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Temperature dependence of the electrical resistivity of the nickel-platinum alloy system
1. Phjs. Chem. SdidsVol. Printed in Gmat Btitairl.
46, No. 12,~~. 1421-1425,
0022~3697/85 s3.00 + al Q 1985 papmon Flwa Ltd.
1985
TEMPERATURE DEPENDENCE OF THE ELECTRICAL RESISTIVITY OF THE NICKEL-PLATINUM ALLOY SYSTEM HANS LIT~CHEL Department of Physics, Sibiu University, 2400 Sibiu Bdul Victoriei nr.5, Romenia
and IULIU POP Department of Physics, Cluj University, 3400 Cluj, Rominia (Received I1 January 1984; accepted in revisedform 22 April 1985) Abstract-The temperature dependence of the electrical resistivity of Nil-& (x = 1,2,3,4, 5,8, 10, 15, 20,25 and 30 at.%) between 77 and 700 K has been investigated. The experimental results are inkrprekd according to the theoretical model developed by Mott. It is shown that for this system Matthiessen’s rule is not obeyed.
tivity of the nickel-platinum alloy system has not been
INTRODUCI’ION It is well-known that the existence of magnetic ordering in a transition metal system gives rise to an important modification of the energy spectrum of the conduction electrons. This modification will influence the electrical properties, especially the electrical resistivity, which will have a greater value than in the ordinary metal, and will also lead to an anomaly in the temperature dependence, corresponding to a second-order phase transition. In the case of metallic nickel, this behaviour may be understood on the basis of the model developed by Mott [l-3]. According to this model, the electrical behavior is determined by the electrons of the s-band, and the main contribution to the electrical resistivity is determined by the s-d transition up to the neighborhood of the critical temperature. In the low-temperature region, conduction electrons with up-spins cannot make a transition to the band of upd-spins, because ail the energy levels of this band are occupied. This is the reason why the average length of the mean free path of the conduction upspin s-electrons is considerably greater than that of the down-spin s-electron current carriers. Since the s-d transition is different for up and down +&ectrons, these two types of electrons may conduct the electric current in parallel. This two-band conduction model developed by Mott [l] has been proved unambiguously. The concept of two current conduction in ferromagnetic materials has been used to explain deviations from Matthiessen’s rule, and resistivity anisotropy, magnetoresistivity and thermoelectric power. In the neighborhood of the Curie temperature there are holes in the d-band, and an s-d transition becomes possible, giving rise to an anomaly in the electrical resistivity of pure metallic nickel. The temperature dependence of the electrical resis-
investigated so far, except for the case of alloys with high Pt concentrations at low temperatures. In this paper we have investigated the temperature dependence of the electrical resistivity of this system between pure nickel and up to 30 at.% Pt. EXPERIMENTAL The samples Nil_& (x = 1, 2, 3, 4, 5, 8, 10, 15, 20,25 and 30 at.%)were obtained by melting the metals purity 99.99% Ni and 99.999% Pt in an aromelting furnace in a pure argon atmosphere. The samples were annealed at 1173 K for 24 h before and a&r lamination and cooled down to room temperature at a rate of 150 K/h, in order to get undeformed solid solutions. The electrical resistivity of the alloys was determined by the four-electrode method in the temperature range from 77 to 700 K on samples of linear dimensions 5 X 8 X 0.15 mm3. RESULTS AND DISCUSSION The temperature dependence between 77 and 700 K of the electrical resistivity for all the samples investigated is given in Fig. 1. One can see that the electrical resistivity graduahy increases with increasing platinum concentration and that the anomaly corresponding to the Curie temperature shifts towards low temperatums. The shape of the temperature dependence curves is very similar in all the samples investigated because nickel and platinum metals are isoelectronic and large band effects are not present. If we consider the concentration dependence of the critical temperature, T,, them is a monotonic decrease of the Curie temperature when the platinum concentration increases, as can be seen in Fig. 2. A similar dependence was obtained previously by
1421
1422
H. LIIXCHEL and I. POP
04 1
100
200
300
100
500
600
TIK) 700
Fig. 1. Temperature dependence of resistivity of Ni,_Pt, alloys. The curves are labelled with the Pt content (at.%). Kussmann and Nitlca 141, but our values are systematically lower, except for the nickel value, which is Te= 628 K, a little higher than that reported by Kussmann and Nitka. The concentration dependence decresses monotonically with increasing platinum concentration, more mpidly than linear at higher platinum concentrations. The general shape of the curve is the same as that obtained by Kussmann and Nitlca. In order to show the deviation from Matthiessen’s rule it was necessary to extrapolate the temperature curves for T = 0 K. The p. values obtained by extrapolation from 77 K to 0 K are in good agreement with
those obtained in other papers by electrical resistivity measurements at 4.2 K [5-91. The concentration dependence of the residual electrical resistivity given in Fig. 3 increases monotonically with increasing platinum concentration. For low-concentration nickelplatinum alloys one can see that the concentration de pendence is almost linear up to 8 at.% Pt. This dependence of the residual electrical resistivity is in agreement with the concentration dependence of the magnetic moments given also in Fig. 3 determined by saturation magnetization measurements. One can see from Fig. 3 that the concentration dependence of the magnetic
1423
0
I
10
I
20 %?APt)
Fig. 2. Concentration dependence of the Curie temperature.
moments falls linearly up to 8 at.% Pt, but for higher concentrations the fall is more rapid. It is possible that in this alloys system, beginning with 8 at.% Pt, the shift
of the Fermi level towards bigb energy is no longer negligible. The numerical values of the residual electrical resistivity for nickel-platinum alloys are much
Fig. 3. Concentration dependence of residual resistivity, closed circles. Plot of magnetic moments asa function of concentration, open circles (dashed curves).
1424
H. LITSCHELand I. POP
smaller than in the other nickel3d alloys [6-g]. This proves that the perturbation potential of the impurity atoms is small. The influence of the solute platinum atoms in NiPt alloys is very clearly demonstrated by the temperature dependence of the solute resistivity pS = p,,&T) - p&T), which is represented in Fig. 4. The general features of the p.(T) are an increase in its value at 77 K to a maximum or plateau near 300 to 400 K, in good agreement with the band model developed by Mott [ 11. Let us mention that large variations in PAT) near T, are due to the ahoy and the standard having different degrees of magnetic order.
A plot of the measured deviations from Matthiessen’s rule, A(C,T), defined as
is presented in Fig. 5, for only four concentrations.
In Fig 6, the deviations from Matthiessen’s rule are analysed and shown as A(C, 297 K)/pO =f(C), where p. is the residual resistivity, in comparison with the other reported experimental results [7].
j_-
I--
20
5--
S--
0
1
100
200
500
=QTF’K)
Fig. 4. Solute resistivity of Nil_,Ptx alloys. The curves are labelled with the Pt content (at.%).
1425
Electrical resistivity of the nickel-platinum alloy system Ak,T) (pm4
t
00
700T(OK)
0
20
1
Fig. 5. Plot of the measured deviations from Matthiessen’s rule A(C,T).
c,297 OKI
These. three figures tell us that Matthiessen’s rule is not obeyed in the case of the nickel-platinum alloy system.
REZERENCES
:!L_:
0
_
.
Mott N. F., Proc. R. Sot. (London) Ser. A 153,699 (1936). :: Mott N. F., Pmt. R. Sot. (London) Ser. A 156,368 (1936). 3. Mott N. F., Adv. Phys. 13,325 (1964).
4. Kussmann A. and Nitka H., Phys. Z. 39,373 (1938). Farrell T. and Greig D., J. Phys. C&r. 2 1,1359 (1968). :: Cadeville M. 0. and Durand J., Solid State Commun. 6, L
Fig.6. Concentration
8
15
$5 cbwo2&)
dependence of [A(C, 297 K)]/po.Filled circles, this study: open circles, Durand and Gautier [7].
399 (1968).
7. Durand J. and Gautier F., J. Phys. C’hem.Solids 31,2773 (1970). Dorleijn J. W. F., Phillips Res. Rep. 31,287 (1976). ;: Beylin V. M. et al., Fiz. Metal. Metallov. 46,1083 (1978).
46, No. 12,~~. 1421-1425,
0022~3697/85 s3.00 + al Q 1985 papmon Flwa Ltd.
1985
TEMPERATURE DEPENDENCE OF THE ELECTRICAL RESISTIVITY OF THE NICKEL-PLATINUM ALLOY SYSTEM HANS LIT~CHEL Department of Physics, Sibiu University, 2400 Sibiu Bdul Victoriei nr.5, Romenia
and IULIU POP Department of Physics, Cluj University, 3400 Cluj, Rominia (Received I1 January 1984; accepted in revisedform 22 April 1985) Abstract-The temperature dependence of the electrical resistivity of Nil-& (x = 1,2,3,4, 5,8, 10, 15, 20,25 and 30 at.%) between 77 and 700 K has been investigated. The experimental results are inkrprekd according to the theoretical model developed by Mott. It is shown that for this system Matthiessen’s rule is not obeyed.
tivity of the nickel-platinum alloy system has not been
INTRODUCI’ION It is well-known that the existence of magnetic ordering in a transition metal system gives rise to an important modification of the energy spectrum of the conduction electrons. This modification will influence the electrical properties, especially the electrical resistivity, which will have a greater value than in the ordinary metal, and will also lead to an anomaly in the temperature dependence, corresponding to a second-order phase transition. In the case of metallic nickel, this behaviour may be understood on the basis of the model developed by Mott [l-3]. According to this model, the electrical behavior is determined by the electrons of the s-band, and the main contribution to the electrical resistivity is determined by the s-d transition up to the neighborhood of the critical temperature. In the low-temperature region, conduction electrons with up-spins cannot make a transition to the band of upd-spins, because ail the energy levels of this band are occupied. This is the reason why the average length of the mean free path of the conduction upspin s-electrons is considerably greater than that of the down-spin s-electron current carriers. Since the s-d transition is different for up and down +&ectrons, these two types of electrons may conduct the electric current in parallel. This two-band conduction model developed by Mott [l] has been proved unambiguously. The concept of two current conduction in ferromagnetic materials has been used to explain deviations from Matthiessen’s rule, and resistivity anisotropy, magnetoresistivity and thermoelectric power. In the neighborhood of the Curie temperature there are holes in the d-band, and an s-d transition becomes possible, giving rise to an anomaly in the electrical resistivity of pure metallic nickel. The temperature dependence of the electrical resis-
investigated so far, except for the case of alloys with high Pt concentrations at low temperatures. In this paper we have investigated the temperature dependence of the electrical resistivity of this system between pure nickel and up to 30 at.% Pt. EXPERIMENTAL The samples Nil_& (x = 1, 2, 3, 4, 5, 8, 10, 15, 20,25 and 30 at.%)were obtained by melting the metals purity 99.99% Ni and 99.999% Pt in an aromelting furnace in a pure argon atmosphere. The samples were annealed at 1173 K for 24 h before and a&r lamination and cooled down to room temperature at a rate of 150 K/h, in order to get undeformed solid solutions. The electrical resistivity of the alloys was determined by the four-electrode method in the temperature range from 77 to 700 K on samples of linear dimensions 5 X 8 X 0.15 mm3. RESULTS AND DISCUSSION The temperature dependence between 77 and 700 K of the electrical resistivity for all the samples investigated is given in Fig. 1. One can see that the electrical resistivity graduahy increases with increasing platinum concentration and that the anomaly corresponding to the Curie temperature shifts towards low temperatums. The shape of the temperature dependence curves is very similar in all the samples investigated because nickel and platinum metals are isoelectronic and large band effects are not present. If we consider the concentration dependence of the critical temperature, T,, them is a monotonic decrease of the Curie temperature when the platinum concentration increases, as can be seen in Fig. 2. A similar dependence was obtained previously by
1421
1422
H. LIIXCHEL and I. POP
04 1
100
200
300
100
500
600
TIK) 700
Fig. 1. Temperature dependence of resistivity of Ni,_Pt, alloys. The curves are labelled with the Pt content (at.%). Kussmann and Nitlca 141, but our values are systematically lower, except for the nickel value, which is Te= 628 K, a little higher than that reported by Kussmann and Nitka. The concentration dependence decresses monotonically with increasing platinum concentration, more mpidly than linear at higher platinum concentrations. The general shape of the curve is the same as that obtained by Kussmann and Nitlca. In order to show the deviation from Matthiessen’s rule it was necessary to extrapolate the temperature curves for T = 0 K. The p. values obtained by extrapolation from 77 K to 0 K are in good agreement with
those obtained in other papers by electrical resistivity measurements at 4.2 K [5-91. The concentration dependence of the residual electrical resistivity given in Fig. 3 increases monotonically with increasing platinum concentration. For low-concentration nickelplatinum alloys one can see that the concentration de pendence is almost linear up to 8 at.% Pt. This dependence of the residual electrical resistivity is in agreement with the concentration dependence of the magnetic moments given also in Fig. 3 determined by saturation magnetization measurements. One can see from Fig. 3 that the concentration dependence of the magnetic
1423
0
I
10
I
20 %?APt)
Fig. 2. Concentration dependence of the Curie temperature.
moments falls linearly up to 8 at.% Pt, but for higher concentrations the fall is more rapid. It is possible that in this alloys system, beginning with 8 at.% Pt, the shift
of the Fermi level towards bigb energy is no longer negligible. The numerical values of the residual electrical resistivity for nickel-platinum alloys are much
Fig. 3. Concentration dependence of residual resistivity, closed circles. Plot of magnetic moments asa function of concentration, open circles (dashed curves).
1424
H. LITSCHELand I. POP
smaller than in the other nickel3d alloys [6-g]. This proves that the perturbation potential of the impurity atoms is small. The influence of the solute platinum atoms in NiPt alloys is very clearly demonstrated by the temperature dependence of the solute resistivity pS = p,,&T) - p&T), which is represented in Fig. 4. The general features of the p.(T) are an increase in its value at 77 K to a maximum or plateau near 300 to 400 K, in good agreement with the band model developed by Mott [ 11. Let us mention that large variations in PAT) near T, are due to the ahoy and the standard having different degrees of magnetic order.
A plot of the measured deviations from Matthiessen’s rule, A(C,T), defined as
is presented in Fig. 5, for only four concentrations.
In Fig 6, the deviations from Matthiessen’s rule are analysed and shown as A(C, 297 K)/pO =f(C), where p. is the residual resistivity, in comparison with the other reported experimental results [7].
j_-
I--
20
5--
S--
0
1
100
200
500
=QTF’K)
Fig. 4. Solute resistivity of Nil_,Ptx alloys. The curves are labelled with the Pt content (at.%).
1425
Electrical resistivity of the nickel-platinum alloy system Ak,T) (pm4
t
00
700T(OK)
0
20
1
Fig. 5. Plot of the measured deviations from Matthiessen’s rule A(C,T).
c,297 OKI
These. three figures tell us that Matthiessen’s rule is not obeyed in the case of the nickel-platinum alloy system.
REZERENCES
:!L_:
0
_
.
Mott N. F., Proc. R. Sot. (London) Ser. A 153,699 (1936). :: Mott N. F., Pmt. R. Sot. (London) Ser. A 156,368 (1936). 3. Mott N. F., Adv. Phys. 13,325 (1964).
4. Kussmann A. and Nitka H., Phys. Z. 39,373 (1938). Farrell T. and Greig D., J. Phys. C&r. 2 1,1359 (1968). :: Cadeville M. 0. and Durand J., Solid State Commun. 6, L
Fig.6. Concentration
8
15
$5 cbwo2&)
dependence of [A(C, 297 K)]/po.Filled circles, this study: open circles, Durand and Gautier [7].
399 (1968).
7. Durand J. and Gautier F., J. Phys. C’hem.Solids 31,2773 (1970). Dorleijn J. W. F., Phillips Res. Rep. 31,287 (1976). ;: Beylin V. M. et al., Fiz. Metal. Metallov. 46,1083 (1978).