- Email: [email protected]
Resistivity anomalies of dilute Zr1−xRExAl2 alloys
Journal of the Less-Common
99
Metals, 162 ( 1990) 99-103
RESISTIVITY ANOMIES
OF DILUTE Zr,_$E,Al,
ALLOYS
A. SLEBARSKI Institute
of Physics,Silesian University, 40.t?iV Katwice (Poland)
D. WOHLLEBEN II Physikalisches Institut, Universittit zu Kiiln, 5iNO Kdn 41 (FAG.) (Received November 8,1989)
In ZrAl, the resistivity increment of stable lanthanum and praseodymium impurities is larger than that of mixed valent cerium impurities. All increments increase with increasing temperature. These results are discussed in terms of charge density contrast scattering and of a reduction in the local phonon frequencies on the rare earth impurities.
1. Introduction In this work, we present data of the resistivity of dilute Zr, _ $EXAl, alloys. The goal is to enlarge the empirical basis of the anomalies of the resistivity increment AP( T ) = ba~loy - Pmatrix) of dilute rare earth (RE) impurities with unstable 4f shells in metals. For cerium and praseodymium impurities the anomalous temperature dependence of A,#( T ) is usually interpreted in terms of the Kondo effect, according to which the effective impurity scattering cross-section increases with decreasing temperature over the normal, temperature independent cross-section owing to potential scattering. This increase (positive resistivity anomaly) is thought to come from the dynamics of the impurity spin on the unstable f shell. However, it was recently found [ 1J that the resistivity anomalies of dilute unstable cerium and prase~ymium in ZrIr, are actually negative, i.e. that their resistivity increment Ap is smaller than that of the other m impurities with stable f shells such as lanthanum and gadolinium. It was therefore suggested in ref. 2 that the resistivity increment Ahp comes primarily from the potential scattering due to the charge density contrast of the unstable impurity against the matrix. A charge density difference between unstable and stable impurities is a necessary consequence of the fractional valence of the impurity, which is the main feature of the 4f ~stability. An unstable cerium or praseodymium atom has fractional valence 3 + Y, while the valence of stable gadolinium (and of stable cerium) is three. Then Ap - Y. The charge density contrast also depends on the valence electron density of the matrix, 0 Elsevier S~uoia/~nted
in The Netherlands
100
and on the compression or dilatation of the impurity in the matrix [3]. Y may be a function of temperature, i.e. Ap( T ) = Y( T ). Furthermore, in ref. 4 it was shown that Ap( T ) correlates with the temperature dependence of the so-called valence fluctuation temperature Tr( T ), via Ap( T ) = T; ‘( T ). Near T= 0, Ap( 0) = 1W12f T,(O), where W= Wii”- W, is the on-site scattering matrix element between the mixed valent cerium atoms and the matrix atoms M. W reflects both the charge density contrast between the impurity and the matrix and the lifetime smearing of the f level described by Tr. Zr, _$F$r, is a good example for the interpretation of Ap( T ) on the basis of the above “dynamic alloy” model [5]. In this system cerium has a strongly fractional valence 3 + Y.At the same time it exhibits the smallest resistivity increment. This can be explained by the fact that since the RE impurities replace nearly tetravalent zirconium, the charge contrast scattering of the Ce3 + ” atoms in ZrIr, is smaller than that of RE3 + impurities. A similar abno~al charge contrast scattering can then be expected for cerium impurities in a ZrAl, matrix.
2. Experimental details The samples of Zr, _,RE$Al, with RE!.= La, Ce and Pr and with 0 < x < 0.4 were prepared by arc melting the pure elements together on a water-cooled copper hearth in a zirconium-gettered argon atmosphere. A Debye-Sherrer X-ray examination showed that all samples were single phase and had the C-14 structure. The resistivity was measured by a standard four lead ac. technique.
3. Results and discussion Figure 1 shows the resistivity increment Ap/x = ( palloy the Apfx data one sees the following.
5
pzrAi,
)/x. Comparing
aREAl
t
I 0
105 Tomporoturc
200
300
cK>
Fig. 1. The resistivity increments Ap( T )/x =(,oallay-,oZrAIJ)/x of dilute lanthanum, cerium and praseodymium as function of temperature.
alloys
of ZrAl,
with
( 1) Ap/x is independent of the concentration x of the RE element within the uncertainty of the absolute resistivity because of cross-sectional errors. (2) The increment of cerium is considerably smaller than those of lanthanum and praseodymium. (3) ho/x depends on temperature. While there is no obvious rise a la Kondo with decreasing T, there is a rise with increasing T, with a point of inflection near 160 K, for all three impurity species (lanthanum, cerium and praseodymium). As expected, the behaviour of the RE impurities observed here has similarities with that observed in ZrIr, [ 11. In the latter system the resistivity increments of trivalent lanthanum, gadolinium and lutetium were 4-6 ,uQ cm %-I. These large increments were attributed in first order to potential scattering due to a charge difference of the outer valence electrons of the trivalent RE (5d’6s2) with respect to tetravalent zirconium (4d25s2) in ZrIr,. There was also a clear increase of the increment with the RE atomic number, which was again interpreted in terms of charge density contrast, this time using an old idea of Blatt [3], who first pointed out that the resistivity increment of impurities with the same valence still measures a difference of charge densities between impurity and matrix: trivalent lanthanum atoms have a larger volume V than trivalent lutetium atoms, but they also have, by the same token, a larger compressibility K. The ratio of the K’S is larger than the ratio of the Vs. Therefore the lanthanum atoms are compressed more strongly than the lutetium atoms by the high lattice pressure (strong chemical binding) in the small unit cell of ZrAl, and have then a larger 5d6s charge density than lutetium impurities and therefore a smaller charge density contrast against zirconium than lutetium. As in ref. 2, one must assume that at T=O, where the scattering is purely elastic, the impurities show the full potential scattering expected from their charge density contrast, considering their valence together with their state of high compression. The value of Ap = 2 Q cm %- ’ for lanthanum and praseodymium in ZrAl, suggests a rather small charge density contrast (high compression at large compressibility). Cerium in ZrAl, is under very high lattice pressure and therefore strongly mixed valent (Y = 0.2-0.3) [6, 71. Ap/x of cerium is observed to be smaller than that of lanthanum by roughly 30% at all temperatures. This is as anticipated from the fractional valence 3 + Y of cerium, which puts its charge density closer to that of zirconium than that of trivalent praseodymium and lanthanum. The value of Ap = 1 8 cm %- ’ for cerium is reasonably consistent with Y= 0.2-0.3, together with the well-known low compressibility of cerium at this valence [7]. At low temperatures, there is no upturn of Ap/x of cerium. This is not surprising in view of the large T, or 7‘,, which is of around 1000 K for strongly mixed valent cerium [6]. The very similar, non-linear upturn of the increment of all impurity species with increasing temperature cannot have anything to do with valence instability or Kondo effect, nor is there any reason to invoke scattering on crystal field excitations, e.g. in praseodymium (because of the similarity of this increment with that of lanthanum) or on cerium ( Tf is much larger than the crystal field splittings). There are two possible explanations: a change of the electronic structure of ZrAl,
102
with increasing temperature or a change of the phononic structure upon alloying, which will change the temperature dependence of the electron phonon scattering. We have no clear frame of thinking for the first possibility, but can suggest a mechanism for the second. In the Zr,_,RE,Al, alloys, the masses of the constituents increase in the sequence MAI=27, Mz,=91, Mr.= 139, MC,= 140, MPr= 141. The mass of the matrix cell is therefore considerably smaller than that of the impurities. When alloying, we replace low mass zirconium by high mass RE atoms. Replacing a tetravalent zirconium atom by a trivalent RE atom also reduces the binding energy with the nearest neighbours, which will reduce the local elastic constants c. We therefore reduce the average optical phonon frequency (c/M)‘/* on each unit cell with an RE atom by 20%-30%. Therefore the optical phonons around the RE atoms will be excited at lower temperatures than on the zirconium unit cells. Near the Debye temperature and above, there will then be additional electron phonon scattering in the alloys. This additional scattering will appear in A,o/x= (,oalloy -pzrA,*)/x. The additional Ap/x should be independent of the concentration at x Q 1, should appear near the Einstein temperature of the RE TE =h(c/M)“*/kB (near 150 K) and should increase linearly with T sufficiently far above this temperature, because in the Dulong Petit limit the number of additional phonons increases linearly with temperature. All these features are as observed. The effect is expected to be much weaker in a matrix like ZrIr,, where the local elastic constants are also reduced by alloying, but where the average optical phonon frequencies are lower from the start (M= 191 for the majority iridium atoms), actually lower than for the RE atoms. Indeed, in Zr, _.ReE,Ir,, a weak linear increase in Ap/x is barely discernible above 150 K.
4. Conclusion In the alloys Zr, -$E@, with RE = La, Ce and Pr the resistivity increment APIX = (Pa,,oy- PZrAI, )/x is about twice as large for the stable valent lanthanum and praseodymium impurities than for the strongly mixed valent cerium impurities. There is no significant temperature dependence of Ap/x at low temperatures. This is consistent with charge density contrast scattering in the dynamic alloy model [4, 51. Beginning at about 100 K, there is a very unusual increase of Ap/x with increasing temperature, which can be explained by a reduction of the optical phonon frequencies on the REAl, unit cells with respect to the ZrAl, unit cells of the matrix.
Acknowledgments This work was supported by SFB 125 of the Deutsche Forschungsgemeinschaft and by the Institute of Physics of the Polish Academy of Sciences, contract CPBP 01.04.
103
References 1 A. Slebarski, D. Wohlleben and P. Weidner, Z. fhys. B: Condensed Mutter, 61(1985) 177. 2 A. Slebarski and D. Wohlleben, Z. f%ys. B: Condensed Mutter, 60 ( 1985) 449. 3 J. F. Blatt, Phys. Rev., 108( 1957) 285. 4 A. Slebarski, E. Zipper and M. Drzazga, J. Magn. Mugn. Mater., 76, 77 (1988) 249. 5 D. Wohlleben and B. Wittershagen, Adv. Whys., 34 (1985) 403. 6 P. Weidner, K. Keulerz, R. Liihe, B. Roden, J. RGhler, B. Wittershagen and D. Wohlleben, J. Mugn. Magn. Muter., 47, 48 (1985) 75. 7 D. Wohlleben and J. Riihler, J. Appl. Phys., 55 (1984) 1904.
99
Metals, 162 ( 1990) 99-103
RESISTIVITY ANOMIES
OF DILUTE Zr,_$E,Al,
ALLOYS
A. SLEBARSKI Institute
of Physics,Silesian University, 40.t?iV Katwice (Poland)
D. WOHLLEBEN II Physikalisches Institut, Universittit zu Kiiln, 5iNO Kdn 41 (FAG.) (Received November 8,1989)
In ZrAl, the resistivity increment of stable lanthanum and praseodymium impurities is larger than that of mixed valent cerium impurities. All increments increase with increasing temperature. These results are discussed in terms of charge density contrast scattering and of a reduction in the local phonon frequencies on the rare earth impurities.
1. Introduction In this work, we present data of the resistivity of dilute Zr, _ $EXAl, alloys. The goal is to enlarge the empirical basis of the anomalies of the resistivity increment AP( T ) = ba~loy - Pmatrix) of dilute rare earth (RE) impurities with unstable 4f shells in metals. For cerium and praseodymium impurities the anomalous temperature dependence of A,#( T ) is usually interpreted in terms of the Kondo effect, according to which the effective impurity scattering cross-section increases with decreasing temperature over the normal, temperature independent cross-section owing to potential scattering. This increase (positive resistivity anomaly) is thought to come from the dynamics of the impurity spin on the unstable f shell. However, it was recently found [ 1J that the resistivity anomalies of dilute unstable cerium and prase~ymium in ZrIr, are actually negative, i.e. that their resistivity increment Ap is smaller than that of the other m impurities with stable f shells such as lanthanum and gadolinium. It was therefore suggested in ref. 2 that the resistivity increment Ahp comes primarily from the potential scattering due to the charge density contrast of the unstable impurity against the matrix. A charge density difference between unstable and stable impurities is a necessary consequence of the fractional valence of the impurity, which is the main feature of the 4f ~stability. An unstable cerium or praseodymium atom has fractional valence 3 + Y, while the valence of stable gadolinium (and of stable cerium) is three. Then Ap - Y. The charge density contrast also depends on the valence electron density of the matrix, 0 Elsevier S~uoia/~nted
in The Netherlands
100
and on the compression or dilatation of the impurity in the matrix [3]. Y may be a function of temperature, i.e. Ap( T ) = Y( T ). Furthermore, in ref. 4 it was shown that Ap( T ) correlates with the temperature dependence of the so-called valence fluctuation temperature Tr( T ), via Ap( T ) = T; ‘( T ). Near T= 0, Ap( 0) = 1W12f T,(O), where W= Wii”- W, is the on-site scattering matrix element between the mixed valent cerium atoms and the matrix atoms M. W reflects both the charge density contrast between the impurity and the matrix and the lifetime smearing of the f level described by Tr. Zr, _$F$r, is a good example for the interpretation of Ap( T ) on the basis of the above “dynamic alloy” model [5]. In this system cerium has a strongly fractional valence 3 + Y.At the same time it exhibits the smallest resistivity increment. This can be explained by the fact that since the RE impurities replace nearly tetravalent zirconium, the charge contrast scattering of the Ce3 + ” atoms in ZrIr, is smaller than that of RE3 + impurities. A similar abno~al charge contrast scattering can then be expected for cerium impurities in a ZrAl, matrix.
2. Experimental details The samples of Zr, _,RE$Al, with RE!.= La, Ce and Pr and with 0 < x < 0.4 were prepared by arc melting the pure elements together on a water-cooled copper hearth in a zirconium-gettered argon atmosphere. A Debye-Sherrer X-ray examination showed that all samples were single phase and had the C-14 structure. The resistivity was measured by a standard four lead ac. technique.
3. Results and discussion Figure 1 shows the resistivity increment Ap/x = ( palloy the Apfx data one sees the following.
5
pzrAi,
)/x. Comparing
aREAl
t
I 0
105 Tomporoturc
200
300
cK>
Fig. 1. The resistivity increments Ap( T )/x =(,oallay-,oZrAIJ)/x of dilute lanthanum, cerium and praseodymium as function of temperature.
alloys
of ZrAl,
with
( 1) Ap/x is independent of the concentration x of the RE element within the uncertainty of the absolute resistivity because of cross-sectional errors. (2) The increment of cerium is considerably smaller than those of lanthanum and praseodymium. (3) ho/x depends on temperature. While there is no obvious rise a la Kondo with decreasing T, there is a rise with increasing T, with a point of inflection near 160 K, for all three impurity species (lanthanum, cerium and praseodymium). As expected, the behaviour of the RE impurities observed here has similarities with that observed in ZrIr, [ 11. In the latter system the resistivity increments of trivalent lanthanum, gadolinium and lutetium were 4-6 ,uQ cm %-I. These large increments were attributed in first order to potential scattering due to a charge difference of the outer valence electrons of the trivalent RE (5d’6s2) with respect to tetravalent zirconium (4d25s2) in ZrIr,. There was also a clear increase of the increment with the RE atomic number, which was again interpreted in terms of charge density contrast, this time using an old idea of Blatt [3], who first pointed out that the resistivity increment of impurities with the same valence still measures a difference of charge densities between impurity and matrix: trivalent lanthanum atoms have a larger volume V than trivalent lutetium atoms, but they also have, by the same token, a larger compressibility K. The ratio of the K’S is larger than the ratio of the Vs. Therefore the lanthanum atoms are compressed more strongly than the lutetium atoms by the high lattice pressure (strong chemical binding) in the small unit cell of ZrAl, and have then a larger 5d6s charge density than lutetium impurities and therefore a smaller charge density contrast against zirconium than lutetium. As in ref. 2, one must assume that at T=O, where the scattering is purely elastic, the impurities show the full potential scattering expected from their charge density contrast, considering their valence together with their state of high compression. The value of Ap = 2 Q cm %- ’ for lanthanum and praseodymium in ZrAl, suggests a rather small charge density contrast (high compression at large compressibility). Cerium in ZrAl, is under very high lattice pressure and therefore strongly mixed valent (Y = 0.2-0.3) [6, 71. Ap/x of cerium is observed to be smaller than that of lanthanum by roughly 30% at all temperatures. This is as anticipated from the fractional valence 3 + Y of cerium, which puts its charge density closer to that of zirconium than that of trivalent praseodymium and lanthanum. The value of Ap = 1 8 cm %- ’ for cerium is reasonably consistent with Y= 0.2-0.3, together with the well-known low compressibility of cerium at this valence [7]. At low temperatures, there is no upturn of Ap/x of cerium. This is not surprising in view of the large T, or 7‘,, which is of around 1000 K for strongly mixed valent cerium [6]. The very similar, non-linear upturn of the increment of all impurity species with increasing temperature cannot have anything to do with valence instability or Kondo effect, nor is there any reason to invoke scattering on crystal field excitations, e.g. in praseodymium (because of the similarity of this increment with that of lanthanum) or on cerium ( Tf is much larger than the crystal field splittings). There are two possible explanations: a change of the electronic structure of ZrAl,
102
with increasing temperature or a change of the phononic structure upon alloying, which will change the temperature dependence of the electron phonon scattering. We have no clear frame of thinking for the first possibility, but can suggest a mechanism for the second. In the Zr,_,RE,Al, alloys, the masses of the constituents increase in the sequence MAI=27, Mz,=91, Mr.= 139, MC,= 140, MPr= 141. The mass of the matrix cell is therefore considerably smaller than that of the impurities. When alloying, we replace low mass zirconium by high mass RE atoms. Replacing a tetravalent zirconium atom by a trivalent RE atom also reduces the binding energy with the nearest neighbours, which will reduce the local elastic constants c. We therefore reduce the average optical phonon frequency (c/M)‘/* on each unit cell with an RE atom by 20%-30%. Therefore the optical phonons around the RE atoms will be excited at lower temperatures than on the zirconium unit cells. Near the Debye temperature and above, there will then be additional electron phonon scattering in the alloys. This additional scattering will appear in A,o/x= (,oalloy -pzrA,*)/x. The additional Ap/x should be independent of the concentration at x Q 1, should appear near the Einstein temperature of the RE TE =h(c/M)“*/kB (near 150 K) and should increase linearly with T sufficiently far above this temperature, because in the Dulong Petit limit the number of additional phonons increases linearly with temperature. All these features are as observed. The effect is expected to be much weaker in a matrix like ZrIr,, where the local elastic constants are also reduced by alloying, but where the average optical phonon frequencies are lower from the start (M= 191 for the majority iridium atoms), actually lower than for the RE atoms. Indeed, in Zr, _.ReE,Ir,, a weak linear increase in Ap/x is barely discernible above 150 K.
4. Conclusion In the alloys Zr, -$E@, with RE = La, Ce and Pr the resistivity increment APIX = (Pa,,oy- PZrAI, )/x is about twice as large for the stable valent lanthanum and praseodymium impurities than for the strongly mixed valent cerium impurities. There is no significant temperature dependence of Ap/x at low temperatures. This is consistent with charge density contrast scattering in the dynamic alloy model [4, 51. Beginning at about 100 K, there is a very unusual increase of Ap/x with increasing temperature, which can be explained by a reduction of the optical phonon frequencies on the REAl, unit cells with respect to the ZrAl, unit cells of the matrix.
Acknowledgments This work was supported by SFB 125 of the Deutsche Forschungsgemeinschaft and by the Institute of Physics of the Polish Academy of Sciences, contract CPBP 01.04.
103
References 1 A. Slebarski, D. Wohlleben and P. Weidner, Z. fhys. B: Condensed Mutter, 61(1985) 177. 2 A. Slebarski and D. Wohlleben, Z. f%ys. B: Condensed Mutter, 60 ( 1985) 449. 3 J. F. Blatt, Phys. Rev., 108( 1957) 285. 4 A. Slebarski, E. Zipper and M. Drzazga, J. Magn. Mugn. Mater., 76, 77 (1988) 249. 5 D. Wohlleben and B. Wittershagen, Adv. Whys., 34 (1985) 403. 6 P. Weidner, K. Keulerz, R. Liihe, B. Roden, J. RGhler, B. Wittershagen and D. Wohlleben, J. Mugn. Magn. Muter., 47, 48 (1985) 75. 7 D. Wohlleben and J. Riihler, J. Appl. Phys., 55 (1984) 1904.