Transcript Document

MAGNETISM OF ROCKS AND
MINERALS
How do rocks record paleomagnetic information?
Paleomagnetism
Rock Magnetism
Solid State Physics
Petrology
Mineralogy
Outline
Basics of magnetism (today)
Magnetic minerals
Magnetization processes in rocks
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Basics of magnetism
Everything should be made
as simple as possible.
But not simpler.
A. Einstein
P. Weiss
H. Onnes
P. Ehrenfest
P. Langevin
At a conference on
magnetism in
Leiden, 1920
(from Physics Today)
Magnetic field
attraction
N
S
N
S
S
N
repulsion
N
S
The field of a force – a property of the space in which the force acts
Magnetic field (force lines)
F
N
S
Magnetic field is not a central field (no free magnetic charges)
Magnetic field definitions
B – magnetic induction
H – magnetic intensity
In vacuum:
Two quantities describing
a magnetic field
B = µ0H (Système Internationale, SI)
µ0 = 4π · 10-7 N A-2 - the permeability of free space
(the permeability constant)
B=H
(cgs: centimeter, gram, second)
Magnetic induction (B) units
FL = q(v X B)
Tesla
q
v
FL
B
Lorentz force (FL )
Gauss
SI:
Tesla (T)
[N A-1 m-1]
cgs:
Gauss (G)
[dyne-1/2 cm-1]
1 γ (gamma) =10-5 Gauss
1 Tesla =104 Gauss
Ampere
Magnetic intensity (H) units
Ørsted
SI: B = µ0H , hence H = B/µ0
[H] =
cgs:
[B]
[µ0]
=
N A-1 m-1
N A-2
A
= m
Ørsted (Oe)
1 A/m = 4π/103 Oersted
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
Magnetic moment (M) units
Emu
m = AIn
A – area, I – current, n – unit vector
m
I
SI:
[m] = Am2
cgs:
[m] = emu
1 Am2 =103 emu
Interaction with magnetic field
B
m = AIn
θ
m = pd
+p
d θ
-p
aligning torque:
τ = m B sinθ
Magnetic field of a current loop (dipole)
=AI
Baxial =
2µ0 m
4πz3
decreases as the cube of
distance
z
m
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)
MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL
Filling a free space with matter…
Rigorous consideration requires quantum-mechanical approach… We go simple…
Mspin
Morbital
nucleus
Orbital magnetic moment
Bohr magneton:
µB = 9.274 ∙ 10-24 Am2
e-
Spin magnetic moment
Atomic moment = orbital
moment + spin moment
MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL
Net magnetic moment of a volume V:
mi
mi
mi
mi
mtotal = ∑ mi
mi
mi
mi
mi
mi
i
mi
mi
mi
mi
mi
mi
mi mi
M = mtotal /V
mi
mi
volume = V
Magnetization - the magnetic
moment per unit volume
A m2
A
SI: [ M ] = m3 = m
cgs: emu / cm3
1 A m-1 =103 emu/cm3
MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL
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
B = µo (H + M)
B = µo H – free space (M = 0)
Magnetic susceptibility
If M and H are parallel and the material is isotropic:
M=κH
κ – magnetic susceptibility (dimensionless in SI)
κ is a measure of the ease with which the
material can be magnetized
Magnetic permeability
M=κH
B = µo(H + M) = µoH (1 + κ) = µoµH
µ = 1 + κ - magnetic permeability
µ is a measure of the ability of a material
to convey a magnetic flux
MAGNETIC UNITS AND CONVERSIONS
Magnetic properties of materials
Pauli’s exclusion principle: each possible electron orbit can be
occupied by up to two electrons with opposite spins
me
e-
me
e-
∑ mspin = 0
me
e-
∑ mspin ≠ 0
Diamagnetism
Magnetization develops in the direction
opposite to the applied magnetic field
M
H
H
M
κ<0
• Exists in all materials (but observable when electron spins are paired)
• Diamagnetic κ (and magnetization) is reversible
• Diamagnetic κ is temperature-independent
Examples of diamagnetic minerals
Mineral
κ (SI)
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
Data from Hunt et al (1995)
Paramagnetism
the partial alignment of permanent atomic magnetic
moments by a magnetic field
H = 0, M = 0
H > 0, M > 0
M
κ>0
H
H
Thermal energy dominates
• 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
Paramagnetism: Temperature dependence
κ
1/κ
C
κ=
T
κ-1 ~ (T – θ)
θ
T
κ=
C
T-θ
κ-1 ~ T
T
The Curie-Weiss law
θ – the paramagnetic Curie temperature (near 0 K for
most paramagnetic solids)
The constant C is material-specific
Examples of paramagnetic minerals
Mineral
κ (SI)
Olivine (Fe,Mg)2SiO4
1.6 · 10-3
Montmorillonite (clay)
0.34 ·10-3
Siderite (FeCO3)
1.3-11.0 · 10-3
Serpentinite
(Mg3Si2O5(OH)4)
3.1-75.0 · 10-3
Chromite (FeCr2O4)
3-120 · 10-3
Data from Hunt et al (1995)
Ferromagnetism
Atomic magnetic moments are always aligned (even for H = 0)
due to exchange interaction (quantum-mechanical effect)
Conditions for ferromagnetism:
H=0
1) Non-compensated spin moments
2) Positive exchange interaction
(i.e. co-directed spins)
M≠ 0
Spontaneous
magnetization
Ferromagnetic elements:
• Iron (Fe)
(κ = 3900000)
• Nickel (Ni)
• Cobalt (Co)
• Gadolinium (Gd)
Ferromagnetism
Exchange interaction (Eex) decreases with temperature
Spontaneous
magnetization, Ms
Ferromagnetism
(Eex > kT)
Paramagnetism
(Eex < kT)
Tc
T
Tc – the ferromagnetic Curie temperature (material-specific)
Ferromagnetism: Magnetic hysteresis
M
Ms
Ms – Saturation
magnetization
Mrs
Mrs – Saturation remanent
magnetization
H
Hc
Hc – Coercive force
(the field needed to
bring the magnetization
back to zero)
Ferromagnetism
(magnetic hysteresis)
M
Ms – Saturation
magnetization
Mrs
Mrs – Saturation remanent
magnetization
Hcr
H
Hc – Coercive force
(the field needed to
bring the magnetization
Ms back to zero)
Hcr – Coercivity of
remanence
(the field needed
to bring Mrs to zero)
Antiferromagnetism
Negative exchange interaction (anti-parallel spin moments)
Conditions for antiferromagnetism:
1) Non-compensated spin moments
2) Negative exchange interaction
(i.e. anti-parallel spins)
M= 0
Antiferromagnetic elements:
• Chromium (Cr)
• Manganese (Mn)
Non-perfect antiferromagnetism
spin-canted
antiferromagnetism
defect
antiferromagnetism
M
M
Eg., Hematite (Fe2O3)
Ferrimagnetism
Super-exchange interaction
Fe2+
O2-
Fe3+
M
Ferrimagnets (ferrites) behave
similar to ferromagnets
5µB
6µB
Eg., Magnetite (Fe3O4)
Summary
Diamagnetism
Paramagnetism
Ferromagnetism
Non-perfect
Antiferromagnetism Antiferromagnetism
Ferrimagnetism
important for rock and
paleomagnetism
Next …
Magnetic minerals
Rock magnetizations