Dr.Ph. Kazova A.M., Zhaksybaeva G.S., Dr.Dr.Ph. Kazova R.A.

 

Kazakh National Technical University, Kazakhstan

 

THE POWER APPROACH TO REVEALING LAWS solidphase OF THERMOCHEMICAL TRANSFORMATIONS

 

Thermodynamic research of system Ña10(ÐÎ4)6F2-SiO2-CaMg(CO3)2-                      KAl2[Al,Si3]O10(OH)2 is executed by a method of physical and chemical modeling [1]. The equilibrium component structure of a multisystem is determined under the program of "Selector" according to a principle of minimization of free energy. The system is in a condition of balance when function of free energy (isobar-isothermal potential of Gibbs) accepts the minimal value. Calculation of equilibrium quantity of each component of a multisystem is received by the decision of system of the equations consisting of the equations of action of weights, balance of weights and an electroneutrality. Participation in system of firm phases, a gas mix and water solutions [1, 2] is taken into account. In table 1 the thermodynamic data for initial components the systems used at drawing up of modeled matrixes are resulted. Dependent components (predicted connections) are determine d experimentally. The elements included in dependent components have been attributed (related) to independent components, and also conditions of an electroneutrality of system and restriction of system on volume. Varied parameters were the maintenance(contents) of components in system. The matrix of planning (table 1) has been broken into seven series on five experiments (table 1) in such a manner that experiences (1-35) were distributed (allocated) on these series, where Õ1 - the maintenance (contents) ftorapatite; Õ2 - quartz; Õ3 - dolomite; Õ4 - muscovite.

Table 1 - Series of experiments of a matrix of planning

Number

Õ1

Õ2

Õ3

Õ4

Number

Õ1

Õ2

Õ3

Õ4

experience

 

 

 

 

experience

 

 

 

 

 

The first five

 

The fifth five

27

0,25

0,5

0,25

0

23

0,5

0,25

0,25

0

17

0,25

0,75

0

0

31

0,25

0,25

0,5

0

5

0,5

0,5

0

0

6

0,5

0

0,5

0

11

0,75

0,25

0

0

12

0,75

0

0,25

0

1

1,0

0

0

0

18

0,25

0

0,75

0

The second five

The sixth five

24

0,5

0,25

0

0,25

26

0

0,5

0,25

0,25

13

0,75

0

0

0,25

34

0

0,25

0,25

0,5

7

0,5

0

0

0,25

9

0

0,5

0

0,5

19

0,25

0

0

0,75

15

0

0,75

0

0,25

4

0

0

0

1,0

21

0

0,25

0

0,75

The third five

The seventh five

33

0,25

0

0,25

0,5

35

0,25

0,25

0,25

0,25

22

0

0

0,25

0,75

25

0,5

0

0,25

0,25

10

0

0

0,5

0,5

29

0,25

0

0,5

0,25

16

0

0

0,75

0,25

28

0,25

0,25

0

0,25

3

0

0

1,0

0

32

0,25

0,25

0

0,5

THE FOURTH FIVE

 

30

0

0,25

0,5

0,25

 

 

 

 

 

20

0

0,25

0,75

0

 

 

 

 

 

8

0

0,5

0,5

0

 

 

 

 

 

14

0

0,75

0,25

0

 

 

 

 

 

2

0

1,0

0

0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Results of thermodynamic modeling of system Ñà10 (ÐÎ4)6F2-SiO2-ÑaÌg(CO3)2-ÊÀl2[Àl,Si3]Î10(ÎÍ)2 are shown in tables 1-3. Characteristics of independent components of an equilibrium condition (chemical potential, relative chemical potential) (table 2) are received.

So, in the first five in end-products are found out: akermanite (Cà2Mg[Si2O7]), ortoanstatite (MgSiO3), forsterite (Mg2SiO4), pyrophosphate of calcium (Ca2P2O7), cuspidin (Ca4 [Si2O7] F2), in part dolo mite (tables 2).

Table 2 - the characteristic of products of interaction in system in an equilibrium condition (the first five)

Phase

Amount

Function ∆Gò, kkal/moth

Mas. %

Î2 (Oxygen)

1,55.10-7

-63433

0,00

CO2 (oxide of carbon)

1,5.10-3

-93917

0,023

CO2 (oxide of carbon)

5,35.10-1

-163617

12,90

SiF (silicon fluoride)

3,33.10-2

-475175

1,83

SiO2 (Quartz)

9,51.10-9

-231762

0,00

Ca2Mg[Si2O7] (akermatite)

2,68.10-1

-1011166

40,07

MgSiO3 (ortoenstatite)

3,63.10-9

-394597

0,00

Ca2P2O7 (pyrophosphate)

2,737.10-1

-921411

38,11

Ca4[Si2O7]F2 (cuspidin)

2,455.10-2

 

4,90

CaMg (CO3) dolomite

2,148.10-2

-680319

2,17

In other series the phase structure, basically, is similar. In the second five are found out periclaz (MgO), aluminate of magnesium (MgAl2O4), oxide  of calcium, mayanid (Ca12Al14O33), bredigite (Ca2SiO4), mervinite (Ca3Mg5SiO8), silicate  of calium (KSi2O5), anortite (CaAl2[Si2O8]), psevdovollastonite (CaSiO3), etc. (the first, fifth variants). In the third five it is revealed, besides the specified connections, ftorflogopite (table 3). In the fourth five (the first variant) in appreciable amount phosphate of calcium, cuspidin and ftorflogopite [(KMg3[AlSi3]O10)F] is formed akermanite, anortite. The similar data are received in series V-VÏ.

In systems investigated by us interaction proceeds in nonequilibrium conditions. With reference to the thermochemical transformations proceeding in conditions of gasedynomic of a mobile layer expediently use of the new power approach. In the multicomponent mix consisting of complex multinuclear mineral components, as criterion of an orientation of interaction energy of a crystal lattice can serve. It is caused by that for the complex connections having polications and polianions parts, determining thermodynamic characteristics is rather problematic, connected to significant methodical difficulties. 

The power approach will allow to compare quantitatively power characteristics of the initial substances participating in the solidphase  reaction and end-products of interaction, to reveal phase structure in nonequilibrium conditions. With this purpose the analysis of reactions of interaction in system is executed by calculation and the comparative analysis of the sum of energy of initial and final connections. Most we accept for similar calculations a method of power constants of ions of A.E.Fersman's. Energetically  constant (EC) - energy of formation (education) of one gram - ion of crystal structure and the ions which are taking place in infinity. It is possib le to enter one more power characteristic - VEC, equal 1 EC, divided on valence. Dependence between size of energy of a crystal lattice and a power constant is described by the equation:                            

U = 256,1 (aEC + bEC);                             (1)

where a and b - numbers cations  and ànions, included in formula unit. Under the formula (1) values of energy of a crystal lattice of initial components (total) and products of interaction for the equations 1-25 are designed. The certain law is revealed: the sum of energy of crystal lattices is more, than the same sum of end-products (table 3), except for reactions in which in end-products it is formed dioxide of carbon. It is possible to explain it to that minerals wi th higher value of energy of a crystal lattice were allocated in initial stages of geochemical process and existed as initial in matrix under influence thermally àctivational processes in thermolitical  conditions initial components of system undergo transformations with reception of mineral components with lower value of total energy crystal lattices (table 3). It is caused by that all processes connected to chemical changes at a nuclear level or as a result of formation of new mineral kinds have one general tendency - to lower free energy of a mineral or a mineral composition under influence of external conditions. Stability appearances connections in the certain degree is defined by size of heat of formation. Allocation of phases at which formation the greatest amount of energy is allocated is preferable.

The table 3 - Energy of a crystal lattice of initial connections

Connection

Amount

Whole atoms

Energy of the crystalline lattice, kkal/moth

cations

ànions

Ca10 (PO4) 6F2 - ftorapatite

16

26

42

36325

α - SiO2 - quartz

1

2

3

2996

CaMg (CO3) 2 - dolomite

4

6

10

9629

KAl[Si3,Al] O10 (OH) 2 - muscovite

8

12

20

14661

Ca3,3 (PO3) 2 [SiO4]F0,6 calsium phosphosilicate

6,3

10,6

16,9

3008

KMg3[Al2,5Si1,5]O10F0,2 - ftorflogopite

6

10,2

16,2

9840

Ca2Mg5Si8O22(OH) 2 - tremolite

17

24

41

30192

CaCÎ3 - calcite

2

3

5

4674

Ca4[Si2O7]F2 - cuspidin

6

9

15

9166

CaMgSi2O6 - diopcid

4

6

10

7785

MgSiO3 - ortoenstatite

2

3

5

3944

Mg3Si4O10(OH) 2 - talc

9

12

21

14621

Mg2SiO4 - forsterite

3

4

7

4892

Ca(OH) 2 - hydroxide of calcium

3

2

5

1406

Ca10 (PO4) 6(OH0,3, F1,7) - hydroxideoccilapatite

16

26

42

36325

Mg3Si2O5(OH) 4 - serpentine

5

9

14

8421

Mg7Si8O22 (OH) 2  - antofillite

15

24

39

21663

Mg2Si2Al2O10(OH)2 - vermiculite

6

2

12

3

18

5

12202

4866/750

H2O→H [OH] - water

1

1

2

16,82

CO2 - dioxide of carbon

1

2

3

3918

CaF2 - Fluorite

1

2

3

638

CaO - oxide of calcium

1

1

2

845

SiF2 - fluoride of silicon

1

4

5

2581

HF - ftor hydrogen

1

1

2

177

Ca3(PO4) 2(OH) - hydroxilapatite

6

9

15

12260

Ca5 [(PO4) 0,7 [SiO4]O1,5F] - britolite

6,7

8,7

15,4

10414

MgO - oxide of magnesium

1

1

2

92

Ca3(PO4) 2 - vitcolite

4

6

10

11101

Mg2Si2O6 - enstatite

4

6

10

7888

Mg0,5Fe0,5[CO3] - breinerite

3

3

6

4863

MgFe [SiO4] - olivin

3

4

10

4884

Mg0,5F0,5 (OH) 2 brucite

2

2

4

738

Minerals of phosphorites (ftorapatite, ftorkarbonatapatite, micas, carbonates) concern to unisodespetical and mesodismetical to structures, i.e. contain the isolated groups of atoms forming complex ions which serve in similar structures structural units. In such ions the central ion is surrounded with the big ions of oxygen (ÐÎ43-, ÑÎ32-, SO42-).

The list of the used sources

1. Karpov I.K., Dorogokupets P.I., Petrov B.V. Problem of correct construction of physical and chemical models - In book: the Thermodynamic mode of metamorphism. -L.: Science, 1976. p. 120-127.

2. Karpov I.K., Haliullina O.A., Kiselyov A.I. Physical and chemical modelling by a method of optimum programming // the Note of the All-Union mineralogical society, 1983. V.4. p. 402-409.