Reactive wetting behaviour between carbon-unsaturated Fe-C

4.3.2.1. Formation of concave geometry at the interface

Fig. 42 shows optical micrographs of the interfacial region between the SN10 substrate and the Fe-C samples of MS1, MS2 and MS3. Fig. 43 shows images of this area for SN0, SN5 and SN10 substrates in contact with the MS1 Fe-C sample.

Concave geometries are clearly formed at the interfacial regions in all cases.

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Concave formations are observed as shown in Figs. 42 and 43. Carbon has obviously dissolved from the substrates into the Fe-C samples without residual ash in the reacted layer to form the concaves. The concave formations have been thought to depend on the amount of carbon dissolved into the Fe-C sample from the substrate. Therefore, it is necessary to estimate the amount of carbon dissolution to evaluate the relationship between this amount and the formation of concave regions. Thus, the method of image analysis was applied to calculate the amount of carbon dissolution from the images. Eq. (19) was used to calculate the

100 μm

100 μm

100 μm Original Interface

Fig. 42. Optical microscope images of concave formation at the interface area between SN10 substrate and (a) MS1, (b) MS2, and (c) MS3 Fe-C samples.

Fig. 43. Optical microscope images of concave formation at the interface area between MS1 Fe-C sample and (a) SN0, (b) SN5, and (c) SN10 substrates.

Original Interface _{100 μm}

100 μm

100 μm

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amount of carbon dissolution. Dintrusion and Riron were determined by image analysis, as shown in Fig. 44.

Fig. 45 shows the effects of the Al2O3 amount in the substrates and the initial carbon concentration of the Fe-C samples on the carbon d-issolution amount. The amount of carbon dissolution decreases with increasing of the Al2O3 amount and the initial carbon concentration of the Fe-C sample. This trend of varied carbon dissolution with the initial carbon concentration of the Fe-C samples agrees well with previous studies.^2-9) From these results, Al2O3 is concluded to prevent carbon transport phenomena from the substrate to the molten Fe-C sample; larger initial carbon concentrations in the Fe-C sample also cause the carbon absorption capacity of the Fe-C sample to decrease.

Fig. 44. Estimation of carbon dissolution amount from the optical micrograph at interface.

100 μm

Dintrusion Riron Riron

Original Interface

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4.3.2.2. Interfacial energy variation

4.3.2.2.1. Initial interfacial energy between liquid phase and solid phase The initial interfacial energy between the liquid and solid phases is defined as an interfacial energy values at the moment of time 0 in the contact between the Fe-C sample and the substrate. The effect of carbon dissolution on the macroscopic morphology is assumed negligible at this moment; the liquid Fe-C sample moves on the flat surface of the substrate. Therefore, Young’s equation (Eq. (1)) can be applied to calculate the interfacial energy between the liquid and solid phases.³¹⁾

The values of γ_LV and γ_SV in Eq. (1) are determined to calculate the value of γ_LS. Firstly, the value of γ_LV is estimated for the Fe-C sample. It is assumed to be Fig. 45. Relationship between Al2O3 amount in the substrate and carbon dissolution

amount.

Al2O3 content (vol%)

MS3 Fe-C sample MS2 Fe-C sample

Amount of carbon dissolution (g/cm2 )

MS1 Fe-C sample

0 2 4 6 8 10

0.01

0.02

0.03

0.04

0.05

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constant with varied carbon content in the Fe-C liquid phase andthe value of γ_LV is 1.73 J/m².³²⁾ Secondly, the values of γ_SV are estimated for the SN0, SN5, and SN10 substrates. The interfacial energy between the solid and vapour phases is assumed to be a combination of the interfacial energies between the solid and vapour phases of graphite and Al2O3 components in the substrate and that the interfacial energies between pores and the vapour phase is negligible. Therefore, the values of γ_SV of the substrates are obtained from Eq. (20).

γ_SV = γ_SVgraphite×^{(100−a−p)}₁₀₀ + γ_SVAl2O3 ×₁₀₀^a (20)

where γ_SVgraphite and γ_SVAl2O3 (J/m²) represent the interfacial energy between

solid graphite-vapour and Al2O3-vapour, respectively. a (%) is the area ratio occupied by Al2O3 area on the surface of the simulant coke substrate. p (%) is the

50 μm

Void area

Graphite area

Al2O3 area

50μm

Fig. 46. Evaluation of the occupied Al2O3 area on the surface of the simulant coke substrate from image analysis of cross-sectional observations.

Graphite area

Al2O3 area Void area

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void ratio of the surface of the substrate. The ‘‘a’’ (%) values were evaluated by image analysis of cross-sectional observations. In SN10 substrate, a had values of 20.1% and in the SN5 substrates, ‘‘a’’ had value of 11.3% . These values of ‘‘a’’

are estimated by the image analysis method, as shown in Fig. 46. The values of

‘‘p’’ were taken from Table 2. Meanwhile, the values of γ_SVgraphite and γ_SVAl2O3 (J/m²) were calculated using Eq. 21³⁵⁾ and Eq. 22³⁵⁾ as functions of the experimental temperature, T (K), as 0.957 and 0.724 J/m², respectively.

γ_SVgraphite = 1.139 − 0.13 × 10⁻³× (T − 273) (21) γ_SVAl2O3 = 0.892 − 0.12 × 10⁻³× (T − 273) (22)

Table 9. Initial interfacial energy of solid-vapour and solid-liquid phases.

Finally, the values of γ_SV were estimated using Eq. (20) as listed in Table 9.

From Eq. (1), the initial value of γ_SL was calculated as given in Table 9.

4.3.2.2.2. Equilibrium interfacial energy between liquid and solid phases Young’s equation can be applied when the melts ideally spread on the perfectly smooth surface substrate. In the contact area between the substrate and carbon-unsaturated Fe-C sample, the formation of concave geometry is observed clearly,

Simulant coke substrate

Liquid iron sample

γ_SV ( J/m²)

γ_SL ( J/m²)

SN0

MS1

0.761

1.482

MS2 1.623

MS3 1.693

SN5

MS1

0.750

1.504

MS2 1.682

MS3 1.731

SN10

MS1

0.754

1.583

MS2 1.752

MS3 1.758

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as shown in Fig. 42 and Fig. 43. When concave are formed at the contact area between carbon-unsaturated liquid Fe-C sample and the simulant coke substrate, Young’s equation could not be applied. Hence, Neumann’s equation, as shown in Eq. (23), is applied in this reactive wetting case.^35,36)

γ_SL

sin θ_V = ^γSV

sin θ_L = ^γLV

sin θ_S (23)

where γ_SL, γ_SV, and γ_LV (J/m²) represent the interfacial energies between solid-liquid, solid-vapour and liquid-vapour phases, respectively. The dihedral angles θV, θL and θS are formed by the planes tangent to the interfaces, as shown in Fig. 47.

The values of the dihedral angles are measured from the cross-sectional images

of the cooled samples, as shown in Fig. 42 and Fig. 43 and given in Table 10. To simplify the contact angle measurement, changes in volume of droplet in solidification process are neglected. The value of the dihedral angles were calculated from 3 images for each value. The error in the measurement is ± 1°.

The values of γ_SV for the SN0, SN5 and SN10 substrates are taken from Table 9.

From Eq. (23), the equilibrium value of γ_SL is calculated as shown in Table 10.

γ_SV

γ_LV

γ_SL

Fig. 47. Schematic of geometry at the triple position.

θ_V θ_S

θ_L

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Table 10. Dihedral contact angles and interfacial energy values between the iron samples and the substrates in the constant stage.

4.3.2.2.3. Interfacial energy between liquid and solid phases variation

The subtraction from the initial interfacial energy to the equilibrium interfacial energy were determined as the variation in interfacial energy. Fig. 48 shows the relationship between the variation of interfacial energy and the amount of Al2O3 in the substrate. Larger amounts of Al2O3 in the substrate cause lager variations in the interfacial energy.

The interfacial energy variation is affected by the amount of Al2O3 in the substrate. Additionally, Al2O3 affects the formation of concave regions at the interfacial area between the carbon-unsaturated liquid Fe-C sample and the simulant coke substrate.

Simulant coke substrate

Liquid iron sample

θV

(°) θL

(°) θS

(°)

γ_SL ( J/m²)

SN0

MS1 98 107 155 0.788 MS2 93 109 158 0.804 MS3 90 110 160 0.810 SN5

MS1 98 104 158 0.765 MS2 93 107 160 0.783 MS3 90 108 163 0.789 SN10

MS1 98 103 159 0.766 MS2 93 105 162 0.780 MS3 90 106 164 0.784

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4.3.3. Role of Al2O3 in the reactive wetting behaviour with concave formation