METAL MELTS STRUCTURAL RESEARCHES
Institute of Metallurgy, Ural’s Division of Russian Academy of Sciences,
101, Amundsen Str., 620016, Ekaterinburg, Russia
Structure of phases is very important for study of speeds and mechanism of phase transitions, and also chemical reactions. The most simple state of substance in this relation is gaseous one, where the substance as separate molecules is regularly distributed in space and at small pressure is simply described by the law of ideal gases. However, at increase of pressure up to tens or hundreds atmospheres, it is hardly possible to speak about completely uniform distribution of particles in volume. Density fluctuations of gas appear, the laws for ideal gas are not available in such systems. The structure of already considerably influences the majority of its properties. It is natural, that the structure of solid state substances for many years is investigated by various methods and this information is concentrated in the numerous reference book.
It is much more difficult to obtaine structure of a liquid, since the space arrangement of atoms is not fixed, as in a solid state body, however atoms are not completely free as in gas. Therefore properties of liquid can approach to gas at overheating or to solid state body close to melting temperatures. In this case it is possible with confidence to speak about the short order existing around of each moving atom that revils in a regular arrangement of fading concentric spheres with alternating density behind the ionic centers of atoms, got in an environment of given atom. It can be defined from experiment by curves of function of radial distribution of atoms (RDF), obtained from diffraction researches, in particular, from x-ray measurements of electron scattering intensity I (S) depending on a wave vector S
S = 4 ； sin ！ / ： , (1)
where ！ - half of angle of scattering; ： - length of a radiation wave.
RDF (~(R)) is the probability of a presence of any atom at
distance R from atom accepted as the centre, is obtaned by Fourier-transformation of curve intensity of scattering.
0Experimental dependence I(S) for molten iron at 1550С and 001750С as well as RDF at 1550С calculated from I(S) are given in a
fig. 1. Distance up to the first maximum on this curve gives average distance between atoms in metal, and the area under this peak determines coordination number, i.e. number of atoms in the first coordination sphere around of atom accepted for central.
The numerous data show, that coordination of atoms in a liquid and the distances between the nearest atoms are close to those of crystal. Therefore many researchers follow J.I.Frenkel concepts about quasicrystal nature of liquid (especially, liquid metals), stated by them at 30-th years .
The liquid metals are usually regarded as simple liquids such as the liquefied inert gases, for which the theory is most full developed.
The liquid differs from crystal state bodies by absence of the long order, i.e. uncorrelated arrangement of any particle concerned as the center. As noted by J.I.Frenkel, character of thermal movement of particles in liquid has dual nature, that unites in itself property attributed to gases (fluidity), and crystal bodies (shift elasticity). The shift elasticity of liquids is usually hidden by their small viscosity. However, if a liquid is quickly cooled, i.e. amorfized, it becomes hard, but not crystal and gets shift elasticity.
The conclusions about structure of pure liquid metals began to occur from experimental researches of temperature dependencies of those or other properties of melts (viscosity, electric conductivity, density, solubility of gases, x-ray structure analysis, overcooling at crystallization etc.).
So, at of aluminum by 130 K above melting temperature T all m
diffraction maximums on curve intensity of electron scattering are moved to the large angles of scattering, the side maximum on the main peak of -1-1the structural factor disappears at S = 31 nm, and at S = 40 nm there
is an additional maximum .
This variations in structure of aluminum accompanied by
changes of viscosity at 1040-1120 K  and density at 1070-1170 K . The solubility of hydrogen in pure aluminum with growth of temperature
is maximal at 1070 K .
Overheating of iron by 130 K above T gets displacement of m
scattering curves maximums, but to the smaller angles of scattering, asymmetry on the part of the large angles of scattering and increases width of the main peak .
-2 I(10, e. un.
-1-1 S, nm S, nm-1S, nm
R, nm R, nm
Fig.1. Intensity change of electron scattering from a surface of liquid
iron (a) and radial distribution function (RDF) of atoms in molten
iron (b). ρ - average nuclear density in system, f - nuclear factor – 00
scattering intensity by the isolated atom.
Numerous x-rays researches stated, that the liquid metals with dense packing (Al, Fe, Au, Pb etc.) keep internuclear distances and coordination numbers close to the appropriate crystals, that often is explained by destroying of a crystal lattice.
Metals with friable packing in a solid state (coordination number 4) such as Bi, Ga, Ge etc. at melting increase coordination number and pass to more dense type of packing.
However it is possible to explain dens packing of a liquid disregarding it crystal lattice-like nature. So Bernall  considers, that the liquid on structure also is far from gas, as well as from a crystal and is the irregularly constructed congestion of molecules not containing any crystal sites, and the coordination number is close to a dens packing type of lattice.
Last years the interpretation of topology amorphous and liquid structures is successfully carried out on the basis of statistical geometry Voronoy polyhedra, which are formed by planes, perpendicular middle of vectors connecting given nuclear unit to its nearest neighbors (fig. 2). The type of polyhedron is designated by a sequence of digits in brackets ( n , 3
n , n n ...), and first digit n shows number of triangular faces in 45,63
polyhedron , second n - tetragonal, n - pentagonal etc. The sum of 45
indexes n defines local geometrical (in difference with average) K
coordination number for given knot of atom. At modeling of melting and crystallizing the most stable Voronoy polyhedrons are b.c.c. type, which are identified by a set of digits (0608). Polyhedrons (0-12), describing f.c.c. structure, it appear to be extremely unstable on thermal movement atoms of tetragonal apex.
The polyhedrons such as (0-12) are transformed under influence of thermal movement in polyhedrons (0446) that are topologically close to (0608), as is observed in experiments with overheating of liquid aluminum. The same way cooling to T and lower the formation of m
microgerms of a crystal phase in iron, aluminum, potassium, sodium at the beginning goes on the basis of growth polyhedron congregations (0608) and relative to it (0446). It is possible, that the direct crystal phase of premelting or at crystallizing, close to liquid, appears structure with prevalence f.c.c. coordination. The given property can be universal, the question only is in a temperature interval from a melting point. Evidence
of this property is probably results of experimental researches, where the crystal systems at the moment of crystallization (interval of several degrees) had b.c.c. structure independently from initial structure at lower temperatures.
Fig.2. The scheme, illustrating construction of Voronoy polyhedron in
two-dimensional space. The asterisks designate atoms, dark points
d - crossing of straight lines NN with a perpendicular plane. ijij
The further heating results in growth of statistical weight of icosahedron type polyhedrons (00-12), for which the uniform distribution of 12 atoms on sphere is proper. Naturally, transition from (0608) with Z = 14 and (0446) with Z = 14 to (00-12) with Z = 12 (Z - coordination number of polyhedron, equal to the sum n + n + n +...) is defined by a 345
nature of melt and can go with a various degree at increase of temperature. So, for iron the icosahedron packing appears with less density, that results in growth of first internuclear distance. It is known, that for the majority of metals this distance remains or constant, or decreases at heating. Such anomaly in iron can be explained by relative conservatism of an electronic condition of system at transition in a liquid state .
In liquid aluminium at increase of temperature above T, as m
show molecular dynamics experiment, there is an increase of a general share of polyhedrons (0446) and icosahedron type polyhedrons due to the residual statistical weights of f.c.c. type polyhedron smashed by thermal background movement. At overheating temperatures 200 K above T the m
growth of polyhedrons (0446) statistical weight stops and further heating results, as well as in case of pure iron, to practically complete prevalence of fifth order symmetry (00-12).
The given changes may not repeat in accuracy at temperature decrease and depending on intensity of cooling, that can be the reason in the certain sort of a structural hysteresis. In case of melt overcooling lower T the maximums of electron scattering intensity functions and m
RDF noticeably grow. In some cases these changes are accompanied by occurrence of a shoulder or inflow on the right side of 2 peak RDF and structural factor. The further overcooling, if it is not accompanied by crystallization (at sufficient intensity of cooling), results to glassing of metal. For a is proper glass it is proper more distinct reveal of the mentioned additional structure, which can be expressed by quasidipersyty of all radial distribution function.
Thus, the icosahedron type short order (and the prevalence of fifth order symmetry) can in some aspect be accepted for the generalized and idealized image of structure of a liquid, proper for high-temperature state, where individual features of liquid substantially disappear. At last, interpretation of structure of liquid and amorphous metals needs to consider conceptually competing individual structural elements being its primary basis. At first that are elements of structural motives with structure close to crystal phases, and at second, formations specific actually to a liquid and amorphous state (icosahedron, Bernal's cavities).
For the theoretical description of liquid metals the numerous modeling theories based on the assumption of quasicrystalline liquid were used. At different approximation it is possible to determine configuration integral Q, and using relation between free energy F and statistical N
integral Q we obtain
F = - kT ln Q, (2)
and also between Q and QN
where m - weight of particles; N - number of particles in system; h - the Plank constant, then it’s possible to calculate F.
Knowing F, it is possible to determine by the known
hermodynamic formulas internal energy of a liquid, entropy, thermal capacity, pressure etc.
The statistical physics has enabled to describe properties of a liquid starting from a nature of forces acting between particles, in account of such approximation, as absence of quantum-mechanical effects, presence only of spherical symmetry of molecules and directed interaction between them ignoring structure of melt. The correlation functions method describing probability or correlation in an arrangement of cooperating particles in system is most advanced for account of properties of a liquid which was offered at 30-40 years in works of, Ivon, Bogolubov, Born and Green etc.
Bogolubov and Kirkwood have derived complicated
integrodifferential equation allowing at given V and T to calculate radial distribution function, of (RDF), if the dependence of interaction energy of two particles (pair potential ，(r)) from distance r between their centers
(fig. 3) is known. Thus it is supposed, that the potential energy of all system is equal to the sum of pair interactions
U = ，， (r). (4) N
With the help of correlation functions method the expressions connecting different thermodynamic properties with u(r) and (RDF) were derived. The accuracy of accounts will depend on accuracy of interparticle potential ， (r) obtaining. The method of pseudo-potential for calculations of interparticle potential is widely used last decade
，(r) = ，(r) + ， (r) , (5) di
where ，(r) ) - potential of direct Coulomb interaction between ions; d
， (r) - potential of indirect interaction between ions with electrons of i
126??dd)?)?Fig.3. 1 – Lennard-Johnes potential , where ，；r，？2;；：?????，?，?rr：?，?
； - minimum energy of potential curve; d - distance at j (r) = 0.
2 - potential in metal with screening of ion by the collective
The model theories, correlation functions method, pseudo potential theory, wide development of scattering researches of liquid metals, the application of molecular dynamics etc. has allowed to accumulate a huge experimental material on properties and structure of pure liquid metals.
Unfortunately, the researchers did not come to common opinion on structure of molten metals, since the results of calculations with all offered models and methods have not revealed those characteristic dependencies between properties of liquid and short order at change of temperature, which is observed for a number of systems in laboratory researches.
In some degree it was essentially to expect, since in all calculations it’s accepted, that ，(r) and the type of model of a liquid does
not vary with temperature. Therefore hardly probable those or other anomalies to be reveled on calculated temperature dependence of any properties, although such anomalies are observed on experimental curves.
Binary melts and glasses
The binary melts structure is reasonable to consider not only in comparison with crystal, but also with structure of their glasses, since the glass structure is not shaded by a thermal movement. Such systems structure, is strongly depends on composition besides temperature and pressure. If in one-component metal liquids a question on a type of short order is not clear and debatable, for binary or multicomponent melts the majority of the researchers unequivocally recognize existence of short order microgroups (clusters). For a qualitative evaluation of interparticle interaction in binary systems the composition-property experimental curves are usually used, which form essentially differs for various type solutions. There are usually three types of melts under consideration: systems with unlimited solubility of components in a crystalline state, eutectic alloys and alloys with chemical interaction of components.
The significant number of properties researches (viscosity, electrical conductivity, molar volume, activity, surface tension, density, magnetic susceptibility, the solubility etc.), have revealed correlation between these properties and phase diagrams. The monotonous change isotherms of properties for melts, and also insignificant deviation (usually negative) from an ideal solution is proper for systems with complete mutual dissolution of components in crystalline state.
For eutectic systems the majority of the authors note change of functional dependence for viscosity in area of eutectic concentration (minimum on isotherm) and positive deviations of thermodynamic properties from ideal solutions (Raul law), that testifies to prevalence in such melts of bond energy of between the same particles above energy between different particles and about occurrence of microareas with primary concentration of one of components.
The presence in a solid state of strong chemical interaction between components, that is accompanied with formation of stable chemical compound, should be revealed substantially in a liquid as well.