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Phonons in the equiatomic Co Ni alloy
Volume 49A, number 4
PHYSICS LETTERS
23 September 1974
PHONONS IN THE EQUIATOMIC Co Ni ALLOY~ L GAMBETTI, F. MENZINGER and F. SACCHETFI Laboratorio Flrica Nucleare Applicata, Cenrro Studi Nucleari della Casaccia del C.N.E.N., Rome, Italy Received 5 July 1974 The longitudinal and transverse branches of the phonon dispersion relation in f.c.c. CoNihave been determined in the [OOz]direction. Appreciable depression of the longitudinal dispersion curve was observed in this alloy with respect to Ni near the zone boundary.
Sofar only a few investigations have been carried on concentrated substitutional binaiy alloys. It has been studied the effect of a large mass difference in the cornponents which have similar chemical characteristics such as Ni-Pd [1] or Ni-Pt [2] alloys and also some alloys where the elements have similar masses but somewhat different chemical and therefore also different binding characteristics such as Ti-Pb [3], Tl-Bi [3], Bi-Pb [3], Cu-Zn [4], Nb-Mo [5], Cu-Ni [6]. The mass disordered alloys Ni-Pt and Ni-Pd have shown widening of the phonon peaks and in Ni-Pt was also observed a splitting of phonons in two branches as predicted in the Taylor’s theory [71. No broadening of the phonon peaks but large effects in the shape of the dispersion relations were observed in the other class of alloys. It was considered of some interest to study an alloy with no mass disorder but only with a different amount of 3d-electrons, to see whether also in this case could be observed any change from the pure metals. An alloy CoNi at the equiatornic composition was chosen; the average masses of Co and Ni are practically the same, the elements are adjacent in the 3d-transition series and have the same valence, therefore any difference that might exist with the pure elements should be ascribed to solid state effects. The sample, produced by Metals Research, Royston, England was a single crystal 20 X 25 X 5 mm3 and the dispersion relations were obtained by means of tripleaxis neutron spectrometry at the 1MW Reactor of C.S.N. Casaccia. The dispersion relation was measured in the [OOz] direction only because of intensity problems arising *
This work was paxtialiy supported by Gruppo Nazionale di Struttura della Materia of Consiglio Nazionale dde Ricerche.
from the weak neutron source and high absorption of the sample. The constant q mode of operation was used. Four different energies of incident neutrons were used in the course of the experiment; they were comprised between 39 and 59 meV. The results are shown in fig. 1 where they are compared with the data obtained by Birgeneau et al. [8] in pure Ni. As it may be observed there is a quite substantial departure of the dispersion relation in Co Ni with respect to Ni particularly in the longitudinal branch near the zone boundary. The change of the dispersion relations cannot be explained on the basis of the mass-disorder because the
THz
—+ Ni
10
~ CON1 -—
L A
T
-
/
~
r
0.2
QL
d& [OO~l
ds
to
X
Fig. 1. Dispersion relations in the [zOO]direction for the longitudinal (L), and transverse (T) branches for CoNi as compared to the results obtained by Birgeneau et al. [111in pure Ni. The curves are the result of a least-squares fit with interplanar force constants as given by equation (1) of text.
327
Volume 49A, number 4
PHYSICS LETTERS
23 September 1974
Table 1 4 dyn/cm). The best Comparison of interplanar force constants for the [zOO] Land [z00] T branches for Ni and CoNi (units of i0 fit as indicated by the cia-square test is that with 4 parameters.
A
2 1
Ni [zOO]L CoNi [zOO]L Ni [zOO]T CoNi [zOO]T
14.30 12.90 7.56 7.34
A2 ±0.16 ±0.09 ±0.07 ±0.03
A3
1.10 2.76 0.16 0.56
±0.07 ±0.06 ±0.03 ±0.02
atomic masses of the two constituentes are very similar. Moreover as noted by Taylor [7] the mass disorder should produce, for a small mass difference, a change of frequency rather uniformly in all the zone as observed, for instance, in Fe-Ni alloys [4]. The interplanar force constants were calculated both for the pure Ni of ref. [8] and for CoNi in the [zOO] direction, least-square-fitting the dispersion relation with the Fourier series suggested by Foreman and Lomer [9]:
—0.03 —1.46 0.05 —0.23
±0.02 ±0.01 ±0.01 ±0.02
A4
x
0.21 ±0.07 0.85 ±0.08 —0.01 ±0.03 0.09 ±0.04
1 6 1 17
ture point mainly towards the next-to nearest neighbrours) decreases from 0.71 to 0.66, going from Ni to CoNi. Further and more extensive work is in progress to obtain a more systematic information on transition element alloys.
-
1
4ir2M
~J~A
[l—cos(nirq/q~)]
(~)
~
where Mis the average atomic mass of the material and A~is the interplanar force constant for the nth neighbour plane and qM = ir/a with a the lattice constant, v and q are respectively the frequency and the modulus of the wavevector of the phonons. The results are given m table 1. As it can be seen the interplanar force constants are appreciably changed and particularly those with the second and following neighbour planes. We think that the large increase of coupling with these planes may be connected with the change in the 3d-band structure. ~ fact it is known [10] from band structure calculations with the coherent potential approximation that the ratio of the number ofeg.electrons (which in this struc-
328
References [1] W.A. Kamitakahara and B.N. Brockhouse, I.A.E.A. symposium, Grenoble p.73(1972). [21 N. Kunitomy, Y. Tsunoda and Y. Hixai, Solid State Comm. 13 (1973) 495. [3] S.C. Ny and B.N. Brockhouse, Solid State Comm. 5 (1967) 79. [4] E.D. Hailman and B.N. Brockhouse, Can. J. Physics 47 (1969) 1117. [~] and A.D.B. Woods, Phys. Rev. [6] M. Sakamoto and Y. Hamaguchi, LA.E.A. symposium, Copenhagen p. 181 (1967). [7] D.W. Taylor, Phys. Rev. 156 (1967) 1017. [8] R.J. Birgeneau, G. Cordes, G. Dolling and A.D.B. Woods, Phys. Rev. 136 (1964) A1359. [9] A.T.E. Foreman and W.M. Lomer, Proc. Phys. Soc. B70 (1957) 1143. [10] F. Leoni and F. Sacchetti, Nuovo Cimento 21B (1974) 97.
PHYSICS LETTERS
23 September 1974
PHONONS IN THE EQUIATOMIC Co Ni ALLOY~ L GAMBETTI, F. MENZINGER and F. SACCHETFI Laboratorio Flrica Nucleare Applicata, Cenrro Studi Nucleari della Casaccia del C.N.E.N., Rome, Italy Received 5 July 1974 The longitudinal and transverse branches of the phonon dispersion relation in f.c.c. CoNihave been determined in the [OOz]direction. Appreciable depression of the longitudinal dispersion curve was observed in this alloy with respect to Ni near the zone boundary.
Sofar only a few investigations have been carried on concentrated substitutional binaiy alloys. It has been studied the effect of a large mass difference in the cornponents which have similar chemical characteristics such as Ni-Pd [1] or Ni-Pt [2] alloys and also some alloys where the elements have similar masses but somewhat different chemical and therefore also different binding characteristics such as Ti-Pb [3], Tl-Bi [3], Bi-Pb [3], Cu-Zn [4], Nb-Mo [5], Cu-Ni [6]. The mass disordered alloys Ni-Pt and Ni-Pd have shown widening of the phonon peaks and in Ni-Pt was also observed a splitting of phonons in two branches as predicted in the Taylor’s theory [71. No broadening of the phonon peaks but large effects in the shape of the dispersion relations were observed in the other class of alloys. It was considered of some interest to study an alloy with no mass disorder but only with a different amount of 3d-electrons, to see whether also in this case could be observed any change from the pure metals. An alloy CoNi at the equiatornic composition was chosen; the average masses of Co and Ni are practically the same, the elements are adjacent in the 3d-transition series and have the same valence, therefore any difference that might exist with the pure elements should be ascribed to solid state effects. The sample, produced by Metals Research, Royston, England was a single crystal 20 X 25 X 5 mm3 and the dispersion relations were obtained by means of tripleaxis neutron spectrometry at the 1MW Reactor of C.S.N. Casaccia. The dispersion relation was measured in the [OOz] direction only because of intensity problems arising *
This work was paxtialiy supported by Gruppo Nazionale di Struttura della Materia of Consiglio Nazionale dde Ricerche.
from the weak neutron source and high absorption of the sample. The constant q mode of operation was used. Four different energies of incident neutrons were used in the course of the experiment; they were comprised between 39 and 59 meV. The results are shown in fig. 1 where they are compared with the data obtained by Birgeneau et al. [8] in pure Ni. As it may be observed there is a quite substantial departure of the dispersion relation in Co Ni with respect to Ni particularly in the longitudinal branch near the zone boundary. The change of the dispersion relations cannot be explained on the basis of the mass-disorder because the
THz
—+ Ni
10
~ CON1 -—
L A
T
-
/
~
r
0.2
QL
d& [OO~l
ds
to
X
Fig. 1. Dispersion relations in the [zOO]direction for the longitudinal (L), and transverse (T) branches for CoNi as compared to the results obtained by Birgeneau et al. [111in pure Ni. The curves are the result of a least-squares fit with interplanar force constants as given by equation (1) of text.
327
Volume 49A, number 4
PHYSICS LETTERS
23 September 1974
Table 1 4 dyn/cm). The best Comparison of interplanar force constants for the [zOO] Land [z00] T branches for Ni and CoNi (units of i0 fit as indicated by the cia-square test is that with 4 parameters.
A
2 1
Ni [zOO]L CoNi [zOO]L Ni [zOO]T CoNi [zOO]T
14.30 12.90 7.56 7.34
A2 ±0.16 ±0.09 ±0.07 ±0.03
A3
1.10 2.76 0.16 0.56
±0.07 ±0.06 ±0.03 ±0.02
atomic masses of the two constituentes are very similar. Moreover as noted by Taylor [7] the mass disorder should produce, for a small mass difference, a change of frequency rather uniformly in all the zone as observed, for instance, in Fe-Ni alloys [4]. The interplanar force constants were calculated both for the pure Ni of ref. [8] and for CoNi in the [zOO] direction, least-square-fitting the dispersion relation with the Fourier series suggested by Foreman and Lomer [9]:
—0.03 —1.46 0.05 —0.23
±0.02 ±0.01 ±0.01 ±0.02
A4
x
0.21 ±0.07 0.85 ±0.08 —0.01 ±0.03 0.09 ±0.04
1 6 1 17
ture point mainly towards the next-to nearest neighbrours) decreases from 0.71 to 0.66, going from Ni to CoNi. Further and more extensive work is in progress to obtain a more systematic information on transition element alloys.
-
1
4ir2M
~J~A
[l—cos(nirq/q~)]
(~)
~
where Mis the average atomic mass of the material and A~is the interplanar force constant for the nth neighbour plane and qM = ir/a with a the lattice constant, v and q are respectively the frequency and the modulus of the wavevector of the phonons. The results are given m table 1. As it can be seen the interplanar force constants are appreciably changed and particularly those with the second and following neighbour planes. We think that the large increase of coupling with these planes may be connected with the change in the 3d-band structure. ~ fact it is known [10] from band structure calculations with the coherent potential approximation that the ratio of the number ofeg.electrons (which in this struc-
328
References [1] W.A. Kamitakahara and B.N. Brockhouse, I.A.E.A. symposium, Grenoble p.73(1972). [21 N. Kunitomy, Y. Tsunoda and Y. Hixai, Solid State Comm. 13 (1973) 495. [3] S.C. Ny and B.N. Brockhouse, Solid State Comm. 5 (1967) 79. [4] E.D. Hailman and B.N. Brockhouse, Can. J. Physics 47 (1969) 1117. [~] and A.D.B. Woods, Phys. Rev. [6] M. Sakamoto and Y. Hamaguchi, LA.E.A. symposium, Copenhagen p. 181 (1967). [7] D.W. Taylor, Phys. Rev. 156 (1967) 1017. [8] R.J. Birgeneau, G. Cordes, G. Dolling and A.D.B. Woods, Phys. Rev. 136 (1964) A1359. [9] A.T.E. Foreman and W.M. Lomer, Proc. Phys. Soc. B70 (1957) 1143. [10] F. Leoni and F. Sacchetti, Nuovo Cimento 21B (1974) 97.