Materials science

2 - laboratory work
OF IRON- CARBON ( CEMENTITE ) STATE DIAGRAM .
The purpose of the work: to acquaint students with the main lines, points and areas present in the status diagram of the iron-cementite system. Learning to analyze the changes that occur in the structure of alloys with different amounts of carbon when heated and cooled using the rule of phases and sections.
Theoretical information
Using the iron-cementite diagram (Figure 6.1), it is possible to understand the changes that occur when heating and cooling iron-carbon alloys (steels and cast irons).
Depending on the temperature and the amount of carbon in the iron, iron-carbon alloys can be composed of the following structures (Table 6.1): ferrite (F), austenite (A), cementite (S), pearlite (P), ledeburite (L)
In this laboratory work, the ferro-cementite diagram is studied in a simplified version (ignoring the upper left part). Tables 6.2 and 6.3 show the phase changes that occur at the main lines and points in the diagram.
Gibbs' phase rule is used to analyze the iron-cementite diagram.

A mathematical expression that shows the relationship between the number of phases (F), the number of components (K), and the number of degrees of freedom (S) of any system at equilibrium.

S = K – F + 1

called the law of phases or Gibbs' law .

At temperatures above the liquidus line (ACD) (Fig. 7.1), since all alloys are in a liquid state, the number of degrees of freedom of the system is two:
S = K – F + 1 = 2 – 1 + 1 = 2
that is, it is possible to heat and cool the alloy within certain temperature ranges without changing the single-phase structure, and to change the amount of its components. In the areas between AS and AES, as well as CD and SF lines, the system is two-phase (liquid alloy and solid alloy). Its number of degrees of freedom is equal to one (S=2–2+1=1), which means that only one of its parameters (temperature or concentration) can be changed to keep the two-phase system unchanged.
In the area between the NJE and GSE lines, the system is single-phase and has two degrees of freedom.
In all other regions of the ferro-cementite state diagram, the alloy is two-phase, with the number of degrees of freedom equal to one. At temperatures corresponding to YeSF and PSK lines (1147 ⁰ С and 727 ⁰ С), the alloy is three-phase, and its number of degrees of freedom is zero.
The rule of sections is used to determine the state of the alloys included in the studied system at a certain temperature, the amount of phases in percent and per mass unit (Fig. 6.2, a).
For example, let the iron-carbon alloy whose chemical composition is determined by point K _{1 (0.4% carbon)} be heated to point b (750 ^{0 C). At point} b , the alloy consists of two solid phases (ferrite and austenite). It is required to find the amount of these phases.
To solve this problem , we draw a horizontal line from point b and continue until it intersects with lines GR and GS . The projection of points a and c on the concentration axis determines the amount of carbon in ferrite and austenite, respectively.
To find the quantitative ratio of austenite and ferrite, the following ratio of sections ab and bs is drawn:
Q _f /Q _aus = bs/ab
here, Q _f is the amount of ferrite, Q _aus is the amount of austenite (at a temperature of 750 ⁰ C). If the mass of the studied alloy is equal to 100 grams, then
Q _f /(100- Q _f ) = bs/ab
Subtracting the amount of sections (bs) and (ab) from the diagram, we can first determine the amount of ferrite, and then austenite.
Cooling curves of alloys can be drawn using the state diagram (Fig. 6.2, b). For this, vertical lines are drawn for each alloy (K ₁ , K ₂ , K ₃ , K ₄ ) and their points of intersection with the main lines of the diagram (1, 2, 3, 4, 5, 6, 7, 8) are determined . These points are moved on the temperature-time axis and the cooling curve of a particular alloy is drawn.

Figure 6.1 . Iron - carbon ( cementite ) system of alloys condition diagram