. The obtained average HHFdecreases with decreasing the particles size, due the decrease ofthe dipole interaction between the magnetic moment of the particles, decreasing the average magnetic field acting on each Fe atom within the particles. Finally, according VSM results,the best magnetic properties of all sixteen prepared samples were foundfor the sample with the average particle size of 60 µm (one of the sieved samples), with the maximum coercive field and a magnetic energy density of 9.611 kOe and 34.45 MGOe, respectively.Reduction of the particle size by mechanical alloying is not favorable because it introduces defects into the sample, degrading the magnetic behavior.

Acknowledgements Special thanks to Universidad del Valle and Colciencias (Colombian Agency) for the research project 110671250407 (CI 71047) and to the project 691235-INAPEM of the H2020 program,which give theeconomic support to this work. Graphical abstract:

Preparation of the samples.

References [1] Lewis LH, Jiménez-Villacorta F.Perspectives on Permanent Magnetic Materials for Energy Conversion and Power Generation.MetalMater Trans A.2013;44A: S1-S20. [2]SaitoT.Electrical resistivity and magnetic properties of Nd–Fe–B alloys produced by meltspinning technique.J Alloys Compd. 2010;505(1): 23. [3]ChenZ, MillerD, and HerchenroederJ.High performance nanostructured Nd–Fe–B fine powder prepared by melt spinning and jet milling.J Appl Phys.2010;107(9): 09A730. [4]Cui WB, Takahashi YK,HonoK.Microstructure optimization to achieve high coercivity in anisotropic Nd–Fe–B thin films.Acta Mater.2011;59(20): 7768. [5]FukagawaT, OhkuboT, HirosawaS, HonoK.Nano-sized disorders in hard magnetic grains and their influence on magnetization reversal at artificial Nd/Nd2Fe14B interfaces.J Magn Magn Mater. 2010;322(21): 3346. [6]PandianS, ChandrasekaranV, MarkandeyuluG, IyerKJL, Rama RaoKVS.Effect of Al, Cu, Ga, and Nb additions on the magnetic properties and microstructural features of sintered NdFeB.JAppl Phys. 2002;92(10):6082. [7]YueM, TianM, ZhangJX, ZhangDT, NiuPL,YangF. Mater Sci Eng B.2006;131(1):18. [8]Oyola Lozano D, Zamora LE, Pérez Alcázar GA, Rojas YA, Bustos H,Greneche JM.Magnetic and structural properties of the mechanically alloyed Nd2(Fe100-xNbx)14B system.Hyp Int.2005;161: 203. [9]Neu V,Schultz L. Two-phase high-performance Nd–Fe–B powders prepared by mechanical milling. J Appl Phys.2001;90(3): 1540. [10]Valcanover JA, Paduani C, Ardisson JD, Pérez CS,Yoshida MI.Mössbauer effect and magnetization studies of Nd16Fe76 − xRuxB8 alloys.ActaMater. 2005;53(9): 2815. [11]Hu Z, Wang H, Ma D,Luo C. The influence of Co and Nb additions on the magnetic properties and thermal stability of ultra-high intrinsic coercivity Nd-Fe-B magnets. J Low Temp Phys. 2013;170(5-6): 313. [12]Trujillo JS, Tabares JA,Pérez Alcázar GA.Comparative magnetic and structural properties study of Nd2Fe14B micro and nanopowders doped with Ni.J Supercond Nov Magn. 2017;303: 423. [13]Harland CL,Davies HA. Magnetic properties of melt-spun Nd-rich NdFeB alloys with Dy and Ga substitutions.J Alloys Compd. 1998;281(1):37. [14] Kneller EF,Hawig R. The exchange-spring magnet: a new material principle for permanent magnets. IEEE TransMagn.1991;27(4): 3588. [15] SkomskiR, Coey JMD. Giant energy product in nanostructured two-phase magnets.Phys Rev B.1993;48(21): 15812. [16] Balamurugan B, Sellmyer DJ, Hadjipanayis GC,Skomski R. Prospects for nanoparticle-based permanent magnets. ScrMater. 2012;67(6): 542.

[17] Simeonidis K, Sarafidis C, Papastergiadis E, Angelakeris M, Tsiaoussis I,Kalogirou O. Intermetal. 2011;19(4):589. [18]Wang Y, Li Y, Rong C, Liu JP.Sm–Co hard magnetic nanoparticles prepared by surfactantassisted ball milling.Nanotech. 2007;18(46): 465701. [19]Feng Y, Lou L, Li M, Song W, Li T, Hua Y, Zhang X. Large-size anisotropic bulk SmCo/Fe(Co) nanocomposite magnets prepared by hot rolling at extreme conditions. JAlloys Comp.2018;744: 104. [20]Li H, Li W, Guo D, Zhang X.Tuning the microstructure and magnetic properties of bulk nanocomposite magnets with large strain deformation.J Magn Magn Mater. 2017;425:84. [21] Jimenez-Villacorta F, Lewis LH. Advanced permanent magnetic materials.In:González JM, ed. Nanomagnetism, Chapter 7, OCP Publishing Group. United Kingdom. 2014.160. [22] Hu BP, Wang YZ, Wang KY, Liu GC,Lai WY.Magnetic properties of NdFe12 − xVx and NdFe12 − xVxNy (x = 1–3).J Magn Magn Mater.1995;140:1023. [23]Scott DW, Ma BM, Liang YL, Bounds CO. The effects of average grain size on the magnetic properties and corrosion resistance of NdFeB sintered magnets.J Appl Phys. 1996; 79:5501. [24] Jurczyk M, Cook JS, Collocott SJ.Application of high energy ball milling to the production of magnetic powders from NdFeB-typealloys.J Magn Magn Mater. 217;1995: 65. [25]LiY, KimYB, WangLS, SuhrbDS, KimbTK, KimbCO. The influence of the powder particle size on the anisotropic properties of NdFeB magnets produced by single-stage hot deformation.J Magn Magn Mater. 2001; 223: 279. [26] Sun Y, Gao RW, Feng WC, Han GB, Bai G, Liu T. Effect of grain size and distribution on the anisotropy and coercivity of nanocrystalline Nd2Fe14B magnets.J Magn Magn Mater. 2006; 306(1): 108. [27] Duan BH,Qu XH,Zhang L,Qin ML,Zhang SG,Li P. Effect of particle size on properties of injection molded bonded NdFeB magnet. Chin. J Nonferrous Met. 2007; 10: 1627. [28]Li WF, Ohkubo T, Hono K, SagawaM. The origin of coercivity decrease in fine grained Nd–Fe– B sintered magnets.J Magn Magn Mater. 2009; 321: 1100. [29]Rong CB, Poudyal N,Ping L.Size-dependent spin-reorientation transition in Nd2Fe14B nanoparticles. Phys Lett A. 2010; 374: 3967. [30]HuangYL,LiuZW,ZhongXC,Yu HY, ZengDC. NdFeB based magnets prepared from nanocrystalline powders with various compositions and particle sizes by spark plasma sintering.Powder Metall. 2012; 55(2): 124. [31]Su KP, Liu ZW, ZengDC, HuoDX, LiLW, ZhangGQ.Structure and size-dependent properties of NdFeB nanoparticles and textured nano-flakes prepared from nanocrystalline ribbons. Phys D: Appl Phys.2013;46(24): 245003. [32] Larson AC, Von Dreele RB. General Structure Analysis System (GSAS), Los Alamos National Laboratory Report LAUR 86-748. 2004. [33]TobyBH. EXPGUI, a graphical user interface for GSAS. J App Crystal.2001;34(2): 210. [34] LutterottiL, MatthiesS, WenkHR. MAUD: a friendly Java program for material analysis using diffraction. IUCr: Newsletter of the CPD.1999; 21(14-15). [35] Varret F,TeilletJ.UnpublishedMOSFIT program, Maine University, France. 2012. [36] XuML, WuQ, LiYQ, LiuWQ, LuQM,YueM.Crystallographic alignment evolution and magnetic properties of anisotropic Sm0.6Pr0.4Co5 nanoflakes prepared by surfactant-assisted ball milling.J Magn Magn Mater. 2015;387:62. [37]YangM, GuoZX, XiongJ, LiuFJ, QiKF.Microstructural changes of (Ti,W)C solid solution induced by ball milling.Int J Refrac Met Hard Mater. 2017;66: 83. [38]CanakciA, ErdemirF, VarolT, PatirA.Determining the effect of process parameters on particle size in mechanical milling using the Taguchi method: measurement and analysis.Measurement.2013;46(9): 3532.

[39] Gialanella S, Amils X, Baro MD, Delcroix P, Le Caër G, Lutterotti L,et al.Microstructural and kinetic aspects of the transformations induced in a FeAl alloy by ball-milling and thermal treatments.Acta Mater. 1998;46(9): 3305. [40]ShashankaR. ChairaD.Optimization of milling parameters for the synthesis of nano-structured duplex and ferritic stainless-steel powders by high energy planetary milling.Powder Technol.2015; 278: 35. [41]SharmaP, BiswasK, MondalAK,ChattopadhyayK.Size effect on the lattice parameter of KCl during mechanical milling. ScrMater. 2009;61(6): 600. [42]BidS,PradhanSK.Preparation of zinc ferrite by high-energy ball-milling and microstructure characterization by Rietveld’s analysis.Mater Chem Phys.2003;82(1): 27. [43]HerbstJF, CroatJJ, PinkertonFE,YelonWB.Relationships between crystal structure and magnetic properties in Nd2Fe14B. Phys Rev B. 1984;29(7):4176. [44] Malfliet A, Cacciamani G, Lebrun N, Rogl P.Boron–iron–neodymium. In Iron Systems, Part 1.Springer, Berlin Heidelberg.2008;pp. 482. [45]JueyunP, ZhengwenL, RuzhangM, ShumingP, ShikuanREN. Mossbauer studies of Nd-Fe-B alloys. In New Frontiers in Rare Earth Science and Applications.1985; 982. [46]PinkertonFE. and DunhamW.R.Mössbauer effect studies of Nd2Fe14B and related melt‐spun permanent magnet alloys,Appl Phys Lett.1984;45(11): 1248. [47]Cadogan JM.Mössbauer spectroscopy and rare-earth permanent magnets.J PhysD: ApplPhys.1996;29(9): 2246. [48] Bustos H, Oyola D, Rojas Y, Pérez Alcázar G.A, González JM,Margineda D.Evidence of dipolar magnetic field in mechanically alloyed Fe50Al50 samples.J Alloys Compd. 2012;536S:S377. [49] Pérez Alcázar GA, Zamora LE, Tabares JA, Piamba JF, González JM, Greneche JM, Marco JF.Evidence of magnetic dipolar interaction in micrometric powders of the Fe50Mn10Al40 system: Melted alloys.JMagn Magn Mater. 2013;327: 137. [50] Ma BM, HerchenroederJW, SmithB, SudaM, BrownDN, ChenZ.Recent development in bonded NdFeB magnets.J Magn Magn Mater.2002;239(1):418. [51] Rave W,RamstöckK. Micromagnetic calculation of the grain size dependence of remanence and coercivity in nanocrystalline permanent magnets.J Magn Magn Mater. 1997; 171: 69.

Fig. Captions Fig. 1. Micrographs and their corresponding particle size distributions for the sample with largest particle size (a, b), sample milled during 20 min (c, d); and sample milled during 20 h (e, f). Fig. 2. Average particle size as a function of the milling time. Fig. 3. Diffractograms of the samples with average particle size of 160 µm, 1056 nm, and 106 nm, respectively. Fig. 4. Mean crystallite size and lattice parameters vs. average particle size for the sieved samples. Fig. 5. Crystallite size and micro strain vs. the average particle size for the milled samples. Fig. 6. Lattice parameters of the milled samples vs mean particle size. Fig. 7. MS for the samples with the mean particle size of 160 µm, 1056 nm, and 106 nm.

Fig. 8. Probability as a function of the hyperfine magnetic field for the samples milled during 4, 10 and 20 h. Fig. 9. 2ε as a function on the average particle size. Fig. 10. HHF of the different sites as function on the average particle size. Fig. 11. as a function of the average particle size. Fig. 12. Hysteresis loops for the samples with mean particle sizes of 160 µm, 1056 nm and 106 nm. Fig. 13. Magnetic properties dependence on the average particle size. From top to bottom, coercive field, saturation magnetization, remnant magnetization, and maximum magnetic energy density.

Table Captions Table 1. Size of the sieved particles (T is the size of the mesh and the particles are on top of the respective mesh, and m400 means that the particles pass through the 400-mesh sieve), lattice parameters, and mean crystallite sizes. Table 2. Milling times, size of the milled particles, lattice parameters, crystallite sizes and micro strain. Table 3. Mössbauer parameters for three prepared samples.

Highlights: Commercial Nd2Fe14B powder was separated in different mean particle sizes, using sieves of different meshes and mechanical alloying assisted by surfactant. The obtained powders present sizes from micro to nanometric values. The different powders were study by XRD, Mössbauer spectrometry and VSM. From the studies it was obtained the dependence of the structural and magnetic properties with the mean particle size. The results shown that powders with a mean particle size of 60 micrometers present the best magnetic properties, inclusive those of the original powder.

The authors declare that they have no conflict of interest.