The electric field gradient at the nucleus in HCP Zr and Hf

Abstract

We use the linear muffin-tin orbital formalism, in the atomic sphere approximation, to obtain the electric field gradient (EFG) at the nucleus for metallic Zr and Hf, in the HCP structure. Combined corrections are included in the calculations. To evaluate the importance of relativistic effects, non-relativistic and scalar relativistic calculations were performed. In agreement with experiment, we find that the EFG for Hf is larger than for Zr by a factor of more than 2. We show that this is mainly due to the behaviour of metallic p and d orbitals, which for Hf have comparatively larger values close to the nuclear region. Because Hf and Zr are in the same group of the periodic table, Hf is often used as a probe in perturbed angular correlation experiments, when investigating the EFG for Zr alloys. We use our results to note that, for similar values of orbital occupations, the EFG at a Hf probe is larger than the EFG at a Zr atom placed at the same site.

Theoretical study of hyperfine and local magnetic properties of Co and Fe clusters in fcc Ag hosts

“…19 The procedure used here for calculating the HF at each site, after the self-consistent electronic structure for a given system is obtained, has been described in detail in previous papers. 12,[20][21][22] As shown in the literature, the hyperfine field for transition metals is usually dominated by the Fermi contact contribution. In a nonrelativistic approach this contribution can be determined by the magnetization density at the nuclear position R through the expression:…”

Study of the EFG Trends in Zr2T (T = Fe, Co, Ni) Intermetallic Compounds

“…We see that I* p is an order of magnitude larger than (reflecting the V tj trend observed in Table 2), and both have almost constant values: I* p varies by not more than two percent from one compound to the other, and I d T d does not vary. The change of can be explained by the small decrease of the WS radius (see Table 1), a more compressed p wave function adding more weight at the region near the nucleus; the I dd are not sensible to such changes, as discussed in [3,4,7,8,13]. Looking now at the T site radial integrals from Table 3, we see that the I] d are much larger than at the Zr site, increasing continuously with the d band filling from Fe to Ni, while I T pp remains almost constant and much smaller than at the Zr sites.…”

“…We note that the probe effect on the EFG results is strong since Ta and Zr have different electronic structure. An attempt to compare the theoretical and experimental results can be made as suggested in [7], The EFG at 181 Ta in hep Zr has been measured by the TDPAC to be 514 x 10 15 V/cm 2 [15], the EFG at Zr in Zr has been measured by NMR to be 368 x 10 15 V/cm 2 [15], The ratio between those two values is around 1.4. By multiplying the theoretical Zr EFG values in Table 4 by this factor we find a very reasonable overall agreement between the theoretical and measured EFG results.…”

“…As it has been pointed out before [3,4,[6][7][8]13], the EFG can conveniently be analysed as a product of two different contributions which are combined to give the p and d contributions: one radial integral (I pp or I dd ) and an angular asymmetry (An p or An d ). The angular asymmetries are mainly given by the difference in occupations of orbitals with different m quantum number (different symmetries) and are responsible for the EFG sign.…”

“…From the LMTO-ASA charge density we calculate the EFG tensor, whereby no empirical factors are used. This procedure to evaluate the EFG may be found in the literature as a successful approach used in different self consistent band structure methods [2][3][4][5][6][7][8].…”