CARBIDE FORMATION DURING CRYSTALLIZATION UPON WELDING

V. Mazurovsky1, M. Zinigrad1, L. Leontiev2, and V. Lisin2
1Materials Research Center, College of Judea and Samaria, Ariel, Israel
2Institute of Metallurgy, Ural Division of the Russian Academy of Sciences, Ekaterinburg, Russia

ABSTRACT. A physicochemical analysis of the carbide-formation processes accompanying the primary and secondary crystallization of a weld metal using quantum-chemical theories that depict the structure of transition metals (d metals) and of carbides as compounds of carbon with d metals is described. The principles governing carbide formation in a rapidly crystallizing weld metal are formulated. The concept of the “carbide-forming ability of a d metal” is introduced, and its application to modeling carbide-formation processes in a weld deposit is examined.

Introduction

An extensive list of consumables (coated electrodes, flux-cored wires, and flux-cored ribbons) has been developed for hardfacing mechanical parts that operate under the conditions of abrasion wear. These consumables ensure the formation of weld deposits of various classes: austenite, martensite, and austenitic-martensitic steels with carbide, carboboride and carbonitride hardening, alloyed cast iron, and composite materials. The amount (volume) of the carbides formed and their structure, composition, and homogeneity region determine the nature of the strengthening of the weld metal and thus its service characteristics. Consequently, modeling of the carbide-formation processes in a weld deposit for the purpose of predicting the composition and amount of the strengthening phases formed is of current interest.

Physicochemical analysis of carbide-formation processes

The carbides in an iron-carbon weld deposit are compounds of carbon with iron and other transition metals (d elements) that have smaller atomic numbers than iron. It has been established [1-3] that the following carbide compounds can form in steels:

  1. Group I carbides – Fe3C, Mn3C, Cr23C6, Cr7C3, Fe3Mo3C, Fe3W3C.
  2. Group II carbides (interstitial phases) – Mo2C, W2C, WC, VC, TiC, NbC, TaC, Ta2C, ZrC.

However, the carbides just listed do not exist in their pure forms in steels. Carbides of all alloying elements contain iron, and when several carbide-forming elements are present, the carbides contain all of those elements. For example, in chrome-manganese steel, a carbide with the formula (Cr, Mn Fe)23C6, which contains iron and manganese, forms instead of the pure carbide Cr23C6.

It has been noted that carbides which have the same general chemical formula dissolve in one another [1-4]. For example, when titanium and niobium are simultaneously present in steel, one combined carbide containing titanium and niobium “in equal proportions,” rather than two separate carbide species, forms. Therefore, there are fewer possible carbide-formation variations than was indicated above, and, in fact, we encounter only carbides of six types in steels:

  1. Group I carbides – M3C, M23C6, M7C3, M6C.
  2. Group II carbides – MC, M2C.

Here M denotes the sum of the carbide-forming (metallic) elements. The ratio between the metallic elements and carbon (for a perfect lattice) is indicated by the formula.

The carbides assigned to group I have a complex crystal structure. Cementite is a typical representative of the carbides of this type.

One special feature of the structure of the group II carbides as interstitial phases is that they have a simple crystal lattice and usually crystallize with a significant carbon deficiency.

It should be noted that interstitial phases are difficultly soluble in austenite [1-4]. This means that upon heating (even to a very high temperature) a significant portion does not pass into the solid solution. This distinguishes them from the group I carbides, which readily dissolve in austenite upon heating. All carbide phases have a high melting point and a high hardness. In this respect, the interstitial phases surpass the group I carbides.

To understand the mechanism of carbide formation in an iron-carbon weld deposit during nonequilibirum crystallization of the weld pool, we must first have a picture of the carbide-forming elements or d metals themselves.

The d elements are known to include elements whose atoms contain valence electrons in their (n–1)d and ns levels and comprise the secondary (IIIB-VIIB, IB, IIB) subgroups, occupying an intermediate position between typical s metals (IA, IIA) and p elements. The electronic structure of the atoms of d elements determines their chemical properties. As the number of d elements increases along a period, they can undergo transitions from one level to another to achieve one of the most stable configurations (d5 or d10) required by Hund's rules [5-8]. Such transitions occur, for example, in the case of Cr(3d54s1) and Mo(4d55s1).

We note several special features of the d elements that are not shared by elements of the major groups [5-8]:

  1. In the d elements, only a small fraction of the valence electrons are delocalized over the entire crystal (while in the alkaline and alkaline-earth metals, the valence electrons are all donated for collective use). The remaining d electrons participate in the formation of directed covalent bonds between neighboring atoms. Thus, these elements have covalent-metallic bonding, rather than purely metallic bonding, in the crystalline state. Therefore, they are all solid (except Hg) and high-melting (with the exception of Zn and Cd) metals. The metals of the VB and VIB subgroups have the highest melting points. In these elements, the d sublevel is half-filled with electrons, and the highest possible number of unpaired electrons and the largest number of covalent bonds are achieved. Further filling results in a decrease in the number of covalent bonds and a drop in the melting point.
  2. As a consequence of the incomplete filling of the d orbitals and the presence of unfilled ns and np levels that are close in energy, d elements tend to form complexes. Their complex compounds are generally colored and paramagnetic.
  3. The d elements form compounds of variable composition (oxides, hydrides, carbides, silicides, nitrides, and borides). Compounds of variable composition are characterized by the following features:

a)The composition of these compounds depends on the way in which they formed. For example, depending on the synthesis conditions, titanium oxides have the formulas TiO1.21.5 and TiO1.9-2.0, titanium carbide and vanadium carbides have the formulas TiC0.6-1.0 and VC0.581.09, titanium nitride has the formula TiN0.45-1.00.

b)The compounds generally have a broad homogeneity region. For example, as follows from its formula, TiC0.6-1.0 maintains the titanium carbide lattice even when there is a 40% shortage of carbon atoms in it.

c)The nature of the bonding in these compounds has not been adequately studied and is determined by the degree of filling of the d orbitals of the metal. The electrons of the nonmetal presumably fill the vacant d orbitals with a resultant increase in the degree of covalent character of the bonds. The occurrence of covalent bonding in them is confirmed by the larger positive heats of formation, higher hardness and melting points, and lower electrical conductivity of these compounds in comparison to the metals forming them.

Carbides, which are typical representatives of these compounds, form when d metals react with carbon. The factors influencing carbide formation can be divided into two groups:

1)physicochemical, which determine the nature of the carbide-formation process itself;

2)technological, which indirectly influence the carbide-formation process by altering parameters of the former group.

Let us examine these groups of factors in somewhat greater detail. First, we must take into account the concentration of each carbide-forming element and its chemical affinity to carbon. The latter is determined by the change in the Gibbs free energy upon formation of the particular carbide under standard conditions. The value of is related to the equilibrium constant of the corresponding carbide-formation reaction by the familiar relation

.(1)

This value of corresponds to the equilibrium, i.e., limiting, concentration of the carbide formed. Since the formation of different carbides of the same element is possible, the order of their formation and the ratio between the concentrations of the carbides formed in the equilibrium state is also determined by the affinity of the element to carbon. Of course, the values of and, accordingly, of are temperature-dependent, as is illustrated by the presence of different stable phases on the binary phase diagram of the carbide-forming-element/carbon system.

However, in a fast welding process, during which melting, the chemical reaction between the phases, and crystallization take place with high rates, an equilibrium state is generally not attained. Therefore, we should take into account kinetic factors, among which we should include the rate constant of the purely chemical step of the heterogeneous carbide-formation reaction, as well as the diffusion coefficients of carbon () and the carbide-forming element ().

The corresponding reaction step can be represented in the simplified form

.(2)

It should be recalled that the rate of a reaction is determined not only by the kinetic constants, , and , but also by how far the state of the system is from equilibrium and, when liquid phases are involved, by the hydrodynamic conditions of the process.

To obtain a more complete picture of the mechanism of carbide formation, let us analyze the electronic structure of d metals and carbides.

The band structure of transition metals has several special features that are related to the presence of unfilled d orbitals [3-8]. When these metals form a crystal lattice, the outer s electrons are completely delocalized. In contrast, the wave functions of the d electrons remain concentrated in the cores of the atoms. However, the crystal field lowers the potential barrier in the interstitial regions of the lattice, providing for the tunneling of some of the d electrons through the potential barrier and the formation of narrow d bands. The width of the d bands formed is of great significance because these bands determine the nature of the binding of electrons and the binding energy in d metals. As we know, the band width depends on the value of the exchange integral Ae according to the expression [7, 8]

,(3)

and the exchange integral increases with increasing values of the principal quantum number n. Thus, the higher is the number of the d sublevel in the expression nd, the higher is the value of the exchange integral and the broader is the d band.If the number of d electrons does not exceed five, electrons fill the lower part of the band, providing a gain in binding energy. This gain is higher, the broader is the band. If the number of d electrons exceeds five, electrons begin to fill the upper part of the band, and the energy gain decreases. Thus, for d metals, the binding energy increases with increasing period (with increasing atomic radius) as long as the number of d electrons does not exceed five. Therefore, the d metals with the largest atomic radii and three or four electrons in the d sublevel form the strongest bonds. Taking into account that only some of the d electrons participate in the formation of the d bands (in metallic bonding), we must assume that there is covalent bonding in transition metals, which further increases the binding energy. This accounts, for example, for the high melting points of tantalum and tungsten. When carbon is inserted into the crystal lattice of a transition metal, the formation of carbides of two types is possible (in accordance with Hagg's rule [1, 2, 4]). If the ratio of the atomic radius of carbon to the atomic radius of the metal is less than 0.59, so-called interstitial phases having the lattice of the solvent metal form. Otherwise, carbides of complex composition with a crystal lattice differing from the lattice of the solvent metal form. These carbides are characteristic of chromium, manganese, and iron, which have five or more d electrons. They have lower melting points and hardness than do carbides of the first group. Carbon atoms occupy tetrahedral or octahedral cavities, depending on the type of crystal lattice. When a carbon atom enters the crystal field of the lattice of a d metal, it experiences the coordinating action of an atom of the d metal. This effect is stronger, the higher is the number of the d sublevel of the metal and the smaller is the number of electrons filling the d sublevel. A covalent bond forms between the carbon atom and the metal atom according to a donor–acceptor mechanism, i.e., carbides form. The carbon atom, in turn, acts on the coordinating atom and removes the degeneracy in the d sublevel, splitting it into two new levels: eg and t2g [2, 3]. This accelerates the chemical reaction and provides an additional gain in binding energy. The smaller is the occupancy of the degenerate d sublevel (before it splits), the greater is the gain in binding energy [7, 8].

Carbide-forming ability (CFA) of the i-th d metal. Modeling of the carbide-formation processes in a weld deposit

Based on the foregoing physicochemical analysis of the carbide-formation processes accompanying the primary and secondary crystallization of a weld metal with reliance on quantum-chemical theories that depict the structure of transition metals (d metals) and carbides as compounds of carbon with d metals, we may assert that the amount of carbon that is used to form the carbide of the i-th d metal is proportional to the atomic radius of the metal (Ri) and is inversely proportional to the number of electrons in the d sublevel of the metal. We introduce the concept of the absolute carbide-forming ability (CFA) of the i-th d metal and represent it as

.(4)

It follows from an analysis of (4) that the carbide-forming ability increases along the series consisting of Fe, Mn, Cr, Mo, W, Nb, V, Ta, Ti, Zr, and Hf, in good agreement with the empirical results in [1-4] and with the calculations of the temperature dependence of the chemical affinity of these elements toward carbon performed within the present study for individual carbide-formation reactions (Fig. 1). At the same time, this series specifies the thermal stability of carbides in alloys. Table1 contains general data on the d elements and their carbide-forming ability.

The distribution of carbon and alloying elements between austenite and the carbides formed should be elucidated. We shall assume that carbide-forming elements tend to bind all the carbon in carbides in accordance with their carbide-forming ability (4).

Fig. 1. Temperature dependence of the change in the standard Gibbs free energy ΔG0, kJ/mol, for carbide-formation reactions.

The amount of carbon bound by any particular carbide-forming element will follow from the stoichiometry of the compound (MexCy). It is reasonable to assume that only the portion of the alloying elements and carbon that cannot be dissolved in austenite at a given temperature is used in carbide formation. That is, the quantity of the alloying element that can be bound in a carbide by the carbon not dissolved in austenite will be used in carbide formation. We shall assume that the distribution of carbon between the carbide phases in an alloy will be proportional to the relative carbide-forming ability of the respective transition element and its atomic concentration in the alloy ai (n is the number of alloying elements in the alloy).

The principles formulated above underlie the phenomenological model of carbide formation that we developed in [9]. The model takes into account the participation of a portion of the alloying d elements and carbon in carbide formation during the primary and secondary crystallization of a weld deposit and permits prediction of the quantitative and qualitative composition of the strengthening phases (carbides). The model is an integral part of the general phenomenological model of the nonequilibrium crystallization of the molten metal in a weld pool described in [9,10], which was used to create a closed algorithm and a computer-aided design system for advanced welding and hardfacing materials [11-14]. The computer-aided design system developed, whose core component is an expert system, permits the solution of a large set of scientific and practical problems, including:

  • modeling of the nonequilibrium crystallization of multicomponnet molten metals with a broad alloying range for various types of fusion welding and for the manufacture of small-sized casts;
  • modeling of the formation of strengthening phases during the nonequilibrium crystallization of multicomponnet molten metals with a broad alloying range;
  • prediction of the composition, structure, and properties of the crystallized weld metal and the metal in small-sized casts;
  • designing new welding and hardfacing matierals for welding steels and iron-based alloys and for producing special protective coatings.

The system significantly shortens the time needed to develop welding and hardfacing materials for the production of intricate welded metal assemblies and multifunctional casts.

CONCLUSION

The principles governing carbide formation in an iron-carbon alloyed weld deposit during nonequilibrium crystallization have been formulated on the basis of a physicochemical analysis of the formation of primary carbides as compounds of carbon with d metals using quantum-chemical theories of the electronic structure of d metals and carbides. These principles provide a basis for the assumption that the amount of carbon that is used to form the carbide of the i-th d metal is proportional to the atomic radius of the metal (Ri) and is inversely proportional to the number of electrons in the d sublevel of the metal (di). The concept of the carbide-forming ability of d elements has been introduced, and a carbide-formation series based on it has been given. These principles underlie the phenomenological model of carbide formation that we developed.