Electro-structural correlations, elastic and optical properties among the nanolaminated ternary carbides Zr2AC

doi:10.1016/j.solidstatesciences.2010.01.035

Solid State Sciences

Volume 12, Issue 5, May 2010, Pages 887-898

https://doi.org/10.1016/j.solidstatesciences.2010.01.035 Get rights and content

Abstract

We have performed ab initio calculations for the nanolaminates Zr₂AC (A = Ti, In, Tl, Si, Ge, Sn, Pb, P, As, S) ceramics to study their electronic structure, elastic and optical properties. In this work, we used the accurate augmented plane wave plus local orbital method with density functional theory to find the equilibrium structural parameters, dielectric functions and to compute the full elastic tensors. The obtained elastic constants were used to quantify the stiffness of the Zr₂AC phases and to appraise their mechanical stability. The relationship between elastic, electronic and valence electron concentration is discussed. Our results show that the bulk modulus and shear modulus increase across the periodic table for Zr₂AC. Furthermore, trends in elastic stiffness are well explained in terms of electronic structure analysis, as occupation of valence electrons in states near the Fermi level of Zr₂AC. We show that increments of bulk moduli originate from additional valence electrons filling states involving Zr d–A p. We show also that Zr d–A p hybridizations are located just below the Fermi level and are weaker bonds than the Zr d–C p hybridizations, which are deeper in energy. As a function of the p-state filling of the A element the Zr d–A p bands are driven to deeper energy. The optical spectra were analyzed by means of the electronic structure, which provides theoretical understanding of the conduction mechanism of these ceramics.

Graphical abstract

Introduction

The M_n₊₁AX_n (MAX) phases (n = 1–3) are layered hexagonal compounds, in which near close-packed layers of M (early transition metals) are interleaved with layers of group A element (mostly IIIA and IVA), with the X-atoms (C and/or N) filling the octahedral sites between the M layers. The MAX phases represent a class of technologically important solids exhibiting unusual properties associated with both metals and ceramics [1]. Generally, the M_n₊₁AX_n phases are machinable, [2] exhibit good damage tolerance, [3] have excellent thermal shock resistance, [4] good corrosion resistance, [5] and they are good thermal and electrical conductors [6], [7]. These materials gained renewed interest since Barsoum and co-workers [8] succeed to synthesize single phase, bulk dense samples of Ti₃SiC₂. Afterwards, many of the roughly 60 M_n₊₁AX_n phases known to date have been studied both experimentally and theoretically [9], [10], [11]. However, individual properties vary from phase to phase. Only limited data are available describing the systematic dependence of the properties on the electronic structure. It has been suggested from ab initio calculations [12] that M₂AC (M = Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W and A = Al, Ga, Ge and Sn) can be classified into two groups: one where the bulk modulus of the binary MC is conserved and the other for which the bulk modulus is decreased. However, the same authors [13] have questioned their own results, the description of the binary carbides MC being very sensitive to the choice of the projector augmented wave (PAW) potentials they used. In the same way, Schneider et al. reported that the bulk modulus increases with p electron concentration at the M site for Ta₂AC [14]. Recently, Hug [15] has studied the electronic properties among ternary carbides Ti-based compounds. All these phases are shown, except for A = Si, P and As, to be stable, a behavior originating from the particularities of the hybridization scheme in these compounds (Ti d–A p and Ti d–C p hybrids). More recently, we have suggested that the 211 M₂SnC (M = Ti, Zr, Hf and Nb) MAX phases hold back about 69% of the bulk modulus of the corresponding binary carbides, a value close to 2/3. Knowing that the bulk moduli of M₃SiC₂ are 3/4 of the corresponding MC, it is curious to remark that the bulk moduli of M_n₊₁AC_n are pretty close to $n + 1 / n + 2$ of the corresponding binary carbides for n = 1 and 2. Such a phenomenological relation will give 4/5 for the bulk moduli of M₄AC₃ compared to the related MC ones [16].

Thus, in the present paper, we focus our intention on the physical properties of nanolaminate Zr₂AC with A = Ti, In, Tl, Si, Ge, Sn, Pb, P, As, and S by mean of full-potential first principles calculations. Specifically, we address the crystal parameters, electronic structure, mechanical behavior and optical properties of these compounds. It is our ambition to contribute towards understanding the relationship between the elastic properties and electronic structure as a function of valence electron population of A element. The elastic properties are of particular interest as they determine the mechanical stability of the material and important macroscopic properties such as hardness, lubrification, friction, and machinability. The electronic structure and chemical bonding investigation will then provide an overall view of electro-structural information that is needed for tailoring and improving the electronic features of these materials. We have to point out that many theoretical calculations have been carried out on the electronic structures of MAX phases, but the optical properties of the MAX phases have not received adequate attention from neither experimentalists nor theorists.

Section snippets

Theoretical method and crystal structure

The present calculations were performed using an all-electron full-potential (linearized) augmented plane waves plus local orbitals (FP-L/APW + lo) method [17], based on the density functional theory (DFT) [18]. The exchange correlation potential was computed with the Wu and Cohen generalized gradient approximation (GGA-WC) [19]. The maximum value l_max for the wave functions expansion inside the atomic spheres is limited to 10. To achieve the energy eigenvalues convergence, the wave functions

Structural properties

To investigate the ground-state properties, we computed the equilibrium lattice configurations of Zr₂AC phases at first optimized lattice parameters for a, c and Z_M are summarized in Table 1 as well as the experimental data [22] for comparison. As a general remark, it can be note that all the Zr₂AC compounds, are intrinsically stable. The deviations are estimated to be about 0.1% and 0.8% for a and c compared to available experimental work. The formation energies ΔE_f of these MAX phases,

Elastic properties

The elastic stiffness determines the response of the crystal to an externally applied strain (or stress) and provides information about the bonding characteristics, mechanical and structural stability. In general, estimating elastic constants from first principles calculation is really tough because it requires accurate methods to evaluate the total energy or stress accompanying strain. Fortunately, state of the art first principles computational modeling permits us to reproduce the elastic

Electronic properties

In order to explain the electronic structure, we have calculated the total density of state (TDOS) using optimized geometry at equilibrium volume. As shown in Fig. 4, the DOS around the Fermi level (E_F) generally lies in a dip. This location may split bonding and antibonding states giving rise to stranger cohesion, the structure stability [41] and higher bulk modulus. However, the TDOS of the alloys with s²p³ A atoms presents a sharp peak at E_F a configuration which is often associated with

Optical properties

A study of the optical properties of solids has been an interesting research topic, both in basic research as well as for industrial applications. While for the former the origin and nature of different excitation processes are of fundamental interest, the latter can make use of them in many optoelectronic devices. Therefore optical properties bring together experiment and theory. The calculation of ɛ₂(ω) requires energy eigenvalues and electron wave functions. These are natural outputs of a

Conclusion

In summary, this work reports on a study of electro-structural correlation, elastic and optical properties of Zr₂AC (A = Ti, In, Tl, Si, Ge, Sn, Pb, P, As, S) through first principles all-electron full-potential linearized augmented plane wave calculations. It has been shown that the structural parameters obtained after relaxation are in good agreement with the experimental ones. Our results show that the increase of p electrons from A elements when moving rightwards along the periodic table

Acknowledgments

The calculations using Wien2k code have been performed on the Interuniversity Scientific Computing Facility (ISCF), installed at the FUNDP for which the authors gratefully acknowledge the financial support of the F.R.S.-FRFC and of the “Loterie Nationale” under Contract No. 2.4.617.07.F, and of the FUNDP (Namur, Belgium). M.B.K and S.G.S acknowledge F. Wautelet (ISCF-FUNDP) for permanent computer assistance. Alberto Otero de la Roza from Universidad de Oviedo (spain) is acknowledged for

References (49)

M.W. Barsoum
Prog. Solid State Chem.
(2000)
C.J. Gilbert et al.
Scr. Mater.
(2000)
M.W. Barsoum et al.
Scr. Mater.
(1997)
J.M. Schneider et al.
Solid State Commun.
(2004)
W. Voigt
Lehrbuch der Kristallphysik
(1928)
O.L. Anderson
J. Phys. Chem. Solids
(1963)
E. Schreiber et al.
Elastic Constants and Their Measurements
(1973)
A.H. Reshak et al.
J. Chem. Phys.
(2008)
B. Chakraborrty et al.
Phys. Rev. B
(1972)
B. Manoun et al.
Appl. Phys. Lett.
(2004)

M.W. Barsoum et al.

Nat. Mater.

(2003)

T. El-Raghy et al.

J. Am. Ceram. Soc.

(1997)

H. Yoo et al.

Nature (London)

(2000)

M.W. Barsoum et al.

J. Am. Ceram. Soc.

(1996)

S.E. Lofland et al.

Appl. Phys. Lett.

(2004)

M.B. Kanoun et al.

J. Phys. Condens. Matter

(2008)

Z. Sun et al.

Phys. Rev. B

(2004)

D. Music et al.

Phys. Rev. B

(2006)

J.M. Schneider et al.

J. Appl. Phys.

(2005)

G. Hug

Phys. Rev. B

(2006)

M.B. Kanoun et al.

J. Phys. Condens. Matter

(2009)

P. Blaha et al.

An Augmented-Plane-Wave + Local Orbitals Program for Calculating Crystal Properties

(2001)

R. Dreizler et al.

Density-Functional Theory

(1990)

Z. Wu et al.

Phys. Rev. B

(2006)

Cited by (42)

Exploring novel Zr<inf>2</inf>GeX (X = C, N, F) MAX phases by first-principles approach
2024, Materials Today Communications
In recent years, there has been a surge of interest in the thermodynamically stable nanolaminate ternary carbides/nitrides known as MAX phases. In this first-principles research work, we focus on the MAX phases with a particular emphasis on Zr₂GeX (X = C, N, F) compounds. These novel Zr₂GeX compounds exhibited considerable values of cohesive energy, demonstrating stability comparable to well-established MAX compounds. Our calculations for the structural parameters of Zr₂GeX agree well with the literature, indicating the reliability of our results. The absorption coefficients for ultraviolet (UV) light are approximately 10⁵/cm and 10⁶/cm, respectively, highlighting their significance for energy harvesting devices. Additionally, these metallic compounds demonstrate impressive reflectivity, reflecting over 50% of infrared and visible light. Similarly, they exhibit the highest refraction for infrared light, with a significant decrease in refraction for visible and UV light. Consequently, the transparency of Zr₂GeX compounds diminishes, rendering them opaque against UV light and highly likely to absorb most incident UV radiation. Results presented in this paper highlight the potential applications of Zr₂GeX MAX phases for optoelectronic devices due to their exceptional electronic and optical properties.
Physical properties of W<inf>2</inf>GaX (X=C, N, and F) based novel MAX phases; potential materials for applications in advanced electronic and optical devices
2024, Computational and Theoretical Chemistry
This study examines the electronic and optical characteristics of W₂GaX (X = C, N, and F) MAX phases using first-principles approach. The cohesive energies of W₂GaC, W₂GaN, and W₂GaF are determined as 7.31, 6.40, and 5.05 eV, respectively, demonstrating excellent agreement with existing literature and confirming their stability. The W-d, Ga-s, and X-p states are symmetrically dispersed across the spin-polarized electronic structures, resulting in a nonmagnetic metallic behavior of W₂GaX. Due to their metallic behavior, they reflect more than 60 % of infrared and up to 50 % of visible light. These compounds demonstrate considerable absorption of infrared, visible, and ultraviolet (UV) light, with absorption coefficients of approximately ∼10⁴ cm⁻¹, ∼10⁵ cm⁻¹, and ∼10⁶ cm⁻¹, respectively. The refractive indices of W₂GaX MAX phases remain greater than one for incident light energies below 10 eV. Additionally, W₂GaC shows the highest optical conductivity among the investigated compounds when exposed to light, making it a promising material for various conduction applications. Our present study sheds light on the optical and electronic properties of W₂GaX MAX phases and highlights their potential for applications in advanced electronic and optical devices.
Overview of structural, electronic, elastic, thermal, optical, and nuclear properties of Zr<inf>2</inf>AC (A= Al, Si, P, S, Ge, As, Se In, Sn, Tl, and Pb) MAX phases: A brief review
2023, Heliyon
The Zr₂AC MAX phases are a family of ternary carbides ceramics that possess layered structures and exhibiting exceptional properties resulting from combining the most desirable features of metals and ceramics. In addition, the Zr₂AC MAX-phases exhibit numerous physical and chemical properties due to their chemical and structural characteristics, a tendency for multiple basal dislocations and exhibiting mobility under ambient conditions. This review extensively analyzes the properties of the Zr₂AC MAX phase, as they are closely linked to the exceptional and potential applications of the MAX phase. For the first time, the present study analyzed various properties of Zr₂AC MAX phases, including structural, electronic, elastic, thermal, optical, self-healing, nuclear, oxidation, and corrosion characteristics. Furthermore, this review included experimental and theoretical work with comparison. It's found that the Zr₂AC lattice parameters a and c are deviations theoretically from 0.1 to 2% and 0.15–2.87% compared with experimental work. Also, the Zr₂AC MAX phases are metallic characters and the conductivity differs depending on the type of the Zr₂AC(different A element) MAX phases. Its concluded that the Zr₂AC MAX phases are stiff, isotropic elastic properties and high machinability with damage tolerance and hardness levels ranging from 3.5 to 13.02 Gpa. The Zr₂AC MAX phases are also resistant to corrosion, thermal shock, and oxidation as well as lightweight. In addition, at elevated temperatures the transition from brittle to plastic behavior can be occurred in the Zr₂AC MAX phase. The Zr₂AC MAX phase's optical properties are anisotropic such as electrical conductivity and mechanical properties. This review study provides a comprehensive details assisting researches to deal with Zr₂AC MAX phase potentially for different applications.
Trends in structural, electronic and elastic properties of Ti<inf>2</inf>AC (A = Al, Zn, Cu, Ni) based on late transition metals substitution
2023, Physica B: Condensed Matter
Recently, the substitutional incorporation of late transition metals in the “A” sublattice of MAX phases further extends the physical properties and diversity of this class of materials. In this study, the structural, electronic and elastic properties of Ti₂AC (A = Al, Zn, Cu, Ni) were investigated using the density functional theory. The calculated results reveal that a large number of d orbital bands of Zn, Cu, and Ni atoms accumulate around −6.5 eV, −2.5 eV, and −2.0 eV, respectively, leading to stronger ionic and metallic characteristics for Ti₂ZnC, Ti₂CuC, and Ti₂NiC. Three Ti₂AC (A = Zn, Cu, Ni) phases are ductile and consequently damage tolerant, whereas Ti₂AlC is brittle in nature. When Al is replaced by Zn, Cu, and Ni, there is a remarkable decrease of hardness and shear modulus, indicating high machinability. Ti₂ZnC, Ti₂CuC, and Ti₂NiC are expected to be promising thermal barrier coating materials.
Trends in mechanical, anisotropic, electronic, and thermal properties of MAX phases: a DFT study on M<inf>2</inf>SX phases
2023, Materials Today Communications
Based on the density functional theory, the structural, mechanical and thermal properties of 27 S-based M₂SX (M=Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W; X = B, C, N) phases have been investigated systematically. The calculated formation enthalpies (ΔH) reveal that W₂SC and W₂SN are thermodynamically unstable phases due to the positive ΔH, and the V₂SN, Nb₂SN, and Mo₂SC are mechanically unstable phases with C₁₂ > C₁₁. The calculated phonon spectrum indicates that 16 phases are dynamically stable phases except M₂SN (M=V, Nb, Ta), M₂SX (M=Cr, W; X = B, C, N), Mo₂SC, and Mo₂SN phases. Among the 16 stable phases, the Ti₂SB, V₂SB, Ta₂SB and Ta₂SC are predicted in this work, for the other 12 stable phases, the physical properties have been reported more or less. From the calculated results, V₂SC, Nb₂SC, and Ta₂SC are resistant to compression and thermal shock, and which exhibit potential application in thermal barrier coatings. All the stable phases are more compressible along the a-axis, which means that c-axis is stiffer owing to strong atomic bond. Electronic structures indicate the stable phases are all metallic, and the Mo₂SB and Ta₂SC can be applied in thermoelectric material with very low lattice thermal conductivity. All the present results could motivate exploration and research on novel S-based MAX phases in the future.
Study of Structural, optoelectronic and elastic properties of MAX phase of Ti<inf>2</inf>BrX (X = B, C and N) by density functional theory
2023, Inorganic Chemistry Communications
The compounds with general formula M_n+1AX_n, where n = 1, 2, 3,…, where M = early transition metals, A = IIIA and IV A group elements like Al, Ga, In or Si, Ge and X = B, C or N for n = 1 and B or C or N for n greater than 1 are known as the compounds having MAX phases. These compounds (MAX phases) are having great potential for many technological applications due to their metallic and ceramic properties along with rare mechanical and chemical properties like damage and oxidation resistance, good thermal and electrical conductivity, reversible deformation and many more. The systematic and detailed study of these compounds gives the knowledge regarding their properties and hence we can search the new compounds for our technological needs. In the present paper, we have made a detailed investigation of the structural, electronic, optical and elastic properties of newly predicted MAX phase compounds Ti₂BrB, Ti₂BrC and Ti₂BrN and also compared the results with the help of first-principles density functional theory. We have found that newly proposed MAX phase compounds Ti₂BrB, Ti₂BrC and Ti₂BrN are chemically and mechanically stable. But the compound Ti₂BrC is dynamically stable while the compounds Ti₂BrB and Ti₂BrN are dynamically unstable.

View all citing articles on Scopus

View full text

Electro-structural correlations, elastic and optical properties among the nanolaminated ternary carbides Zr2AC

Abstract

Graphical abstract

Introduction

Section snippets

Theoretical method and crystal structure

Structural properties

Elastic properties

Electronic properties

Optical properties

Conclusion

Acknowledgments

Prog. Solid State Chem.

Scr. Mater.

Scr. Mater.

Solid State Commun.

J. Phys. Chem. Solids

J. Chem. Phys.

Phys. Rev. B

Appl. Phys. Lett.

Nat. Mater.

J. Am. Ceram. Soc.

Nature (London)

J. Am. Ceram. Soc.

Appl. Phys. Lett.

J. Phys. Condens. Matter

Phys. Rev. B

Phys. Rev. B

J. Appl. Phys.

Phys. Rev. B

J. Phys. Condens. Matter

An Augmented-Plane-Wave + Local Orbitals Program for Calculating Crystal Properties

Density-Functional Theory

Phys. Rev. B

Electro-structural correlations, elastic and optical properties among the nanolaminated ternary carbides Zr₂AC