From theoretical chemistry to nuclear physics and back

Transcription

1 From theoretical chemistry to nuclear physics and back H. Haas CICECO, Universidade de Aveiro, Aveiro, Portugal and CERN/PH-IS, CH-1211 Geneve-23, Switzerland

2 Nuclear quadrupole interaction p-electron cloud electric field gradient (EFG) V zz = d 2 V/dz 2 [V/m 2 ] nucleus nuclear quadrupole moment Q [b] low energy high energy interaction energy E = eqv zz Interaction frequency eqv zz /h typically 1 MHz RF spectroscopy NQR

3 Interest from (theoretical) chemistry: Ionic bond: NaCl Covalent bond: Cl 2 EFG = EFG = atomic value Transition metal halides: CuCl 2, NiCl 2,... EFG measures covalency! More interesting: Fluorides but 19 F has I = ½, thus Q =! Measure other state by nuclear technique!

4 Nuclear decay Source (isomeric) state T 1/2 3 seconds to years PAC state, Spin > 1/2 T 1/2 2 ns to 5 ns

5 Angular correlation

6 PAC coincidence time spectrum 9 o detector 18 o detector

7 The Berkeley trick two start detectors two stop detectors four time spectra simultaneously! made possible by 16 channel MCA, and of course some electronics

8 Typical PAC spectra (Berkeley 1969)

9 A bit of history: Temperature dependence of QI in Cd Used T 1.5 law for extrapolation to T=

10 The hexagonal crystal structure of Zn and Cd Zn Cd a[a] c[a] c c/a hcp a

11 nn configuration Positive point charges would give negative EFG!

12 The breakthrough in experiment The EFG for Cd in Cd is positive!

13 EFG at impurities in cadmium: Our data 15 EFG [1 21 V/m 2 ] 5sp Cd 1 5 Ru Rh Pd Ag Cd In Sn Sb Te I Xe -5

14 Back to Townes and Dailey: p orbitals at central atom

15 Tight binding model for Cd

16 Model: The whole story 2 1 EFG [1 21 V/m 2 ] 5sp Cd Ru Rh Pd Ag Cd In Sn Sb Te I Xe

17 The breakthrough in theory This triggered my retirement project!

18 Theoretical EFG for 5sp impurities in Cd [1 21 V/m 2 ] 2 1 Cd Pd Ag Cd In Sn Sb Te Ii Xe 3x3x2 norel 3x3x2 rel 4x4x2 rel 4x4x3 rel 5x5x2 rel 5x5x3 rel Conclusion: No large dependence on supercell size and local lattice relaxation!

19 Final FLAPW results 2 1 EFG [1 21 V/m 2 ] 5sp Cd Ru Rh Pd Ag Cd In Sn Sb Te I Xe

20 Local volume change (%) by sp impurities 5 Zn 5 Cd sp sp 4sp 1 1 Zn Ga Ge As Se Br Kr Rb Sr Yy Zn Ga Ge As Se Br Kr Rb Sr Yy -1-1

21 Local c/a change (%) by sp-impurities 6 Zn 6 Cd Zn Ga Ge As Se Br Kr Rb Sr Yy Zn Ga Ge As Se Br Kr Rb Sr Yy

22 5sp EFG compared to experiments in Zn and Cd 2 Zn 2 Cd 1 1 Ru Rh Pd Ag Cd In Sn Sb Te I Xe Ru Rh Pd Ag Cd In Sn Sb Te I Xe

23 4sp EFG compared to experiments in Zn and Cd 1 Zn 1 Cd 5 5 Fe Co Ni Cu Zn Ga Ge As Se Br Kr Fe Co Ni Cu Zn Ga Ge As Se Br Kr

24 Conclusions from 4sp and 5sp cases For the cases where the nuclear quadrupole moments (Q) are reliably known the calculations reproduce quantitatively the data, with the exceptions of Sb in Zn and I in Zn and Cd. Whenever Q has only been estimated, strong disagreement is found. In three cases ( 67 Ge, 77 Br, 123 Xe) it is felt that the present work results in the first reliable value for Q. All the qualitative features found in the present investigation can be understood in the rigid band model earlier proposed.

25 EFG ratio, plotted: XZn / (XZn + XCd) 1.5 Fe Co Ni Cu Zn Ga Ge As Se Br Kr 1.5 Ru Rh Pd Ag Cd In Sn Sb Te Ii Xe Also confirms conclusion about incorrect Q values (purple)

26 6sp EFG compared to experiments 6 Zn 6 Cd Os Ir Pt Au Hg Tl Pb Bi Po At Rn Os Ir Pt Au Hg Tl Pb Bi Po At Rn

27 Conclusions from 6sp cases The inclusion of spin-orbit interaction in the calculations changes the results only by a very small amount, typically 5%. For the cases measured with time-differential PAC perfect agreement is obtained. For all cases measured with NO (nuclear orientation) the experiments should be ignored!

28 6sp EFG ratio, plotted: XZn / (XZn + XCd) 1.5 Os Ir Pt Au Hg Tl Pb Bi Po At Rn Also confirms conclusion about NO experiments (squares)!

29 Summary The electric field gradients (EFG) at the impurities Fe Kr, Ru Xe, and Os Rn in the hcp metals Zn and Cd were calculated with the WIEN2k full-potential linearized augmented plane waves (FLAPW) code. The generalized gradient approximation was used throughout. Supercells with 36(45), 64(48), 96(15), 1(14) and 15(21) atoms were constructed with the low temperature lattice constants for all cases in order to test the influence on the resultant EFG (number of k-points in the reduced Brillouin zone in parentheses). The positional parameters were relaxed to small resultant forces acting on all atoms in the supercell, requiring typically 3-4 structural iterations. The calculations reproduce the experiments remarkably well!

30 Thank you Dave! (for putting me on the track)