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Magnetism of SolidsE h F d M ti
Today’s Schedule
Exchange Forces and Magnetic Ordering in Minerals
AntiferromagnetismFerrimagnetism
Magnetic Minerals
y, iRocks.com
Magnetic Characterization of Magnetic Minerals (Part I)
Magnetite octahedra from Cerro Huanaquino, Bolivia.
Photo by
Rob
Lavinsky
Paramagnetism: Molecular Field Theory and Exchange Interactions
Curie Law of Paramagnetism
CT
Curie‐Weiss Law of C Paramagnetism: T
Produced by interactions between electron ‘neighbors’: Hm=M (=const.)Total field acting on an internal “molecular” moment: H=Ha+M
Assume a Molecular field acts on the magnetic ions (Hmis very large)
CApplied field + Molecular Field
,
( )
,
a a m
a a
CM H H H H HT
CH H MTC C C
T C T
FerromagnetismTheory of Ferromagnetism must explain
Magnetite
Shape of M‐H curve Shape of M‐T curve1.0
a. SDMagnetite50
Tauxe, 2009
‐1.0
‐0.5
0.0
0.5
‐0.5 ‐0.25 0 0.25 0.5
M/M
s
Field (T)
50 nm
Large magnetic moments in low magnetic fields (< 1 T) and high temperatures (300K)Spontaneous (saturation) Magnetization
(M0,B=0)
Fe3O4 480 kA/mFe 1700 kA/mParamagnet <1 A/m
Magnetic Ordering Temperature(Tc, Curie Temperature)
Fe3O4 580CFe 780CNi 358CCo 1121CT>Tc Curie‐Weiss law
Molecular Field Theory and Exchange Interactions
The interaction constant from Curie‐Weiss Law can be:
=0 paramagnetism unpaired spins independent (Curie‐Law)>0 ferromagnetism unpaired spins align parallel<0 antiferromagnetism unpaired spins align antiparallel
FerromagnetismCurie Temperature
Ferromagnetism T<Tc Paramagnetism T>Tc
Lowrie, 2007
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Weiss Molecular Field Theory of Ferromagnetism
Start with Langevin Equation for M(T,H)s
BM M LkT
Assume a molecular field dependent on Mw=molecular field constant mH wM
Total field H=Ha+HmMagnetization exists even when Ha=0 and T<Tc
w M0
0 1, ( 0)
s
s
wM LkT
wM M H MkT
MM
All spins are aligned
Weiss Molecular Field Theory of FerromagnetismTo solve for M when T<TcTwo simultaneous equations for M
0
(1) ( )
(2)
sM M L
kTMw
TT
T1T2
T3M/Ms
0.4
0.6
0.8
1.0
L(
)
T1T2
T3T4
Em>>kT Em<<kTEq (2)
Eq (1)
T4
Temperature0.0
0.2
0 2 4 6 8 10
T>T4, no solution, M=0, Ha=0, T4=Curie temperatureT=0 K, solution at =, L()=1, M=Ms
m
Weiss Molecular Field Theory of Ferromagnetism
T>TC
Ferromagnetism
CT
Antiferromagnetism
O’Reilly, 1984
Weiss Molecular Field Theory of Ferromagnetism
Curie TemperatureSlope of line at T=T4=slope of Langevin Function at origin
kT kTM
0 0
0
0
,
lim ( ) / 3, / 3
3
c c
s
sc
kT kTMMw w
ML M
M wTk
M it d f M l l Fi ld t 0 K3 ckTH wM w kT Magnitude of Molecular Field at 0 K
0
,m s cH wM w kT
Fe: Tc=1063 K, =2.2B: H~108 A/m, B~ 1000 T
Field is much larger than that produced by magnetic dipole‐dipole interaction between spins (a=lattice spacing, ~0.3 nm)
5
310 A/m (0.1 T)B
a
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FerromagnetismTheory of Ferromagnetism must explain
Large magnetic moments in low magnetic
Shape of M‐H curve1.0
a SDMagnetite Large magnetic moments in low magnetic fields (< 1 T) and high temperatures (300K)Spontaneous (saturation) Magnetization
(M0,B=0)
Fe3O4 480 kA/mFe 1700 kA/mParamagnet <1 A/m‐1.0
‐0.5
0.0
0.5
‐0.5 ‐0.25 0 0.25 0.5
M/M
s
Fi ld (T)
a. SDMagnetite50 nm
Field (T)
Weiss Domains: How to explain the demagnetized stateMagnetic Domains and Walls
Fe3O4
13x13 m (110) Fe3O4
Fe3O4
(100) Titanomagnetite
http://www.ifwdresden.de/institutes/imw/sections/24/members/schaefer/magnetic‐domains/5
(100)‐oriented silicon iron crystal
Some ways to image domainsBitter patterns
Magnetic Force MicroscopyMagnetooptic Kerr effect
Quantum Theory of Magnetically Ordered Materials
The source of the molecular field is exchange interactions between
1. Direct Exchange between neighboring electron spins
overlapping electron orbitals resulting in:
2. Superexchange between unpaired electrons spins couple through covalent interactions with intervening ligand (e.g. O2‐)
Tauxe [2008]
Exchange Forces
12 1 22
exe J s s Exchange energy: energy related to the exchange of
two electron spins (s) between atoms
J12 is the exchange integral (constant)f d>0 ferromagnetic ordering
<0 antiferromagnetic ordering
Depends on degree of orbital overlap between electrons
ra=interactomic distancer3d=mean radius of 3d orbital
ra/r3dSmall AF orderingLarger values FM ordering
ll l l d /Tc=631 K
Tc=1403KTc=1043K
Bethe‐Slater curve
Still larger values dia/paramagnetism
Cullity, 1972
Tc=96KCurie Temperature is related to strength of exchange integral
12 B cJ k T
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Magnetically Ordered Materials
When the applied field is zero, the internal field is still present and leads to Positivemagnetic ordering and spontaneous magnetization.
Positive interactions
Negative Interactions
Ferromagnetism Fe, Ni, Co, NiFe, Gd
Antiferromagnetism MnO, FeTiO3
Ferrimagnetism Fe3O4, MOFe2O3, where M=transition metal
Main Types of Magnetic Ordering
Egli
Antiferromagnetism
Two separate magnetic sublattices (A and B) with negative (antiparallel) magnetic superexchange coupling
A
p g
MB=‐MA at all temperaturesMs=MB‐MA =0
CT
B
MB
Néel Temperature (Tn)
M=0
MA
Molecular Field Theory of Antiferromagnetism (Néel Theory)
Molecular Field “seen” by A and B ions on A and B sublattices
molecular field constant (>0)
( / 2) AB
CTC
T>TN
00( ) B A
A A JA Ag JM T M B HkT
Brillouin Functions
A AB B
B AB A
H MH M
AB = molecular field constant (>0)
Applied Field to spin axis
1
AB
T<TN
T/TN
Cullity, 1972; Dunlop and Özdemir, 1997
0
00
( )
( )
( ) ( ) ( ) 0
A A JA A
B BB B JB B
S B A
kTg JM T M B HkT
M T M T M T
Applied Field // to spin axis
MAMB
MAMB
// ( 0) 0T
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1 00
1.20
1.40
Marcasite (FeS2)
axAntiferromagnetism
Tn
T>TN
Goethite (‐FeOOH)Özdemir and Dunlop (1996)
0.20
0.40
0.60
0.80
1.00
0 50 100 150 200 250 300
X/X
ma
Temperature (K)
TN=393 K
CT
1 2||3 3p
Temperature (K)
Mineral TN (K) Ms (Am2/kg)
Type
Ilmenite (FeTiO3) 40 0 AFM
Ulvospinel (Fe TiO 120 0 AFM
Antiferromagnetic Minerals
Ulvospinel (Fe2TiO4 120 0 AFM
Hematite (‐Fe2O3) 948 0.4 canted
Goethite (‐FeOOH) 393 ~0.5 defect
Lepidocrocite (‐FeOOH) 52 ~0.1 defect
Siderite (FeCO3) 37 0.38 canted
Rhodocrosite (MnCO3) 34 0.46 canted
Vivianite (Fe3[PO4]28H2O ~12 0.06 (?) defect?( 3[ 4]2 2 ( )
Ferrihydrite (Fe5HO84H2O) ~500 6‐12 non‐compensated
Data from various sources
FerrimagnetismTwo separate magnetic sublattices (A and B) with negative (antiparallel) magnetic superexchange coupling
Different numbers or kinds of cations or valence states on h bl tti diff t it di tieach sublattice + different site coordination
MAMB at all temperaturesMs=MB ‐MA > 0
T>TC FerrimagnetismT<TcC
T
Ferromagnetism
O’Reilly, 1984
Similar magnetic properties to ferromagnetic materials (Ms, hysteresis, remanence) C
T
Ferrimagnetism
( ) ( )~ 0 3 0 5s cM T T T
0.0
0.5
1.0
/Ms
a. SDMagnetite50 nm
Magnetite
0.3 0.5
‐1.0
‐0.5
‐0.5 ‐0.25 0 0.25 0.5M
Field (T)
Tauxe, 2008
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Molecular Field Theory of Ferrimagnetism
Cullity, 1972
Molecular fields acting between ions (AA, BB, and AB)
Molecular Field Theory of Ferrimagnetism (T<TN)
H M M
00( ) B A
A A JA Ag JM T M B HkTg J
Molecular Field “seen” by A and B ions on A and B sublattices
AA , BB , and AB : molecular field constants for interactions
Brillouin Functions JA, JB= quantum spin numbers
A AA A AB B
B BB B AB A
H M MH M M
00( )
( ) ( ) ( )
B BB B JB B
S B A
g JM T M B HkT
M T M T M T
Q‐TYPEAA=BB
P‐TYPEAA > BB
N‐TYPEAA < BB
Different combinations of AB, AA, BB interactions give rise different types of Ms‐T curves
Temperature Dependence of Magnetization
Q
QP
Néel Model
Q
N
Q
Harrison
, 2000
Nickel‐Iron Vanadates (NiFe2‐xVxO4 )Variation as a function of composition (O’Handley, 2000)
Titanomaghemite (Fe2.3Ti0.7O4)Variation as a function of oxidation (Readman and O’Reilly, 1972)
P
Mineral TN (K) Ms (Am2/kg)at 300 K
Magnetite (Fe3O4) 853 92
M h it ( F O ) 863 948 73
Ferrimagnetic Minerals
Maghemite (‐Fe2O3) 863‐948 73
Greigite (Fe3S4) Unknown, >593 59
Pyrrhotite (Fe7S8) 593 20
Jacobsite (MnFe2O4) 673 77
Trevorite (NiFe2O4) 713 51
Daubreelite (FeCr2S4) ~170 ~30 (at 70 K)
Fe O ~510 ~15‐Fe2O3 510 15
Feroxyhyte (‐FeOOH) 440‐460 ~12
Data from various sources
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SummaryMagnetic Ordering in Solids
– Diamagnetism: No unpaired e‐
– Paramagnetism: Unpaired e‐, disordered and fluctuating– Ferromagnetism: All unpaired e‐ spins aligned parallel– Antiferromagnetism: Unpaired e‐ aligned antiparallel– Antiferromagnetism: Unpaired e aligned antiparallel– Ferrimagnetism: Unpaired e‐ aligned antiparallel but don’t fully cancel out
Magnetic Mineralogy
Magnetite and Titanomagnetites (Fe3‐xTixO4)Hematite and Titanohematites (Fe2‐yTiyO3)Maghemite and TitanomaghemitesMaghemite and TitanomaghemitesChemical Change
ExsolutionHigh temperature oxidation , T>600 C (oxy‐exsolution)Low temperature oxidation (titanomaghemites)
Magnetic Oxyhydroxides, Sulfides, and Fe‐Ni
Exsolved titanomagnetite grain (width of image =320m)
Magnetite (Sicily Strait, Dinare‐Turell et al., 2003)
Magnetic Mineralogy
Sources of magnetic minerals Igneous and metamorphic processesSoil formation and diagenesis
Magnetic minerals follow the rock cycle
gCosmic dustBiomineralizationIndustrial pollutionarcheological materials
Transformation of magnetic phaseschemical weatheringlow/high temperature oxidation
/dissolution/precipitationbiogenic formation/alteration
Magnetic Minerals can undergo significant chemical/physical changes after formationPhysical/Chemical changes can destroy primary remanence or produce new remanence
Ternary diagram for iron‐oxides
Most Important Magnetic Phases
Fe‐Ti oxidesFe‐sulfidesFe‐oxyhydroxides
Tauxe, 2008
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Titanomagnetites
Solid Solution Series (T>600 C)Cubic mineralsSpinel crystal structure
3 4
3 4 2 4(1 )
x xFe Ti O
x Fe O xFe TiO
Spinel crystal structure
Tauxe, 2008
TM0= magnetiteTM60= Fe2.4Ti0.6O4
Spinel Crystal Structure
S i l i th M Al bSpinel is the Mg-Al member of the larger spinel group of minerals.
MgAl2O4
A‐sites: tetrahedral coordination
http://en.wikipedia.org/wiki/File:Spinel.GIF
A sites: tetrahedral coordinationB‐sites: octahedral coordination
Superexchange Interactions in Spinels
Superexchange between unpaired electrons spins couple through covalent interactions with intervening ligand (e.g. O2‐)
Dunlop & Özdemir, 1997; Tauxe [2008]
Bond angles in Magnetite
Angles near 90 are unfavorable for superexchange interactions
AB, BB, and AA interactions
Crystal Structure of Magnetite
Magnetite octohedra from Cerro Huanaquino Bolivia
Unit cell contains 32 O2‐ anions arranged in a face‐center cubic network
Cerro Huanaquino, Bolivia.
Two types of cation sitesA‐sites: tetrahedral coordination (8 sites per unit cell)B‐sites: octahedral coordination (16 sites per unit cell)
Butler, 1992; Walz, 2002
2 4( )[ ]A B OGeneral Structural Formula:
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Magnetite
Fe3O4(Fe3+,Fe3+,Fe2+)O 4
2‐
In magnetite, there are 16 Fe3+ and eight Fe2+ cations per unit cell
Fe2+ : S=2, = 4BFe3+ : S=5/2, = 5BWhat’s the magnetic structure of Magnetite?
Ferromagnetism (all spins are aligned)Ferrimagnetism (A and B sites are AF coupled)
Coupling Spin Moment
Ferromagnetic All spins aligned 4+5+5 =14B
Ferrimagnetic (5+5)‐4=6B
Ferrimagnetic (5+4)‐5=4B
2 2
4( ) [ , ]
A BFe O 3+ 3+Fe Fe
2 2
4( ) [ , ]
A BFe O 3+ 3+Fe Fe Observed value
~4.1B
Temperature dependence of the sublattice magnetizations
Magnetite
Stacey and Banerjee 1974
Curie Temperature: 853 K (580 C)Saturation Magnetization at 23 C
92 Am2/kg480 kA/m
Stacey and Banerjee , 1974
Tauxe, 2008
0.70
0.80
dM/dT
Verwey Transition in MagnetiteChange in lattice symmetry at Tv=121 K Monoclinic Magnetite
1990
0.20
0.30
0.40
0.50
0.60
SIRM
(AM
2 /kg)
T>Tv CubicT<Tv
Monoclinic
3 mm Single Crystal
dM/dT
Relationship between the low‐T monoclinic axes (a, b and c), the h b h d ll di t t d ll ( lid
Kakol,
0.00
0.10
0 50 100 150 200 250 300
Temperature
Saturation IRM (SRM) given at 10 KMeasurement on warming to 300 K
rhombohedrally distorted cell (solid line), and the high‐T cubic unit cell (dashed line)
c‐axis is tilted ~0.2° from cubic <100>
Maghemite (‐Fe2O3 )
Isochemical with hematite (‐Fe2O3 ) but maintains the inverse spinel structure of magnetite.
C ll F 2+F 3+ d i i h b l
Partially oxidized magnetitesz=0 magnetite; z=1 maghemite
op and
Özdem
ir, 1997
Convert all Fe2+Fe3+ and maintain charge balance
3 2 3 2 3 3 2
4 5/3 1/3 4( )[ , ] ( )[ ]Fe Fe Fe O Fe Fe O
3 2 31 1 2 /3 /3 4[Fe ] [Fe Fe ] OA z z z B
Dunlo
Ms (300K)= 74.3 Am2/kgT ~ 863 948 K (590 675 ° C)
0.8
1.0
0)
maghemite
TC 863‐948 K (590‐675 C)No Verwey like transition
0.0
0.2
0.4
0.6
0 50 100 150 200 250 300
Sirm
/Sir
m(2
0
Temperature (K)
magnetite
Magnetite is oxidized to maghemite by changing the valence state of two thirds of the original Fe2+ to Fe3+ while simultaneously removing one third of the original Fe2+ from the B sublattice.
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‐Fe2O3 is metastable and typically inverts to ‐Fe2O3 (hematite) when heated to T> 300° C
Maghemite (‐Fe2O3 )
Synthetic maghemite
mir and Du
nlop
, 1988
Inversion to ‐Fe2O3
Synthetic maghemiteD~0.025 m
Özdem
ir, 1990
Synthetic maghemiteD~0.47 m
Axial ratio 9:1
Tc=645°C
Özdem
Differential thermal analysis (DTA) heated in 02.
Inversion T>Tc
Distribution of cation between A and B sites and the exchange coupling between/within sublattices control intrinsic magnetic properties ( e.g., Msand Tc) of titanomagnetites
Cation Distribution and Magnetization in Titanomagnetites
Normal spinel: similar cations/ occupy the same sublatticeInverse spinel: different cations occupy the same sublattice
3 2 3 2 4 21 (2 2 ) 4( ) [ ]b b x b b x xFe Fe Fe Fe Ti O A B
Generalized Cation Distribution Formula for Titanomagnetites
b= distribution parameter (no. of A‐site Fe3+ )x= compositional parameter
Generalized Cation Distribution Formula for Titanomagnetites
Cation Distribution and Magnetization in Titanomagnetites
Single‐crystal data3 2 3 2 4 2
1 (2 2 ) 4( ) [ ]b b x b b x xFe Fe Fe Fe Ti O A B
b= distribution parameter (no. of A‐site Fe3+ )x= compositional parameter
2 2
4( ) [ , ]
A BFe O 3+ 3+Fe Fe
For example (x=0, Magnetite)
b=0: normal spinel
Kakol et a
l., 1991
2 2
4( ) [ , ]
A BFe O 3+ 3+Fe Feb=1: inverse spinel
Variation in saturation magnetization (Bohr magnetons pfu at 0K)
6(1 ) 2x b
Variation of saturation magnetization with composition x for various models of cation distributions.
Crystal Chemistry in Spinels: Cation Site‐Preference for transition metal ions in A and B Sites
8Certain cations have a preference for
Navrotsky and
Klepp
a, 1968
B‐sites
3 3 2 24
2 2 4 24
( ) [ ]
( ) [ ]
Fe Fe Fe O
Fe Fe Ti O
A B
A B
Certain cations have a preference for occupying a particular coordination site
A‐sites
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Magnetic Properties of Titanomagnetites
In the titanomagnetite series (Fe3–xTixO4)
Ti4+ substitutes for Fe3+ as Ti content increases. The ionic substitution is 2Fe3+ Fe2+ + Ti4+
30
40
50
60
70
80
90
100
Ms(Am
2 /kg)
Saturation Magnetization at 300 K
Lattard et al., 2006Natural titanomagnetites can also contain Al3+,Mg2+, Mn2+
0
10
20
30
0 0.2 0.4 0.6 0.8 1x‐parameter
Data from various sources
Different combinations of AB, AA, BB interactions give rise different types of Ms‐T curves
Néel Classification of Ms‐T curves
Magnetic Properties of Titanomagnetites
Temperature dependences of the sublattice magnetizations are not always the same, but all go to 0 as TTc
1.02
1.04
1.06
nt
TM60
P‐type behavior in TM60
0.90
0.92
0.94
0.96
0.98
1.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Normalized
Mom
en
T/Tc
Dunlop and Özdemir, 1997
Hematite: Fe2O3
Canted AntiferromagnetismSEM image of hematite. Image is ~800 m across.
Wikipedia Com
mon
sFe3+
Weak ferromagnetism
T > 263 K T < 263 K
Dunlop and Özdemir, 1997; Butler, 1992
pure cantedAF AF
Morin Transition
Curie Temperature: 948 K (675 C)Saturation Magnetization at 300 K
0.5 Am2/kg2 kA/m
T > 263 K T < 263 K
Morin TransitionSpin‐flop transition
Hematite: Fe2O3
Özdemir et al, 2008
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Titanohematites: Fe2‐yTiyO3TN= 953 K TN= 63 K
Phase diagram for titanohematites
Dunlop and Özdemir, 1997; Lagroix et al., 2004
Magnetic Structure
Both end‐members have rhombohedral crystal structures and are antiferromagnetic below TNOrdered Phase: Fe2+ uniquely distributed within the A layer and Ti4+ within the B layer
mir, 2007
Titanohematites: Fe2‐yTiyO3
y=0.7
Tc=418 K 04
Dunlop
and
Özdem
Canted‐AF
temperature
d2M
/dT2
Lagroix et al., 200
Compositions around y=0.5 have the property of self‐reversed thermoremanent magnetization
Applied a field in the positive direction and cool through Curie temperature an negative remanence is produced!
Primary Fe‐Ti oxidesOriginally crystallized from igneous melts
~1‐5% by volumecrystallize T~1300C > > Tc
Cooling rate has major impact on grain size and microstructureextrusive volcanic rocks: TM grain sizes < 50 m many <1mextrusive volcanic rocks: TM grain sizes < 50 m, many <1mintrusive igneous rocks : TM grain sizes > 100m
Composition of the melt
Mafic magmas (enriched in Fe, low Si)Basalts and Gabbros TM’s 0<x~0.8 ,Ferrimagnetic, Tc >0CTH’s 0.8<y<0.95, Paramagnetic, T> 0C
Felsic magmas (higher in SiO2)rhyolites, granitesTM’s x~0TH’s 0 <y<0.8
Tauxe, 2008
Magnetic Inclusions in Paramagnetic Silicate Minerals
Ti‐poor TM (< 1m) can be exsolved from silicate minerals
Dunlop and Özdemir, 1997; 2007
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Chemical Change
O’Reilly, 1984
Chemical Change and Exsolution (T>500C)Quench by rapid cooling (volcanic rocks)
single phase composition
Exsolution by slow cooling (t>106 yr) Igneous intrusionsmultiphase compositionsmultiphase compositions
Hemoilmenite(two‐phase composition
Important ChangesMagnetic properties due to change in compositionDecrease in effective magnetic grain size
Tauxe, 2008
Ilmenite‐Hematite Exsolution in granulites from S. Sweden
McEnroe et al., Elements, 2009
Lamellar MagnetismExsolution in Titanohematites
Lamellar magnetism is associated with boundary
Monte Carlo simulation of cation ordering and resulting magnetic signal of hematite‐rich and ilmenite‐rich phases in exsolved titanohematite
Lamellar magnetism in the hematite‐ilmenite series as an explanation for strong remanent magnetization (up to 55 kA/m)
layers between the exsolved phases.
Robinson et al. (2002)
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Slow Cooling and Oxy‐Exsolution
Solid solution between magnetite
Oxidation that occurs during original cooling of an igneous rock is deuteric oxidation
Solid solution between magnetite and ulvospinel exists in principle, intergrowths of these two minerals are rare
Natural titanomagnetites interact with oxygen in the melt to form intergrowths of low Ti magnetite with Ilmenite (deuteric oxidation)
Ti‐rich ilmenite
Fe‐rich TM
Tauxe, 2008
Titanomagnetite grain displaying typical high temperature oxidation texture (i.e. produced during cooling).
Titanomagnetite (brown) is sub‐divided b il it ( l b ) S l llby ilmenite (pale brown). Some lamellae and patches of hematite are also present (width of image =320m).
http://geography.lancs.ac.uk/cemp/atlas/atlas_frm1.htm
Optical photomicrograph of ilmenite lamellae within titanomagnetite grain; note the symmetrywithin titanomagnetite grain; note the symmetry of the ilmenite planes that are parallel to (111) planes of the host titanomagnetite.
Butler, 1992
Low‐Temperature (T<300C)Titanomaghemites
Weathering at ambient surface conditionsHydrothermal alteration Ocean floor basalts
MaghemitizationNo change in crystal structure (spinel)Convert all Fe2+Fe3+ & maintain charge balance
Ph ll d cation deficient spinels (non stoichiometric TM)
titanomaghemites
Phases are called cation‐deficient spinels (non‐stoichiometric TM)
3 2 3 2 4 21 (2 2 ) 2 (3 ) ( ) (9 ) (1 ) 3 4( ) [ ]
0 (1 ) / (9 )b b x x b b x x xFe Fe Fe Fe Ti O
x x
A B
Tauxe, 2008
Oxidation parameter: 0 ≤ z≤ 1, z=9For x=0: z=0 magnetite
z=1maghemite
Consequences of Maghemitization
MSTca
Titanomagnetite ( x = 0.6) is the dominant primary FeTi oxide in oceanic pillow basalts (upper 0.5 km of oceanic crust).
A magnetite crystal (∼ 30 μm) undergoing maghemitization. Because of the change in volume, the crystal begins to crack. [From Gapeyev and Tsel’movich, 1988.]
Tauxe, 2008
During seafloor weathering, titanomagnetites oxidize totitanomaghemite.
Titanomaghemite is one of the most abundant FeTi oxides in the earth’s crust.
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Cell‐parameter
Curie‐Temperature and Cell‐parameter contours for titanomagnetites‐titanomaghemites
Curie‐Temperature
Readman and O’Reilly, 1972
Ocean‐Floor Basalts
Temperature dependence of magnetizationInversion of titanomaghemite
i t th f F i h TM d Ti i h il it
If titanomaghemites are heated, by burial beneath later flows on the seafloor for example, they become unstable and ‘invert’.
intergrowth of Fe‐rich TM and Ti‐rich ilmenite
TMht
TM0
Inversion
Dunlop and Özdemir, 1997
Inversion temperature
Other Common Magnetic Phases
TN=393 KGoethite (‐FeOOH)
Common weathering product and precursor to hematite in sediments and soils.
Saturation Magnetization ~0.1 Am2/kg1‐2 kA/m
Özdemir and Dunlop (1996)
Goethite (‐FeOOH)Néel and Curie Temperature
Thermomagnetic heating
TC=120° C
Thermomagnetic heating curve (strong field) Step‐wise thermal demagnetization of
thermoremanent magnetization (TRM)
Özdemir and Dunlop, GRL, 23, 921‐924, 1996
Weak ferromagnetism has a TC=TN
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Iron‐Sulfides: Pyrrhotite
Monoclinic pyrrhotite (Fe7S8): FerrimagneticTc=593 K (320C)Ms=~20 Am2/kg ( 80 kA/m)
○ vacancies
Hexagonal pyrrhotite (Fe10S11 ,Fe9S10)structural transition from an (imperfect) antiferromagnet to ferrimagnet at about 200C.
Fe cations are FM coupled within c planes and AF coupled
Fe2+
Tauxe, 2008; Dunlop and Özdemir, 1997
within c‐planes and AF coupled between layers via S2‐ ions
0.8
1.0
(20)
“Besnus” Transition (T=34 K) in Monoclinic Pyrrhotite
Thermal demagnetization of 20 K SIRM
0.0
0.2
0.4
0.6
0 50 100 150 200 250 300
Sirm
/Sirm
(
Temperature (K)
pyrrhotite
Transition ~34K is diagnostic of the
Room‐Temperature SIRM
Transition 34K is diagnostic of the presence of monoclinic pyrrhotite
Rochette et al, 1990
Physical Origin of transition is likely related to crystallographic transformation
Pierre Rochette, Gérard Fillion, and Mark J. Dekkers, IRM Quarterly, 21:1, Spring 2011
Crystal Structure: Cubic, Inverse spinel Magnetic Structure: Ferrimagnetic
Iron‐Sulfides: Greigite (Fe3S4)Ro
berts e
t al., 2010
Ms=125 kA/m, 59 Am2/kg
Tetrahedral (A) site Octahedral (B) site
Chang et al., 2008
Low‐temperature measurements of Ms
Synthetic greigite
Iron‐Sulfides: Greigite (Fe3S4)Tc unknown but must be T> 603 K (330C)Chemically unstable at high T and decomposes at T< Tc
High‐field M‐T curves (heated in air)
High‐temperature hysteresis data (measured in air)
Robe
rts e
t al., 2010
Chang et al., 2008
Natural Greigite Samples Synthetic Greigite
Formation of high Hc phase
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1.0
Iron‐Sulfides: Greigite (Fe3S4)
No low‐Temperature transition
Coarse grained
0.2
0.4
0.6
0.8
Sirm
/Sir
m(2
0)
greigite
magnetite
t al., 2010
Coarse grained SD/PSD/MD samples
0.00 50 100 150 200 250 300
Temperature (K)
Low‐temperature SIRM
Robe
rts e
t
NanophaseUnblocking behavior
Biogenic greigite produced by bacteria Sedimentary greigite and pyrite
Iron‐Sulfides
Greigite and Pyrrhotite occur in reducing environments and both tend to oxidize to various iron oxides leaving paramagnetic pyrite as the sulfide component.
Bazylinski et al., 1994; Moskowitz et al,2008 Roberts et al., 2010
Iron and Iron–NickelFerromagnetism
Iron and iron–nickel are the principal NRM carriers in lunar rocks and most meteorites.
AFM
FM FM
Phase diagram of Fe–Ni
Dunlop
and
Özdem
ir, 2007
Body‐centered cubic kamacite (‐Fe) does not exist for >30 mol.% Ni. Face centered cubic taenite (‐Fe) is the stable phase at high T and at all T for >30 mol.% Ni. The ordered phase tetrataenite can exist for 50–55 mol.% Ni.
Phase Formula Ms (Am2/kg) Tc (K)
Gibeon IVA fine octahedrite
Phase Formula Ms (Am /kg) Tc (K)
Kamacite Fe (bcc cubic)Low‐T phase
218 1038
Taenite Fe (fcc cubic)High‐T phase
AFM
tetrataenite Fe0.5Ni0.5 ~823
Awarunite Ni2Fe to Ni3Fe 120 893
http://www.meteorlab.com/METEORLAB2001dev/widpatrn.htm
Widmanstätten pattern of a polished and etched slice showing kamacite (light bands) taenite (dark areas)
Magnetic Mineral Identification: Part 1
Different Approaches:
ImagingDiffraction ck
s.com
DiffractionMagnetic Characterization
Looking for changes in magnetic behavior at characteristic temperatures (2‐1000 K)
High‐Temperature (>300 K) methodsMagnetite octohedra from Cerro Huanaquino, Bolivia.
Photo by
Rob
Lavinsky, iRoc
Most magnetic minerals that carry stable remanence (SD/PSD) are small (< 10 μm) and in low concentrations ( < 1%)
The challenge is to associate a particular component of NRM (identified from partial demagnetization) with a particular ferrimagnetic mineral.
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Imaging Magnetic Minerals
Exsolved magnetic & ilmenite in an igneous rock
Detrital titano‐magnetites from Chinese loess.
Hematite rosettes on a smectite grain.
Industrial pollutant (“fly‐ash”)
Interstellar Dust Particle (IDP)
Just looking at your samples in a microscope can help explainJust looking at your samples in a microscope can help explain A LOT about the magnetic behavior of your samples.
The shape, grain‐size, texture, and associated non‐magnetic minerals all give clues to the magnetic mineralogy in a sample and their origins.
Imaging Magnetic Minerals
Exsolved magnetic & ilmenite in an igneous rock
Detrital titano‐magnetites from Chinese loess.
Hematite rosettes on a smectite grain.
Industrial pollutant (“fly‐ash”)
Interstellar Dust Particle (IDP)
Frequently used modes of
Tauxe, 2008
Frequently used modes of imaging:
Reflected light microscopy.
Easy, cheap, fast! Reflected light image of ilmenite hematite intergrowths.http://www.ngu.no/prosjekter/Geode/Tellnes/Tellnes%20ore%20photographs.htm
Imaging Magnetic Minerals
Exsolved magnetic & ilmenite in an igneous rock
Detrital titano‐magnetites from Chinese loess.
Hematite rosettes on a smectite grain.
Industrial pollutant (“fly‐ash”)
Interstellar Dust Particle (IDP)
Tauxe, 2008
Frequently used modes of imaging:
Scanning Electron Microscopy (SEM)Electron MicroProbe Analysis (EMPA)
Better spatial resolution (~0.1 µm), observation of 3D morphology of grains, and ability to measure composition (EDS) and crystal structure (via EBSD)
EDS: Energy‐dispersive X‐ray spectroscopy, EBSD: Electron backscatter diffraction
Imaging Magnetic Minerals
Exsolved magnetic & ilmenite in an igneous rock
Detrital titano‐magnetites from Chinese loess.
Hematite rosettes on a smectite grain.
Industrial pollutant (“fly‐ash”)
Interstellar Dust Particle (IDP)
Tauxe, 2008
Frequently used modes of imaging:
Transmission Electron Microscopy (TEM)Synchrotron Radiation
Best spatial resolution (0.1‐5 nm), ability to measure composition (EDS or EELS), and crystal structure (SAED).
EELS: electron energy loss spectroscopy, SAED: selected area electron diffraction
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Magnetic Characterization of Minerals
Characteristic Temperature Changes
All FM minerals have a Curie or Néel point 08
Derivative curves
Typical Strong‐field (~1 T) thermomagnetic experiment.
or Néel point
One of the ways we characterize samples is by heating them up and determining these key temperature transitions.
Tauxe 20
0
Measurement of Ms(T) in whole rock samples.
Experiment measures induced magnetization in a very strong field.
Peak shows temperature of maximum curvature, interpreted as the Curie temperature
Vibrating sample magnetometer
Magnetic Characterization of Minerals
lop & Özdem
ir, 2007
Identification of Magnetic Minerals by thermomagnetic analysis is complicated by two main factors
1. Each magnetic mineral has its own unique Curie (or Neel) temperature, but different minerals can
Dun
Normalized Ms(T ) dependences for five common magnetic minerals
have the same Tc or Tn (solid solution series titanomagnetites and titanohematites
2. Chemical alteration of samples can occur during thermomagnetic analysis (heating samples up to 500‐700 °C
Mineral Tc or TnMagnetite (Fe O ) 580° C
TitanomagnetitesMagnetite (Fe3O4) 580 C
TM60 120
Pyrrhotite (Fe7S8) 320
Maghemite (‐Fe2O3) 600?
Greigite (F3S4) 350(?)
Hematite (‐Fe2O3) 675
Goethite (‐FeOOh) 120
Tauxe, 2008
Magnetic Characterization of MineralsExamples of thermomagnetic curves
Standard Experimental practice is to measure thermomagnetic curves during a heating and cooling cycle
Butle
r 199
2 The Curie temperature is the same on both heating and cooling (~575˚C). This is termed reversible behavior.
Heating in air (not typically recommended)Heating in vacuum, or inert gas (N2, Ar) to reduce effects of oxidation
No (likely) chemical alteration occurred during heating and cooling cycle
Magnetic Characterization of Minerals
Examples of thermomagnetic curves
The Curie temperature of ~200˚C is observed with reversible behavior.
Could be either titanomagnetite (x~0.55) or titanohematite (y~0.5)
(Optical microscopy shows that titanohematite is the dominant magnetic phase in the sample.)
Butler 1992
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Magnetic Characterization of Minerals
Examples of thermomagnetic curves
Non‐reversible behavior
Usually indicates a change in the magnetic mineralogy has occurred during heating (oxidation, reduction, crystallographic change).
This sample contains intergrowths of Fe7S8 and Fe9S10
The change 225‐320˚C is a transition from antiferromagnetism to ferrimagnetism in the Fe9S10
Butler 1992
Irreversible Behavior: Titanomaghemites
TMAGH Fe‐rich TM + Ti‐rich ilmenite
Magnetic Characterization of Minerals
Titanomaghemite (ocean floor basalts from DSDP site 417D (Moskowitz, 1980)
Characteristic irreversible thermomagnetic curve of a partially oxidized TM60 (Özdemir and O’Reilly, 1982)
Irreversible Behavior: ‐FeOOH ‐Fe2O3‐Fe2O3
Magnetic Characterization of Minerals
Özdemir and Dunlop, 1993
“Irreversible” Behavior: Sluggish (reversible) phase transformations producing thermal hysteresis
Fe Fe‐Ni
Dunlop and Özdemir, 1997
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Magnetic Characterization of Minerals
Examples of thermomagnetic curves
Some samples have more than one magnetic phase
Curie temps at 580˚C and 680˚C are due to magnetite and hematite respectively.
This is a nice example where you can see a mineral with a large Ms (magnetite) and a low Ms (hematite).
Sometimes, the stronger Ms mineral
Butler 1992
, gswamps the signal, making it hard to detect the presence of other magnetic phases.
Often, you need to combine information from different kinds of experiments.
Magnetic Characterization of MineralsExamples of thermomagnetic curves
Identification of the ferromagnetic minerals in a pelagic limestone by determination of their Curie temperatures in concentratedextracts Lo
wrie
, 2007
Magnetic Characterization of Minerals ‐ Susceptibility
Tauxe 2008Hopkinson Peak
Tauxe, 2008
Paramagnetism has a 1/T dependence.
So the χ100 should be twice as large as χ200
χ100
χ200
T
Susceptibility experiments measure induced magnetization in a very weak field.
Diamagnetism is independent of T
1.00
1.20
Susceptibility Measurements
0 20
0.40
0.60
0.80
X/X
300
Titanomagnetite (TM28)Fe
2.72Ti
0.28O
4
0.00
0.20
300 400 500 600 700 800 900
Temperature (K)
increases with rising T because wall pinning decreases and resistance to wall motion decreases
2013 SSRM 5/29/2013
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coolingheating
FG_1951_02_04_BOT_05
/kg]
1.3e0
1.2e0
1.1e0
1.0e0
9.0e-1
8.0e-1
FG_1951_01_01_BOT_01
m3/
kg]
1.20e-5
1.10e-5
1.00e-5
9.00e-6
8.00e-6
B=1500 mTB=0.375 mT (ac)
Problems with Paramagnetism and high‐field measurements
Susceptibility Measurements
Paramagnetic (~1/T)
coolingheating
FG_1951_02_04_BOT_041.1e01.0e0
9.5e-19 0e 1
T [K]900800700600500400300
M [A
m2/
7.0e-1
6.0e-1
5.0e-1
4.0e-1
3.0e-1
2.0e-1
1.0e-1
T [C]700600500400300200100
susc
eptib
ility
[m 7.00e-6
6.00e-6
5.00e-6
4.00e-6
3.00e-6
2.00e-6
1.00e-6
B=500 mT
Paramagnetic ( 1/T) “contamination”
T [K]900800700600500400300
M [A
m2/
kg]
9.0e-18.5e-18.0e-17.5e-17.0e-16.5e-16.0e-15.5e-15.0e-14.5e-14.0e-13.5e-13.0e-12.5e-12.0e-11.5e-11.0e-15.0e-2
B 500 mTLooks more like a Tc
High‐field thermomagnetic (Ms) and NRM unblocking Temperature curves
Young Oceanic CrustEast‐Pacific Rise
Magnetic Characterization of Minerals
NRM unblocking Temperature curves
Hi h Fi ld R lt T ~150 C idi d TM60
Kent and Gee, Science, 1994
High‐Field Results: Tc~150 C, unoxidized TM60NRM unblocking: TB >300 C, oxidized TM60
Why discrepancy between High‐field results and NRM results?
Isothermal Remanent Magnetization (IRM)The magnetization acquired during
exposure to a short‐lived magnetizing field.
Usually at room T and in large fields. -0.1
0.0
0.1
0.2
M
(Am
2 /kg)
05E1 05E305E4
2005
Room temperature
Low‐coercivity minerals
Saturation <300 mTferrimagnetsFe3O4, ‐Fe2O3
High coerci it minerals007
-1000 -500 0 500 1000-0.2
Applied Field (mT)
05E4
Dust on Snow (Red Mountain Pass, San Juans CO)
High‐coercivity minerals
Saturation >1000 mTOpen loop to high fields‘imperfect’ Antiferromagnets‐Fe2O3, ‐FeOOH
Natural goethite
Berquo
et a
l., 2006, 20
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23
Imparting IRMs in the Lab
Isothermal Remanent Magnetization
ASC Impulse MagnetizerASC Impulse MagnetizerThe magnetic field is produced by discharge of energy from a capacitor
ElectromagnetsBmax ~2 T
Superconducting MagnetsBmax ~ 5‐20 Tg gy p
bank through a coil surrounding the sample cavity. The capacitor bank is first charged to the desired voltage (corresponding to the desired field). It is then discharged through the coil very quickly (Bmax~ 1‐2 T)
Bmax 2 T Bmax 5 20 T
Highest magnetic field for a continuous field magnet (Guinness World Record) 45 T
Highest field for a resistive magnet 36.2 T
Highest field for a long‐pulse magnet 60 T
Highest field for a non‐destructive magnet 90 T
Highest field for superconducting magnet 33.8 T
National High Magnetic Field Laboratory www.magnet.fsu.edu
IRM Acquisition: Samples can be exposed to progressively higher fields
IRMs can be very useful in the lab.
Isothermal Remanent Magnetization
SIRM and the resulting magnetization can be measured.
The magnitude of the IRM is sensitive to the magnetic mineralogy, concentration, and grain size of the assemblage.
M i IRM i k SIRM
Irm Acquisition
Tauxe, 2008
Maximum IRM is known as SIRM (saturation IRM) or Mr
IRM Demagnetization After saturation has been reached, the sample can be turned around and subjected to increasingly large back‐fields
Isothermal Remanent Magnetization
Back‐field CurveIRM demagnetization
xe, 2008
fields.
A some point the back‐field strength will be strong enough to flip half of the moments in a sample, resulting in a net moment of zero. This is the Coercivity of Remanence (Hcr).
Sometimes people use a term called ’’’ hi h i h fi ld i d
Taux
H’’’cr, which is the field required to impart half the SIRM.
The acquisition of IRM is one of the many tools we use to characterize the magnetic minerals in a sample
Coercivity of Remanence (Hcr).
Verosub and Ro
berts, 1995
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IRM Acquisition and Demagnetization Curves
Slope ~ 2~0.5
Henkel plot : graphs IRM (demag) as a function of IRM (acq) at equivalent field levels
Cisowski plot: simultaneously graphs the acquisition curve together with the AF or DC demagnetization curve as a function of field
Wohlfarth (1958) Relationships for Non Interacting SD grains
Slope =~‐2
Wohlfarth (1958) Relationships for Non‐Interacting SD grains
MIRB= DC back field demagnetization MIRA= DC acquisition MIR(HAF)= AF demagnetization
IRB IRA
IR IRA
( ) 2 ( )
( ) ( )AF
M H SIRM M H
M H SIRM M H
Slope of Henkel plot =‐2Crossover point for Cisowski plot =0.5
Jackson, 2007
IRM Acquisition and Demagnetization CurvesCisowski Test for magnetic interactions
A crossover ratio R < 0.5 (equivalent to a trajectory on the Henkel
SD MDR
R
A crossover ratio R < 0.5 (equivalent to a trajectory on the Henkel plot that “sags” below the line of slope 2) indicates that MAF > MDF
Ensemble is harder to magnetize than to demagnetize
Such behavior is a hallmark of either a negatively interacting SD population or MD carriers (for which self‐demagnetization produces the equivalent effect)
Cisowski, S., 1981. Interacting vs. non‐interacting single‐domain behavior in natural and synthetic samples. Physics of the Earth and Planetary Interiors, 26: 77–83.
Coercivity Analysis (IRM acquisition curves)
Coercivity in AFM phases like hematite and goethite is much larger than that observed in ferrimagnetic phases like (titano)magnetite i li tphases like (titano)magnetite.
During IRM acquisition, it is more difficult to saturate AFM phases than magnetite.
marine limestone containing magnetite
Butle
r, 1992
Note the change in scale on the x‐axis (titano)magnetite: Hcmax ~ 300 mT Hematite/ goethite: Hcmax >1 T.
Jurassic limestone containing goethite
So the point at which an IRM curve reaches a plateau tells you something about the mineralogy in a sample.
IRM acquisition curves up to 57 TRoom‐Temperature
Non‐saturation of the defect moment of goethite and fine‐grained hematite up to 57 T (Rochette et al, 2005)
Goethite powders
Rock samples
Anomalous decrease in between 34=39 T is due to field reversal between the two coils used.
Rock samples RR,RD: goethiteTO: fine‐grained hematite
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Magnetic Characterization ‐ IRM and Coercivity Analysis
In (a) we see an IRM experiment that is rapidly magnetized up to ~200‐250 mT
Butle
r 199
2
rapidly magnetized up to 200 250 mT.
At this point, the acquisition of IRM slows down considerably, but does not plateau (even by 800 mT).
This is evidence for the presence of hematite or goethite.
It does not exclude the presence of magnetite.
A Curie temperature of 580°C is evident, but there is no indication of hematite (680°C ) or goethite (120°C)
Magnetic Characterization ‐ IRM and Coercivity Analysis
(b) thermal demagnetization experiment for the IRM acquired in (a).
Butle
r 199
2
This experiment measures the remaining magnetization after the sample is heated in zero field to progressively higher temperatures.
Most of the remanence is gone by the Curie temperature of magnetite (580˚C).
However, a portion of the magnetization is still present at temps >580˚C.
This is the remanence held by hematite.
Magnetic Characterization ‐ IRM and Coercivity Analysis
(c) strong‐field thermoremanent experiment for the same sample.
We see a Curie temperature around 580˚C (and also near 425˚C), but no sign of a Curie temperature associated with hematite or goethite.
This highlights the need for complementary experiments!
Butler 1992
Combining thermal and isothermal Magnetizations
3D IRM Test:
Acquisition of 3‐component IRM (‘Triaxial’ IRM)
Magnetic Characterization ‐ IRM and Coercivity Analysis
1. Apply 2 T field along z‐axis2. Apply 0.4 T along y‐axis3. Apply 0.12 T along x‐axis
Thermal demagnetization of a 3‐axis IRM. Each component is plotted separately. (Ta
uxe 2008)
2 T field: AFM phases (hematite/goethite)0.4 T0.4 T field: (titano)magnetite0.12 T field: MD magnetite
Curve is dominated by a phase with a TBmax = 550◦ ‐600◦C and coercivity < 0.4 T, but > 0.12 T (PSD Magnetite)
Small fraction of a high coercivity (>0.4T) mineral with a maximum unblocking temperature > 650C (Hematite)
2013 SSRM 5/29/2013
26
Hematite is present in both (a) and (b), because SIRM requires fields > 1T and
Examples of the identification of magnetic minerals by acquisition and subsequent thermal demagnetization of IRM
because SIRM requires fields 1T and thermal demagnetization of the hard fraction persists to T= 675°C
In (a) the soft fraction that demagnetizes at T= 575°C is magnetite
In (b) no magnetite is indicated but pyrrhotite is present in all three
Lowrie
, 2007
fractions, shown by thermal unblocking at T = 300‐330°C