Rock Magnetism Solid State Physics Paleomagnetism PetrologyMineralogy MAGNETISM OF ROCKS AND...
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Transcript of Rock Magnetism Solid State Physics Paleomagnetism PetrologyMineralogy MAGNETISM OF ROCKS AND...
Rock Magnetism
Solid State Physics
Paleomagnetism
Petrology Mineralogy
MAGNETISM OF ROCKS MAGNETISM OF ROCKS AND MINERALSAND MINERALS
How do rocks record paleomagnetic information?
OutlineOutline
Basics of magnetism (today)
Magnetic minerals
Magnetization processes in rocks
Basics of magnetismBasics of magnetism
At a conference on magnetism in Leiden, 1920 (from Physics Today)
A. Einstein
P. Ehrenfest
P. Langevin
H. Onnes
P. Weiss
Everything should be made as simple as possible.
But not simpler.
S S
SSN
N N
N
The field of a force – a property of the space in which the force acts
Magnetic field
attraction
repulsion
Magnetic field definitions
B – magnetic induction
H – magnetic intensityTwo quantities describing a magnetic field
In vacuum:
B = H
B = µ0H
(cgs: centimeter, gram, second)
(Système Internationale, SI)
µ0 = 4π · 10-7 N A-2 - the permeability of free space (the permeability constant)
Magnetic induction (B) units
B
qv
FL
FL = q(v X B)
SI: Tesla (T) [N A-1 m-1]
cgs: Gauss (G) [dyne-1/2 cm-1]
1 γ (gamma) =10-5 Gauss
Lorentz force (FL )1 Tesla =104 Gauss
Tesla Gauss
[µ0]
[B]
Magnetic intensity (H) units
SI:
cgs: Ørsted (Oe)
1 A/m = 4π/103 Oersted
B = µ0H , hence H = B/µ0
[H] =
Ampere
Ørsted
A=N A-1 m-1
N A-2 = m
Magnetic moment (M)
No free magnetic poles can exist, hence the dipole field is the simplest configuration
Real source of magnetism is moving electrical charges (electrical currents)
Thin bar magnet (dipole)
Electric current loop
Uniformly magnetized sphere
I
Magnetic moment (M) units
m
m = AIn
[m] = Am2SI:
cgs: [m] = emu
1 Am2 =103 emu
A – area, I – current, n – unit vector
Emu
Magnetic field of a current loop (dipole)
Baxial =2µ0 m4πz3
z
decreases as the cube of distance
m
=AI
The Earth as a big magnet
MEarth ≈ 8∙1022 Am2
Earth magnetic field at the surface:
≈ 5 ∙ 10-5 T (0.5 G)
Magnetic fields in the universe
Sun surface: ~10-4 T (~10 G)
Sun spot: 10-2 - 10-1 T (~102-103 G)
At Earth’s orbit: ≈ 5∙10-9 T (~10-5 G)
Neutron Star: ~108 T (~1012 G)
Magnetar: ~1011 T (~1015 G) (strongest known field)
Galactic field: ~10-10 - 10-9 T (~10-6 – 10-5 G)
Filling a free space with matter…
Rigorous consideration requires quantum-mechanical approach… We go simple…
e-nucleus
Orbital magnetic moment
Morbital Mspin
Spin magnetic moment
Bohr magneton:
µB = 9.274 ∙ 10-24 Am2
MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL
Atomic moment = orbital
moment + spin moment
A m2
m3
mi
mi
mi
mi
mi
mi
mi
mi mi
mi
mi
mimi
mimi
mi
mimi
mi
volume = V
Magnetization - the magnetic moment per unit volume
M = mtotal /V
Net magnetic moment of a volume V:
imtotal = ∑ mi
[ M ] = =
MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL
SI:
cgs: emu / cm3
1 A m-1 =103 emu/cm3
Am
B = µo (H + M)
B = µo H – free space (M = 0)
In a magnetizable material the induction (B) has two sources:
1. Magnetizing field H (external sources)
2. Set of internal atomic moment, causing magnetization M
MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL
Magnetic susceptibility
M = κ H
If M and H are parallel and the material is isotropic:
κ – magnetic susceptibility (dimensionless in SI)
κ is a measure of the ease with which the material can be magnetized
Magnetic permeability
B = µo(H + M) = µoH (1 + κ) = µoµH
µ = 1 + κ - magnetic permeability
M = κ H
µ is a measure of the ability of a material to convey a magnetic flux
Magnetic properties of materials
Pauli’s exclusion principle: each possible electron orbit can be occupied by up to two electrons with opposite spins
e- e-
me me
e-
me
∑ mspin = 0 ∑ mspin ≠ 0
Diamagnetism
M
H
κ < 0
Magnetization develops in the direction opposite to the applied magnetic field
• Exists in all materials (but observable when electron spins are paired)
• Diamagnetic κ (and magnetization) is reversible
• Diamagnetic κ is temperature-independent
H M
Quartz (SiO2) - (13-17) · 10-6
Calcite (CaCO3) - (8-39) · 10-6
Graphite (C) - (80-200) · 10-6
Halite (NaCl) - (10-16) · 10-6
Sphalerite (ZnS) - (0.77-19) · 10-6
Examples of diamagnetic mineralsκ (SI)Mineral
Data from Hunt et al (1995)
the partial alignment of permanent atomic magnetic moments by a magnetic field
M
H
κ > 0
Paramagnetism
• One or more electron spins is unpaired (the atomic net moment is not zero)
• Paramagnetic κ (and magnetization) is reversible
• Very large H or very low T is required to align all the moments (saturation)
• Paramagnetic κ is temperature-dependent
H = 0, M = 0 H > 0, M > 0
H
Thermal energy dominates
Paramagnetism: Temperature dependence
κ
T T
1/κ κ-1 ~ T
κ-1 ~ (T – θ)κ =
CT
The constant C is material-specific
θ
κ = CT - θ
The Curie-Weiss law
θ – the paramagnetic Curie temperature (near 0 K for most paramagnetic solids)
Examples of paramagnetic minerals
Olivine (Fe,Mg)2SiO4 1.6 · 10-3
Montmorillonite (clay) 0.34 ·10-3
Siderite (FeCO3) 1.3-11.0 · 10-3
Serpentinite 3.1-75.0 · 10-3 (Mg3Si2O5(OH)4)
Chromite (FeCr2O4) 3-120 · 10-3
Data from Hunt et al (1995)
κ (SI)Mineral
FerromagnetismAtomic magnetic moments are always aligned (even for H = 0)
due to exchange interaction (quantum-mechanical effect)
M ≠ 0
Conditions for ferromagnetism:
1) Non-compensated spin moments
2) Positive exchange interaction (i.e. co-directed spins)
Ferromagnetic elements:
• Iron (Fe) (κ = 3900000)
• Nickel (Ni)
• Cobalt (Co)
• Gadolinium (Gd)
Spontaneous magnetization
H = 0
FerromagnetismExchange interaction (Eex) decreases with temperature
Spontaneous magnetization, Ms
T
Ferromagnetism (Eex > kT)
Paramagnetism (Eex < kT)
Tc
Tc – the ferromagnetic Curie temperature (material-specific)
Ferromagnetism: Magnetic hysteresis
M
H
Ms – Saturation magnetizationMrs
HcHc – Coercive force (the field needed to bring the magnetization back to zero)
Mrs – Saturation remanent magnetization
Ms
Ferromagnetism (magnetic hysteresis)
M
HHcr
Ms – Saturation magnetizationMrs
Hc – Coercive force (the field needed to bring the magnetization Ms back to zero)
Mrs – Saturation remanent magnetization
Hcr – Coercivity of remanence
(the field needed to bring Mrs to zero)
AntiferromagnetismNegative exchange interaction (anti-parallel spin moments)
M = 0Antiferromagnetic elements:
• Chromium (Cr)
• Manganese (Mn)
Conditions for antiferromagnetism:
1) Non-compensated spin moments
2) Negative exchange interaction (i.e. anti-parallel spins)
Non-perfect antiferromagnetism
spin-canted antiferromagnetism
defect antiferromagnetism
M
M
Eg., Hematite (Fe2O3)
Ferrimagnetism
Ferrimagnets (ferrites) behave similar to ferromagnets
M
Super-exchange interaction
Eg., Magnetite (Fe3O4)
5µB 6µB
O2-Fe2+ Fe3+
Summary
Ferromagnetism Antiferromagnetism
Non-perfect Antiferromagnetism Ferrimagnetism
important for rock and paleomagnetism
Diamagnetism
Paramagnetism