Experimental methods for the determination of magnetic electrical

Experimental methods for the determination of magnetic, electrical and thermal transport properties of condensed matter Janez Dolinšek FMF Uni-Ljubljana & J. Stefan Institute, Ljubljana

Magnetic, electrical and thermal transport properties - Magnetic susceptibility Electrical resistivity Thermoelectric power Hall coefficient Thermal conductivity

Introduction • Why to measure magnetic, electrical and thermal transport properties of solid materials ? • Ever-present demand for new materials with novel/improved physicalchemical-mechanical properties • • Novel materials preparation techniques were developed High-quality single crystals available • Complex metallic alloys (CMAs) and quasicrystals (QCs) offer unique physical properties or combinations of properties Electrical conductor + thermal insulator Combination of hardness + elasticity+ small friction coefficient • Potential applications in high technology

Complex Metallic Alloys • • Intermetallic compounds Giant unit cells Cluster arrangement of atoms Inherent disorder: • Configurational • Chemical or substitutional • Partial or split occupation Mg 32(Al, Zn)49 quasicrystals Yb. Cu 4. 5 Ψ-Al-Pd-Mn β-Al 3 Mg 2 λ-Al 4 Mn Al 39 Fe 2 Pd 21 Mg 32(Al, Zn)49 Re 14 Al 57 elem. metals ∞ 7448 at. / u. c. 1480 at. / u. c. 1168 at. / u. c. 586 at. / u. c. 248 at. / u. c. 162 at. / u. c. 71 at. / u. c. <5 at. / u. c.

Quasicrystals • Discovered in 1984 • Thermodynamically stable samples have appeared after 1990 • Well-ordered but nonperiodic solids • Diffraction patterns with non-crystallographic point symmetry Periodic tiling Penrose tiling (quasiperiodic) Diffraction pattern of a decagonal quasicrystal

Sample preparation Bridgman method Czochralski method Flux-grown method • The first solidification zone • Coexistence of solid and liquid phases Single-crystal is cut in bar-shaped samples

Al-Co-Ni decagonal QC Czochralski method

Experimental methods Magnetization and magnetic susceptibility measurement … magnetic susceptibility SQUID magnetometer 5 T

Experimental methods Measurement of the electrical conductivity Electrical resistance: R = U/I Specific resistivity: PPMS – Physical Property Measurement System 9 T

Experimental methods Thermoelectric effect

Experimental methods Measurement of thermoelectric power Thermal conductivity measurement

Experimental methods Measurement of the Hall coefficient

Magnetization vs. magnetic field Y-Al-Ni-Co o-Al 13 Co 4 FM contribution linear term i-Al 64 Cu 23 Fe 13 Al 4(Cr, Fe) ferromagnetic component Curie magnetizations linear term

Magnetic susceptibility Y-Al-Ni-Co i-Al 64 Cu 23 Fe 13 temperature-independent term Curie-Weiss susceptibility temperature-dependent correction o-Al 13 Co 4 Al 4(Cr, Fe) temperature-independent term Curie-Weiss susceptibility

Electrical resistivity Y-Al-Ni-Co o-Al 13 Co 4 PTC of the resistivity – predominant role of electron-phonon scattering mechanism (Boltzmann type)

Electrical resistivity Al 4(Cr, Fe) i-Al 64 Cu 23 Fe 13 r is nonmetallic with NTC slow charge carriers pseudogap in s(e) specific distribution of Fe

Thermoelectric power Y-Al-Ni-Co Al 4(Cr, Fe) o-Al 13 Co 4 i-Al 64 Cu 23 Fe 13

Hall coefficient • RH values of QCs and CMAs are typical metallic • RH’s exhibits pronounced anisotropy • Fermi surface is strongly anisotropic • consists of hole-like and electron-like parts Y-Al-Ni-Co Al 4(Cr, Fe) o-Al 13 Co 4

Thermal conductivity • Total k is a sum of the electronic kel and the phononic kph contribution • kel is estimated from the Wiedemann-Franz law: kel=p 2 k. B 2 Ts(T)/3 e 2 • WF law valid when elastic scattering of electrons is dominant Y-Al-Ni-Co o-Al 13 Co 4 Al 4(Cr, Fe)

Thermal conductivity i-Al 64 Cu 23 Fe 13 electronic part hopping of localized vibrations long wave phonons (Debye model) • k 300 K < 1. 7 W/m. K lower than Si. O 2 (2. 8 W/m. K)

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