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The effect of transition metal impurities on the low-field hall coefficient of aluminum
Physica I07B (1981) 499-500 North-Holland Publishing Company
ID 2
THE EFFECT OF TRANSITION METAL IMPURITIES ON THE LOW-FIELD HALL COEFFICIENT
Constantinos
Papastaikoudis,
Damlanos Papadimitropoulos
Nuclear Research Center "Demokritos"
OF ALUMINUM
and Elsa Rocofyllou
Aghia Paraskevi Attikis,
Greece
o .
The change of the low-fleld Hall coeff.lcient P ~ o f polycrystalline aluminum due to the addition of 3d transitional impurities Ti, Cr,-~n, Fe, Ni and Cu is measured at 4.2 K. The results show that ~ depends systematically on the valence of the impurities, and has the lowest value for chromium. An analysis of the results is given using a three group model of the Fermi surface of AI and the Friedel-Anderson model for a localized virtual bound state. n
I.
INTRODUCTION
The addition of small amounts of transition elements impurities into aluminum, gives rise to relatively large changes in various physical parameters, like electrical resistivity, thermopower, magnetic susceptibility, specific heat, and superconducting critical temperature. This behavior has been interpreted by Friedel (I) as due to resonant scattering effects which gives rice to virtually bound d-states (VBS). Anderson (2) has shown that broadening of atomic dlevels in a metal due to admixture of conduction (s) and d-electrons results in similar virtual states.
determined with an optical microscope. The Hall voltage measurements were performed at 4.2 K in a superconducting solenoid which produces a magnetic field up to 40 kG (5). The low-field Hall coefficients ~ of the AI-Ti and AI-Ni alloys together with values of the earlier investigations for AI-Cr, AI-Mn, AI-Fe and AI-Cu are plotted in Fig. 1 as a function of the atomic number of the 3d impurity. The ~ values of the present alloys are negative and lle on a parabolic curve, with the lowest value at Cr impurity.
3.
DISCUSSION O
Until now only few measurements of the Hall coefficient have been made in aluminum-based 3d transition-metal alloys. Kedves et al. (3) and McAlister et al. (4) have measured the Hall coefficient of AI-Cr and AI-Mn alloys at 77 and 6 K respectively, while Papastalkoudls et al. (5,6) have measured the Hall coefficient of AICu, AI-Cr, AI-Mn and AI-Fe at 4.2 K and it is found that the low-fleld Hall coefficient shows a distinct systematic dependence on t~e valence of the impurities, similar to those found in the residual resistivity, the thermopower and the superconducting transition tempeo rature. R~ becomes negative and even achieves the free-electron value of aluminum, when going from Cu impurities to Cr impurities in the 3d transition series. The present work shows new experiments of low-fleld Hall coefficient R~ on AITi and AINi alloys.
2.
EXPERIMENTAL
In order t o explain this behavior of R~ we u ~ the Friedel-Anderson model of the v i r t U 1 3d bound states together with the three-group model of the Fermi surface of AI (7,8). We will assume here that the nonresonant part of the mean free paths are small relative to the resonant
Papastaikoudis et al
IJ
&o
,~ouE1- •McAlister et al / | B present result . / I
PROCEDURE AND RESULTS
The investigated AI-Ti and AI-Ni alloys are prepared by HF-levitation melting and then rolled into polycrystalline foils about I00 ~m thick. The nominal concentrations were obtained by weight analysis and we have concentrated on very dilute samples with impurity concentrations reasonably removed from the solubility limit. The concentrations of Ti and Hi lle between I0 and 20 ppm. The thickness of the samples was
0378.4363/81/0000-0000/$02-50
© North-Holland Publishing Company
~3
_/
~
~
i
I
I
I
I
I
I
I
Sc Ti V CP MnFeCo Ni Cu
Figure 1 : coefficient impurity.
The dependence of the low-field Hall ~ of aluminum on the valence of the
499
500
n
part and thus the low-fleld Hall coefficient &R~ l in the three-group model of the Fermi surface (8) can be written as
F 3
R F : -3.47 x 10 -5 cm /A's is the free electron va~ue of the Hall coefficient, A = 6 . 5 1 × 10 -5 cm3/ A-s, (£ ) , (£ ) and (£ ) . are the resres res -re~ ~-~ pectlve mean free paths due to the resonant scattering on the free-electron-llke, strongly electron-like and strongly hole-llke Fermi surface regions. For (£ )~_~ : (£ ) the R~. res ~ res ->~ value can be obtained, while for (£res)++ ~ > RFE and for (£res)++<(£res)__ is (£res)-- is --
RI~ < RFEThe s y s t e m a t i c
e d e p e n d e n c e o f t h e RH o f t h e A1-3d
alloys on the atomic number of solutes can be readily attributed to the differences in the scattering probabilities of the VBS near the second and third zone Fermi surface edges. When the atomic number of the solute increases, from titanium to copper the corresponding VBS sinks into the Fermi sea of the AI conduction band. At chromium the VBS cross the Fermi level, where the resonant energy coincides with this level. R~ has the lowest values for the AICr and AIMn alloys and even tend to RFE. If it may be assumed that this result is not highly accidental then it implies that (£res)++~(£res)__. The Hall coefficient R~ increases at both sides of the Cr impurity (see fig. I) and in the case of Cu even changes sign and becomes positive. This means that the mean free paths on both sides of Cr must always obey the relation (£res)++>(£res)__ •
Thus in the case of AICr the electrons on the hole-like edges in the second zone and the electrons on the electron-like edges in the third zone will be scattered approximately with similar probability on Cr impurities. When going a way from Cr, the 3d-VBS moves away from the Fermi level of AI and then the VBS begins to scatter the electrons on the electron-like edges in the third zone at the expense of the electrons on the hole-like edges in the second zone.
REFERENCES I.
J. Friedel,
2.
(1958). P.W. Anderson, Phys. Rev. 124, 41 (1961).
3. 4. 5.
6. 7. 8.
Nuovo Cimento Suppl. ~, 287
F.J. Kedves and L. GergaZy, Phys. Status Solidi A 38, K31 (1976). C.P. McAllster, C.M. Hurd and L.M. Lupton, J.Phys. F 9, 1849 (1979). C. Papastalkoudis, E. Thanou, D. Tsamakis and W. Tselfes, J. Low Temp. Phys. 34, 429 (1979). C. Papastaikoudls, D. Papadimitropoulos and E. Rocofyllou, Phys. Rev. B 22, 2670 (1980). K. BSnlng, K. Pf~nder, P. Rosner and M. SchlSter, J. Phys. F 5, 1176 (1976). W. Kesternich, Phys. Rev. B 13, 4227 (1976).
ID 2
THE EFFECT OF TRANSITION METAL IMPURITIES ON THE LOW-FIELD HALL COEFFICIENT
Constantinos
Papastaikoudis,
Damlanos Papadimitropoulos
Nuclear Research Center "Demokritos"
OF ALUMINUM
and Elsa Rocofyllou
Aghia Paraskevi Attikis,
Greece
o .
The change of the low-fleld Hall coeff.lcient P ~ o f polycrystalline aluminum due to the addition of 3d transitional impurities Ti, Cr,-~n, Fe, Ni and Cu is measured at 4.2 K. The results show that ~ depends systematically on the valence of the impurities, and has the lowest value for chromium. An analysis of the results is given using a three group model of the Fermi surface of AI and the Friedel-Anderson model for a localized virtual bound state. n
I.
INTRODUCTION
The addition of small amounts of transition elements impurities into aluminum, gives rise to relatively large changes in various physical parameters, like electrical resistivity, thermopower, magnetic susceptibility, specific heat, and superconducting critical temperature. This behavior has been interpreted by Friedel (I) as due to resonant scattering effects which gives rice to virtually bound d-states (VBS). Anderson (2) has shown that broadening of atomic dlevels in a metal due to admixture of conduction (s) and d-electrons results in similar virtual states.
determined with an optical microscope. The Hall voltage measurements were performed at 4.2 K in a superconducting solenoid which produces a magnetic field up to 40 kG (5). The low-field Hall coefficients ~ of the AI-Ti and AI-Ni alloys together with values of the earlier investigations for AI-Cr, AI-Mn, AI-Fe and AI-Cu are plotted in Fig. 1 as a function of the atomic number of the 3d impurity. The ~ values of the present alloys are negative and lle on a parabolic curve, with the lowest value at Cr impurity.
3.
DISCUSSION O
Until now only few measurements of the Hall coefficient have been made in aluminum-based 3d transition-metal alloys. Kedves et al. (3) and McAlister et al. (4) have measured the Hall coefficient of AI-Cr and AI-Mn alloys at 77 and 6 K respectively, while Papastalkoudls et al. (5,6) have measured the Hall coefficient of AICu, AI-Cr, AI-Mn and AI-Fe at 4.2 K and it is found that the low-fleld Hall coefficient shows a distinct systematic dependence on t~e valence of the impurities, similar to those found in the residual resistivity, the thermopower and the superconducting transition tempeo rature. R~ becomes negative and even achieves the free-electron value of aluminum, when going from Cu impurities to Cr impurities in the 3d transition series. The present work shows new experiments of low-fleld Hall coefficient R~ on AITi and AINi alloys.
2.
EXPERIMENTAL
In order t o explain this behavior of R~ we u ~ the Friedel-Anderson model of the v i r t U 1 3d bound states together with the three-group model of the Fermi surface of AI (7,8). We will assume here that the nonresonant part of the mean free paths are small relative to the resonant
Papastaikoudis et al
IJ
&o
,~ouE1- •McAlister et al / | B present result . / I
PROCEDURE AND RESULTS
The investigated AI-Ti and AI-Ni alloys are prepared by HF-levitation melting and then rolled into polycrystalline foils about I00 ~m thick. The nominal concentrations were obtained by weight analysis and we have concentrated on very dilute samples with impurity concentrations reasonably removed from the solubility limit. The concentrations of Ti and Hi lle between I0 and 20 ppm. The thickness of the samples was
0378.4363/81/0000-0000/$02-50
© North-Holland Publishing Company
~3
_/
~
~
i
I
I
I
I
I
I
I
Sc Ti V CP MnFeCo Ni Cu
Figure 1 : coefficient impurity.
The dependence of the low-field Hall ~ of aluminum on the valence of the
499
500
n
part and thus the low-fleld Hall coefficient &R~ l in the three-group model of the Fermi surface (8) can be written as
F 3
R F : -3.47 x 10 -5 cm /A's is the free electron va~ue of the Hall coefficient, A = 6 . 5 1 × 10 -5 cm3/ A-s, (£ ) , (£ ) and (£ ) . are the resres res -re~ ~-~ pectlve mean free paths due to the resonant scattering on the free-electron-llke, strongly electron-like and strongly hole-llke Fermi surface regions. For (£ )~_~ : (£ ) the R~. res ~ res ->~ value can be obtained, while for (£res)++ ~ > RFE and for (£res)++<(£res)__ is (£res)-- is --
RI~ < RFEThe s y s t e m a t i c
e d e p e n d e n c e o f t h e RH o f t h e A1-3d
alloys on the atomic number of solutes can be readily attributed to the differences in the scattering probabilities of the VBS near the second and third zone Fermi surface edges. When the atomic number of the solute increases, from titanium to copper the corresponding VBS sinks into the Fermi sea of the AI conduction band. At chromium the VBS cross the Fermi level, where the resonant energy coincides with this level. R~ has the lowest values for the AICr and AIMn alloys and even tend to RFE. If it may be assumed that this result is not highly accidental then it implies that (£res)++~(£res)__. The Hall coefficient R~ increases at both sides of the Cr impurity (see fig. I) and in the case of Cu even changes sign and becomes positive. This means that the mean free paths on both sides of Cr must always obey the relation (£res)++>(£res)__ •
Thus in the case of AICr the electrons on the hole-like edges in the second zone and the electrons on the electron-like edges in the third zone will be scattered approximately with similar probability on Cr impurities. When going a way from Cr, the 3d-VBS moves away from the Fermi level of AI and then the VBS begins to scatter the electrons on the electron-like edges in the third zone at the expense of the electrons on the hole-like edges in the second zone.
REFERENCES I.
J. Friedel,
2.
(1958). P.W. Anderson, Phys. Rev. 124, 41 (1961).
3. 4. 5.
6. 7. 8.
Nuovo Cimento Suppl. ~, 287
F.J. Kedves and L. GergaZy, Phys. Status Solidi A 38, K31 (1976). C.P. McAllster, C.M. Hurd and L.M. Lupton, J.Phys. F 9, 1849 (1979). C. Papastalkoudis, E. Thanou, D. Tsamakis and W. Tselfes, J. Low Temp. Phys. 34, 429 (1979). C. Papastaikoudls, D. Papadimitropoulos and E. Rocofyllou, Phys. Rev. B 22, 2670 (1980). K. BSnlng, K. Pf~nder, P. Rosner and M. SchlSter, J. Phys. F 5, 1176 (1976). W. Kesternich, Phys. Rev. B 13, 4227 (1976).