Metallurgical Analysis

The mounted samples were ground by P100, P600, P800, P1000, P1200, P1500 and P2000 grinding-paper. After polished by 1μm, 0.3μm and 0.05μm

alumina abrasives, the arc bead samples were mechanically ground and soaked for 60 s in an etchant solution [25% ammonium hydroxide (5 mL), 30% hydrogen peroxide (2 mL), pure water (5 mL)]. The samples were removed for cleaning and drying and then a metallurgical microscope was used to observe the morphologies of the cross sections of the arc bead samples.

The samples were obtained from two ends of the load-side wire at short circuit site. In the metallography observation of the cross sections of the samples through metallurgical microscope, the λ values of samples were measured for every sample at 5 sites by magnified 100× object lens. The sampling number, N, was more than 100 times for the FCAB at each wire diameter. Finally, the average λ value of FCABs at each diameter, λɑve, and the standard deviations,

√ ∑ , are calculated.

Chapter 4 Results

4.1 Experimental Observation

When the power supply was turned on, the two copper wires sparked instantly due to the short circuit, until the short-circuit current blew out the two conductors. The arc bead samples were obtained from the blown part of the wire.

As copper wires were short-circuited and blown out, the melted copper liquid formed arc beads and marks at the blown part of the wire under the effect of surface tension [40].

4.2 Classified Generalization

The exterior morphologies of the samples were investigated preliminarily using the field-emission SEM. In the solidification process, the FCABs can be divided into the non-faceted and the faceted surfaces of FCABs, namely, the two molten marks at ambient atmosphere.

4.2.1 FCABs with Non-faceted Surface

4.2.1.1 XRD Analysis

The XRD patterns of the non-faceted surface FCABs (Figure 4-1) reveal that the peaks at the 2θ values of 43.33°, 50.47°, and 74.20° pertain to the copper planes of (111), (200), and (220), respectively. Because the growth rates of high-index planes with high surface energy were quicker than those of low-index planes in the solidified copper, the low-index planes of copper were left in the final solidification. The peak at a value of 2θ of 50.47° was the strongest, suggesting that the (200) plane was the preferred crystallographic plane.

4.2.1.2 FIB-SEM conduct

The surface morphologies of the arc bead samples exhibited the single-phase growth of primary dendritic crystals. Figure 4-2 reveals that the primary dendrites possessed a non-faceted growth surface morphology, with outward growth derived from the unfused wire [41]. We used a FIB for ion-bombardment cutting of the primary dendrite tips to prepare TEM specimens.

4.2.1.3 TEM-EDS Analysis

We used EDS to analyze the element of the primary dendrite tips specimen.

The main element in the primary crystal specimens was copper (Figure 4-3a). We employed electron diffraction through TEM for structural analysis of the primary crystal specimens (Figures 4-3b.c.d), measuring the values of L and θ from the diffraction pattern and calculating the corresponding plane indices (hkl) from Equations (1)–(4). Matching the data from JCPDS cards to the inter-planar spacing confirmed that the primary crystal was a copper phase with a face-centered cubic crystal structure and a lattice constant of 0.3615 nm (Table 4-1).

4.2.1.4 Metallurgical Analysis

From the metallography microscope of the load-side FCABs with non-faceted surface, the internal microstructure constituted by the columnar crystalline structure is displayed in Figure 4-4.

We repeated the short-circuit experiments 10 times for each wire diameter.

The samples were obtained from the short-circuit site at two ends of the load-side wire. We used metallography to measure the values of λ of the FCABs at five sites for each sample as shown in Figure 4-5. The sampling number, N, was more than 100 for the FCABs at each wire diameter. Table 4-2 lists the average value of λ of the FCABs at each diameter, λɑve, and the standard deviations, √ ∑ , are calculated.

4.2.1.5 A Section Result

Although plate-like primary crystallites are often observed during solid-state precipitation, the primary crystallites in our present experiment grew into rod-like shapes. The conducting wire was a good thermal extracting material. Heat from the melted copper liquid was extracted into the super-cooled melt through a conduction effect; the solid-liquid interface generated a temperature inversion [42, 43]. As the latent heat was released from the solid-liquid interface, the temperature at the interface became hotter than that on the liquid side. Therefore, an unstable interface appeared because the interface front produced a negative temperature gradient that led to part of the heat flowing toward the super-cooled liquid [44].

When the crystallization of copper occurred toward the super-cooled liquid region, the primary dendrites crystallized rapidly in rod-like form, while the secondary branch cell body grew in the <001> preferred direction, out of the surface where the primary trunk contacted the super-cooled liquid. The latent heat released from the dendrite growth of the secondary branch increased the temperature of the liquid nearby obstructing the formation of other protruding interfaces [45]. As a result, the secondary branch dendrites competed with, and restricted, one another in terms of their growth. The direction anti-parallel to the heat flow became the dominant growth direction. Therefore, the primary trunks of the thermal dendrites grew in a parallel manner to form the columnar crystalline structure displayed in Figure 4-4. The formation of thermal dendrites is the unique fingerprint of FCABs with non-faceted surface in the load-side wire.

Via the above-mentioned experimental result, the FCABs with non-faceted surface is non-permeated by oxygen. Their internal microstructure is constituted by the thermal dendrites of copper.

4.2.2 FCABs with Faceted Surface

4.2.2.1 XRD Analysis

The XRD patterns of the faceted surface FCABs (Figure 4-6) reveal that the peaks at values of 2θ = 29.549°, 36.413°, 61.349° and 73.534° are respectively belonged to the plane indexes of Cu2O (110), (111), (220) and (311); and the peak at 2θ=43.552° is pertaining to Cu (111). Because the growth rates of high-index planes with high surface energy were quicker than those of low-index planes in the

solidified copper, the low-index planes of copper were left in the final solidification.

4.2.2.2 FIB-SEM Conduct

By using FIB-SEM to observe the microstructure constituents of those load side FCAB samples, which exhibit the faceted morphology layer on the surface of the samples, and the faceted layer is about 6μm thick (Fig. 4-7a.b). The microstructure under the faceted layer is a mixture consisted of two microstructure constituents, namely poly-phase eutectic structure (Fig. 4-7b, 4-8a) and dendrite with surface precipitate (Fig. 4-9a). The poly-phase eutectic structure is characterized by two phases, which are rod-shaped phase and a matrix of continuous phase.

Gallium ion beam was used for bombardment cutting on the surface layer (Fig. 4-7b); the eutectic structure (Fig. 4-8a), and the dendrite tip with precipitate (Fig. 4-9a) of above FCAB samples for TEM analysis sampling.

4.2.2.3 TEM-EDS Analysis

Gallium ion beam was used for bombardment cutting on the surface layer of above FCAB samples for TEM analysis sampling (Fig. 4-7b). According to EDS analysis, the surface layer specimen of arc bead is composed of copper and oxygen elements (Fig. 4-7c). TEM electron diffraction analysis was also conducted on the specimen (Fig. 4-7f). By checking JCPDS cards corresponding inter-planar

spacing, it was found that the faceted layer on the surface of the arc bead samples is the cuprous oxide of lattice constant 0.4269 nm with simple cubic structure.

In Figure 4-8a, the poly-phase eutectic structure under the cuprous oxide layer of the arc bead samples was observed by FIB-SEM. From TEM electron diffraction results, Fig. 4-8c, 4-8d and 4-8e, the eutectic matrix is the Cu phase with a face-centered cubic structure, and a lattice constant of 0.3613 nm, and the rod-shaped phase is the cuprous oxide with a simple cubic structure, Fig. 4-8g, 4-8h, 4-8i, at a lattice constant of 0.4269 nm. The corresponding EDS spectrum, Fig. 4-8b and 4-8f, also confirmed the chemical composition of the eutectic matrix and the rod-shaped phase, respectively.

In Figure 4-9, the dendrite, tipped with precipitate, is the microstructure of another constituent under the oxide layer of the arc bead. These dendrites exhibit the non-faceted growth morphology, and outward growth derived from the unfused wire end, and immersed in eutectic [46]. The chemical compositions of dendritic second arm and precipitate in the specimen are copper element (Fig. 4-9c) and including copper-oxygen elements respectively (Fig. 4-9g). The structure analysis of the dendritic second arm (Fig. 4-9d, 4-9e, 4-9f) and tipped precipitate (Fig. 4-9h, 4-9i, 4-9j) show that the dendrite is the Cu phase with a face-centered cubic structure, at a lattice constant of 0.3615nm, and the precipitate on the dendritic surface is the cuprous oxide with a simple cubic structure, at a lattice constant of 0.4269 nm (Fig. 4-9g. 4-9j and Table 4-3).

4.2.2.4 A Section Result

The non-melted part of conductor is the heat extraction direction, when the molten mark solution temperature is lower than 1358K, the copper atoms in liquid will be heterogeneously nucleated as crystal embryos on the interface at the solid end of conducting wire that is not yet melted, and then grow towards〈100〉

direction to form columnar crystals. When the columnar crystals grow, the oxygen atoms are rejected continuously into the liquid and the solute concentration of solution between columnar crystals is therefore enhanced (Figure 4-9b). Thus the solution forms constitutional undercooling between columnar crystals. The secondary arms grow along〈100〉direction perpendicular to primary crystals. This kind of dendrite also is known as solutal dendrite.

The experimental results showed that due to high current density overheating, the liquid copper at the melting site of the short-circuited wire adsorb oxygen from air. According to the above identification results, the surface layer of the fire causing arc bead is the faceted cuprous oxide. The microstructure under the faceted cuprous oxide layer is a mixture consisted of two constituents, which are copper-cuprite eutectic structure and solutal Cu dendrites; the schematic diagram is shown as Fig. 4-10.

When wiring short circuit occurred at atmosphere, the dissolved oxygen in liquid copper on the molten end of the electrical copper wire follows the Sievert's law. The solubility of the dissolved diatomic gases in melt is proportional to the square root of partial pressure of oxygen, C_g= K (p_o)^1/2, and it is also the temperature function, Cg= B exp(-Q/RT) [47]. According Cu-O phase diagram [48], the oxygen solubility enhances in the liquid copper at high temperature as the instant short-circuit current heating wire rapidly.

Via the above-mentioned experimental result, the FCABs with faceted surface are permeated by oxygen. Their internal microstructures are constituted by the solutal dendrites of copper and the Cu-κ eutectic. Their faceted surface are the cuprous oxide flake.

Chapter 5 Discussions

5.1 Non-Oxygen-permeated FCAB

Although the kinetics of atomic addition plays a key role in some materials, we assumed that the diffusion of atoms from the liquid phase to the crystalline phase was rapid so that the kinetics model could be neglected [49–54] because the dendrite morphologies clearly exhibited ―non-faceted‖ growth.

Because heat diffusivity is much faster than mass diffusivity [55], the solid-liquid interface of a pure metal will always be unstable if the temperature gradient is negative. Perturbations will grow if the temperature gradient is negative at the interface, resulting from the heat flux due to the temperature gradient (G = dT/dz) [56]. The total undercooling (∆T0) of the melt is equal to the difference between T_m (the melting point) and T_l (the liquid temperature).

The perturbations have an infinitesimal critical amplitude r*, a quarter wave length, which does not affect the diffusion fields. The perturbed interface can be described by a simple sine function (Figure 5-1):

where ω = π/2r* is the wave number.

The interface temperature Ti can be deduced from the assumption of local equilibrium:

The T_i is the difference between the melting point (T_m) and the curvature undercooling ∆TR = ΓK, where the Gibbs–Thomson coefficient (Γ) is equal to γTm

/∆ _f, and the curvature K is ; γ is the solid/liquid interface energy and ∆ _f is the latent heat of fusion per unit volume.

The temperature difference between the tips (at point t) and depressions (at point d) of the interface is given by:

√

When a protrusion appears on the solid (Figure 5-1), the negative temperature gradient in the liquid becomes even more negative. The advancing perturbations then continuously evolve into the cell, with the cell radius Rc having twice the value of r* at ∆T₀, √ . The tip growth at the cell is isothermal; the

thermal diffusion equation in cylindrical coordinates at the solid-liquid interface of the growing tip can be written [57, 58]:

a: thermal diffusivity; ∆Tt: the temperature difference due to heat flow.

The heat moving away from the interface through the liquid must balance the sum of the heat from the solidification and the latent heat generated at the interface:

( )

ν: growth velocity; c: volumetric specific heat.

The cell grows continuously into dendrite, due to the temperature difference

∆Tt at the tips of the solid–liquid interface. From the Gibbs–Thomson effect, the equilibrium across the dendritic tip radius occurs at a curvature undercooling (∆T_R) below the melting point Tm is given by .

The total undercooling of melt ( ) equals the sum of the undercooling due to curvature (∆T_R) and the temperature difference from the heat flow (∆Tt):

The growth of a thermal dendrite at marginal stability is given by

: dendrite radius at marginal stability.

The primary trunk tip radius of thermal dendrite growth at marginal stability is obtained [59–63]:

√

(1)

(

)

(2)

Gs is the temperature gradient of dendritic tip at marginal stability, and ∆Tts

is the temperature difference of dendritic tip at marginal stability due to heat flow.

Our experiment revealed the relationship between the wire diameter and the primary spacing of the thermal dendrite of the short-circuit arc bead samples, as proportional to λ. The proportionality constant depends on the geometrical arrangement of the dendrites grown in steady state. From the hexagonal arrangement in Figure 4-4, it is likely that the last liquid solidifies at the gravity center of the equilateral triangle that is formed by the three densely packed dendrites [63]. This assumption leads to the value of

√ (4)

A cylinder having a hemispherical tip (Figure 5-1) growing along its axis is the simplest approximation that can be adapted to the growth of a dendrite tip [64, 65]. The cross-section of the cylinder, , determines the volume that grows in a time and is responsible for the rejection of thermal heat. The surface area of the hemispherical cap, , determines the amount of

radial thermal diffusion. Thus, the flux due to thermal rejection J1 equals the thermal diffusion in the liquid ahead of tip (J₂) which can be written by:

ν_s: growth velocity of thermal dendrite at marginal stability.

Under steady-state conditions, the heat flux balance must lead to the thermal Péclet numbers (P_t) which are defined by the dimensionless ratio of the radius R to the thermal-diffusion distance 2a/ν at thermal diffusion-limited growth [66–69]:

(5)

Because the stability limit of the dendrite tip lies at a larger tip radius than that of the extremum, the capillarity effect can be neglected [70, 71].

At marginal stability, the thermal supersaturation Ω can be defined as the ratio of the thermal undercooling to the unit undercooling (θ_t = ∆ _f/c). The relationship defining the thermal diffusion at the tip for the marginally stable growth of a thermal dendrite is given by . Thus, the temperature difference due to heat flow can be written as ∆Tt = P_tθ_t; the temperature difference due to the heat flow of dendrite growth at stability is obtained by

(6)

Combining Equations (6), (9), and (10) into Equation (5), the growth velocity and the radius of thermal dendrite growth at marginal stability are obtained

respectively by

(11)

√ (12)

Table 4-2 lists the growth velocities (ν_s) of the thermal dendrites in the

FCABs. The growth velocities of the thermal dendrites of the melted beads having diameters ranging from 0.1 to 1.2 mm are inversely proportional to the square of the wire diameter (Figure 5-3). That is, as the diameter of the wire increases, the growth velocity of the thermal dendrite decreases.

√

(7)

As listed in Table 4-2, the values of ∆Tts due to the thermal dendrite growth of the melted beads having diameters from 0.1 to 1.2 mm are inversely proportional to the wire diameters (Figure 5-4). Thus, when the diameter of the wire increases, the value of ∆Tts also decreases.

The extremum growth of a thermal dendrite is influenced by diffusion, capillarity effects, and the degree of thermal supersaturation (Ω). This thermal supersaturation is defined by the equation

Ω_e = Pt_e + 2Γ/R_eθ_t

The temperature difference ∆Tte due to the heat flow of extremum growth is equal to Ω_eθt. The extremum of growth velocity (ν_e) is used to define the tip radius (R_e). The maximum velocity in an isothermal environment corresponds to a minimum in the total undercooling (∆T0) for constant-velocity growth. Therefore, minimizing ∆T₀ will give the extremum radius (R_e) and the temperature difference due to heat flow (∆Tt_e)

√

(8)

√

(9)

Figure 5-5 presents the overall relationships between the wire diameter (D), the total undercooling (∆T₀), the tip radius ( ), and the growth velocity (ν) of thermal dendrites at various growth stages [72].

5.2 Oxygen-Permeated FCABs

From the gas/liquid interface (the surface of FCAB), the oxygen dissolved in the liquid copper of the arc bead to form Cu-O solution. The liquid copper is the solvent, and the dissolved oxygen atom is the solute. The oxygen concentration of the molten arc bead profile forms diffusion distributed curve, decreases with an increasing diffusion distance from the surface of arc bead. Therefore, the oxygen concentration is highest on surface of the melting the arc bead at ambient atmosphere.

In Cu-O solution, copper dendrites grows up, oxygen solute is being repelled from the Cu-dendrites tip constantly, and form cuprous oxide on dendritic surface (Fig. 4-9a and 4-9b). These dendrites are solutal dendrites. Since the growth of the high-index planes with higher surface energy are quicker than low-index planes in the solidified Cu phase solutal dendrites, thus leaving the low-index｛111｝plane of copper in the final solidification [73-74], so XRD results exhibited strong Cu (111) texture in the arc bead.

According to the Cu-O phase diagram [75], as shown in Figure 5-4, when hypoeutectic composition between κ-phase and τ-phase. In this experiment, the surface of the arc bead is the cuprous oxide (κ-phase) coating layer, and the constituents of the arc bead includes Cu-κ eutectic structure and solutal Cu-dendrites, meanwhile, the eutectic structure consist of rod-shaped κ-phase and Cu phase matrix. During the local equilibrium solidification of the rapid cooling process, the melted solution is cooled below T = 1618 K (critical point), L→ L1+

L2, the liquid solution forms two-phase miscibility gap. When the surface temperature is decreased below T=1502 K (freezing point of cuprous oxide), L2→

κ, L2 is solidified into cuprous oxide layer, which prevents the oxygen at ambient atmosphere from further dissolving into the molten arc bead continuously. When the molten arc bead solution is cooled below T= 1496 K (monotectic point), L1+L2→ L1+ κ [76], the cuprous oxide layer becomes thick by the monotectic transformation. The oxygen content of arc bead is 0.33 (Xo=0.33), and therefore, the molar fraction of oxygen inside the arc bead is less than 0.33 (Xo< 0.33).

When the melt solution inside the arc bead is further cooled below T=1358 K (melting point of copper), copper atoms in liquid heterogeneously nucleate at the melted/non-melted interface of wire [77]. The solid end of wire becomes the heat conductor (the heat sink). The copper atoms on the liquid side near the interface are likely to attach to crystallize by the capillarity and thermal conduction. The kinetics of transfer of atoms from the liquid to the crystal is rapid so that it can be neglected, thus, the solidified Cu phase dendrites appear to be non-faceted crystal.

The growth direction of cellular dendrites is opposite to the direction of heat flow [76]. The solutal Cu-dendrites grow rapidly toward the molten arc bead surface layer from the non-melted solid end section of wire. The solutal Cu-dendrites form

The growth direction of cellular dendrites is opposite to the direction of heat flow [76]. The solutal Cu-dendrites grow rapidly toward the molten arc bead surface layer from the non-melted solid end section of wire. The solutal Cu-dendrites form