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Suez University
Faculty of Petroleum & Mining Engineering
Magnetic Properties
Student
Belal Farouk El-saied Ibrahim
Class / III
Section / Engineering Geology and Geophysics
Presented to Prof. Dr. / Ali Abbas
Rock Magnetism
Solid State Physics
Paleomagnetism
Petrology Mineralogy
MAGNETISM OF ROCKS MAGNETISM OF ROCKS AND MINERALSAND MINERALS
How do rocks record paleomagnetic information?
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 Retentivity
Also called permanence; how long a magnet retains its magnetism
Materials that are hard to magnetize generally retain their magnetism longer
Relates to the amount of force needed to align magnetic domains
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
Permeability of Magnetic Materials
• High permeability– Iron, steel, nickel, cobalt – Commercially made alloys of iron, nickel, cobalt, and other
elements• Silicon steel (used in transformers)• Alnico (used in audio speakers)
• Medium permeability– Aluminum, platinum, manganese, and chromium
• Low permeability– Bismuth, antimony, copper, and zinc – Rare metals (mercury, gold, and silver)
• Nonmagnetic materials (diamagnetic)– Glass, paper, rubber, wood, and air
Relative permeability µr
The ratio of permeability of medium to the permeability of free space is called relative permeability µr of the solid.
00
0
B
B
HBHB
r
r
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)
Hysteresis
The striking property of Ferro Magnetic materials is the relation between Magnetization and the strength of Magnetic field. This property is called Hysteresis.
P
Q
R
S
H
MSaturation Magnetization
Residual Magnetization
Coercivity
Ferro Magnetic Material
Hs
-Hs
oHc
Ms
Mr
-Ms
• If we start with no Magnetized specimen (M= 0) with the increasing values of magnetizing field H.
• The Magnetization of the specimen increases from zero to higher values and attains its maximum value at a point P, at this point the Magnetization referred as Saturation Magnetization..
• When we increase Magnetic field H there is no further increment in Magnetic moment.
• When we decrease Magnetic field H to Zero, the Magnetization M attains point Q.
• At this point Magnetization referred as residual Magnetization Mr.
• Further if we increase the Magnetic field from zero to negative values, the Magnetization of material becomes zero at a point R, at that point the Magnetic field Hc is referred as Coercivity of the specimen.
• If we increase Magnetic field H in reverse direction Magnetization of material reaches its peak value at a points S.
• On reversing the polarities of Magnetic field and increasing its strength the Magnetization slowly decreases first to residual value then to zero and finally increases to saturation state and touches the original saturation curve.
• The area of loop indicates the amount of energy wasted in one cycle of operation.
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+