Stability, electronic and mechanical properties of Fe2B

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Physica B 403 (2008) 1723–1730 www.elsevier.com/locate/physb

Stability, electronic and mechanical properties of Fe2B B. Xiaoa, J.D. Xinga,, S.F. Dingb, W. Sua a

State Key Laboratory of Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China b Institute of Opto-Electronic Materials and Technology, South China Normal University, Guangzhou 510631, China Received 1 July 2007; received in revised form 4 September 2007; accepted 1 October 2007

Abstract In this paper, the stability, electronic and mechanical properties of three polymorphs of Fe2B were studied using CASTEP code. The calculated binding energy and formation energy values showed that Tp2 (Space group, I42m) and Tp3 (Space group, I4=mcm) structures of Fe2B are more stable than Tp1 ðI42mÞ. Structural analysis results indicated that Tp2 and Tp3 have the same atom coordinate numbers. Electronic structure calculations revealed that both Tp2 and Tp3 have very similar chemical bonding states, the d orbital splitting reduced DOS density at Fermi surface result in total energy reduction when compared with that of Tp1, and is consistent with thermodynamical results. The covalent bonds in these structures are due to orbital overlap between p bands of B and d bands of Fe, but the whole system has a metallic character and DOS at Fermi level are dominated by d bands of Iron. Elastic constants were also evaluated and indicated that in order to improve the abrasive property of boron casting irons; Tp1 is better than the other two structures and has the largest bulk modulus and Young modulus values. r 2007 Published by Elsevier B.V. PACS: 71.20.b; 71.15.Nc; 71.20.Be; 62.20.Dc; 65.40.Gr Keywords: Density functional theory; Semi-iron boride; Thermodynamical properties; Electronic structures; Elastic constants

1. Introduction Until now, for many wearing resistance materials, their superior mechanical properties are usually due to precipitation phases or compounds with high hardness and high melting point, but most importantly the stability [1–4]. These requirements cannot be always fulfilled simultaneously, before we began to modify these compounds compositions or to control microstructures of second phases, basic properties, such as stability, chemical bonds and mechanical parameters must be known firstly. Casting iron and related materials have many applications in various industry fields, for example can be used as structural materials, machine building blocks, wearing resistance devices [1,5]. For casting irons containing certain concentrations of carbon or boron element, transition metal compounds with these impurities can be easily formed during solidification process; these are including Corresponding author. Tel.: +86 29 82665479; fax: +86 29 82663453.

E-mail addresses: [email protected], [email protected] (J.D. Xing). 0921-4526/$ - see front matter r 2007 Published by Elsevier B.V. doi:10.1016/j.physb.2007.10.014

carbides with cementite like structure (Fe3C), borides like FeB, Fe2B and Fe3B, M7C3(M=Fe, Cr and Mn) type carbides in high content chromium casting irons and also some mixture compounds (FeCxBy) [6–9]. When considering the abrasive performance of carbon steels, casting irons, these compounds may play a key role to improve the final mechanical properties of products. However, experimental values on stability or mechanical properties of these compounds are limited since it is very difficult to extract these compounds from bulk casting irons or to develop an effective method to obtain large bulk samples. Due to above reasons, to understand various properties of these compounds become important. Several authors have been applied first principle calculations to investigate fundamental properties of Fe3C, Fe3B and other carbide forms in casting irons [10–16]. For Fe2B, main issues were focused on experiments and subsequent heat treatment, but lack of theoretical study [17–20]. In this paper, the ground state properties of Fe2B were evaluated using CASTEP code in order to provide a guard lines for microstructure modifications of various boron casting iron products.

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This paper is organized as follows: calculation methods and crystal structures will be briefly discussed in Section 2, stability, electronic and mechanical properties are illustrated in Section 3 and conclusions are presented in Section 4.

2. Crystal structures and calculation details In this study we carried out first principle calculations based on Density Functional Theory, as implemented in CASTEP code which uses a plane wave basis set for expansion of effective single particle Kohn–Sham energy [21–24]. Ultrasoft pseudopotentials were used to describe the interactions of ionic core and valence electrons. Valence states considered in this study are including iron 3d64s24p and B 2s22p1. For comparisons, both local density approximation (LDA) of CA-PZ and generalized gradient approximation (GGA) within PBE scheme were employed to evaluate exchange-correlation energy. A kinetic energy cut-off 300 eV was used for plane wave expansions in reciprocal space. Magnetic state of Fe2B was not considered in this paper because each of these structures has even number of valence electrons and below the Fermi level the corresponded Kohn–Sham orbits were fully occupied. As a result, computational costs were reduced greatly. Energy calculations in the first irreducible Brillouin zone were performed using a special k point sampling methods of Monkhorst–Pack scheme and set as 5  5  5, which equivalent to 18k-points for bulk calculations [25]. BFGS optimization method was used to find the ground state of Fe2B crystals which both atom positions and lattice parameters were optimized simultaneously [26]. Total energy changes were finally reduced less than 0.2  105 eV/atom, and Hellman–Feynman forces acting on atoms were converged less than 0.05 eV/A˚. In order to calculate binding energy and formation enthalpy of these structures, we also carried out calculations for B and body centered cubic iron crystal in order to get bulk binding energy values of pure elements. Total energy of isolated B and Fe atoms were directly achieved from CASTEP output files.

Usually, binding energy and formation enthalpy are defined as E Binding ðFe2 BÞ ¼

E total ðFe2 B; cellÞ  nE iso ðBÞ  2nE iso ðFeÞ , n (1)

DH r ðFe2 B; 0 KÞ E Binding ðFe2 B; cellÞ  nE binding ðBÞ  2nE Binding ðFeÞ , ¼ n ð2Þ where E Binding ðFe2 BÞ is binding energy of Fe2B per formula, E total ðFe2 B; cellÞ is total energy of calculated cell, E iso ðX Þ represents total energy of isolated atom X, DH r ðFe2 B; 0 KÞ is formation enthalpy of Fe2B evaluated at 0 K, E binding ðX Þ refers to binding energy of X crystal and finally n is total number of Fe2B formula contains in crystal. A collection of crystal structures of iron boride are shown in Table 1, they belong to one crystal systemtetragonal but with different space group [27–29]. Here we designated these structures as Type1 (Tp1, Space group: 121), Tp2 (1 2 1) and Tp3 (1 4 0) in order to avoid misuse. There are four formula unit of Fe2B in each cell. Fe atoms are at 8i site both in Tp1 and Tp2 structures, and for B they are at Wyckoff site of 2a and 2b for Tp1 and 4c for Tp2. Because of higher point symmetry of 2a, 2b and 4c site of 121 space group, they are independent on any additional variable, but for 8 h site which determined by other two parameters x and z. For Tp3, eight iron atoms are in general positions (8 h), four boron atoms are in special positions (4a). It is interesting that both Tp2 and Tp3 have very similar crystal structure although they are quite different in space group. Tp3 has an inverse element which lost in Tp1 and Tp2 space group. The crystal structures of these borides are illustrated in Fig. 1. The lattice relationships between Tp3 and Tp2 are also shown. Actually, the atomic configurations in Tp3 and Tp2 are completely the same, we can easily find conventional cell of Tp3 in Tp2 when views the lattice projection along z direction. On the other hand, we can find the lost symmetry element in Tp2 cell by a rigid movement of Fe and B atom layers in Tp2

Table 1 Crystal structures of semi-iron boride Species

Space group

International table number

Atom positions Wyckoff symbols

Lattice parameter (A˚)

ICSD number

Fe2B

I-42m

121

B Fe

2a 2b 8i

a ¼ b ¼ 5.088 c ¼ 4.232

16 809

Fe2B

I-42m

121

B Fe

4c 8i

a ¼ b ¼ 5.099 c ¼ 4.24

30 446

Fe2B

I-4/mcm

140

B Fe

4a 8h

a ¼ b ¼ 5.11 c ¼ 4.249

42 530

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Fig. 1. Crystal structures of Fe2B studied in this paper: (a) Tp1; (b) Tp2; and (c) Tp3.The upper panel shown the view along y direction and corresponding down part is the project along z-axis. The big ball is boron and the small refers to iron atoms.

3. Results and discussions Since the accuracy of the first principle calculations may dependent on many parameters, such as kinetic energy cut off value for plane wave expansions, exchange-correlation energy scheme and k point grid, etc. We calculated the variations of binding energy of Tp3 as a function of energy cut off values, both the GGA and LDA are used in order to assure the accuracy of our results (for the other two structures, this trend also valid). As shown in Fig. 2, the calculated binding energy values oscillated slightly as energy cut off increased from 300 to 420 eV. On the other hand, in Fig. 3 we also plotted the relationships between cell parameters and energy cut-off values, a very tiny variation of calculated values are obtained. Although, in this paper we used the minimum value of 300 eV for the stability and electronic investigations, but our conclusions are reasonable.

-26.5 -27.0 Binding energy (eV)

along z-axis by 0.25c and also along x- and y- directions by 0.5a and 0.5b, the final structure will automatically convert to Tp3 cell. We noticed that the above operations are in fact unnecessary, Wyckoff site of 4c in Tp2 are equivalent to 4a positions of Tp3, also valid for iron atoms. The chemical bond environment is very similar in Tp2 and Tp3, each B has eight nearest Fe atoms, and the coordinate numbers of Fe is 15, four of them are Fe–B bonds and again verified our result that Tp2 and Tp3 have the same atomic configuration. For Tp1, B atoms are four coordinated with Fe, Fe atoms are 11 coordinated with two Fe–B bonds and nine Fe–Fe bonds. Both numbers are less than Tp2 and Tp3. The relative stability of these crystals will be clarified in next section.

-27.5 LDA-Tp3 GGA-Tp3

-28.0 -28.5 -29.0 -29.5 -30.0 300

320

340 360 380 400 Kinetic energy cut-off (eV)

420

Fig. 2. The calculated binding energy of Tp3 as a function of energy cutoff values, both GGA and LDA scheme were used and compared.

First we illustrated the calculated equilibrium lattice parameters and cell volumes in Table 2 and corresponding exchange correlation energy schemes also indicated. When compared with experimental values in Table 1, theoretical parameters all contract within x- and y-axis, but elongate parallel to z-axis only for Tp1 structure within two different methods, the other two structures are slightly compressed in this direction. The deviation between experimental and evaluated values of cell parameters is varied from 6.63% to 7.15% along x and y directions and from 3% to 10% for c values using LDA scheme, within GGA scheme, it is changed from 4.94% to 5.32% and 0.75% to 11% for a ¼ b and c, respectively. Very large deviation values appeared for Tp1 results are

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caused by enormous atomic displacement of iron during relaxations. The calculated cell volume values in LDA case are smaller than GGA results. It is well accepted that LDA method usually overestimates the cohesive energy and result in small cell parameters [30,31]. As for GGA, lattice expansions are the common results [22]. But in this study, cell parameters evaluated using different methods shown rather complicated relations, besides Tp1, cell parameters of Tp2 and Tp3 are underestimated along all directions either LDA or GGA was used. On the other hand, the same degree of agreement of Tp2 and Tp3 with respect to experimental values is due to atomic configuration similarity and also because Tp1 is a metastable structure. In addition, both Tp2 and Tp3 are less overestimated within GGA method especially for c-axis. Now we are going to discuss the relative stability of these Fe2B structures based on energy calculations. Common features for a ground state of matter are low in free energy; both binding energy and formation enthalpy have negative values as defined in Eqs. (1) and (2). The calculated results are listed in Table 3, also included binding energies of bulk iron and boron. From Table 3, it is evident that these energy parameters calculated using different exchange-correlation energy are quite different; GGA results of total energy are generally

4.9

Cell parameter (0.1nm)

4.8 4.7

Tp3-a axis LDA Tp3-c axis LDA Tp3-a axis GGA Tp3-c axis GGA

4.6 4.5 4.4 4.3 4.2 4.1 300

320

340 360 380 Energy cut off value (eV)

400

420

Fig. 3. The variations of cell parameters as a function of energy cut-off values.

smaller than LDA method, and again Tp2 and Tp3 have very close values not only in total energy but also for binding energy and heat of formation which are consistent with the discussions in Section 2 that they have similar chemical bonding state. We noticed that for bulk B, two stable crystal structures exist, aB (Space group: P6/m) and bB (Space group: R-3 m) [32–34], since each of them has a large number of atoms in unit cell and in order to save computational cost, the binding energy was cited directly from references. When considering total energy values, we found that both GGA-PBE and LDA-CA-PZ method revealed the same stability ordering, total energy decreased from Tp1 to Tp3. Therefore Tp1 is less stable and probably the observed structure in experiments is Tp2 or Tp3. Binding energy generally has a negative value, because when compared with that of isolate atom, bonding state is always lower in energy. PBE (CA-PZ) results of binding energy are 25.078 (28.28), 26.67 (30.05) and 26.67 eV (30.07) for Tp1, Tp2 and Tp3, respectively. Tp1 is again unstable; the other two structures are the ground state. As the calculated equilibrium lattice values are not consistent with common expectations, we are not sure whether over binding problems may dominate these values. But it is less ‘‘over binding’’ in GGA-PBE method. According to thermodynamical theory, the stability of Fe2B can be uniquely determined by its formation enthalpy (also called heat of formation) below certain temperature (G=H-TS, free energy is also depend on T and S) [30]. The results clearly show that Tp1 has a positive value corresponding to an endothermic reaction both within GGA and LDA algorithms. Hence Tp2 and Tp3 are more stable when compared with that of Tp1, and the calculated energy values are very close to each other, the average deviation between theoretical and experimental values are 70 and 14 K J/mol for LDA and GGA results, respectively. A good agreement with experimental results can be achieved using GGA methods rather than LDA; hence we assure that the overbinding errors really exist. Due to the above results and discussions in Section 3, we suspect that crystal structure differences of Tp2 and Tp3 could be caused by some experimental uncertainties which may attribute to temperature effects, and in many cases this leads to lowering the space group of solids. In order to

Table 2 Cell parameters and equilibrium volume after relaxation with different methods Species

Opt. method

Cell parameters (A˚)

Cell volume (A˚)

a, b

c

Tp1

CASTEP-LDA CA-PZ CASTEP-GGA PBE

4.7238 (7.15%) 4.817 (5.32%)

4.668 (10.8%) 4.737 (11.9%)

104.169 109.921

Tp2

CASTEP-LDA CA-PZ CASTEP-GGA PBE

4.769 (6.47%) 4.847 (4.94%)

4.124 (2.7%) 4.211 (0.68%)

93.786 98.947

Tp3

CASTEP-LDA CA-PZ CASTEP-GGA PBE

4.771 (6.63%) 4.838 (5.32%)

4.121 (3%) 4.208 (0.75%)

93.785 98.488

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Table 3 Total energy, binding energy and formation enthalpy of Fe2B crystals evaluated using different methods; useful energy parameters for pure elements are also shown Species

Methods

Total energy (eV/Cell)

Binding energy (eV/Unit)

Formation enthalpy (eV/Unit)

Formation enthalpy (KJ/mol)

Fe (BCC)

LDA-CA-PZ GGA-PBE

1720.422 1732.399

10.56 9.4

B (a)

LDA-CA-PZ GGA-PW91

Tp1

LDA-CA-PZ GGA-PBE

7190.3557 7236.6336

28.28 25.078

Tp2

LDA-CA-PZ GGA-PBE

7197.449 7243.0299

30.05 26.67

1.45 0.89

139.66 85.7

Tp3

LDA-CA-PZ GGA-PBE

7197.4453 7243.0117

30.07 26.67

1.47 0.891

141.59 85.8

7.48a 6.98b 0.3 0.702

28.896 67.6

71.13c

Fe2B a

Evaluated using total energy value of B with R-3M B12 crystal structure in Ref. [33]. From Ref. [32]. c Experimental value at 298 K in Ref. [34]. b

verify this conclusion, high accuracy X-ray diffraction or selected area electron diffraction method should be applied to boron casting irons to provide insightful informations on its crystal structure. In this part, the calculated electronic structure will be discussed. Here we are only concerning density of states and electron density distribution maps for studied structures, since band structures are rather complicated and confused due to large number of atoms in each Fe2B cell. Total DOS and angular projected DOS of Fe and B are depicted in Fig. 4. DOS of Tp3 are not shown as it is almost identical to Tp2. For many carbides, borides formed by transition metals, such as XC (X represents Ti, Nb, V, W, Mo and Fe, etc.), Y3C (Y refers to Fe, Co and Ni), Y3B (Fe, Co Ni) and XB2 (X ¼ Ti, Nb, V, Fe and Y, etc.), DOS near the Fermi surface are dominated by d like bands of transition metals [15,16]. Otherwise, the stability or chemical reactivity of bulk crystal is totally determined by d bands of metal, while the contributions from nonmetal atoms cannot be negligible. Only valence orbitals for all considered compounds are projected according to angular component for constitutions. In Fig. 4 it is evident that all of the considered structures have a metallic character and 3d bands of Fe determined the ground properties. 2s and 2p bands of B are low in energy and overlapped to each other in some degrees. The covalency in these crystals is mainly caused by 2p and 3d hybridizations which leads to the decrease of DOS at Fermi surface and sometimes affect magnetic properties. In reference [15], the author proposed that as carbon concentrations increased from Fe8C to FeC, a remarkable band splitting effect occurring due to competition of metal–metal bonds and metal–carbon bonds. We expect that this mechanism is also valid for the row of iron borides (Fe3B–Fe2B–FeB).

As shown in Fig. 4, overlapping of 2p and 3d orbital in Tp2 and Tp3 are stronger than that of Tp1 and 3d bands appearing as double peak shape which is in contrast to an intensive DOS peak located at Fermi level of Tp1. Usually, sharp DOS intensity at Fermi level could raise total energy of the whole structure and considered as a destabilized factor. This is consistent with energy calculations that Tp1 is less stable than the others. Population analysis provides further informations on chemical binding properties for these compounds, the calculated bond lengths are quite anisotropy for Fe2B. The interactions among Fe atoms respond for longer bond length as from 2.334 to 2.362 A˚ and 2.238 to 2.559 A˚ for Tp1 and other two structures, respectively. Fe–B and B–B have a bonding character because of positive orbital overlap values. The average bond length of Fe–B is 2.037 A˚ (2.0559 A˚) for Tp1 (Tp2 and Tp3), for B–B bond, the value is 2.334 A˚ (2.061 A˚). The largest overlapping values in those compounds are due to B–B bonds, which are 0.37 and 0.73 for Tp1 and the others. When compared the overlap populations of Fe–B of Tp1 with that of Tp2 and Tp3, it is found that the covalency between iron and boron atoms are slightly decreased. In Section 2, we verified that the coordinate numbers of Fe and B in these structures are quite different, in Tp1, B has four nearest Fe atoms and this number increased to eight for Tp2 and Tp3. Based on group theory, combinations or hybridizations of different orbitals intra or inter atoms are not only decided by energy differences but also depend on symmetric properties. In other words, these electron waves must have the same irreducible representations and also compatible with the point group of crystal. As Fe and B in these crystals occupied different Wyckoff sites and have different site symmetry features, orbital splitting behavior in Tp1 and Tp2 (Tp3) can be understood based on these

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30 TDOS

DOS/Cell

DOS/Cell

20 15 10

0 25

Fe:4s Fe:4p Fe:3d DOS/Cell

20 DOS/Cell

15 10 5

5

15 10 5 0 B:2s B:2p

0 18 16 14 12 10 8 6 4 2 0 2.5

Fe:4s Fe:4p Fe:3d

B:2s B:2p

2.0 DOS/Cell

3 DOS/Cell

TDOS

20

25

2

1.5 1.0

1 0.5 0.0

0 -15

-10

-5

0

5

10

15

Energy (eV)

20

-20

-15

-10

-5

0

5

10

15

20

25

Energy (eV)

Fig. 4. Total density of states (TDOS) and angular projected density of states (PDOS) of iron and boron atoms. (a) TDOS and PDOS of semi-iron boride of Tp1 and (b) PDOS and TDOS of Tp2. Dotted lines represent Fermi energy level.

Fig. 5. Total electron density distribution contour for three low index planes of Tp1: (a) (0 0 1); (b) (1 0 0); and (c) (1 1 0). These planes are plotted in order to illustrate the interactions of Fe–Fe, B–B and Fe–B, respectively. The density value is from 0.00 to 1.00 e/A3.

reasons. Since the electronegativity values are different in Pauling scale as 1.8 and 2.0 for Fe and B, a charge transfer mechanism can be easily proposed when checking the population results, metal atoms are all positive charged and B carried exceed negative charges. Total electron density map are shown in Figs. 5 and 6. Only Tp1 and Tp2

are depicted due to the same reason mentioned above. The core regions for both Fe and B have large values and smaller in interstitial area. Covalent bond features can be seen clearly in the picture between metal and B atoms. In summary, according to energy calculations and electronic structure results, we conclude that Tp1 is not the ground

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Fig. 6. Electron distribution map for Tp2 structure of selected planes: (a) (0 0 1) Fe–Fe; (b) (1 0 0), B–B bonds; and (c) (1 2 0), Fe–B bonds. All figures plotted with density value from 0.00 to 1.00 e/A˚3.

Table 4 Summarized elastic constants and other mechanical parameters Species

Tp1 Tp2 Tp3

Methods

GGA-PBE GGA-PBE GGA-PBE

Energy cutoff (eV)

500 500 500

k-Point grid

15  15  15 15  15  15 15  15  15

B (GPa)

Cij C11

C33

C44

C66

C12

C13

337.2 336.3 324.0

866.3 205.6 194.6

100.2 97.6 94.1

109.5 60.2 43.5

144.3 141.3 135.3

213.9 211.2 198.7

239.7 204.2 194.0

E (GPa)

G (GPa)

Ex

Ey

Ez

254.9 71.1 83.3

254.9 71.1 83.3

676.3 18.7 22.7

126.5 72.0 67.0

B: isothermal bulk modulus; E: Young modulus; and G: shearing modulus.

state of Fe2B at ambient conditions; this compound could be synthesized by applying non-equilibrium methods. Finally, the mechanical properties of these compounds will be briefly discussed in this part. In order to get reliable values, we used different k point grid to conduct elastic constants calculations using CASTEP code, we started with a k point grid as 5  5  5, and then increased to 10  10  10, but unfortunately the calculated bulk Young modulus values were very unstable with respect to k point used. They have opposite values in these two cases. Finally, a 15  15  15k point sampling grid was used for all crystals to get relatively satisfied results. All of elastic constants are summarized in Table 4 and exchangecorrelation scheme also included. The independent elastic constants number usually depends on the symmetry properties of crystal class according to Neumann’s rule. Concretely speaking, it is closely related to 32 point groups and transformation matrix elements for a tensor with a rank of 4. The fundamental theory behind elastic constant evaluations is Hook’s law: a linear relationship between two tensors, stress and strain, and a proportional coefficient Cijkl. In CASTEP code, in order get each independent elastic constant value, appropriate number of strain patterns will be imposed on crystal cell. The total energy associated

with each strain pattern is optimized and then fitted with [35–38] sij ¼ C ijkl kl .

(3)

For tetragonal crystal structures studied in this paper, there are six independent Cijkl values, C11, C12, C13, C33, C44 and C66. Bulk modulus, Young modulus and shearing modulus values are directly calculated within these constants. The calculated isothermal bulk modulus of Tp1 has the largest value as 239.7 GPa, in contrast to 204.2 and 194.0 GPa for the other two crystals. Since tetragonal structure has a lower symmetry than cubic class. Consequently, Young modulus is isotropy at xy plane but anisotropy perpendicular to this plane. The calculated Young modulus values are quite different for Tp1 and Tp2 (Tp3). Very similar to bulk modulus results, for Tp1 it is 254.9 GPa along x- and y-axis and 676.3 GPa parallel to z-axis, all are the largest values among studied structures. Mechanical properties for Tp2 and Tp3 are very similar and again due to structure features discussed previously. In other words, the chemical structures of Tp2 and Tp3 are identical but they have different space group due to some experimental uncertainties (temperature effects). The evaluated elastic constants matrix has positive values which indicate that they are mechanically stable structures. This is true for Tp2 and

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Tp3, but for Tp1, more accurate method should be applied to verify this conclusion. Although, the relationship between hardness and bulk modulus is still unclear, in most cases, this value is large enough for superhard compounds or intermetallics. For casting irons used under heavy abrasive service conditions, the mechanical properties of reinforced particles must be superior to wearing medium. From this point of view, Tp1 is better for wearing resistance casting irons to achieve a good performance in practice. In order to improve the stability of this structure, other elements should be introduced such as carbon, nitrogen and many other carbides forming elements; on the other hand we can use non-equilibrium solidification process to change thermodynamical conditions and promote synthesis. 4. Conclusions In this paper, the authors have been used first principle calculations based on density functional theory to investigate the ground state properties of Fe2B such as binding energy, formation enthalpy, electronic structure and elastic constants. The calculated equilibrium lattice parameters with different exchange-correlation energy conflict with general expectations that LDA results were underestimated and GGA overestimated it. Binding energy and heat of formation results revealed that Tp2 and Tp3 are more stable than Tp1. The calculated formation enthalpy energy of Tp1 is 0.3 and 0.702 eV/Fe2B using LDA and GGA, respectively. Electronic structure indicated that covalency in these compounds is due to 2p and 3d hybridizations of B and Fe. A decreasing of DOS intensity at Fermi energy in Tp2 (Tp3) is accomplished with a remarkable splitting effect of 3d bands and population analysis clearly verified that Fe–B and B–B bonds have large positive overlap population values. Although Tp1 is not the ground state, it has the largest mechanical properties such as bulk modulus and Young modulus. In other words, in order to improve abrasive properties of boron casting irons, Tp1 is superior to the other structures. A non-equilibrium processing should be involved for its synthesis. Acknowledgments The authors would like to thank Professor Y.H. Chen and Dr. X.J. Xie for useful discussions and also appreciated for providing CASTEP code and SGI working station. We also thank Dr. Liang.Yu from Northeastern University (Sheng Yang, PRC) provided useful data for this calculations. References [1] C.E. Campbell, G.B. Olson, Comput. Aided Mater. 7 (2001) 145.

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