Positron Annihilation in Copper Alloys

Abstract

The long-slit geometry has been used to measure the angular correlation of annihilation radiation from copper alloys. The alloys 0.975 Cu-0.025 Al, 0.95 Cu-0.05 Al, and 0.77 Cu-0.23 Ni display "necks" in momentum space. In units of the copper Fermi-surface neck, the measured neck radii of 1.3, 1.5, and 0.8, respectively, are consistent with the assumption that the energy-momentum relation is unchanged upon alloying.Recent investigations 1 " 4 of annihilation radiation from oriented single crystals of copper and copper alloys have shown anisotropies which are apparently produced by "necks" where the Fermi surface (F.S.) makes contact with the [111] Brillouin zone boundaries. It therefore seems that the positron method, if applied with sufficient angular resolution, could provide useful data on changes in the F.S., and particularly in the necks, as copper is alloyed with other metals. Other methods 5 of studying these changes have been restricted to solute concentrations of about 0.1% or less, but the positron method imposes no such restriction; the only limitation lies in our ability to interpret the results. We have used the method to study the following alloys: 0.975 Cu-0.025 Al, 0.95 Cu-0.05 Al, 0.78 Cu-0.22 Zn, and 0.77 Cu-0.23 Ni. Decimals indicate atomic percentages in all constituents.Our data were obtained by a "long-slit" angular correlation apparatus in which the angles were defined by slits 30 cm long and 1.0 mm wide, at a distance of 4.0 m from the sample. Single crystals of the above alloys, as well as a single crystal of pure Cu, were oriented with respect to the slits in such a way that the angle 6 was proportional to the component of momentum parallel to the [110] axis (or, in one case, to the [111] axis). Our angular correlation curve for copper is in agreement with the results of Berko, Cushner, and Erskine, 1 who used the same geometry.Each single-crystal sample was also used as the source of positrons; in each case about 1.5 Ci of Cu 64 was produced in the sample by thermal-neutron irradiation. After irradiation the source sample was placed in a pocket constructed with identically oriented (nonirradiated) pieces of the same alloy crystal, so that all of the positrons were annihilated in the assembly in a volume whose width parallel to the selected momentum component was about 0.3 mm. The resulting angular-resolution function had a full width at half-maximum of about 0.3 mrad, for the mo-mentum component in the selected direction. The whole assembly was cooled to liquid-nitrogen temperature in order to minimize the contribution of the positron to the momentum of an annihilating pair. Figure 1 shows the angular correlation curve obtained for the [111] axis of the Cu-Ni alloy. Data for 6<0 are folded over onto the data for 6 >0; the clear agreement between the two sets of points provides a good check on the experimental technique and on the treatment of the data-e.g., the correction for decay of the source. Each point near the peak represents about 60 000 coincidence counts, and the entire curve ...

Dependence on Fermi surface dimensions of oscillatory exchange coupling in Co/Cu1−xOkuno1, Inomata2 1993Phys. Rev. Lett.

“…In the light of the theory [16], we discuss the relation between the measured oscillation periods and the extremal points at the spacer [21]; and closed triangles give the calculated results from KKR-CPA [20]. An open inverted triangle is the neck diameter of pure Cu from the de Haas-van Alphen effect [22].…”

The Fermi surface of random-metallic alloys and the oscillatory magnetic coupling across alloy spacers

“…Indeed, it has been proven that this is the typical case for random binary alloys, so the k-space description of the electronic states, on average, is valid and the Fermi surface of many of these systems is well defined. As we discuss later, even small necks and pockets of the pure-host-metal Fermi surface survive in alloying even for large concentrations of the solute and these features are identified in ACAR [8,9] as well as oscillatory magnetic coupling experiments [25][26][27]. Since for most of the binary alloys the Fermi surface is well defined across the whole range of concentrations, it is of great interest to see how the shape and connectivity of the Fermi surface change with concentration.…”

“…In figure 2 the calculated neck diameter as well as the one measured using ACAR [8,9] and the one predicted from the oscillatory magnetic coupling period for the (110) direction [27] are plotted as functions of the Ni concentration. The agreement between the three different sets of data is striking.…”

“…The method up to now has had to rely on theoretical calculations of the Fermi surface for the comparison of its measurements [5][6][7]. For example in reference [5] the neck of the Fermi surface of Cu 1−x Ni x calculated with KKR-CPA electronic structure method was compared with ACAR measurements [8,9]. These theoretical calculations usually combine an electronic structure method (usually ab initio) with the CPA 'mean-field' approach which is the most accurate 'single-site' approximation to the random-binary-alloy problem [10,11].…”

Positron–annihilation measurements of the Fermi surface of copper‐base solid solutions with gallium, germanium, and nickel

“…From the data concerning the resolution of the present apparatus (Section 3.1), it is evident that a decrease of kNp below the one of pure Cu could have been easily detected. A possible explanation as to why Hasegawa et al [22] and Murray and McGervey [26] found that adding Ni t o Cu decreases kft, is the difficulty of deriving k, from I ( @ curves. Moreover, the two groups had poor vertical resolutions: 5.4 mrad and infinite in comparison, respectively.…”