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The value of the spontaneous magnetization of binary nickel alloys as a function of temperature
Physica X V I I , no 6
J uni 1951
T H E VALUE OF T H E SPONTANEOUS MAGNETIZATION OF BINARY NICKEL ALLOYS AS A FUNCTION OF T E M P E R A T U R E b y J. J. W E N T *) Natuurkundig Laboratorium N.V. Philips' Gloeilampenfabrieken,Eindhoven, Nederland
Synopsis The I s versus T curve for pure nickel is more concave towards the T-axis than that for any binary nickel alloy, with only one exception, viz. completely ordered alloys, such as slowly-cooled Ni3Fe. For pure nickel the form of the I s vs T curve can be explained by the occurrence of an order-disorder phenomenon of the magnetic moments where.the latter can be placed only parallel or anti-parallel. It is suggested that all the other I s vs T curves must be explained as being a result of this order-disorder phenomenon and the statistical fluctuations of the concentration of dissolved atoms. In the case of Ni3Fe two different order-disorder phenomena (a crystallographic and a magnetic) act simultaneously. § 1. T h e value of the s p o n t a n e o u s m a g n e t i z a t i o n decreases cont i n u o u s l y as a function of t e m p e r a t u r e until the Curie t e m p e r a t u r e is reached. At the Curie t e m p e r a t u r e the s p o n t a n e o u s m a g n e t i z a t i o n d i s a p p e a r s c o m p l e t e l y , which m e a n s t h a t the long-range a r d e r of the m a g n e t i c m o m e n t s is destroyed. Since this Curie point is related to an order-disorder t r a n s f o r m a t i o n , it is a so-called t r a n s f o r m a t i o n of t h e second order. T h e r e is a p e a k in the specific h e a t b u t no h e a t of t r a n s f o r m a t i o n is found. M e a s u r e m e n t s on p u r e nickel b y W e i s s and Forrerl), on p u r e iron b y W e i s s and Forrer 2) a n d b y P o t t e r 3 ) , a n d on a p u r e single c r y s t a l of cobalt m e a s u r e d in the direction of p r e f e r r e d m a g n e t i z a t i o n b y M y e r s and Sucksmith4) show t h a t in all these cases there is a relation b e t w e e n the spont a n e o u s m a g n e t i z a t i o n a n d the t e m p e r a t u r e , which can fairly well be described b y t h e Brillouin f u n c t i o n I r / I o = B s ( a S 13 I o / k T ) if for t h e spin q u a n t u m - n u m b e r S the value ½ is chosen. I n this f o r m u l a *) Present address: N.V.K.E.M.A., Arnhem, Nedcrland. - - 596 - -
MAGNETIZATIONOF NICKEL ALLOYSAS FUNCTION OF TEMPERATURE 597 I T and I 0 represent the values of the spontaneous m a g n e t i z a t i o n
respectively at T and 0 ° K ; B,(x) = (2S + l ) / 2 S . t g h {(2S + 1)/2 S . x } - - 1/2 S . t g h {1/2 S . x } ; a = c o n s t a n t of the Weiss molecular field; fl = the magnetic m o m e n t of one B o h r magneton. T h e value S = ½ means t h a t only two positions of the spins, parallel and anti-parallel, are admissible. Minor systematic deviations from this Brillouin function observed in the case of pure metals are not t a k e n into consideration because the p h e n o m e n a mentioned in this p a p e r show m u c h larger deviations. § 2. F o r a large n u m b e r of b i n a r y nickel-alloys in which different a m o u n t of Cu, Pd, Co, Fe, Mn, Cr, Mo, W,' V, A1, Si or Sn are disI.G
=
a5
Fig. 1. I s vs T curves in reduced coordinates for pure nickel and a nickel alloy with 9.2 at % Si. The two asterisks indicate the two points of the theoretical curves for S = ½ and S = co. 0.5
ZO
solved it was found, without exception, t h a t the I s vs T curves when drawn on a reduced induction vs t e m p e r a t u r e scale ( I ~ / I o vs T/Tc) are less concave towards the t e m p e r a t u r e axis t h a n the same curve for pure nickel, iron or cobalt 5). In fig. 1 two e x t r e m e cases are given, viz. the curves for pure nickel and for a Ni - - Si alloy. If the numerical value Q at which 17-/lo = T / T c = Q is t a k e n as a measure for the shape of the curve (fig. 1), the results of all our experiments can be collected in one single diagram (fig. 2). In this diagram the Q value is given as a function of the atomic composition for different b i n a r y systems. The following points are of interest, starting from the fact t h a t the pure nickel curve with Q = 0.765 can be described fairly well with formula (1) with S -- ½, which formula results in Q = 0,755.
598
J . J . WENT
1. A l l Is vs T curves are less concave towards the x-axis than the pure nickel curve; the Q-value decreases continuously, and usually even roughly linearly with an increasing amount of the alloying element. 2. For a specific atomic percentage of the alloying element Q decreases in the order given in the series of elements C o - F e Mn - - Cr. 3. The Q-values become ver y small, even much smaller than can be calculated from the Brillouin function with S = oo, for a 0.8
/_z=_ TM
0.7
Cb
"~Mn
a~
w si
O2
0
~9
20
ato~ ~ic % I
Fig. 2. Q-value of homogeneous nickel alloys as a function of the concentration of different dissolved elements. For a nickel-iron alloy with the composition Ni3Fe two points are given for the ordered and disordered state respectively. high amount of an alloying element without a magnetic moment, such as Si. The shape of the I , vs T curve is altered in such a way t h a t in the neighbourhood of the Curie temperature only a very gradual decrease of saturation with temperature is found. An explanation of these experimental facts can be given b y assuming that t h e y are due to the statistical fluctuations of the concentration of the dissolved atoms in a solid solution .However,
MAGNETIZATION OF NICKEL ALLOYS AS F U N C T I O N OF T E M P E R A T U R E 5 9 9
if such fluctuations determines the change in the shape of the I s vs T curve, a crystaUographically ordered alloy must possess a curve much more like t h a t of pure nickel than the same curve of the same alloy in the disordered state. In order to verify this Ni3Fe was investigated in the ordered and disordered form. In order to Obtain the ordered state an extremely pure Ni-Fe alloy of the correct atomic composition, prepared by sintering a mixture of carbonyl nickel and carbonyl iron, is heated during one hour at 800°C and then quenched in cold water; it is heated again to 490°C and then during 260 hours slowly cooled down to 450°C. In order to obtain the disordered state the same sample is heated again at 800°C and quenched in cold water. The comparison of the I s vs T curves, however, is difficult since the Curie temperature of the disordered state is about 600°C, which is higher than the order-disorder transformation temperature of Ni3Fe, which lies in the neighbourhood of 500°C. Therefore it is impossible to measure the Curie temperature of the ordered state, because only the Curie temperature of the disordered state is found. A rather pronounced change of the slope in the I s vs T curve for the ordered state at about 500°C is found. The direction of this discontinuity shows a pronounced bend towards the temperature axis and suggests t h a t the Curie temperature of the ordered state is 1.0
~~
Fig. 3. I s vs T curves in reduced coordinates for Ni3Fe in the disordered state (curve a) and in the ordered state (curbe b or b'). For curve b' the experimental Curie temperatures has been used, this being the Curie temperature of the disordered state; curve b, with a hypothetical Curie temperature, about 50° higher to satisfy the theoretical curve with S = ½.
'
0.5
T
-'We 0
a5
i.o
higher than that of the disordered state (fig. 3). A reliable reduction to T / T s for the ordered state is therefore impossible. It is even to be expected, as is indeed found, that by using the Curie temperature of the disordered state a higher Q-value will result for the incorrectly
600
j . j . WENT
reduced curve relative to the ordered state t h a n with the value for pure nickel (0.785 instead of 0.775). A reduction of this Q-value to t h a t of pure nickel corresponds to an increase of the Curie t e m p e r a ture of a b o u t 50°C. F o r the disordered state of the same alloy a Q-value of 0.735 is found. Thus there is strong evidence t h a t the I s vs T curve of an alloy in the ordered state is indeed m u c h more concave towards the T-axis t h a n is the case for the same alloy in the disordered state. As already mentioned, we assume t h a t the large m e a s u r e d deviations from the theoretical curve with S = ½ are related to fluctuations in the local c o n c e n t r a t i o n of the solid atoms. § 3. W e m a y suggest the following two possibilities regarding the physical b a c k g r o u n d responsible f~r this influence. F o k k e r has calculated the change of order-disorder p h e n o m e n a which take place when t h e n u m b e r of particles to be ordered is m a d e v e r y small s). As a result of such calculations it is to be e x p e c t e d t h a t in the n e i g h b o u r h o o d of the Curie t e m p e r a t u r e the order-disorder 1.0
0£"
x
~.all
0
05
~0
1.5
Fig. 4. aa' Theoretical I, vs T curve for S = ½. aa" Curve a with a large tail corresponding to a deviation connected with very small ferromagnetic particles. b Reduced curve aa'" t r a n s f o r m a t i o n is a v e r y gradual function of t e m p e r a t u r e as shown in fig. 4 (dotted line). This effect is large for isolated particles with a small n u m b e r of atoms or, in our case, a small n u m b e r of magnetic moments, and small for large particles with m a n y atoms. If the new
MAGNETIZATION OF NICKEL ALLOYS AS FUNCTION OF TEMPERATURE 601
order-disorder curve with its tail a a " is reduced on the same T I T c scale as used for the normal order-disorder transformation curve, a less convex curve b results, as indicated by the flat curve in fig. 4. The form of this new curve is very much the same as that of the curve for the Ni-Si alloy shown in fig. 1. Of course this reduction is somewhat artificial owing to an incorrect Curie temperature being used. Now it seems possible that similar effects are present in our nickel alloys. Although ferromagnetism is a long-range order effect, it is well known that the electrostatic interaction responsible for the magnetic ordering in nickel is an interaction between nearest neighbours only. If the fluctuations in the concentration of the dissolved foreign atoms were such that small isolated particles of pure nickel exist, this Fokker effect must be present. Although such a fluctuation is highly improbable, the formation of partly closed regions containing a small number of Ni atoms is quite possible. It is probable that these partly closed regions will show an effect similar to that mentioned above as calculated by F o k k e r. Taking this effect into account, pure nickel, iron or cobalt must show I s v s T curves more convex towards the T-axis than disordered Ni alloys. On the other hand I s v s T curves for completely ordered alloys must be comparable with the curves for pure ferromagnetic metals, in close agreement with our observations on Ni3Fe. It is immediately clear that the Fokker effect, if present, must be stronger for large amounts of foreign atoms than for small amounts; the undisturbed regions of Ni atoms are smaller. It is also probable that this effect is more pronounced for foreign atoms not having a magnetic moment themselves like Si, than for these with a magnetic moment like Co. In the first case the Ni regions are more isolated. The great difference between the influence of Si and A1, both atoms without a magnetic moment, may be related with the extremely large heat of formation of Ni-A1. Therefore it is improbable that two A1 atoms will be neighbours ; at higher Ni contents a strong tendency to a crystallografic ordering exists and large fluctuations in these Ni-A1 alloys, responsible for the flat I s v s T curve, are not present. Goldman and S m o l u c h o w s k y ~ ) have g i v e n a q u a l i t a tive explanation of the change in saturation magnetization, Curie temperature and magnetostriction observed when crystallographically ordered alloys are disordered. They consider the fluctuation
602
MAGNETIZATION OF N I C K E L ALLOYS AS F U N C T I O N OF T E M P E R A T U R E
of the exchange force acting on an atom with a magnetic moment caused by the nearest neighbours to fluctuations of the type of surrounding atoms. If a nickel atom is surrounded by 12 nearest Ni atoms this exchange energy must be larger than when it is surrounded by 11 Ni atoms and one Si atom. This exchange energy is a direct measure for the value of the Curie temperature. N ~ e 111) has calculated the influence of fluctuations of the W e i s z molecular field on the spontaneous magnetization in the neighbourhood of the Curie temperature. This kind of reasoning just as the calculations of F o k k e r w h i c h are not independent m a y explain the facts observed in this paper. In two respects, even for pure nickel, small deviations from the theoretical curve with S = ½ are observed. For low temperature the value of the spontaneous magnetization is slightly too high and for high temperatures too low. Furthermore a small tail is found above the Curie temperature 8). According to the picture given above this small tail is perhaps related to dislocations and m a y then be explained in a similar way as suggested above. Finally it is of interest to note t h a t such deformations of the I s v s T curves are not confined to metallic ferromagnetic alloys alone. Similar effects are present in the ferromagnetic oxides. The I s v s T curve for pure Ni is more convex towards the T-axis than those for Mn or Ni ferrites, while mixed MnZn or NiZn ferrites are even more flat 9). N 6 e 1 ~o) has calculated the shape of the I s v s T curve for these ferrites. His values should be compared with the experimental data however only after a correction for the ~tbovementioned effects. Eindhoven, 1st December 1950. Received 13-2-51. REFERENCES l) 2) ;3) 4) 5) 6) 7) 8) 9) 10) 11)
W e i s s , P. and F o r r e r , R., Ann. de Phys. 5(1926)153. W e i s s , P. and F o r r e r , R., Ann. d e P h y s , l°(1929) 279. Potter, H . H . , Proc. roy. Soc. A. 146(1934) 362. S u c k s m i t h, W., Communications Conference on Magnetism, Grenoble 1950. W e n t, J. J., Physica 17 (1951) 98; in this paper more experimental details are described. Fokker, A . D . , Physiea 8 (1941) 109 and 159. Goldman, J. E. and S m o l u c h o w s k y , R., Phys. Rev. ~5 (1949) 140. Gerlach, W., Z. Elektroehemie 45 (1939) 151. Guillaud, Ch. and R o u x , M., C.R. Ac. Sc. Paris °21J (1949)1133. N 6 e l , L., Ann. de Phys. 3 (1948) 137. N 6 e l , L., J. Physique, 5 1934 104.
J uni 1951
T H E VALUE OF T H E SPONTANEOUS MAGNETIZATION OF BINARY NICKEL ALLOYS AS A FUNCTION OF T E M P E R A T U R E b y J. J. W E N T *) Natuurkundig Laboratorium N.V. Philips' Gloeilampenfabrieken,Eindhoven, Nederland
Synopsis The I s versus T curve for pure nickel is more concave towards the T-axis than that for any binary nickel alloy, with only one exception, viz. completely ordered alloys, such as slowly-cooled Ni3Fe. For pure nickel the form of the I s vs T curve can be explained by the occurrence of an order-disorder phenomenon of the magnetic moments where.the latter can be placed only parallel or anti-parallel. It is suggested that all the other I s vs T curves must be explained as being a result of this order-disorder phenomenon and the statistical fluctuations of the concentration of dissolved atoms. In the case of Ni3Fe two different order-disorder phenomena (a crystallographic and a magnetic) act simultaneously. § 1. T h e value of the s p o n t a n e o u s m a g n e t i z a t i o n decreases cont i n u o u s l y as a function of t e m p e r a t u r e until the Curie t e m p e r a t u r e is reached. At the Curie t e m p e r a t u r e the s p o n t a n e o u s m a g n e t i z a t i o n d i s a p p e a r s c o m p l e t e l y , which m e a n s t h a t the long-range a r d e r of the m a g n e t i c m o m e n t s is destroyed. Since this Curie point is related to an order-disorder t r a n s f o r m a t i o n , it is a so-called t r a n s f o r m a t i o n of t h e second order. T h e r e is a p e a k in the specific h e a t b u t no h e a t of t r a n s f o r m a t i o n is found. M e a s u r e m e n t s on p u r e nickel b y W e i s s and Forrerl), on p u r e iron b y W e i s s and Forrer 2) a n d b y P o t t e r 3 ) , a n d on a p u r e single c r y s t a l of cobalt m e a s u r e d in the direction of p r e f e r r e d m a g n e t i z a t i o n b y M y e r s and Sucksmith4) show t h a t in all these cases there is a relation b e t w e e n the spont a n e o u s m a g n e t i z a t i o n a n d the t e m p e r a t u r e , which can fairly well be described b y t h e Brillouin f u n c t i o n I r / I o = B s ( a S 13 I o / k T ) if for t h e spin q u a n t u m - n u m b e r S the value ½ is chosen. I n this f o r m u l a *) Present address: N.V.K.E.M.A., Arnhem, Nedcrland. - - 596 - -
MAGNETIZATIONOF NICKEL ALLOYSAS FUNCTION OF TEMPERATURE 597 I T and I 0 represent the values of the spontaneous m a g n e t i z a t i o n
respectively at T and 0 ° K ; B,(x) = (2S + l ) / 2 S . t g h {(2S + 1)/2 S . x } - - 1/2 S . t g h {1/2 S . x } ; a = c o n s t a n t of the Weiss molecular field; fl = the magnetic m o m e n t of one B o h r magneton. T h e value S = ½ means t h a t only two positions of the spins, parallel and anti-parallel, are admissible. Minor systematic deviations from this Brillouin function observed in the case of pure metals are not t a k e n into consideration because the p h e n o m e n a mentioned in this p a p e r show m u c h larger deviations. § 2. F o r a large n u m b e r of b i n a r y nickel-alloys in which different a m o u n t of Cu, Pd, Co, Fe, Mn, Cr, Mo, W,' V, A1, Si or Sn are disI.G
=
a5
Fig. 1. I s vs T curves in reduced coordinates for pure nickel and a nickel alloy with 9.2 at % Si. The two asterisks indicate the two points of the theoretical curves for S = ½ and S = co. 0.5
ZO
solved it was found, without exception, t h a t the I s vs T curves when drawn on a reduced induction vs t e m p e r a t u r e scale ( I ~ / I o vs T/Tc) are less concave towards the t e m p e r a t u r e axis t h a n the same curve for pure nickel, iron or cobalt 5). In fig. 1 two e x t r e m e cases are given, viz. the curves for pure nickel and for a Ni - - Si alloy. If the numerical value Q at which 17-/lo = T / T c = Q is t a k e n as a measure for the shape of the curve (fig. 1), the results of all our experiments can be collected in one single diagram (fig. 2). In this diagram the Q value is given as a function of the atomic composition for different b i n a r y systems. The following points are of interest, starting from the fact t h a t the pure nickel curve with Q = 0.765 can be described fairly well with formula (1) with S -- ½, which formula results in Q = 0,755.
598
J . J . WENT
1. A l l Is vs T curves are less concave towards the x-axis than the pure nickel curve; the Q-value decreases continuously, and usually even roughly linearly with an increasing amount of the alloying element. 2. For a specific atomic percentage of the alloying element Q decreases in the order given in the series of elements C o - F e Mn - - Cr. 3. The Q-values become ver y small, even much smaller than can be calculated from the Brillouin function with S = oo, for a 0.8
/_z=_ TM
0.7
Cb
"~Mn
a~
w si
O2
0
~9
20
ato~ ~ic % I
Fig. 2. Q-value of homogeneous nickel alloys as a function of the concentration of different dissolved elements. For a nickel-iron alloy with the composition Ni3Fe two points are given for the ordered and disordered state respectively. high amount of an alloying element without a magnetic moment, such as Si. The shape of the I , vs T curve is altered in such a way t h a t in the neighbourhood of the Curie temperature only a very gradual decrease of saturation with temperature is found. An explanation of these experimental facts can be given b y assuming that t h e y are due to the statistical fluctuations of the concentration of the dissolved atoms in a solid solution .However,
MAGNETIZATION OF NICKEL ALLOYS AS F U N C T I O N OF T E M P E R A T U R E 5 9 9
if such fluctuations determines the change in the shape of the I s vs T curve, a crystaUographically ordered alloy must possess a curve much more like t h a t of pure nickel than the same curve of the same alloy in the disordered state. In order to verify this Ni3Fe was investigated in the ordered and disordered form. In order to Obtain the ordered state an extremely pure Ni-Fe alloy of the correct atomic composition, prepared by sintering a mixture of carbonyl nickel and carbonyl iron, is heated during one hour at 800°C and then quenched in cold water; it is heated again to 490°C and then during 260 hours slowly cooled down to 450°C. In order to obtain the disordered state the same sample is heated again at 800°C and quenched in cold water. The comparison of the I s vs T curves, however, is difficult since the Curie temperature of the disordered state is about 600°C, which is higher than the order-disorder transformation temperature of Ni3Fe, which lies in the neighbourhood of 500°C. Therefore it is impossible to measure the Curie temperature of the ordered state, because only the Curie temperature of the disordered state is found. A rather pronounced change of the slope in the I s vs T curve for the ordered state at about 500°C is found. The direction of this discontinuity shows a pronounced bend towards the temperature axis and suggests t h a t the Curie temperature of the ordered state is 1.0
~~
Fig. 3. I s vs T curves in reduced coordinates for Ni3Fe in the disordered state (curve a) and in the ordered state (curbe b or b'). For curve b' the experimental Curie temperatures has been used, this being the Curie temperature of the disordered state; curve b, with a hypothetical Curie temperature, about 50° higher to satisfy the theoretical curve with S = ½.
'
0.5
T
-'We 0
a5
i.o
higher than that of the disordered state (fig. 3). A reliable reduction to T / T s for the ordered state is therefore impossible. It is even to be expected, as is indeed found, that by using the Curie temperature of the disordered state a higher Q-value will result for the incorrectly
600
j . j . WENT
reduced curve relative to the ordered state t h a n with the value for pure nickel (0.785 instead of 0.775). A reduction of this Q-value to t h a t of pure nickel corresponds to an increase of the Curie t e m p e r a ture of a b o u t 50°C. F o r the disordered state of the same alloy a Q-value of 0.735 is found. Thus there is strong evidence t h a t the I s vs T curve of an alloy in the ordered state is indeed m u c h more concave towards the T-axis t h a n is the case for the same alloy in the disordered state. As already mentioned, we assume t h a t the large m e a s u r e d deviations from the theoretical curve with S = ½ are related to fluctuations in the local c o n c e n t r a t i o n of the solid atoms. § 3. W e m a y suggest the following two possibilities regarding the physical b a c k g r o u n d responsible f~r this influence. F o k k e r has calculated the change of order-disorder p h e n o m e n a which take place when t h e n u m b e r of particles to be ordered is m a d e v e r y small s). As a result of such calculations it is to be e x p e c t e d t h a t in the n e i g h b o u r h o o d of the Curie t e m p e r a t u r e the order-disorder 1.0
0£"
x
~.all
0
05
~0
1.5
Fig. 4. aa' Theoretical I, vs T curve for S = ½. aa" Curve a with a large tail corresponding to a deviation connected with very small ferromagnetic particles. b Reduced curve aa'" t r a n s f o r m a t i o n is a v e r y gradual function of t e m p e r a t u r e as shown in fig. 4 (dotted line). This effect is large for isolated particles with a small n u m b e r of atoms or, in our case, a small n u m b e r of magnetic moments, and small for large particles with m a n y atoms. If the new
MAGNETIZATION OF NICKEL ALLOYS AS FUNCTION OF TEMPERATURE 601
order-disorder curve with its tail a a " is reduced on the same T I T c scale as used for the normal order-disorder transformation curve, a less convex curve b results, as indicated by the flat curve in fig. 4. The form of this new curve is very much the same as that of the curve for the Ni-Si alloy shown in fig. 1. Of course this reduction is somewhat artificial owing to an incorrect Curie temperature being used. Now it seems possible that similar effects are present in our nickel alloys. Although ferromagnetism is a long-range order effect, it is well known that the electrostatic interaction responsible for the magnetic ordering in nickel is an interaction between nearest neighbours only. If the fluctuations in the concentration of the dissolved foreign atoms were such that small isolated particles of pure nickel exist, this Fokker effect must be present. Although such a fluctuation is highly improbable, the formation of partly closed regions containing a small number of Ni atoms is quite possible. It is probable that these partly closed regions will show an effect similar to that mentioned above as calculated by F o k k e r. Taking this effect into account, pure nickel, iron or cobalt must show I s v s T curves more convex towards the T-axis than disordered Ni alloys. On the other hand I s v s T curves for completely ordered alloys must be comparable with the curves for pure ferromagnetic metals, in close agreement with our observations on Ni3Fe. It is immediately clear that the Fokker effect, if present, must be stronger for large amounts of foreign atoms than for small amounts; the undisturbed regions of Ni atoms are smaller. It is also probable that this effect is more pronounced for foreign atoms not having a magnetic moment themselves like Si, than for these with a magnetic moment like Co. In the first case the Ni regions are more isolated. The great difference between the influence of Si and A1, both atoms without a magnetic moment, may be related with the extremely large heat of formation of Ni-A1. Therefore it is improbable that two A1 atoms will be neighbours ; at higher Ni contents a strong tendency to a crystallografic ordering exists and large fluctuations in these Ni-A1 alloys, responsible for the flat I s v s T curve, are not present. Goldman and S m o l u c h o w s k y ~ ) have g i v e n a q u a l i t a tive explanation of the change in saturation magnetization, Curie temperature and magnetostriction observed when crystallographically ordered alloys are disordered. They consider the fluctuation
602
MAGNETIZATION OF N I C K E L ALLOYS AS F U N C T I O N OF T E M P E R A T U R E
of the exchange force acting on an atom with a magnetic moment caused by the nearest neighbours to fluctuations of the type of surrounding atoms. If a nickel atom is surrounded by 12 nearest Ni atoms this exchange energy must be larger than when it is surrounded by 11 Ni atoms and one Si atom. This exchange energy is a direct measure for the value of the Curie temperature. N ~ e 111) has calculated the influence of fluctuations of the W e i s z molecular field on the spontaneous magnetization in the neighbourhood of the Curie temperature. This kind of reasoning just as the calculations of F o k k e r w h i c h are not independent m a y explain the facts observed in this paper. In two respects, even for pure nickel, small deviations from the theoretical curve with S = ½ are observed. For low temperature the value of the spontaneous magnetization is slightly too high and for high temperatures too low. Furthermore a small tail is found above the Curie temperature 8). According to the picture given above this small tail is perhaps related to dislocations and m a y then be explained in a similar way as suggested above. Finally it is of interest to note t h a t such deformations of the I s v s T curves are not confined to metallic ferromagnetic alloys alone. Similar effects are present in the ferromagnetic oxides. The I s v s T curve for pure Ni is more convex towards the T-axis than those for Mn or Ni ferrites, while mixed MnZn or NiZn ferrites are even more flat 9). N 6 e 1 ~o) has calculated the shape of the I s v s T curve for these ferrites. His values should be compared with the experimental data however only after a correction for the ~tbovementioned effects. Eindhoven, 1st December 1950. Received 13-2-51. REFERENCES l) 2) ;3) 4) 5) 6) 7) 8) 9) 10) 11)
W e i s s , P. and F o r r e r , R., Ann. de Phys. 5(1926)153. W e i s s , P. and F o r r e r , R., Ann. d e P h y s , l°(1929) 279. Potter, H . H . , Proc. roy. Soc. A. 146(1934) 362. S u c k s m i t h, W., Communications Conference on Magnetism, Grenoble 1950. W e n t, J. J., Physica 17 (1951) 98; in this paper more experimental details are described. Fokker, A . D . , Physiea 8 (1941) 109 and 159. Goldman, J. E. and S m o l u c h o w s k y , R., Phys. Rev. ~5 (1949) 140. Gerlach, W., Z. Elektroehemie 45 (1939) 151. Guillaud, Ch. and R o u x , M., C.R. Ac. Sc. Paris °21J (1949)1133. N 6 e l , L., Ann. de Phys. 3 (1948) 137. N 6 e l , L., J. Physique, 5 1934 104.