CARBIDE FORMATION DURING CRYSTALLIZATION UPON WELDING
V. Mazurovsky1, M. Zinigrad1, L. Leontiev2, and V. Lisin2
1
Materials Research Center, College of Judea and Samaria, Ariel, Israel
2
Institute 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.
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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 [14]. 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 covalentmetallic 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 halffilled 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 TiO1.2-1.5 and TiO1.9-2.0, titanium
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carbide and vanadium carbides have the formulas TiC0.6-1.0 and
VC0.58-1.09, 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 G 0 upon formation of the particular carbide under standard conditions. The
value of G 0 is related to the equilibrium constant K eq of the corresponding
carbide-formation reaction by the familiar relation
(1)
G 0  RT ln K eq .
This value of G 0 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 G 0 and, accordingly, of K eq 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 K C of the purely
chemical step of the heterogeneous carbide-formation reaction, as well as the
diffusion coefficients of carbon ( DC ) and the carbide-forming element ( DEi ).
The corresponding reaction step can be represented in the simplified form
xEi  yC  ( Ei ) x C y .
(2)
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It should be recalled that the rate of a reaction is determined not only by the
kinetic constants K C , DC , and DEi , 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)
Ed  12 Ae ,
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].
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Carbide-forming ability (CFA) of the i-th d metal. Modeling of the carbideformation 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
R
(4)
i  i .
di
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.
Table 1 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).
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ΔG0, kJ/ mol
50
Cr23C6
0
HfC
Ta2C
ZrC
Nb2C
Cr7C3
-50
TiC
V2C
TaC
NbC
Mn7C3
Cr4C
-100
VC
Mo2C
WC
W2C
Mn3C
-150
MoC
Fe3C
Fe3(alfa)C
Ni3C
-200
-250
0
200
400
600
800
1000
1200
1400
1600
1800
T, K
,K
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 n i and its atomic
 i
i 1
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
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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:
o 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;
o modeling of the formation of strengthening phases during the
nonequilibrium crystallization of multicomponnet molten metals with a
broad alloying range;
o prediction of the composition, structure, and properties of the
crystallized weld metal and the metal in small-sized casts;
o 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.
α→γ
912
γ→α(δ)
1394
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BCC(α)
2,861
FCC(γ)
3,564
CFA
Lattice parameter, Å
1536
Crystal lattice structure
1,26
Transformation
Electron configuration
3d64s2
Melting point
26
Temperature, Со
Atomic radius, Å
Fe
Atomic number
The element
Table 1. Some properties of carbide-forming elements
0,210
Mn
25
3d54s2
1,27
1245
α→β
727
β→γ
1100
γ→δ
1138
SC(α)
8,894
SC(β)
6,300
FCC (γ)
3,774
BCC (δ)
3,720
0,254
Cr
24
3d54s1
1,28
1875
BCC
2,885
0,256
Mo
42
4d55s1
1,39
2620
BCC
3,140
0,278
W
74
5d46s2
1,39
3380
BCC
3,160
0,347
Nb
41
4d45s1
1,46
2468
BCC
3,294
0,365
V
23
3d34s2
1,34
1919
BCC
3,034
0,447
Ta
73
5d36s2
1,46
2996
BCC
3,296
0,487
HCP(α)
22
2
a = 2,945
c = 4,667
BCC (β)
3,313
HCP (α)
a = 3,223
c = 5,123
Ti
Zr
Hf
40
72
2
3d 4s
4d25s2
5d26s2
1,45
1,59
1,59
1688
1852
2231
α→β
882
α→β
865
α→β
1743
BCC (β)
3,61
HCP (α)
a = 3,197
c = 5,057
BCC (β)
3,615
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