DETERMINATION OF THE DEGREE OF CRYSTALLITES ORIENTATION IN PERMANENT MAGNETS BY X-RAY SCATTERING AND MAGNETIC MEASUREMENTS

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DETERMINATION OF THE DEGREE OF

CRYSTALLITES ORIENTATION IN PERMANENT MAGNETS BY X-RAY SCATTERING AND

MAGNETIC MEASUREMENTS

D. Givord, A. Liénard, R. de la Bâthie, P. Tenaud, T. Viadieu

To cite this version:

D. Givord, A. Liénard, R. de la Bâthie, P. Tenaud, T. Viadieu. DETERMINATION OF THE

DEGREE OF CRYSTALLITES ORIENTATION IN PERMANENT MAGNETS BY X-RAY SCAT-

TERING AND MAGNETIC MEASUREMENTS. Journal de Physique Colloques, 1985, 46 (C6),

pp.C6-313-C6-317. �10.1051/jphyscol:1985656�. �jpa-00224911�

DETERMINATION OF THE DEGREE OF CRYSTALLITES ORIENTATION I N PERMANENT MAGNETS BY X-RAY SCATTERING AND MAGNETIC MEASUREMENTS

D.

Givord,

Lignard,

P e r r i e r de l a Bzthie,

~ e n a u d * and T. Viadieu

X,

R6sumB - ^{Les aimants} permanents s o n t e s s e n t i e l l e m e n t des compos4s ferromagnetiques e t uniaxiaux. C e r t a i n s aimants s o n t Blabores en f r i t t a n t d e s poudres prealablement o r i e n t 6 e s e t comprim6es sous champ. La v a l e u r de l ' i n d u c t i o n remanente Br depend directement du degrd d'alignement des c r i s t a l l i t e s e t nous prgsentons dans c e t a r t i c l e deux mdthodes q u a n t i t a t i v e s d i f f e r e n t e s pour l e d8terminer.Ltanalyse aux rayons X permet de comparer l e s i n t e n s i t e s des r e f l e x i o n s de Bragg pour l e s d i f f e r e n t e s v a l e u r s de l ' a n g l e e n t r e une d i r e c t i o n [ h k l l e t l ' a x e c r i s t a l l o g r a p h i q u e p r i n c i p a l . L'analyse magnetique permet de comparer l e s courbes d'aimantation experimentales e t c e l l e s c a l c u l 8 e s , pour d i f f e r e n t e s d i s t r i b u t i o n s s t a t i s t i q u e s des o r i e n t a t i o n s des g r a i n s . Les deux methodes ont 6 t 6 appliquees & des aimants Nd-Fe-B e t SmCo5. E l l e s r e v e l e n t que l a d e s o r i e n t a t i o n des p a r t i c u l e s dans c e s systSmes conduit b une r e d u c t i o n d'environ 10 % de l ' i n d u c t i o n remanente.

Abstract - Permanent magnet compounds a r e b a s i c a l l y ferromagnets with u n i a x i a l a n i s o t r o p y . I n d i f f e r e n t c a s e s , the magnets a r e e l a b o r a t e d by s i n t e r i n g of powders previously o r i e n t e d and compressed under f i e l d . The value of t h e remanent induction Br is d i r e c t l y dependent on t h e degree of c r y s t a l l i t e s alignment, and we present i n t h i s paper two d i f f e r e n t q u a n t i t a t i v e methods t o determine i t . X-ray a n a l y s i s involves t h e comparison of t h e i n t e n s i t i e s of Bragg r e f l e c t i o n s , f o r d i f f e r e n t values of t h e angle of a d i r e c t i o n [hkl] with r e s p e c t t o the unique c r y s t a l l o g r a p h i c a x i s of t h e compound. Magnetic a n a l y s i s involves t h e comparison between experimental magnetization curves and c a l c u l a t e d ones f o r d i f f e r e n t s t a t i s t i c a l d i s t r i b u t i o n s of c r y s t a l l i t e s o r i e n t a t i o n s . Both methods were applied t o NdFeB and SmCo5 magnets. They r e v e a l t h a t t h e m i s o r i e n t a t i o n of p a r t i c l e s i n t h e s e systems l e a d s t o a r e d u c t i o n of t h e remanent induction

about 10 8 .

I - INTRODUCTION

Permanent magnet compounds a r e b a s i c a l l y ferromagnets with u n i a x i a l anisotropy. The c o e r c i v i t y of the magnets, c l o s e l y r e l a t e d t o t h i s a n i s o t r o p y , develops i n m a t e r i a l s which a r e inhomogeneous a t a microscopic s c a l e . Such a property

i n p a r t i c u l a r obtained i n f e r r i t e s and r a r e e a r t h - t r a n s i t i o n metal magnets, by s i n t e r i n g of powders previously o r i e n t e d and compressed under f i e l d . The value of t h e remanent induction

is d i r e c t l y dependent on t h e degree of c r y s t a l l i t e s alignment.

quick method t o determine a n average value of t h e i r degree of alignment c o n s i s t s i n measuring t h e remanent induction Br of t h e magnet with r e s p e c t t o t h e spontaneous induction of t h e compound / I / . We p r e s e n t i n t h i s paper a more q u a n t i t a t i v e a n a l y s i s of t h e s t a t i s t i c a l d i s t r i b u t i o n of g r a i n s o r i e n t a t i o n , which was obtained by X-ray a n a l y s i s and magnetostatic measurements, on NdFeB and SmCo5 magnets.

I1 - ^X-RAY DETERMINATION OF THE DEGREE OF G R A I N ALIGNMENT

For a r e f l e c t i o n Q k l , Bragg s c a t t e r i n g occurs i f t h e d i r e c t i o n [hkl] is along t h e s c a t t e r i n g v e c t o r K , defined a s t h e b i s s e c t r i c e of t h e angle between t h e d i r e c t i o n of the i n c i d e n t beam and t h a t of the s c a t t e r e d beam. I n a p o l y c r y s t a l l i n e sample, i n

* p a r t l y supported by a fellowship from "Aimants UGIMAG S.A.", France

JOURNAL DE PHYSIQUE

6

8 Nd-Fe-B magnet

3

i

Fig. 1 - X-ray diffractogram of a Nd-Fe-B magnet obtained with t h e Co r a d i a t i o n

1.7903

which c r y s t a l l i t e s o r i e n t a t i q n s a r e p e r f e c t l y a t random, t h e p r o b a b i l i t y f o r any d i r e c t i o n [ h k l l t o be along

c o n s t a n t . I n t h e case of a s i n g l e c r y s t a l 4 i t is necessary t o a d j u s t t h e c r y s t a l o r i e n t a t i o n i n o r d e r t o a l i g n [hkl] along K.

Permanent magnets e l a b o r a t e d by s i n t e r i n g of powders, can be,considered a s an assembly of s i n g l e c r y s t a l s , f o r which t h e c r y s t a l l o g r a p h i c c-axes, i . e . t h e d i r e c t i o n s [0011 of t h e r e c i p r o c a l space, a r e d i s t r i b u t e d w%thin a c e r t a i n s o l i d angle. I f t h e a x i s of t h e s o l i d a n g l e , z , is a l i g n e d along K,+the p r o b a b i l i t y p(w

f o r c r y s t a l l o g r a p h i c c-axes t o be along a

given d i r e c t i o n a t an angle

with r e s p e c t t o

is simply equal t o t h e p r o b a b i l i t y f o r a d i r e c t i o n Lhkl] a t an+angle whkl

from COO11 t o be along

Thus t h e compa- r i s o n of the i n t e n s i t y of a r e f l e c t i o n

[hkl], ~ ~ t o t h a t observed i n a ~ g ~ ~ ~ , p o l y c r y s ~ ! $ ~ l i n e sample, 01y, is a measu-

rement of the

along any d i r e c t i o n a t w// from

We used t h i s method t o determine t h e degree of g r a i n alignment i n Nd-Fe-B and SmCog magnets. X-ray diffractograms were recorded on s l i c e s of Nd-Fe-B permanent magnets, c u t a t d i f f e r e n t t h i c k n e s s e s p e r p e n d i c u l a r l y t o

z .

The r e s u l t s obtained show t h a t t h e degree

of g r a i n alignment is a c o n s t a n t over t h e volume of t h e magnet, except on a very t h i n s k i n of about 0.1 mm a t the s u r f a c e . Typical X-ray p a t t e r n i s presented i n f i g u r e 1 . Comparison t o the i n t e n s i t i e s measured on a non-oriented powder /2,3/ l e a d s t o t h e determination of Ima net/lpoly which i s

hkB hkl

C

p l o t t e d a s a f u n c t i o n of whkl

c V

A s shown i n f i g u r e 3, the decrease of Fig.

- ~ m a g n e t / ~ P o l Y a s f u n c t i o n of

Ib,fnet/ipoly

hkl hkl

the angle whkl between d i r e c t i o n s Lhkll hkl and C0011.

"the sample Of SmCog was kindly provided t o u s by "Aimants

S.A."

angle s m a l l e r tQan 55O with r e s p e c t t o t h e z-axis of t h e magnet. However, t h e

observation of weak r e f l e c t i o n s with w// > 45O r e v e a l s a n a d d i t i o n a l small c o n t r i b u t i o n of another gaussian with

36O, corresponding t o a much broader d i s t r i b u t i o n of c r y s t a l l i t e s o r i e n t a t i o n

(Figure 3 ) . The proportion of

approximately 15

of t h e t o t a l number of c r y s t a l l i t e s . This property can be

understood by considering

0 4000 8000

t h a t a proportion of

c r y s t a l l i t e s obtained a f t e r Fig. 3 -

dependence of t h e logarithm of grinding of t h e bulk i n g o t s normalized Bragg r e f l e c t i o n s i n Nd-Fe-B and a r e not s i n g l e c r y s t a l s . Such

SmCo5 magnets. c r y s t a l l i t e s a r e not

e f f i c i e n t l y o r i e n t e d i n t h e f i e l d a p p l i e d during the compression.

The same a n a l y s i s was performed f o r a SmCo5 magnet. The r e s u l t s a r e presented i n f i g u r e s

and 3. Very s i m i l a r r e s u l t s a r e obtained. The main gaussian d e s c r i b i n g t h e s t a t i s t i c a l d i s t r i b u t i o n of g r a i n s o r i e n t a t i o n is determined by a

14". The

accuracy of the r e s u l t s is not s u f f i c i e n t t o r e v e a l a p o s s i b l e a d d i t i o n a l contribu- t i o n from another gaussian d e s c r i b i n g a broader d i s t r i b u t i o n of g r a i n s o r i e n t a t i o n . Such a c o n t r i b u t i o n is i n any case much weaker than i n NdFeB, and suggests t h e r e f o r e t h a t , i n SmCo5 magnets, almost a l l g r a i n s can be considered a s s i n g l e c r y s t a l s .

-

DETERMINATION OF

OF GRAINS ALIGNMENT

The f i e l d dependence of t h e magnetization of an u n i a x i a l s i n g l e - c r y s t a l l i n e compound h a s been z a l c u l a t e d by N6el e t a 1

f o r any angle between t h e applied f i e l d and t h e easy c-axis. The f i r s t magnetization curve can be divided i n t o two p a r t s a s s o c i a t e d with d i f f e r e n t p h y s i c a l processes. I n low f i e l d s , t h e c r y s t a l i s

decomposed i n t o s e v e r a l domains, and t h e magnetization measured along t h e f i e l d H i s

2 2

m(4, H )

H x ~ ~ C c o s 4/HD

s i n $/(HD

HA)]

1

where MS is t h e spontaneous magnetization, HD t h e demagnetizing f i e l d f o r s a t u r a t e d magnetization and HA t h e anisotropy f i e l d . The magnetization follows t h i s law u n t i l a threshold f i e l d , Hs($), f o r which t h e c r y s t a l becomes s i n g l e domain. Above

t h e angle

between t h e magnetization and t h e easy a x i s is given by

and the magnetization measured along the f i e l d is

The c a l c u l a t e d r e c o i l magnetization curve, assuming t h a t t h e c o e r c i v i t y impedes t h e n u c l e a t i o n of r e v e r s e domains, corresponds t o t h e second process alone.

A s described i n t h e previous s e c t i o n , t h e permanent magnets considered h e r e a r e

formed of independent c r y s t a l l i t e s whose easy axes a r e d i s t r i b u t e d about a p r e f e r r e d

d i r e c t i o n

When t h e f i e l d is a p p l i e d along z , c r y s t a l l i t e s which make t h e same

angle

with r e s p e c t t o z , i . e . with r e s p e c t t o t h e f i e l d , e x h i b i t i d e n t i c a l

magnetization law. The number of C r y s t a l l i t e S between w// and w//+ is obtained

by i n t e g r a t i n g over a around t h e z-axis

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where p(wN) is t h e s t a t i s t i c a l d i s t r i b u t i o n o f c r y s t a l l i t e s . When t h e f i e l d is a p p l i e d p e r p e n d i c u l a r t o z , t h e c r y s t a l l i t e s behaving i d e n t i c a l l y make t h e same a n g l e w w i t h r e s p e c t t o t h e f i e l d . The number o f c r y s t a l l i t e s between w and

+

d d i s

I

I

w i t h w// depending on a t h r o u g h

c o s w l

s i n w// x c o s a ( 6 )

I n Both c a s e s , t h e c a l c u l a t e d m a g n e t i z a t i o n of t h e magnet is t h e r e f o r e

r r / 2

where m ( w , H) is deduced from r e l a t i o n s

t o ( 3 ) w i t h

o r Y depending whether t h e f i e l d is a l o n g o r p e r p e n d i c u l a r t o H.

S u b s e q u e n t l y , t h i s method was u s e d t o deduce t h e d e g r e e o f g r a i n s o r i e n t a t i o n from m a g n e t i c measurements. The f i e l d dependence o f t h e m a g n e t i z a t i o n f o r a Nd-Fe-B magnet, under f i e l d s a p p l i e d r e s p e c t i v e l y a l o n g z and p e r p e n d i c u l a r t o z , a r e p r e s e n t e d i n f i g u r e 4 . S a t i s f a c t o r y agreement between c a l c u l a t e d f i r s t m a g n e t i z a t i o n c u r v e s and e x p e r i m e n t a l r e s u l t s c a n b e o b t a i n e d i f c o n s i d e r i n g a unique g a u s s i a n d i s t r i b u t i o n f o r p(w//). However a b e t t e r f i t is o b t a i n e d w i t h t h e s u p e r p o s i t i o n o f

M (uem / g )

150 -

Nd-Fe-B magnet

100-

.

T=300 K

SmCog magnet

T=300 K

Fig.

- Experimental (---I and F i g . 5 - Experimental

and c a l c u l a t e d c a l c u l a t e d

m a g n e t i z a t i o n c u r v e s

m a g n e t i z a t i o n c u r v e s o f a SmCo5 o f a NdFeB magnet. C a l c u l a t i o n p a r a - magnet. C a l c u l a t i o n p a r a m e t e r s

m e t e r s

M,

150 e.m.u./g, M,

98 e.m.u./g, HA

350 kOe.

HA

7 3 k0e.

two g a u s s i a n s w i t h a

and

28O, and r e s p e c t i v e weight 90

and 10 % ( F i g u r e

The d i f f e r e n c e s between e x p e r i m e n t a l a n d c a l c u l a t e d m a g n e t i z a t i o n c u r v e s i n i n t e r m e d i a t e f i e l d s c a n b e a t t r i b u t e d t o t h e i n h o m o g e n e i t i e s o f t h e demagnetizing f i e l d i n t h e c u b i c specimen s t u d i e d , a s v e r i f i e d by measuring a n Fe sample of i d e n t i c a l s h a p e .

A

same a n a l y s i s f o r SmCog magnet is p r e s e n t e d i n f i g u r e 5. The c a l c u l a t e d c u r v e s

were o b t a i n e d f o r a main

g a u s s i a n w i t h

and a weak a d d i t i o n a l

c o n t r i b u t i o n ( 5

w i t h

30°.

obtained. The r e d u c t i o n of t h e remanent induction B,, due t o misalignment of t h e g r a i n s , reaches about 10 i n both Nd-Fe-B and SmCo5 magnets. Comparing both

methods, X-ray a n a l y s i s is more q u a n t i t a t i v e , but not a s e a s y t o r e a l i z e a s magnetic a n a l y s i s . I t is worth r e c a l l i n g t h a t t h e usual way t o determine g r a i n s o r i e n t a t i o n involves a d i r e c t measurement of B,. The r e s u l t may be a f f e c t e d by a p o s s i b l e decrease of t h e induction r e s u l t i n g from domain n u c l e a t i o n i n g r a i n s of small c o e r c i v i t y . The measurement of t h e f i r s t magnetization curve considered i n t h i s s t u d y , is obviously not a f f e c t e d by such a phenomenon. F i n a l l y , a s t r a i g h t

g e n e r a l i z a t i o n of t h i s method would permit a more q u a n t i t a t i v e a n a l y s i s of magnetic p r o p e r t i e s i n u n i a x i a l systems where s i n g l e c r y s t a l s a r e not a v a i l a b l e /3,5/.

REFERENCES

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Appl. Phys. 52

(1981) 73'14.

/2/

Sagawa, M., Fujimura, S., Yamamoto, H. Matsuura.

and Hiraga,

I.E.E.E.

Trans. Mag. 20 ( 5 ) (1984) 1584.

/3/ Sinnema, S.. Radwanski, R.J., Franse,

.J.M., de Mooij,

and Buschow, K.H.J., J . Magn. Magn. Mat. 44 (198'1) 333.

/'1/

Nkel, L . , Pauthenet,

Rimet, G., son, ^V.S.,

Appl. Phys. 2 Suppl.,

(1960).

/5/ DBportes, J . , T h e s i s , University of Grenoble (1977).