Materials Science and Engineering A318 (2001) 264– 276

www.elsevier.com/locate/msea

Influence of solidification variables on the microstructure,

macrosegregation, and porosity of directionally solidified
Mar-M247
H.S. Whitesell, R.A. Overfelt *
Materials Engineering Program, Mechanical Engineering Department, Auburn Uni6ersity, 201 Ross Hall, Auburn, AL 36849 -5341, USA

Received 27 November 2000; received in revised form 8 February 2001

Abstract

The solidification microstructure is critical in determining the amount and distribution of porosity that develops during the
freezing of castings. As the solidification velocity Vs increases, the microstructural length scales (primary and secondary dendrite
arm spacings) decrease; thus (1) the mushy zone permeability would be expected to decrease; and (2) nucleated pores would be
increasingly isolated. Although the first effect would tend to increase the observed porosity, the second effect would tend to
decrease the porosity. To better understand these competitive mechanisms, a series of controlled unidirectional solidification
experiments were performed on bars of nickel-base superalloy Mar-M247. Samples were produced with constant dendrite arm
spacing throughout an extended length of each cast bar. The axial thermal gradient and withdrawal velocity imposed on each
casting were varied between castings to produce a range of microstructures from aligned cellular dendritic to aligned dendritic to
mis-aligned dendritic. Macrosegregation effects along the lengths of the bars were evaluated and the resultant impact upon the
density along the length of each casting was also characterized. The density measurements were found to be very sensitive to both
(1) compositional macrosegregation in these castings and (2) internal porosity. Statistical analyses of microporosity in the castings
were based upon metallographic measurements. The development of microporosity in the unidirectionally solidified castings is
shown to be dependent upon the hydrogen gas content of the samples and the imposed solidification velocity through the sample’s
cast microstructures. An optimum intermediate withdrawal velocity of 0.005– 0.01 cm s − 1 was found, which led to closely spaced
dendrite arms, a large number of very small pores and a minimum total porosity level. Lower velocities lead to increased porosity
from larger pores whereas higher velocities lead to macroporosity due to centerline shrinkage. © 2001 Elsevier Science B.V. All
rights reserved.

Keywords: Solidification; Porosity; Dendrite; Segregation; Superalloy; Mar-M247

1. Introduction solidification process parameters on microstructural de-

velopment during casting of these complex superalloys
Nickel-based superalloys have evolved into compli- are important because the as-solidified microstructure
cated alloy systems due to manufacturers’ efforts to dictates subsequent heat treatments and the ultimate
obtain the best combination of high temperature engineering performance of the casting. The dendrite
strength and oxidation resistance to enable higher oper- arm spacings (primary and secondary), macro/mi-
ating temperatures in turbines. More recently, consider- crosegregation, distribution and morphologies of pre-
able research has concentrated on better understanding cipitates as well as porosity all influence subsequent
of the manufacturing processes to improve productivity mechanical properties.
and lower costs. Fundamental studies of the effect of Although equiaxed and chill castings have been
widely used to study porosity formation, such castings
exhibit coupled thermal gradients and solidification ve-
* Corresponding author. Tel.: + 1-334-8445940; fax: +1-334-
8443400. locities that change over time. As reviewed by Sigworth
E-mail address: overfra@auburn.edu (R.A. Overfelt). and Wang [1], these attempts to quantitatively relate

0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 1 2 6 4 - 3
 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276 265

As noted by Piwonka and Flemings [6], the space

between aligned cells during directional solidification
can be most simply modeled as capillary tubes with
lengths approximately equal to the lengths of the
aligned cells and diameters approximately equal to the
intercellular spaces. Liquid metal flows down the inter-
cellular space to feed the solidification shrinkage near
the roots of the cells. The Hagen–Poiseuille equation
describes pressure drop down a capillary tube as
8vLU
DP = (2)
r2
Fig. 1. Schematic of aligned dendritic and cellular growth.
where DP is the pressure drop, v is the viscosity of
liquid, U is the velocity of liquid in the capillary tube,
porosity in equiaxed castings to the imposed process
and r is the radius of the capillary tube. If the length of
parameters by means of the pressure drop through the
the interdendritic capillary tube is described in terms of
mushy zone via Darcy’s law have met with only limited
solidification variables (L DTo/G), and the solidifica-
success. Sigworth and Wang concluded that although
tion velocity (Vs) is used, then the equation for pressure
Darcy’s law can be applied to porous media flow of
drop becomes
liquid metal through a mushy zone, the pressure drops
associated with flow through the mushy zone are simply 8viDToVs
DPMZ = (3)
too small to contribute to porosity formation. These Gr 2
authors proposed an alternative ‘geometric model’ that
where DTo is the freezing range of alloy, G is the
predicted increased probabilities of isolated pools of
thermal gradient, i= (zS − zL)/zS, and zS and zL are
liquid metal as thermal gradients decreased.
the densities of the solid and liquid, respectively. Once
Unidirectional solidification is a powerful technique
an alloy is specified, the important metallurgical charac-
for studying solidification phenomena since the thermal
teristics of equilibrium freezing range and equilibrium
gradient and the solidification velocity can be de-cou-
amount of eutectic are fixed. The only means remaining
pled. In addition, the mushy zone’s interdendritic feed-
to exert control of microstructure in unidirectional
ing geometry is simplified with respect to complex,
solidification is in modifying the process parameters:
equiaxed mushy zones. The aligned dendritic or cellular
thermal gradient and solidification velocity. The applied
growth expected from careful unidirectional solidifica-
thermal variables play important roles in the formation
tion experiments is shown schematically in Fig. 1. Un-
of dendrite spacings during freezing. Higher velocities
fortunately, few experimentalists (e.g. Lecomte-Beckers
promote the formation of secondary arms since there is
[2], Kao et al. [3], Lin and Sekhar [4], and Ho and
less time for solute diffusion [7]. The simple models of
Sekhar [5]) have applied directional solidification tech-
Hunt [8] and Kurz and Fisher [9] indicate that the
niques to investigate porosity formation.
primary dendrite arm spacing, u1, should be propor-
Porosity is generally expected to nucleate heteroge-
tional to G − 1/2V − 1/4. Recently Bouchard and Kirkaldy
neously when the local pressure tending to close pores
[10], Ma and Sahm [11], and Hunt and Lu [12] have
is exceeded by the local pressure to open pores. The
shown that the exponent for G varies from −0.27 to
overall ambient pressure (Po 1 atm), the metallostatic
− 0.54 and V from − 0.11 to − 0.75 for many alloys.
head pressure (Pz =zLgh) and the liquid– vapor surface
The authors’ measurements [13] with a number of
tension pressure (P| =2|LV/r for a spherical bubble of
superalloys yielded exponents for G and V of −0.39
local radius r) all tend to close pores. Gas pressure (Pg)
and −0.082, respectively.
from partitioned gaseous species and the pressure drop
The dendrite arm spacing also influences the develop-
in the mushy zone (DPMZ) both tend to overcome the
ment of porosity during freezing. Although the presence
closure pressures and open pores. When the total net
of secondary dendritic arms decreases the permeability
pressure to nucleate becomes higher than the combined
of the mushy zone for liquid metal flow normal to the
pressures to close, conditions for pore nucleation are
primary dendritic arms, no effect on permeability for
favorable and can be represented as
flow parallel to the primary arms has been reported
2| [14,15]. Secondary arm formation may actually reduce
PT = Po + LV +zLgh − Pg −DPMZ (1)
r porosity by isolating pores and simply preventing their
where zL is the liquid metal density, g is the gravita- continued growth. Bachelet et al. [16] proposed that
tional constant, h is the height of liquid metal, and |LV there should be optimum casting conditions between
is the liquid–vapor surface tension. Thus, when PT B 0, fast and slow cooling leading to small evenly dis-
porosity would be expected. tributed micropores.
266 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276

argon gas. An Applied Test Systems Inc. box furnace

(maximum temperature of 1600°C) provided the hot
zone and was controlled by a digital computer, which
enables multiple set points. A second booster furnace
was utilized beneath the box furnace to modify the
thermal conditions imposed on the samples and obtain
low thermal gradients. An insulated adiabatic zone
between the two furnaces was used to provide flat
isotherms in that region. Sample temperatures and ther-
mal gradients were recorded with a computer data
acquisition system and dual 0.38 mm dia. B-type (Pt–
30% Rh/Pt –15% Rh) thermocouples axially spaced 10-
mm apart and inserted into the center of the samples.
The thermocouple data showed that when the dendrites
are aligned antiparallel to the thermal gradient, solidifi-
cation takes place in the adiabatic region. The use of
Bridgman directional solidification was critical for the
present investigation because of the need for steady
state solidification conditions (i.e. constant thermal gra-
dients and constant solidification velocities) after allow-
ing for the initial and final transients.
Fig. 2. Schematic of the directional solidification apparatus utilized in Table 1 gives the composition of the Mar-M247 alloy
this investigation. utilized in the present experiments. A series of twelve
experiments were performed with three different hot
Accurate porosity data from aligned unidirectional zone temperatures (1600, 1500, 1400°C) and four differ-
solidification samples cast with a range of thermal ent withdrawal velocities (0.0005, 0.005, 0.01, 0.1 cm
gradients and solidification velocities are a prerequisite s − 1). The experimental data on microstructure,
to understand the important coupling phenomena macrosegregation and density for the 0.01 and 0.005 cm
among the process parameters and microstructural de- s − 1 bars were comparable and only the data for the
velopment that affect porosity in nickel-base superal- 0.005 cm s − 1 samples will be discussed below. Each
loys for turbine applications. The material chosen for as-cast cylindrical bar (length, 20 cm; diameter, 12.7
this research is the often-studied, nickel-based superal- mm) was sectioned down the middle using wire EDM
loy Mar-M247. The present paper reports on the roles and 6.4-mm-thick semicircular samples taken every 3
of the process parameters on axial macrosegregation mm from one side. The other half of the bar was cut
and the development of microstructure and porosity in into 2.5-cm samples and mounted longitudinally for
Mar-M247. metallographic examination. Each sample was ground
and polished using standard metallographic techniques.
The etchant used to analyze microstructures was 10 ml
2. Experimental procedure HCl, 10 ml HNO3, 0.3 g molybdic acid, and 15 ml
distilled H2O. An Olympus PME3 inverted metallurgi-
The experimental arrangement for the casting experi- cal microscope was used to examine and photograph
ments is illustrated schematically in Fig. 2. A vertical the samples. Primary dendrite arm spacings were esti-
Bridgman furnace was used to melt and resolidify the mated by averaging five transverse photomicrographs
samples. The withdrawal velocity was monitored and using the relationship u1 = (A/N)0.5, where A is the
precisely controlled by personal computer. The sample cross-sectional area of the photograph and N is the
was enclosed in an alumina retort, which isolated the number of primary arms in the photograph [17]. This
sample from the oxidizing atmosphere. A vacuum was relationship is valid for a square array [18]. Secondary
drawn on the retort for each sample prior to melting dendrite arm spacings were measured from longitudinal
and then the retort was backfilled with high purity sections by counting the number of secondary arms

Table 1
Composition of the samples utilized in this investigation

Element Ni W Co Cr Al Ta Hf Ti Mo C Zr B H N

Wt.% Bal. 10.0 10.1 8.35 5.7 3.07 1.23 0.99 0.80 0.16 0.045 0.015 0.0008 0.0022
 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276 267

over a measured length on a minimum of three well- crostructure is cellular-dendritic with no secondary
aligned dendrite trunks. dendrite arms as verified by the corresponding longitu-
A number of samples were hot-isostatically-pressed dinal micrograph (Fig. 3f). When the samples are with-
(HIP) to close internal porosity. Samples were hot drawn at the highest velocity of 0.1 cm s − 1, cooling
isostatically pressed in a commercial unit using typical curves from in situ thermocouples indicated that freez-
hip parameters of 10393.4 MPa at 12189 3.9°C for ing occurs outside of the adiabatic zone and most of the
4.25 h. heat is extracted in the radial direction. Such cooling
Image analysis of porosity was performed on as-pol- conditions lead to predominantly dendritic growth in-
ished longitudinal sections to determine the number ward from the sample surface to the sample centerline
and shape of pores in a sample. Images were taken by as shown in Fig. 3a and b and such conditions can
a CCD camera mounted to the metallurgical micro- produce extensive centerline porosity. Porosity originat-
scope and connected to a personal computer. Greyscale ing from this mechanism was not the focus of this
8-bit images from the CCD camera were analyzed using work.
image analysis software. On each image, the threshold The primary dendrite arm spacings were measured
was adjusted to remove the light areas and leave only along the lengths of a number of samples and these
the dark pores. Careful manual control of the image data are shown in Fig. 4. Fig. 4 confirms that the
processing assured that carbide shadows were rejected experimental arrangement results in reasonably con-
from the measurements of the pores. Pores under two stant primary dendrite arm spacing over a large portion
pixels in size (i.e. approximately 4.7-mm diameter) were of the casting lengths. The influence of G and V on the
rejected. A total of 48 images were captured and ana- primary and secondary dendrite arm spacing have been
lyzed for each sample corresponding to  40% of the reported in another publication [13] and will not be
polished area. repeated here.
Porosity measurements in castings are sometimes
made by measuring the density of samples followed by 3.2. Density measurements
a comparison with the density determined after hot-iso-
static-pressing. The density of every 3-mm semicircular The density of each semi-circular disc from along the
sample was measured a minimum of five times via length of each sample was measured to compare the
Archimedes principle. The samples were carefully mea- as-cast density against (1) the as-received density of the
sured in air and in absolute ethanol with the tempera- original samples, (2) density measurements obtained
ture monitored by a thermometer. from selected samples after hot isostatic pressing, and
Qualitative compositions of the primary segregating (3) theoretical predictions of the density from measure-
elements along the length of the samples were deter- ments of the composition. The as-received density was
mined on transverse cross-sections using a JEOL 840 determined to be 8.57 g cm − 3. Hot-isostatic-pressing
scanning electron microscope with an Oxford Instru- increased the density only slightly to 8.58 g cm − 3. Fig.
ments energy dispersive spectroscopy (EDS) system 5a–c show the density versus position from the bottom
with programming to adjust for atomic number, ab- to the top of the unidirectionally solidified bars cast
sorption and fluorescence (ZAF) effects. Quantitative under each condition of withdrawal velocity and ther-
compositions of the primary segregating elements were mal gradient. The standard deviation of each density
determined on selected samples by direct current determination is included in the figures. All three of the
plasma emission spectrometry. Analyses of hydrogen highest velocity samples (Fig. 5a, V= 0.1 cm s − 1)
and nitrogen were performed using the inert gas fusion exhibited density values near the bottom of the bars that
technique. were comparable to the density of the as-received and
hot-isostatically-pressed value. However, all three of the
highest velocity samples exhibited significant reductions
3. Experimental results in density values near the top of the bars. As noted
above, metallographic examination of the tops of the
3.1. Microstructural characterization bars revealed an equiaxed microstructure and signifi-
cant porosity from the development of extensive center-
Fig. 3a–f are typical transverse (a, c, and e) and line shrinkage.
longitudinal (b, d, and f) microstructures for the three Castings withdrawn at 0.01 and 0.005 cm s − 1 were
withdrawal velocities. Transverse micrographs in Fig. 3 considered intermediate velocity samples and their den-
show that the primary dendritic spacing increases as the sity versus distance data exhibited similar trends. As
withdrawal velocity decreases. The samples shown in shown in Fig. 5b for the 0.005 cm s − 1 samples, except
Fig. 3c and d demonstrate that increased solidification for three density datapoints near the tops of the bars
velocities result in secondary and tertiary arm forma- where preferential cooling out the end (top) of the
tion to enhance solute rejection. In Fig. 3e the mi- crucible created a local ‘mini-pipe’ end-effect, each sam-
268 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276

Fig. 3. Typical microstructures of directionally solidified samples, (a, b) Vs =0.1 cm s − 1, G =19°C cm − 1 (transverse and longitudinal,
respectively); (c, d) Vs = 0.005 cm s − 1, G=39°C cm − 1 (transverse and longitudinal, respectively); (e, f) Vs =0.0005 cm s − 1, G =43°C cm − 1
(transverse and longitudinal, respectively).

ple’s density was essentially constant along the length hot-isostatically-pressed, as-received sample. However,
of the bar. These density values are comparable to the each sample displayed a decreasing density towards the
as-received, hot-isostatically-pressed density value. The top of the sample. The density of the 1400°C sample
density data shown in Fig. 5c for samples solidified at remained constant from the bottom to a position of
V =0.0005 cm s − 1 is extremely interesting. This was approximately 3–4 cm while the density of the 1500°C
the slowest velocity investigated and each sample exhib- sample remained constant from the bottom to a posi-
ited a cellular-dendritic microstructure with no sec- tion of approximately 5–6 cm. The density of the
ondary arm formation (Fig. 3e and f). The density of all 1600°C sample appears to begin to decrease almost
three samples at each furnace setting exhibited a density from the very beginning of solidification (i.e. bottom of
at their bottoms comparable to the density of the the sample). These decreases in density could be due to
 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276 269

one or both of the following, (1) macrosegregation of

lighter elements near the top and denser elements
near the bottom of each bar; and/or (2) increases in
porosity up the bar. These effects will be treated sepa-
rately next.

3.3. Longitudinal macrosegregation measurements

To assess the level of longitudinal macrosegregation

present, pieces from along samples grown at velocities
of 0.005, and 0.0005 cm s − 1 length were mounted,
polished and examined using EDS via the scanning
electron microscope. The X-ray data showed that tung-
sten preferentially segregates to the matrix gamma and
that tantalum segregates to the liquid while the remain-
ing elements exhibited partition ratios approximately
equal to 1. This behavior is consistent with the segrega-
tion analyses of Zeisler-Mashl [19]. The weight percent-
ages of each element were averaged and plotted versus
position along the unidirectionally solidified bars in
Fig. 6 for these two withdrawal velocities. The longitu-
dinal segregation of tungsten and tantalum was greatest
in the slowest velocity samples (Fig. 6b), and may
influence the density measurements. However, as seen
in Fig. 6a, segregation of tungsten and tantalum is not
as large in the higher velocity sample and, therefore,
would not influence the measured densities as
significantly.
At the slowest velocity of 0.0005 cm s − 1, there is
sufficient time for transport of species by both diffusion
and advection in the liquid. The EDS measurements in
Fig. 6b indicate that tungsten is depleted in the liquid
(i.e. inverse segregation to k) and tantalum is rejected
into the liquid as solidification progresses. To further

Fig. 5. Density along the sample length for samples withdrawn at (a)
Vs =0.1; (b) Vs =0.005; (c) Vs =0.0005 cm s − 1.

investigate this effect on the 0.0005 cm s − 1 castings,

samples from along the length of the castings were
Fig. 4. Primary dendritic spacing along selected sample lengths. carefully analyzed for composition using direct current
270 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276

plasma emission spectroscopy with standards. In addi- tion along the length of the bars significantly lowers the
tion, selected samples from along the length of the same measured density for the samples grown at 0.0005 cm
castings were also hot-isostatically-pressed. The density s − 1.
of the as-cast bars and the as-cast and hot-isostatically-
pressed samples are shown in Fig. 7. In addition, the 3.4. Metallographic porosity characterization
theoretical density based upon the composition of the
samples was estimated using the methodology of Sung Extensive metallographic measurements of porosity
and Poirier [20] and these data are also shown in Fig. 7 from the bottom and top regions of bars solidified at
for comparison. The as-cast density, the as-cast and V= 0.005 and 0.0005 cm s − 1 and G=25–43°C cm − 1
hot-isostatically-pressed density, and the theoretical es- were also performed. These data are shown in Fig. 8a
timate of the density all decrease with distance from the and b. Fig. 8a shows low levels of porosity along the
bottom of the cast bars. Thus compositional segrega- length of the bars until centerline shrinkage occurs at

Fig. 6. Longitudinal segregation measurements (wt.%) for samples withdrawn at (a) Vs =0.005; (b) Vs =0.0005 cm s − 1.
 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276 271

thermal gradient were exhibited at the 95% confidence

level only for the bottom regions of samples solidified
at velocities of 0.005 and 0.0005 cm s − 1.
Even more unclear is any potential difference be-
tween the bottom and the top regions of castings.
Although Fig. 8a shows a clear propensity for large
levels of macroporosity due to centerline shrinkage, the
microporosity data of Table 3 and Fig. 8b exhibit no
statistically significant distinction between the amount
of microporosity in the bottom regions of bars versus
the top regions of samples. However, analysis of the
variances by the ‘F’ test shows that the scatter in the
data is greater in the tops of the samples than the
bottom of the samples at the 99% confidence level. The
population of pores in the tops of the bars may be
composed of a bimodal distribution of micropores and
Fig. 7. Comparison of density measurements and theoretical predic-
tions of density from local composition measurements along the
length of samples withdrawn with Vs = 0.0005 cm s − 1.

the tops of three bars where the porosity values are

greater than 1%. The porosity scale is expanded in Fig.
8b and shows the measured variation of microporosity
for the six samples — porosity levels greater than 0.5%
were eliminated from the data sets to minimize the
influence of centerline shrinkage. These microporosity
data exhibit considerable scatter that is typical of
porosity data in general.
Table 2 shows the means and Standard deviation for
the microporosity data shown in Fig. 8b. All samples
solidified at 0.005 cm s − 1 exhibited less microporosity
than the corresponding samples solidified at 0.0005 cm
s − 1. Analyses of the means by the Welch Test [21]
indicate that this conclusion is highly significant at the
99% confidence level for both the top and bottom
regions of all samples except only the top of the sam-
ples solidified using a furnace setting of 1400°C. The
reductions in porosity average approximately 55% by
increasing the solidification velocity from 0.0005 to
0.005 cm s − 1. Comparison of the S.D. (|) of porosity
between the 0.005 and the 0.0005 cm s − 1 samples
shows that the 0.005 cm s − 1 samples typically exhibit
less scatter than the 0.0005 cm s − 1 samples. Analysis of
the variances (| 2) by the ‘F’ test indicates that this
conclusion is correct at the 99% confidence level for the
tops and bottom of the samples except for the top
region of samples cast using a furnace setting of
1400°C. Fig. 9a and b show the population distribu-
tions for pore radii for the 0.005 and 0.0005 cm s − 1
samples cast using all three furnace settings (1400–
1600°C). Clearly, the higher velocity samples exhibits a
larger number of smaller pores than the lower velocity
samples.
Fig. 8. (a) Metallographic measurements of porosity for samples
The influence in thermal gradient (i.e. furnace set- withdrawn with Vs =0.005 and 0.0005 cm s − 1; (b) metallographic
ting) on porosity levels was not as clear. Statistically measurements of porosity for samples withdrawn with Vs = 0.005 and
significant reductions in porosity due to an increase in 0.0005 cm s − 1 (expanded scale).
272 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276

Table 2
Statistical data on metallographic measurements of porosity in samples withdrawn at 0.005 and 0.0005 cm s−1

V (cm s−1) G (°C cm−1) Bottom of sample Top of sample

n Mean | n Mean |

0.0005 26 55 0.21 0.20 39 0.23 0.31

0.0005 38 52 0.19 0.18 50 0.19 0.21
0.0005 43 58 0.13 0.14 58 0.22 0.25
0.005 25 59 0.10 0.086 53 0.17 0.46
0.005 35 57 0.050 0.046 42 0.084 0.12
0.005 40 60 0.070 0.056 58 0.046 0.030

incipient cases of macropores, perhaps from the begin- ity certainly forms in the 0.0005 cm s − 1 samples to
ning of centerline shrinkage. Additional investigation of overall levels of approximately 0.1–0.4%
the transition from aligned axial dendritic growth to A straightforward capillary flow analysis of the
misaligned and radial dendritic growth is required to 0.0005 cm s − 1 samples provides insight into the pore
assess this possibility.

4. Discussion

4.1. High 6elocity samples: Vs = 0.1 cm s − 1

The samples withdrawn at 0.1 cm s − 1 did not exhibit

aligned directional solidification since the withdrawal
velocity was too high for solidification to be completed
within the adiabatic zone. Heat extraction was princi-
pally from the sides of the cylindrical samples and the
dendrites grew radially inward. Near the top of each of
these samples, extensive macroporosity developed to
form severe centerline shrinkage. Porosity of this type
can be interpreted from the simplified geometrical
model of Sigworth and Wang [1]. As shown in Fig. 10,
withdrawal velocities too high to enable directional
solidification will induce radial dendritic growth and
created a tapered liquid feeding channel down through
the center of the bar. Such a tapered channel can be
characterized by an angle and molten metal feeding
could be assumed to occur as long as the angle was
greater than a certain critical angle qc. As noted by
Sigworth and Wang, local variations in the contraction
of the casting from the mold and the orientations of the
radially growing grains would cause uneven solidifica-
tion and allow isolated ‘pools’ of liquid metal to freeze
without feeding and exhibit shrinkage.

4.2. Low 6elocity samples: Vs = 0.0005 cm s − 1

The castings withdrawn at velocities less than 0.1 cm

s − 1 all exhibited aligned growth of dendrites and/or
cellular-dendrites as shown schematically in Fig. 1. As
noted above, the decrease in density from the bottom
towards the top of the 0.0005 cm s − 1 bars was princi-
pally due to macrosegregation effects and not porosity. Fig. 9. Distribution of pore sizes for samples withdrawn with (a)
However, as shown in Fig. 8b and Fig. 9b, microporos- Vs =0.005 and (b) Vs =0.0005 cm s − 1.
 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276 273

Table 3 and exhibit typical diameters from 20 to 40 mm. Eq. (3)

Properties of MAR-M247 used in the calculations
was utilized to theoretically predict the pressure drop
Property Value Reference through the mushy zone by assuming that the interden-
dritic spaces formed small circular ‘pipes’ through
Liquid density, zL (g cm−3) 7.43 [26] which liquid metal flowed to feed solidification at the
Solid density, zS (g cm−3) 7.95 [26]
eutectic temperature. The thermophysical property and
Viscosity, v (mPa s) 8.5 [27]
Surface tension, |LV (N m−1) 1.7 [28] relevant process data utilized for Mar-M247 are shown
Liquidus temperature (K) 1628 [26] in Table 3. Calculations were performed for a range of
Eutectic temperature (K) 1549 [26] solidification velocities from 0.0005 to 0.05 cm s − 1 and
the predicted local pressures at the bottom of the
mushy zone are presented in Fig. 11b. The maximum
local pressure is shown as Po + zgh. Note that the
metallostatic head only increases the maximum local
pressure by approximately 10 kPa (or 10% of 1 atm).
At the experimental velocity utilized here (0.0005 cm
s − 1), the local pressure is predicted to remain positive

Fig. 10. (a) Cross-section of a vertical bar casting where the presence
of an axial thermal gradient creates a tapered liquid pool in the center
to feed the casting (after Sigworth and Wang [1]); (b) cross-section of
a vertical bar casting where lack of an axial thermal gradient and
uneven freezing leaves isolated pools of liquid.

formation processes. The lack of secondary arms en-

ables the interdendritic spaces of the 0.0005 cm s − 1
samples to be approximated as capillary tubes. This is
an important aspect of the cellular-dendritic growth
since it obviates the necessity of evaluating the transient
permeability of a tortuous mushy zone during solidifi-
cation and greatly simplifies calculation of pressure Fig. 11. (a) Lightly etched transverse cross-section near the eutectic
drops through the mushy zone. Fig. 11a shows a lightly freezing isotherm of a quenched DS sample showing the interden-
etched transverse section through a sample solidified at dritic spaces available to feed final solidification (V = 0.0005 cm s − 1,
G =41°C cm − 1); (b) calculations of the local pressure due to capil-
0.0005 cm s − 1 and a thermal gradient of 38°C cm − 1. lary flow through assumed cylindrical interdendritic spaces for the
The smallest interdendritic regions are circular in shape withdrawal velocities shown.
274 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276

Table 4 where CH is the hydrogen concentration in wt.%, KH is

Hydrogen and nitrogen activity coefficients
the equilibrium constant, fH is the activity coefficient
Property Hydrogen Nitrogen and PH2 is the local pressure of hydrogen gas in equi-
librium with the hydrogen dissolved in the liquid. The
dx −2.97302 18.8573 activity of hydrogen in liquid Mar-M247 was estimated
fx 0.008199 −34.8763 as
ex 12956.4 −70200.4
gx 18495.6 89008.10 (exq+ gxq 2)
Element b iH b iN
ln fH = dxq+ fxq 2 + (5)
T
Co 0.171 0.0642 where
Al 0.47 −0.354 N
Ti −0.075 2.83
q= % b iHX i (6)
Ta 0.52 0.85 i=1
Mo 0.334 0.86
W 0.52 0.85 and dx, fx, ex, gx, and b iH are constants obtained from
Cr 0.143 1 Schurmann et al. [22] and given in Table 4 for both
Hfa 0.52 0.85 hydrogen and nitrogen; X i is the atomic fraction of
a
element i and T is temperature in Kelvin. The Sieverts’
Estimated from Ta and W.
equilibrium constants [23] for hydrogen and nitrogen
are
2613 4972
ln KH = − 4.154− ; ln KN = − 4.106−
T T
(7)
Fig. 12 plots the results of calculations of gas pres-
sures at the eutectic temperature for hydrogen and
nitrogen for a wide range of gas contents. The gas
pressure in the liquid is seen to be highly influenced by
the amount of hydrogen in the samples; the influence of
nitrogen on the gas pressure is minimal and can be
neglected. Brandes [24] gives a partition coefficient for
hydrogen in pure nickel as k= 0.44. Assuming that
hydrogen partitioning in Mar-M247 is similar yields an
interdendritic liquid hydrogen content of 2.3 times the
average alloy composition. Thus hydrogen levels of
Fig. 12. Theoretical predictions of gas pressure at the eutectic temper- 5–11 ppm in the bulk alloy would yield values from 11
ature due to rejection of dissolved hydrogen and nitrogen.
to 25 ppm hydrogen in the interdendritic liquid. Fig. 12
unless the capillary diameter decreases to 0.1 mm. This shows that these interdendritic hydrogen contents at the
value is approximately two orders of magnitude smaller eutectic temperature would produce equivalent gas
than the interdendritic sizes exhibited by the samples pressures of 65–350 kPa. Such high local gas pressures
and the corresponding pore diameters (10 mm). Higher are the same order as the local metallostatic pressure
velocities of 0.05 cm s − 1 are theoretically shown to (Po + zgh) and would be expected to play an important
require capillary diameters of the order of 1 mm before role in pore nucleation.
the local pressures are predicted to be negative, again Chen et al. [25] note that carbides can heteroge-
smaller than the actual pore diameters. Thus the pres- neously nucleate in nickel-based superalloys at tempera-
sure drop due to capillary flow is not expected to tures from within the mushy zone to temperatures
exhibit a meaningful effect on pore formation. higher than the liquidus depending upon the nucleation
The segregation of dissolved gases and precipitation potential of the liquid. During the low velocity cellular-
of gas bubbles can play a dominant role in formation of dendritic solidification of MAR-M247 LC alloy, Chen
porosity. The gas pressure PG due to rejection of dis- et al. [25] found that carbides tend to become preferen-
solved gases was calculated following the work of Sung tially trapped by the advancing solid at the bottom of
et al. [22] utilizing the equivalence method developed by the mushy zone. This observation is consistent with the
Schurmann et al. [23]. Sievert’s law was used to calcu- present series of samples. This is not surprising since
late PG as follows. the density of the liquid is 7.4 g cm − 3 and the density
of HfC, TaC, and W2C are 12.7, 14.5 g cm − 3, and W2C
CH fH
KH = (4) is 17.2 g cm − 3, respectively [19]. Thus carbides nucleat-
(PH2)1/2 ing in the enriched interdendritic liquid would tend to
 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276 275

settle to the bottom of the mushy zone. Fig. 13a and b The secondary and tertiary arm development of the
are SEM micrographs showing two typical interden- 0.005 cm s − 1 samples also prevented significant growth
dritic carbide particles associated with porosity (behind and coalescence of micropores that resulted in a larger
the carbides with respect to the direction of dendritic number of smaller pores as compared with the samples
growth). The extensive metallographic characterization grown at 0.0005 cm s − 1. Since the volume of each
of porosity in this investigation revealed that a high isolated micropore would scale as d 3, reducing the size
percentage of pores were located adjacent to carbide of pores dramatically reduces their effect on the mea-
particles. This close association of porosity with car- sured porosity and density of any given sample. As
bides suggests that the particles may be settling to the noted above, Bachelet et al. [16] proposed that there
bottom of the interdendritic spaces during cellular-den- should be optimum casting conditions between fast and
dritic growth and block off the feeding path to feed the slow cooling leading to small evenly distributed microp-
final solidification at the eutectic temperature behind ores. These conditions appear to have been met for the
the carbide particle. Thus interdendritic carbides may samples withdrawn at 0.005 cm s − 1.
create isolated micropools of liquid metal that then
become micropores during final solidification. Addi-
tional studies with varying amounts of carbon and 5. Conclusions
carbide forming elements are required to test this
possibility. As originally proposed by Bachelet et al. [16], there
appears to be an optimum directional solidification
4.3. Intermediate 6elocity samples: Vs = 0.005 cm s − 1 velocity for MAR-M247 of 0.005–0.01 cm s − 1 that
(and 0.01 cm s − 1) leads to small evenly distributed micropores with mini-
mum total porosity. Micropore growth appears to be
Interestingly, none of the samples withdrawn at 0.005 limited by the isolating effects of secondary and tertiary
cm s − 1 exhibited significant density variation with posi- dendrite arms.
tion along the length of the bars. Perhaps the decreased Directional solidification velocities higher than 0.01
permeability of the mushy zone due to secondary and cm s − 1 for MAR-M247 in the present apparatus enable
tertiary arm development prevented significant penetra- solidification outside of the adiabatic zone, radial den-
tion of bulk convection into the mushy zone and al- dritic growth, and severe centerline shrinkage.
lowed microsegregation to develop in a quiescent Directional solidification velocities for MAR-M247
liquid. Additional studies utilizing computational mod- lower than 0.005 cm s − 1 lead to cellular-dendritic
els of the present experiments are necessary to quantify solidification, greater levels of overall porosity, and a
this effect. smaller number of larger pores than at the optimum
velocity. In addition, greater levels of axial macrosegre-
gation are found in these samples as compared with the
higher withdrawal velocity samples. The macrosegrega-
tion levels are great enough to significantly impact
density measurements of the castings.
Applied thermal gradients of 19–34°C cm − 1 for
MAR-M247 in the present apparatus do not appear to
exert significant influence on either macrosegregation or
porosity.
Dissolved hydrogen levels of 5–11 ppm in the bulk
alloy can theoretically produce local hydrogen gas pres-
sures from 65 to 350 kPa in the interdendritic regions.
Such pressures are comparable to the local metallostatic
pressures at the bottom of the mushy zones.
Carbides appear to be highly associated with microp-
ores in MAR-M247. Further studies are required to
assess the statistical significance of this association and
any possible implications regarding cause and effect.

Acknowledgements

Fig. 13. Typical as-cast pores associated with large carbide particles This material is based upon work supported by, or in
(Vs =0.0005 cm s − 1, G =43°C cm − 1). part by, the US Army Research Office under grant
276 H.S. Whitesell, R.A. O6erfelt / Materials Science and Engineering A318 (2001) 264–276

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