3. Three-component systems

A. Definition of ways of crystallization in state diagrams of three-component systems

Equilibrium phase composition of three-component systems depending on temperature and concentrations in space diagrams.

As foundation of this diagram equilateral concentration triangle is chosen more often, in which concentrations of components are described in the same scale. The compositions f points of pure components are located on the vertexes of the triangle, concentrations of dual compositions – on corresponding side of the triangle, triple compositions – inside the triangle. All points inside the triangle describe any correlations of three components. The sides of the triangle are divided into 100 parts to count any concentrations of mixtures.

The temperatures of full melting of mixtures are shown by the points of vertexes of perpendicular, erected in the certain scale to the concentration triangle in corresponding compositions of mixtures. The space diagram is limited by three flat two-component diagrams from sides, and from the vertex – space liquation, above of which only one-phase space of liquid is located.

Taking into account difficulties of employment of similar space diagrams projection diagrams are usually used instead of them. The last ones get projection with the help of perpendiculars on the plane of triangle of concentration of non-variant points, boundary lines, crossings of space liquation of isothermal planes, parallel planes of the triangle of concentration.

To define the composition of mixture in any point inside the triangle of concentration it is necessary to draw two straight, parallel to any two sides of the triangle. Then on the third side of the triangle three cuts will be chipped out, corresponding to the percentage content of mixture components in the representative point.

Example 21. In equilateral triangle of concentration the point D is given (pic.11).

To define the percentage composition of mixture, represented by the point D.

Solution. We draw two lines fk _║ AC and lg _║ BC through the point. Then on the side of AB we get three cuts, the cut Af corresponds to the percentage content of the component B, the cut Bg – to the percentage content of the component A, and the cut fg – to the content of the component C.

Thus, taking the side AB for 100%, the composition of mixture in the point D will contain 52,5% of A, 22,5% of B and 25% of C.

Pic.11. Equilateral triangle of concentrations

Example 22. The composition of the given mixture corresponds to 51% of B, 24% of A and 25% of C.

To define the representative point of this mixture in the triangle, responsible for the given mixture (see pic.11).

Solution. On the side of the triangle AB or on any other one of sides of the triangle from the point A we put aside the cut An, corresponding to 51% of B, from the point B – the cut Bp, corresponding to 24% of A. We draw straight lines, parallel to two other sides of the triangle, that is AC and BC from obtained points n and p. The crossing point O will be the desired point, responsible for the given composition.

B. The processes of crystallization in three-component systems

While defining the ways of crystallization it is necessary to use the following rule: at the primary crystallization of any component from mixture, located in the filed of releasing of this component or any crystallized phase, the composition of liquid phase changes in straight lines, passing through the vertex of this component and representative point of the mixture, moving away from the point of this component (or another phase).

The composition of solid substance, released from liquid initial mixture (the given composition), on the boundary curve it is shown by the crossing point of straight line, drawn through the point of compositions of liquid and initial mixture, with straight line, connecting both points of released crystalline phases.

Crystallization finishes in such non-variant point (in eutectic one as well), to which converge fields of primary crystallization of three phases, lying in vertexes of three-phase (elementary) triangle, inside of which points of initial mixture regardless of that fact whether these phases independently form triple systems.

While solving tasks it is necessary to use the set of rules as well:

1. In case of congruently melted combination of A_mB_n the point of its composition is within the contour E₃E₄E₆E₅ (pic.12) of the field of primary crystallization, and in case of non-congruently melted combination – beyond the contour E₁UGE₄ (pic.13) of the field of its primary crystallization.

2. If the straight line, connecting points of compositions of two solid phases, or continuation of this straight line crosses the boundary curve (or its continuation), dividing the fields of primary crystallization of those two phases, temperatures always fall on the boundary curve according to withdrawal from the specified crossing point.

3. The feature of triple eutectic point E_t is the location of arrows in three converging boundary curves, shown in pic.14. The triangle ABC is an elementary phase triangle, in the vertexes of which those phases are located, fields of primary crystallization of which converge in eutectic point. Therefore the reaction in this point can be presented as

E_t A + B + C

that is at withdrawing heat from eutectics the specified three equilibrium phases are simultaneously crystallized.

4. The feature of non-variant point of dual lifting G₁ serves as the location of arrows on the boundary curves (pic.15). The point of dual lifting G₁ lies beyond its elementary phase triangle ABC and lies opposite the vertex of the phase A. The further way of crystallization from G₁ along boundary curve (where liquid is simultaneously equilibrium with B and C) leaves the field of primary crystallization A. Therefore in the point G₁ the reaction flows as

G₁ B + C – A

that is at withdrawing heat phases B and C are crystallized, and phase A is dissolved.

5. The feature of non-variant point of dual lowering of G₂ is location of arrows on boundary curves (pic.16).

Pic.12. The diagram of the state of three-component system with congruently melted dual chemical compound

Pic.13. The diagram of the state of three-component system with dual chemical compound, melted incongruently

Pic.14. Position of the eutectic point

Pic.15. Position of the point of dual lifting

Pic.16. Position of the point of dual lowering

The point of dual lowering G₂ lies beyond its elementary phase triangle ABC, is located in external corner of the triangle at the vertex of the phase C and lie opposite the side with phases A – B. The way of crystallization from G₂ at cooling can flow along boundary curve, where liquid is equilibrium with solid phases A and C, or along curve with equilibrium solid phases B and C and liquid. On both boundary curves, and therefore, in the point of their crossing G₂ the phase C releases. In the point G₂ the following reaction flows

G₂ C – A – B

that is at withdrawing heat the phase C is crystallized, phases A and B are dissolved.

6. At graphic definition of correlation of quantities of phases or their percentage content lever rule is used, similarly as it is done in diagrams of state of two-component systems.

Pic.17. The diagram of the state of three-component system with one triple eutectics

Example 23. The diagram of the state of three-component system with eutectics and without chemical compounds (pic.17).

To construct a way of crystallization of the fusion of composition, responsible for the point m (see pic.17).

Solution. At cooling of the fusion, responsible for the composition of the point m, to the temperature t of the space liquation crystals C will begin to release. According to the further cooling the fusion will combine with crystals C and, therefore, will be enriched with components A and B at conserving of their initial correlation. The composition of the fusion will change along the straight line mm´, which is the continuation of the straight line C_m, connecting the point of initial fusion with the point of the corresponding component, in the field of crystallization of which it is located. At achieving the temperature, corresponding to the point m´, on the boundary curve E₃E₄, the component A with the component C will begin to release. The further way of crystallization will flow along the boundary curve from m´ to triple eutectics E₄. According to the removal of the composition of the fusion from the point m´ the total composition of released solid phases will transfer along the straight line CA in the direction from C to E₃ (up to the point n). At achieving the representative point of the fusion of eutectics E₄ the composition of mixtures of solid phases will be responsible for the point n, lying in the point of crossing of straight lines AC and continuation of mE₄. The third component B will also begin to release in the eutectic point E₄. In this case the composition of the mixture of three solid phases begins to transfer along the line nm, and when crystallization will finish, coincides with the point, corresponding to the initial composition of m.

All this way of crystallization at cooling of the fusion in such projection diagram (see pic.17) is presented in the table.

Representative point of the mixture	The composition of liquid phase	Solid phases	The composition of solid substance (mixtures of solid phases), released from the beginning of crystallization up to the present moment

Example 24. The diagram of the state of systems with one dual chemical compound, melted without decomposition, that is congruently (see pic.12).

Solution. Let’s consider the definition of ways of crystallization. The fusion of the composition of representative point k is crystallized in the way of continuation of straight line Ak up to the point k´ to the boundary curve E₄E₆ releasing crystals A. In the point k´ on the boundary curve crystals A are released and A_mB_n appears.

The further ways of crystallization will flow along the curve E₄E₆ from k´ to the triple eutectics E_6. The composition of solid phase, released from the beginning of crystallization, will change by AB from A in the direction of the point of the composition of the phase A_mB_n to the point p. The finite fusion will be crystallized in the triple eutectics E₆ with simultaneous release of crystals A, A_mB_n and C. The composition of mixture of solid phases will transfer from p to the point k. The fusion of the composition of the representative point f is crystallized in the way of ff´E₅. At the beginning crystals A_mB_n will drop out, as the point f is in the field of the primary crystallization A_mB_n. Then, when the composition of the fusion will achieve the boundary line E₃E₅, in the point f´ crystals B will begin to drop out and finally the fusion will be crystallized in the point E₅, where simultaneously crystals A_mB_n, B and C will be released. The composition of mixture of solid phases according to the crystallization of the eutectics E₅ will transfer from the point n to the point f.

Example 25. The diagram of the state of three-component system with one dual chemical compound, melted incongruently (see pic.13).

Solution. In the given diagram there are congruent and incongruent boundary curves. One judges about congruence and incongruence by the tangent line, drawn to the boundary curves. If these tangent lines cross the connecting line of two equilibrium solid phases between representative points, the curve is congruent and both solid phases are released at cooling of the fusion along the same curve. In case the tangent lines lie of the continuation of the connecting line of equilibrium solid phases, the curve is incongruent. At cooling of the fusion one phase, the representative point of which lies near the tangent lines, is crystallized, and the second phase, which point lies farther from tangent lines, is dissolved.

The boundary curve UG therefore is incongruent, and at cooling of crystallized fusion on it the phase A_mB_n is released, and the phase A is dissolved.

At cooling of the fusion, represented by the point O, its composition will transfer in the way of oo´G and finally it is crystallized in the point G. In fact, according to the given rule, the point of the composition of initial mixture o lies in elementary triangle A – A_mB_n – C and to the point G the field of primary crystallization of those phases A, A_mB_n and C converge.

In the representative point b of initial fusion is in elementary phase triangle A_mB_n – B – C, in accordance to that rule, the end of the way of crystallization will be in triple eutectics E₄.

As the point b is in the field of crystallization A, crystals A will be the first to appear at cooling. In the point b´, except crystals A, also crystals A_mB_n will appear, and crystals A will begin to dissolve, as the boundary curve UG is incongruent curve unlike boundary curve, for example E₁E₄, which is congruent curve. The further way of crystallization will flow along the boundary curve UG. The composition of solid phase will change along the line A – A_mB_n. At transferring of the point b´ to the point b´´ on the boundary curve UG A_mB_n will be crystallized, whereas A is dissolved. In the point b´´ the solid phase A will be fully dissolved (in solid phase only A_mB_n remains). In the point b´´ the way of crystallization transfers from boundary curve, crosses along b´´ - b´´´, that is in continuation of the straight line A_mB_nb´´, the field A_mB_n falls into the boundary curve GE₄ in the point b´´´. At this the composition of solid phase, corresponding to A_mB_n, will not change.

Representative point of the mixture and its elementary three-phase triangle	The composition of liquid phase	Solid phases	The composition of solid substance, released from the beginning and up to the given point of the way of crystallization	Comments

Thus, the following rule can be used: the way of crystallization, flowing along incongruent boundary curve, leaves the latter in that case, if primarily released phase is fully dissolved. This happens, when the point of the way of crystallization on the incongruent curve, the point of initial mixture and point of the second equilibrium phase (released at cooling along incongruent curve) lie on tone straight line.

Pic.18. The part of the diagram of the state of the system MgO – A₃S₂ – SiO₂ and the way of crystallization of the mixture of the composition of the point g in it

After this the way of crystallization crosses the filed of primary crystallization of the released crystalline phase along the connoda, passing thought the point of the composition of this phase and initial mixture. In the point b´´´, except A_mB_n, also crystals C appear, and the further way of crystallization will flow along boundary curve GE₄ to the point E₄. The composition of solid phase before the beginning of crystallization of eutectics, at this, changes from the point A_mB_n along the line A_mB_n – C to the point p´. In the point E₄, except crystals A_mB_n and C crystals B appear, and fusion will be fully crystallized. The composition of solid phases will transfer from p´ to the point b. The table in page 30 shows the ways of crystallization of mixtures of points o and b (see pic.13).

Example 26. To define the ways of crystallization of fusion, responsible for the composition, represented by the point g in the diagram M – A – S (pic.18).

Solution. The representative point g is in elementary phase triangle A₃S₂ – M₄A₅S₂ – M₂A₂S₅. Therefore, the end of the crystallized way will lie in the point of dual lifting 9. As the point g is in the field A, corundum will be the primary crystalline phase. At cooling of fusion its composition first will change along the straight line gg´, drawn through the point of initial mixture g and the point of corundum A till the crossing with incongruent boundary curve 8-7 in the point g´. At this corundum will drop out as solid phase. In the point g´ on the boundary curve of corundum-mullite crystals of mullite will appear. The further way of crystallization will flow along the curve 8-7 in the direction of the point 7, besides A will be dissolved, and A₃S₂ will be released. The composition of solid phase at this will change from the point A in the direction of A₃S₂ to the point A₃S₂. The composition of liquid phase g´´ will correspond to this position of solid phase, when all the amount of A is dissolved and only mullite remains.

Further, the way of crystallization leaves the boundary curve, continuing the straight line A₃S₂ - g´´ and crosses the field A₃S₂ to the boundary curve 7-3 in the point g´´. In the point g´´, besides crystals A₃S₂ crystals MA begin to drop out. Then the way of crystallization flows along the boundary curve 7-3 from g´´ to the point 3. The composition of solid substance (two phases) at this will change from A₃S₂ along the straight line A₃S₂ – MA to the point p. In the point of dual lowering 3 crystals MA are fully reabsorbed (dissolved), crystals A₃S₂ are dissolved partly, and a new solid phase M₄A₅S₂ appears. The composition of solid phase (two phases) at this will change from p to p´.

Further, the way of crystallization will flow along the boundary curve 3-9 to the point 9 releasing A₃S₂ and M₄A₅S₂. The composition of solid substance (two phases) at this will change from the point p´ to the point p´´.

In the point of dual lifting 9 the third crystalline phase M₂A₂S₅ appears and full crystallization of fusion (mullite partly dissolves) occurs. The composition of solid substance at this transfers from the point p´ to the point p´´.

The table in page 33 shows the way of crystallization of the mixture of the composition of the point g in the diagram in pic.18.

Example 27. To define the way of crystallization of fusion, responsible for the composition of the point k in the diagram C – A – S (pic.19).

Solution. The point k lies inside the elementary phase triangle C₃S – C₂S – C₃A. The process of crystallization of the indicated fusion will finish in the point of dual lifting 34. Tricalium silicate, dicalcium silicate and tricalcium aluminate will be the finite products of crystallization.

Representative point of the mixture and its elementary phase triangle	The composition of liquid phase	Solid phases	The composition of substance, released from the moment of the beginning of crystallization
(the end of crystallization must begin in the point 9)

* A₃S₂ partly dissolves

Pic.19. The part of the diagram of the state of the system CaO – A₃S₂ – SiO2 and ways of crystallization of the mixture of compositions of points k and f in it

The point k lies in the field of crystallization of calcium oxide, and therefore CaO will be the primarily released solid phase. To define changes of the composition of liquid phase at this from the point CaO through the stated point k we draw the straight line to the crossing with the curve 4-33 in the point k´. At changing of the composition of liquid phase from k to k´ the solid phase CaO will drop out. At further decreasing of the temperature the composition of fusion will transfer along the curve 4-33 from k´ to k´´. The composition of solid phase will change, moving away from CaO, in the direction of SiO₂ and to C₃S.

In the point k´´ CaO will fully dissolve and in solid phase only C₃S will remain. The further way of crystallization will flow along the straight line, drawn through the points C₃S and k´´ to the point k´´´. At this only C₃S will drop out as solid phase. In the point k´´´, besides C₃S, solid phase C₂S will appear. The further way of crystallization will flow from the point k´´´ along the curve 3-34 to the point 34. The composition of solid phase at this will change from C₃S to the point p. In the point 34, besides solid phases C₃S (is partly dissolved) and C₂S (is crystallized), C₃A will begin to crystallize. At this the composition of solid phase will change from the point p to k. Thereon crystallization will finish.

The table shows the way of crystallization of fusion of the point composition (see pic.19).

Representative point of the mixture and its elementary three-phase triangle	The composition of liquid phase	Solid phases	The composition of substance, released from the moment of the beginning of crystallization to the given point of the way of crystallization
K, elementary triangle C3S – C2S - C3A (the end of crystallization must begin in the point 34)

Example 28. To construct the way of crystallization of fusion of the composition of the point f in triple diagram, in which one two-component system shows liquation (pic.20).

Solution. From triple diagram (pic.20) it can be seen, that adding of the third component C gradually narrows the filed of liquation adb, adjoining the side AB, and in the critical point d the compositions of two layers of liquid coincide. The compositions of equilibrium liquids are indicated by the ends of experimentally applied cannodas, lying on the curve of the boundary of the field of liquation.

Pic.20. The diagram of the state of three-component system, in which one two-component system shows liquation

At decreasing of the temperature and crystallization A the composition of liquid phase changes from f to l₁. In the point l₁ liquid phase breaks down into two liquids of the composition of the points l₁ and l₂. The further decreasing of the temperature changes the compositions of liquid phases along curves l₂ → l₂ and l₁ → l_1. In the point l₂ liquid l₁ disappears and the change of the composition of liquid phase continues along the straight line Al₂ to the point k. In solid phase the component A drops out all the time.

In the point k the second solid phase B appears. The further way of crystallization flows along the line kE_t. At this the composition of solid phase changes from A to n.

In the point E_t the full crystallization of fusion occurs, and the composition of solid phase changes from n to f.

The table presents the way of crystallization of the mixture of the composition of the point f (see pic.20).

Representative point of the mixture and its three-phase triangle	The composition of liquid phase	Solid phases	The composition of substance, released from the moment of the beginning of crystallization

C. Definition of quantative composition of phases

Example 29. Triple mixture of the composition 8% of Al₂O₃, 8% of SiO₂ and 84% of CaO (see pic.19) is given.

To define analytically percentage content of fusion and solid phases, released to the moment of achieving the boundary curve in the way of crystallization, and also the compositions of these phases.

Solution. In the diagram (see pic.19) CaO - Al₂O₃ - SiO₂ we find the point f, responsible for the composition of the stated mixture. For this on the side of CaO - Al₂O₃ we put aside from 84% of CaO (the point α) the point Al₂O₃ and draw a straight line, parallel to the side of Al₂O₃ - SiO₂; on the same side of CaO - Al₂O₃ we put aside 8% of Al₂O₃ from the point CaO (the point b) and draw a straight line parallel to the side CaO - SiO₂. The crossing point of these two lines will correspond to the desired point in the diagram (the point f). The point f is in the field of the primary crystallization CaO.

Through the point f of initial mixture and vertex of CaO of the triangle we draw the straight line to the crossing with the boundary curve. The composition of fusion on the boundary curve is responsible for the point f´. We find the composition of liquid in the point f´ graphically. For this through the point f´ we draw two straight lines: one – parallel to the side CaO - SiO₂, and the second one parallel to Al₂O₃ - SiO₂. On the side of CaO - Al₂O₃ we find the composition of fusion of the point f´, corresponding to 16,5% of Al₂O₃ (cut CaO - d), 16,5% of SiO₂ (cut dc) and 67,0% of CaO. As in solid phase only CaO drops out, components of SiO₂ and Al₂O₃ don’t drop out. We find the amount of fusion by the formula (I, 5)

The amount of solid phase will be

Example 30. To define analytically and graphically compositions and quantities of fusion and solid substance, released by the moment of reaching of the finite point of crystallized way, for triple mixture of the point f in the system CaO – Al₂O₃ – SiO₂ (see pic.19) but before the beginning of crystallization in this point.

Solution. We find the point of the end of crystallization way. As the point f is located in the elementary phase triangle C – C₃S – C₃A, the end of crystallization way will be in the point of dual lifting 33 (in this point fields of primary crystallization of three phases, lying in the vertexes of the indicated elementary triangle converge).

We define the composition of the fusion in the point of dual lifting 33 graphically. The composition corresponds to 61,0% of CaO; 6,8% SiO₂ and 32,2% of Al₂O₃. (It can be taken by the table data).

We draw a straight line from the point 33 through the point of initial mixture f to the crossing from the side of the triangle CaO – SiO₂ in the point n to define the indicated compositions of solid substance. The point n corresponds to 7,9% of SiO₂ and 92,1% of CaO. We calculate the amount of fusion analytically, we make the solution, taking into account, that the component Al₂O₃ is absent in solid substance.

graphically

The amount of solid substance will be

Example 31. The point of the fusion n, which is in equilibrium with solid CS is taken on the isotherm 1400º in the field of crystallization CS (pic.21)

To calculate for this point the composition of initial mixture, giving 25% of fusion at this temperature.

Solution. This task can be solved by analytical method, taking into account, that Al₂O₃ is a non-dropped component.

The composition of fusion in the point is defined graphically. It corresponds to 52,5% of SiO₂; 12,5% of Al₂O₃ and 35% of CaO. Using the formula (I,5), we define

Pic.21. The diagram of the state of the system CaO – Al₂O₃ – SiO₂

The second component C is present both in liquid and in solid phases. Therefore it should be defined by the expanded formula (I,7).

The amount of SiO₂ in initial mixture will be

This task can be solved graphically by the lever rule. We connect the point n with the point CS. As the amount of fusion comprises 25% of the total mixture, all the cut CS is divided into four equal parts. We put one part aside representative point of solid phase CS and find the point e, which will correspond to the composition of initial mixture.

Pic.22. The part of the state diagram of the system CaO – Al₂O₃ – SiO₂

Assignments

1. Densities of solid and liquid iron at melting temperature correspondingly equal to 7,865 and 6,880 g/cm³. The change of entropy at melting comprises 2cal/deg·g-atom.

To define the change of melting temperature at increasing pressure for 1atm.

2. Pressure of mercury vapour (mm ) depending on the temperature is expressed by the equation

To define the heat of mercury evaporation at boiling temperature 630ºK.

3. The temperature of transformation of α-quartz in α- tridymite is 1140ºK, in the point of transformation comprises 1,29 kg/cm² ·deg, the change of the volume Δυ – 3,489 cm³/mole.

4. The temperature of transformation β-quartz in α-quartz is 846ºK; in the point of transformation comprises 64,7 kg/cm²·deg; υ₂ – υ₁ – 0,295 cm³/mole.

To calculate heat effect Q at transformation of β-quartz in α-quartz.

5. The mixture consists of 80% of CaO and 20% of SiO₂ (see pic.2). To define the number of phases and number of freedom degrees at heating of the given mixture to 2400º.

6. To comprise the table of ways of crystallization in the diagram of the state of the system Li₂O – SiO₂ (pic.25), for fusions, the compositions of which lie:

1. between 85 and 100% of SiO₂;

2. between Li₂O·SiO₂ and eutectics 2Li₂O·SiO₂ - Li₂O·SiO₂;

3. between Li₂O·SiO₂ and peritectic point;

4. between 2Li₂O·SiO₂ and eutectics 2Li₂O·SiO₂ - Li₂O·SiO₂;

7. To compose the table of ways of crystallization of fusions, for the diagram of the state of the system Na2O – SiO2 (see pic.7), the compositions of which lie:

1. between eutectics Na₂O·SiO₂ - Na₂O·2SiO₂ and Na₂O·2SiO₂;

2. between eutectics Na₂O·2SiO₂ - SiO₂ and SiO₂;

3. between eutectics Na₂O·SiO₂ - 2Na₂O·SiO₂ and 2Na₂O·SiO₂

4. between Na₂O·2SiO₂ and Na₂O·SiO₂

5. between Na₂O·2SiO₂ and SiO₂

8. To compose a table of the ways of crystallization and for fusion in the diagram of the state of the systems K₂O – SiO₂ (pic.26), the compositions of which lie:

1. between eutectics K₂O·SiO₂ - K₂O·2SiO₂ and K₂O·2SiO₂

2. between eutectics K₂O·4SiO₂ – SiO₂ and SiO₂

3. between eutectics K₂O·4SiO₂ – K₂O·2SiO₂ and K₂O·2SiO₂

9. Toe compose a table of the way of crystallization in the diagram of the state of the system MgO – SiO₂ (see pic.1) for fusions, the compositions of which lie:

1. between the compositions MgO·SiO₂ and 2MgO·SiO₂;

2. in the field of liquation;

3. between peritectic point D and eutectics MgO·SiO₂ - SiO₂;

4. between eutectics MgO - 2MgO·SiO₂ and 2MgO·SiO_2.

10. To compose the table of the ways of crystallization in the state diagram of the systems CaO-SiO₂ (see pic.2) for fusions, the compositions of which lie:

1. between 3CaO·2SiO₂ and 2CaO·SiO₂;

2. between 3CaO·2SiO₂ and peritectic point H΄;

3. between CaO and 3CaO·SiO₂;

4. in the field of liquation;

5. between CaO2SiO₂ and eutectics CaO·SiO₂ - SiO₂;

6. between 2CaO·SiO₂ and eutectics 2CaO·SiO₂ - 3CaO·SiO₂;

7. between 3CaO·SiO₂ and a peritectic point;

11. To compose a table of the ways of crystallization in the state diagram of the system SrO – SiO₂ (pic.27) for fusions, the compositions of which lie:

1. between SrO-SiO₂ and eutectics SrO·SiO₂ - SiO₂;

2. between 2SrO·SiO₂ and eutectics 2SrO·SiO₂ - SrO·SiO₂;

3. in the field of liquation;

4. between eutectics SrO·SiO₂ - SiO₂ and the finite composition of the liquation field.

12. The composition of initial fusion corresponds to 64% of CaO and 36% of SiO₂ (see pic.2). The fusion has been cooled to full crystallization.

To define, what type of cement (alite or belite) this mixture will give.

13. The fusion consists of 75% of SiO₂ and 25% of CaO (see pic.2). What amount (in per cent) should be added to the fusion of CaO, so that it begins to crystallize at the temperature 1500ºC?

14. The composition of initial fusion is 52% of SiO₂ and 48% of MgO (see pic.1). To define analytically and graphically percentage content of solid phases before the beginning and at the end of the reaction at peritectic temperature 1557º.

15. To define the temperature, up to that it is necessary to cool the fusion of the composition 50% of MgO and 50% of SiO₂ (see pic.1), so that the half of all fusion will be in solid phase.

In equilibrium with the fusion of what composition will crystallized solid phase be?

16. The mixture from 50% of Al₂O₃ and 50% of sillimanite Al₂O₃·SiO₂ (see pic.33) has been composed to produce high-aluminous products.

What amount (in per cent) of liquid phase at heating of this mixture to 1850 and 1900° will be formed? What solid phases will drop out and what amount (in per cent) each phase at cooling of the fusion to 1750° will contain?

17. To compose a table of ways of crystallization of mixtures (see.pic.53), represented by points, lying:

1. inside the triangle CS – NC₂S₃ – NC₃S₆;

2. on the isotherm 1000°, in the field of crystallization NC₃S₆;

3. inside the triangle NS₂ – NC₂S₃ – NC₃S₆;

4. on the isotherm 1400°, lying in the field of crystallization α-CS.

18. To compose a table of ways of crystallization for mixtures (see.pic.53), representative points of which lie:

1. in the field of crystallization N₂CS₃;

2. in the field of crystallization NS₂.

19. To compose a table of ways of crystallization for mixtures (see.pic.53), representative points of which lie:

1. in the field of crystallization α-CS on the isotherm 1200°;

2. in the field of crystallization NC₃S₆ between isotherms 900 and 1000°.

20. To compose a table of ways of crystallization for fusions (see.pic.53), containing:

1. 75% of SiO₂, 16% of Na₂O and 9% of CaO;

2. 60% of SiO₂, 20% of Na₂O and 20% of CaO;

3. 60% of SiO₂, 10% of Na₂O and 30% of CaO.

21. To compose a table of ways of crystallization of fusion (see.pic.53), representative point of which lies on the connecting straight line NC₃S₆ – NS₂ in the field of crystallization α-CS:

1. in the field of crystallization N₂CS₃;

2. in the field of crystallization NS₂.

22. To compose a table of ways of crystallization of fusion (see.pic.53), representative point of which lies on the isotherm 1400° in the field of crystallization α-tridymite:

1. in the field of crystallization N₂CS₃;

2. in the field of crystallization NS₂.

23. To compose a table of ways of crystallization of fusions (see.pic.53) for mixtures, representative points of which lie inside the triangle:

1. KS₄ – KAS₆ – S;

2. A₃S₂ – KAS₆ – S in the field of crystallization of mullite;

3. KAS₂ – KAS₄ – KS₂.

24. To compose a table of ways of crystallization for points of mixtures (see.pic.54), lying:

1. in the field of crystallization KAS₆;

2. on the isotherm 1100° in the field of crystallization KAS₄;

3. on the isotherm 900° in the field KAS₆.

25. The mixture, consisting of 30% of Al₂O₃; 60% of SiO₂ and 10% of MgO (see pic.55), heated to 1470°.

26. The mixture consists of 70% of orthoclase K₂O·Al₂O₃·6SiO₂ and 30% of K₂O·2SiO₂ (see pic.54).

27. The mixture, consisting of 15% of Al₂O₃, 15% of SiO₂ and 70% of ZnO (see pic.57), heated to 1600°.

28. The mixture of initial mixture (weight, %): Na₂O is 10; SiO₂ is 45; FeO is 45 (pic.62).

29. The composition of the fusion (weight, %): Al₂O₃ is 30; SiO₂ is 30; FeO is 40 (see pic.65). The equilibrium temperature is 1500°. The amount of solid substance if 60%.

To define the composition of initial mixture.

30. The mixture, consisting of 30 g of Al₂O₃, 60 g of FeO and 10 g of SiO₂ (see pic.65). The mixture is heated to 1600°.

Will the mixture be fused fully at this temperature?