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where
m
is grain moment;
B
is the Earth's fi eld strength;
k
is Boltzmann's constant;
T
is temperature; pDRM is
post-depositional remanent magnetization; and pDRM
sat
is saturated pDRM for all the particles in the sediment
perfectly aligned (Johnson
et al
. 1948). Basically, a mis-
aligning force (in this case the randomizing effects of
thermal energy or Brownian motion of water mole-
cules,
kT
) counteracts the aligning torque of the geo-
magnetic fi eld acting on the magnetic moment of the
magnetic particle,
mB
.
This approach does a good job of fi tting experimen-
tal results of re-deposited glacial clays (Verosub 1977)
if a uniform distribution of magnetic moments with a
maximum cut-off value is used (Stacey 1972). The
hidden assumption of using this model is the magnetic
moments of the detrital magnetic nano-particles.
We used 5 × 1 0
− 17
A m
2
in our calculated estimate of
the alignment time of a magnetite particle. There we
assumed that the grain was one micron (μm) in diam-
eter (10
− 6
m) and the magnetization
J
of this grain was
0.1 × 1 0
3
A/m. If the grains are truly single domain it
would be reasonable to use the spontaneous magneti-
zation of magnetite (
J
= 480 × 1 0
3
A/m) or, more
accurately, calculate it from micromagnetic modeling
(Tauxe
et al
. 2002 ) (
J
= (340 - 480) × 1 0
3
A/m; see
Tauxe 2010 , fi g. 4.5, p. 56). If the grains are in the
pseudo-single domain or very small multi-domain
grain-size range, i.e. submicron to 1-2 microns in
size, then the subdivision of the grain into a small
number of domains would decrease the grain moment
from the spontaneous magnetization or micromag-
netic modeling values; the exact magnetic moment
would depend on the number of domains and their
confi guration.
Hence the estimate of
J
= 0.1 × 1 0
3
A/m used by
Butler (1992) and here in the alignment time calcula-
tion for small multi-domain grains. A maximum grain
moment of 7.4 × 1 0
− 17
A m
2
(Stacey 1972 ; Butler
1992, p. 72) used in the Langevin description of
Brownian motion yields a curve (Fig. 2.2) that fi ts the
re-deposition data of Johnson
et al
. (1948) and assumes
something close to
J
= 0.1 × 1 0
3
A/m for the magneti-
zation of the magnetic grains (
J
= 0.07 × 1 0
3
A/m).
The Brownian motion modifi cation of classical DRM
theory usually describes a post-depositional remanent
magnetization in sediments and sedimentary rocks, so
the alignment is envisioned to occur in the pore spaces
of the sediment after the grains have been deposited.
Post-depositional remanence will be covered in more
detail in the next chapter.
Fig. 2.2
Plot of Langevin description of Brownian motion
affecting the alignment of particles in a pDRM. The curve
plotted here comes from Stacey's (FD Stacey, On the role of
Brownian motion in the control of detrital remanent
magnetization of sediments,
Pure Applied Geophysics
, 98,
139-145, 1972, John Wiley & Sons) adaptation of the
Langevin description of Brownian motion, assuming a
uniform grain moment distribution with a maximum
moment (
m
in equation for
x
in the fi gure) of
7.4
1 0
− 17
A m
2
. Johnson
et al
. ' s (1948) re - deposition data
for glacial sediments fi ts this curve quite nicely.
×
FLOCCULATION MODEL OF DRM FOR
MAGNETITE-BEARING ROCKS
Lisa Tauxe has provided an alternative model for DRM
acquisition (Tauxe
et al
. 2006) that gets around the
problem of classical DRM theory which predicts nearly
instantaneous alignment of grain magnetic moments
with the geomagnetic fi eld. The main idea of her model
is that the effective magnetic moment of a magnetic
grain is signifi cantly reduced because it is embedded in
non - magnetic sediment fl occules. The composition of
the fl occules is not discussed in her 2006 paper, but
they could be organics, clay particles or both. Mitra &
Tauxe (2009) take the fl occulation idea a step further
and envision clay fl occules with an internal hierarchi-
cal structure. They also show through a series of re-
deposition experiments in solutions of varying salinity
that the size of the fl occules (small fl occules at low
salinity, large fl occules at higher salinities) controls the
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