First-Principles Study of the Interfaces between Fe and Transition

Subscriber access provided by FORDHAM UNIVERSITY

Article

First-Principles Study of the Interfaces Between Fe and Transition Metal Carbides Na-Young Park, Jung-Hae Choi, Pil-Ryung Cha, Woo-Sang Jung, Soon-Hyo Chung, and Seung-Cheol Lee J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp306859n • Publication Date (Web): 19 Nov 2012 Downloaded from http://pubs.acs.org on December 12, 2012

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

First-Principles Study of the Interfaces between Fe and Transition Metal Carbides

Na-Young Park1,2, Jung-Hae Choi3, Pil-Ryung Cha2, Woo-Sang Jung4, Soon-Hyo Chung4, and Seung-Cheol Lee3,*

1

Computational Science Research Center, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea

2 3

School of Advanced Materials Engineering, Kookmin University, Seoul 136-702, Republic of Korea

Electronic Materials Research Center, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea 4

High Temperature Energy Materials Center, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT The interface energies and electronic structures of the interfaces between BCC Fe and transition metal carbides have been investigated using first-principles calculations based on density functional theory. The effects of the composition and configuration of the carbides on the interface properties have been determined. It was shown that the Fe/TiC interface has the highest interface energy and the formation of complex carbides leads to a significant decrease in the interface energy. The complex carbide of (Ti0.5Mo0.5)C, which has Mo present at the interface, has been found to be the most stable. From the analysis of the density of states, the stability of the Mo-segregated (Ti0.5Mo0.5)C carbides has been revealed to be due to the hybridization of the d-orbitals in the t2g local symmetry between Mo and its first nearest neighboring Fe atoms.

Keywords: interface energy, metallic carbides, orbital hybridization, density functional theory


Page 2 of 22

Page 3 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1. INTRODUCTION For decades, the synthesis and applications of metallic carbides (MCs) have received much attention in materials chemistry and nano-engineering due to their superior mechanical properties1-5. It is well known that the MCs dispersed in the Fe-based matrix enhance the strength of alloys by impeding the movement of dislocations. Use of Ti, Nb, V, Mo, and W as alloying elements is widespread6-9. In earlier experiments, an addition of Mo in Ti-based steels has been shown to result in a significant enhancement of the strength and excellent thermal stability due to a fine dispersion of the nanometersized (Ti0.5Mo0.5)C carbides10-12. However, to the best of the author’s knowledge, the role of Mo in the enhancement of the mechanical properties remains unclear. Furthermore, the nucleation mechanism of the (Ti0.5Mo0.5)C carbides in the matrix are not yet completely understood. The interfaces between the MCs and Fe-based matrix play important roles in the mechanical and thermal properties of alloys13, but it is difficult to measure the interface energy in experiments. From the theoretical side, the first-principles calculation based on density functional theory (DFT) has been used to investigate the interface characteristics of metal/TMCs14-17. It has been found that the hardness of the TMCs is attributed to the strong chemical bonding between transition metals (TMs) (e.g., Ti, V, and Zr) and C18. In addition, the interface properties of Fe/TMCs are primarily governed by the covalent bonding between the Fe d-orbital and the C p-orbital of the atoms present at the interface, that is, pdσ hybridization14. However, theoretical studies for explaining the stability of the (Ti0.5Mo0.5)C complex carbides exhibiting excellent mechanical properties are still lacking. In the present study, we perform first-principles calculations based on DFT for the energetics on the binary carbides of Ti, V, Nb, Mo, and W and for the energetics on the complex carbides that contain Ti and the other TMs mentioned above, in order to reveal the role of Mo. The interface energy is calculated on the equilibrium atomic structure that is determined by the minimization of the total energy under the three-dimensional strain, as applied in earlier studies15,19. The electronic structures and characteristics of the chemical bonding are analyzed on the complex carbide interfaces, which are energetically favorable, in terms of the site-projected density of states (DOS) and partial electron density contour close to the Fermi level.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2. THEORETICAL METHODS Theoretical investigations were performed within the framework of DFT20,21 as implemented in the Vienna Ab-initio Simulation Package (VASP)22,23 based on the pseudo-potential plane-wave basis set total energy first-principles method. The electron-ion interactions were described by projector augmented-wave (PAW) potentials23,24, and the exchange-correlation terms were employed with the generalized gradient approximation (GGA) proposed by Perdew and Wang (PW91)25. The planewave energy cutoff was set to be 350 eV and the Brillouin zone sampling was fixed at a 16 × 16 × 8 special k-point mesh. Spin-polarized calculations were performed for all systems because the ground state of BCC Fe is ferromagnetic. The changes in the site-projected density of states and partial valence electron density resulting from the formation of interfaces were explored. The interfaces between BCC Fe and NaCl-type carbides are known to follow the Baker-Nütting (cube-on-edge) relationship, which is as follows: {100}TMC//{100}Fe, TMC//Fe26,27. Because the binding energy of Fe and C is much higher than that of Fe and Ti or Fe and the other TMs, the C atoms lay directly next to the Fe atoms at the interface. The supercell structure of Fe/TiC interface system and the atomic configurations of various compositions of the TMCs are presented in Figure 1. Each interface system was composed of eight atomic layers; four unit cells of Fe and four layers of the TMC. Each TMC layer contains one TM and one C atom. The colors orange, blue, pink, and brown in Figure 1 represent Fe, Ti, alloying TM and C, respectively. The composition of the complex carbides, Ti1-xTMxC were set to be x=0, 0.25, 0.50 and 1. For the dependence of the atomic configurations of TMCs, various stacking sequences were considered at a given composition shown in Figure 1 (b), (c) and (d). In Figure 1, T and m denote Ti and the alloying TMs, respectively. For complex carbides, the selected atomic configurations were as follows: mTTT and TmTT for x=0.25, mmTT, mTmT, TmmT, and mTTm for x=0.5, and mmmT and mmTm for x=0.75. To investigate the structures and the interface energies of the Fe/TMCs, cell parameters of the system were fitted to consider the different lattice parameters of the Fe and the TMCs. The total energies of both the bulk Fe and the TMC were calculated separately as a function of the cell parameters along the plane parallel to the interface ( and directions for bulk Fe, and directions for bulk TMC). The changes in the total energies with respect to the cell parameter perpendicular to the interface, along the direction, were also considered. By adding the total


Page 4 of 22

Page 5 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


energies of both the bulk Fe and the bulk TMC for each cell parameter examined, the dimensions of the minimum total energy were obtained. The Fe and TMC layers were then combined within the period boundary condition. The interlayer spacing between the Fe and the TMC layers at the interface was evaluated by determining the minimum total energy for the given cell parameters. These procedures were applied to all Fe/TMC systems, which means that each Fe/TMC system had different cell parameters and interlayer spacings. The interface energy, σ, was calculated by using the following equation15,19:

σ = (E Fe /TMC − E Fe,bulk − ETMC,bulk )/2A

(1),

where A refers to the interface area. EFe/TMC is the total energy of the interface system, EFe,bulk and ETMC,bulk are the total energies of bulk Fe and the TMCs having the same cell parameters with the corresponding interface system.

3. RESULTS AND DISCUSSION

3.1. Energetics on the interfaces of binary carbides and Ti-based complex carbides. The calculated lattice parameters and bulk moduli for bulk BCC Fe and binary carbides of TiC, VC, NbC, MoC, and WC are presented in Table 1. The calculated lattice parameter for Fe with the GGA pseudo-potential is slightly smaller than the experimental value with an error of 1%. For the TMCs, slightly overestimated lattice parameters were obtained and compared with the experimental values, with errors less than 3 %. In the case of the magnetic moment of the ferromagnetic BCC Fe, the calculated value of 2.17 µB agree well with the 2.12 µB measured by experiments28. Because the semi-coherent interface followed the Baker-Nütting relationship in which the Fe plane is parallel to the TMC plane, a cell parameter of a0/√2 was also investigated for the TMCs. A comparison between the a0 of Fe and the a0/√2 of the TMCs shows that a lattice mismatch is expected occur when a semi-coherent interface forms. The calculated bulk moduli for the TMCs were in good agreement with the experimental values, with an error less than 5 %. It is noted that higher bulk moduli for TMCs means that they have a higher resistance to compression than Fe with a strong tendency of increasing the bulk modulus with an increasing number of d electrons in the TMs. The structural parameters for the interface systems are summarized in Table 2. The cell parameter, a, is the lattice parameter for Fe and a/√2 is that of the carbides in each interface system. It is noted that



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

the Fe and the carbides are under tensile and compressive strains, respectively, due to the lattice mismatch occurring during the process of minimization of internal energy for the interface system. The tensile strain induced in Fe (δ) is highest at the Fe/NbC interface, and lowest at the Fe/VC interface. Note that the magnitudes of the tensile strain ranging from 2.51 to 9.19 % were much higher than those of the compressive strain of 1.16-2.18 % induced in the TMCs. This strain asymmetry can be explained by the lower bulk modulus of Fe (172 GPa) relative to the TMs (235390 GPa). Furthermore, after the atomic relaxation of the interface systems, it was observed that the TM atoms for TiC, VC, and NbC slightly moved away from the interface, whereas those of MoC and WC also slightly toward the interface. The movement of interface atoms was determined by comparing the z coordinates between the TM and its neighboring C atoms. The results were expressed as zTM-zC, as shown in Table 2. The positive values of zTM-zC in the Fe/MoC and Fe/WC interface systems indicate the presence of strong chemical bonding between Mo or W and Fe at the interface. Apparently, the binary carbides of MoC and WC in the NaCl-type structure have positive formation energies36,37, indicating their unstable states. These positive values of zTM-zC and positive formation energies of MoC and WC originate from the fact that the ground states of those carbides are hexagonal structures. There were little differences on the interface Fe-C bond length, dFe-C, in the range of 1.845-1.889 Å with the deviation of 1 %. The calculated interface energies between BCC Fe and the binary carbides are presented in Figure 2. The interface energy is highest for the Fe/TiC interface system and decreases in the order of Fe/VC, Fe/NbC, Fe/MoC, and Fe/WC. It should be noted that a positive interface energy value was obtained for the Fe/TiC system, indicating that the separate bulk states of Fe and TiC are preferred rather than forming an interface. Negative values were obtained in the other binary carbide systems, meaning that there exists a relatively strong bonding between Fe and those TMCs. Considering the fact that the interface contains many structural defects such as vacancies, the lack of those impurities, which increases the internal energy of the interface system (EFe/TMC), causes a small decrease in the interface energy35. Therefore, the Fe/TiC interface system showing the highest interface energy could be present in the positive value ranges. The significantly low interface energies of the Fe/WC and Fe/MoC systems are explained by the fact that the stable structures of MoC and WC are not of the NaCl-type structure but hexagonal structure, which induces an increase in ETMC,bulk and consequently a decrease in the interface energy38. The tendency of the formation of strong bonds in the Fe/MoC and Fe/WC interface systems can be substantiated by a positive zTM-zC as described in Table 2. These calculation results demonstrated that the interface energies were not strongly affected by the


Page 6 of 22

Page 7 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


magnitude of strain arising from the lattice mismatch between Fe and the carbides. Therefore, only the chemical contribution from the carbides to the interface energy will be considered hereafter. The calculated interface energies for Ti-based complex carbides containing TMs (e.g., V, Nb, Mo, and W) are presented in Figure 3. The composition and the configuration at a given composition were determined. For each composition, the energetically favorable configuration corresponding to the lowest interface energy was connected with a solid line. To concentrate on the influence of the added TMs on the stability, the interface energies for complex carbides were compared with those of the Fe/TiC system. The results showed that the addition of TMs by 50 % in Ti-based carbide resulted in a decrease in the interface energies for all the systems. For the Fe/(Ti, Nb)C and Fe/(Ti, Mo)C systems, the lowest interface energies were found at a composition of (Ti0.5m0.5)C, where m represents Nb and Mo. Those values were far beneath the virtual lines generated between 0 % and 100 %, indicating that the influence of the TMs is maximized at a concentration of 50 %. Particularly for Mo, the Fe/(Ti0.5Mo0.5)C system with the Fe/MTTM configuration showed a maximum decrease of 1.04 J/m2 in the interface energy compared to the Fe/TiC system. It was also found that such a low interface energy for the Fe/MTTM system corresponds to a shorter bond length between the interface Fe and Mo atoms (2.79 Å) compared to that between the Fe and Ti (3.17 Å) in the Fe/TiC system. The interface energy for the Fe/(Ti, W)C system decreased monotonically with the concentration of W, indicating that the formation of binary carbide of WC is always preferred over formation of the complex carbides of (Ti, W)C. Figure 4 shows the lowest interface energies among the all compositions and configurations for a given Fe/TMC system. The lowest interface energies were obtained for the Fe/VTVV, Fe/NTTN, Fe/MTTM, and Fe/WTWW configuration with relative decreases of 0.44 J/m2, 0.76 J/m2, 1.04 J/m2, and 0.80 J/m2, respectively, from the interface energy of Fe/TiC. A remarkable finding was that the TMs added to the Ti-based carbides prefer to be present at the interfaces, forming a chemical bond with the Fe atom, indicating the segregation of TMs at the interface. This result implies that the segregation of the TMs significantly contributes to the coherence of the TMCs in the Fe matrix by forming TM-Fe bonds in addition to Fe-C bonds. The influence of the TMs on the stability of the interface was clearly observed in the Fe/(Ti, Mo)C system. It was found that a significant decrease in the interface energy observed in the Fe/(Ti0.5Mo0.5)C system with the Fe/MTTM configuration coincides with experimental reports on the enhancement of strength by the dispersion of nanometersized (Ti0.5Mo0.5)C10.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3.2. Electronic structure analysis of Fe/(Ti, Mo)C interfaces. To understand the bonding characteristics, electronic structure analysis was performed. In this section, we present the site-projected partial density of states (PDOS) for the interface atoms of the Fe/TiC, Fe/MTTM corresponding to the composition of Fe/(Ti0.5Mo0.5)C, and Fe/MoC systems. Each density of states was compared to those of strained bulk Fe and TMCs. It should be noted that the Fe/MTTM system showed the lowest interface energy among the interfaces investigated. First we note that the concentration of the neighboring Mo was shown to hardly affect the bonding character of Fe-C at the interface from the line profile analysis of the electron density between the Fe and C atoms in the Fe/TiC, Fe/MTTM, and Fe/MoC systems. Hence, the present study focuses on the characteristic features of TM-C and TM-Fe bonds at the interface, except those of Fe-C that have been well established in previous publications14. The PDOSs for the interface atoms of the Fe/TiC, Fe/MTTM and Fe/MoC systems are presented in Figure 5. The colored lines represent the interface system and the grey lines represent the bulk system. The Fermi level was aligned to zero eV. The results showed that most of the bulk features remained for all the systems when the strained Fe and TMCs formed the interface, in spite of the strong covalent Fe-C bonding present at the interface. Moreover, a pseudogap between the bonding and antibonding states was clearly observed in the bulk TMCs. This pseudogap is related to the hybridization between the d-orbital of the TMs and the p-orbital of the C, stabilizing the TMCs with a NaCl-type structure16. This hybridization in the TMCs is believed to possess high resistance to shear strain18. Detailed electronic structure analysis for bulk TiC and MoC at the equilibrium state have been conducted in previous publications36,38,39 and were in agreement with our results. As observed in Figure 5 (a) for the Fe/TiC system, the PDOSs of the interface and the bulk agree well except for a small peak at the Fermi level. Pseudogaps in the Fe/MTTM and Fe/MoC systems [Figure 5 (b) and (c)] shifted down because Mo has two more d electrons than Ti. For the Fe/MoC system, a pseudogap was observed at -3 eV, leading to the partial occupation of the antibonding states. This electronic structure causes the destabilization of the NaCl-type MTTM and MoC carbides in contrast to the stable TiC in the NaCl-type structure. This phase stability is consistent with the fact that the hexagonal-type Mo2C or MoC carbides are thermodynamically more stable than their NaCl-type counterparts34.


Page 8 of 22

Page 9 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The PDOS of Fe/TiC in Figure 5 (a) showed that the pseudogap state was occupied to a small extent and new resonance peaks were found relative to the bulk PDOS. The bonding states of C were shifted to slightly lower energies than those of bulk TiC. As a result, the p-orbital of C overlapped with the d-orbital of Fe at the interface at -2.2 eV and -3.2 eV in majority spin and -2.1 eV in minority spin (thin arrows), maintaining the Ti-C bonding states. Moreover, the hybridization between the d-orbital of Ti and the d-orbital of Fe was found at -1.5 eV in the minority spin (thick arrows), which is associated with the second nearest neighbor interaction (2NN) of Fe (refer to Figure 1). For the Fe/MTTM in Figure 5 (b), hybridization was clearly observed among Ti, Mo, and C atoms at -4.7 eV and -3.2 eV for majority spin and at -4.4 eV and -3.3 eV for minority spin (thin arrows). These hybridizations were contributed by the rigid shift of both the d-orbital of Mo and the p-orbital of C to higher energies. Meanwhile, for the Fe/MoC in Figure 5 (c), the interface PDOS resembled that of the bulk except in the antibonding states of Mo and C. The hybridization between the dorbital of Mo and the p-orbital of C at antibonding states was shifted to higher energies. Therefore, new resonance peaks were found at -4.0 eV and -2.0 eV for majority spin, and -4.0 eV for minority spin (thin arrows). It is noted that an increase in the density of states were clearly observed for the dorbital of Mo, which are at -1.19 eV for Fe/MTTM and -1.51 eV for Fe/MoC in minority spin (thick arrows). To examine the bonding characteristics in more detail, the PDOSs in minority spin for the Mo and 1NN Fe atoms shown in Figure 5 (b) were decomposed into the t2g (dxy, dyz, and dzx) and eg (dz2 and dx2-y2) orbitals. The representative results for the Fe/MTTM interface system are presented in Figure 6. It can be clearly observed that the hybridization of the d-orbitals for the Mo-Fe bonding results from the t2g interaction (-1.19 eV). No significant hybridization by the t2g interaction was found in the TiFe bonding, which is not shown in this paper. To understand the spatial electronic structure for the hybridization of the d-orbital between the Fe and the TMC interface, the partial electron densities from the Fermi level to -2 eV were plotted. Figure 7 (a) and (b) show the calculated partial electron density contours on a (110) cross section for the interfaces of Fe/TiC and Fe/MTTM, respectively. The contour levels are shown within the ranges of 0.00 (black) and 0.02 electrons/Å3 (white). For the Fe/TiC interface presented in Figure 5 (a), the localized bonding states between the Ti and the 2NN Fe were observed with a high electron density along a normal direction with respect to the interface with a bond length of 3.17 Å. This bond



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

corresponds to the resonance peak of Ti-Fe at -1.5 eV (minority spin) in the PDOS of Figure 5 (a). However, the electron density between the Ti and the first nearest neighbor (1NN) Fe atoms are quite low. On the contrary, a distinctive electron contour was obtained for the Fe/MTTM interface, as shown in Figure 7 (b). The localized bonding states between the Mo and 1NN Fe atoms were formed along the four oblique directions with respect to the interface with a bond length of 2.79 Å. The electron density contour for the Fe/MoC system was similar to that of the Fe/MTTM and is not presented in this paper. Consequently, the orbital hybridization between the Mo and 1NN Fe atoms makes the Mo-segregated interface more stable, resulting in the stronger adhesion and shorter bond length than the Ti-segregated interface. These electronic structures are in accordance with the energetics showing the lowest interface energy of the Mo-segregated system. The DFT results are highly supportive of previous experimental reports on the enhancement of mechanical properties by the addition of Mo in Ti-based steel. However, the calculated phase diagram of Ti-Mo-C alloys by the CALPHAD method has shown that the (Ti0.85Mo0.15)C, which is Ti-rich phase, is thermodynamically equilibrium. The discrepancy between (Ti0.5Mo0.5)C obtained from DFT and experiments and (Ti0.85Mo0.15)C obtained from CALPHAD is explained by the size effect. Phase diagrams are a useful tool for explaining the thermodynamic state of a system. However, the direct explanation using the calculated phase diagram for nanometer-sized materials having high surface to volume ratio is unreasonable. Because, in the CALPHAD approach, the determination of the equilibrium composition is accomplished with bulk phases. Moreover, the elastic strain field occurring in lattice of the semi-coherent interface can significantly influence the physical properties as well as their chemical composition and crystal structure of nanometer-sized materials. Considering the fact that Mo prefers to be segregated at the interface as observed in the present study, the proportion of Mo in (Ti, Mo)C is predicted to increase as decreasing the size of the carbide. Eventually, the equilibrium composition could reach the level of (Ti0.5Mo0.5)C due to an increase in the proportion of the interface, when the carbides are formed in the nanometer-size with few atomic layers. In addition, we suggest one possible mechanism for the nucleation of the complex carbides of (Ti, Mo)C in the perspective of the interface energy. In general, MCs are precipitated by moletn alloys that cool from high temperatures. In the process of solidification, the NaCl-type TiC carbides are formed earlier than the molybdenum carbide in the Fe matrix because the precipitation temperature of TiC is much higher than that of MoC (above 1250 °C)41. During the subsequent solidification, MoC would be epitaxially segregated at the interface between the pre-precipitated NaCl-type TiC


Page 10 of 22

Page 11 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and the Fe matrix as forms of complex carbides of (Ti, Mo)C to reduce the interface energy. Hence, the fine dispersion of the (Ti, Mo)C at the more energetically stable state than TiC or other complex carbides leads to the enhancement of the strength of these materials.

4. CONCLUSIONS First principles calculations based on DFT have been performed to investigate the interface energy of Ti-based MCs containing V, Nb, Mo, and W in the BCC Fe matrix. The effects of composition and configuration of the TMCs on the interface properties have been determined. The electronic structures of the Fe/(Ti, Mo)C interfaces have been investigated to identify the bonding characteristics of Mo at the interface. From the energetics of the various carbides, the formation of complex carbides has led to a significant decrease in the interface energy compared to TiC. In particular, the (Ti0.5Mo0.5)C, where Mo is segregated at the interface (MTTM), has been found to be the most stable. From the electronic structure analysis, this stability of the Mo-segregated carbides has been shown to be due to the d-orbital hybridization between the Mo and 1NN Fe atoms at the interface. In particular, the t2g interaction in Mo-Fe bonding has been found to play a crucial role in reducing the interface energy but has not been observed at the Fe/TiC interface.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACKNOWLEDGMENT This study was supported by a grant from the Fundamental R&D Program for Core Technology of Materials funded by the Ministry of Knowledge Economy, Republic of Korea. This study was also supported by the Future-based Technology Development Program (Nano Fields) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. 2011-0019162).


Page 12 of 22

Page 13 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


REFERENCES (1) Toth, L. E. Transition Metal Carbides and Nitrides, Academic; New York, 1971. (2) Levy, R. B.; Boudart, M. Science, 1973, 181, 547-549. (3) Hanif, A.; Xiao, T.; York, A. P. E.; Sloan, J.; Green, M. L. H. Chem. Mater. 2002, 14 (3), 1009-1015. (4) Zaoui, A.; Bouhafs, B.; Ruterana, P. Mater. Chem. Phys. 2005, 91, 108-115. (5) El Zahhidl, M.; Oudghiri-Hassani, H.; McBreen, P. H. Nature. 2001, 409, 1023-1026. (6) Priestner, R.; Zhou, C.; Ibraheem, A.K. Titanium Technology in Microalloyed Steels, Institute of Materials; London, 1997. (7) Mishra(Pathak), S. K.; Ranganathan, S.; Das, S. K. Scripta Mater. 1998, 39, 253-259. (8) Poths, R. M.; Higginson, R. L.; Palmiere, E. J. Scripta Mater. 2001, 44, 147-151. (9) Sun, J.; Boyd, J. D. Int. J. Press. Vessels Piping 2000, 77, 369-377. (10) Funakawa, Y.; Shiozaki, T.; Tomita, K.; Yamamoto, T.; Maeda, E. ISIJ Int., 2004, 44, 19451951. (11) Chen, C.Y.; Yen, H.W.; Kao, F.H.; Li, W.C.; Huang, C.Y.; Yang, J.R.; Wang, S.H. Mater. Sci. Eng. A, 2009, 499, 162-166. (12) Yen, H.-W; Huang, C.-Y.; Yang, J.-R. Scripta Mater. 2009, 61, 616-619. (13) Sutton, A.P.; Balluffi, R.W. Interfaces in Crystalline Materials, Clarendon Press; Oxford , 1995. (14) Lee, J.-H.; Shishidou, T.; Zhao, Y.-J.; Freeman, A. J.; Olson, G. B. Phil. Mag. 2005, 85, 36833697. (15) Jung, W.-S.; Chung, S.-H. Modelling Simul. Mater. Sci. Eng. 2010, 18, 075008(1-7). (16) Dudiy, S.V.; Lundqvist, B.I. Phys. Rev. B 2001, 64, 045403(1-14). (17) Siegel, D.J.; Hector Jr, L.G.; Adams, J.B. Acta Mater. 2002, 50, 619-631. (18) Jhi, S.; Ihm, J.; Louie, S. G.; Cohen, M. Nature 1999, 399, 132-134. (19) Hartford, J. Phys. Rev. B 2000, 6, 2221-2229. (20) Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864-871. (21) Kohn, W.; Sham, L.J. Phys. Rev. 1965, 140, A1133-1138. (22) Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15-50. (23) Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169-11186. (24) Blöchl, P.E. Phys. Rev. B 1994, 50, 17953-17979. (25) Perdew, J.P.; Wang, Y. Phys. Rev. B 1992, 45, 13244-13249. (26) Ishikawa, F.; Takahashi, T.; Ochi, T. Metall. Trans. A 1994, 25A, 929-936. (27) Yang, Z.-G.; Enomoto, M. Mater. Sci. Eng. A 2002, 332, 184-192.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(28) Wyckoff, R.W.G. Crystal Structure, Wiley; New York, 1963. (29) American Institute of Physics, American Institute of Physics Handbook, McGrow-Hill; New York, 1970. (30) Sha, X.; Cohen, R.E. Phys. Rev. B 2006, 74, 214111(1-6). (31) Villars, P.; and Calvet, L. D. Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, American Society for Metals; Metals Park, OH, 1985. (32) Zhukov V. P. Transition Metal Carbides and Nitrides, Academic; New York, 1971. (33) Hare, J.P.; Hsu, W.K.; Kroto, H.W.; Lappas, A.; Prassides, K.; Terrones, M.; Walton, D.R.M. Chem. Mater. 1996, 8, 6-8. (34) Hugosson, H. W.; Eriksson, O.; Nordström, L.; Jansson, U.; Fast, L.; Delin, A.; Wills, J. M.; Johansson, B. J. Appl. Phys. 1999, 86, 3758-3767. (35) Price, D. L.; and Copper, B. P. Phys. Rev. B: Condens. Matter 1989, 39, 4945-4957. (36) Hugosson HW, Eriksson O, Jansson U, Johansson B. Phys Rev B 2001, 63, 134108(1-11). (37) Jang, J. H.; Lee, C.-H.; Heo, Y.-U.; Suh, D.-W. Acta Mater. 2012, 62, 208-217. (38) Velikanova, T. Y.; Kublii, V. Z.; Khaenko, B. V.; Sov. Powder Metall. Metal Ceramics, 1988, 27(11), 891-896. (39) Guillermet, A. F.; Grimvall, G. Phys. Rev. B 1989, 40, 10582-10593. (40) Shim, J.-H.; Oh, C.-S.; Lee, D.-N. Met. Mater. Trans. B 1996, 27B, 955-966. (41) Shim, J.-H. (Private communication)


Page 14 of 22

Page 15 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TABLES Table 1. Calculated lattice parameters and bulk moduli for Fe and NaCl-type TMCs. Experimental data are in parentheses. The a0/√2 values of the TMs are also presented to show the Baker-Nütting relationship.

Bulk Fe TiC VC NbC MoC WC

Lattice parameter (Å) a0

B (GPa)

2a0 / 2

2.836 (2.8628) 4.338 (4.3230) 4.163 (4.1631) 4.511 (4.4731) 4.390 (4.2533) 4.393 (4.3835)

3.067 2.943 3.189 3.104 3.106

172 (17029) 235 (24028) 307 (30332) 301 (30232) 381 (36434) 390 (36531)

Table 2. Cell parameters (a), induced strain in Fe due to the lattice mismatch with carbides (δ), relative z-coordinate of the TM atoms compared to that of the C atoms (zTM-zC), and interlayer spacing at the interface (dFe-C) of the interface systems. Interface system Fe/TiC Fe/VC Fe/NbC

a (Å)

δ (%)

zTM-zC (Å)

dFe-C (Å)

3.000 2.909 3.123

5.467 2.509 9.190

-0.058 -0.078 -0.004

1.880 1.845 1.889

Fe/MoC Fe/WC

3.044 3.053

6.833 7.108

0.098 0.215

1.879 1.870



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

FIGURE CAPTIONS Figure 1. (Color online) (a) Supercell structures of Fe/TiC consisting of 8 Fe atoms, 4 Ti and 4 C atoms. Atomic configurations of (b) (Ti0.75m0.25)C, (c) (Ti0.5m0.5)C, and (d) (Ti0.25m0.75)C. T and m denote Fe and TMs (e.g., V, Nb, Mo, and W), respectively. The sequence of stacking of the TMCs is represented from the top to the bottom. Figure 2. Interface energies between the BCC Fe matrix and the NaCl-type binary carbides of TiC, VC, NbC, MoC, and WC. Figure 3. Interface energies of the (a) Fe/(Ti1-xVx)C, (b) Fe/(Ti1-xNbx)C, (c) Fe/(Ti1-xMox)C, and (d) Fe/(Ti1-xWx)C systems with various layer configurations. For each interface system, the lowest interface energies at a given composition are connected with solid lines. T, N and M denote Ti, Nb and Mo, respectively. Figure 4. The lowest interface energies for various compositions and configurations of the Fe/(Ti1xmx)C

systems. T, N and M denote Ti, Nb and Mo, respectively.

Figure 5. (Color online) Projected density of states (PDOS) of the atoms at the interfaces of (a) Fe/TiC, (b) Fe/MTTM (Ti0.5Mo0.5C), and (c) Fe/MoC. The PDOS in the bulk structures are represented using grey lines. The left and right panels show the majority and minority spins, respectively. Figure 6. The d-orbitals divided into t2g and eg local symmetries in the minority spin for the interface Mo and Fe atoms of the Fe/MTTM system. Figure 7. Partial electron density contours on a (110) cross section in the range within 2 eV below the Fermi level (-2 eV < E-EF < 0 eV) for the (a) Fe/TiC and (b) Fe/MTTM interface systems.


Page 16 of 22

Page 17 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


FIGURES

Figure 2. (Color online) (a) Supercell structures of Fe/TiC consisting of 8 Fe atoms, 4 Ti and 4 C atoms. Atomic configurations of (b) (Ti0.75m0.25)C, (c) (Ti0.5m0.5)C, and (d) (Ti0.25m0.75)C. T and m denote Fe and TMs (e.g., V, Nb, Mo, and W), respectively. The sequence of stacking of the TMCs is represented from the top to the bottom.

Figure 2. Interface energies between the BCC Fe matrix and the NaCl-type binary carbides of TiC, VC, NbC, MoC, and WC.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3. Interface energies of the (a) Fe/(Ti1-xVx)C, (b) Fe/(Ti1-xNbx)C, (c) Fe/(Ti1-xMox)C, and (d) Fe/(Ti1-xWx)C systems with various layer configurations. For each interface system, the lowest interface energies at a given composition are connected with solid lines. T, N and M denote Ti, Nb and Mo, respectively.


Page 18 of 22

Page 19 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. The lowest interface energies for various compositions and configurations of the Fe/(Ti1xmx)C

systems. T, N and M denote Ti, Nb and Mo, respectively.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5. Projected density of states (PDOS) of the atoms at the interfaces of (a) Fe/TiC, (b) Fe/MTTM (Ti0.5Mo0.5C), and (c) Fe/MoC. The PDOS in the bulk structures are represented using grey lines. The left and right panels show the majority and minority spins, respectively.


Page 20 of 22

Page 21 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6. The d-orbitals divided into t2g and eg local symmetries in the minority spin for the interface Mo and Fe atoms of the Fe/MTTM system.

Figure 7. Partial electron density contours on a (110) cross section in the range within 2 eV below the Fermi level (-2 eV < E-EF < 0 eV) for the (a) Fe/TiC and (b) Fe/MTTM interface systems.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

TABLE OF CONTENTS IMAGE


Page 22 of 22

First-Principles Study of the Interfaces between Fe and Transition

Recommend Documents