KINETICS OF THE TRANSPORT PHENOMENA IN MELTS OF METALS 

Nikolaev, Ukraine

Kharkov, Ukraine

www.geociies.com/fond_nauka

The problem of making new steals and alloys is intimately bound to search of the efficient physical analogs adequately featuring converting of energy of exterior action at phase modular transferrings. One of the most perspective expedients of formation of expresses metal materials based on few - dendrites matrixes is electrocurrent pulsing treatment /ECPT/ on a method of academician D.I.Korneev [1-3, 7]. Innovational substance of ECPT consists in special algorithms of delivering of series of superhigh-energy electroimpulses through hardening metal and is accompanied by a series of not trivial physical processes. The analysis of these processes has allowed revealing features of their phenomenological thermodynamics, the bound with kinetic of temperature fields and oscillation of thermo-undular packages [3 - 6].

Further, we shall consider the thermal diffusion effects incipient at complex action of destabilizing factors /CADF/ and their influence on formation of subfinely divided matrixes. As it was already repeatedly scored, basic elements of a pattern of redistribution of thermal fields during embodying ECPT are dynamic both static of thermo-waves and heterogeneous temperature gradients. In such statement of a problem search of precise analytical solutions for the equations of diffusive mass-transport will be considerably difficult, therefore everywhere, except for expressly stipulated cases, we shall use concept of locally average temperature. Well-known, that thermal diffusion to the general case can be described by a series of the magnetohydrodynamic equations for continuous medium of molten metal:

dp(m) / dt = - divF *[t, T, q(i)], (1)

where F * - an integrated stream of thermal diffusion conduction. F *[t, T, q (i)] it is possible to receive apparent view the analysis of parametric changes of system's entropy of a hardening melt at CADF. In this case we shall take advantage of elements of thermodynamics of irreversible processes /TDIP/ and it is comparable to molten metal fixed set of some parameters x(i), i = 1, 2, 3, …, n. Similar parameters will define a local thermodynamic equilibrium in course ECPT and can become quantities of temperature, heat capacity, electric conductivity, viscosity, density, etc. Accordingly, at passage of a diffusive stream the system of amorphous metal will be wedged from initial equilibrium with parameters x[i(0)], i = 1, 2, 3, …, n on conditional quantity

Δx(t,T) = S {x(i) – x[i(0)]}. (2)

Then blanket entropic performances of system of a hardening melt will become

S[Δx(t, T)] = S{S {x(i) – x[i(0)]}}. (3)

Hence, velocity of change of entropy of a viewed thermodynamic system can be submitted as

dS / dt = S dS / dΔx(i) dx(i) / dt. (4)

Received formulas allow estimating theoretically velocity of change of thermodynamic generalized parameters of a congealing melt:

dΔx / dt = S Δx(i) v[x(i)], (5)

where v[x(i)] - velocity of change of quantity x(i). Accordingly, expression (5) can compare concept of an integral parametric fluency:

F (x) = S F [x(i)]. (6)

Guessing, that the subset of locally allocated thermodynamical coordinates will consist from invariant concerning frequency of CADF of builders, we shall write down:

dΔx(i) / dt = dx(i) / dr(g) dr(g) / dt, (7)

where r(g) - thickness of the allocated modular phase. Based on formulas (5) - (7) it is possible to enter the most blanket thermodynamic definition for change of entropy of quasi-closed system of molten metal at ECPT:

dS / dt = S F[T(i)] F [x(i)], (8)

where F[T(i)] - the generalized thermodynamic forces initiating diffusive conduction. The physical shape and an analytical view of similar forces undergo essential changes during all cycle of ECPT and substantially depend on field of their terminating localization.

Standard reception of an establishment of analytical connection between the generalized quantities of thermodynamic forces and parametric streams is their decomposition on degrees of parameters with the subsequent linearization:

F[T(i)] = S y(ji) Δx(j); F [x(i)] = S y*(ij) Δx(i). (9)

Expressions (9) can be presented as:

F[T(i)] = S K(ij) F [x(i)]; F [x(i)] = S K*(ji) F[T(j)], (10)

where K(ij), K*(ji) - the conjugate kinetic coefficients independent of entropic streams and thermodynamic forces. Their interior structure can contain matrix shapes on a parametric subset of values determined only characteristic properties of a hardening melt.

The conceptual approach from positions TDIP allows to take into account difficultly identifiable effects of superposition incipient at CADF. For example, at a stage of leader - streamer counteraction /LSC/ and formations of electropulse's discharges channels trunk /EDCT/ essential value have magneto-hydrodynamic effects /MHDE/. During stabilization of a thermodynamic system of a melt, there is a redistribution of thermal fields and chemical potentials. Relaxation processes are intimately interlinked to convective and diffusive conduction during which the apparent view of kinetic coefficients varies. At final stage of ECPT, phenomenological parameters of TDIP will correspond to transport of ions of metal in the initial hardened melt with the vector's fields of mechanical pressure.

As a completely phenomenological kinetic coefficients and thermodynamic forces are characterized by fixed allocation of chemical potential in a liquid melt:

F(T) = S Ñ (f* / T); F * = S N[D(i)] v[D(i)], ( 11)

where f* - chemical potential; N[D(i)] - efficiency concentration of diffusing particles. Accordingly, it is possible to enter concept of the module of a diffusion current density:

|F *| = {S K(ij) Ñ [f*(j) / T]} / t. (12)

The topology of thermal fields of an amorphous polycrystallite supposes dissection into separate local isothermal areas for which the equation (12) will be valid as:

|F *| = {S K(ij) Ñ [f*(j)]} / t T. (13)

As already it has above been shown, development of last relaxation stage of a solidus results in change of chemical potentials owing to occurrence of concentration gradients and elastic mechanical pressure. Similar force fields arise at modular transferrings alloys from amorphous phases in polycrystalline. In this case, the lapse rate of chemical potential will have the shape [1, 3]:

Ñ f* = S df*(i) / dN[D(i)] Ñ N[D(i)] + S df*(i) / dG*(j) Ñ G*(j), (14)

where G* - elastic mechanical pressure. Apparently, those formulas (13) and (14) can be transformed in

|F *| = {S K(ij) {S df*(i) / dN[D(i)] Ñ N[D(i)] + S df*(i) / dG*(j) Ñ G*(j)}} / t T. (15)

In bands of an arrangement of nonequilibrium, fields with distinctly expressed temperature gradients there will be padding thermal diffusion flows:

F * = {S K(ij) S df*(i) / dT(j) Ñ T(j)} / t T. (16)

Use of expression for chemical potential in a relaxation period (14) together with functional connections of local inhomogeneities of the distributed thermal field, allows to extend obtained relations as follows:

Ñ f* = S df*(i) / dN[D(i)] Ñ N[D(i)] + S df*(j) / dG*(j) Ñ G*(j) S df*(j) / dT(j) Ñ T(j). (17)

It is similarly possible to deduce the blanket formula for the module of a diffusive stream based on the equations (15) and (16):

|F *| = {S K(ij) {S df*(i) / dN[D(i)] Ñ N[D(i)] + S df*(j) / dG*(j) Ñ G*(j) + S df*(j) / dT(j) Ñ T(j)}} / t T. (18)

Quality examination of processes of thermal diffusion conduction at ECPT of allows making some preliminary deductions. In particular, at activation LSC there is an oscillation of the plasma formations accepting the immediate participation in subsequent of MHDE. Development of LSC is intimately bound to formation of vortex's system of the boundary layer generatored near to EDCT; streamline a stream of molten metal. In subsequent drift of the charged plasmoids is replaced their pulsing effusion through treelike to crown of EDCT. In the field of equilibrium a liquidus - a solidus thermal diffusion processes are limited by effusion of a liquid melt through microscopic capillaries on a demarcation of modular phases. Near to the boundary unit of a solidus on mass-transport, affect the secondary phenomena of sweat and tertiary changes of a degree of lyophilic property and a dilatation of amorphous microcrystallites. At transferring from the mixed modular intermediate phase in a band of the complete initial solidus activity of diffusing builders will be determined by tensor fields of elastic stresses and a nonequilibrium drain of heat.

As a whole, the thermodynamic pattern of processes of thermal diffusion conduction is defined by all courses CADF and is relative dependents on all surveyed heterogeneous and homogeneous mechanisms of activation. Thus, general enough semiempirical models of the diffusive phenomena at ECPT of melt can be generated based on a synergetic principles. We shall note that in the physical essence, the constructed model of diffusive factors is comparable on the action to the general-purpose catalytic protectors labilizing change of this or that group of crystallographic parameters of the hardening melts.

Electrophysical effects at ECPT are defined first by level of CADF, i.e. a spectrum, quantity, density and a period of inlet electromagnetic energy. In volume of a hardening, melt the electrophysical phenomena are proportioned depending on integrated electrical resistance of modular phases. By the form prevailing modular state the volume of a melt can be broken on three characteristic bands including states of a liquidus and a solidus. Accordingly, for a band of a liquid melt magnetohydrodynamic phenomena and magneto-hydrodynamic for plasma of EDCT will be characteristic. The second band of conditional equilibrium a solidus - a liquidus includes cloud of amorphous polycrystallites for which inversion polarization is characteristic, induction warming up and directs thermal effects. The third band of the perfect solidus propagates on surface layers of primarily hardened metal; here it is possible to observe the above-mentioned effects of a dispersion of charge carriers and a skin effect.

The tentative electrophysical phenomena at ECPT are observed already at a stage of formation of EDCT. Superhigh-energy electroimpulses cause occurrence of linearly extended areas of strongly ionization hot plasma of discharge merging as LSC. During the further propagation, similar plasma formations get under action vortical MHDE, twisting forces in current-carrying cords. Braids of plasma merge in a braid of EDCT, terminating a cycle of unitary discharge of ECPT. Model build-ups for electrophysical phenomena of ECPT can be begun with the analysis of balance of energy of oscillations of EDCT plasma under action of exterior and interior electromagnetic fields [6]:

q(pl) Δf E ~ N(pl) [q(pl) l(e)]^2, (19)

where q(pl) and N(pl) - a charge and concentration of collective charge carriers; Δf and E - potential difference and intensity of an interior electromagnetic field; l(e) - efficient length of LSC. From a relation (19) follows that stable maximal linear dimensions for plasma will make:

l(e) < [Δf E cos b / N(pl) q(pl)]^0,5, (20)

where b - angle between a direction of an electromagnetic field and an axis formatived EDCT.

The important characteristic parameter of an initial metastable state of EDCT cords is the lifetime of local plasma formations:

t(pl) ~ q(pl) [N(pl) / m(pl)]^0,5, (21)

where m(pl) - efficient mass of a plasmoids. One of determining requirements of development of an impulsing discharge of the composite branchy type is kinetic mobility of charge carriers. For oscillatory process of coupling of plasma, velocity of drift of charged particles of EDCT in a peak-a-boo magnetic field will make:

V(e,i) ~ {m(pl) c(g) [v*(e,i) / B(H)]^2 / q(pl)} dB(H) / dl(e), (22)

where c(g) - rate of propagation of an electromagnetic field in medium of a melt; v*(e, i) - cross a builder of velocity of drift of carriers; B(H) - a magnetic induction.

Dynamic stability of model of local plasma coupling inside EDCT will depend on a lifetime of charge carriers in diffusive approach:

t(e, i) ~ l(e)^2 / {s*(pl) D(0) exp[E*(e, i) / kT]}, (23)

where s*(pl) - section of interaction of plasma charge carriers with ions of a melt; D(0) - frequency factor as a diffusivity approximated to absolute zero of temperature; E*(e, i) - critical increment of energy of process of bipolar diffusive migration of charge carriers.

Spending correlation comparison of a lifetime initial EDCT with frequency ECPT it is possible to receive on the basis of formulas (22) - (23) system of the following equations:

C / a[A(I)] L ~ q(pl) [N(pl) / m(pl)]^0,5; a[A(I)] L l(e)^2 /RC ~ s*(pl) D(0) exp[E*(e,i) / kT], (24)

where R, C and L - technical parameters of the complete of electrical resistance, capacity and inductance of exterior discharge circuit; a [A(I)] - a logarithmic damping ratio of amplitude of an electrocurrent impulse. Solutions of system (24) allow establishing functionally - analytical connections between group of the basic electrotechnical parameters of exterior contour and integrated performances of plasma of discharge. Essential value for hipping system (24) is represented with natural topology of exterior electromagnetic fields for various variants of connection of electrodes - spark gaps. Procedure of reception of solutions in such approach appears intimately the bound with build-up of vectograms for efficient components of an electromagnetic field. It is simple to show, that the direction and quantity field a builder renders determining influence on stability of restricted plasma configurations of EDCT. They will define also system of the electrodynamic forces incipient owing to expressed magnetic properties of plasma.

Dynamics of EDCT development, as the substantial physical system automatically adjusting with partial diamagnetism of charge carriers, caused by the Larmor currents rotary the charged plasmoids. Because of the given rotary movement, there is a blanket peak-a-boo moment of magnet, directional against variations of an external field. Hence, intensity of a resulting magnetic field inside plasma braids of EDCT will decrease. As a first approximation, incipient system of forces will counterpoise difference of pressures in volume of plasma of discharge, and to submit to the magneto-hydrodynamic equations of a view:

[I(pl) x B(H)] / c(m) = [dv(pl) / dt] [N(e) + N(i)] + Ñ P(e, i), (25)

where P(e) - magneto-hydrodynamic forces. From the equations (25), we shall transfer to more high level of model approach for multicomponent composition of plasma ÊÝÐ:

N(e) {E + [v(e) x B(H)] / c(m)} = Ñ P(e) + F – v(e) N(e); N(i) {E + [v(i) x B(H)] / c(m)} = Ñ P(i) + F – v(i) N(i);

N(pl) {E + [v(pl) x B(H)] / c(m) = Ñ P(pl) + F – v(pl) N(pl), (26)

here F - the forces effective between charge carriers. The system of the magneto-hydrodynamic equations (26) allows describing multipleparameter kinetic legitimacies of activity of electromagnetic forces on a critical state of a hardening melt.

Let us consider in more detail energy exterior of CADF. On the basis of author's methodical development of academician D.I.Korneev it is possible to present as the total of the following summands:

E(w) = E(1) + E(2) + E(3) + E(x). (27)

The left-hand part of equality (27) represents energy of the electroimpulses generated by exterior discharge circuit [9 - 11]:

E(w) = R C / L ò U² exp( - R t* / L) sin^2(t* / L C) dt / {C – (C / L)^0,5 ò U exp[sin(t* / L C)^(-at)] dt}. (28)

In turn, the first summand from a right part determines the energy transferred by plasma charge carriers through various modular phases of the hardening melt:

E(1) = S I[pl(i)] p[pl(i)] N[pl(i)]. (29)

Hereinafter summation is spent on all allocated areas of a dissipation of electromagnetic energy. The second summand is bound to a dispersion of plasmoids on phase inhomogeneities of medium of a melt:

E(2) = S I(pl) exp[E*(pl) / kT]. (30)

The third summand from equality (27) features energy of the magneto-hydrodynamic phenomena accompanying discharges:

E(3) = N(pl) [P(pl) d(pl)^2 t*], (31)

where P(pl) - interior pressures of plasma; d(pl) - diameter of EDCT.

The detailed analysis of integral balance (27) shows, that all energy builders included in it have a dual view. They are represented functionally dependent as from parameters of ECPT, and changes of a phase state of a hardening polycrystallite. Thus, examination of mathematical model (27) - (31) allows to draw a deduction on its adequacy to processes of occurrence and development of close-grained packing and practically a without - dendrites structure of recrystallized metal. Separate and in many respects, the question of principle is made with a correlation between frequency of following of electrocurrent impulses and frequency of modular-phase changes. In more detail given theme irradiated in the subsequent partitions, and here we shall specify, that in the modern theory of phase changes similar questions be considered methods of renormalization group with reference to examination of critical phenomenas.

Last summand of a right part of equality (27) represents energy of difficultly identifiable processes. To the similar phenomenon, it is necessary to relate oscillation of the frontal magnetohydrodynamic impulses with efficient pressure:

ΔP ~ t* v(p) P(pl) {1 – exp[- r(d) / t* v(p)]} / r(d), (32)

where v(p) - velocity of perturbation's propagation in liquid medium of a melt; r(d) - a distance between front of a magnetohydrodynamic wave and shell of EDCT.

The separate class of electrophysical effects at ECPT is made with the phenomena of indirect electrostimulation of diffusive conduction. Thus, diffusive processes are characterized by a complex structure of interaction potentials, energy barriers, and mechanisms of catalytic activation. Kinetic instability of diffusive profiles demands application of express phenomenological research techniques among which it is possible to term the analytical means of the theory of irreversible processes. Briefly enough it can be formulated as invariance of the thermodynamic system including fluctuations of extrinsic profiles, the mixed modular phases, eutectics, and peritectics. Tendencies to alignment of chemical potentials of metastable system of a melt result in pinch of probability of indirect activation of thermodiffusion. Thus, mass transfer is accompanied by change of the physicochemical properties of medium and catalytic quasichemical reactions on boundaries of modular phases.

Electrophysical regularity of ECPT on structural parameters of formatived lattice matrixes of a hardening crystalline-amorphous melt find expressed displays in comparative mechanical performances. Experimental researches of a static and dynamic tension, an arcuation the concentrated loading, local hardness, and impact strength. Influence of the aggregate size making structure of textures, on elastic - mechanical characteristics of alloys speaks their influence on isotropy of textures, allocation of micropores and heterogeneous inserts. Similar stoichiometrical infringements of the polycrystalline centres order have the expressed centres of concentration concentrating on boundaries of grains. From here follows, that in large and medium-grained structural matrixes there is a grid of preferable trajectories of the break worsening mechanical service performances. However recently there were new physical concepts guessing, that the distance between grains non-linearly influences parameters of recrystallization. In a basis of such sights the empirical datas linking changes of velocities of a crystalline-amorphous solidification with quantity of characteristic distances between branches of dendrites of the highest orders lay.

Given quasichemical reactions, evidently enough show all basic stages of environmental change of a melt in fluxion of ECPT Korneev. More detailed viewing of the schema (24) shows, that primary responses are limited by activity of mechanisms of passage of electrocurrent impulses through a liquid melt as a quasi-equilibrium modular phase with sites of local supercoolings in a border zone of a solidus. In accordance with depressing temperature of metal, the probability of occurrence of initial heterogeneous micro-crystallites increases. Simultaneously there is a dispelling of collective charge carriers on inhomogeneities of a melt to pinch of its temperature and subsequent collapse of EDCT. The given processes are accompanied by oscillation of bull frontal magnetohydrodynamic oscillations and metastable waves of heat. The thermodynamics of the similar phenomena reflexes in initial responses of system (24) and dynamic equations (20) - (23). At following, stage the secondary stream of plasma formations attacks hardening metal with cloud of in part associate polycrystallites. In accordance with pulsing input of electromagnetic energy, process of a metastable solidification of metal gets quasicyclic character. Closing stage results in formation of the abnormal matrix structures including polycrystallites in scoured borders of crushed fragments of initial dendrites. It is possible to assume, that the given phenomenon is interlinked to processes of a relaxation dissipation of electromagnetic energy. Thus, the thermodynamic energy transferred along lapse rates of metastable thermal fields and evolved at a dispersion of macroplasmoids on a conglomerate of crystallites limits velocity of modular transferrings. Simultaneously, magnetohydrodynamic impulses and a vortical peak-a-boo electromagnetic interaction destroy a formatived lattice matrix, by intensive stirring a hardening melt. It is necessary to note, that the fixed role in embodying a close-grained polycrystalline structure is played with the phenomena of polymorphism. In their bottom, embodying of polycrystalline modifications of a standard lattice matrix minimized on enthalpy lays. It is rather probable, that such crystallographic arrangement of elementary fragmentary meshes concentration of an equilibrium solid phase will have more high density of packing.

1. Feygin O.O. Action of high-energy electroimpulses on metal melts// SciTecLibrary. com. 2003. - http://www.sciteclibrary.ru/rus/catalog/pages/5294.html 

2. Korneev D.I., Feygin O.O. Korneev D.I., Feygin O.O. Paradoxical physics of super-power impulsing discharges// Ibid. - http://www.sciteclibrary.ru/rus/catalog/pages/5347.html 

3. Korneev D.I., Feygin O.O. Phenomenological thermodynamics of super-energy electroimpulses in metal melt// Ibid. - http://www.sciteclibrary.ru/rus/catalog/pages/5422.html 

4. Korneev D.I., Feygin O.O. Òåðìîäèíàìèêà æèäêèõ ìåòàëëîâ ïðè ñâåðõâûñîêèõ ýíåðãèÿõ ýëåêòðîòîêîâîãî âîçäåéñòâèÿ// Ibid. - http://www.sciteclibrary.ru/rus/catalog/pages/5454.html 

5. Petrenko S.S., Feygin O.O. Nonequilibrium crystallization of metal melts// Ibid. - http://www.sciteclibrary.ru/rus/catalog/pages/5687.html 

6. Korneev D.I., Feygin O.O. Quasicrystallization of metals at ultrahigh energy of action// Ibid. - http://www.sciteclibrary.ru/rus/catalog/pages/6078.html 

7. Korneev D.I., Feygin O.O. Electrophysical methods of control by the crystallization of welded metal// Ibid. - http://www.sciteclibrary.ru/rus/catalog/pages/6302.html 

8. Korneev D.I., Feygin O.O. Theoretical explorations of processes high-energy electrophysical treatments of metal’s melts// Ibid. - http://www.sciteclibrary.ru/rus/catalog/pages/6436.html 

9. Korneev D.I., Feygin O.O. Mechanisms of the operation of electroimpulses channels in the metal's melts// Ibid. - http://www.sciteclibrary.ru/rus/catalog/pages/6586.html 

10. Korneev D.I., Feygin O.O. Superhigh-energy electroimpulses in the metal's melt// Ibid. - http://www.sciteclibrary.ru/rus/catalog/pages/6649.html 

11. Petrenko S.S., Feygin O.O. Macro-nonequilibrium model of the quasicyclic solidification of metal-alloys// Ibid. -  http://www.sciteclibrary.ru/rus/catalog/pages/6651.html 

12. Korneev D.I., Feygin O.O. Superenergy electropulsing treatment of weld joints// Ibid. - http://www.sciteclibrary.ru/rus/catalog/pages/6669.html

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