Download microhardness studies

Chapter 4
MICROHARDNESS STUDIES
4.1. Introduction
The microhardness of a substance is an important parameter to define the
strength of its material. This property is basically related to the crystal structure of
the material or in other words, the way in which the atoms are packed and the
electronic factors operating to make the structure ~tab1e.l.~
Physically speaking,
hardness is the resistance offered by the crystal for the movement of dislocations
and practically it is the resistance offered by the crystal for localized plastic
deformation. Hardness testing provides useful information about the mechanical
properties like elastic constants, yield strength etc of materials.
Elastic deformation developed in a material when subjected to indentation is
~ e r n h a r d suggested
t~
that a part of
directly proportional to the plastic def~rmation.~
the energy absorbed during indentation is used in producing plastic deformation and
the rest increases the surface free energy. Hardness value depends on the method of
measurement that in turn determines the scale of hardness obtained. In metals,
polymers and organic solids, an indenter is pressed in to the surface and the size of
the permanent indentation mark formed is measured. In certain materials, the
indenter is pressed in to the material and the hardness is determined by the extent to
which it had penetrated under load. In the case of minerals and brittle solids,
hardness is calculated on the basis of scratch produced in one material by another of
specific hardness number.
4.2. Various Testing Methods
There are many methods for measuring hardiless of materids but the most
commonly used form of measuring hardness ir: che indexation type. ~ a b o r ~
discusses an elaborate description of these methods with f&ir aLvan:-ges and
limitations as follows.
Static Indentation Tests
In these tests, a ball, cone or pyramid is used as an indenter, which is forced in to
the surface and the load per unit area of the impression measures the hardness of the
surface. The Brinel, Vickers, Rockwell, Monotron and Knoop tests are of this type.
,
spherical indenter is pressed under a
In the Brinell hardness ~ e s t a~hard
fixed normal load on to the smooth surface of the material under examination.
When equilibrium has been reached the load and the indenter are removed and the
diameter of the impression is measured. The Brinell hardness number HBis defined
as the maximum applied load per contact area. Another type of indenter, which is
most commonly used, is the conical or pyramidal indenter in the ludwick and
Vickers Hardness Testers. In the Knoop indenter, the indentation is in the form of
an elongated pyramidal impression, its length been seven times its width. This
indenter is particularly suitable for the study of anisotropy in hardness.
Scratch Tests
In this test it is observed whether one material is capable of scratching another.
If a material is able to scratch the other it is said to be harder than the other.
Plowing Tests
In these tests a blunt element (usually diamond) is moved across a surface
under controlled conditions of load and geometry and the width of the groove is the
measure of hardners. The Bierbaum Test is of this type.
Rebound Tests
In these tests, an object of standard mass and dimension is bounced from the
tests surface and tile height of rebound is taken as the measure of hardness. The
Shore Sceloroscop. is an instrument of this type.
Damping Tests
Ir r'lese te?ts, a change in amplitude of a pendulum having a hard pivot
~estingon the test swface is the measure of hardness. The Herbert pendulum test is
ot this type.
93
Microhardness Studies
Cutting Tests
In these tests, a sharp tool of given geometry is used to remove a chip of
standard dimensions.
Abrasion Test
In this test, hardness is defined as the resistance to mechanical wear, a
measure of which is the amount of material removed under specified conditions.
For example, a specimen under test is loaded against a rotating disc, and the rate of
wear is a measure of hardness.
Erosion Tests
In these tests, sand or abrasive grain is made to strike the specimen under
standard condition and the loss of material in a given time is taken as a measure of
hardness. This method is used to measure the hardness of grinding wheels. Recent
reports have shown that an ultrasonic hardness tester consisting of the modification
of the Brine11 indenter has been developed which enables instantaneous automatic
readout using ultrasonics7.
Hardness usually implies resistance to deformation, which in turn denotes
the ability of one body to resist penetration by another. It depends on the elastic and
plastic properties of both the indenter and the indented material. Among the various
methods for hardness measurements as described above, the most common method
is the microindentation method; and pyramid indenters are found to be best suited
for hardness tests due to two reasons; (a) the contact pressure for a pyramid indenter
is independent of indent size and (b) pyramid indenters are less affected by elastic
release than other indenters. The Vickers pyramid indenter, whose opposite faces
contain an angle of 136". is the most widely accepted pyramid indenter.
Nanostructered metals and ceramics cm have improved mechanical properties
compared to conventional materials as a result of the ultrafine micro~tructure~-~.
Many
materials.
studied the micro lrardness behavior of different nanostructered
For example Nieman,
Weertman
and
siegels reported
that
nanocrystalline palladium samples (20 nm) show a four-fold increase in hardness
compared to coarse- grained (100 pm) palladium and a doubling in hardness for
nanocrystalline copper samples (25 nm) over coarse-grained (50 pm) copper.
Nanocrystalline materials provide a promising way to generate ductile ceramics but,
poses new problems to physicists and material scientists on the property-structure
relationship. In studying the mechanical behaviour of nanocrystalline metals and
alloys, conflicting results have been obtained for the dependence of hardness on
grain size. For example the Jang and ~ o c h " , Qin, Wu and zhangll', Ganapathy and
~ i ~ e n c ~found
",
an increase in hardness with decrease in grain size. The
conventional relationship for this behaviour in coarse-grained materials is described
by the Hall-Petch equation8-"
where Hv is the hardness, Ho and k are constants, and dl is the average grain size.
According to these investigators, the increase in hardness with decreasing grain size
is observed to the finest grained material examined, although its variation with
grain size may be less than that in the case of conventional grain size materials.
Obviously, the equation has limitations because the strength cannot increase
indefinitely with decreasing grain size. From a practical viewpoint, for example, the
strength value cannot exceed the theoretical strength, i.e., the strength of a perfect
whisker. Additionally, any relaxational processes at grain boundaries, associated
with an extremely fine grain size, could lead to a decrease in strength and this could
result in an inverse d relationship below some critical grain size. In the absence of
-
such grain boundary relaxation mechanism, a region of constant strength with
decreasing grain size may be expected. In the case of the Hall-Petch relation, there
is an inherent upper limit on strength, that is, below the theoretical strength. This is
because the strengthing mechanism is based on dislocation pile-ups at physical
obstacles such as grain boundaries. As the grain size of a polyc~ystallinematerial
decreases, a stage will be reached at whjch each individual grain will no longer be
able to support more than one dislocation. At this point the Hall-Petch relation will
no longer hold". From another point of view, when the grain size approaches zero,
the material essentially becomes amorphous. The grain boundary strengthing effect
will then disappear. The hardness of an amorphous material is ir~deedlower than its
crystalline counterpart. In summary, strength (or hardness) may be expected to
Microhardness Studies
95
decrease or at least be constant when the grain size is below the critical value for
dislocation pile-ups and at this critical value the Hall-Petch relation would no
longer be observed.
Depth sensing indenter devices, known as nanoindenters, mainly using
Vickers diamond pyrarnid~,'~-~~are
now employed for studying mechanical
properties of materials. The hardness number Hv is defined as the ratio of applied
load, P to contact area A between the indenter and sample, i.e.,
Hv
= P/A
(4.2)
This area is defined by the pyramid geometry. In the case of a square base Vickers
pyramid, the contact area is
A = dSZ sin (8/2)
(4.3)
where 0 = 136" is the angle between opposite faces, and d is the diagonal length of
impression. Thus, the Vickers hardness number is given by
Hv = 1.8544 P / & ~ ~ / r n r n '
(4.4)
In apparent contrast to this behavior, Lu, Wei and wang'', Christman and
Jain
14,
and Chokshi, Rosen, Karch and ~leiter", reported that decreasing the grain
size produces softening in nanocrystalline materials. Softening with decreasing
grain size has been attributed to the increasing contribution of diffusional
accommodation to deformation processes at the finest grains. Hardness of a
material is closely related to its plastic deformation and the fracture properties.
Significantly increased strength and ductilities have been predicted for
nanophase microstructures. The strengtk. of nanophase microstructures is estimated
from the Hall-Petch strengthing theory to be up to 30 times that of the coarse grai~r
standard.14 The increased ductility (from Coble creep mechanism) is proposed to
occur due to the large volume fraction of atoms occupying grain boundary sites and
increased diffusion rates along these boundaries " Experimental evidence remains
contradictory regarding b?ti~of these theoretical suggestions. ~ l e i t e r 'reported
~
deformation studies of :.acccrystalline Ti02 where he describes significantly
enhanced plasticity and formability in this nanophase ceramic during compressive
96
Chapter 4
loading. Nieman, Weertman and Siege1 have reported tensile test results only for
nanophase materials. Their work on nanophase Pd and Cu suggests increased
strength and decreased ductility as a result of the drastic decrease in grain size.
4.3. Microhardness of Nanocrystaliine Metal Phosphates
Nano-sized metallic phosphates, aluminium phosphate (AlP04), copper
pyrophosphate (Cu2P207)and magnesium pyrophosphate (MgzP207) are prepared
from the thermolysis of new polymer matrix based precursor solutions. The
resulting powders are nano-sized, and are of high purity. The details of
preparation24are given in the synthesis part in section 2.2. In the present study
stoichiometric amounts of the reactants were taken such that the concentration of
the reactants were 1.0 OIL-', 0.5 mol~.' and 0.1 mol~.' to produce nanosized
Alp04 samples of average grain sizes16.34nm. 13.59 nm and 12.04 nm (samples
Al, A2 & A3). Nano-sized powders of Cu~P20,with average grain sizes 33.34 nm,
30.16 nm and 25.5 nm (samples C1, C2 & C3) and Mg2P207 with average grain
sizes 25.7 nm, 22.3 nm and 20.8 nm (samples M1, M2 & M3) were also prepared
by changing the concentration of the reactants, as described in section 2.2.
The microhardness studies of the samples were carried out, using Leitz
hardness tester type P 1191 fitted with a Vickers pyramidal diamond intender.25The
load P was varied from 0.1 N to 5 N, and the time of indentation was the same (30
sec.) for all trials and samples. For each sample, several trials of indentation with
each load were made and the average values of the diagonal lengths of indentation
marks were obtained. The Vickers microhardness number Hv at each load was
calculated using the relation
Hv = 1.8544 p/d2 (GPa)
(4.5)
where P is the applied load in N and d is the diagonal length of the indentation in
m. In this study, the nanopowders of the samples obtained by chemical method as
described earlier, were collected and compacted9 for 2 minutes under pressures of
0.3 GPa, 0.34 GPa, 0.38 GPa and 0.41 GPa. The specimens were disc shaped, 13
mm in diameter and 1 to 2 mm in thickness. The densi~ymeasurements of each
specimen were made based on Archimedes principle.
Microhardness Studies
97
4.4. Results and Discussion
Fig 4.1 presents the variation of Vickers microhardness number Hv with
indentation loads of the n-A1PO4 sample A1 compacted under different pressures.
The hardness shows an increase up to a load of about 2N, and then becomes
practically independent of load. The nature of variation of hardness is similar at
higher compacting pressures but when the compacting pressure is gradually
increased, the hardness also is seen to increase. It is found that the hardness for 0.45
GPa is about two orders greater than that for the same sample compacted under 0.3
GPa. This result indicates that the hardness of Alp04 is strongly related to
compacting pressure. Fig.4.2 gives the variation of Hv with indentation loads for
different compacting pressures for sample A3. Here also the nature of variation of
Hv is similar to sample Al, but Hv has a five-fold increase when compacting
pressure is increased from 0.3 GPa to 0.45 GPa. Fig.4.3 and Fig.4.4 give the
variation of microhardness with compacting pressures for the Cu2P207samples C1
and C3. In this case, for both samples, the hardness increases up to a load of about 2
N and thereafter remains steady. But Hv increases h m about 500 GPa to 800 GPa
when compacting pressure is increased from 0.3 GPa to 0.45 GPa for sample C1.
For sample C3 it is from about 600 GPa to 900 GPa when the compacting pressure
is increased from 0.3 GPa to 0.45 GPa. These variations are plotted in Fig.4.3 and
Fig.4.4. The variation of microhardness with compacting pressures for the Mg2P207
samples MI and M3 are plotted in Fig. 4.5 and Fig.4.6. Both the samples in this
case also show an increase of hardness up to a load of'about 2 N and thereafter
remain almost steady. Here Hv increases from about 900 GPa to 1100 GPa when
the compacting pressure is increased from 0.3 GPa to 0.45 GPa for sample M 1. For
sample M3, it is from about 900 GPa to 1200 GPa when the compacting pressure is
increased from 0.3 GPa to 0.45 GPa.
An important challenge faced in the fabrication of nanoshuctured materials
is how to achieve full densification of the powder while simultaneously retaining
the nanoscale microstruct~re~~.
High densities can be achieved, but are
accompanied by significant grain growth. To reduce grain growth at high densities,
98
Chapter 4
Fig.4.1. Variation of microhardness with indentation loads
for various compacting pressures of the n-AIR34 sample Al
Fig.4.2. Variation of microhardness with indentation loads
for various compacting pressures of the n-Alp04 sample A3
99
Microhardness Studies
Load (N)
Fig.4.3. Variation of microhardness with indentation loads
for various compacting pressures of the n- Cu~P207sample C1
Laad (N)
Fig.4.4. Variation of microhardness with indentation loads
for various compacting pressures of the n- CuzPz07 sample C3
100
Chapter 4
+I
I
0
1
2
1
3
4
5
Load (N)
Fig.4.5. Variation of microhardness with indentation loads
for various compacting pressures of the n- MgzPz07 sample M1
j r
0
7'
I
1
2
I
I
I
3
4
5
Load (N)
Fig.4.6.Variatxon of microhardness with indentation loads
for various compacting pressures of the n- MgzP207 sample M3
Microhordness Studies
random close packing of the nanosize particles in the material is to be achieved
prior to sintering. One way to achieve this condition is by compaction of the
powder at high pressures. A high-strength piston-cylinder die was used to compact
the powder samples and thus high density is achieved in the material. The increase
of compacting pressure inevitably leads to further densification of the specimen.27-29
To prove this result, the densities of all the specimens compacted under different
pressures were measured. The density increases almost linearly with pressure. In
order to show the influence of density on microhardness of the Alp04 sample, the
hardness is plotted as a function of density for sample A1 (Fig.4.7). It can be seen
that the hardness of n-Alp04 increased from 0.38 GPa to 0.79 GPa as the density
changes from 1.48~10"kg/m
to 1 . 5 5 ~ 1 0kg/m3.
~
This increase of microhardness
with increasing compact pressure actually reflects the effect of density on hardness.
This result indicates that the density of n - Alp04 specimen is an important factor
affecting its hardness. The variation of microhardness with compacting pressure
and density is further intensified as the grain size of the sample is reduced. Fig.4.8
shows that the hardness of n-A1PO4 sample A3 (grain size 12 nm), increased from
0.38 GPa to 1.7 GPa for a variation of density from 1 . 5 1 ~ 1 0kg/m
~
' to 1 . 6 2 ~ 1 0 ~
kg/m3.
Fig.4.9 and Fig 4.10 show the variation of microhardness with densities for
Cu2P207 samples C1 and C3. It can be seen from Fig.4.9 that the hardness of
sample C1 increases from about 0.4 GPa to 0.75 GPa as the density changes from
1 . 6 2 5 ~ 1 0kg/m
~
to 1 . 7 2 ~ 1 0kg/m3.
~
The corresponding variation for sample C3
(Fig.4.10) is from 0.4 (;Pa to 0.9 GPa for a change of density from 1.685~10'kglm
to 1 . 8 ~ 1 0kg/m3.
~
A similar variation of microhardness with density is observed
for M g 2 P ~ qsamples M1 and M3 as shown in Fig. 4.1 1 and Fig.4.12. For sample
MI, the hardness increases from 0.6 GPa to 1.0 GPa for an increase in density from
1 . 6 7 5 ~ 1 0kg/m3
~
to 1 . 7 5 ~ 1 0kg/m3
~
(Fig.4.11). For sample M2 (Fig.4.12) the
corresponding variation is from 0.675 GPa to 1.175 GPa when density changes
0~
to 1 . 7 6 5 ~ 1 kg/m3.
0~
from 1 . 6 8 5 ~ 1kg/m
Indentation hardness testing is probably the most widespread of all the
testing techniques, to assess the mechanical properties of materials. Applications of
Chapter 4
102
Fig.4.7. Variation of ~nicrohardnesswith density for
various compacting pressures of n-Alp04 sample A l .
Fig.4.8. Variation of microhardness with density for
various compacting pressures of n-Alp04 sample A3.
103
Microhardness Studies
Fig.4.9. Variation of microhardness with density for
various conipacting pressures of n- CuzPz07 sample C1.
-v-
0.41GPa
800
>
I
/
1680
1700
I
I
I
I
I
1720
1740
1760
1780
1800
Density (Kg m")
Fig.4.10. Variation of microhardness with density for
various co~npactingpressures of n- Cu2P207sample C3.
Chapter 4
104
-
microhardness indentation techniques, however, experience the load/size effect at
low levels of the testing load and have been traditionally described by the power
law,
P=Adn
(4.6)
where P is the indentation test load and d is the resulting indentation size3'. A and n
are descriptive parameters derived from the curve fitting of experimental results.
Equation (4.6) is r e f e d to as Mayer's law. For virtually all materials, the
power law exponent, n, is experimentally observed to be between 1 and 2, which
indicates that lower indentation test loads result in higher apparent microhardness.
This load dependence of hardness has been frequently reported.
The indentation loadlsize effect (ISE) on the microhardness has been
considered on the basis of a variety of phenomena, including work hardening
during indentation, the load to initiate plastic deformation, indentation plastic
recovery, the activation energy for dislocation nucleation, surface dislocation
pinning, and plastic deformation band spacing. Application of equation 1 yields an
n value that is less than 2, indicative of an increasing apparent microhardness at
lower indentation test loads. To examine the ISE critically, it is necessary to
evaluate an extensive set of experimental microhardness measurements on the
material to be studied. A plot of log P versus log d provides a straight tine, the slope
of which gives the work hardening coefficient n. These graphs, for the different
samples studied, are plotted in Fig.4.13 to Fig. 4.18.
Kick proposed a constant value for n =2 for all the indenters and for all
0 2 in the
geometrically similar impressions. However, according to ~rodzinski~',
region where Hv decreases with increase in load. In the present study, work
hardening coefficient n is obtained using least square fit method and is found to be
less than 2 for all the samples as given in table 4.1. According tn the Onstrich
concept, 32 the lattice is soft if n>2 and the lattice is hard if n <2. h i the high load
region, classical Mayer's law is insufficient to explain the variations as the
microhardness tends to be load independent.
Microhardness Studies
105
Density (Kg m")
Fig.4.1 1. Variation of microhardness with density for
Various compacting pressures of n- Mg2P207 sample MI.
Fig.4.12. Variation of microhardness with density for
various compacting pressures of n- Mg2P26sample M3.
Chapter 4
106
-
log d
Fig.4.13.log d vs log P graph for various compacting
pressures of n-A1PO4sample A l .
log d
Fig.4.14.log d vs log P graph for various compacting
pressures of n-AlP04 sample A3.
Microhardness Studies
107
-
log d
Fig.4.15.log d vs log P graph for various compacting
pressures of n- CuzPz07 sample C1.
Fig.4.16.1og d vs log P graph for various compat%ng
pressures of n- Cu2P~&saniple C3.
Chapter 4
108
1
log d
Fig.4.17.log d vs log P graph for various compacting
pressures of n- Mg2P207 sample MI.
Fig.4.18.log d vs log .? glaph for various compacting
pressures of n - hfg2P207 sample M3.
109
Microhardness Studies
l
Sample
I
a i n size
(nm)
I
Val:
of
I
Table 4.1. Work hardening coeficient determined for different samples.
In this region the indentation test load P related to indentation size d as,
Where a1 is the proportionality constant in the load dependent region, a2 that in the
load dependent region, PC is the critical applied test load above that the
microhardness becomes load independent and do is the corresponding diagonal
length. The first term in the equation represents the surface energy contribution
while the second term represents the volume energy contribution. Eqn. (4.7) can be
rearranged to give
P/d = a1 + (PC/'&') d
(4.8)
Hence a plot of P/d versus d is a straight line and the slope of which gives
the value of load dependent microhardness, which when multiplied by the Vicker's
conversion factor 1.854 gives the load independent microhardness H,.
To investigate the effect of grain size on the
the values of the
micro hardness number (Hv)are plotted with grain size (dlR)for all the samples as
a function of indentation loads (Fig.4.19, Fig.4.20 and Fig.4.21). It can be seen
110
Chapter 4
from the figures that the plots are more or less straight lines with positive slopes,
showing that microhardness of each sample increases with decrease of grain size in
accordance with the normal Hall-Petch relationship,
Fig.4.19 shows the variation of microhardness of n-A1P04 when the grain
size changes for various compacting pressures. The value of Hv changes from 545
GPa to 718 GPa when the grain size changes from 16.34 nm to 12.04 nm for the
compacting pressure 0.98 N. 'l'he corresponding change in Hv is from 657 GPa to
1260 GPa for the compacting pressure 2.4 N.
Fig.4.20 shows the variation of microhardness of nanocrystalline copper
phosphate for different grain sizes and compacting pressures. In this case the value
of Hv changes from 257 GPa to 298 GPa when the grain size changes from 33.34
nm to 25.5 nm for the compacting pressure 0.98 N. For the compacting pressure 2.4
N, the change in Hv is from 395 GPa to 470 GPa.
Fig.4.19. Variation of microhardness with grain size for
various compacting pressures of n-AlP84 sample
Microhardness Studies
Fig.4.20. Variation of microhardness with grain size for
various compacting pressures of n- CuzP~07sample
Fig.4.21. Variation of microhardness with grain size for
various compacting pressures of n- MgzPz07 sample
111
The variation of microhardness of nanocrystalline magnesium phosphate for
different grain sizes and compacting pressures is given in fig.3.21. Here the value of
Hv changes from 514 GPa to 553 GPa when the grain size changes from 25.7 nm to
20.8 nm for the compacting pressure 0.98 N. The change in Hv is from 621 GPa to
680 GPa, for the compacting pressure 2.4 N.
From the experiment.al results obtained above, it can be seen that the
microhardness of all the samples studied, is mainly affected by compacting pressure
and change in grain size of the material. When the grain size is constant, the
hardness behavior is dominated by density due to compacting pressure. On the
contrary, when the density of the material is constant, the hardness behavior is
controlled by grain size. It is evident that densification and reduction of grain size
would increase the hardness of all the nano-sized samples studied.
4.5. Conclusion
Indentation hardness testing is the most important testing techniques, to
assess the mechanical properties of materials. Among the various indentation
hardness testing methods, the Vickers hardness testing method is employed in the
present investigation. The microhardness behaviour of all the nanocrystalline
samples are studied in terms of various parameters. The hardness number depends
on the elastic and plastic properties of both the indenter and the indented material.
The variation of Vickers micro hardness numbers (Hv) with indentation loads of all
the studied specimens, show an increase of hardness up to a load of about 2 N, and
then remains practically constant, independent of load. The hardness shows an
increase of two orders when the compacting pressure is increased from 0.3GPa to
0.45GPa for AlP04 sample A1. The corresponding increase is five fold in the case
of sample A3. Similar variations are observed for n-CuzP207 samples and for nMg2P207. These variations are explained with the help of the Hall-Petch equation,
in which the strengthing mechanism is derived in terms of dislocation pile-ups at
grain boundaries.
In order to show the influence of density on microhardness, all the specimens
are compacted with varying pressures to obtain samples with different densities.
The strength of nanophase microstructures having different densities is estimated
Microhardness Studies
113
using the Hall-Petch strengthing theory. For sample A l , it is found that the hardness
increases from 0.38 GPa to 0.79 GPa as the density is increased from 1 . 4 8 ~ 1 0 ~
kg/m3 to 1 . 5 5 ~ 1 0kg/m3.
~
Similar variations of microhardness with densities are
observed for n-CuzP207 and for n-Mg2P207 samples. The variation of
microhardness with compacting pressure and density is further enhanced as the
grain size of the sample is reduced.
A plot of log P ve:rsus log d provides a straight line, the slope of which gives
the work hardening coefficient n. Work hardening during indentation is explained
on the basis of the theo~yof indentation loadlsize effect (ISE). In the present study,
work hardening coefficient n is found to be less than 2 for all the samples,
indicating that the lattices are hard.
To study the effect of grain size on hardness, the values of the micro
hardness number (Hv) are plotted with grain size (dln)for all the samples as a
function of indentation loads. It is found that the plots are more or less straight lines
with positive slopes, showing that microhardness of each sample increases with
decrease of grain size in accordance with the normal Hall-Petch relationship.
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1.
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C W Nieman, J R Weertman & R W Siegel, scripta Met. et Muter. 23(12),
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Chapter 4
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--
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