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Magneto-elastic properties and invar anomaly of Fe-Pd alloys
Physica B 161 (1989) 53-59 North-Holland, Amsterdam
MAGNETO-ELASTIC
PROPERTIES
AND INVAR ANOMALY
OF Fe-Pd
ALLOYS
Masaaki MATSUI Department
of Iron and Steel Engineering,
Faculty of Engineering,
Nagoya University, Nagoya 464, Japan
Kengo ADACHI Department of Physics, Faculty of Science, Nagoya University, Nagoya 464, Japan
The magnetic
properties
and thermal
expansion
of disordered
Fe-Pd
alloys have been measured.
Elastic
constants
for
the invar region have been also measured. The results suggest that the Fe-Pd system is a conventional ferromagnet. The magnitude of the volume magnetostriction and the coupling constant KC were smallest in the Fe-based invar alloys. A large lattice softening takes place around fee-fct phase boundary. The different magnetic, volume and structural instabilities among Fe-based invar alloys are discussed.
1. Introduction
The Fe-Pd system is one of the famous Febased fee invar alloys. Magnetic and thermal invar anomalies of Fe-Pd alloys were first investigated by Kussman and Jessen [ 11. Typical invar anomalies are large spontaneous volume magnetostriction below T,. and abrupt decrease of spontaneous magnetization deviating from the Slater-Pauling curve for Fe-Ni alloys. The dependence of volume on magnetization is also observed in the forced magnetostriction and in the elastic constants below Tc [2]. Many theoretical approaches for understanding these invar anomalies have been proposed based on localized moment models [3-51 and on itinerant moment Stoner models [S, 91. We also proposed a two state model modified from the Weiss model [6,7]. Nakamura et al. [lo] have claimed that Fe-Pt alloys are magnetically and compositionally homogeneous and that the invar anomaly is essentially the spontaneous volume magnetostriction arising from the 3d band polarization. Moriya also proposed a spin fluctuation model [ll] which could explain the magnetic phenomena at high temperatures. Williams et al. [12] calculated the total energy contours using a relation between the magnetic moment and volume estimated by the precise band structure
calculation and claimed that the microscopic origin of the invar effect is the degenerate nature of the non-magnetic state with the ferromagnetic ground state [12]. Morruzi et al. also calculated total energy contours for fee and bee Fe and pointed out that there are three minima of total energy at non-magnetic, low spin and high spin states for fee Fe [13]. Since our previous two state model [7] was based on a localized model, it was not a correct description. However, the degeneracy of two or three states could presumably cause an invar anomaly. As for Fe-Pd alloys, we previously reported the magnetic properties [14], low temperature structural transformation, [15], thermal expansion [16], magnetic anisotropy [ 171, and low temperature specific heat [18]. In this paper, we describe magnetic, thermal and elastic properties for the whole composition range of disordered Fe-Pd alloys and discuss the magnetic anomaly and lattice instability connected with the low temperature phase diagram shown in fig. 1 [1419].
2. Magnetic properties
and specific heat
The temperature dependence of the magnetization of Fe I_XPd, alloys is shown in fig. 2 for
0921-4526/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
54
1.0 0.9 :
0.8 0.7
\ I I
0.22
bee
_
M. Matsui and K. Adachi
I Invar anomaly of Fe-Pd
and 0.80, respectively. The magnetic moment at 4.2 K is plotted along with the lattice constant in fig. 3. The magnetic moment changes linearly and shows no distinct change at the phase boundaries between fee-fct and fct-bee and has no decrease around x = 0.30. The results suggest that the magnetic moment of Fe-Pd does not decrease, in the invar composition region and thus, cannot be explained by a weak itinerant ferromagnetic model [8,9]. The linear dependence of magnetic moment on composition can be explained by assuming pr+ = 2.70~~ and pr,d = 0.56~~. The moment of Fe is in agreement with that of Fe-Pt and Fe-Ni systems. No ferromagnetism instability is observed for the Fe-Pd system. The ratio P,,,/P, is shown in the lower parts in fig. 3, where P, = gj/m. S was estimated from the saturation magnetization at 4.2 K. The ratio increases near the invar region and suggests that the susceptibility of Fe-Pd alloys should be described by an itinerant electron model and approaches that of y-Fe with decreasing Pd concentration. The composition dependence of the Curie temperature of the Fe-Pd system is shown in fig. 4 and resembles that for Fe-Pt and Fe-Ni systems, though T, is
1
+ I
i
I
I
fct
j fee
,
I
0.26
1
,
i
I 4
0.30 X
0.34
I
Fig. 1. Low temperature phase diagram of Fe-Pd alloys. The upper part shows the c/a ratio based upon the fct phase.
the whole composition range. The magnetization at 4.2 K increases with decreasing Pd concentration. The effective magnetic moments estimated by the Curie-Weiss law were 4.54, 4.15, 3.99, 3.70 and 2.84 for x = 0.30, 0.32, 0.34, 0.40
Fig.
2. Temperature
dependence
of the
magnetization
alloys
of
Fe-Pd
alloys.
Arrows
indicate
the Curie
temperature
T,
llodal aM Jaded s!q, UI *[cl ‘3al II! pavodal alaM s)uawamseatu uoymedxa pmlaql hreupuga~d uoy+qsoyau%mu
auuqoa snoauquodg
*c
aDylel e %ugsa%ns OSIB‘k~epunoq aseqd mq-333 aql%_uq3eoldde uo saseamap “0 ammadtual aq) ‘tua@ !N-ad aql u! sv 71oysue~1 v3-m3 aql30 hpunoq aseqd aql kqcwoldde uaqw paluasqo SBM Zhqual3os acywl aqL ‘x ~I!M saseamap dlIEj -II.IIISstuajslis 1col1cqloq 103 amw~adwa~ alCqaa aqL *sho~le !N-ad 30 leql ueql ssal s! uoysod -u103 .mu! aql .wau slCojp2pd-ad aq, us aseam! aql 3nq ‘x %!seamap t.pt~ saseamuy X.,uapg3ao:, aqL *[L]suramis !N-ad ~03 Jpsal aqt qyy laqla% -01 9 2%~II! UMoqs ale “0 amqe~adwal ahqaa aqi pw X. luapg3ao3 vaq Dypads D!uo.wala aql 103 s4lnsal pm ‘[fjl] ‘1” la Bumy 1cq pamseatu uaaq seq way 3yyDads amw~adwal MOI aqJ .“J leau iuapy3ao:, uors -uedxa pmuaql aql IIF aseamap dleqs E sampold pm? ‘snopmow s! id-ad 103 uogc?!Aap pmwdn aqL ‘uoyun3 u!nollp~ aqi 01 as013 s! pd-aA 30 leql apqm ‘suogDa.up al!soddo III lnq ‘lo!aeq -aq uoyun3 uIno11y8 1 = s 1.11013wdap qtoq id-ad pm IN-ad 30 uoy2zgau%uI aqL waas a.m slcolp~ .wauy aalqi aqt 2k1ou1e samala33Ip ~mgs!p ‘am%y s!qi UI sdo~le I~AU~ !N-ad pue Id-ad uaamaq aiwpaurlaiui s! lC011epd-aA aql
aq1 U! pamseaur
SBM
.sl(o[le parapros!p aq) .103TJOM luasard Ula)sKsJ&a.J ‘03 3-z pm [I] ‘3aJ uloq amlwadmal au ‘(id ‘pd ‘!N = fly)
S!S.iOlIE IN-a.J aql ‘03 “J
“@‘ad
103 Y 30 uogx~y
e se ampxadmq
apn3
‘p %?!d
f
30 amapuadap amwadwal uogezgau%w aqA *[rz] put2 [oz] 53al ~013 a.w id-ad pm TN-ad 103 elep aqL .a.mwadwal pampal 30 uoyun3 I! Sl? S ‘&J II! UMOqS S! ShOIj&? lt2AI.I~ 333 pZSt?q-a+J II?:, -IdAl 30 uogezyau%mu pampal aql woysoduIo3 ad awes aqi ie ruaisds lay10 aqi u! ueqi laq%iq ‘(1 + Sk/v = ‘d 01 “‘, .l~qUInU 'qO$J aA!JX33a 30 O!W aq? SMOqS 30 lmd JaMoI aqL 'x 30 uo!ixq e se u PI~ISUOD ‘LIIO~Elad warnour qau9em uvam ‘c ‘8y
a&y
aylq
aql
pue d
0’1
8’0
TOX
YO
Z’O
0
O
0’1
SE
56
T!
x10-: Fe, _XPdx .
l
x 0: *.
1t
X=030 032 0.34 040
i
l( Is C . ,-
0
o-
I
03
0.4
06
05
0.7
0
08
X
Fig. 6. Electronic specific heat coefficient perature as a function of x for Fe, \Pd. alloys (m) (see ref. [lg]).
and Debye tem(01 and Fe, ,Ni,
new measurements and values of the spontaneous volume magnetostriction. In fig. 7, results for thermal expansion in invar region are shown.
0
400 T
Fig. 7. Linear thermal for Fe-Pd alloys.
expansion
2 a,’ (emu*/,*
800 (K) as a function
1200 of temperature
3
1
x104
Fig. 8. Spontaneous volume magnetostriction w> as a function of square of magnetization for Fe-Pd alloys.
The broken lines represent the phonon term we estimated by the Gruneisen equation utilizing high temperature date above T,.. A large spontaneous volume magnetostriction, o,~, was observed for the invar compositions, with a maximum around x = 0.32. A plot of w,~ versus the square of the magnetization, (cri) is shown in fig. 8 and shows a linear dependence. The coupling constant KC was calculated from w, = KCCT’ and gave values of 4.44, 5.12, 5.03 and 3.23 x lo-” (cm”/emu2) for x = 0.30, 0.32, 0.34 and 0.40, respectively. It is interesting that the coupling constant is maximal not at x = 0.30 but at x = 0.32. The values of the coupling constant are smaller than that of Fe-Pt invar (6.3 x lo-‘) and of Fe-Ni invar (9 x lo-‘) [lo]. In fig. 9 the thermal expansion coefficient of three Fe-based invar systems is shown. The data for Fe-28%Pt and Fe-34.6%Ni are from refs. [22] and [23]. The invar anomaly in the spontaneous volume magnetostriction for Fe-Pd is the smallest of the three alloy systems. However, it is noted that the sharpness of the anomaly at T, is intermediate between Fe-Pt and Fe-Ni systems. The sharpness is associated with the change of magnetization near T, as shown in fig. 5.
M. Matsui and K. Adachi
T (K)
Fig. 9. Thermal expansion coefficient for typical invar alloys as a function of temperature. Curves for Fe-28%Pt and Fe-34.6%Ni are from refs. [22] and [23].
4. Elastic and magnetic stiffness constants
The elastic constants Cii, C,, and C,, of the Fe-Pd alloys were measured by the rectangular parallelepiped resonance method [7]. In the measurement, a magnetic field was applied in order to eliminate the AE effect. The result is shown in fig. 10. Both the shear mode constant C’ = (C,, --C,,) /2 and the longitudinal mode r-,l.oo H
=lOkOe
I
9
$i
0.75 ‘; 6
OJO-
I Invar anomaly of Fe-Pd
alloys
57
constant C, = (C,, + C,, + 2C,,)/2 decrease with decreasing temperature. As shown in fig. 1, the fee-fct structural transition temperature is 180 K for x = 0.32 and no transition takes place for x = 0.34. The frequency shift in the measurement for x = 0.32 was too large to follow the resonant peaks around the transition temperature. Accordingly, C, for x = 0.32 could not be obtained. The coefficient C’ for x = 0.34 is presumably almost zero at 0 K. The present results suggest that the driving force for the transition is the softening of the phonon shear mode. It should be noted that such a remarkable change in elastic constants has never been observed for other Fe-based invar alloys. Ohta has suggested recently that local changes in the elastic constants can be induced by substitution of an impurity Fe atom and leads to a local lattice instability [24]. In fig. 11, X-ray diffraction patterns for well annealed (200 hours at 450°C following a quench from 11OO’C) alloys of x = 0.32 to 0.40. The ordered fct FePd phase and bee CYphases co-exist for all samples, while the disordered phase also exists at the lower x. It&hould be noted that the ordered fct FePd is different from the low temperature fct phase shown in fig. 1. The present result suggests that the disordered fee phase is unstable in the invar region and transforms either to the disordered fct or ordered fct phase. Thus the lattice instability of Fe-Pd invar alloys is most remarkable in Fe-based invar systems. The lattice instability is presumably attributed to the local electronic structure induced by Fe-Pd bonds.
5. Invar anomaly and lattice instability
0
100
200
300
T(K)
Fig. 10. Elastic constants as a function of temperature for x = 0.32 and 0.34, where C’ = (C,,-CT,,)/2 and CL = (C,, + C,, + 2C,,) /2. The temperature T, denotes the fee-fct transformation temperature.
The invar anomaly of the Fe-Pd system can be summarized by the following: 1) No anomalous behavior of the magnetic properties is observed except for the P,,,lP, ratio, and the elastic stiffness constant D which shows a softening effect around the fee-fct phase boundary [18]. The internal field obtained from the Mossbauer effect is almost independent of x in the invar region [16,25].
M. Matsui
30
40
50
and
K. Adachi
60
I lnvur
anomaly
of
Fe-Pd
alloys
sumably due to the bond between Fe and solute atoms. The local lattice instability for the Fe-Pd alloys is caused by the Fe-Pd bonds produced by the substitution of the Pd site by Fe atoms [24]. Accordingly, the pair interaction of Fe and solute atom is important for understanding the invar problem. The Fe-Pt system forms a Fe,Pt while the other invar alloys ordered phase, exhibit no such ordered phases. On the other hand, disordered Fe-Pd invar transforms either to an ordered FePd + bee phase or to a disordered fct phase, while Fe-Ni directly transforms to a bee phase. Thus, the final structural transition is different for Fe-Pt, Fe-Pd and FeNi alloys. According to Williams et al. and Morruzi et al.. it is possible that the degeneracy of two states of nonmagnetic and ferromagnetic Fe causes the invar anomaly. The magnitude of anomaly presumably depends on the solute atoms. Different pair interactions will result in different local band structure and thus different magnitudes of the invar anomaly or lattice softening.
26 (degree)
Fig. 11. X-ray diffraction patterns for well annealed samples of Fe,_,Pd, alloys (see text). The peak (1 1 1) for x < 0.40 is split into two peaks, the lower angle peak belongs to the ordered FePd phase and the upper one to the disordered phase.
2)
The half width of the distribution of internal fields is about 50 kOe which is not unusual. These results for the magnetic properties suggest that the Fe-Pd system is a conventional ferromagnet. The magnitude of the volume magnetostriction and the coupling constant KC were smallest in the Fe-based invar binary alloy systems. The small forced volume magnetostriction 1.5 x 10m9(0e-‘) was also reported in ref.
F'61. 3) A large
lattice softening takes place around fee-fct phase boundry. The softening is presumably one of the pre-martensitic transformation phenomena [24,27]. The different magnetic volume and structural instabilities among Fe-based invar alloys are pre-
Acknowledgement A part of this work was supported by Grantin-Aid for Scientific Research on Priority Areas, Ministry of Education, Science and Culture, Japan.
References [I] A. Kussman and K. Jessen. J. Phys. Sot. Jpn. 17 suppl. B-l (1962) 136. [2] Cr. Hausch and H. Warlimont, Acta Met. 21 (1973) 401. [3] E.I. Kondorsky and V.L. Sedov. J. Appl. Phys. 31 (1960) 331s. [4] S. Kachi and H. Asano, J. Phys. Sot. Jpn. 27 (1969) 536. [5] R.J. Weiss, Proc. Phys. Sot. 82 (1963) 281. [h] M. Matsui and S. Chikzumi, J. Phys. Sot. Jpn. 45 (1978) 458. (71 M. Matsui, K. Adachi and S. Chikazumi, J. Appl. Phys. 51 (1980) 6319. [8] E.P. Wohlfarth, J. Appl. Phys. 39 (1968) 1061. [9] E.P. Wohlfarth, Phys. Lett. 28 (1969) 569.
M. Matsui and K. Adachi
I Invar anomaly of Fe-Pd
[lo] Y. Nakamura, K. Smiyama and M. Shiga, J. Magn. Magn. Mat. 12 (1979) 127. [ll] See for instance, T. Moriya, Electron Correlation and Magnetism in Narrow-Band Systems (Springer, Berlin, 1981)p. 2. [12] A.R. Williams, VL. Morruzi, J. Kfibler and K. Schwarz, Bull. Am. Phys. Sot. 29 (1984) 278. [13] V.L. Morruzi, P.M. Marcus, K. Schwarz and P. Mohn, Phys. Rev. B 34 (1986) 1784. [14] M. Matsui, T. Schimizu, H. Yamada and K. Adachi, J. Magn. Magn. Mat. 15-18 (1980) 1201. [15] M. Matsui, T. Shimizu, H. Yamada and K. Adachi, J. Phys. Sot. Jpn. 48 (1980) 2161. [16] M. Matsui, T. Shimizu and K. Adachi, Physica B 119 (1983) 84. [17] M. Matsui, J. P. Kuang, T. Totani and K. Adachi, J. Magn. Magn. Mat. 54-57 (1986) 911.
alloys
59
[18] J. P. Kuang, M. Kontani, M. Matsui and K. Adachi, Physica B 149 (1988) 209. [19] T. Sohmura, R. Ohshima and F.E. Fujita, Scripta Met. 14 (1980) 855. [20] K. Sumiyama, M. Shiga and Y. Nakamura, J. Phys. Sot. Jpn. 40 (1976) 996. [21] J. Crangle and G.C. Hallam, Proc. Phys. Sot. A 272 (1963) 119. [22] K. Sumiyama, M. Shiga, M. Muraoka and Y. Nakamura, J. Phys. F 9 (1979) 1665. [23] Y. Tanji, J. Phys. Sot. Jpn. 31 (1971) 1366. [24] Y. Ohta, Physica B 161 (1989) 60 (these Proceedings). [25] N.V. Nair and D.C. Khan, J. Phys. F13 (1983) 1965. [26] M. Matsui and K. Adachi, J. Magn. Magn. Mat. 32-34 (1983) 115. [27] M. Sugiyama, R. Ohshima and E.F. Fujita, Trans. JIM. 27 (1986) 719.
MAGNETO-ELASTIC
PROPERTIES
AND INVAR ANOMALY
OF Fe-Pd
ALLOYS
Masaaki MATSUI Department
of Iron and Steel Engineering,
Faculty of Engineering,
Nagoya University, Nagoya 464, Japan
Kengo ADACHI Department of Physics, Faculty of Science, Nagoya University, Nagoya 464, Japan
The magnetic
properties
and thermal
expansion
of disordered
Fe-Pd
alloys have been measured.
Elastic
constants
for
the invar region have been also measured. The results suggest that the Fe-Pd system is a conventional ferromagnet. The magnitude of the volume magnetostriction and the coupling constant KC were smallest in the Fe-based invar alloys. A large lattice softening takes place around fee-fct phase boundary. The different magnetic, volume and structural instabilities among Fe-based invar alloys are discussed.
1. Introduction
The Fe-Pd system is one of the famous Febased fee invar alloys. Magnetic and thermal invar anomalies of Fe-Pd alloys were first investigated by Kussman and Jessen [ 11. Typical invar anomalies are large spontaneous volume magnetostriction below T,. and abrupt decrease of spontaneous magnetization deviating from the Slater-Pauling curve for Fe-Ni alloys. The dependence of volume on magnetization is also observed in the forced magnetostriction and in the elastic constants below Tc [2]. Many theoretical approaches for understanding these invar anomalies have been proposed based on localized moment models [3-51 and on itinerant moment Stoner models [S, 91. We also proposed a two state model modified from the Weiss model [6,7]. Nakamura et al. [lo] have claimed that Fe-Pt alloys are magnetically and compositionally homogeneous and that the invar anomaly is essentially the spontaneous volume magnetostriction arising from the 3d band polarization. Moriya also proposed a spin fluctuation model [ll] which could explain the magnetic phenomena at high temperatures. Williams et al. [12] calculated the total energy contours using a relation between the magnetic moment and volume estimated by the precise band structure
calculation and claimed that the microscopic origin of the invar effect is the degenerate nature of the non-magnetic state with the ferromagnetic ground state [12]. Morruzi et al. also calculated total energy contours for fee and bee Fe and pointed out that there are three minima of total energy at non-magnetic, low spin and high spin states for fee Fe [13]. Since our previous two state model [7] was based on a localized model, it was not a correct description. However, the degeneracy of two or three states could presumably cause an invar anomaly. As for Fe-Pd alloys, we previously reported the magnetic properties [14], low temperature structural transformation, [15], thermal expansion [16], magnetic anisotropy [ 171, and low temperature specific heat [18]. In this paper, we describe magnetic, thermal and elastic properties for the whole composition range of disordered Fe-Pd alloys and discuss the magnetic anomaly and lattice instability connected with the low temperature phase diagram shown in fig. 1 [1419].
2. Magnetic properties
and specific heat
The temperature dependence of the magnetization of Fe I_XPd, alloys is shown in fig. 2 for
0921-4526/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
54
1.0 0.9 :
0.8 0.7
\ I I
0.22
bee
_
M. Matsui and K. Adachi
I Invar anomaly of Fe-Pd
and 0.80, respectively. The magnetic moment at 4.2 K is plotted along with the lattice constant in fig. 3. The magnetic moment changes linearly and shows no distinct change at the phase boundaries between fee-fct and fct-bee and has no decrease around x = 0.30. The results suggest that the magnetic moment of Fe-Pd does not decrease, in the invar composition region and thus, cannot be explained by a weak itinerant ferromagnetic model [8,9]. The linear dependence of magnetic moment on composition can be explained by assuming pr+ = 2.70~~ and pr,d = 0.56~~. The moment of Fe is in agreement with that of Fe-Pt and Fe-Ni systems. No ferromagnetism instability is observed for the Fe-Pd system. The ratio P,,,/P, is shown in the lower parts in fig. 3, where P, = gj/m. S was estimated from the saturation magnetization at 4.2 K. The ratio increases near the invar region and suggests that the susceptibility of Fe-Pd alloys should be described by an itinerant electron model and approaches that of y-Fe with decreasing Pd concentration. The composition dependence of the Curie temperature of the Fe-Pd system is shown in fig. 4 and resembles that for Fe-Pt and Fe-Ni systems, though T, is
1
+ I
i
I
I
fct
j fee
,
I
0.26
1
,
i
I 4
0.30 X
0.34
I
Fig. 1. Low temperature phase diagram of Fe-Pd alloys. The upper part shows the c/a ratio based upon the fct phase.
the whole composition range. The magnetization at 4.2 K increases with decreasing Pd concentration. The effective magnetic moments estimated by the Curie-Weiss law were 4.54, 4.15, 3.99, 3.70 and 2.84 for x = 0.30, 0.32, 0.34, 0.40
Fig.
2. Temperature
dependence
of the
magnetization
alloys
of
Fe-Pd
alloys.
Arrows
indicate
the Curie
temperature
T,
llodal aM Jaded s!q, UI *[cl ‘3al II! pavodal alaM s)uawamseatu uoymedxa pmlaql hreupuga~d uoy+qsoyau%mu
auuqoa snoauquodg
*c
aDylel e %ugsa%ns OSIB‘k~epunoq aseqd mq-333 aql%_uq3eoldde uo saseamap “0 ammadtual aq) ‘tua@ !N-ad aql u! sv 71oysue~1 v3-m3 aql30 hpunoq aseqd aql kqcwoldde uaqw paluasqo SBM Zhqual3os acywl aqL ‘x ~I!M saseamap dlIEj -II.IIISstuajslis 1col1cqloq 103 amw~adwa~ alCqaa aqL *sho~le !N-ad 30 leql ueql ssal s! uoysod -u103 .mu! aql .wau slCojp2pd-ad aq, us aseam! aql 3nq ‘x %!seamap t.pt~ saseamuy X.,uapg3ao:, aqL *[L]suramis !N-ad ~03 Jpsal aqt qyy laqla% -01 9 2%~II! UMoqs ale “0 amqe~adwal ahqaa aqi pw X. luapg3ao3 vaq Dypads D!uo.wala aql 103 s4lnsal pm ‘[fjl] ‘1” la Bumy 1cq pamseatu uaaq seq way 3yyDads amw~adwal MOI aqJ .“J leau iuapy3ao:, uors -uedxa pmuaql aql IIF aseamap dleqs E sampold pm? ‘snopmow s! id-ad 103 uogc?!Aap pmwdn aqL ‘uoyun3 u!nollp~ aqi 01 as013 s! pd-aA 30 leql apqm ‘suogDa.up al!soddo III lnq ‘lo!aeq -aq uoyun3 uIno11y8 1 = s 1.11013wdap qtoq id-ad pm IN-ad 30 uoy2zgau%uI aqL waas a.m slcolp~ .wauy aalqi aqt 2k1ou1e samala33Ip ~mgs!p ‘am%y s!qi UI sdo~le I~AU~ !N-ad pue Id-ad uaamaq aiwpaurlaiui s! lC011epd-aA aql
aq1 U! pamseaur
SBM
.sl(o[le parapros!p aq) .103TJOM luasard Ula)sKsJ&a.J ‘03 3-z pm [I] ‘3aJ uloq amlwadmal au ‘(id ‘pd ‘!N = fly)
S!S.iOlIE IN-a.J aql ‘03 “J
“@‘ad
103 Y 30 uogx~y
e se ampxadmq
apn3
‘p %?!d
f
30 amapuadap amwadwal uogezgau%w aqA *[rz] put2 [oz] 53al ~013 a.w id-ad pm TN-ad 103 elep aqL .a.mwadwal pampal 30 uoyun3 I! Sl? S ‘&J II! UMOqS S! ShOIj&? lt2AI.I~ 333 pZSt?q-a+J II?:, -IdAl 30 uogezyau%mu pampal aql woysoduIo3 ad awes aqi ie ruaisds lay10 aqi u! ueqi laq%iq ‘(1 + Sk/v = ‘d 01 “‘, .l~qUInU 'qO$J aA!JX33a 30 O!W aq? SMOqS 30 lmd JaMoI aqL 'x 30 uo!ixq e se u PI~ISUOD ‘LIIO~Elad warnour qau9em uvam ‘c ‘8y
a&y
aylq
aql
pue d
0’1
8’0
TOX
YO
Z’O
0
O
0’1
SE
56
T!
x10-: Fe, _XPdx .
l
x 0: *.
1t
X=030 032 0.34 040
i
l( Is C . ,-
0
o-
I
03
0.4
06
05
0.7
0
08
X
Fig. 6. Electronic specific heat coefficient perature as a function of x for Fe, \Pd. alloys (m) (see ref. [lg]).
and Debye tem(01 and Fe, ,Ni,
new measurements and values of the spontaneous volume magnetostriction. In fig. 7, results for thermal expansion in invar region are shown.
0
400 T
Fig. 7. Linear thermal for Fe-Pd alloys.
expansion
2 a,’ (emu*/,*
800 (K) as a function
1200 of temperature
3
1
x104
Fig. 8. Spontaneous volume magnetostriction w> as a function of square of magnetization for Fe-Pd alloys.
The broken lines represent the phonon term we estimated by the Gruneisen equation utilizing high temperature date above T,.. A large spontaneous volume magnetostriction, o,~, was observed for the invar compositions, with a maximum around x = 0.32. A plot of w,~ versus the square of the magnetization, (cri) is shown in fig. 8 and shows a linear dependence. The coupling constant KC was calculated from w, = KCCT’ and gave values of 4.44, 5.12, 5.03 and 3.23 x lo-” (cm”/emu2) for x = 0.30, 0.32, 0.34 and 0.40, respectively. It is interesting that the coupling constant is maximal not at x = 0.30 but at x = 0.32. The values of the coupling constant are smaller than that of Fe-Pt invar (6.3 x lo-‘) and of Fe-Ni invar (9 x lo-‘) [lo]. In fig. 9 the thermal expansion coefficient of three Fe-based invar systems is shown. The data for Fe-28%Pt and Fe-34.6%Ni are from refs. [22] and [23]. The invar anomaly in the spontaneous volume magnetostriction for Fe-Pd is the smallest of the three alloy systems. However, it is noted that the sharpness of the anomaly at T, is intermediate between Fe-Pt and Fe-Ni systems. The sharpness is associated with the change of magnetization near T, as shown in fig. 5.
M. Matsui and K. Adachi
T (K)
Fig. 9. Thermal expansion coefficient for typical invar alloys as a function of temperature. Curves for Fe-28%Pt and Fe-34.6%Ni are from refs. [22] and [23].
4. Elastic and magnetic stiffness constants
The elastic constants Cii, C,, and C,, of the Fe-Pd alloys were measured by the rectangular parallelepiped resonance method [7]. In the measurement, a magnetic field was applied in order to eliminate the AE effect. The result is shown in fig. 10. Both the shear mode constant C’ = (C,, --C,,) /2 and the longitudinal mode r-,l.oo H
=lOkOe
I
9
$i
0.75 ‘; 6
OJO-
I Invar anomaly of Fe-Pd
alloys
57
constant C, = (C,, + C,, + 2C,,)/2 decrease with decreasing temperature. As shown in fig. 1, the fee-fct structural transition temperature is 180 K for x = 0.32 and no transition takes place for x = 0.34. The frequency shift in the measurement for x = 0.32 was too large to follow the resonant peaks around the transition temperature. Accordingly, C, for x = 0.32 could not be obtained. The coefficient C’ for x = 0.34 is presumably almost zero at 0 K. The present results suggest that the driving force for the transition is the softening of the phonon shear mode. It should be noted that such a remarkable change in elastic constants has never been observed for other Fe-based invar alloys. Ohta has suggested recently that local changes in the elastic constants can be induced by substitution of an impurity Fe atom and leads to a local lattice instability [24]. In fig. 11, X-ray diffraction patterns for well annealed (200 hours at 450°C following a quench from 11OO’C) alloys of x = 0.32 to 0.40. The ordered fct FePd phase and bee CYphases co-exist for all samples, while the disordered phase also exists at the lower x. It&hould be noted that the ordered fct FePd is different from the low temperature fct phase shown in fig. 1. The present result suggests that the disordered fee phase is unstable in the invar region and transforms either to the disordered fct or ordered fct phase. Thus the lattice instability of Fe-Pd invar alloys is most remarkable in Fe-based invar systems. The lattice instability is presumably attributed to the local electronic structure induced by Fe-Pd bonds.
5. Invar anomaly and lattice instability
0
100
200
300
T(K)
Fig. 10. Elastic constants as a function of temperature for x = 0.32 and 0.34, where C’ = (C,,-CT,,)/2 and CL = (C,, + C,, + 2C,,) /2. The temperature T, denotes the fee-fct transformation temperature.
The invar anomaly of the Fe-Pd system can be summarized by the following: 1) No anomalous behavior of the magnetic properties is observed except for the P,,,lP, ratio, and the elastic stiffness constant D which shows a softening effect around the fee-fct phase boundary [18]. The internal field obtained from the Mossbauer effect is almost independent of x in the invar region [16,25].
M. Matsui
30
40
50
and
K. Adachi
60
I lnvur
anomaly
of
Fe-Pd
alloys
sumably due to the bond between Fe and solute atoms. The local lattice instability for the Fe-Pd alloys is caused by the Fe-Pd bonds produced by the substitution of the Pd site by Fe atoms [24]. Accordingly, the pair interaction of Fe and solute atom is important for understanding the invar problem. The Fe-Pt system forms a Fe,Pt while the other invar alloys ordered phase, exhibit no such ordered phases. On the other hand, disordered Fe-Pd invar transforms either to an ordered FePd + bee phase or to a disordered fct phase, while Fe-Ni directly transforms to a bee phase. Thus, the final structural transition is different for Fe-Pt, Fe-Pd and FeNi alloys. According to Williams et al. and Morruzi et al.. it is possible that the degeneracy of two states of nonmagnetic and ferromagnetic Fe causes the invar anomaly. The magnitude of anomaly presumably depends on the solute atoms. Different pair interactions will result in different local band structure and thus different magnitudes of the invar anomaly or lattice softening.
26 (degree)
Fig. 11. X-ray diffraction patterns for well annealed samples of Fe,_,Pd, alloys (see text). The peak (1 1 1) for x < 0.40 is split into two peaks, the lower angle peak belongs to the ordered FePd phase and the upper one to the disordered phase.
2)
The half width of the distribution of internal fields is about 50 kOe which is not unusual. These results for the magnetic properties suggest that the Fe-Pd system is a conventional ferromagnet. The magnitude of the volume magnetostriction and the coupling constant KC were smallest in the Fe-based invar binary alloy systems. The small forced volume magnetostriction 1.5 x 10m9(0e-‘) was also reported in ref.
F'61. 3) A large
lattice softening takes place around fee-fct phase boundry. The softening is presumably one of the pre-martensitic transformation phenomena [24,27]. The different magnetic volume and structural instabilities among Fe-based invar alloys are pre-
Acknowledgement A part of this work was supported by Grantin-Aid for Scientific Research on Priority Areas, Ministry of Education, Science and Culture, Japan.
References [I] A. Kussman and K. Jessen. J. Phys. Sot. Jpn. 17 suppl. B-l (1962) 136. [2] Cr. Hausch and H. Warlimont, Acta Met. 21 (1973) 401. [3] E.I. Kondorsky and V.L. Sedov. J. Appl. Phys. 31 (1960) 331s. [4] S. Kachi and H. Asano, J. Phys. Sot. Jpn. 27 (1969) 536. [5] R.J. Weiss, Proc. Phys. Sot. 82 (1963) 281. [h] M. Matsui and S. Chikzumi, J. Phys. Sot. Jpn. 45 (1978) 458. (71 M. Matsui, K. Adachi and S. Chikazumi, J. Appl. Phys. 51 (1980) 6319. [8] E.P. Wohlfarth, J. Appl. Phys. 39 (1968) 1061. [9] E.P. Wohlfarth, Phys. Lett. 28 (1969) 569.
M. Matsui and K. Adachi
I Invar anomaly of Fe-Pd
[lo] Y. Nakamura, K. Smiyama and M. Shiga, J. Magn. Magn. Mat. 12 (1979) 127. [ll] See for instance, T. Moriya, Electron Correlation and Magnetism in Narrow-Band Systems (Springer, Berlin, 1981)p. 2. [12] A.R. Williams, VL. Morruzi, J. Kfibler and K. Schwarz, Bull. Am. Phys. Sot. 29 (1984) 278. [13] V.L. Morruzi, P.M. Marcus, K. Schwarz and P. Mohn, Phys. Rev. B 34 (1986) 1784. [14] M. Matsui, T. Schimizu, H. Yamada and K. Adachi, J. Magn. Magn. Mat. 15-18 (1980) 1201. [15] M. Matsui, T. Shimizu, H. Yamada and K. Adachi, J. Phys. Sot. Jpn. 48 (1980) 2161. [16] M. Matsui, T. Shimizu and K. Adachi, Physica B 119 (1983) 84. [17] M. Matsui, J. P. Kuang, T. Totani and K. Adachi, J. Magn. Magn. Mat. 54-57 (1986) 911.
alloys
59
[18] J. P. Kuang, M. Kontani, M. Matsui and K. Adachi, Physica B 149 (1988) 209. [19] T. Sohmura, R. Ohshima and F.E. Fujita, Scripta Met. 14 (1980) 855. [20] K. Sumiyama, M. Shiga and Y. Nakamura, J. Phys. Sot. Jpn. 40 (1976) 996. [21] J. Crangle and G.C. Hallam, Proc. Phys. Sot. A 272 (1963) 119. [22] K. Sumiyama, M. Shiga, M. Muraoka and Y. Nakamura, J. Phys. F 9 (1979) 1665. [23] Y. Tanji, J. Phys. Sot. Jpn. 31 (1971) 1366. [24] Y. Ohta, Physica B 161 (1989) 60 (these Proceedings). [25] N.V. Nair and D.C. Khan, J. Phys. F13 (1983) 1965. [26] M. Matsui and K. Adachi, J. Magn. Magn. Mat. 32-34 (1983) 115. [27] M. Sugiyama, R. Ohshima and E.F. Fujita, Trans. JIM. 27 (1986) 719.