Diffusion behavior of N atoms in Sm2Fe17

Journal of

ALLOYS AND CONPOUJND5 ELSEVIER

Journal of Alloys and Compounds 222 (1995) 10%112

Diffusion behavior of N atoms in

Sm2Fe17

H. Uchida a, S. Tachibana a T. Kawanabe a, y . Matsumura a V. Koeninger a, H.H. Uchida b, H. Kaneko c, T. Kurino c Department of Applied Physics, Tokai University, 1117 Kita-Kaname, Hiratsuka, Kanagawa 259-12, Japan bDepartment of Human Development, Tokai University, 1117 I~'ta-Kaname, Hiratsuka, Kanagawa 259-12, Japan Society of Non-Traditional Technology, 1-2-8 Toranomon, Minato-ku, Tokyo 105, Japan

Abstract The rate of N diffusion in Sm2Fel7 was measured using an Sm2Fe17Nz4 sample with a particle size of 5 /xm. At this N concentration, the two Sm2Fe~TNa and Sm2Fe~7N3 phases were assumed to coexist. The measured diffusion coefficient yielded a value. D = 2 . 7 × 10 -12 cm 2 s -~ at 623 K which is much higher than those measured for larger particle sizes of the sample. The marked change in the diffusivity can be attributed to the contribution of the pre-exponential factor Do to the diffusion coefficient. The sample size dependence of the N diffusivity suggests strong interactions of the diffusing N atoms with defects induced and accumulated in the nitrided sample. The rate of the N diffusion seems to change depending on the readiness of strain relief of the sample in the nitride formation, resulting in a different diffusion process depending on the N concentration and the particle size.

Keyword~,: Nitrogen diffusion; Stress

1. Introduction

SmzFel7Nx is usually prepared by the exposure of Sm2Fe~7 to N2, N 2 + Ha, NH3 or NH3 + H2 gas. N atoms have to pass various intermediate states before they reach lheir final positions in the bulk in the overall reactions x

N2 + Sm2Fe'7

, Sm2Fe17Nx

or

NH 3 + SmeFe17

)

x1 Sm2Fe17Nx+ ~3 H2 --

In such gas-metal reactions, the following partial steps should be considered as the rate-controlling steps in the gas atom uptake by SmzFea7 [1]. For a metal sample with a clean surface, (1) N 2 or NH3 transport in the gas phase and molecular adsorption (physisorption) to the metal surface, (2) N 2 or NH3 dissociation and chemisorptions of N and H atoms on the surface, (3) transition of N and/or H into the metal, (4) N and/or H diffusion in the metal where H atoms preferentially are desorbed because of SmzFelvN. [2] has a higher thermodynamic stability than Sm2Fe~7Hx 0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(94)04928-9

[3] at the usual nitriding temperatures, (5) formation of N solid solution phases SmzFelv(Nx) if an appreciable solubility limit would exists at low N concentrations (otherwise, step (6) would follow immediately after step (4)), (6) formation of a nitride phase (if the N concentration is not yet in an equilibrium state, additional partial steps are still active), (7) transition of N atoms from the nitride to the metal and (8) N diffusion in metal of N solid solutions. For the metal covered with oxide and/or hydroxide surface layers, the following steps should be added [4]: (2a) transition of N and/or H into the surface layer and (2b) N and/or H diffusion in the layer. In this case, nitride formation might take place at the surface layer-metal interface without the formation of an N solid solution phase because the precipitation of the compound tends to begin at incoherent sites such as misfits and interfaces. However, the preparation of SmzFe17Nx generally is carried out above 600 K; therefore, the effects of such surface layers on the N2 dissociation may be small because these layers are decomposed by the diffusion of O atoms into the metal

[41. For these partial steps described above, the surface processes are decisive in initiating the overall reactions. In the N2 absorption by Sm2Fe17, two distinctly different

108

H. Uchida et al. / Journal of Alloys and Compounds 222 (1995) 107-112

rate-controlling steps are present [5,6]: the N 2 dissociation at the initial stage and the N diffusion in the bulk at increased N concentrations. The dissociation of a covalent gas molecule is the result of interaction between the antibonding orbitals of a molecule and the lobe-shaped orbitals of the d electrons of the metal surface [7] where electron transfer between the surface and a molecule seems to be the essential step for dissociation of the molecule [8]. The enormously high rates of N uptake by SmzFe17 in an NH3 atmosphere [9] indicate the importance of the generation of N atoms with high activities from the NH3 dissociation. The synthesis of NH3 on the surface also seems possible by the exposure of cyclically hydrided SmzFe~7 to N2, which enhances the N solubility [10]. At increased N concentrations, the rate-controlling step shifts from Nz dissociation to N diffusion in the bulk as can be seen by the linear relation between the N amount absorbed and the square root of reaction time [5,6]. The diffusion-controlled kinetics was measured also by gravimetric and metallographic measurements of the growth rate of nitride layers, and both measurements yielded consistent results [11]. The decrease in particle size increased the diffusivity of N in the Sm2Fea7 where the contribution of the vibrational term of the diffusion coefficient seemed to be dominant while the activation energy of the N diffusion was almost constant in the range from 108.5 to 118.5 kJ (mol N atoms)-1 and independent of the N uptake process in N2, N2+H2 or NH3 [9,12]. This means that the effect of the H atoms dissolved in the Sm2Fe17 or Sm2Fe~vNx bulk prior to the N uptake does not seem to affect the diffusion process of N in Sm2F%7 [9]. On the contrary, a much lower activation energy of 66.1 kJ (tool N) -~ and a low pre-exponential factor of 2.15×10 5 cm 2 s-1 were measured in the N diffusion at [N]/[SmzFe17] = 1.8 using a block sample in a glow discharge spectroscopy (GDS) study [13]. These results suggest that the N diffusion process markedly depends on the N concentration in the sample. Thus the N diffusion in Sm2Felv should be investigated with respect to the influences of sample particle size and N concentration where the stress or strain accumulation and relaxation in the lattice may play important roles. In this study, the N diffusion coefficient was measured from the N uptake rate in the transition between two different equilibrium states where Sm2Fe17N2 and Sm2Fe~7N3 phases were assumed to coexist [2]. Discussions are given with respect to the diffusion behavior of N atoms in SmzFea7 under various constrained lattice conditions depending on the sample size and N concentrations.

compositions of the samples were determined by inductively coupled plasma (ICP) emission spectroscopy. Microstructure and the N distributions of the samples before and after N2 exposure were observed by secondary electron microscopy (SEM) and electron probe microanalysis (EPMA). The structure of the samples and the changes in the lattice parameters were determined by X-ray diffraction (XRD) analysis. The produced block samples were pulverized by ball mill in an Ar atmosphere and powder samples with a particle size of about 5 /xm were subjected to the measurement. Details of the sample preparation and control have been reported elsewhere [2]. The rate of the N uptake was measured in the course of the measurements of the pressure P-concentration C-temperature T relations for the Sm2Fe17-N system at 623 and 673 K. Details of this measurement have been described elsewhere [2]. The sample was nitrided at 673 K up to an equilibrium condition at about [N]/ [Sm2Fe17] = 2.4. Then, the temperature of the reaction cell was set within a short time from 673 to 623 K. The time needed for stabilization of the cell temperature was within 5 rain and was short enough to allow subsequent measurement of the slow rate of N uptake at 623 K. The total amount of N atoms absorbed by the sample was determined volumetrically by the pressure decrease using a calibrated reaction cell, and the precision of the measurement of the N concentration by the sample was of the order of + 10 -4 in the mole ratio [14]. The confirmation of equilibrium state was made by the observation of the homogeneous distribution of N atoms in the sample using EPMA [2].

3. Results and discussion

Fig. 1 shows the plateau pressure regions of the P--C-T isotherms of the Sm2FelT-N system measured at 623 and 673 K [2]. On the basis of the thermodynamic 3

10

673KoDA~ 623K

&

Sm2Fe17 alloy was prepared by arc melting and annealed at 1373 K in Ar gas for 6 h. The chemical

-

©

ID-

10

2

J

2.2 2. Experimental process

• ,,A.

'

'

'

2.4

t

2.6

,

2.8

N/St%FelT Fig. 1. Two plateau pressures at 623 and 673 K and the region where the rate of N uptake was measured.

H. Uchida et aL / Journal of Alloys and Compounds 222 (1995) 107-112

phase rule, two Sm2Fe17N2 and Sm2FeavN3 phases are assumed to coexist in this region. The N uptake reaction was initiated at N concentrations corresponding to about [N]/[Sm2Fe17] = 2.4 and 623 K where the N2 pressure decreased from one plateau pressure of 4.8x 102 Pa to another of 2.7x 102 Pa as indicated in Fig. 1. The total amount of N atoms transferred was 2.5 × 10 -3 in the mole ratio of [N]/[Sm2Fe17]. A linear relation can be seen between the measured N concentration absorbed and the square root of the reaction time t up to tm=: 160 s1/2 in Fig. 2. The N distribution of the sample used was examined by EPMA and the presence of two different phases could not be found although the coexistence of two Sm2Fe17N2 and SmgFe~TN3 phases was assumed in this plateau region [2]. In addition, no splitting of XRD peaks of the sample was found [2]. When only a small differer.ce between the lattice parameters of these two phases and the high compressive stresses in these phases [2] are taken into account, the differences between the densities of N atoms and the lattice structures of the two phases may also be very small. This argument seems consistent with the result of the observation of homogeneous magnetic domains in SmzFea7N2.6 [15]. Therefore the measured rate may be assumed to be rather the N diffusion rate through a constrained Sm2FearN3-, lattice than the growth rate of the nitride layer growing at the interface of two nitride phases with quite different concentrations. On the basis of this assumption, we applied the measured data to the fol-

2.398

2. 397 O3 I1 E O0 Z

2.396

2. 395 0

t 50

t 100

t 150

J 200

t 250

300

~/U [ s e c ~ ] Fig. 2. T h e N a m o u n t a b s o r b e d vs. the s q u a r e root o f t h e r e a c t i o n time.

109

lowing equation: (1)

2 t X "2 = D t

where the mean square kX 2 of the displacement of N atoms is given as a result of brownian movement [16], D is the diffusion coefficient and t is the reaction time. The calculated diffusion coefficient D at 623 K for the sample with a particle size of 5 /zm was D = 2.5 × 10-12 cm2 S- 1 The pre-exponential factor Do of the diffusion coefficient was calculated from the following temperature dependence of D:

o=ooexp( ) where Q is the activation energy for the N diffusion and was assumed to be equal to 118.5 kJ (mol N atoms) -1 [9,11] as shown in Table 1 and R is the gas constant. From this, at 623 K, Do=2.2×10 -z was obtained. Then the diffusion coefficient of N in the pressure plateau region was obtained as D = 2 . 2 × 10-2 exp

(

]cmZs -

(3)

Using Eq. (3), the diffusion coefficients for the SmzFe~7N, sample with a particle size of 5 /xm were calculated at different temperatures and listed in Table 1 with the previously reported diffusion data [11]. Figs. 3 and 4 show the dependences of the N diffusivity D and the pre-exponential factor Do respectively on the particle size d. The apparent diffusivity markedly increases with decreasing particle size and tends to become constant for smaller particle sizes. A similar size dependence can be seen also in the change in Do. As can be seen in Table 1, the activation energy Q is almost constant and independent of the particle size. This effect cannot be attributed to the surface diffusion or grain boundary diffusion because these fast diffusion processes depend strongly on the particle size and the activation energies are much lower than that of lattice diffusion, which is measured from the growth rate of nitride layers in the grains. Thus the marked increase in D can be attributed to the increase in the preexponential factor Do. This result seems to be strongly connected with the induction of anisotropic internal stresses or strains in the lattice [2] and the generation of defects such as dislocations and microcracks in the samples with increasing N concentration. The arguments that the diffusion process may vary in the interactions of N atoms with such defects in the lattice, and that the interactions change depending on the sample size and the N concentration are now discussed.

H. Uchida et al. /Journal of Alloys and Compounds 222 (1995) 107-112

110

Table 1 T h e d e p e n d e n c e s of the N diffusion coefficient D, p r e - e x p o n e n t i a l factor Do a n d a c t i v a t i o n e n e r g y Q on the p a r t i c l e size of Sm2Fe17 s a m p l e s P a r t i c l e size d

D (cm / s -~)

(cm2 s-')

Q (kJ (mol N)-')

2.2X 1.6 X 4.8 X 1.0X 5.4 X

118.5 118.5 118.5 111.0 108.5

Do

(,~m) 5 <75 75-150 150-250 250-500

623 K

673 K

723 K

773 K

2.6X 1.8 X 5.5 X 4.9X 4.3 x

l A X 10 -H 1.0 X 10 -,2 3.0 X 1 0 - i3 2.4 X 10 -~3 2.0 x 10-13

6.0X 4.1 X 1.3 X 9.6X 7.5 X

2.2X 10 - m 1.5 X 10 - u 4.5 X 10-12 3.2X 10 -,2 2.4 X 1 0 - ,2

10 -12 10 -,3 1 0 - ,4 10 -,4 10-14

10 - u 10 -,2 1 0 - ,2 10 -13 10-13

10!

~ 1 773K

-10

~

10

r'~

Kaneko letat [13]

10 -2 10 -3 10 -4 10 -4 10-s

773K

C0eyetal~[20]~ .

NNN~ Coey

l [20

,-g • A • O

-14

10

0

10

773K 723K 673K 623K

% "~

J

i

10

10

1

Particle

2

¢"4E O t--.l O r-,,

10 3

3

10

size

Fig. 3. C h a n g e in the N diffusion coefficient D in Sm2Fe,7 as a f u n c t i o n o f the p a r t i c l e size d of Sm2Fe,7 s a m p l e . Kanek0 et al [13]

3.1. N diffusion at low N concentrations [N]/ [Sm2Fe17] <2 or at the initial stage in the growth of S m 2 F e 1 7 N x nitride layers with 0
105 10 0

, 10 1

, 10 2

, 10 a

Particle

size

d[ttm]

I 10 4

Fig. 4. C h a n g e in the p r e - e x p o n e n t i a l factor Do of the N a t o m s in SmzFe,7 as a f u n c t i o n of the particle size d of the SmzFe~7 sample.

interstitial H solubility [14]. In these less constrained samples, the diffusion of a first and second N atom in the 9e site occupancy would readily proceed under the less constrained condition. Additional evidence for the stress effect can be seen in the diffusion data obtained in a GDS study by Kaneko et al. [13]. Their data shown for D in Fig. 3 and for Do in Fig. 4 were obtained by measurement of the temporal change in the N distribution profile at the N concentration [N]/[SmzFe17] = 1.8 using a large block sample (greater than 1 cm) at the initial stage of the N uptake. This rate corresponds to the growth rate of the Sm2Fea7Na.8 nitride layer. The activation energy for the N diffusion was 66.1 kJ (mol N) -~ which is much lower than the data measured in the growth of the Sm2Fea7Nx nitride layers with 2
H. Uchida et al. / Journal of Alloys and Compounds 222 (1995) 107-112

1. The diffusion coefficients of 9 . 4 × 1 0 - n - 1 . 6 × 1 0 -9 cm2 s- 1 measured at 673-873 K and [N]/[Sm2Fe~7] = 1.8 are quite high compared with those measured at higher N concentrations and similar particle sizes of 102-103 tzm as shown in Fig. 3. In this GDS study, however, the high diffusivity resulted from the low activation energy rather than from the small pre-exponential factor Do, which was of the order of 10 -5 cm 2 s -1. The interpretation of the pre-exponential (frequency) factor Do is not simple. When a model based on interstitial diffusion through disordered lattices is considered [18], under the compressive stress, Do may also change by several orders of magnitude resulted from a slight increase in repulsive potential energy due to a change in the lattice distance. The surface or grain boundary effect may be omitted from the consideration because the GDS study was made by measuring temporal changes in N concentration. Thus the argument of the large effect of internal stress or strain on Do seems reasonable. Arother simple interpretation may be given from the change in the entropy term of Do. If the bonding of N to metal atoms is weakened, the vibrational frequency of ar N atom in an interstitial site decreases on considering the Einstein model for the N-metal atom bonding, and which increases the entropy term and Do. In this connection, the Do value measured by GDS was obtained at low N concentrations (i.e. [N]/[Sm2Fe17] < 2) and lhe sample was not under highly constrained conditions; the jump frequency and the bonding states of N to metal atoms may not be seriously influenced by the stress accumulation in the sample. 3.2. N diffusion at increased N concentrations 2 < [N]/ [SmeFelT] <3 or in the growth of the SmeFelTNx nitride layers with 2
As shown in Figs. 3 and 4, the diffusion data for Sm2Fea7N2.3 obtained by Coey et al. [19] are in good agreement with our data measured from the growth rate of nitride layers where the D and Do values obtained by Coey et al. were calculated using a particle size of about 1/,m [20] and D = 1.02 × 10 -2 e x p ( - 123000/RT) cm2 s -1 [19]. In Table 1, the activation energy Q slightly decreases (118.5--+108.5 kJ (mol N atoms) -1) with increasing sample size (5--+500 txm). This might be in good agreement with the generally accepted theory [18,21] that the pre-exponential factor is associated with Q or the energy barrier on the lattices. However, this change in Q is too small to affect Do. Therefore the marked dependence of D and Do seems to be attributed to the ease of lattice strain relaxation which depends on the particle size of the sample. As the N concentration is increased or the nitride layer grows, the induced stresses increase and accu-

1t 1

mulate. In the Sm2Fe17Nx nitride layers with 2 < x < 3 , the lattice seems to be highly constrained and the defect density may be almost saturated as can be seen in the inclined plateau pressures [2]. At such high N concentrations and high densities of defects, no difference may be present in the N chemical potentials between small powder and large block samples [2,14]. However, the activation energy for N diffusion in SmzFe17N, is constant and almost independent of the particle size as shown in Table 1. Therefore the predominant effect of the pre-exponential term Do on the diffusion coefficient D should be considered. As already mentioned, the increase in repulsive potential or weakened bonding of N to metal atoms by large lattice strains may cause the increase in Do. At high N concentrations, the effect of anelastic strains should also be considered because anelastic strains become large in the vicinity of equilibrium state or when interstitial atoms take fixed sites in the lattice [22]. The difference between the small and large particle samples with almost saturated defect densities may be the ease of relaxation of elastic and anelastic strains in the increasing N uptake. The relation between the diffusion coefficient D and the relaxation time r can be written [22] Do~ r -1

(4)

where r is the time that it takes the anelastic strain to fall to 1/e of its original strain and is directly proportional to the mean time of stay of an atom in an interstitial position. If r is large, the strain relaxes very slowly and interstitial diffusion is slow and, if r is small, the strain relaxes quickly and interstitial diffusion is fast. This relation is consistent with the jump frequency change in the pre-exponential factor depending on the sample size. For small particles, more elastic expansion of volume is possible in the additional N uptake, and the strain relaxation may also be easier, resulting in small r values and large D. The larger samples may have much higher anelastic strains in the lattice because these samples accumulate high densities of defects in the lattice with which N atoms interact. This yields a larger r value, resulting in a lower jump frequency and Do.

4. Conclusion

The N diffusion in Sm2Fea7 markedly depends on the particle size of the sample. The contribution of the pre-exponential factor of the diffusion coefficient, which is sensitive to anelastic internal stresses, is predominant. This may be attributed to the inductions and

112

H. Uchida et al. / Journal of Alloys and Compounds 222 (1995) 107-112

accumulations of defects such as strains, dislocations and microcracks in the sample on the N uptake. The diffusion data measured for the Sm2Fea7Nx samples with 2 < x < 3 indicate a diffusion process under highly constrained lattice conditions. The jump of a third N atom in the 9e site occupancy may proceed through the highly distorted and constrained Sm2Fe17N/lattice with 2
[7] [8] [9] [10]

[11]

[12]

Acknowledgment The authors are grateful to Kanagawa Academy of Science and Technology, Kanagawa, Japan, for financial support of this study.

[13]

[14]

References [1] G. Hoerz, in E. Gebhardt and E. Fromm (eds.), Gase und Kohlenstoff in Metallen, Springer, Berlin, 1976, p. 115. [2] H. Uchida, T. Yanagisawa, S. Kise, S. Tachibana, T. Kawanabe, Y. Matsumura, H.H. Uchida, V. Koeninger, H. Kaneko and T. Kurino, J. Alloys Comp., 222 (1995) 33. [3] V. Koeninger, U. Koike, K. Kamada, Y. Matsumura, T. Noguchi, T. Kurino, H. Kaneko, T. Yanagisawa, H.H. Uchida and H. Uchida, Z. Phys. Chem., 181 (1993) 299. [4] H. Uchida, Y. Ohtani, M. Ozawa, T. Kawahata and T. Suzuki, J. Less-Common Met., 172 (1991) 983. [5] H.H. Uchida, H. Uchida, T. Yanagisawa, S. Kise, T. Suzuki, Y. Matsumura, U. Koike, K. Kamada, T. Kurino and H. Kaneko, J. Alloys and Comp., 196 (1993) 71. [6] H.H. Uchida, H. Uchida, T. Yanagisawa, S. Kise, V. Koeninger, Y. Matsumura, U, Koike, K. Kamada, T. Kurino and H. Kaneko, Proc. 7th Int. Syrup. on Magnetic Anisotropy and Coercivity in

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[21] [22]

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