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The work of adhesion and the interface energy of NiAl/V coherent interface systems have been investigated using first-principles methods. The adhesion of the Ni-terminated interface is larger than the Al-terminated interface. The difference in charge density and the density of states show that the Ni-terminated interface is dominated by metallic bonds, and the Al-terminated interface is dominated by metallic and covalent bonds. To account for the effects of misfit dislocations on the semicoherent interfaces, the Peierls–Nabarro model combined with generalized stacking fault energy is employed to determine the interface energy. It is found that misfit dislocations can reduce the adhesion of the interface, and the reduction increases with the maximum of the restoring force.

Nickel aluminum (NiAl) is a promising material for high temperature structure materials, especially applied in the aerospace industry, due to its superior properties, including high melting temperature, high temperature strength, low density and good oxidation resistance [

As we know, there exists a discrepancy of the lattice constants between NiAl and V. The misfit will introduce strain and a periodic array of dislocations at the interface, and thus, the interface becomes semicoherent. Therefore, it is indispensable to analyze the misfit dislocations at the interface. The semicoherent interfaces have been investigated by some researchers using first-principles methods [

An alternative method to address this problem is based on the Peierls–Nabarro (PN) framework. The original PN model describes the motion of the dislocation core through the sinusoidal potential function; whereas, the local relaxation of atoms is neglected due to the one-dimensional constraint path approximation. The modification of the original PN model has been proposed by many researchers in which the nonlinear displacement field is considered [

In this paper, we have investigated the coherent and semicoherent interface energy. The work of adhesion and the interface energy of coherent NiAl/V interfaces have been calculated using the first-principles methods. The difference in the charge density and the states of density (DOS) have been used to analyze the interfacial bonding. In order to determine the adhesive properties of semicoherent NiAl/V interfaces, the misfit dislocations and interface energy have been investigated within the framework of the PN theory. The effects of misfit dislocations on the adhesive properties of interfaces have been also discussed.

The first-principles calculations were employed with the Vienna

The optimized lattice parameters are listed in

The bulk modulus

To investigate the interface, it is necessary to make sure that the two slabs are thick enough to represent the bulk-like interiors. Therefore, we conducted convergence tests on NiAl (001) and V (001) slabs. To acquire the suitable thickness necessary for bulk-like NiAl and V slabs, the dependence of layer relaxation on the atom layers has been explored. In

As for the NiAl (001) surface, the situation is more complicated. The (001) surface of NiAl is distinguished by its terminated surface layer consisting of a Ni layer or a Al layer. Thus, its surface energy, which is calculated by using Equation (1), is the average value of the two terminations, and we could not obtain the surface energy for Ni-terminated or Al-terminated. What is more, the asymmetric slab will induce the spurious dipole effect [

The calculated Δ

Our geometry of the NiAl/V interface was established by a supercell enclosing a sequence of eight NiAl and six V (001) layers stacked in the

There are two fundamental quantities widely used to describe the mechanical and thermodynamic properties of the interface. One is the ideal work of adhesion

The

The other one is interface energy

In order to state the details of the interfaces, the difference of the charge density is used to examine the interfacial electronic structure and bonding. The difference of the charge density can be given by the following equation:

To further reveal the interfacial bonding characteristics, the calculated Layer-Projected Density of States (LPDOS) of the NiAl/V interface with Ni-terminated and Al-terminated surfaces are presented in

As we know, there is a discrepancy of the lattice constants between NiAl and V, and the misfit is

To analyze the dislocation core structure, it is necessary to calculate the Generalized-Stacking-Fault-Energy(GSFE). We calculated the GSFE along

It is difficult to calculate the work of adhesion of semicoherent interfaces through first-principles methods in that the unit cells required for the semicoherent interface are beyond the capacity of our computer. According to Yao

Foreman’s method applied to solve the dislocation equation is given as follows [

The parameter

The mean total energy (per unit area) of the interface due to the forming of misfit dislocation is called the interface energy and can be divided into two parts: the elastic strain energy

The misfit energy (per unit area) can be obtained from:

The calculated elastic strain energy, misfit energy and interface energy are listed in

The first-principles density functional calculations were employed to investigate the surface properties of NiAl (001) and V (001), as well as the interfacial properties of coherent NiAl/V interfaces. The models of Ni-terminated and Al-terminated surfaces were both considered. The work of adhesion, the interface energy, the difference charge density and the layer-projected density of states were calculated. Furthermore, the semicoherent interfacial properties of NiAl/V interfaces were also investigated within the framework of PN theory for misfit dislocations. The summarized results are given as follows:

(1) Surface tests reveal that the V slab with more than five layers and the NiAl slab with more than seven atomic layers exhibit a bulk-like interior feature, and the surface energy of the Ni-terminated surface is larger than the Al-terminated one for the NiAl slab, which means that the Ni-terminated interface is more active.

(2) The calculated work of adhesion for the Ni-terminated surface (5.01 J/m

(3) The work of adhesion for both semicoherent Ni-terminated and Al-terminated interfaces is smaller than coherent interfaces. It is found that misfit dislocations can reduce the adhesion of interfaces.

The work is supported by the Natural Science Foundation of China (11104361, 11304403, 11547305) and Projects supported by the Fundamental Research Funds for the Central Universities (CDJZR14328801).

Yaoyao Linghu, Xiaozhi Wu and Rui Wang performed the theoretical calculations; Weiguo Li and Qing Liu analyzed the data; Yaoyao Linghu wrote the paper.

The authors declare no conflict of interest.

_{2}interfaces

_{5}Si

_{3}(001) interface: A first-principles study

_{4}/FePO

_{4}interfaces

_{3}V (001) interface

_{2}O

_{3}interfaces: A first-principles study

_{3}Zr(111)/Pt (111) interfaces: A first-principles study

_{5}Si

_{6}/

_{2}

_{2}O

_{3}(0001) interface: A first principles study

_{2}/Si substrates

_{3}Al interface alloying with Re and Ru

The supercell models for the (

The work of adhesion of the NiAlV and AlNiV interface systems.

Charge density difference for (

Layer-Projected Density of States (LPDOS) for (

The generalized stacking fault energy curves and the corresponding restoring forces for the NiAlV interface AlNiV interface slip along

The density of misfit dislocations: (

Summary of the lattice constants

Materials | ||||||||
---|---|---|---|---|---|---|---|---|

NiAl | 2.89 | 205.1 | 136.1 | 116.9 | 83.9 | 159.1 | 214.2 | 0.40 |

[ |
2.89 | 203 | 140 | 113 | 80.4 | 161.0 | 206.8 | 0.41 |

[ |
2.89 | 233 | 121 | 114 | 85 | 159 | 218 | 0.34 |

V | 3.01 | 253.7 | 134.7 | 19.9 | 35.7 | 174.3 | 100.4 | 0.35 |

[ |
3.04 | 228.0 | 118.8 | 42.6 | 47.4 | 155.2 | 129.0 | 0.34 |

[ |
– | 228 | 119 | 42.6 | 47.4 | 155.3 | 129.0 | 0.34 |

The relaxed atomic arrangements of 7-layer NiAl, AlNi and V for surface energy calculations. We only show the atomic arrangements of the top four layers due to the symmetry of the supercell. The atomic position is given with respect to the basis vector of the supercell for surface calculations (Aln, Al atoms of the n-th layer; Nin, Ni atoms of the n-th layer; Vn, V atoms of the n-th layer).

Systems | Symbol | Atomic Position | ||
---|---|---|---|---|

x | y | z | ||

NiAl (Al-terminated) | Al1 | 0.0000 | 0.0000 | 0.0018 |

Ni1 | 0.5000 | 0.5000 | 0.0743 | |

Al2 | 0.0000 | 0.0000 | 0.1536 | |

Ni2 | 0.5000 | 0.5000 | 0.2308 | |

AlNi (Ni-terminated) | Ni1 | 0.0000 | 0.0000 | 0.0042 |

Al1 | 0.5000 | 0.5000 | 0.0730 | |

Ni2 | 0.0000 | 0.0000 | 0.1548 | |

Al2 | 0.5000 | 0.5000 | 0.2308 | |

V | V1 | 0.0000 | 0.0000 | 0.0108 |

V2 | 0.5000 | 0.5000 | 0.0770 | |

V3 | 0.0000 | 0.0000 | 0.1539 | |

V4 | 0.5000 | 0.5000 | 0.2308 |

The interlayer relaxation change (

Systems | Interlayer | Atom Layers of Slab | ||||
---|---|---|---|---|---|---|

3 | 5 | 7 | 9 | 11 | ||

NiAl (Al terminated) | −1.4% | −6.6% | −5.7% | −6.4% | −7.0% | |

– | 4.2% | 3.1% | 3.6% | 4.1% | ||

– | – | 0.3% | 1.1% | 1.0% | ||

– | – | – | −1.3% | −0.5% | ||

– | – | – | – | −0.3% | ||

AlNi (Ni terminated) | −5.3% | −10.0% | −10.7% | −10.3% | −10.9% | |

– | 4.8% | 6.3% | 7.0% | 6.1% | ||

– | – | −1.2% | −2.8% | −1.9% | ||

– | – | – | 0.7% | 1.2% | ||

– | – | – | – | 0.0% | ||

V | −13.6% | −15.2% | −13.9% | −14.2% | −14.3% | |

– | 0.7% | 0.2% | −0.7% | −0.2% | ||

– | – | 0.3% | 1.9% | 2.0% | ||

– | – | – | −1.8% | −3.0% | ||

– | – | – | – | 0.7% |

Convergence of the surface energy

Number of Layers; n | ||||||
---|---|---|---|---|---|---|

Stoichiometric | Non-Stoichiometric | Stoichiometric | Non-Stoichiometric | |||

3 | – | – | – | |||

4 | 2.27 | – | 2.27 | – | 2.61 | |

5 | – | – | – | |||

6 | 2.31 | – | 2.31 | – | 2.36 | |

7 | – | – | – | |||

8 | 2.30 | – | 2.30 | – | 2.36 | |

9 | – | – | – | |||

10 | 2.30 | – | 2.30 | – | 2.36 | |

11 | – | – | – |

Interfacial distance

Interfaces | Unrelaxed | Relaxed | |||||
---|---|---|---|---|---|---|---|

NiAlV | 1.769 | 4.09 | 1.775 | 4.03 | |||

AlNiV | 1.515 | 5.01 | 1.506 | 4.85 |

The unstable stacking fault energy

Misfit Dislocations | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

NiAlV |
3.06 | 2.89 | 72.5 | 0.029 | 0.048 | 1.83 | 0.75 | 2.57 | ||

NiAlV |
10.60 | 4.09 | 102.5 | 0.010 | 0.018 | 3.63 | 1.07 | 4.70 | ||

AlNiV |
4.18 | 2.89 | 72.5 | 0.021 | 0.035 | 2.06 | 0.75 | 2.81 | ||

AlNiV |
20.10 | 4.09 | 102.5 | 0.005 | 0.008 | 4.43 | 1.08 | 5.51 |