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Positron annihilation in superconductive niobium-aluminium alloys
Volume 29A,
number 3
before the matter tion monotonously
PHYSICS
begins too.
to collapse
POSITRON
in this
direc-
LETTERS
21 April 1969
1. J. V. Narlikar, in Evidence for gravitational theories (Academic Press, New York and London, 1962) pp. 222-227.
ANNIHILATION IN SUPERCONDUCTIVE NIOBIUM-ALUMINIUM ALLOYS
I. J. DEKHTJAR, V. S. MIKHALENKOV, S. G. SAKHAROVA Institute
of the Physics
of Metals,
Academy
Received
of Sciences
25 February
of the Ukrainian
SSR, Kiev
1969
The angular correlation of positron annihilation radiation was studied in the superconductive Nb-Al alloys. From the results of the work the estimation of narameters of the equation for the critical temperature of superconductive transition has been made. -
The method of electron-positron annihilation which have been developed during the recent years turned to be a rather effective one for the study of electron structure of metals [l] and especially the Fermi surface. The attempts made to detect the change of the Fermi surface at the superconductive transformation allow to state [a] that this change is too little to be revealed with the mentioned method. In the present work this method was used for the investigation of superconductive alloys of the system Nb-Al with the structure of B-W type. The curves of the angular correlation of gammaquanta caused by the positron annihilation were obtained with the method of shielded emitter. The intensity of emitted photons, Z(o), may be expressed by a sum of two functions: a parabolic Zp(“) and a Gaussian Zg(u) curve describing the contribution respectively of conduction and core electrons to annihilation [l], Z(o) = Zp(o) + Zg(a) = 27rA(gm -02) + B exp(-a2/c)
,
where cz is the deviation of photon momenta from anticolinearity, em corresponds to the electron momentum lying on the Fermi surface and A, B and C are constants. This expression provides to separate the curve of angular correlation into the parabolic and Gaussian parts, the relative contribution of conduction electrons to the annihilation process corresponding to the ratio of the area under the parabolic part (S,) to the total area (So) under the curve of angular correlation Fig. 1 shows dependence of values (Ymand 148
Fig. 1. Dependence of: IV on I’, (I); Wp on the concentration of Al [2]; am on R, e concentration of Al [3].
Wp =S /So, which characterized the probability of anm*R* elation with conduction electrons, on the aluminium concentration in the alloy, as well as the dependence of Wp on the critical temperature of transformation (Tc) into the superconductive state for alloys with the structure p - W*. The curve Wp(C~l) shows in the range of stoichiometric composition an apparent trend to have an extremum, while the curves W (Tc) and om(CAl) have distinct trends to “satur al!ion”. Fig. 2 gives the dependence of the critical temperature on om, which has for alloys in the region of phase type /3- W an obvious exponential character and may be approximated by the ex* The values of T, are taken from the work of Pan et al. [3].
Volume
29A,
number
3
PHYSICS
LETTERS
21 April
N(Ef) = 8nm2cvatam/h
.
1969
(3)
For alloys Nb-Al in a narrow concentration range with the 6-W structure one may suppose that the parameter V in (2) has a constant value [5]. We’ll assume further that (% W&/k = $8~ [5], where 8~ the Debye temperature. Then we get from eqs. (2) and (3): l-C
M
0.6 81) e-(-b/a,
V)
(4)
where b = h3/8n dCv&. Comparison of eq. (4) and (1) gives the values of the parameters A and B : Fig.
2. Dependenues
of: lg Tc on fX2 [l],
A cs 0.6 8D andB =h3/8ndCv,tV.
Tc on Or, [2].
From the data obtained in the present work we have: at Vat = 10.6 cm3/g. at, am = 6 mrd, N(Ef) = 0.36 eV-1 at-‘, V=1eVandb=490°K. These values are quite acceptable and may be compared with the known data for a series of alloys published in [6], from where it follows that V = 0.4 eV. These results are in a good agreement with the existing theory [4,5] and show in general that it is worthy to use the method of positron snnfhilation for the investigation of superconductors.
pression: Tc =A exp(-B/a,) where
(1)
A and B ttre some parameters for a given
system. The obtained dependence may be readjly explained in terms of the microscopic BCS theory [4], which sets a relation between Tc and the parameters of the electronic structure of a superconduction metal: kTc = (h WD) exp (- l/N(Ef)V)
(5)
(2)
where N(Ef) is the density of electron state at the Fermi level; V ‘the parameter of electron-phonon interaction, which involvs both the shielded Coulomb’s collfsion between electrons and attraction between them inducted by phonons near the Fermi surface and @ WD) the average energy of phonons which scatter electrons at the Fermi level. In the free electrons approximation the method of positron annfhilation allows to estimate the electron state density at the Fermi level [l] from the data for am8and the atomic volume vat:
References Czechoslovak J. Phys. 18 (1968) 1. I. Ja.Dekhtjar, 1509. G. M. Beardslay and A. T. Stewart, 2. C. V. Bristol, Phys. Rev. 141 (1966) 141. A. I. Sudowstov and V.I. 3. V. M. Pan, V.I. Latisheva, Melnikov, Metalurgy, physical chemistry and physsits of superconductors, (Idz. “Nauka”, Moscow), to be published. L. Copper and I. R. Schriffer, Phys. Rev. 4. I. Bardeen, 106 (1967) 162. Phys. Rev. 106 (1958) 280. 5. D. Pines, 6. F. I. Morin and J. P. Maita, Phys. Rev. 129 (1963) 1115.
*****
149
number 3
before the matter tion monotonously
PHYSICS
begins too.
to collapse
POSITRON
in this
direc-
LETTERS
21 April 1969
1. J. V. Narlikar, in Evidence for gravitational theories (Academic Press, New York and London, 1962) pp. 222-227.
ANNIHILATION IN SUPERCONDUCTIVE NIOBIUM-ALUMINIUM ALLOYS
I. J. DEKHTJAR, V. S. MIKHALENKOV, S. G. SAKHAROVA Institute
of the Physics
of Metals,
Academy
Received
of Sciences
25 February
of the Ukrainian
SSR, Kiev
1969
The angular correlation of positron annihilation radiation was studied in the superconductive Nb-Al alloys. From the results of the work the estimation of narameters of the equation for the critical temperature of superconductive transition has been made. -
The method of electron-positron annihilation which have been developed during the recent years turned to be a rather effective one for the study of electron structure of metals [l] and especially the Fermi surface. The attempts made to detect the change of the Fermi surface at the superconductive transformation allow to state [a] that this change is too little to be revealed with the mentioned method. In the present work this method was used for the investigation of superconductive alloys of the system Nb-Al with the structure of B-W type. The curves of the angular correlation of gammaquanta caused by the positron annihilation were obtained with the method of shielded emitter. The intensity of emitted photons, Z(o), may be expressed by a sum of two functions: a parabolic Zp(“) and a Gaussian Zg(u) curve describing the contribution respectively of conduction and core electrons to annihilation [l], Z(o) = Zp(o) + Zg(a) = 27rA(gm -02) + B exp(-a2/c)
,
where cz is the deviation of photon momenta from anticolinearity, em corresponds to the electron momentum lying on the Fermi surface and A, B and C are constants. This expression provides to separate the curve of angular correlation into the parabolic and Gaussian parts, the relative contribution of conduction electrons to the annihilation process corresponding to the ratio of the area under the parabolic part (S,) to the total area (So) under the curve of angular correlation Fig. 1 shows dependence of values (Ymand 148
Fig. 1. Dependence of: IV on I’, (I); Wp on the concentration of Al [2]; am on R, e concentration of Al [3].
Wp =S /So, which characterized the probability of anm*R* elation with conduction electrons, on the aluminium concentration in the alloy, as well as the dependence of Wp on the critical temperature of transformation (Tc) into the superconductive state for alloys with the structure p - W*. The curve Wp(C~l) shows in the range of stoichiometric composition an apparent trend to have an extremum, while the curves W (Tc) and om(CAl) have distinct trends to “satur al!ion”. Fig. 2 gives the dependence of the critical temperature on om, which has for alloys in the region of phase type /3- W an obvious exponential character and may be approximated by the ex* The values of T, are taken from the work of Pan et al. [3].
Volume
29A,
number
3
PHYSICS
LETTERS
21 April
N(Ef) = 8nm2cvatam/h
.
1969
(3)
For alloys Nb-Al in a narrow concentration range with the 6-W structure one may suppose that the parameter V in (2) has a constant value [5]. We’ll assume further that (% W&/k = $8~ [5], where 8~ the Debye temperature. Then we get from eqs. (2) and (3): l-C
M
0.6 81) e-(-b/a,
V)
(4)
where b = h3/8n dCv&. Comparison of eq. (4) and (1) gives the values of the parameters A and B : Fig.
2. Dependenues
of: lg Tc on fX2 [l],
A cs 0.6 8D andB =h3/8ndCv,tV.
Tc on Or, [2].
From the data obtained in the present work we have: at Vat = 10.6 cm3/g. at, am = 6 mrd, N(Ef) = 0.36 eV-1 at-‘, V=1eVandb=490°K. These values are quite acceptable and may be compared with the known data for a series of alloys published in [6], from where it follows that V = 0.4 eV. These results are in a good agreement with the existing theory [4,5] and show in general that it is worthy to use the method of positron snnfhilation for the investigation of superconductors.
pression: Tc =A exp(-B/a,) where
(1)
A and B ttre some parameters for a given
system. The obtained dependence may be readjly explained in terms of the microscopic BCS theory [4], which sets a relation between Tc and the parameters of the electronic structure of a superconduction metal: kTc = (h WD) exp (- l/N(Ef)V)
(5)
(2)
where N(Ef) is the density of electron state at the Fermi level; V ‘the parameter of electron-phonon interaction, which involvs both the shielded Coulomb’s collfsion between electrons and attraction between them inducted by phonons near the Fermi surface and @ WD) the average energy of phonons which scatter electrons at the Fermi level. In the free electrons approximation the method of positron annfhilation allows to estimate the electron state density at the Fermi level [l] from the data for am8and the atomic volume vat:
References Czechoslovak J. Phys. 18 (1968) 1. I. Ja.Dekhtjar, 1509. G. M. Beardslay and A. T. Stewart, 2. C. V. Bristol, Phys. Rev. 141 (1966) 141. A. I. Sudowstov and V.I. 3. V. M. Pan, V.I. Latisheva, Melnikov, Metalurgy, physical chemistry and physsits of superconductors, (Idz. “Nauka”, Moscow), to be published. L. Copper and I. R. Schriffer, Phys. Rev. 4. I. Bardeen, 106 (1967) 162. Phys. Rev. 106 (1958) 280. 5. D. Pines, 6. F. I. Morin and J. P. Maita, Phys. Rev. 129 (1963) 1115.
*****
149