J. Mater. Sci. Technol. ›› 2018, Vol. 34 ›› Issue (4): 613-619.DOI: 10.1016/j.jmst.2017.09.003
Special Issue: Nanomaterials 2018
• Orginal Article • Previous Articles Next Articles
Guibin Shan, Yuzeng Chen*(), Mingming Gong, Hao Dong, Feng Liu*()
Received:
2016-12-21
Revised:
2017-02-21
Accepted:
2017-02-23
Online:
2018-04-20
Published:
2018-05-04
Contact:
Chen Yuzeng,Liu Feng
Guibin Shan, Yuzeng Chen, Mingming Gong, Hao Dong, Feng Liu. Modelling thermodynamics of nanocrystalline binary interstitial alloys[J]. J. Mater. Sci. Technol., 2018, 34(4): 613-619.
Fig. 1. Schematic of the atomic and lattice site configurations of a NC system, which is divided into the bulk and intergranular regions that are connected by the transitional bonds [16]. The system consists of two sublattices [21], i.e., α sublattice (closed blue circles) and β sublattice (open circles and closed green circles, open circles and closed green circles represent the vacant sublattice and the sublattice occupied by solute atoms, respectively).
Region | Bond type | Bond energy | Probability of the bonds | Bond number |
---|---|---|---|---|
Bulk | NbD-VaNbD-Va | ED-Va | 2Xb(1-Xb) | z2N0CXb(1-Xb)(1-fig) |
Intergranular | NigD-D | ED-D | Xig2 | (1-2ν)z22N0CXig2fig |
NigVa-Va | EVa-Va | (1-Xig)2 | (1-2ν)z22N0C(1-Xig)2fig | |
NigA-A | EA-A | 1 | (1-2ν)z12N0fig | |
NigD-Va | ED-Va | 2Xig(1-Xig) | (1-2ν)z2N0CXig(1-Xig)fig | |
Transitional | NtD-D | ED-D | XbXig | νz2N0CXbXigfig |
NtVa-Va | EVa-Va | (1-Xb)(1-Xig) | νz2N0C(1-Xb)(1-Xig)fig | |
NtA-A | EA-A | 1 | νz1N0fig | |
NtD-Va | ED-Va | Xig(1-Xb)+Xb(1-Xig) | νz2N0C[Xig(1-Xb)+Xb(1-Xig)]fig |
Table 1 Bond type, bond energy, bond probability, and bond number that are derived in terms of the defined solute concentrations in the respective regions.
Region | Bond type | Bond energy | Probability of the bonds | Bond number |
---|---|---|---|---|
Bulk | NbD-VaNbD-Va | ED-Va | 2Xb(1-Xb) | z2N0CXb(1-Xb)(1-fig) |
Intergranular | NigD-D | ED-D | Xig2 | (1-2ν)z22N0CXig2fig |
NigVa-Va | EVa-Va | (1-Xig)2 | (1-2ν)z22N0C(1-Xig)2fig | |
NigA-A | EA-A | 1 | (1-2ν)z12N0fig | |
NigD-Va | ED-Va | 2Xig(1-Xig) | (1-2ν)z2N0CXig(1-Xig)fig | |
Transitional | NtD-D | ED-D | XbXig | νz2N0CXbXigfig |
NtVa-Va | EVa-Va | (1-Xb)(1-Xig) | νz2N0C(1-Xb)(1-Xig)fig | |
NtA-A | EA-A | 1 | νz1N0fig | |
NtD-Va | ED-Va | Xig(1-Xb)+Xb(1-Xig) | νz2N0C[Xig(1-Xb)+Xb(1-Xig)]fig |
parameter | γA (J/m2) | γD (J/m2) | ω (kJ/mol) | σ (m2/mol) | T (K) | t (nm) | υ | z2 | C | l |
---|---|---|---|---|---|---|---|---|---|---|
value | 0.805 | 0.4 | 12.5 | 30000 | 573 | 0.3 | 0.3 | 12 | 3 | 0.4 |
Table 2 Values of the physical parameters for the Fe-C alloy [16,26].
parameter | γA (J/m2) | γD (J/m2) | ω (kJ/mol) | σ (m2/mol) | T (K) | t (nm) | υ | z2 | C | l |
---|---|---|---|---|---|---|---|---|---|---|
value | 0.805 | 0.4 | 12.5 | 30000 | 573 | 0.3 | 0.3 | 12 | 3 | 0.4 |
Parameters | Γ (10-5 mol/m2) | Xb (at. %C) | ΔHseg (kJ/mol) |
---|---|---|---|
Calculated values using the current model | 1.06 | 2.5 × 10-5 | 68 |
Experimental values from Ref. [ | 1.3 | 0.35 | 74 |
Table 3 Comparisons of calculated values of Γ, Xb and ΔHseg of the nanocrystalline Fe-C system with the experimental data cited from Ref. [25].
Parameters | Γ (10-5 mol/m2) | Xb (at. %C) | ΔHseg (kJ/mol) |
---|---|---|---|
Calculated values using the current model | 1.06 | 2.5 × 10-5 | 68 |
Experimental values from Ref. [ | 1.3 | 0.35 | 74 |
Fig. 3. Effect of ω on (a) deq and (b) Γ. The values of the parameters used in calculations are t = 0.4 nm, υ = 0.5, z2 = 12, σ = 30000 m2/mol, γA = γD = 0.8 J/m2, l = 0.6, C = 3, X0 = 0.02 and R = 8.3145 J/mol K.
Fig. 4. Effect of X0 on (a) deq and (b) Γ. The values of the parameters used in calculations are t = 0.4 nm, υ = 0.5, z2 = 12, σ = 30000 m2/mol, γA = γD = 0.8 J/m2, l = 0.6, C = 3, ω=10 kJ/mol and R = 8.3145 J/(mol K).
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