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Experimental methods for the determination of magnetic, electrical and thermal transport properties of
condensed matterJanez DolinšekJanez Dolinšek
FMF Uni-Ljubljana & J. Stefan Institute, LjubljanaFMF Uni-Ljubljana & J. Stefan Institute, Ljubljana
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Magnetic, electrical and thermal transport properties
- Magnetic susceptibility- Electrical resistivity- Thermoelectric power- Hall coefficient- Thermal conductivity
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Introduction
• Why to measure magnetic, electrical and thermal transport properties of solid materials ?
• Ever-present demand for new materials with novel/improved physical-chemical-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 insulatorCombination of hardness + elasticity+ small friction coefficient
• Potential applications in high technology
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Complex Metallic Alloys
• Intermetallic compounds• Giant unit cells• Cluster arrangement of atoms• Inherent disorder:
• Configurational• Chemical or substitutional• Partial or split occupation
quasicrystals ∞YbCu4.5 7448 at. / u. c.Ψ-Al-Pd-Mn 1480 at. / u. c.β-Al3Mg2 1168 at. / u. c.λ-Al4Mn 586 at. / u. c.Al39Fe2Pd21 248 at. / u. c.Mg32(Al,Zn)49 162 at. / u. c.Re14Al57 71 at. / u. c.elem. metals <5 at. / u. c.
Mg32(Al,Zn)49
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Quasicrystals
• Discovered in1984
• Thermodynamically stable samples have appeared after 1990
• Well-ordered but nonperiodic solids
• Diffraction patterns with non-crystallographic point symmetry
Penrose tiling (quasiperiodic)Periodic tiling Diffraction pattern of a decagonal quasicrystal
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Sample preparation
Czochralski methodBridgman method Flux-grown method
Single-crystal is cut in bar-shaped samples
•The first solidification zone
•Coexistence of solid and liquid phases
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Czochralski method
Al-Co-Ni decagonal QC
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Experimental methods
Magnetization and magnetic susceptibility measurement
H
M … magnetic susceptibility
SQUID magnetometer 5 T
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Experimental methods
Measurement of the electrical conductivity
Electrical resistance:
R = U/I
l
SR
Specific resistivity:
PPMS – Physical Property Measurement System 9 T
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Experimental methods
Thermoelectric effect
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Experimental methods
Measurement of the thermoelectric power
Thermal conductivity measurement
TS
P qj
TSU
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Experimental methods
Measurement of the Hall coefficient
BI
dU
Bj
E
BR
H
x
yHH
Hall coefficient
neH1
R
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Magnetization vs. magnetic fieldY-Al-Ni-Co o-Al13Co4
Al4(Cr,Fe)
i-Al64Cu23Fe13
kHTHLMM ),,(0
kHJgBMJgBMM ),(),( 222111
FM contribution linear term
Curie magnetizations
ferromagnetic component
linear term
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Magnetic susceptibilityY-Al-Ni-Co
o-Al13Co4Al4(Cr,Fe)
i-Al64Cu23Fe13
44
220)( TATA
T
CT
j
j0j T
C
Curie-Weisssusceptibility
temperature-independent term
temperature-dependent correction
Curie-Weisssusceptibility
temperature-independent term
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Electrical resistivityY-Al-Ni-Co o-Al13Co4
PTC of the resistivity – predominant role of electron-phonon scattering mechanism (Boltzmann type)
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Electrical resistivityAl4(Cr,Fe) i-Al64Cu23Fe13
is nonmetallic with NTC
slow charge carriers
j
j2j2
j2j
2
NBjBjj
Lgevge
)(
)()( FF
wpLvτ
pseudogap in ()
22
22
2
21
21
1 11)(
A
specific distribution of Fe
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Thermoelectric power Y-Al-Ni-Co o-Al13Co4
Al4(Cr,Fe) i-Al64Cu23Fe13
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Hall coefficient
Y-Al-Ni-Co o-Al13Co4Al4(Cr,Fe)
• 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
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Thermal conductivity
Y-Al-Ni-Co o-Al13Co4 Al4(Cr,Fe)
• Total is a sum of the electronic el and the phononic ph contribution
• el is estimated from the Wiedemann-Franz law: el=2kB2T(T)/3e2
• WF law valid when elastic scattering of electrons is dominant
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Thermal conductivity
i-Al64Cu23Fe13
)()()()( HDel TTTT
long wave phonons
(Debye model)
electronic part hopping of localized vibrations
• 300K < 1.7 W/mK lower than SiO2 (2.8 W/mK)
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Thank you for your attention !