Accepted Manuscript Electronic structure, bonding behavior and optical properties of (HfC)mAl4C3 (m�=�1, 2, 3) carbides Salman Mehmood, Athar Javed, Muhammad Nasir Rasul, Muhammad Azhar Khan, Altaf Hussain PII:
S0925-8388(18)30091-4
DOI:
10.1016/j.jallcom.2018.01.090
Reference:
JALCOM 44554
To appear in:
Journal of Alloys and Compounds
Received Date: 24 November 2017 Accepted Date: 6 January 2018
Please cite this article as: S. Mehmood, A. Javed, M.N. Rasul, M.A. Khan, A. Hussain, Electronic structure, bonding behavior and optical properties of (HfC)mAl4C3 (m�=�1, 2, 3) carbides, Journal of Alloys and Compounds (2018), doi: 10.1016/j.jallcom.2018.01.090. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
(b) Hf2Al4C5
C2 2.164 Å (0.233)
99.12°
o
116.27
M AN U
C3
(c) Hf3Al4C6
SC
(a) HfAl4C4
RI PT
Graphical abstract
1.882 Å (0.310)
C3 115.38o
Al1
C3
C2
C2
TE D
Al3
C2
Al1 2.087 Å (0.825)
C2
C2
o
101.89
EP
117.54°
2.108 Å (0.801)
C3
AC C
C3
1.934 Å (0.974)
1.919 Å (0.294)
102.96o
C2
ACCEPTED MANUSCRIPT 1
Electronic structure, bonding behavior and optical properties of (HfC)mAl4C3 (m = 1, 2, 3) carbides Salman Mehmood1,*, Athar Javed2, Muhammad Nasir Rasul1, Muhammad Azhar Khan1, and
RI PT
Altaf Hussain1,* *
Department of Physics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
2
Department of Physics, University of the Punjab, Lahore, 54590-Pakistan
Corresponding authors: *
SC
1
Salman Mehmood (
[email protected]); * *A. Hussain (
[email protected])
M AN U
ABSTRACT
This paper reports results from the study of the electronic structure, bonding and optical properties of ternary (HfC)mAl4C3 (m = 1, 2, 3) carbides. The interatomic bonding and bond order is studied to elucidate the role to atoms in the structure. The band structures of all three
TE D
(HfAl4C4, Hf2Al4C5 and Hf3Al4C6) carbides show conducting nature. All three carbides exhibit direct band gap. Density of states (DOS) spectra of HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides reveal that the total number of states, N(EF) at Fermi level are 2.84, 6.51 and 6.37 states/eV,
EP
respectively. The electronic charge transfer from Hf and Al atomic sites to C atomic site has been found in all three carbides. The bond order (BO) calculation of these carbides shows the
AC C
dominating role of Al-C bonds in to the cohesion of crystal structures. Localization index (LI) calculation reflects highly delocalized states near the Fermi level. The dependence of dielectric function and optical conductivity on photon energy show anisotropic behavior of HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides. Keywords: Carbides; ab-initio calculations; Electronic Structure; bonding behavior; Optical Properties
ACCEPTED MANUSCRIPT 2
1.
Introduction
Hafnium carbide (HfC) is the most refractory binary ceramic carbide which belongs to the transition metal carbides (TMCs) group [1,2]. Being a ceramic material with high melting point
RI PT
(~3900ºC), HfC has excellent mechanical and chemical properties. A good wear resistance and chemical inertness of HfC makes it a promising ceramic material for various applications [3-7]. For example, HfC has applications in ultra-high temperature environment such as in rockets,
SC
scramjet engines, re-entry vehicles and thermal protecting system for hypersonic vehicles. The HfC has also potential application as a fuel and structural matrix material in nuclear reactors [8-
M AN U
12]. However, poor degree of oxidation resistance and brittleness limits its applications and reliability [13,14]. To overcome these weaknesses, several efforts have been made by various research groups, see for example Refs. [15,16]. Similar to TAX or MAX phase materials [16], the ternary carbides generally represented by formula Tn+1AXn (where T = element from early
TE D
transition metals, A = A group element such as aluminum, X = C or N and n = 1, 2, 3. . .) offers to improve the ductility and degree of oxidation resistance by adding Al in binary carbides [1719]. Ternary aluminum carbides such as ZrAlC and HfAlC with different compositions have
EP
been successfully synthesized in laboratory and experimental results on structural and mechanical properties have been reported in Refs. [20-26]. Studies show that the degree of
AC C
oxidation resistance, mechanical strength, specific stiffness and/or fracture toughness of ternary (HfAlC and ZrAlC) carbides has significantly improved as compared to binary (ZrC and HfC) carbides [25-31].
Ternary Hf-Al-C system has several crystallographic phases. For example, ternary Hf2Al3C4 and Hf3Al3C5 carbides exhibit hexagonal symmetry with space group P63/mmc. Both Hf2Al3C4 and Hf3Al3C5 systems are iso-structural to Zr2Al3C4 and Zr3Al3C5 [32–35]. He et al. [25] found new
ACCEPTED MANUSCRIPT 3
phases (Hf2Al4C5 and Hf3Al4C6) of Hf–Al–C ceramics. Hf2Al4C5 and Hf3Al4C6 are similar to Zr2Al4C5 [36] and Zr3Al4C6 [37], respectively but dissimilar to Hf2Al3C4 and Hf3Al3C5 ceramics. m; while Hf2Al3C4 and Hf3Al3C5 Both Hf2Al4C5 and Hf3Al4C6 carbides exhibit space group R3
RI PT
carbides has space group P63/mmc. The Hf2Al3C4 and Hf3Al3C5 belong to homologous series of HfAlC phases [20,21,38] with general formula (HfC)mAl3C2 (m = 2 and 3); whereas Hf2Al4C5 and Hf3Al4C6, have chemical formula (HfC)mAl4C3 (m = 2 and 3).
SC
Nian et al. [39] synthesized new HfAl4C4 ternary carbide and studied its microstructural properties using XRD and TEM. They also studied the mechanical properties of HfAl4C4 by first
M AN U
principles approach [39]. He et al. [25] also reported the elastic and mechanical properties of Hf2Al4C5, Hf3Al4C6, Hf2Al3C4 and Hf3Al3C5 carbides along with HfC (cubic), HfC (hexagonal) and Al4C3. They found that the mechanical properties (elastic stiffness constants, bulk modulus, shear modulus and elastic modulus) depended on the Al-C and Hf-C slab thickness in Hf-Al-C
TE D
structure. Further, they concluded that the Hf3Al4C6 was stiffer and stronger as compared to Hf2Al4C5 [25]. Until now, though some theoretical calculations have been carried-out to study the elastic and mechanical behavior of Hf-Al-C carbides [25,39], the electronic structure,
studied so far.
EP
bonding behavior and optical properties of HfAl4C4, Hf2Al4C5 and Hf3Al4C6 have not been
AC C
In this paper, theoretical results on the electronic structure, bonding and optical properties of three ternary HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides are reported. First principles calculations have been performed by implementing the orthogonalized linear combination of atomic orbitals (OLCAO) method [40]. The band structures, bonding and optical properties of HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides are discussed and correlated with structural properties. The
ACCEPTED MANUSCRIPT 4
localization index (LI) and effective charge (Q∗) behavior is also discussed for better understanding of electronic and optical behavior of HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides. 2.
Computational detail
RI PT
For theoretical calculations of ternary (HfC)mAl4C3 (m = 1, 2, 3) carbides, first principles calculations were performed by implementing OLCAO method based on density functional theory [40,41]. In order to study the structure, bonding and optical behavior of three ternary
SC
HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides, results were produced by applying OLCAO method. OLCAO is a well-established code which offers to calculate electronic structure, chemical
M AN U
bonding and optical properties of crystalline [42,43] materials [42-4544,45]. The exchangecorrelation energy functional is calculated by applying local density approximation (LDA) [46]. For (HfC)mAl4C3 (m = 1, 2, 3) carbides, the initial structural model with lowest energy has been utilized as described by Nian et al. [39]. In OLCAO method, the wave functions of atomic
TE D
orbitals are expanded considering Gaussian type orbitals (GTOs). The quantization of angular momentum is applicable to spherical harmonics. To extract different properties, three basis sets are implemented in OLCAO method. Firstly, the full basis (FB) set is used in the calculation of
EP
self-consistent field (SCF) potential, band structures and density of states (DOS). For each atom, the FB set consists of core electron orbitals, occupied valence electron orbitals and empty shell
AC C
of unoccupied electron orbitals. For Hf-Al-C system, the FB set consists of Hf-(1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 5s, 5p, 4f, 5d, 6s, 6p, 6d, 7s, 7p, 7d, 8s and 8p), Al-(1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 5s and 5p) and C-(1s, 2s, 2p, 3s, 3p, 4s and 4p). Secondly, an extended basis (EB) set is applied in calculating optical properties. In this case, one additional shell of empty orbitals is included in order to improve the accuracy of higher energy states in the conduction band. Third one is a minimal basis (MB) set which is used for effective charge (Q*) and bond order (BO)
ACCEPTED MANUSCRIPT 5
calculations using Mulliken analysis [47]. MB set provides more localized basis in calculating Q* and BO. To obtain self-consistency in calculating the crystal potential, the total energy is allowed to converge to minimum value 0.0001a.u. To run simulations, a sufficient number of k-points are
3.
Results and Discussion
3.1
Crystal structure and atomic bonding
SC
calculated by using the method described elsewhere [43].
RI PT
necessary for SCF iterations and to obtain optical spectra (see Table 1). The BO and Q* are
Ternary (HfC)mAl4C3 (m = 1, 2, 3) carbides have hexagonal (a = b ≠ c) crystal structures. The
M AN U
HfAl4C4 has space group P3m1 (SG. No. 164) while both Hf2Al4C5 and Hf3Al4C6 carbides have space group R3m (SG. No. 166) [25,39]. There are two formula units with 18 atoms and 10 nonequivalent atomic sites (Hf = 1, Al = 4, C = 5) per unit cell of HfAl4C4. In Hf2Al4C5 and Hf3Al4C6, there are three formula units but Hf2Al4C5 has 33 atoms and 6 non-equivalent sites (Hf
TE D
= 1, Al = 2, C = 3) while Hf3Al4C6 has 39 atoms and 7 non-equivalent sites (Hf = 2, Al = 2, C = 3) in the unit cell. Table 1 presents the crystal structures and bonding data of HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides. The crystal structure of HfAl4C4 consists of (HfC)2 and Al4C3 layers as
EP
shown in Fig. 1a. In the crystal structure of HfAl4C4 carbide, Hf-C4 bonds are the longest bonds (bond length, BL = 4.183 Å) and Al1-C2 bonds are the shortest bonds (BL = 1.901 Å). Fig. 2a
AC C
shows the local bonding environment in the vicinity of Al3 atom. From Fig. 2a, it can be seen that the C3-Al3-C3 angle (117.54 ) is larger than C2-Al3-C3 angle (99.12 ). Moreover, the Al3-C2 bond is longer (BL = 2.164 Å) than that of Al3-C3 bond (BL = 1.934 Å). Fig. 2b-c depicts the local bonding environment in the vicinity of Al1 in Hf2Al4C5 and Hf3Al4C6. The Al1C2 bonds in the basal plane are longer (BL = 2.108 and 2.087 Å in Hf2Al4C5 and Hf3Al4C6, respectively) than Al1-C3 bonds (BL = 1.882 and 1.919 Å in Hf2Al4C5 and Hf3Al4C6,
ACCEPTED MANUSCRIPT 6
respectively) along c-axis. The C2-Al1-C3 bond is larger (116.27 ) in Hf2Al4C5 than Hf3Al4C6 (115.38 ). However, the situation is reversed in case of C2-Al1-C2 bond in Hf2Al4C5 (101.89 ) and Hf3Al4C6 (102.96 ). The detailed picture of self-consistent field (SCF) k-points, OLCAO k-
3.2
Electronic structure
3.2.1
Band structure
RI PT
points and lattice parameters along with cell volume is given in Table-1.
SC
Fig. 3 presents the calculated band structures of ternary (HfC)mAl4C3 (m = 1, 2 and 3) carbides. The Fermi level (EF) is fixed at 0.0eV (see dashed horizontal line in Fig. 3). All three band
M AN U
structures reflect the overlapping of valence band (VB) and conduction band (CB) leading to the conducting nature of HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides. This fact can be seen from the lower and upper set (from EF) of bands. Six bands are observed to cross the Fermi level (EF = 0.0 eV) and inter-mix with each other in band structure of HfAl4C4 (Fig. 3a). In band structure of
TE D
Hf2Al4C5 (Fig. 3b), ten bands cross the Fermi level while sixteen bands cross the Fermi level in Hf3Al4C6 (Fig. 3c). It is observed that the number of bands crossing the Fermi level increase with the increasing value of m in ternary (HfC)mAl4C3 carbides. Ternary (HfC)mAl4C3 (m = 1, 2 and
EP
3) carbides exhibit orbital overlapping to some extent, which means that the valence electrons/bands share some energy states with conduction electrons/bands. Further, the VB splits
AC C
into two parts; the upper VB and lower VB with an energy gap, Eg = 1.065, 1.98 and 191 eV for HfAl4C4, Hf2Al4C5 and Hf3Al4C6, respectively. The width of upper and lower VB decreases from 8.13 to 6.92 eV and 4.94 to 4.55 eV as the value of m increases (1 to 3) in ternary (HfC)mAl4C3 carbides (Table 1). Further, the upper VB is denser as compared to lower VB in all three HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides (see Fig. 3 a-c).
ACCEPTED MANUSCRIPT 7
3.2.2
Density of states
Fig. 4 shows the partial density of states (PDOS) along with total density of states (TDOS) for HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides. In TDOS spectra of these carbides, four peaks
RI PT
marked as A, B, C and D are observed at different energies. For HfAl4C4, the peaks A, B, C and D appear at energies -9.70, -5.78, -2.70 and 5.22 eV, respectively. Out of these four peaks, three peaks (A, B and C) lie in the VB region while one peak (D) lies in the CB region. Carbon (C)
SC
atomic sites C2, C3, C4 and C5 (see Fig.1) are the major contributors to peak A in HfAl4C4, Hf, C1 and C3 sites dominantly contribute to this peak in Hf2Al4C5 while in Hf3Al4C6, the main
M AN U
contribution comes from C1 and C3 sites to peak A. Similarly, different non-equivalent sites contribute to the appearance of peaks B, and C in DOS spectra of ternary HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides (Fig. 4 a-c). Peak D mainly appears from the Hf atomic sites in all these ternary carbides.
TE D
The total number of energy states, N(EF) at EF are 2.84, 6.51 and 6.31 states/eV per unit cell in HfAl4C4, Hf2Al4C5 and Hf3Al4C6, respectively. In HfAl4C4, most of the contribution to N(EF) comes from C2 (0.63 states/eV) and C3 (0.77 states/eV) atomic sites. Similarly, in Hf2Al4C5
EP
carbide, the main contribution comes from C2 (1.21 states/eV) and C3 (2.26 states/eV) sites. However, in Hf3Al4C6, the dominant contributor in to N(EF) are C3 (2.32 states/eV) sites. Some
AC C
minor contribution into N(EF) also comes from Hf and Al atomic sites. Further, the top of VB is much more broadened and gets its shape mainly due to C2 and C3 atomic sites in these carbides. The bottom of the CB seems to carry less energy states and is found very less occupied. 3.2.3
Localization index
Localization index (LI) which measures the electronic charge distribution around an atom, is calculated as follows:
ACCEPTED MANUSCRIPT 8 = ∑ !
/
(1)
where is the αth atom’s electronic charge according to Mulliken’s model [47]. Under normalization conditions: ∑ = 1, for complete localized electronic states, = 1 and
near the VB edge is also used order to estimate mobility edge [40].
RI PT
= 1 ⁄ $ for complete delocalized states. The distribution of localization of electron states
Fig. 5 shows the dependence of localization index (LI) on energy for HfAl4C4, Hf2Al4C5 and
SC
Hf3Al4C6 carbides. In the energy range -15.0 to 9.0 eV, the dominant contribution of Hf-3d states and formation of bands with aluminum atoms are observed in all three carbides. In HfAl4C4,
M AN U
some localized states are observed in the energy range -12.4 to -6.5 eV (Fig. 5a). In HfAl4C4 carbide, highly delocalized states are also observed to occur in energy range -6.2 to -0.4 eV. However, in Hf2Al4C5 and Hf3Al4C6, the localized states are present in energy range of -12.0 to 9.0 eV while energy states in between -6.5 and -0.3 eV are relatively delocalized. The energy
TE D
states above EF are also delocalized inHfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides. Further, the top of VB and bottom of CB is mainly formed by delocalized energy states while the bottom of VB carries highly localized energy states.
Effective charge (Q*) and bond order (BO)
EP
3.2.4
To study the behavior of Hf, Al and C atoms in (HfC)mAl4C3 (m = 1, 2, 3) carbides, the effective
AC C
charge, % ∗ on any atom α = Hf, Al, C and bond order (BO) between different atoms are also calculated. The charge transfer, ∆% ∗ = % ∗ − %( (where %( indicates the valence electrons in neutral Hf, Al, and C atoms) are also calculated for all atoms in HfAl4C4, Hf2Al4C5 and Hf3Al4C6. Table 2 presents the summary of effective charge, % ∗ of Hf, Al and C along with charge transfer in the ternary HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides. Both Hf and Al have charge losing trends (negative values of ∆Q∗ ) in these ternary carbides. However, Al sites are
ACCEPTED MANUSCRIPT 9
found to lose more charge as compared to Hf sites. For example, in HfAl4C4, ∆Q∗ = −0.948 for Al as compared to ∆Q∗ = −0.648 for Hf. The C atoms gain on average charge equals to1.11, 0.97 and 0.92 electrons in HfAl4C4, Hf2Al4C5 and Hf3Al4C6, respectively. It has been observed
RI PT
that the highest charge transfer takes place in HfAl4C4 while Hf3Al4C6 exhibit the lowest charge transfer. Due to charge loss, Hf and Al exhibit cationic behavior and C as anionic, due to charge gaining behavior in HfAl4C4, Hf2Al4C5 and Hf3Al4C6. For Hf, Al and C atoms, the average
SC
values of % ∗ are 3.352, 2.052 and 5.110 electrons respectively in HfAl4C4, 3.276, 2.144 and 4.974 electrons respectively in Hf2Al4C5 and 3.300, 2.140 and 4.924 electrons respectively in
M AN U
Hf3Al4C6. In HfAl4C4 and Hf2Al4C5, all sites of Hf carry same value of % ∗ (see Table 2), while this is not true in case of Hf3Al4C6 carbide. However, all non-equivalent Al sites exhibit different character in bonding and carry different values of % ∗ in HfAl4C4, Hf2Al4C5 and Hf3Al4C6. Similar behavior of C atoms has been observed in these ternary carbides (Table 2).
TE D
The BO data (Table 3) show that the Al-C bonds are stronger than Al-Al bonds. For HfAl4C4, Hf2Al4C5 and Hf3Al4C6, the calculated BO of Al-C bonds is 8.624, 13.329 and 13.421, respectively) while for Al-Al bond, the calculated BO = 0.140, 0.234 and 0.209 for HfAl4C4,
EP
Hf2Al4C5 and Hf3Al4C6, respectively. The Hf-C bond exhibit BO = 2.438, 7.510 and 11.308 in HfAl4C4, Hf2Al4C5 and Hf3Al4C6 respectively. Comparison of calculated BO of Al-C, Al-Al and
AC C
Hf-C bonds confirms that the Al-C bonds have dominant role in the stability of HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides. Further, the Al-C bonds in basal plane (Fig. 2) are stronger (BO = 0.974, 0.801 and 0.825 in HfAl4C4, Hf2Al4C5 and Hf3Al4C6, respectively) than those of Al-C bonds (BO = 0.233, 0.310 and 0.294 in HfAl4C4, Hf2Al4C5 and Hf3Al4C6 respectively) along the c-axis. In order to see the overall cohesion of ternary carbides, the total bond order
ACCEPTED MANUSCRIPT 10
(TBO) and total bond order density (TBOD) is also calculated and presented in Table 3. TBOD
3.3
Optical properties
3.3.1
Dielectric behavior
RI PT
in Hf2Al4C5 and Hf3Al4C6 is very similar and higher than HfAl4C4.
To study the optical behavior of (HfC)mAl4C3 carbides, the dielectric function, optical conductivity and loss function are also calculated as a function of energy. The dielectric function
SC
(*) has two parts; the real (* ) and imaginary (* ) part which are related to each other by relation: * ℏ, = * ℏ, + .* ℏ,. The * ℏ, gives the information about the polarization in
M AN U
material under applied electric field while absorption features are understood by * ℏ,. The imaginary part, * ℏ, of dielectric function is obtained from density of states of occupied and un-occupied electronic eigen-states and momentum matrix elements as follows [48]: /0 1
* ℏ, = 2ℏ314 1 5 67 8 ∑,A |〈8;| 10.0 eV, the behavior of * ℏ, and * ℏ, as a function of energy in (HfC)mAl4C3 carbides is isotropic. Close to 0.0 eV, ternary carbides show
RI PT
metal like behavior due to intra-band transitions of conduction electrons. From Fig. 6a-c, it is clear that the * ℏ, goes through zero in low energy range indicating the metallic nature of ternary HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides. Further, transitions between the unoccupied
SC
and occupied bands can be understood from * ℏ, as a function of energy plot. The most interesting feature of * ℏ, plot appears at photon energies close to zero where there is a
M AN U
sudden rise in spectra. This reflects the intra-band optical absorption in HfAl4C4, Hf2Al4C5 and Hf3Al4C6. However, the spectra almost become flatten for energy > 10.0 eV. 3.3.2
Optical conductivity and electron energy loss function
Fig. 7 a-c shows optical conductivity N( as the function of energy for (HfC)mAl4C3 carbides.
TE D
To observe optical anisotropy, the spectra are resolved into ab-plane and along c-axis. For HfAl4C4 carbide, two absorption peaks marked as A and B appear at photon energies 5.79 and 7.44 eV, respectively in ab-plane. Similarly, two peaks marked as C and D appear at energies
EP
5.24 and 7.41 eV, respectively along c-axis (Fig. 7-a). For Hf2Al4C5, a single peak marked as A appears at 7.45 eV while a shoulder peak marked as S appears at low energy (~1.80 eV) in ab-
AC C
plane. However, along c-axis, there appear two peaks C and D at energies equal to 5.69 and 7.45 eV, respectively (Fig. 7-b). The σ spectra are richer in structures in Hf3Al4C6, especially at energies below 4.0 eV (Fig.7-c). In ab-plane, there appears a single absorption peak marked as A at 7.35 eV (similar to appear in Hf2Al4C5) and two peaks C and D at 5.76 and 7.60 eV, respectively along c-axis. The analysis of spectra (Fig.7) leads to conclude that the anisotropy exists at energies < 13.0 eV. Above 13.0 eV, the two spectra seem to be almost overlapped
ACCEPTED MANUSCRIPT 12
reflecting isotropic behavior of conductivity in all three carbides. Further, the conductivity spectra (Fig. 7 a-c) indicate the identical behavior near 0.0 eV where σ curves rise-up showing
Hf2Al4C5 and Hf3Al4C6 carbides shown above in Fig. 3.
RI PT
intra-band transitions. The conductivity behavior validates the band structures of HfAl4C4,
the following relation [49]: J 4
1 , = Im P− QJ4RS = TJ14VJ 1 4W U
1
SC
The electron energy loss , can be calculated by taking dielectric function in to account using
(4)
M AN U
Fig. 8 shows the , as a function of energy for (HfC)mAl4C3 (m = 1, 2 and 3) carbides. For HfAl4C4 carbide, the peaks appear at almost the same photon energy (44.37 and 47.14 eV) along ab-plane and c-axis (Fig. 8-a). However, the height of the peaks from c-axis is larger than height of the peaks appearing from ab-plane. The , spectra of Hf2Al4C5 and Hf3Al4C6 are almost identical with the appearance of single peak from ab-plane at 20.28 and 21.73 eV, respectively.
TE D
These peaks reflect plasma resonance. As compared to HfAl4C4 carbide, the position of peaks in , spectra shifts towards lower energies in Hf2Al4C5 and Hf3Al4C6 carbide. 3.4
Conclusions
EP
The electronic band structures, bonding and optical behavior of (HfC)mAl4C3 (m = 1, 2, 3)
AC C
carbides is studied by applying density functional theory. OLCAO method has been implemented by following the local density approximation (LDA). The band structure spectra show the conducting nature of HfAl4C4, Hf2Al4C5 and Hf3Al4C6 carbides. The localization index calculation shows the presence of highly delocalized states in the vicinity of Fermi level (EF = 0). The effective charge, % ∗ calculation reflects the cationic behavior of Hf and Al atoms and anionic nature of C atoms in structure. The bond order calculation of these carbides show the dominating role of Al-C bonds in stability of the structure. In basal plane, Al-C bonds are found
ACCEPTED MANUSCRIPT 13
to be stronger than Al-C bonds along the c-axis. On the basis of bonding behavior, these carbides are expected to have anisotropic mechanical properties. However, the optical properties
RI PT
(dielectric behavior and conductivity) show anisotropic behavior of these carbides.
Acknowledgments
A. Hussain is thankful to Dr. Paul Rulis (Assistant Professor, University of Missouri-Kansas
SC
City, MO, USA) for extending support to perform these calculations using OLCAO. Authors also acknowledge the financial assistance from Higher Education Commission (HEC),
AC C
EP
TE D
M AN U
Government of Pakistan and The Islamia University of Bahawalpur (IUB), Pakistan.
ACCEPTED MANUSCRIPT 14
REFERENCES [1] X.X. Yu, C.R. Weinberger, G.B. Thompson, Ab initio investigations of the phase stability in group IVB and VB transition metal carbides, Comp. Mater. Sci. 112 (2016) 318–326.
RI PT
[2] V.I. Razumovskiy, M.N. Popov, H. Ding, J. Odqvist, Formation and interaction of point defects in group IVb transition metal carbides and nitrides, Comp. Mater. Sci. 104 (2015) 147–154. [3] W.G. Fahrenholtz, G.E. Hilmas, I.G. Talmy, J.A. Zaykoski, Refractory diborides of
SC
zirconium and hafnium, J. Am. Ceram. Soc. 90 (2007) 1347–1364.
Nucl. Mater. 389 (2009) 317–325.
M AN U
[4] J. Gan, Y. Yang, C. Dickson, T. Allen, Proton irradiation study of GFR candidate ceramics, J.
[5] H.O. Pierson, Handbook of Refractory Carbides and Nitrides Properties, Characteristics, Processing and Applications, Noyes Publications Westwood, New Jersey, 2001. [6] Von L.E. Toth, Transition Metal Carbides and Nitrides, Academic Press, New York-London,
TE D
1971.
[7] E.K. Storms, The Refractory Carbides, Vol. 2, Academic Press, New York-London, 1967. [8] E. Sani, L. Mercatelli, P. Sansoni, L. Silvestroni, D. Sciti, Spectrally selective ultra-high
EP
temperature ceramic absorbers for high-temperature solar plants, J. Renewable and Sustainable Energy, 4 (2012) 033104.
AC C
[9] E. Sani, L. Mercatelli, D. Fontani, J.L. Sans, D. Sciti, Hafnium and tantalum carbides for high temperature solar receivers, J. Renewable and Sustainable Energy, 3 (2011) 063107. [10] E. Sani, L. Mercatelli, F. Francini, J.L. Sans, D. Sciti, Ultra-refractory ceramics for high temperature solar absorbers, Scr. Mater. 65 (2011) 775–778. [11] D. Sciti, S. Guicciardi, M. Nygren, Densification and mechanical behavior of HfC and HfB2 fabricated by spark plasma sintering, J. Am. Ceram. Soc. 91 (2008) 1433–1440.
ACCEPTED MANUSCRIPT 15
[12] X. Xu, Y. Bai, P. Jin, L. Li, X. Bai, G. Liu, C. Tang, First-principles calculations on the structural, elastic and electronic properties of a class of ternary carbides: A survey investigation, Materials and Design 116 (2017) 331 –339.
RI PT
[13] D. Sciti, S. Guicciardi, M. Nygren, Spark plasma sintering and mechanical behavior of ZrCbased composites, Scripta Mater. 59 (2008) 638-641.
[14] V.V. Bannikov, I.R. Shein, D.V. Suetin, Structural, elastic and electronic properties of Ir-
calculations, Comp. Cond. Matter 11 (2017) 60-68.
SC
based carbides-antiperovskites Ir3MC (M = Ti, Zr, Nb and Ta) as predicted from first principles
M AN U
[15] T. Liao, J. Wang, Y. Zhou, Superior mechanical properties of Nb2AsC to those of other layered ternary carbides: a first-principles study, J. Phys.: Condens. Matter 18 (2006) L527. [16] C.C. Lai, Thin Film Synthesis of New Nanolaminated Ternary Carbides, Linköping Studies in Science and Technology, Licentiate Thesis No. 1728, Thin Film Physics Division, Department
(2015).
TE D
of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden
[17] M.W. Barsoum, The MN+1AXN phases: a new class of solids: thermodynamically stable
EP
nanolaminates, Prog. Solid State Chem. 28 (2000) 201-281. [18] J.Y. Wang, Y.C. Zhou, Recent progress in theoretical prediction, preparation, and
AC C
characterization of layered ternary transition-metal carbides, Annul Rev. Mater. Res. 39 (2009) 415-443.
[19] H.B. Zhang, Y.C. Zhou, Current status in layered ternary carbide Ti3SiC2, a review, J. Mater. Sci. Technol. 25 (2009) 1–38. [20] Th. M. Gesing, W. Jeitschko, The crystal structure of Zr3Al3C5, ScAl3C3, and UAl3C3 and their relation to the structure of U2Al3C4 and Al4C3, J. Solid State Chem. 140 (1998) 396–401.
ACCEPTED MANUSCRIPT 16
[21] K. Fukuda, S. Mori, S. Hashimoto, Crystal structure of Zr2Al3C4, J. Am. Ceram. Soc. 88 (2005) 3528–3530.
layered carbide ZrAl8C7, J. Am. Ceram. Soc. 91 (2008) 3758–3761.
RI PT
[22] T. Iwata, K. Sugiura, S. Hashimoto, K. Fukuda, Synthesis and crystal structure of a new
[23] T. Iwata, E. Hattori, S. Hashimoto, K. Fukuda, Synthesis and crystal structure of a new layered carbide ZrAl4C4, J. Am. Ceram. Soc. 91 (2008) 2713–2715.
SC
[24] K. Sugiura, T. Iwata, H. Yoshida, S. Hashimoto, K. Fukuda, Syntheses, crystal structures and Si solubilities of new layered carbides Zr2Al4C5 and Zr3Al4C6, J. Solid State Chem. 181
M AN U
(2008) 2864–2868.
[25] L.F. He, Z.J. Lin, J.Y. Wang, Y.W. Bao, Y.C. Zhou, Crystal structure and theoretical elastic property of two new ternary ceramics Hf3Al4C6 and Hf2Al4C5, Scripta Mater. 58 (2008) 679– 682.
TE D
[26] L.F. He, Y.W. Bao, J.Y. Wang, M.S. Li, Y.C. Zhou, Microstructure, mechanical and thermal properties of ternary carbides in Hf–Al–C System, Acta Mater. 57 (2009) 2765–2774. [27] L.F. He, Y.C. Zhou, Y.W. Bao, J.Y. Wang, M.S. Li, Synthesis and oxidation of Zr3Al3C5
EP
powders, Int. J. Mater. Res. 98 (2007) 3–9.
[28] L.F. He, Y.C. Zhou, Y.W. Bao, Z.J. Lin, J.Y. Wang, Synthesis, physical and mechanical
AC C
properties of bulk Zr3Al3C5 ceramic, J. Am. Ceram. Soc. 90 (2007) 1164–1170. [29] L.F. He, Z.J. Lin, J.Y. Wang, Y.W. Bao, M.S. Li, Y.C. Zhou, Synthesis and characterization of bulk Zr2Al3C4 ceramic, J. Am. Ceram. Soc. 90 (2007) 3687–3689. [30] L.F. He, H.B. Zhong, J.J. Xu, M.S. Li, Y.W. Bao, J.Y. Wang, Y.C. Zhou, Ultrahightemperature oxidation of Zr2Al3C4 via rapid induction heating, Scripta Mater. 60 (2009) 547– 550.
ACCEPTED MANUSCRIPT 17
[31] L.F. He, X.P. Lu, Y.W. Bao, J.Y. Wang, Y.C. Zhou, High-temperature internal friction, stiffness and strength of Zr–Al(Si)–C ceramics, Scripta Mater. 61 (2009) 60–63.
studies on complex carbides, Z. Metallkd. 71 (1980) 341-346.
RI PT
[32] J.C. Schuster, H. Nowotny, Investigations of the ternary systems (Zr, Hf, Nb, Ta)–Al–C and
[33] E. Parthe, B. Chabot, Zr2Al3C5-x and Hf2Al3C5-x described with higher symmetrical space group P63/mmc, Acta Cryst. C44 (1988) 774–775.
SC
[34] J.Y. Wang, Y.C. Zhou, Z.J. Lin, T. Liao, L.F. He, First-principles prediction of the mechanical properties and electronic structure of ternary aluminum carbide Zr3Al3C5, Phys. Rev.
M AN U
B 73 (2006) 134107.
[35] Z.J. Lin, M.J. Zhuo, L.F. He, Y.C. Zhou, M.S. Li, J.Y. Wang, Atomic-scale microstructures of Zr2Al3C4 and Zr3Al3C5 ceramics, Acta Mater. 54 (2006) 3843–3851. [36] K. Fukuda, M. Hisamura, T. Iwata, N. Tera, K. Sato, Synthesis, crystal structure and
TE D
thermoelectric properties of a new carbide Zr2[Al3.56Si0.44]C5, J. Solid State Chem. 180 (2007) 1809–1815.
[37] K. Fukuda, M. Hisamura, Y. Kawamoto, T. Iwata, Synthesis, crystal structure and
(2007) 2888–2894.
EP
thermoelectric properties of a new layered carbide (ZrC)3[Al3.56 Si0.44]C3, J. Mater. Res. 22
AC C
[38] K. Sugiura, T. Iwata, H. Nakano, K. Fukuda, [Zr0.72Y0.28]Al4C4: A new member of the homologous series (MC)l(T4C3)m (M = Zr, Y and Hf, T = Al, Si and Ge), J. Solid State Chem. 182 (2009) 1619–1623.
[39] H. Nian, L. He, F. Li, J. Wang, Y. Zhou, Crystal structure and theoretical elastic property of a new ternary ceramic HfAl4C4, J. Am. Ceram. Soc. 93 (2010) 1164–1168.
ACCEPTED MANUSCRIPT 18
[40] W.Y. Ching, P. Rulis, Electronic Structure Methods for Complex Materials: The Orthogonalized Linear Combination of Atomic Orbitals, Oxford University Press, Oxford, 2012. [41] W.Y. Ching, Theoretical studies of electronic properties of ceramic materials, J. Am.
RI PT
Ceram. Soc. 73 (1990) 3135-3160.
[42] A. Hussain, S.S. Hayat, M.A. Choudhry, Phys. B 406 (2011) 1961-1965.
[43] A. Hussain, A. Javed, S. Mehmood, M.N. Rasool, M.A. Khan, F. Iqbal, Structure,
SC
electronic, mechanical and optical properties of ternary YAl3C3 carbide, J. of Solid State Chem. 237 (2016) 336-342.
M AN U
[44] K. Baral, P. Adhikari, W.Y. Ching, Ab initio modeling of the electronic structures and physical properties of a-Si1− xGexO2 glass (x = 0 to 1), J. Am. Ceram. Soc. 99 (2016) 3677-3684. [45] A. Hussain, S. Aryal, P. Rulis, M.A. Choudhry, J. Chen, W.Y. Ching, Ab initio electronic structure calculations and optical properties of ordered and disordered Ni3Al, J. Alloys and
TE D
Comp. 509 (2011) 5230-5237.
[46] M.D. Segall, P.J. Lindan, First-principles simulation: ideas, illustrations and the CASTEP code, J. of Phys.: Cond. Matter 14 (2002) 2717-2744.
EP
[47] R.S. Mulliken, Electronic population analysis on LCAO–MO molecular wave functions. I, J. Am. Chem. Soc. 23 (1955) 1833-1840.
AC C
[48] Z.Y. Jiao, Y.M. Li, S.H. Ma, First-principle s investigation s of phase stability, mechanical, thermal and optical properties of Ti3(Al1-xSix)C2 solid solutions, J. Alloys and Comp. 724 (2017) 603-613.
[49] P. Rulis, Computational studies of bioceramic crystals & related materials, PhD thesis, University of Missouri-Kansas City, USA (2005).
ACCEPTED MANUSCRIPT 19
FIGURE CAPTIONS Figure 1. Crystal structures of (a) HfAl4C4, (b) Hf2Al4C5 and (c) Hf3Al4C6. Here the yellow, blue and red balls represent the Hf, Al and C atoms respectively.
RI PT
Figure 2. Bonding features in the vicinity of Al3 of (a) HfAl4C4, Al1 of (b) Hf2Al4C5, and (c) Hf3Al4C6. The values outside the parenthesis are the bond lengths, while the values inside the parenthesis are the bond order (in electron). The curved dotted lines indicate the bond angles
SC
with the values given in degrees.
carbides along high symmetry lines.
M AN U
Figure 3. Calculated band structures of (a) HfAl4C4, (b) Hf2Al4C5 and (c) Hf3Al4C6 ternary
Figure 4. Calculated total and element resolved partial DOS spectra of (a) HfAl4C4, (b) Hf2Al4C5 and (c) Hf3Al4C6 crystals.
Figure 5. LI plots as a function of photon energy: (a) HfAl4C4, (b) Hf2Al4C5 and (c) Hf3Al4C5.
TE D
Figure 6. Calculated complex dielectric function of HfAl4C4, Hf2Al4C5 and Hf3Al4C5. Figure 7. The optical conductivity (σ) spectra of (a) HfAl4C4, (b) Hf2Al4C5 and (c) Hf3Al4C6 ternary carbides.
EP
Figure 8. Calculated electron energy loss function as a function of energy for ternary (a)
AC C
HfAl4C4 (b) Hf2Al4C5 and (c) Hf3Al4C6 carbides.
ACCEPTED MANUSCRIPT 20
Figures:
(c)
M AN U
SC
RI PT
(b)
AC C
EP
TE D
(a)
Figure 1 Crystal structures of ternary (a) HfAl4C4 (b) Hf2Al4C5 and (c) Hf3Al4C6 carbides showing the atomic positions of Hf, Al and C atoms in the unit cell. The yellow, blue and red spheres represent the Hf, Al and C atoms, respectively.
ACCEPTED MANUSCRIPT
(b) Hf2Al4C5
C2
C3 o
116.27
1.882 Å (0.310)
M AN U
2.164 Å (0.233)
99.12°
(c) Hf3Al4C6
SC
(a) HfAl4C4
RI PT
21
115.38o
Al1
C3
1.934 Å (0.974)
2.108 Å (0.801)
C3
Al3
C2
C3
C2
1.919 Å (0.294)
Al1 2.087 Å (0.825)
C2
C2
C2
o
101.89
TE D
117.54°
C2
C3
102.96o
AC C
EP
Figure 2 Bonding features in the vicinity of Al3 atom of (a) HfAl4C4 and Al1 atom of (b) Hf2Al4C5 and (c) Hf3Al4C6. The values outside the parenthesis are the bond lengths, while the values inside the parenthesis are the bond order (in electron). The dotted curves indicate the bond angles in degrees.
ACCEPTED MANUSCRIPT
9
RI PT
22
(a) HfAl4C4
SC
6
Fermi Level
-3
Χ
Γ
Ζ
Α
Γ
∆
Α Χ
AC C
-15
Wave vector
Γ
4.55 eV
4.941 eV
-9
1.91 eV
1.98 eV
4.59 eV
1.065 eV
TE D
-6
-12
Fermi level
M AN U
Fermi level
EP
Energy (eV)
3 0
(c) Hf3Al4C6
(b) Hf2Al4C5
Ζ
Α
Γ
Wave vector
∆
Α Χ
Γ
Ζ
Α
Γ
∆
Wave vector
Figure 3 Calculated band structures of ternary (a) HfAl4C4 (b) Hf2Al4C5 and (c) Hf3Al4C6 carbides along high symmetry lines.
Α
ACCEPTED MANUSCRIPT
23
(a) HfAl4C4 B
C
Al1
C A
D Total
0 2
Al3
10 0 15
Al1
M AN U
5 0 15
Al4
10 5
0 2
C1
0 2
0 15
0 2
C3
0 2
C4
TE D
10
C2
5 0 15
Al2
C1
C2
EP
10 5
0 2
0 15
C3
10
C5
5 0
0 -15 -12
-9
-6
-3
0
Energy (eV)
3
6
9
D Total
B
0 15 10 5 0 15 10 5 0 15 10 5 0 15 10 5 0 15 10 5 0 15 10 5 0 15 10 5 0
Hf
10
0 2
C
15
SC
Al2
A
30
B
5
0 2
(c) Hf3Al4C6
45
RI PT
A
(b) Hf2Al4C5
D Total 35 28 21 14 Hf 7 0 15
AC C
PDOS [States/(eV Cell)]
15 10 5 0 4 2 0 2
-15
-12
-9
-6
-3
0
Energy (eV)
3
6
9
Hf1
Hf2
Al1
Al2
C1
C2
C3
-15
-12
-9
-6
-3
0
Energy (eV)
3
Figure 4 Calculated total density of states (TDOS) and element resolved partial density of states (PDOS) spectra of ternary (a) HfAl4C4 (b) Hf2Al4C5 and (c) Hf3Al4C6 carbides.
6
9
ACCEPTED MANUSCRIPT 24
0.30 0.24
RI PT
0.18 0.12 0.06 0.00 0.15 -15
-12
-9
-6
-3
SC
Localization Index
(a) HfAl4C4
0
3
6
9
M AN U
0.12 0.09 0.06 0.03
-9
-6
-3
0
3
6
9
(c) Hf3Al4C6
EP
-12
0.06
0.04
AC C
Localization index
0.00 0.08 -15
TE D
Localization Index
(b) Hf2Al4C5
0.02
0.00 -15
-12
-9
-6
-3
0
3
6
9
Energy (eV) Figure 5 Localization index (LI) plot as a function of photon energy for ternary (a) HfAl4C4 (b) Hf2Al4C5 and (c) Hf3Al4C5 carbides.
ACCEPTED MANUSCRIPT
15 ab-plane
11
45
(a) HfAl4C4
55
(b) Hf2Al4C5 35
c-axis
c-axis
9
25 ab-plane
SC
5
1 -5
-1 0
2
4
6
8
10
12
14
16
18
0
20
2
4
8
10
12
14
15 5 -5
16
18
0
20
2
25
25
(d) HfAl4C4 20
10 5
AC C
2
4
6
8
10
12
Energy (eV)
14
16
18
20
0
16
18
20
c-axis 30 ab-plane
20 10
0
0
14
40
5
0
12
(f) Hf3Al4C6
EP
10
10
50
TE D
15 ab-plane
8
Energy (eV)
c-axis
c-axis
6
(e) Hf2Al4C5
ab-plane
20
15
4
Energy (eV)
Energy (eV) Imaginary part of dielectric function
6
ab-plane
25
15
3
c-axis
35
7 5
(c) Hf3Al4C6
45
RI PT
13
M AN U
Real part of dielectric function
25
0 2
4
6
8
10
12
Energy (eV)
14
16
18
20
0
2
4
6
8
10
12
Energy (eV)
Figure 6 Calculated complex dielectric function of ternary HfAl4C4, Hf2Al4C5 and Hf3Al4C5 carbides.
14
16
18
20
ACCEPTED MANUSCRIPT 26
0.35 B
0.30
(a) HfAl4C4
ab-plane
A
0.25
D
C
RI PT
0.20 0.15 0.10
0.00 0.45 D
A
M AN U
0.36
(b) Hf2Al4C5
c-axis
C
ab-plane
0.27 0.18
S
0.09
TE D
5
-1
Opt. Cond. [10 (Ohm.m) ]
SC
c-axis
0.05
0.45 0.00 0.36
(c) Hf3Al4C6
c-axis
C
EP
AD
ab-plane
0.27
AC C
0.18 0.09 0.00
0
3
6
9
12
15
18
21
24
27
30
Energy (eV) Figure 7 The optical conductivity (σ) spectra as a function of photon energy for ternary (a) HfAl4C4 (b) Hf2Al4C5 and (c) Hf3Al4C6 carbides.
26
ACCEPTED MANUSCRIPT 27
10
(a) HfAl4C4
6 4
RI PT
ab -p la ne
Loss function
is ax c-
8
2
10 5
20
30
4
50
60
70
Energy (eV)
ab-plane
c-axis
3 2 1 0 5 0
5
TE D
Loss function
40
M AN U
(b) Hf2Al4C5
SC
0
10
15
20
25
30
35
40
45
50
35
40
45
50
(c) Hf3Al4C6
2
ne la -p ab
AC C
3
c-axis
EP
4
1 0
0
5
10
15
20
25
30
Energy (eV)
Figure 8 Calculated energy loss function as a function of energy for ternary (a) HfAl4C4 (b) Hf2Al4C5 and (c) Hf3Al4C6 carbides.
27
ACCEPTED MANUSCRIPT 28
Table 1. Crystal and electronic structure data of HfAl4C4, Hf2Al4C5 and Hf3Al4C6. XYZ[ \]^ Z_
`=a
`=b
`=_
HfAl4C4
Hf2Al4C5
Hf3Al4C6
Hexagonal P3m1 (No. 164)
Hexagonal R3m (No. 166)
Hexagonal R3m (No. 166)
3.308 3.308 21.900 90.00 90.00 120.00
3.274 3.274 40.220 90.00o 90.00o 120.00o 373.362 3 33 148 (12 × 12 × 2) 1160 (24 × 24 × 4) 6
3.265 3.265 48.090 90.00o 90.00o 120.00o 443.968 3 39 148 (12 × 12 × 2) 1160 (24 × 24 × 4) 7
1 (6) 2 (6, 6) 3 (3, 6, 6)
2 (3, 6) 2 (6, 6) 3 (6, 6, 6)
8.13 4.94
6.98 4.59
6.92 4.55
1.06
1.98
1.91
2.84
6.51
6.37
a (Å) b (Å) c (Å) α β γ Volume (Å3) Formula units/unit cell Atoms/unit cell SCF k-points OLCAO k-points Non-equivalent sites
207.536 2 18 513 (18 × 18 × 3) 1201 (24 × 24 × 4)
10 Atom types (no. of atoms of different type) Hf Al C
SC
Lattice parameters
M AN U
Crystal system Space group
RI PT
Crystal Structure data
1 (2) 4 (2, 2, 2, 2) 5 (1, 2, 2, 2, 1)
Electronic structure information
AC C
EP
TE D
Upper VB width (eV) Lower VB width (eV) Energy gap between lower and upper VB (eV) DOS at Fermi level N(EF)
28
ACCEPTED MANUSCRIPT 29
Table 2. The effective charge % ∗ data of HfAl4C4, Hf2Al4C5 and Hf3Al4C6. XYZ[ \]^ Z_
`=a
`=b
`=_
HfAl4C4
Hf2Al4C5
Hf3Al4C6
Min. %∗ Max. % ∗ Mean %∗ Charge transfer ∆%∗
3.352 3.352 3.352 -0.648
3.276 3.276 3.276 -0.724
3.273 3.356 3.300 -0.700
Min. %∗ Max. % ∗ Mean %∗ Charge transfer ∆%∗
1.959 2.149 2.052 -0.948
2.023 2.265 2.144 -0.856
Min. %∗ Max. % ∗ Mean %∗ Charge transfer ∆%∗
4.767 5.244 5.110 +1.110
4.752 5.160 4.974 +0.974
∗
AC C
EP
TE D
M AN U
C
29
2.014 2.266 2.140 -0.860
SC
Al
RI PT
Effective Charge (c ) Hf
4.759 5.111 4.924 +0.924
ACCEPTED MANUSCRIPT 30
Table 3. Bond order (BO) data of HfAl4C4, Hf2Al4C5 and Hf3Al4C6.
Bond order (BO) Bond Al-C Hf-C Al-Al Hf-Hf Total BO
`=a
HfAl4C4
`=b
Hf2Al4C5
BO
BO
BO
8.624 2.438 0.140 0.000 11.202
13.329 7.510 0.234 0.000 21.073
13.421 11.308 0.209 0.411 25.349
77.00 21.80 1.20 0.00
63.25 35.64 1.11 0.00
52.94 44.61 0.82 1.62
Bond order density (BOD)
0.036 0.020 0.001 0.000 373.362 0.057
0.030 0.026 0.000 0.001 443.968 0.057
M AN U
0.042 0.012 0.001 0.000 207.536 0.054
AC C
EP
TE D
Al-C Hf-C Al-Al Hf-Hf Cell volume (Å7) TBOD (TBO/Vol.)
SC
BO% Al-C Hf-C Al-Al Hf-Hf
`=_
Hf3Al4C6
RI PT
XYZ[ \]^ Z_
30
ACCEPTED MANUSCRIPT Highlights
EP
TE D
M AN U
SC
RI PT
(HfC)mAl4C3 (m = 1, 2, 3) carbides are studied by first principles All three carbides exhibit conduction nature by exhibiting direct band gap. Charge transfer from Hf and Al to C atom is found to exist in these carbides. Dielectric function and optical conductivity exhibit anisotropic behavior.
AC C
• • • •
