Electric Field Gradients in Metals -'Ą
Total Page：16
File Type：pdf, Size：1020Kb
HYPERFINE INTERACTIONS PROCEEDINGS OF XVII WINTER SCHOOL February 19 - March 3, 1979 Bielsko - Biała, POLAND Edited by : R. Kulessa and K. Królas Cracow; September 1979 4 NAKŁADEM INSTYTUTU FIZYKI JĄDROWEJ W KRAKOWIE v UL. RADZIKOWSKIEGO 152 Wydanie pierwsze. Nakład 220 egzemplarzy Arkuszy wydawniczych 25,5. Arkuszy drukarskich 22,4. Papier offsetowy kl. III, 70 g. 70 x 100. Oddano do druku w październiku 1979 roku. Druk ukończono w listopadzie 1979 roku. Zamówienie nr 295/79. Kopię kserograficzną, druk i oprawę wykonano w INSTYTUCIE FIZYKI JĄDROWEJ W KRAKOWIE SCHOOL HOSTS Institute of Nuclear Physics, Kraków Institute of Physics, Jagellonian University, Kraków SCHOOL ADDRESS Ośrodek Wdrażania Postępu Technicznego w Energetyce, Bielsko-Biała, ul. Brygadzistów 170 '\ OHSANIZIWG COMMITTEE Chairmen: R. Kulessa A.Z. Hrynkiewioz Members: E. Bożek M. Lach E. GOrlioh M» Marszałek H. Kmieć B. Haydell J. Kraczka K. Tomala K. Królas J. Wrzesiński Secretary: Z. Natkanieo 1. Electric Quadrupole Interaction ELECTRIC PIELD GRADIENTS IN METAIS G. Schatz 3 ELECTRIC FIELD GRADIENTS IN CUBIC ALLOTS K. Krdlas 21 SOME HYPERFINE INTERACTION STUDIES IN OXIDE GLASSES R. Kamal .............. 37 Panel Discussion: RESULTS OP QUADHUPOLE INTERACTION MEASUREMENTS IN METALS E. Bodenstedt ........ .. 48 REMARKS ON QUADRUPOLAR ELEMENTARY EXCITATIONS IN NONCOBIC METALS G. Schatz 61 2. Magnetic Dipole Interaction HYPERFINE FIELDS IN HEUSLER ALLOYS I.A. Campbell 67 MOSSBAUER SPECTROSCOPY IN INTERMETALLIC COMPOUNDS AND ALLOYS OP RARE EARTHS Z. Tomala ........ ....... 71 INVESTIGATIONS OP HYPERFINE INTERACTIONS IN NICKEL- FERRITE-ALUMINATES BY THE MOSSBAUER EPPECT METHOD J. Bara 93 MOSSBAUER STUDIES ON IRON BASE ALLOYS E. YJieser 105 MAGNETIC MOMENTS OP ns-ISOMERS IN 105Ag AND 1O3P<3 L. Schneider ........ ..115 3. lattice Defects APPLICATION OP HYPERFINE INTERACTIONS TO DEFECT STUDIES G. Vogl . 12? THE NATURE OP IRON STOPPING SITES IN METAS STUDIED BY MOSSBAUEH SPECTROSCOPY B.D. Sawicka ...... 147 ANNEALING BEHAVIOUR RADIATION DAMAGED k11^11 - AND IZ IV V A B C2 - COMPOUND SEMICONDUCTORS MEASURED BY 111Cd - TDPAC S. Unterrioker 174 Panel Discussion: ION IMPLANTATION AND RADIATION DAMAGE J. Sawicki 181 CONTRIBUTION TO THE PANEL DISCUSSION E. Bodenstedt 184 4. Some Aspects of the MBssbauer Effect MOSSBAUER SPECTROSCOPY H. de Waard 189 NON-CONVENTIONAL MOSSBAUER SPECTROSCOPY AND APPLICATIONS TO METALS U. Gonser 216 PILTRATIONAL PROPERTIES OP NUCLEAR RESONANCE SCATTERING OP GAMMA RAYS 3, Bara 226 5. Special Topics ELECTRIC QUADRUPOLE INTERACTIONS MEASURED BY NUCLEAR ORIENTATION AND NMR ON ORIENTED NUCLEI N.J. Stone - 251 VI RECENT DEV3L0ROTTS IK RADIATIVE DETECTION OF NUCLEAR MAGNETIC RESONANCE Vf.D.Brewer . 271 ;iSR - SPECTROSCOPY Th. V/iohert . , 312 Panel Dlsonssion: HYPERPIKE INTERACTION MEASUREMENTS AT LOW TEMPERATURES I. Katila 334 CONTRIBUTIONS TO THE PANEL DISCUSSION E. Bodenstedt 336 W.D. Brewer 339 J. Sawicki 346 N.J. Stone 348 List of Participants ......... 351 vii >:?! n 1. ELECTRIC QUADRUPOLE INTERACTION Electric field gradients In metals -'Ą-. • . G. Schatz, Dftpt. of Physics, University of Konstanc, Fed. Rep. of Germany 1. Introduction . Tremendous interest in electric, field gradients (efg) in metals is do¬ cumented by numerous experiments, which were done in recent years. This field is a rather complex and heterogeneous one, containing nu¬ merous aspects, such as contributions from different sources to the efg, sign of the efg, dependence on temperature and pressure. In this lecture, only few of them can be treated, detailed reviews on this sub¬ ject can be found in literature (Ref. 1,2); the most recent one was published by Kaufmann and Viaiiden (Ref.3). In the following, the main emphasis shall lay on the temperature dependence of the efg in nonmag¬ netic metals. Some of the selected experimental examples are untypical, they are however well suited to demonstrate the actual interest in this largely growing field. 2. Definition of the efg The electric tieid gradient at a certain position - nere we axe unxy ir-tcrcctcd in the cf~ »t s nv.?!?**- «<•»•» - •<« define* »•>• v <?i * a2V (r) (1) with the electrostatic potential Vi?) at the nuciear site (a,B denote Cartesian coordinates). Very often also the notation eqag = Vag is used. These Cartesian components form a symmetric 3x3 matrix with a vanishing trace; this is due to the Laplace equation for t f 0 electrons: iV«O (s-electrons do not contribute to the efg). The efg can also be re¬ presented in terms of the components of a second rank tensor. In the principle axis system the tensor components are: V ' 2,±1 "° . {2) V (v 2,±2 ~i i^f xx - V • i with the asymmetry parameter n - (V^ - vyy)/VM. Usually, the convention |VZZI >. IVyyl^jV.^1 is adopted, which results in O£ ujt 1. The expression for the tensor components shows that the efg can fully be described by only two parameters, V2Z and n, for axial symmetry (n - O) only the parameter V"zz has to be considered. 3. Contribution to the efg in metals The efg in A metal can be imagined to be governed by three main contri¬ butions: the point charges from the metal ions, the conduction electrons and the antishielding effect in the atomic shell of the metal ion. How these contributions can be taken into account is schematically illustrated in Fig. 1. Starting from a noncubic lattice, where the metal ions are represented by point charges, the efg can easily be calculated by the sura of all efg's originating from each ion, acting at the probe site. This lattice sum depends on the lattice parameter, these are generally temperature dependent (upper part of Fig.1). After filling in conduction electrons, the charge of the fcetax ions is partially screened. This effect can be taken into account by an effective point charge Z • e. Inside a certain volume (e.g. the Wigner-Seitz cell) around the probe ion, however, the explicit con¬ duction electron density has to be calculated using for instance the band structure of the metal (middle part of Fig.1). Roth. t-h«» nn-fnł- ch<*rg*n and the conduction electrons produce an efg at the probe atom site. The atomic shell of the probe atom will react in an antishielding of this efg, and therefore enhances the efg felt by the nucleus. The antishielding (Sternheimer) factor (1 - y^) for the efg from the point charges can be taken as the antishielding factors for the free ions, the antishielding factor d-y') for the conduction electron contribution is close to 1, because the sources for the efg overlap largely which the localized electrons of the probe atoms (lower part of Fig.1). These contributions lead to the socalled con- point charges Ze 2^ ; - i Sto r> lattice sum, depends on o o o o lattice parameters a(T), c(T) point charges + conduction electrons 3cos*-e - band structure calculation point chargen + liii conduction electrons + antishielding nit Sternheimer factors: Fig. 1 : Illustration of the contributions to the efg in a metal. ventional parametrizatlon (3) Recently, two experimental results however have shown, that the con- ventional parametrization is not adequate. The two results are: 1) Correlation between ionic and electronic part of the efg (Raghavan et al, Ref.4) (1 >Yi) . vjj£ «-x(1- YjV^*" with K s 2 ii) Temperature dependence of efg of the form: (Christiansen et al, Ref.5) As an example, for the host system tin the temperature dependencies for 12oSb(Ref.6}, 69Ge(Ref.7), 111Cd(Ref.5), and 115Te(Ref.8) impu¬ rities are shown in Fig.2. TEMPERATURE (K) 100 200 300 400 500 Fig. 2 : -1-5 temperature depen¬ dence of the efg for 120,Sb , 69Ge, 111Cd , and 115- Te probe nuclei in tin (Courtesy of W. Witthuhn, Erlangen). O2fl 2 4 6 ,._ 8 .10 4. Charge screening approach and temperature dependence of the efg In the charge screening approach the effect of conduction electrons Is taken into account by an effective ion potential. This potential of a lattice ion, screened by conduction electrons, is givoa by use of the static dielectric function e(ic), as: v ( V(r) ' -\1 )f -c V* > *ik r dk* (4) 3 ' (> Vc(k) is the Fourier transform of the unscreened ion potential. • (r). The tensor components of the efg are then found by differentiation of Eg. 4 : 2 2 lkr V2rn(r) - - VEJ7?/ 24w J-S-g- k Y2łffl t^) e dk i 151 In case of a central potential VQ(r) and a spherical Fermi surflanae (e(k) » e(k)) the efg components can be given in a factorized SScmas where In the asymptotic limit for large r, V(r) can be calculated usftng e(k) for a free electron gas (kp Fermi momentum), resulting in tflbe second derivative (Kef.9): , cos(2kpr) . | V"(r) s - 2k)2 s-s- <2kpr)3 The total efg acting at a nucleus in a metal is then produced by all the individual screened Jons at distances x^ j1 0: (9, An effective antishielding factor a•(1 - Y«) is introduced since the screening of the ions makes them more neutral and therefore a higher antishielding effect is expected (see Ref.3; |al'v- 6", Ref. 10). The above sketched concept of screened potentials is very useful for discussing the temperature dependence of the efg (Ref.11,10). If we now allow the ions to vibrate, the distance of an efg producing ion to the probe nucleus has to be expressed in terms of deviations from equilibrium position r° * + (10) • Uj(t) and u_(t) are the displacements of the i-th ion and the probe ion respectively. The effect onto the temperature dependence can now be imagined in the following way. A probe ion feeling a V"(r) in a region of a maximum or minimum (see Fig.3) will see a V"(r) averaged over the vibrations which depends strongly on the vibrations and therefore on temperature.