How to read Fe-Fe3C diagram ??
More specifically, what happens during the solidification for different compositions ? Or why there are different phase fields in different regions of the diagram ? Why do we get mixtures of different phases ?
Insort, this post is all about the technical stuff just so one can understand what the hack does the diagram show !?
There are millions of iron-carbide diagrams having slight variations based on the parameters, but still there is not a universal standard. So here we will consider the diagram shown in 'Journal of phase equilibria, vol-13-1992 by ASM' as standard.
Solid lines represents the Fe-C diagram & dotted lines represents slight variations in Fe-Fe3C diagram from Fe-C diagram.
Melting point of pure-Fe = 1538 °C
Melting point of Fe3C = 1252 °C
There are 3 invariant reactions take place in the Fe-Fe3C phase equilibrium diagram,
1) Peritectic reaction | at 1493 °C | 0.16 %C
2) Eutectic reaction | at 1147 °C | 4.3 %C
3) Eutectoid reaction | at 727 °C | 0.76 %C
1) Peritectic reaction
here,
point P is called peritectic point,
line MPB is called invariant line
\[\underset{(of\,0.53\,\%C)}{Liquid}\,\,+\,\,\underset{(of\,0.09\,\%C)}{\delta-Ferrite}\,\,\xrightarrow[cooling]{1493\,^{\circ}C}\,\,\underset{(of\,0.16\,\%C)}{\gamma-Austenite}\]
According to the reaction, at 1493 °C and 0.16 %C, mixture of liquid and δ-Ferrite ( i.e. L+δ ) completely transforms into γ-Austenite. There is no surplus δ-Ferrite or liquid.
That's why steel having 0.16 %C is known as peritectic steel.
During cooling of liquid, first δ-Ferrite nucleates and that grows with cooling, upto peritectic temperature ( i.e. 1493 °C ). So at that temperature before completely transforming into γ-Austenite, there exists fixed amounts of liquid and δ-Ferrite.
We can calculate the amount of L and δ in peritectic mixture just before 1493 °C by help of the lever-rule. We can see the tie-line MPB ties two phases, L & δ, and point P acts as a fulcrum.
\[\underset{(of\,0.53\,\%C)}{Liquid\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.16\,-\,0.09}{0.53\,-\,0.09}\,\,\times\,\,100\,\,\,\,\,=\,\,\,15.90\%\]\[\underset{(of\,0.09\,\%C)}{\delta-Ferrite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.53\,-\,0.16}{0.53\,-\,0.09}\,\,\times\,\,100\,\,\,\,\,=\,\,\,84.10\%\]
That's why steel having 0.16 %C is known as peritectic steel.
During cooling of liquid, first δ-Ferrite nucleates and that grows with cooling, upto peritectic temperature ( i.e. 1493 °C ). So at that temperature before completely transforming into γ-Austenite, there exists fixed amounts of liquid and δ-Ferrite.
We can calculate the amount of L and δ in peritectic mixture just before 1493 °C by help of the lever-rule. We can see the tie-line MPB ties two phases, L & δ, and point P acts as a fulcrum.
\[\underset{(of\,0.53\,\%C)}{Liquid\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.16\,-\,0.09}{0.53\,-\,0.09}\,\,\times\,\,100\,\,\,\,\,=\,\,\,15.90\%\]\[\underset{(of\,0.09\,\%C)}{\delta-Ferrite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.53\,-\,0.16}{0.53\,-\,0.09}\,\,\times\,\,100\,\,\,\,\,=\,\,\,84.10\%\]
∴ %L = 15.90% & %δ-Ferrite = 84.10%
Insort, the this alloy at peritectic temperature, 1493 °C undergoes the peritectic transformation completely, i.e. 84.10% of δ-Ferrite reacts with 15.90% of liquid and gives 100% solid γ-Austenite.
∴ for peritectic reation, ratio of δ-Ferrite and L = 5.29 : 1
Insort, the this alloy at peritectic temperature, 1493 °C undergoes the peritectic transformation completely, i.e. 84.10% of δ-Ferrite reacts with 15.90% of liquid and gives 100% solid γ-Austenite.
∴ for peritectic reation, ratio of δ-Ferrite and L = 5.29 : 1
Steel having carbon between 0.09% and 0.16% are called hypo-peritectic steels & steels having carbon between 0.16% and 0.53% are called hyper-peritectic steels.
- Hypo means less than,
- Hyper means greater than
-> Hypo-peritectic steels have more amount of δ-Ferrite than required for the peritectic reaction, and thus, extra unreacted δ-Ferrite along with peritectically formed austenite are present after the peritectic reaction is completed.
Let say, for steel of carbon 0.14%, there exist the region of δ + Austenite after the peritectic reaction. That δ is the extra unreacted δ-Ferrite which we discussed just before.
we can prove this in two ways,
1) Indirect way
let's consider lever MOB having O as fulcrum,
that's why by applying lever-rule we get that,
\[\underset{(of\,0.53\,\%C)}{Liquid\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.14\,-\,0.09}{0.53\,-\,0.09}\,\,\times\,\,100\,\,\,\,\,=\,\,\,11.36\%\]\[\underset{(of\,0.09\,\%C)}{\delta-Ferrite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.53\,-\,0.14}{0.53\,-\,0.09}\,\,\times\,\,100\,\,\,\,\,=\,\,\,88.64\%\]
but we know that for 1 part of liquid 5.29 parts of δ-Ferrite is required for preritectic reation.
∴ required δ-Ferrite = %L * 5.29
∴ = 11.36% * 5.29
∴ = 60.09%
but we have 88.64% of δ-Ferrite,
that's why 88.64% - 60.09% = 28.59% δ-Ferrite is extra unreacted one.
2) Direct way
let's consider lever MOP having O as fulcrum,
that's why by applying lever-rule we get that,
\[\underset{(of\,0.09\,\%C)}{\delta-Ferrite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.16\,-\,0.14}{0.16\,-\,0.09}\,\,\times\,\,100\,\,\,\,\,=\,\,\,28.59\%\]
thus we can conclude that, for 0.14 %C just after peritectic reaction, 28.59% of δ-Ferrite remains unreacted and does not transform into γ-Austenite.
-> Hyper-peritectic steels have more amount of liuid than required for the peritectic reaction, and thus, extra unreacted liquid along with peritectically formed austenite are present after the peritectic reaction is completed.
Steels having carbon lower than 0.09% and more than 0.53% do not undergo peritectic reaction.
2) Eutectic reaction
here,
point C is called eutectic point,
line QCR is called invariant line.
\[\underset{(of\,4.3\,\%C)}{Liquid}\,\,\xrightarrow[cooling]{1147\,^{\circ}C}\,\,\underset{(of\,2.11\,\%C)}{\gamma-Austenite}+\,\,\underset{(of\,6.67\,\%C)}{Fe_{3}C}\,\,\]
Mixture of austenite and cementite is called ledeburite.
According to the reaction, at 1147 °C and 4.3 %C, liquid completely transforms into γ-Austenite and cementite. There is no surplus liquid.
Generally alloy of iron and carbon having more than 2.11 %C is called cast-iron.
That's why here alloy having 4.3 %C is known as eutectic cast-iron.
During cooling of liquid, after 1147 °C, liquid is completely transformed into mixture of γ-Austenite and cementite . So at that temperature after completely transforming into γ-Austenite and cementite, the amount of both components in the solid mixture is definite.
We can calculate amount of Austenite and Cementite in eutectic alloy just after the eutectic reaction i.e. below 1147 °C, by the help of lever-rule.
Consider a tie-line QCR which ties two phases, Austenite and Cementite, and point C acts as fulcrum.
\[\underset{(of\,2.11\,\%C)}{\gamma-Austenite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{6.67\,-\,4.3}{6.67\,-\,2.11}\,\,\times\,\,100\,\,\,\,\,=\,\,\,51.97\%\]\[\underset{(of\,6.67\,\%C)}{Cementite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{4.3\,-\,2.11}{6.67\,-\,2.11}\,\,\times\,\,100\,\,\,\,\,=\,\,\,48.03\%\]
Fe-C alloys having carbon between 2.11% and 4.3% are called hypo-eutectic cast-irons and the alloys having carbon between 4.3% to 6.67% is called hyper-eutectic cast-irons.
-> A hypo-eutectic cast-iron, say, having carbon 3.3%, starts solidifying on cooling from molten state, at point H and the first solid to nucleate is Austenite. As cooling proceeds, more austenite called proeutectic austenite, solidifies. Proeutectic austenite is the austenite formed from liquid alloy before the eutectic reaction takes place of the remaining liquid in alloy.
Composition of proeutectic austenite changes with cooling along the austenite line upto point Q. At 1147 °C, the composition of austenite is 2.11 %C and the liquid have 4.3 %C. Lever-rule is use to calculate the amount of both phases.
\[\underset{(of\,2.11\,\%C)}{Proeutectic\,austenite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{4.3\,-\,3.3}{4.3\,-\,2.11}\,\,\times\,\,100\,\,\,\,\,=\,\,\,45.66\%\]\[\underset{(of\,4.3\,\%C)}{Liquid\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{3.3\,-\,2.11}{4.3\,-\,2.11}\,\,\times\,\,100\,\,\,\,\,=\,\,\,54.34\%\]
Thus, only liquid ( i.e. 54.34% of the mixture ) will transform into ledeburite, proeutectic austenite will remain unreacted.
That's why in the hypo-eutectic cast-iron, below eutectic line we get mixture of extra unreacted austenite and ledeburite.
-> A hyper-eutectic cast-iron, say, having carbon 5.0%, cementite starts nucleating on cooling from molten state, at point M. As cooling proceeds, more cementite called primary cementite, solidifies from liquid. Primary cementite is the cementite formed from liquid alloy before the eutectic reaction takes place of the remaining liquid in alloy.
At 1147 °C, the composition of primary cementite is 2.11 %C and the liquid have 4.3 %C. Lever-rule is use to calculate the amount of both phases.
\[\underset{(of\,6.67\,\%C)}{Primary\,cementite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{5.0\,-\,4.3}{6.67\,-\,4.3}\,\,\times\,\,100\,\,\,\,\,=\,\,\,29.53\%\]\[\underset{(of\,4.3\,\%C)}{Liquid\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{6.67\,-\,5.0}{6.67\,-\,4.3}\,\,\times\,\,100\,\,\,\,\,=\,\,\,70.47\%\]
Thus, only liquid ( i.e. 70.47% of the mixture ) will transform into ledeburite, primary cementite will remain unreacted.
That's why in the hyper-eutectic cast-iron, below eutectic line we get mixture of extra unreacted cementite and ledeburite.
3) Eutectoid Reaction
here,
\[\underset{(of\,0.77\,\%C)}{Austenite}\,\,\xrightarrow[cooling]{727\,^{\circ}C}\,\,\underset{(of\,0.022\,\%C)}{\alpha-Ferrite}+\,\,\underset{(of\,6.67\,\%C)}{Fe_{3}C}\,\,\]
Mixture of austenite and cementite is called pearlite.
According to the reaction, at 727 °C and 0.77 %C, austenite completely transforms into α-Ferrite and cementite. There is no surplus austenite.
Generally alloy of iron and carbon having less than 2.11 %C is called steels.
That's why here alloy having 0.77 %C is known as eutectoid steel.
During cooling of austenite, after 727 °C, it is completely transformed into mixture of α-Ferrite and cementite . So at that temperature after completely transforming into α-Ferrite and cementite, the amount of both components in the solid mixture is definite.
\[\underset{(of\,4.3\,\%C)}{Liquid}\,\,\xrightarrow[cooling]{1147\,^{\circ}C}\,\,\underset{(of\,2.11\,\%C)}{\gamma-Austenite}+\,\,\underset{(of\,6.67\,\%C)}{Fe_{3}C}\,\,\]
Mixture of austenite and cementite is called ledeburite.
According to the reaction, at 1147 °C and 4.3 %C, liquid completely transforms into γ-Austenite and cementite. There is no surplus liquid.
Generally alloy of iron and carbon having more than 2.11 %C is called cast-iron.
That's why here alloy having 4.3 %C is known as eutectic cast-iron.
During cooling of liquid, after 1147 °C, liquid is completely transformed into mixture of γ-Austenite and cementite . So at that temperature after completely transforming into γ-Austenite and cementite, the amount of both components in the solid mixture is definite.
We can calculate amount of Austenite and Cementite in eutectic alloy just after the eutectic reaction i.e. below 1147 °C, by the help of lever-rule.
Consider a tie-line QCR which ties two phases, Austenite and Cementite, and point C acts as fulcrum.
\[\underset{(of\,2.11\,\%C)}{\gamma-Austenite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{6.67\,-\,4.3}{6.67\,-\,2.11}\,\,\times\,\,100\,\,\,\,\,=\,\,\,51.97\%\]\[\underset{(of\,6.67\,\%C)}{Cementite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{4.3\,-\,2.11}{6.67\,-\,2.11}\,\,\times\,\,100\,\,\,\,\,=\,\,\,48.03\%\]
Fe-C alloys having carbon between 2.11% and 4.3% are called hypo-eutectic cast-irons and the alloys having carbon between 4.3% to 6.67% is called hyper-eutectic cast-irons.
-> A hypo-eutectic cast-iron, say, having carbon 3.3%, starts solidifying on cooling from molten state, at point H and the first solid to nucleate is Austenite. As cooling proceeds, more austenite called proeutectic austenite, solidifies. Proeutectic austenite is the austenite formed from liquid alloy before the eutectic reaction takes place of the remaining liquid in alloy.
Composition of proeutectic austenite changes with cooling along the austenite line upto point Q. At 1147 °C, the composition of austenite is 2.11 %C and the liquid have 4.3 %C. Lever-rule is use to calculate the amount of both phases.
\[\underset{(of\,2.11\,\%C)}{Proeutectic\,austenite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{4.3\,-\,3.3}{4.3\,-\,2.11}\,\,\times\,\,100\,\,\,\,\,=\,\,\,45.66\%\]\[\underset{(of\,4.3\,\%C)}{Liquid\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{3.3\,-\,2.11}{4.3\,-\,2.11}\,\,\times\,\,100\,\,\,\,\,=\,\,\,54.34\%\]
Thus, only liquid ( i.e. 54.34% of the mixture ) will transform into ledeburite, proeutectic austenite will remain unreacted.
That's why in the hypo-eutectic cast-iron, below eutectic line we get mixture of extra unreacted austenite and ledeburite.
-> A hyper-eutectic cast-iron, say, having carbon 5.0%, cementite starts nucleating on cooling from molten state, at point M. As cooling proceeds, more cementite called primary cementite, solidifies from liquid. Primary cementite is the cementite formed from liquid alloy before the eutectic reaction takes place of the remaining liquid in alloy.
At 1147 °C, the composition of primary cementite is 2.11 %C and the liquid have 4.3 %C. Lever-rule is use to calculate the amount of both phases.
\[\underset{(of\,6.67\,\%C)}{Primary\,cementite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{5.0\,-\,4.3}{6.67\,-\,4.3}\,\,\times\,\,100\,\,\,\,\,=\,\,\,29.53\%\]\[\underset{(of\,4.3\,\%C)}{Liquid\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{6.67\,-\,5.0}{6.67\,-\,4.3}\,\,\times\,\,100\,\,\,\,\,=\,\,\,70.47\%\]
Thus, only liquid ( i.e. 70.47% of the mixture ) will transform into ledeburite, primary cementite will remain unreacted.
That's why in the hyper-eutectic cast-iron, below eutectic line we get mixture of extra unreacted cementite and ledeburite.
3) Eutectoid Reaction
here,
point Y is called eutectoid point,
line EYP is called invariant line
\[\underset{(of\,0.77\,\%C)}{Austenite}\,\,\xrightarrow[cooling]{727\,^{\circ}C}\,\,\underset{(of\,0.022\,\%C)}{\alpha-Ferrite}+\,\,\underset{(of\,6.67\,\%C)}{Fe_{3}C}\,\,\]
Mixture of austenite and cementite is called pearlite.
According to the reaction, at 727 °C and 0.77 %C, austenite completely transforms into α-Ferrite and cementite. There is no surplus austenite.
Generally alloy of iron and carbon having less than 2.11 %C is called steels.
That's why here alloy having 0.77 %C is known as eutectoid steel.
During cooling of austenite, after 727 °C, it is completely transformed into mixture of α-Ferrite and cementite . So at that temperature after completely transforming into α-Ferrite and cementite, the amount of both components in the solid mixture is definite.
We can calculate amount of Ferrite and Cementite in eutectoid alloy just after the eutectoid reaction i.e. below 727 °C, by the help of lever-rule.
Consider a tie-line EYP which ties two phases, Ferrite and Cementite, and point Y acts as fulcrum.
\[\underset{(of\,0.022\,\%C)}{\alpha-Ferrite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{6.67\,-\,0.77}{6.67\,-\,0.022}\,\,\times\,\,100\,\,\,\,\,=\,\,\,89\%\]\[\underset{(of\,6.67\,\%C)}{Cementite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.77\,-\,0.022}{6.67\,-\,0.022}\,\,\times\,\,100\,\,\,\,\,=\,\,\,11\%\]
Fe-C alloys having carbon between 0.022% and 0.77% are called hypo-eutectic cast-irons and the alloys having carbon between 0.77% to 2.11% is called hyper-eutectic cast-irons.
-> A hypo-eutectoid steel, say, having carbon 0.4%, austenite transforms into solid mixture of α-Ferrite and cementite. Proeutectoid ferrite is the ferrite formed from austenite before the eutectoid reaction takes place of the remaining austenite in alloy.
Composition of proeutectoid ferrite changes with cooling along the ferrite line upto point E. At 727 °C, the composition of ferrite is 0.022 %C and the austenit have 0.77 %C. Lever-rule is use to calculate the amount of both phases.
\[\underset{(of\,0.022\,\%C)}{\alpha-ferrite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.77\,-\,0.4}{0.77\,-\,0.022}\,\,\times\,\,100\,\,\,\,\,=\,\,\,49.33\%\]\[\underset{(of\,0.77\,\%C)}{Austenite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.4\,-\,0.022}{0.4\,-\,0.022}\,\,\times\,\,100\,\,\,\,\,=\,\,\,50.67\%\]
Thus, only austenite ( i.e. 50.67% of the mixture ) will transform into pearlite, proeutectoid ferrite will remain unreacted.
That's why in the hypo-eutectoid steels, below eutectoid line we get mixture of extra unreacted ferrite and pearlite.
-> A hyper-eutectoid steel, say, having carbon 1.2% austenite transforms into solid mixture of austenite and cementite. Transformed ledeburite is the pearlite formed from secondary ledeburite after the eutectoid reaction takes place of the remaining ledeburite in alloy.
At 727 °C, the composition of Proeutectoid cementite is 6.67 %C and the Austenite have 0.77 %C. Lever-rule is use to calculate the amount of both phases.
\[\underset{(of\,0.77\,\%C)}{Austenite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{6.67\,-\,1.2}{6.67\,-\,0.77}\,\,\times\,\,100\,\,\,\,\,=\,\,\,92.71\%\]\[\underset{(of\,6.67\,\%C)}{Proeutectoid\,cementite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{1.2\,-\,0.77}{6.67\,-\,0.77}\,\,\times\,\,100\,\,\,\,\,=\,\,\,7.29\%\]
Thus, only asutenite ( i.e. 92.71% of the mixture ) will transform into pearlite, secondary cementite will remain unreacted.
That's why in the hyper-eutectoid steel, below eutectoid line we get mixture of extra unreacted cementite and ledeburite.
Consider a tie-line EYP which ties two phases, Ferrite and Cementite, and point Y acts as fulcrum.
\[\underset{(of\,0.022\,\%C)}{\alpha-Ferrite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{6.67\,-\,0.77}{6.67\,-\,0.022}\,\,\times\,\,100\,\,\,\,\,=\,\,\,89\%\]\[\underset{(of\,6.67\,\%C)}{Cementite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.77\,-\,0.022}{6.67\,-\,0.022}\,\,\times\,\,100\,\,\,\,\,=\,\,\,11\%\]
Fe-C alloys having carbon between 0.022% and 0.77% are called hypo-eutectic cast-irons and the alloys having carbon between 0.77% to 2.11% is called hyper-eutectic cast-irons.
-> A hypo-eutectoid steel, say, having carbon 0.4%, austenite transforms into solid mixture of α-Ferrite and cementite. Proeutectoid ferrite is the ferrite formed from austenite before the eutectoid reaction takes place of the remaining austenite in alloy.
Composition of proeutectoid ferrite changes with cooling along the ferrite line upto point E. At 727 °C, the composition of ferrite is 0.022 %C and the austenit have 0.77 %C. Lever-rule is use to calculate the amount of both phases.
\[\underset{(of\,0.022\,\%C)}{\alpha-ferrite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.77\,-\,0.4}{0.77\,-\,0.022}\,\,\times\,\,100\,\,\,\,\,=\,\,\,49.33\%\]\[\underset{(of\,0.77\,\%C)}{Austenite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{0.4\,-\,0.022}{0.4\,-\,0.022}\,\,\times\,\,100\,\,\,\,\,=\,\,\,50.67\%\]
Thus, only austenite ( i.e. 50.67% of the mixture ) will transform into pearlite, proeutectoid ferrite will remain unreacted.
That's why in the hypo-eutectoid steels, below eutectoid line we get mixture of extra unreacted ferrite and pearlite.
At 727 °C, the composition of Proeutectoid cementite is 6.67 %C and the Austenite have 0.77 %C. Lever-rule is use to calculate the amount of both phases.
\[\underset{(of\,0.77\,\%C)}{Austenite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{6.67\,-\,1.2}{6.67\,-\,0.77}\,\,\times\,\,100\,\,\,\,\,=\,\,\,92.71\%\]\[\underset{(of\,6.67\,\%C)}{Proeutectoid\,cementite\,\,wt\%}\,\,\,\,\,=\,\,\,\frac{1.2\,-\,0.77}{6.67\,-\,0.77}\,\,\times\,\,100\,\,\,\,\,=\,\,\,7.29\%\]
Thus, only asutenite ( i.e. 92.71% of the mixture ) will transform into pearlite, secondary cementite will remain unreacted.
That's why in the hyper-eutectoid steel, below eutectoid line we get mixture of extra unreacted cementite and ledeburite.