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Spatial dispersion of graphite particles in cast iron
337
M E ? A L L O G R A P H Y 11,337-346 (1978)
Spatial Dispersion of Graphite Particles in Cast Iron
G. E. HI~NEIN AND J. E. HILLIARD
Materials Research Center and Department o f Materials Science and Engineering, Northwestern University, Evanston, Illinois 60201
The distribution of intercept lengths in the matrix constituent has been determined for eight cast-iron specimens with graphite nodularity ranging from 0 to 100%. For all specimens the distribution f(L) of intercept lengths was found to be that corresponding to a random dispersion of graphite particles, the distribution being of the form f(L) - ( l / L ) e x p ( - L / L ) for L greater than the average intercept length in the particles. From this result it was possible to infer that nucleation of graphite had occurred in the melt.
Introduction Although graphite growth in cast iron is now well understood, the circumstances of its nucleation remain in dispute. As an aid in resolving the issue of whether nucleation occurs in the liquid or the solid, we have studied the spatial distribution of graphite particles. If nucleation occurs in a solid matrix, one would expect the graphite to be found at preferential sites (grain boundaries for instance) and the particles will therefore be clustered. On the other hand, if nucleation occurs in the melt, the spatial dispersion will be random. In this case the distribution f(L) of linear intercept lengths in the matrix between successive particles will correspond approximately to the distribution of random points on a line which is given by [1]:
f(L)
= (l/L)exp (-
L/L)
(1)
where L is the average intercept length. We have chosen this last expression as the starting point of our study for the two following reasons: In the case of randomness a plot of the logarithm of f(L) versus L is linear with a slope - 1/L as is a plot of Ln [1 - F(L)] versus L where F(L) © Elsevier North-Holland, Inc., 1 9 7 8
0026-0800/78/0011-0337501.25
G. E. Hdnein and J. E. Hilliard
338
is the cumulative distribution function, i.e.: ¢, L
F(L) = Jo f(L)dL = 1 - exp ( - L/L)
(2)
The ratio 8 of the standard deviation o-(L) to the average intercept length L is a useful measure of the degree of randomness in general; for a perfectly random distribution this ratio is unity. If the experimental value of this ratio is found much smaller than one, on the other hand, it is an indication that the particles are distributed more homogeneously (that is, the deviations of the intercept lengths from the mean are small). On the contrary, in most cases of clustering this ratio will be greater than unity.
Experimental Procedure SPECIMENS Eight cast irons were studied having visual nodularity ratings varying from 0 to 100 percent. The structures of two of the samples are shown in Figs. 1 and 2. All specimens had a pearlitic-ferritic matrix.
F~G. 1. Specimen D: gray cast iron, 100% flakes, 750x.
Spatial Dispersion of Graphite Particles in Cast Iron :" o
i''"
"
O-
_.a
"
"
•" ~
4
"~"
",.,..o
'* l b .
•
,~ ~
":i,~,
-"O
" Q
..
Q
#
.'.
"~ " ~
--"
• ,
~" .
_II
. re.
"
339 •
f4
O).
P
~ ".~'"* W
.",'.,e :.',:--',-*,
"
" ...
Fnc. 2. SpecimenK: vermicules + nodules (40~/~),300×.
The specimens were ground first on a " D i s c o p l a n " and then by hand on 24 and 17 tzm silicon carbide papers. They were then alternately polished and etched on 5 and 1 micron diamond wheels and given a short final polish on a slow wheel using 0.05 micron cerium oxide. With patience it was possible to obtain almost 100 percent graphite retention, which is an essential requirement for reliable measurements. INSTRUMENTATION The instrument used for the stereological measurements consisted of a " D i g i s c a n " optical-stage scanning microscope interfaced to a DEC PDP8/e computer [2]. The stage is driven in the X and Y directions by pulsed DC motors having a speed variation of 150: 1. The location of the stage is monitored by optical encoders with a resolution of 0.5 txm. Although the instrument is capable of automatic discrimination, the measurements were made using visual discrimination at 400× magnification in order to ensure maximum resolution and to avoid errors due to counting inclusions other than graphite. The instrument was operated as fol-
340
G. E. Hdnein and J. E. Hilliard
lows. The X and Y motions of the stage were controlled by a variablespeed joystick. When a particle boundary reached the cross-hair inscribed on the eyepiece reticule, the stage was stopped and the event signaled to the computer by pressing a key. The traverse was then continued, and a second key was pressed when the opposite boundary was reached. This operation was continued until the required number of measurements had been accumulated. The distributions of intercept lengths in the graphite particles and matrix were stored by the computer on histograms with 128 class intervals. (The width of the class intervals was automatically adjusted to accomodate the longest intercept encountered in each constituent.) Provision was made when outputting the data for regrouping into any smaller number of intervals which is a power of 2. The optimum number of intervals was determined by a balance between two factors. As the number of intervals is increased the resolution of the distribution is improved but the scatter is increased. In the present case, 16 and 32 intervals provided the best compromise.
~-~o
SPECIMEN
D
Z
~
a I-N=2000
r__,= 5z,18~
0
I
I
64
128
FIG. 3.
o
22 I
192 L(Fm)
I
I
256
320
Specimen D: 100% flakes.
,84
Spatial Dispersion of Graphite Particles in Cast Iron
341
The complete data were also stored on magnetic tape for later use and for combination with additional measurements. The program we used in this study yielded, among other statistical parameters, the average lengths traversed in the matrix constituent and the particles, respectively L~ and Lp, along with the sample standard deviations o(Lu)and ALp).
Experimental Results Plots of L n N f ( L ) a n d LnN[1 - f(L)] vs. L for three of the specimens are shown in Figs. 3, 4, and 5. It will be noted that the plots are close to being linear, indicating that Eq. (1) for a random dispersion is obeyed. However, the first point in each of the plots for LnNf(L)falls below the extrapolation of the frequencies for longer intercept lengths. We believe that this is due to a breakdown in our model at short intercept lengths.
SPECIMEN K \o
\o
X~O\o\/
"~0
-~tx
..°'°-~ ,
N ['-F(L~/50
\
7 S
o\
&
°\% o ~o,,,
Nf(L) X
Z N=2000 Ls= 112.74/~m
0
I
64
I
128
I
192
I
256
I
320
L (~m)
FIG. 4. Specimen K: 40% nodules.
384
G. E. HOnein and J. E. Hilliard
342
SPECIMEN A ~o
\o ~o~
O 10
,,
"
o~
a"~,,
°~°
ts
\
~
0
Nf
N=2000 Ls=153.61/,Lm
0
6'4
' 128 L
IcJ2
2~56
' 320
384
(/Lm)
FiG. 5. Specimen A: 100~ nodules.
As illustrated in Fig. 6 there is a geometrical factor that also contributes to the distribution of intercept lengths, and this factor becomes proportionately more important as the separation distance between particles decreases (Fig. 7). As would be expected, the intercept length LR at which the deviation occurred was approximately equal to the average intercept length Lp in the particles (Table 1). The plots for the remaining specimens were also linear, except for the first one or two points. The results for all the specimens are given in Table 1. The average intercept length in the matrix, Lu, is the one calculated from the distribution and Zu' the one determined from the slope of a linear least-squares fit to the LnN[1 - F(L)] vs. L plots. With one exception, Lu is greater than LM' which can be accounted for by the deviations from the theoretical distribution at short intercept lengths previously noted. The average intercept length in the matrix phase is related [3] to the surface area, Sv, of the
Spatial Dispersion of Graphite Particles in Cast Iron
343
FIG. 6. Effect of the geometry of the particles on the distribution of very short intercepts in the matrix.
particles per unit volume of the specimen by LM = 4(1 - Vv)/Sv
(3)
where Vv is the volume fraction of the particles. Since the latter was approximately the same for all specimens, the observed increase of LM with the percent of nodularity is to be expected since, for a given size distribution, Sv is a minimum for spherical particles. Also, as one would expect, the average intercept length in the particles increased. Values of the dispersion index 6 = (r(L)/Lu for the various samples are listed in Table 1. The values ranged from 0.88 to 1.04 with an average of 0.95 and with all samples but one exhibiting a 8 slightly less than unity. The Kolmogoroff test of goodness of fit [4] was used both for determining the number of profiles, N, to be sampled in each specimen and for setting up confidence limits for the distribution function. This test showed that the assumption of a random dispersion of the graphite particles could be accepted with great confidence.
ca,
(b)
( ~
FIG. 7. Effect of the geometry of the particles on the distribution of intercept lengths in the matrix: (a) negligible effect for long intercepts, (b) important effect for short intercepts.
G. E. Hdnein and J. E. Hilliard
344
TABLE 1 Results for Eight Specimens. (Symbols are defined in the text.) Nodularity %
LM
LM'
Lp
Spec.
/zm
~zm
tzm
¢r(LM) ¢r(Le) ttm
tzm
D G H 1 J K L A
0 15 15 23 35 40 65 100
59.82 83.87 101.31 108.46 115.71 119.64 139.88 161.30
57.18 79.55 102.00 105.04 108.25 112.74 127.28 153.61
5.03 13.59 19.63 17.2 22.2 21.6 23.1 31.26
1.22 1.75 2.21 2.52 2.28 2.57 2.83 3.51
0.11 0.23 0.33 0.27 0.31 0.31 0.27 0.40
~
0.91 0.93 0.98 1.04 0.88 0.96 0.90 0.97
4.5 4.0 ~ N
\
3.5
\
\
50
N 2.5 ¢n
~
2.0
1.5 1.0
0"50
I
2
3
4
5
6
7
8
SILICON, WT. PCT. FIG. 8.
LB /zm
Composition variation of the eutectic melt line of a F e - C - S i alloy.
10 12 20 18 24 20 28 32
345
Spatial Dispersion of Graphite Particles in Cast Iron Conditions
of G r a p h i t e
Nucleation
The spatial dispersion of graphite in cast iron is governed by the conditions in which these particles have nucleated and by the state of the matrix when the nucleation occurred. A random dispersion is a strong indication that the graphite nucleated in the melt, in which nucleation centers and fluctuations of carbon concentration are likely to be distributed randomly. Indeed this interpretation is supported by the phase diagram corresponding to the composition of our samples. The composition variation of eutectic melt line [5] (Fig. 8) shows that a 3.6 wt.% alloy is slightly above the eutectic composition of a Fe-C-Si alloy containing 2.6 wt.% Si. However, the presence of additional elements such as manganese ( - 0.9 wt.%) modifies the phase diagram, and our samples were in fact slightly hypo-eutectic. Therefore, upon cooling, a small amount of austenite will appear in the liquid before the eutectic temperature. Figure 9 shows the relevant part of the phase diagram [4] for 2.3 wt.% Si which is close to the composition of our samples. The volume fraction of austenite present in the liquid at the eutectic temperature is given by the ratio of the lengths B C / A C ~ 2-3 vol.% austenite and 9798 vol.% liquid, and therefore, upon further cooling, the eutectic graphite nucleates in a medium almost entirely liquid.
1500
o
laoo
~
1300
~
a+y+L
\
),+L
W I'--
1200
I I I I
11oo i o FIG. 9.
//
y+ L + C-'---q /
y+C
,'
Lo z.o 30 CARBON, WT. PeT.
~'
I 3.6 4.0
Part of the Fe-C-Si phase diagram pertaining to the cast-iron specimens studied.
346
G. E. H~nein and J. E. Hilliard
Conclusion T h e spatial dispersion o f graphite particles in cast iron has b e e n f o u n d to be r a n d o m . This c o n f i r m s the fact that, in slightly h y p o - e u t e c t i c cast irons, nucleation o f flake, vermicular, and n o d u l a r graphite takes place in the melt.
We wish to thank J. M. Duffy who wrote the programs. We are grateful to the American Foundrymen Society for allowing us to use its library in Des Plaines, Illinois. This study was supported in part by Gould, Inc. Gratitude is expressed to the Northwestern University Materials Research Center for the use o f its facilities as supported by the National Science Foundation.
References 1. M. G. Kendall and P. A. P. Moran, Geometrical Probability, Hafner Publishing Co., New York (1963) p. 27. 2. J. M. Duffy and J. E. HiUiard, A Computer Microscope Partnership, Optical Spectra (October 1977)pp. 32-35. 3. E. E. Underwood, Quantitative Sterology, Addison Wesley Publishing Co. (1970) p. 82. 4. M. G. Kendall and A. Stuart, The Advanced Theory of Statistics, 3rd Ed., Vol. 2, Charles Griffin and Co., Ltd., London (1973) p. 468. 5. J. E. Hilliard and W. S. Owen, A Thermal and Microscopic Study of the Iron-CarbonSilicon System, Journal of the Iron and Steel Institute, 172, 272-275 (1952).
Received January 1978
M E ? A L L O G R A P H Y 11,337-346 (1978)
Spatial Dispersion of Graphite Particles in Cast Iron
G. E. HI~NEIN AND J. E. HILLIARD
Materials Research Center and Department o f Materials Science and Engineering, Northwestern University, Evanston, Illinois 60201
The distribution of intercept lengths in the matrix constituent has been determined for eight cast-iron specimens with graphite nodularity ranging from 0 to 100%. For all specimens the distribution f(L) of intercept lengths was found to be that corresponding to a random dispersion of graphite particles, the distribution being of the form f(L) - ( l / L ) e x p ( - L / L ) for L greater than the average intercept length in the particles. From this result it was possible to infer that nucleation of graphite had occurred in the melt.
Introduction Although graphite growth in cast iron is now well understood, the circumstances of its nucleation remain in dispute. As an aid in resolving the issue of whether nucleation occurs in the liquid or the solid, we have studied the spatial distribution of graphite particles. If nucleation occurs in a solid matrix, one would expect the graphite to be found at preferential sites (grain boundaries for instance) and the particles will therefore be clustered. On the other hand, if nucleation occurs in the melt, the spatial dispersion will be random. In this case the distribution f(L) of linear intercept lengths in the matrix between successive particles will correspond approximately to the distribution of random points on a line which is given by [1]:
f(L)
= (l/L)exp (-
L/L)
(1)
where L is the average intercept length. We have chosen this last expression as the starting point of our study for the two following reasons: In the case of randomness a plot of the logarithm of f(L) versus L is linear with a slope - 1/L as is a plot of Ln [1 - F(L)] versus L where F(L) © Elsevier North-Holland, Inc., 1 9 7 8
0026-0800/78/0011-0337501.25
G. E. Hdnein and J. E. Hilliard
338
is the cumulative distribution function, i.e.: ¢, L
F(L) = Jo f(L)dL = 1 - exp ( - L/L)
(2)
The ratio 8 of the standard deviation o-(L) to the average intercept length L is a useful measure of the degree of randomness in general; for a perfectly random distribution this ratio is unity. If the experimental value of this ratio is found much smaller than one, on the other hand, it is an indication that the particles are distributed more homogeneously (that is, the deviations of the intercept lengths from the mean are small). On the contrary, in most cases of clustering this ratio will be greater than unity.
Experimental Procedure SPECIMENS Eight cast irons were studied having visual nodularity ratings varying from 0 to 100 percent. The structures of two of the samples are shown in Figs. 1 and 2. All specimens had a pearlitic-ferritic matrix.
F~G. 1. Specimen D: gray cast iron, 100% flakes, 750x.
Spatial Dispersion of Graphite Particles in Cast Iron :" o
i''"
"
O-
_.a
"
"
•" ~
4
"~"
",.,..o
'* l b .
•
,~ ~
":i,~,
-"O
" Q
..
Q
#
.'.
"~ " ~
--"
• ,
~" .
_II
. re.
"
339 •
f4
O).
P
~ ".~'"* W
.",'.,e :.',:--',-*,
"
" ...
Fnc. 2. SpecimenK: vermicules + nodules (40~/~),300×.
The specimens were ground first on a " D i s c o p l a n " and then by hand on 24 and 17 tzm silicon carbide papers. They were then alternately polished and etched on 5 and 1 micron diamond wheels and given a short final polish on a slow wheel using 0.05 micron cerium oxide. With patience it was possible to obtain almost 100 percent graphite retention, which is an essential requirement for reliable measurements. INSTRUMENTATION The instrument used for the stereological measurements consisted of a " D i g i s c a n " optical-stage scanning microscope interfaced to a DEC PDP8/e computer [2]. The stage is driven in the X and Y directions by pulsed DC motors having a speed variation of 150: 1. The location of the stage is monitored by optical encoders with a resolution of 0.5 txm. Although the instrument is capable of automatic discrimination, the measurements were made using visual discrimination at 400× magnification in order to ensure maximum resolution and to avoid errors due to counting inclusions other than graphite. The instrument was operated as fol-
340
G. E. Hdnein and J. E. Hilliard
lows. The X and Y motions of the stage were controlled by a variablespeed joystick. When a particle boundary reached the cross-hair inscribed on the eyepiece reticule, the stage was stopped and the event signaled to the computer by pressing a key. The traverse was then continued, and a second key was pressed when the opposite boundary was reached. This operation was continued until the required number of measurements had been accumulated. The distributions of intercept lengths in the graphite particles and matrix were stored by the computer on histograms with 128 class intervals. (The width of the class intervals was automatically adjusted to accomodate the longest intercept encountered in each constituent.) Provision was made when outputting the data for regrouping into any smaller number of intervals which is a power of 2. The optimum number of intervals was determined by a balance between two factors. As the number of intervals is increased the resolution of the distribution is improved but the scatter is increased. In the present case, 16 and 32 intervals provided the best compromise.
~-~o
SPECIMEN
D
Z
~
a I-N=2000
r__,= 5z,18~
0
I
I
64
128
FIG. 3.
o
22 I
192 L(Fm)
I
I
256
320
Specimen D: 100% flakes.
,84
Spatial Dispersion of Graphite Particles in Cast Iron
341
The complete data were also stored on magnetic tape for later use and for combination with additional measurements. The program we used in this study yielded, among other statistical parameters, the average lengths traversed in the matrix constituent and the particles, respectively L~ and Lp, along with the sample standard deviations o(Lu)and ALp).
Experimental Results Plots of L n N f ( L ) a n d LnN[1 - f(L)] vs. L for three of the specimens are shown in Figs. 3, 4, and 5. It will be noted that the plots are close to being linear, indicating that Eq. (1) for a random dispersion is obeyed. However, the first point in each of the plots for LnNf(L)falls below the extrapolation of the frequencies for longer intercept lengths. We believe that this is due to a breakdown in our model at short intercept lengths.
SPECIMEN K \o
\o
X~O\o\/
"~0
-~tx
..°'°-~ ,
N ['-F(L~/50
\
7 S
o\
&
°\% o ~o,,,
Nf(L) X
Z N=2000 Ls= 112.74/~m
0
I
64
I
128
I
192
I
256
I
320
L (~m)
FIG. 4. Specimen K: 40% nodules.
384
G. E. HOnein and J. E. Hilliard
342
SPECIMEN A ~o
\o ~o~
O 10
,,
"
o~
a"~,,
°~°
ts
\
~
0
Nf
N=2000 Ls=153.61/,Lm
0
6'4
' 128 L
IcJ2
2~56
' 320
384
(/Lm)
FiG. 5. Specimen A: 100~ nodules.
As illustrated in Fig. 6 there is a geometrical factor that also contributes to the distribution of intercept lengths, and this factor becomes proportionately more important as the separation distance between particles decreases (Fig. 7). As would be expected, the intercept length LR at which the deviation occurred was approximately equal to the average intercept length Lp in the particles (Table 1). The plots for the remaining specimens were also linear, except for the first one or two points. The results for all the specimens are given in Table 1. The average intercept length in the matrix, Lu, is the one calculated from the distribution and Zu' the one determined from the slope of a linear least-squares fit to the LnN[1 - F(L)] vs. L plots. With one exception, Lu is greater than LM' which can be accounted for by the deviations from the theoretical distribution at short intercept lengths previously noted. The average intercept length in the matrix phase is related [3] to the surface area, Sv, of the
Spatial Dispersion of Graphite Particles in Cast Iron
343
FIG. 6. Effect of the geometry of the particles on the distribution of very short intercepts in the matrix.
particles per unit volume of the specimen by LM = 4(1 - Vv)/Sv
(3)
where Vv is the volume fraction of the particles. Since the latter was approximately the same for all specimens, the observed increase of LM with the percent of nodularity is to be expected since, for a given size distribution, Sv is a minimum for spherical particles. Also, as one would expect, the average intercept length in the particles increased. Values of the dispersion index 6 = (r(L)/Lu for the various samples are listed in Table 1. The values ranged from 0.88 to 1.04 with an average of 0.95 and with all samples but one exhibiting a 8 slightly less than unity. The Kolmogoroff test of goodness of fit [4] was used both for determining the number of profiles, N, to be sampled in each specimen and for setting up confidence limits for the distribution function. This test showed that the assumption of a random dispersion of the graphite particles could be accepted with great confidence.
ca,
(b)
( ~
FIG. 7. Effect of the geometry of the particles on the distribution of intercept lengths in the matrix: (a) negligible effect for long intercepts, (b) important effect for short intercepts.
G. E. Hdnein and J. E. Hilliard
344
TABLE 1 Results for Eight Specimens. (Symbols are defined in the text.) Nodularity %
LM
LM'
Lp
Spec.
/zm
~zm
tzm
¢r(LM) ¢r(Le) ttm
tzm
D G H 1 J K L A
0 15 15 23 35 40 65 100
59.82 83.87 101.31 108.46 115.71 119.64 139.88 161.30
57.18 79.55 102.00 105.04 108.25 112.74 127.28 153.61
5.03 13.59 19.63 17.2 22.2 21.6 23.1 31.26
1.22 1.75 2.21 2.52 2.28 2.57 2.83 3.51
0.11 0.23 0.33 0.27 0.31 0.31 0.27 0.40
~
0.91 0.93 0.98 1.04 0.88 0.96 0.90 0.97
4.5 4.0 ~ N
\
3.5
\
\
50
N 2.5 ¢n
~
2.0
1.5 1.0
0"50
I
2
3
4
5
6
7
8
SILICON, WT. PCT. FIG. 8.
LB /zm
Composition variation of the eutectic melt line of a F e - C - S i alloy.
10 12 20 18 24 20 28 32
345
Spatial Dispersion of Graphite Particles in Cast Iron Conditions
of G r a p h i t e
Nucleation
The spatial dispersion of graphite in cast iron is governed by the conditions in which these particles have nucleated and by the state of the matrix when the nucleation occurred. A random dispersion is a strong indication that the graphite nucleated in the melt, in which nucleation centers and fluctuations of carbon concentration are likely to be distributed randomly. Indeed this interpretation is supported by the phase diagram corresponding to the composition of our samples. The composition variation of eutectic melt line [5] (Fig. 8) shows that a 3.6 wt.% alloy is slightly above the eutectic composition of a Fe-C-Si alloy containing 2.6 wt.% Si. However, the presence of additional elements such as manganese ( - 0.9 wt.%) modifies the phase diagram, and our samples were in fact slightly hypo-eutectic. Therefore, upon cooling, a small amount of austenite will appear in the liquid before the eutectic temperature. Figure 9 shows the relevant part of the phase diagram [4] for 2.3 wt.% Si which is close to the composition of our samples. The volume fraction of austenite present in the liquid at the eutectic temperature is given by the ratio of the lengths B C / A C ~ 2-3 vol.% austenite and 9798 vol.% liquid, and therefore, upon further cooling, the eutectic graphite nucleates in a medium almost entirely liquid.
1500
o
laoo
~
1300
~
a+y+L
\
),+L
W I'--
1200
I I I I
11oo i o FIG. 9.
//
y+ L + C-'---q /
y+C
,'
Lo z.o 30 CARBON, WT. PeT.
~'
I 3.6 4.0
Part of the Fe-C-Si phase diagram pertaining to the cast-iron specimens studied.
346
G. E. H~nein and J. E. Hilliard
Conclusion T h e spatial dispersion o f graphite particles in cast iron has b e e n f o u n d to be r a n d o m . This c o n f i r m s the fact that, in slightly h y p o - e u t e c t i c cast irons, nucleation o f flake, vermicular, and n o d u l a r graphite takes place in the melt.
We wish to thank J. M. Duffy who wrote the programs. We are grateful to the American Foundrymen Society for allowing us to use its library in Des Plaines, Illinois. This study was supported in part by Gould, Inc. Gratitude is expressed to the Northwestern University Materials Research Center for the use o f its facilities as supported by the National Science Foundation.
References 1. M. G. Kendall and P. A. P. Moran, Geometrical Probability, Hafner Publishing Co., New York (1963) p. 27. 2. J. M. Duffy and J. E. HiUiard, A Computer Microscope Partnership, Optical Spectra (October 1977)pp. 32-35. 3. E. E. Underwood, Quantitative Sterology, Addison Wesley Publishing Co. (1970) p. 82. 4. M. G. Kendall and A. Stuart, The Advanced Theory of Statistics, 3rd Ed., Vol. 2, Charles Griffin and Co., Ltd., London (1973) p. 468. 5. J. E. Hilliard and W. S. Owen, A Thermal and Microscopic Study of the Iron-CarbonSilicon System, Journal of the Iron and Steel Institute, 172, 272-275 (1952).
Received January 1978