**Theory**

**An alloy** is a substance obtained by fusing several chemical elements (in our case, two).

The chemical elements that make up an alloy are called its **components** . In general, we will denote them as A and B.

For the same components, many alloys that differ only in the concentration of components make up **the alloy system** , which is commonly referred to as the list of components. For example, alloys of the A – B system are a set of alloys from components A and B, differing in the content of A and B. Since the total concentration of components in binary alloys is 100%:

%A + %B= 100%,

then any particular alloy of the A – B system is usually indicated by the content of component B in it (for example: an alloy containing 10% B).

Inside the alloy, its components are generally unevenly distributed (an alloy is not just a mixture of components), they are located inside various **structural and phase components.** The properties of an alloy are completely determined by its internal components (phase composition, structure), which can be determined by analyzing the state diagram.

**The state diagram of** alloys of the A – B system is a graphical representation of the possible phase and structural states of any alloys of the A – B system at any temperature. State diagrams are displayed in coordinates: temperature – chemical. alloy composition. In our case, chem. the composition of any alloy is uniquely specified by indicating the content of component B in it. Thus, the coordinates of the state diagram are: temperature of the alloy – content of component B in it.

The form of the state diagram is completely determined by the nature of the physicochemical interaction of its components with each other. In the future, we will consider only those alloys that can be completely melted. Then we can assume that at sufficiently high temperatures, any alloys are a homogeneous liquid solution of components, which in all diagrams will be denoted by L (liquid).

In the solid state, the components within an alloy can generally interact as follows:

1) chemically react with each other to form a new substance – a **chemical compound** A _{m} B _{n} :

A + B u003d A _{m} B _{n} ;

2) dissolve in the crystal lattice of each other completely or partially, while **solid solutions** are formed (for example, a solid solution of A in B);

3) form a fusible mechanical mixture, which is called a **eutectic.**

The most important elements of the internal structure of any alloys are its phase components (or, in short, phases).

**A phase** is a homogeneous (sometimes very small in size) part of an alloy, separated from other parts by an interface, at the transition of which a jump in the physical and mechanical properties of the substance is observed.

In accordance with this definition, in the general case, phases in alloys can be:

1) components A, B;

2) liquid solution of components – liquid L;

3) solid solutions of components in each other – a, β.

4) chemical compounds A _{m} B _{n} .

It should be noted that the mechanical mixture is not homogeneous, therefore, **the eutectic is not a phase** ! (This is a mixture of several phases).

Each phase, the existence of which is possible in the alloys of the A-B system, corresponds to a single- **phase region** on the state diagram of this system, that is, the region of temperatures and compositions at which the phase is able to exist with its inherent physical properties.

When analyzing a state diagram, it is first necessary to determine the type of interaction of components in the alloys of a given system using the characteristic lines of the diagram, then to identify single-phase regions in the diagram. After that, using the rule of segments (see below), determine the phase composition of the alloys in the remaining (two-phase) regions of the state diagram and, finally, by constructing cooling curves for specific alloys of the system, determine the possible structures of the alloys in the cooled state.

**Segment rule**

The segment rule is used to determine:

1) the phase composition of the alloy at a given point in the state diagram;

2) the chemical composition of the phases present in the alloy;

3)weight fraction of each phase

To this end, first, from a given point on the state diagram, it is necessary to draw a horizontal segment to the left and right until it intersects with the boundaries of the nearest single-phase regions, and then on this segment it is necessary to determine all points of its contact (i.e., intersection and touch) with single-phase regions ( Fig. 1).

^{}0 s ^{‘} l ^{‘} 100

Rice. 1. Application of the rule of segments in the analysis of state diagrams.

Examples:

1. Point *a* is given, a segment is drawn *bac* , points *b* and *c* are determined.

2. Point *d* is given, segment *fde* is drawn, points *f* and *e* are marked.

3. Point *q* is given, segment *hiqk* is drawn, points *h, i, k* are marked.

In the future, according to certain (marked) points of intersection and contact with single-phase regions, it is possible for a given starting point to determine the phase composition of the alloy, the chemical composition of the phases in the alloy, and the weight fraction of each phase.

1) The phase composition of the alloy is determined by the belonging of each marked point to a single-phase region

In example 1: i.e. *b* indicates phase A, i.e. *c* – phase L, i.e. at a given point a, the alloy has a phase composition of A+L.

In example 2: in a given point *d* , the phase composition of the alloy: A + B.

In example 3: given t. *q* , the phase composition of the alloy: A+B+L.

2) The chemical composition of the phases is determined by the projections of the marked points onto the concentration axis.

In example 1: in phase A (t. *b* contains 0% B, in phase L (t *. c* ) – c’% B.

In example 2: in phase A (t. *O* – 0% B, in phase B (i.e. *)* – 100% B.

In example 3: in A (t. *h* ) – 0% B, in L (t. *i* ) – ‘% B, in B (t. *to* ) – 100% B.

3) The weight fraction of the phase is determined according to the lever rule, as the ratio of the part of the segment opposite to the phase to its entire length

In example 1: Q _{A} = Q _{L} =

In example 2: Q _{A} = 100% _{QB} = 100%.

Note: if there are more than two phases in the alloy, the rule of leverage should not be applied.

In addition to determining the phase composition of the alloy, the segmentation rule can also be used to determine the structural composition. In this case, the horizontal segment must be drawn up to the intersection with the boundaries of the regions of structural components. For example, if point *l* is given (Fig. 2), then we draw a segment *nlm* , and the marked points *n* and *m* indicate that at a given point *l* the alloy has the structure: eut (A + B) + crystals B; the eutectic contains *n ^{‘}* % B (projection t.

*n*); in crystals B-100% B (projection

*m*);

100% B (projection t. *t* ); weight fraction of eutectic in a structural alloy

Q _{eut} =

The proportion of B crystals in the alloy structure

Q _{B} _{= 100%}

**Phase** rule (Gibbs rule)

In this work, this rule is mainly used to control the behavior of the cooling curves of alloys. The rule looks like:

C u003d K-F + 1,

where K is the number of components in the alloy;

Ф is the number of phases in the considered state of the alloy;

C – the number of degrees of freedom of the alloy, in our simplest case of analysis – this is the number of opportunities for the alloy to reduce its temperature when removing heat from it.

If C>0 (i.e. C = 1 or 2), then the temperature of the alloy will decrease monotonically as heat is removed from the alloy. If at some point there is a change from C = 1 to C = 2 or vice versa, then the rate of decrease in the temperature of the alloy changes, i.e. there will be breaks in the cooling curve at these points.

If C = 0, then despite the removal of heat from the alloy, its temperature will remain constant until some process inside the alloy is completed, due to which the number of phases in it will decrease and C>0 will turn out. On the cooling curve of the alloy, this process will correspond to a horizontal section.

**Construction of cooling curves for alloys**

Consider, as an example, the construction of a cooling curve for an alloy of the eutectic type (Fig. 2).

Fig. 2. An example of constructing a cooling curve

On the vertical section I of the state diagram passing through the point a, we arbitrarily choose the starting point in the region L and then sequentially number the critical points of the alloy, i.e. points 1, 2 of the intersection of section I with the lines of the diagram. We draw the coordinate axes: temperature T – time t, in which the cooling curve will be built; we project temperature levels at critical points on them.

The initial section of the cooling curve (above point 1). For any point of this section, the phase composition of the alloy is: L, since this section is located in the single-phase region of the diagram. Consequently, the number of phases in the alloy is Ф = 1, and according to the phase rule, the number of degrees of freedom of the alloy is C = 2. Therefore, when heat is removed, the temperature of the alloy decreases monotonically and this section of the cooling curve is depicted as a smooth falling line: near this section on the cooling curve, we indicate the phase composition and number of degrees of freedom of the alloy: L, C = 2.

Plot 1-2. For any point *b* in this section, according to the rule of segments, we set the phase composition of the alloy: L (i. *e* ) + A (t. *d* ), therefore, Ф u003d 2 and according to the phase rule C u003d 1. This means that this section of the cooling curve, as and the previous one, will be displayed as a smooth line, near which you should indicate: L + A, C = 1. At point 1 of the cooling curve there will be a break, because here the number of degrees of freedom of the alloy changes from C = 2 to C = 1.

Moving point *b* from point *1* to point *2* and determining the weight fraction of solid crystals A

(Q _{A} = 100%) and the chemical composition of the liquid in the alloy ^{(} e % B), it can be easily established that in this section of the cooling curve, starting from point 1, solid crystals A are released from the liquid, and the content of component B in the remaining liquid in the alloy gradually increases from a % B in point *1* to the value *c’* % B for point *2* , i.e. crystals of a component that is excessive in relation to the eutectic composition stand out from the liquid. At the end of section 1-2, the alloy will consist of crystals A and the remaining eutectic liquid.

Plot 2-2 ^{‘} . At point 2 on the state diagram, according to the rule of segments, it is easy to establish that three phases are in equilibrium in the alloy: A (point F), Tst. C) and B (t. G), with L=L _{3} _{BT} (C ^{/ 0} / o B). Thus, according to the phase rule, Ф=3 and С=0. Consequently, at the temperature of the critical point 2 on the cooling curve there will be a horizontal section 2 -2 ^{‘} with a constant temperature of the alloy. The nature of the process occurring inside the alloy in this area will be clarified as follows. As can be seen from the state diagram, below point 2 (that is, below the temperature level of the FCG line), the existence of a liquid phase L in the alloy is impossible. Therefore, it is clear that in the section 2 -2 ^{‘} , on the one hand, the phase L _{3} _{BT} should “disappear” , on the other hand, since C = 1 should be at the end of the process (so that the alloy can further reduce its temperature), this phase should turn into a mixture of the other two:

L _{eut} > eut (A + B),

that is, in the section 2-2 ^{/} , a eutectic transformation takes place in the alloy.

End section of the cooling curve (after point 2 ^{/} ). After the end of the eutectic transformation, two phases remain in the alloy: A and B, which is easily verified by the rule of segments for any point of the diagram in section 2-a. Thus, F = 2 and C = 1, so that the alloy monotonically reduces its temperature to room temperature.

In this section, it is necessary to indicate the final structure of the alloy. In this simple case, this can be done according to the rule of segments (for structural components) in section 2-a of the diagram.

In a more general case, the final structure is established by the totality of solid crystals that precipitated in different parts of the cooling curve, and were not subjected to internal change after that. In our case, the structure of the alloy is formed by crystals A, precipitated in section 1 – 2, and eutectic crystals, formed in section 2 -2 ^{‘} : A + eut (A + B).

## Be First to Comment