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The Debije temperature of pure Pd and dilute PdNi alloys
PHYSICS LETTERS
Volume 45A, number 2
10 September 1973
THE DEBIJE TEMPERATURE OF PURE Pd AND DILUTE Pd-Ni ALLOYS* J.E. Van DAM and M.F. PIKART Kamerlingh Onnes Laboratorium,
Leiden,
The Netherlands
Received 29 June 1973 The temperature dependence of the Debije temperature, deduced from specific-heat data of dilute (c < 2.2 at.% Ni) Pd-Ni alloys, is presented. Comparing these data with results for pure Pd and a PdCu ahoy we conclude that in pure Pd no observable paramagnon contribution to the apparent lattice specific heat exists.
Contrary to most metals pure Pd shows only a small variation of the effective Debije temperature O(T) with temperature [ 1,2] . It has been suggested by Doniach that this anomaly could be due to a contribution of electronic origin (“paramagnons?), see ref. [3] . This contribution was assumed to decrease the apparent lattice specific heat and hence to increase O(T). In order to verify this suggestion we have measured [4] the specific heat of some dilute Pd-Ni alloys (c < 2.2 at.% Ni) over a wider temperature range (1.3 K- 25 K) than in previous work [5,6]. For comparison we also measured a Pd - 5 at.% Cu alloy:These alloyd systems were chosen because in Pd-Ni the electronic contribution suggested by Doniach would be enhanced compared with the value in pure Pd, while in Pd-Cu it would be decreased. We expected therefore that the variation of 0 with temperature for Pd-Ni would be even smaller than for pure Pd, while for Pd-Cu the opposite would happen. We have computer-fitted our specific-heat data (AC/C = 0.4%) with a least-squares programme to the following expression: C/T=
~~iT2i-2 i=l
From this representation of the data (RMSD = 0.3%) O(T) was calculated at one degree intervals from the apparent lattice specific heat CL(CL E C-a, 7’) comparing it with the known Debije function. As we are in this letter only interested in the temperature * This work is part of the research program of FOM, sup ported by ZWO and TN0 (Metaahnstituut).
o P&Ni
lot
Pd-Ni 1.5
v Pd-Ni 2.15
0
L5
O
at
at O/o
10
I5
20
K
25
Fig. 1. Temperature dependence of the normalized Debije temperature @(T)/@(O). variation of @(the other aspects will be discussed
elsewhere [4]), we have normalized O(T)to its value at T = 0.The results of this procedure,are shown in fig. 1. It is clear from this figure that the expected changes in O(T) do not occur. For Pd-Cu no change is observed (this is also the case of a Pd-1 at.% Ag alloy [41). while for Pd-Ni the depth of the minimum in the 0 versus temperature curve is larger instead of smaller than in pure Pd. Taking into account the above considerations we conclude that the suggestion by Doniach is not confirmed by our experiments. Therefore an interpretation of the anomalous behaviour of O(T) in pure Pd in terms of a particular temperature dependence of the lattice specific heat seems appropriate. It is significant in this respect that 0 derived from values of CL, which were calculated by Miiller and Brockhouse [7] from their neutron scattering experiments, does not vary much with temperature (see fig. 2). 147
Volume 45A, number 2
PHYSICS LETTERS
KJ
r
““W 260
Pd
o cup. (Boerstoel et al)
250
I\
240
-
220’
-
theor. (Pal)
0
data from Mtlller and
I 1
I 0 T_
IO
20
30
K
Fig. 2. Comparison of the experimental and theoretical variation with temperature of the Debije temperature of pure Pd. The line connecting the circles merely serves to guide the eye; the uninterrupted line is from ref. [ 8 ] .
Also the absolute values of 0 are in good agreement with those derived from the specific heat. The discrepancy between experiment and theory [8] apparent from fig. 2 is typical for the present state of the art of lattice dynamics of metals, so no conclusions can be drawn from this difference. The changes in O(T) noticeable in fig. 1 for the Pd-Ni alloys are most probably due to an electronic contribution of magnetic origin since alloying Pd with 5% Cu has no effect on O(T)/@(O). The previous experiments on Pd-Ni [ 5,6] have shown a large negative contribution to the T3 term of the specific heat, which was attributed to localized spin fluctuations. The changes in O(T)/@(O) which we have observed are consistent with a positive contribution to the fl term, i.e. an increase of u3 with increasing concentration of Ni. The presence of both contributions with opposite sign explains why C, at about 15 K for the Pd-Ni alloys is nearly equal to the value for pure Pd [4]. The magnetic character of the contribution to the fi term is also evident from the
148
10 September 1973
influence of a magnetic field, which causes a decrease of a3 [4] . The contribution to the p term can therefore be considered as a higher order term of the contribution of the localized spin fluctuations (LSF): (C/T)LSF = r(0) [1 -@/Td)2 + +B(T/T&4 + ...I. where Ts~ is the local spin fluctuation temperature. Recently, the influence of higher order terms has been noticed in the resistivity of dilute Pd-Ni alloys [9]. We have checked the theoretical prediction of a term in the LSF contribution proportional to T31n(T/T&. (Due to the limited temperature range in the previous measurements [5,6] this term was indistinguishable from the T3 term.) Fitting our data to eq. (1) with a term T31nT included does not improve the fits, so the presence of this term is very questionable. The same conclusion can be drawn from a plot of CL/T3 versus lnT, which shows for the 1.85 at.% Ni alloy a strong deviation above about 5 K from a linear behaviour (below 5 K the accuracy of CL/T3 is too low to make any definite conclusions about a linear behaviour because CL/T3 is almost constant) [4]. This behaviour is certainly due to inter-impurity interactions, which do not justify a comparison with LSF theory, although the interactions can as a first approximation be accounted for by a renormalized value of Td [4].
References [l] B.M. Boerstoel, J.J. Zwart and J; Hansen, Physica 54
[2] [3] [4] [S] (61 [7] [8] [9]
(1971) 442 (Commun. Kamerlingh Onnes Lab., Leiden, No. 385). B.W. Veal and J.A. Rayne, Phys. Rev. 135 (1964) A442. G.E. Shoemake and J.A. Rayne, Phys. Lett. 26A (1968) 222. J.E. Van Dam, thesis, University of Leiden, 1973; Physica to be published. A.I. Schindler and C.A. Mackliet, Phys. Rev.‘Lett. 20 (1968) 15. G. Couteau, R. Fourneaux, R. Tournier and P. Lederer, Phys. Rev. Lett. 21 (1968) 1082. A.P. Miiller and B.N. Brockhouse, Canad. J. Phys. 49 (1971) 704. S. Pal, J. Phys. Fl (1971) 558. R.A. Beyerlein and D. Lazarus, Phys. Rev. B7 (1973) 511.
Volume 45A, number 2
10 September 1973
THE DEBIJE TEMPERATURE OF PURE Pd AND DILUTE Pd-Ni ALLOYS* J.E. Van DAM and M.F. PIKART Kamerlingh Onnes Laboratorium,
Leiden,
The Netherlands
Received 29 June 1973 The temperature dependence of the Debije temperature, deduced from specific-heat data of dilute (c < 2.2 at.% Ni) Pd-Ni alloys, is presented. Comparing these data with results for pure Pd and a PdCu ahoy we conclude that in pure Pd no observable paramagnon contribution to the apparent lattice specific heat exists.
Contrary to most metals pure Pd shows only a small variation of the effective Debije temperature O(T) with temperature [ 1,2] . It has been suggested by Doniach that this anomaly could be due to a contribution of electronic origin (“paramagnons?), see ref. [3] . This contribution was assumed to decrease the apparent lattice specific heat and hence to increase O(T). In order to verify this suggestion we have measured [4] the specific heat of some dilute Pd-Ni alloys (c < 2.2 at.% Ni) over a wider temperature range (1.3 K- 25 K) than in previous work [5,6]. For comparison we also measured a Pd - 5 at.% Cu alloy:These alloyd systems were chosen because in Pd-Ni the electronic contribution suggested by Doniach would be enhanced compared with the value in pure Pd, while in Pd-Cu it would be decreased. We expected therefore that the variation of 0 with temperature for Pd-Ni would be even smaller than for pure Pd, while for Pd-Cu the opposite would happen. We have computer-fitted our specific-heat data (AC/C = 0.4%) with a least-squares programme to the following expression: C/T=
~~iT2i-2 i=l
From this representation of the data (RMSD = 0.3%) O(T) was calculated at one degree intervals from the apparent lattice specific heat CL(CL E C-a, 7’) comparing it with the known Debije function. As we are in this letter only interested in the temperature * This work is part of the research program of FOM, sup ported by ZWO and TN0 (Metaahnstituut).
o P&Ni
lot
Pd-Ni 1.5
v Pd-Ni 2.15
0
L5
O
at
at O/o
10
I5
20
K
25
Fig. 1. Temperature dependence of the normalized Debije temperature @(T)/@(O). variation of @(the other aspects will be discussed
elsewhere [4]), we have normalized O(T)to its value at T = 0.The results of this procedure,are shown in fig. 1. It is clear from this figure that the expected changes in O(T) do not occur. For Pd-Cu no change is observed (this is also the case of a Pd-1 at.% Ag alloy [41). while for Pd-Ni the depth of the minimum in the 0 versus temperature curve is larger instead of smaller than in pure Pd. Taking into account the above considerations we conclude that the suggestion by Doniach is not confirmed by our experiments. Therefore an interpretation of the anomalous behaviour of O(T) in pure Pd in terms of a particular temperature dependence of the lattice specific heat seems appropriate. It is significant in this respect that 0 derived from values of CL, which were calculated by Miiller and Brockhouse [7] from their neutron scattering experiments, does not vary much with temperature (see fig. 2). 147
Volume 45A, number 2
PHYSICS LETTERS
KJ
r
““W 260
Pd
o cup. (Boerstoel et al)
250
I\
240
-
220’
-
theor. (Pal)
0
data from Mtlller and
I 1
I 0 T_
IO
20
30
K
Fig. 2. Comparison of the experimental and theoretical variation with temperature of the Debije temperature of pure Pd. The line connecting the circles merely serves to guide the eye; the uninterrupted line is from ref. [ 8 ] .
Also the absolute values of 0 are in good agreement with those derived from the specific heat. The discrepancy between experiment and theory [8] apparent from fig. 2 is typical for the present state of the art of lattice dynamics of metals, so no conclusions can be drawn from this difference. The changes in O(T) noticeable in fig. 1 for the Pd-Ni alloys are most probably due to an electronic contribution of magnetic origin since alloying Pd with 5% Cu has no effect on O(T)/@(O). The previous experiments on Pd-Ni [ 5,6] have shown a large negative contribution to the T3 term of the specific heat, which was attributed to localized spin fluctuations. The changes in O(T)/@(O) which we have observed are consistent with a positive contribution to the fl term, i.e. an increase of u3 with increasing concentration of Ni. The presence of both contributions with opposite sign explains why C, at about 15 K for the Pd-Ni alloys is nearly equal to the value for pure Pd [4]. The magnetic character of the contribution to the fi term is also evident from the
148
10 September 1973
influence of a magnetic field, which causes a decrease of a3 [4] . The contribution to the p term can therefore be considered as a higher order term of the contribution of the localized spin fluctuations (LSF): (C/T)LSF = r(0) [1 -@/Td)2 + +B(T/T&4 + ...I. where Ts~ is the local spin fluctuation temperature. Recently, the influence of higher order terms has been noticed in the resistivity of dilute Pd-Ni alloys [9]. We have checked the theoretical prediction of a term in the LSF contribution proportional to T31n(T/T&. (Due to the limited temperature range in the previous measurements [5,6] this term was indistinguishable from the T3 term.) Fitting our data to eq. (1) with a term T31nT included does not improve the fits, so the presence of this term is very questionable. The same conclusion can be drawn from a plot of CL/T3 versus lnT, which shows for the 1.85 at.% Ni alloy a strong deviation above about 5 K from a linear behaviour (below 5 K the accuracy of CL/T3 is too low to make any definite conclusions about a linear behaviour because CL/T3 is almost constant) [4]. This behaviour is certainly due to inter-impurity interactions, which do not justify a comparison with LSF theory, although the interactions can as a first approximation be accounted for by a renormalized value of Td [4].
References [l] B.M. Boerstoel, J.J. Zwart and J; Hansen, Physica 54
[2] [3] [4] [S] (61 [7] [8] [9]
(1971) 442 (Commun. Kamerlingh Onnes Lab., Leiden, No. 385). B.W. Veal and J.A. Rayne, Phys. Rev. 135 (1964) A442. G.E. Shoemake and J.A. Rayne, Phys. Lett. 26A (1968) 222. J.E. Van Dam, thesis, University of Leiden, 1973; Physica to be published. A.I. Schindler and C.A. Mackliet, Phys. Rev.‘Lett. 20 (1968) 15. G. Couteau, R. Fourneaux, R. Tournier and P. Lederer, Phys. Rev. Lett. 21 (1968) 1082. A.P. Miiller and B.N. Brockhouse, Canad. J. Phys. 49 (1971) 704. S. Pal, J. Phys. Fl (1971) 558. R.A. Beyerlein and D. Lazarus, Phys. Rev. B7 (1973) 511.