3.1 Atomic Structure, Bonding & Solid-Solution Thermodynamics

3.1 Atomic Structure, Periodic Trends & Chemical Bonding in Alloys

Welding metallurgy operates at the intersection of quantum chemistry, thermodynamics, and solid-state physics. Every arc phenomenon, molten slag-metal partition reaction, solidification structure, and solid-state phase transformation originates from the electronic structure of the participating atoms and the nature of their interatomic bonds.

---

1. Atomic Structure & Electronic Configurations of Transition Metals

An atom is defined by its atomic number $Z$ (number of protons in the nucleus) and its mass number $A$ (total protons plus neutrons). For welding engineers, the distribution of electrons within principal quantum shells ($n = 1, 2, 3, 4\dots$) and subshells ($s, p, d, f$) dictates chemical bonding, magnetic behavior, and alloying characteristics.

Electrons occupy orbitals following three fundamental principles:

1. Aufbau Principle: Orbitals fill in order of increasing energy levels ($1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d$).
2. Pauli Exclusion Principle: No two electrons in an atom can possess identical sets of four quantum numbers; an orbital holds a maximum of two electrons with opposing spins ($+\frac{1}{2}, -\frac{1}{2}$).
3. Hund's Rule of Maximum Multiplicity: Orbitals of equal energy (degenerate orbitals) are each occupied by one electron with parallel spins before any orbital receives a second electron.

In the first transition series (Period 4), the $4s$ subshell fills before the $3d$ subshell because the spherical $4s$ orbital has a higher probability density near the nucleus, lowering its electrostatic energy. However, once the $3d$ orbitals begin filling, their energy drops below that of $4s$. Transition metals exhibit valence electrons in both their outermost $s$ shell and their incompletely filled $(n-1)d$ subshell.

Element      Z    Ground-State Electron Configuration       Unpaired 3d Electrons
Titanium    22    [Ar] 3d² 4s²                               2
Vanadium    23    [Ar] 3d³ 4s²                               3
Chromium    24    [Ar] 3d⁵ 4s¹  (half-filled stability)      5
Manganese   25    [Ar] 3d⁵ 4s²                               5
Iron        26    [Ar] 3d⁶ 4s²                               4
Cobalt      27    [Ar] 3d⁷ 4s²                               3
Nickel      28    [Ar] 3d⁸ 4s²                               2
Copper      29    [Ar] 3d¹⁰ 4s¹ (completely filled d shell)  0
Molybdenum  42    [Kr] 4d⁵ 5s¹                               5

The Role of Partially Filled d-Orbitals

The incompletely filled $d$-orbitals of transition metals give rise to several critical welding behaviors:

• Variable Oxidation States: Iron readily shifts between $\text{Fe}^{0}$ (metallic), $\text{Fe}^{2+}$ (ferrous, as in $\text{FeO}$), and $\text{Fe}^{3+}$ (ferric, as in $\text{Fe}_2\text{O}_3$). Chromium displays states from $+2$ to $+6$, and manganese operates from $+2$ to $+7$. These multi-valent capabilities drive oxidation-reduction reactions between the molten weld pool and covering slag.
• Strong Metallic Cohesion: Delocalization of both $4s$ and $3d$ electrons produces intense interatomic bonding, resulting in high melting points ($T_m$ of $\text{Fe} = 1538^\circ\text{C}$, $\text{Cr} = 1907^\circ\text{C}$, $\text{Mo} = 2623^\circ\text{C}$) and substantial cohesive lattice energy.
• Catalytic Dissociation: Transition metal surfaces act as catalysts that lower the activation energy for the dissociation of diatomic shielding gases ($\text{H}_2, \text{N}_2, \text{O}_2$) at the arc-metal interface.

---

2. Chemical Bonding Mechanisms in Weldments

Interatomic bonding in welded joints and consumables spans three primary classifications: metallic, covalent, and ionic.

Bond Type     Electron Distribution            Typical Occurrence in Welding          Key Engineering Attributes
Metallic      Delocalized electron sea         Base metal and weld bead matrix         High electrical/thermal conduction,
              shared across lattice ions       (Fe-Cr-Ni, Al, Cu, Ti)                  dislocation mobility, ductility

Covalent      Localized, highly directional    Precipitates and non-metallic           High hardness, extreme melting point,
              shared electron pairs            inclusions (TiC, NbC, TiN, SiC, Fe₃C)   brittle cleavage, high Peierls barrier

Ionic         Electrostatic transfer of        Welding flux systems and slag           Molten ionic conduction (ESW),
electrons (cations/anions)      components (CaO, CaF₂, MgO, BaO, Al₂O₃) high slag viscosity control, cleavage

Metallic Bonding & Dislocation Plasticity

In metallic crystals, positively charged ion cores are immersed in a pervasive, delocalized "electron sea." Because the bonding forces are non-directional, atoms can slide past one another under shear stress without disrupting electrostatic cohesion. This low Peierls-Nabarro lattice friction stress facilitates dislocation glide, providing the macroscopic ductility, high toughness, and formability required for structural weldments. The free electrons also provide the thermal and electrical conductivities essential for resistance welding and electric arc operation.

Covalent Bonding in Inclusions and Microconstituents

Covalent bonds involve quantum-mechanical hybridization of atomic orbitals ($sp, sp^2, sp^3, d^2sp^3$) to share localized electron pairs. Because these bonds possess strict directional orientation, displacing atoms requires breaking high-energy orbital overlaps. Consequently, covalent compounds exhibit extreme hardness, high melting points, and minimal dislocation mobility at room temperature.

In microalloyed steel weldments, covalent precipitates such as titanium nitride ($\text{TiN}$), niobium carbide ($\text{NbC}$), and vanadium carbonitride ($\text{V(C,N)}$) play dual roles:

• Grain Boundary Pinning: Fine, nanoscale covalent particles ($10\text{--}50\text{ nm}$) resist coarsening up to $1350^\circ\text{C}$, pinning prior austenite grain boundaries via Zener drag and preventing grain growth in the heat-affected zone (HAZ).
• Cleavage Initiation: Coarse, angular covalent inclusions ($> 1\ \mu\text{m}$), such as primary $\text{TiN}$ cubes formed in the liquid puddle, act as stress concentrators that trigger microcracks under impact loading, degrading low-temperature fracture toughness.

Ionic Bonding in Slags and Flux Formulations

Ionic bonding arises from the electrostatic Coulomb attraction between positively charged metal cations (e.g., $\text{Ca}^{2+}, \text{Mg}^{2+}, \text{Na}^{+}$) and negatively charged anions (e.g., $\text{O}^{2-}, \text{F}^{-}$). Ionic compounds form rigid crystalline lattices that are electrical insulators at room temperature. However, upon melting in the welding arc, the ionic lattice dissociates into mobile, liquid ions: $\text{CaF}_2(l) \longrightarrow \text{Ca}^{2+} + 2\text{F}^- \qquad \text{CaO}(l) \longrightarrow \text{Ca}^{2+} + \text{O}^{2-}$

This molten dissociation enables electroslag welding (ESW) and electroslag remelting (ESR), where resistive heat generation depends directly on the ionic conductivity of the molten slag pool.

Pauling established that no bond between dissimilar elements is purely ionic or purely covalent; instead, bonds exhibit a degree of ionic character that depends on the electronegativity difference $\Delta \chi$: $\text{Fractional Ionic Character} = 1 - \exp\left[-0.25(\chi_A - \chi_B)^2\right]$ When $\Delta \chi > 1.7$, the bond possesses greater than 50% ionic character (e.g., in $\text{CaO}$, $\Delta \chi = 3.44 - 1.00 = 2.44$, yielding $\sim 77%$ ionic character).

---

3. Periodic Trends & Welding Arc Physics

Predicting metallurgical reactions requires mastery of three periodic properties:

Periodic Property       Definition                                     Periodic Trend                     Direct Impact on Welding Systems
Electronegativity (χ)   Tendency of an atom to attract shared electrons Increases across a period;       Governs deoxidation hierarchy, oxide
                        in a chemical bond (Pauling scale)             decreases down a group             inclusion stability, and flux basicity

Atomic Radius (r)       Half the internuclear distance between identical Decreases across a period (Z_eff); Dictates solid solution solubility limits
                        neighboring atoms in a crystal lattice         increases down a group (shells)    (Hume-Rothery rules) and lattice strain

First Ionization        Minimum energy required to remove the most     Increases across a period;         Controls arc initiation, arc column
Potential (IP)          loosely bound valence electron from gas atom   decreases down a group             breakdown voltage, and cathode stability

Ionization Potential and Arc Stabilization

The first ionization potential determines how readily an atom sheds an electron to generate free charge carriers (electrons and ions) within the arc column plasma. Shielding gases such as helium ($24.59\text{ eV}$) and argon ($15.76\text{ eV}$) have high ionization potentials, requiring high open-circuit voltages ($60\text{--}80\text{ V}$) and high-frequency discharge to ignite an arc.

In contrast, flux coatings for Shielded Metal Arc Welding (SMAW) and Flux-Cored Arc Welding (FCAW) incorporate compounds containing alkali and alkaline earth metals:

• Potassium ($K$): $\text{IP} = 4.34\text{ eV}$ (added as potassium silicate, $\text{K}_2\text{SiO}_3$, in AWS E7018 and EXX16/EXX18 electrodes)
• Sodium ($Na$): $\text{IP} = 5.14\text{ eV}$ (added as sodium silicate, $\text{Na}_2\text{SiO}_3$, in EXX15 electrodes)
• Cesium ($Cs$): $\text{IP} = 3.89\text{ eV}$ (experimental and high-stability arc applications)

Because of their low ionization potentials, these elements ionize thermally within the outer periphery of the arc column at modest temperatures ($2500\text{--}4000\text{ K}$). This continuous release of free electrons maintains electrical conductivity across the electrode gap, stabilizing cathode roots, minimizing spatter, and enabling alternating current (AC) welding by sustaining arc reignition as voltage cycles through zero.

---

4. Solid Solution Thermodynamics: Substitutional vs. Interstitial

When alloying elements dissolve into a base metal matrix, they form solid solutions classified by crystallographic occupancy into substitutional or interstitial types.

Parameter             Substitutional Solid Solutions                     Interstitial Solid Solutions
Solute Location       Replaces solvent atom on regular lattice sites    Occupies interatomic void spaces (octahedral/tetrahedral)
Solute Elements       Ni, Cr, Mo, Mn, V, Cu in Iron                     H, C, N, O, B in Iron
Solute Radius (r)     Comparable to solvent (r_solute ≈ r_Fe)           Much smaller than solvent (r_solute / r_Fe < 0.59)
Lattice Distortion    Moderate, spherically symmetric                   Severe, anisotropic (asymmetric tetragonal distortion in BCC)
Strengthening Effect  Moderate solid solution strengthening             Potent strengthening per atom; drives strain aging and quench hardening

Hume-Rothery Rules for Substitutional Solid Solubility

Extensive or complete substitutional solid solubility (such as the continuous solid solution observed in the copper-nickel or iron-chromium systems at elevated temperatures) requires satisfaction of four empirical criteria established by William Hume-Rothery:

1. Atomic Size Factor: The atomic radius of solute and solvent must not differ by more than 15%: $\delta = \frac{|r_{\text{solute}} - r_{\text{solvent}}|}{r_{\text{solvent}}} \times 100\% \le 15\%$ If $\delta > 15%$, lattice strain energy exceeds the chemical driving force, and substitutional solubility is severely restricted (typically $< 1\text{ at}%$).
2. Crystal Structure Rule: Solute and solvent must possess identical crystal lattices (e.g., both Face-Centered Cubic [FCC] or both Body-Centered Cubic [BCC]) for complete isomorphous solubility across all compositions.
3. Electronegativity Difference: Solute and solvent must have similar electronegativities ($\Delta \chi < 0.4$). Large electronegativity differences promote the formation of stable, brittle intermetallic compounds (e.g., sigma phase $\text{FeCr}$, or $\text{Fe}_2\text{Ti}$) rather than an extensive solid solution.
4. Relative Valency Factor: A metal dissolves a solute of higher valency more readily than one of lower valency. For example, aluminum ($+3$) dissolves more zinc ($+2$) than zinc dissolves aluminum.

Interstitial Solid Solutions: Hagg's Rule and Iron Crystallography

Interstitial solid solutions occur when small non-metallic or metalloid atoms fit into the interstitial spaces between solvent atoms. Gunnar Hägg established that interstitial phases form only when the ratio of solute radius to solvent radius is less than 0.59: $\frac{r_{\text{solute}}}{r_{\text{solvent}}} < 0.59$ In iron ($r_{\text{Fe}} = 1.26\ \text{Å} = 0.126\text{ nm}$):

• Hydrogen ($H$): $r = 0.37\ \text{Å} \implies r/r_{\text{Fe}} = 0.29$
• Carbon ($C$): $r = 0.77\ \text{Å} \implies r/r_{\text{Fe}} = 0.61$ (slightly above the strict 0.59 threshold, forcing extreme lattice strain)
• Nitrogen ($N$): $r = 0.74\ \text{Å} \implies r/r_{\text{Fe}} = 0.59$
• Oxygen ($O$): $r = 0.66\ \text{Å} \implies r/r_{\text{Fe}} = 0.52$

Octahedral vs. Tetrahedral Interstice Occupancy in Iron

The behavior of interstitial solutes in iron depends heavily on the host crystal structure:

Crystal Phase     Structure  Packing Factor  Octahedral Void Radius  Tetrahedral Void Radius  Max Carbon Solubility (T)
Austenite (γ-Fe)  FCC        0.74            0.52 Å (0.414 · r_Fe)   0.28 Å (0.225 · r_Fe)    2.14 wt% (1147°C) / 0.77 wt% (727°C)
Ferrite (α-Fe)    BCC        0.68            0.19 Å (0.154 · r_Fe)   0.36 Å (0.291 · r_Fe)    0.022 wt% (727°C) / 0.005 wt% (20°C)

In FCC austenite, the largest void is the octahedral site ($r_{\text{void}} = 0.52\ \text{Å}$), located at the center of the unit cell and the midpoints of the cube edges. The void is spherically symmetric, surrounded by six equidistant iron atoms. Although a carbon atom ($0.77\ \text{Å}$) dilates the cell, the strain is isotropic and distributed evenly, permitting up to $2.14\text{ wt}%$ carbon solubility.

In BCC ferrite, the crystal packing factor ($0.68$) is lower than FCC ($0.74$), meaning BCC has more total empty space. However, that empty space is divided into smaller individual pockets. The tetrahedral site in BCC is geometrically larger ($r_{\text{void}} = 0.36\ \text{Å}$) than the octahedral site ($r_{\text{void}} = 0.19\ \text{Å}$).

Yet, carbon and nitrogen preferentially occupy the smaller octahedral sites in BCC ferrite. The octahedral site in BCC is located at the face centers and edge centers. It is bounded by two iron atoms at an extremely close distance of $a/2 = 1.43\ \text{Å}$ along the $[001]$ direction, and four iron atoms at a farther distance of $a/\sqrt{2} = 2.03\ \text{Å}$ in the $(001)$ plane.

Displacing only two collinear iron atoms requires less elastic strain energy than symmetrically displacing four atoms in tetrahedral coordination. However, this asymmetric displacement forces severe unidirectional expansion along a single cube axis ($c$-axis), causing tetragonal distortion. When austenite transforms diffusionlessly to martensite during rapid weld cooling, this trapped carbon locks the lattice into a Body-Centered Tetragonal (BCT) configuration with exceptional hardness and high susceptibility to hydrogen-induced cold cracking (HICC).

---