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MASTER
OCT 51909
STIG ON FABF.ICATION SCIENCE
Exigaton i2th October, 1964
"material Transport in Sintering" *
C. S. vorüan, B.S., Ph.D
Group Leades, Applied Research Section
C. J. ichlarsue, 3.8., *.3., D.Eng.
Head, Applied Rescarca Section
C. S. Yust, B.S., A.S.
metallurgist, Applied Research Section
Ketáls and Ceramics Division
Oak Ridge National Laboratory
Oak Ridge, Tennessee, U.S.A.

TEGAL NOTICE
TNI set mot red u an seal of Covenant otorid work. Nolter the Unid
MW, sur command, Mr au portat kung ano Con Nooku!
A. MA wymrunt or numewauation, a nd or impued, nu repart to the sou
#ky, coupons, or watum.. intornton could ta werurt, or that the we
of wlabration, menta, who or more delenud on we upon my no latring
Miniatyr or
2. AMU W uues with name to the wol, or for
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renume in
M a Worth, n , that or
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As the home parno stan nu doak" lind my Me
Morse or cour douanku. Hapenen el contractor, the one that
wel om magte or contractor of the most or empero c h cairktar report,
demum , or morti m e , w miarnation mural NI MNoget continet
w Onajomon. * No employuni wa much contractor.
* Research sponsored by the U.S.Atomic Enerly
it Research sponsored by the U.S. Atomic Enerty Commission under contract
*
**
.

ABSTRACT
MATERIAL TRANSPORT IL SINDIRITO
C. S. organ, C. J. Harcuc, C. S. Yust
Investigation of the consification kinetics of Tho, pouder compacis con-
taining varying arouts or coprecipitačeà Cao indicates that the initial
densification as the temperature is being raised is primarily by dislocation
movement, as is thought to be the case with pure Thog. The 'ino, -cao
com.acts.sinter more readily than pure To, compacts. The extent to which
dislocation transport of matcrial continues after attainment or isothermal
conditions is considered. Reasons are advanced to show that nodel study
results indicating volune diffusion transport of material do not rule
out a substantial disiocation contribution.
.
I*
.
Y
S
-
UURIAL RASPORT III SINTERING
C. S. Korcan, C. J. rcllargue
anci C. S. Yust
I. IKPRODUCATOR
Knowlcube oỉ the mechanism oz material transport in sintering is
of fundamental interest and should also contribute to the solution of
practical sintering problems. Workers in this field agree that the
driving force for material transpori is i'urnished by the surface
energy of the material. They also agree that there are four principal
mechanisms of material transport: plastic or viscous flow, volune
diffusion, evaporation-condensation, and surface diffusion. Of these
mechanisms only the first two can cause aerification of a powder compact,
other than in the surface layer. The predominant densification mechanism
and the contribution of supplementary transport processes, such as grain-
boundary diffusion, are still of treat interest. Apparently many investi-
cators nou believe volume diffusion to be the method of material trans-
port in metals and crystalline ceramics. The wide acceptance of volume
diffusion as the principal sintering mechanism is due, to a great extent,
to model studies in which the weld-neck growth between simple forms such as
two spheres is observed. For weld-neck growth between geometrically simple
forms Kuczynski has established the well-known relationship between the
mechanism of material transport and the exponent n in the following equation');
yn - I(T)t
where F(T) is a function of temperature and of the material, and
n = 2 for viscous or plastic flow,
12 À 3 for evaporation-condensation,
na for volume diffusion,
n = 7 for surface diffusion.
.
.
.
.
1
VA
The results oữ sinterinck tesis with metals and crystalline ceramics
have usually indicated volume diffusion to be the sintering mechanism.
In this paper Tho, sintering studies previously reported ) are
extended to include Tho, containing varying amounts of Cagʻand a
mechanistic interpretation of the results is given.
II. EXPERIZONTAL PROCEDURE
Thoria powder containing calcium as prepared by coprecipitation
YES
as the oxalates from nitrate solutions. The thorium ritrate contained
about 150 ppm total impurities. The precipitate vas dried and heated
stepwise in air to 650°C to allow conversion to the oxide and to remove
residual nitrate. Pellets 0.3 in. in diameter and 0.1 to 0.2-in. high
were prepared by cold pressing at 15,300 psi without binder.
The specimens vere placed in a cold furnace and brought to
w
temperature at the desired heating rate. A small platinum-rhodium
resistance wire furnace served for this purpose. For heating rates
greater than 4°C/sec, the specimens were moved at a regulated rate
into a high temperature furnace. A thermocouple embedded in a l'ho,
compact on which the specimen to be sintered was placed was usually
employed for temperature measurement. The specimens were brought
to the desired temperature, then rapidly withdrawn from the furnace.
All firings were carried out in air.
Densities were determined by an immersion technique or were
determined by geometrical measurement if the specimen shape permitted.
III. RESULTS
The densities of Thog-CaO specimens heated to 1600°c at different
heating rates are shown in Fig. 2. Specimens were brought to temperature
but not held there a measurable time. Results of Tho,-1.84 wt 's Cao
heated at l'aster rates to 1400°C are includca. Note that at heating rates
below 1°C/sec, the increase of coccity with decreasing neating rate
w
accelerates. In many tests iü baw sound that the fraction of theoretical
density rocched usually increased with increasing Cao content; however,
direct comparison among oxides vith different Cao contents is obscured
by unavoidable differences in materials resulting from slight differences
TO
in preparation.
Coinpacts of Inon-CaO showed a disproportionate increase in density
with increase in temperature. For example, iho,-1.37 vt Cao compacts
had an average density of 8.744 g/cc wien brought to 1450°c at a rate of
2°c/sec and held at 14:50°C for 10 minutes. Similar compacts had an
average density of 8.746 when held li min and 10 sec at 1450°C, but an
average den sity or 8.938 c/cc resulted when Tho,-1.37 wt Cao powder
compacts were held 10 min at 14:50°c and raised at a uniform rate to 1600°C
in 1 min and 11 sec (not held at 1600°c). The densification effected
during the 70-second period during which the temperature is increased from
14:50°C is significantly greater, by a factor of 10 or unore, than that
achieved when the pellet remains at 14:50°C for the same additional 70
seconds. The ratio of diffusion coefficients at the temperatures con-
f
cerned is only approximately 2.0; hence, it is indicated that some factor
other than the increased rate of diffusion with temperature is responsible
for the additional densification with increasing temperature. Similar
tests at lover temperatures on Tho,-0.84 wt cao powder compacts gave
the following results:
Heated to
and hela 10 min
- 5.14 g/cc
Heated to 1200°c and held 11 min and 20 sec
- 5.15 g/cc
Heated to 2100°c and held 20 mir., then heated to 1250° - 5.49 &/co
.-
-.
It has been rcported that tho, containing small amounts of Cao had
an inflection in the density vs. temperature curve for powder compacts
broucht to temperature at a uniform heating rate but not held at the
da
temyerature. 12.) ricure 2 shows that the inflection disep pears as the
amount oi' Caŭ in the Tho, is increased.
BLOU
You
IV. DISCUSSION
:::
These cata and the discussion are applicable to the initial
densification that occurs on heat up and are not to be confused with
the results of long isotherma. enneals.
Thoria containing cao, except for extremely sınall quantities,
sintered more readily in the initial states than "pure" Thog. Ease of
thoria creep was also creatly enhanced by addition of Cao.15Although
the material sintered to a higher fraction of theoretical density at a
given temperature, observation of the densification kinetics of Thog-Cao
powder revealed the three distinctive effects previously noted with Thoz.12)
The Thoz-Cao compacts had a temperature-dependent densification end point
I'or the initial period; that is, over a wide range of heating rates the
density at a given temperature varied much less than the heating rate.
pared to the increase in diffusion coefficient when the temperature was
increased; and for low Cao concentrations a maximun and minimum occurred
in the densification rate as the temperature was being increased at a
uniform rate.
These distinctive effects do not fit the expected characteristics
of a difusion-controlled reaction, but can be explained on the basis
of dislocation properties, particularly the sensitivity of dislocation
movement to temperature, stress, and impurity content. As the temperature
is increased, the stress required to move dislocations decreases and
110VES
SS
iraterial moves until Crowth of the weld neck between particles reduces
the stress (approximately equivalent to , where y is the surface
tension und po radius of curvature of the neck) below the required level.
Then rapid dislocation motion stops and further material transport to
cirect densification is by volume diffusion and/or by dislocation
:
movement involving diffusional processes such as climb. When the terper-
mo-
-
ature is raisca, the same sequence of events is repeated. The density
is largely temperature dependent as long as the heating rate is surfi-
ciently rapid so that not much diffusion-controlled densification takes
place. As yet, explanation of the minimum in the densification rate
can be given only by invoking a number of ad hoc assumptions which must
be clarified by Turther experiments.
Just how small quantities of Cao increase the sinterability and the
ease oỉ creep of tho, is not known. X-ray diffraction and petrographic
examination indicate that the calcium ions simply replace the thoriun
ions in the lattice 14) with only a very small change in the lattice
constant, e.5. Thog = 5.5970 : 0.0002, mnog-0.84 wt % cao = 5.5972 A +
0.0002. The calcium possibly facilitates dislocation motion by providing
sites in the lattice where other impurity ions can segregate, thus reducing
impurity segregation at dislocations. When present in small quantities,
calciwn appears to act as an impurity and reduces sinterability. In creep
tests, the ease of creep of Tho -CaO speci...ens became greatly reduced
after long periods of time. Petrographic examination indicated that the
Ca had segregated into small zones..
The increase in density with decrease in heating rate of Tho, powder
compacts brought to temperature and then cooled became more evident at
heating rates below about 5°C/sec but was not pronounced until the heating
.02
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rate was below 1°c/sec. "The inereasc in density of especially pure Tho,
was more pronounced at higher heating rates, i.e. 5°C/sec and below, as
was the case with in0,-1.37 wt i cao.
These results from measurement ou decification kinetics sucgest
that plastic i'low (in this paper plastic flow reſers to material trans-
OVO
port by dislocation movement) makes the principal contribution to material
transport during the initial sintering, i.e. as the temperature of the
specimen is being increased. This initial densification may be a sub-
stantial part of the total densification in the case of active ceramics
powders such as small particle size Thos. Examples were given in Ref. 2
in which 76 to 855 01 the total densification occurred in this stage.
In the case of large particles it may be so small as to be undetectable.
It has been fashionable toconduct model.-type experiments, i.e.
ord
studies of initial changes in systems of 'simple and uniform geometry,
and to apply their results to powder compacte. Vost such studies have
led to the conclusion that the main transport mechanism is volume
airTusion." Let us consider the use of inodel studies to differentiate
between two or more mechanisms of material transport during isothermal
sintering. Kuczynski derived rate equations for isothermal densification
when the changes were due to volune diffusion, evaporation-condensation,
and surface diffusion. (1) He cited Frenkel's results (6) to show an exponent
of two for viscous or plastic flow. However, Frenkel considered only viscous
flow in his derivation and did not treat dislocation movement. Kuczynski
states that an equation with an exponent of two can be derived for plastic
flow but he does not do so.') It is assumed that the exponent is two
for plastic as well as viscous flow. That this is actually the case is
not apparent to the authors. In fact, the derivations in Seigler's paper
imply that for dislocation transport of material, n is greater than two
and for certain ranges of particle and neck size have values between
four and six,
Y
There is no doubt that volume ciiffusion occurs but the fact that
the exponent for dislocation movement transport of material is unknown
makes it difficult to determine iſ this is instead of or in addition to
other processes. The exponent five, often o served and considered to re-
prescnt volume diffusion, could represent plastic flow or a combination
of plasstic flow and/or volume diffusion with surface diffusion. Surface
diffusion would be expected to always contribute to the growth of every
neck although this contribution can not be large if substantial densifi...
cation is to occur. The exponent for surface diffusion during neck growth
is not inown with any certainty itself since different analysts have
obtained values from three to se
to
coven.
The results of this investigation are interpreted as indicating that
plastic flow is the primary mechanism a material transport as the compacts
(Tho, and Tho -Cao) are being heated. It can be argued that plastic flow
will also contribute to isothermal sintering. However, during isothermal
sintering, the plastic flow contribution to densification can not be
distinguished from the volume-diffusion contribution by kinetic studies
of the type used here, because diffusion I processes, which cause dis-
location climb and permit.jogged and otherwise immobile dislocations to
move, control the rate of material transport. This restricted status
of dislocation mobility is in contrast to the fast movement of dislocations
which takes place with little or no apparent support from diffusion pro-
cesses during the initial stages. As the temperature is increased, the
resistance to dislocation movement is reduced so that movement continues,
*
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although this is counter-balanced by york-hardening. By the time that
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the elevated temperature has been reached, most or the easy movement of
--
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.
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dislocations will be completed because of the reduced stress caused by
changes in the geometry of the compact and the work-hardening. Murther
äislocation movement without a temperature increase will require that
MOVO
diffusion processes make it easier for the dislocations to move. As
sinterins continues and the geometry changes, i.e. the weld necks grow and
.
the increased radius of neck curvature continues to reduce the stress
available to cause material transport, more recovery by diffusion processes
will be required before additional dislocation movement will take place.
During sintering the surface tension stays approximately the same
so that the stress is related to the geometry of the powder compact.
If
the powder particles are small (small radius of curvature), appreciable
dcnsiſi.cation can take place at high temperature' by plastic flow before
vold-neck growth causes the stress to fall below the macroscopic yield
stress. Some dislocation motion can take place at stresses well below
the macroscopic yield stress. For instance, in room temperature bonding
studies of N80, Stokes, et al, observed dislocation loop expansion at
approximately one-third of the macroscopiq yield stress. Above one-hall
of the yield stress, simple multiplicacion commenced, and above two-thirds
of the yield stress gross multiplication developed short slip-line segments.
At al.evated temperatures one would expect to see more movement of clis.ocations
.
:
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.
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---
below the yield stress because of recovery processes. In l'act, creep of
-
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crystalline solids is the result of such behavior. Thus, the movement of
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dis.locations would be expected to continue well after the geometry 01 the
-
powder compact has changed so as to reduce the stress to a value below the
.-
the yiela stress.
,
K
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ti.
V, COZ.CLUSIONS
mie censiricatior Kinetics of th0,-Cao powder compacts as well as
2.0 Power Contacts cuacest that the initial sintering which occurs as
who weature is scinc zaised is primarily by dislocation movement.
.
min
. 00:02:01 treatment of powder compacts.
The fact that model
Chinese uchy
terorcted to indicate a volume diffusion mechanism
SC
.
w atu isomeado sinterins is not thought to rule out an appreciable
povrtic . Contribution, and in fact, both contrioutions are undoubtedly
museni. Because te exponent, n, in model study equations is not known
25: bic r0W aid is uncertain for surface diffusion, its value may
ovels with that for volume alifusion, and one can not determine the
cateri..., mechanism by nodel studies with any certainty in most cases.
It is argued that dislocation motion continues to make important
contributions after the start of isothermal annealing. The further
overe
con dislocations after the initial rapid movement occurs as
üresünü o dislocation climb and other diffusion-controlled processes.
The relative extent of plastic i lov and o volume diffusion would depend,
icast in part, on the particle size and shape of the powder.
5
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'
ACKNOWLEDGEMENTS
i
.,
.,
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*
The authors thans Dr. L. L. Seigle of General Telephone and Electronics
24.5.
-
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Laboratories for a pre-publication copy of his paper and for comments on
Its interpretation, and express appreciation of the diligent efforts of
-.-
-
-
-
-
L. L. Hall in the preparation and measurement of numerous specimens.
.
.
NET
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WELL
: ROTERENCES
1. a. Kuczynski, G. C., Trans. AIPC, 185, 169, 1949.
b. Kuczynski, G. C., "Theory of Solid State Sintering"
(New York: Interscience, 1961) p. ll.
2. Morgan, C. S., and Yust, C. S., J. Nuclear Materials, 10, 182, 1963.
3. Morgan, C. S., and Yust, C. S., Unpublished results.
4. Johnson, J. R., and Curtis, C. E., J. Amer. Cer. Soc., 37, 611, 1954..
5. Johnson, D. L., and Cutler, I. B., J. Amer. Cer. Soc., 46, (11),
541, 1963.
6. Frenkel, J., J. Phys. (USSR), 9. (5), 385, 1945.
7. a. Seigle, L. L., "Atom Movement During. Solid State Sintering" ..
presented at 20th Annual Powder Metallurgy Technical Conference,
April 28, 1964, Chicago, Illinois.
b. Seigle, L. L., Private communication.
8. a. Cabrera, N., J. Metals, 2, 667, 1950.
i b. Schwed, P., J. Metals, 3 245, 1951.
9. Stokes, R. J., Johnson, T. L., and Li, C. H., Trans. Met. Soc. AIME,
215, 437, 1959.
-
.
PN
XX
.
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.
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CAPTIONS
Fig. 1. Densities Achieved by Tho,-Cao Specimens Heated to Temperature
at Various Rates. . Specimens were not held a measurable time
at temperature.
Fib. 2. Density vs. Temperature for Tho,-0.053 wt% Cao and Th0,-1.84
wt% Cao Specimen. Specimen brought to temperature at 2°C/sec.
No hold at temperature.
(Printed previously in Journal of Nuclear Materials, 10,(3),
185, 1963.
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UNCLASSIFIED
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" HEATING RATE (°C/sec)
8 12 16 20 24 28 32
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DENSITY (g/cc)
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DATE FILMED
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