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Available online at www.sciencedirect.com

Materials Chemistry and Physics 108 (2008) 120–123

The first-principles study on the LaN

Y.O. Ciftci ∗, K. Colakoglu, E. Deligoz, H. OzisikGazi University, Department Of Physics, Teknikokullar, 06500 Ankara, Turkey

Received 8 May 2007; received in revised form 6 September 2007; accepted 14 September 2007

bstract

We present the results of ab-initio study on the structural, elastic, thermodynamics, and electronic properties of the nonmagnetic Lanthanumitride (LaN) using the plane-wave pseudopotential approach to the density-functional theory within the generalized-gradient approximationmplemented in VASP (Viena Ab-initio Simulation Package). The calculated structural parameters (the lattice constant, bulk modulus, cohesive

nergy), the phase transition pressure from NaCl (B1) to CsCl (B2) phase, elastic constants, Zener anisotropy factor (A), Poisson ratio (ν), Young’sodulus (Y), Shear modulus (C′), Debye temperature, and band structures are presented. The obtained results are compared with the available

xperimental and the other theoretical results. 2007 Elsevier B.V. All rights reserved.

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eywords: Nitrides; Ab-initio calculations; Band structures; Mechanical prope

. Introduction

Transition metal mononitrides are known as refractory com-ounds, and they have, relatively, high hardness, brittleness,elting point, and superconducting transition temperature, and

hey also have interesting optical, electronic, catalytic, and mag-etic properties [1]. Because of these properties, they find wideechnological application areas. Lanthanum nitride (LaN), is a

ember of the 5d transition metal group, and its stoichiom-try [2] still has some problems, and crystallizes in rocksaltB1) structure with space group Fm3m (2 2 5). Lanthanum atoms positioned at (0,0,0) and the nitride atom at (1/2,1/2,1/2).nder pressure, the LaN undergoes the structural phase tran-

ition from rocksalt (B1) structure to CsCl-type (B2) structureith the space group symmetry Pm3m (2 2 1). In the B2 phase,itride (N) atom is again positioned at (1/2,1/2,1/2). Some mea-ured data on LaN compound shows both semi-metallic andemi-conducting behaviour [3]. Stampfl et al. [4] have per-ormed ab-initio (FLAPW) calculations on the structural andlectronic properties of the some early transition metal monon-trides. Norman et al. [5] found that LaN has a band overlap

f approximately 40 mRy making it semi-metal. Hasegawa [6]ade band structural calculations, by using the self-consistent

lane wave (APW) method, and it shows a band overlap of

∗ Corresponding author. Tel.: +90 312 2021266; fax: +90 312 2122279.E-mail address: yasemin@gazi.edu.tr (Y.O. Ciftci).

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254-0584/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.matchemphys.2007.09.012

mRy. Vaitheeswaran et al. [7] have reported the structural phasetability and superconductivity of LaN, and predicted that LaNndergoes a crystallographic transition from NaCl type to CsClype structure at 26.9 GPa. When this work is just completedasegawa et al. [8] have reported an experimental work, on LaN,

t high pressure (about 30 GPa) and high temperature (about000 K) using a diamond anvil cell and YAG laser heating sys-em, and synthesized two new phases for LaN. These Pa3 and la3hases are found to be stable down to 5 GPa and about 300 Kn a nitrogen atmosphere with lattice constants a = 11.979 A,nd a = 3.889 A and c = 6.691 A, respectively. In the same work,he B1-type NaCl is identified unambiguously, and its latticearameter is given as a = 5.638 A.

The main goal of the present paper, using the first principlesalculations, is to reveal some more details for the structuralnd the mechanical properties of LaN. The layout of this papers given as follows: the method of calculation is given in Section. The results and overall conclusion are presented in Sectionsand 4, respectively.

. Method of calculation

These calculations have been performed using the augmented

lane-wave pseudopotential approach to the density functionalheory (DFT) implemented in Vienna Ab-initio Simulationackage (VASP) [9–12]. We use the exchange-correlation poten-

ial within the generalized-gradient approximation by Perdew

Y.O. Ciftci et al. / Materials Chemistry and Physics 108 (2008) 120–123 121

awsyz

3

3

bvsdnaptt3pib

TCm

C

L

L

mifs

E

wleg−T[

bttGsp

Fig. 1. Energy vs. volume constant curves of LaN.

nd Wang (GGA). The wave functions are expanded in the planeaves up to a kinetic-energy cutoff of 500 eV. The k-point is

ampled according to the Monkhorst–Pack scheme [12], whichields 16 × 16 × 16 k-points in the irreducible edge of Brillouinone.

. Results and discussion

.1. Structural and electronic properties

Firstly, the equilibrium lattice parameter has been computedy minimizing the crystal total energy calculated for differentalues of lattice constant by means of Murnaghan’s equation oftate (eos) [13] as in Fig. 1. The bulk modulus, and its pressureerivative have also been calculated based on the same Mur-aghan’s equation of state, and the results are given in Table 1long with the experimental and other theoretical values. Theresent value of the bulk modulus is much smaller than that ofhe other theoretical work [6] and values of some simple transi-ion metal nitrides (PtN: 372 GPa [14],YN: 126 GPa [15], TaN:28 GPa [16]). The present value of lattice parameter for B1

hase is found to be 5,307 A, and it quite accords with the exper-mental values of Refs. [8,17] in B1 phase and the agreement isetter than the other theoretical result in Ref. [7].

able 1alculated lattice constants (a), bulk modulus (B), pressure derivative of bulkodulus (B′), cohesive energy of LaN

rystal Reference a (A) B(GPa)

B′ Ecoh

(eV/pair)

aN (B1)

Present 5.307 116.947 3.657 −17.5Theorya 5.150 152 – −16.59Theoryb 5.32 148 – −15.7Experimentc 5.301 – –Experimentd 5.638

aN (B2)Present 3.167 114.18 4.406 −15.43Theorya 2.969 282 – −16.29Experiment – – – –

a Ref. [7].b Ref. [4].c Ref. [17].d Ref. [8].

cpi(

p

Fig. 2. Pressure vs. volume curves of LaN.

The cohesive energy (Ecoh) of a given phase is known as aeasure of the strength of the forces, which bind atoms together

n the solid state. In this connection, the cohesive energy of LaNor both B1 and B2 structures is calculated by using the followingtandard relation:ABcoh = [EA

atom + EBatom − EAB

total]

here EABtotal is the total energy of the LaN compound at equi-

ibrium lattice constant and EAatom and EB

atom are the atomicnergies of the pure constituents. The computed cohesive ener-ies (Ecoh) for B1 and B2 structures are found to be −17.5 and15.43 eV/atom, respectively, and they are also listed in Table 1.hese values are lower than other calculations in Refs. [4] and

7].We have plotted the phase diagrams (equation of state) for

oth B1 and B2 phases in Fig. 2. The discontinuity in volumeakes place at the phase transition pressure. The phase transi-ion pressure from B1 to B2 structure is calculated from theibbs free energy at 0 K, and the related enthalpy versus pres-

ure graphs for the both phases are shown in Fig. 3. The transitionressure is a pressure at which H(p) curves for both phasesrosses. The present value (25.25 GPa) of the phase transitionressure is in agreement with other theoretical result (26.9 GPa)

n Ref. [7], and it is very close to the value found experimentally25 GPa) for LaS in Ref. [18].

We have also calculated the band structures of LaN, for bothhases, along the high symmetry directions using the calculated

Fig. 3. Estimation of phase transition pressure from B1 to B2.

122 Y.O. Ciftci et al. / Materials Chemistry and Physics 108 (2008) 120–123

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Table 2Elastic constants (in GPa) for LaN in B1 structure

Materials Reference C11 C12 C44

LaN (B1) Present 213 84 71HfN (B1)a Experiment 679 119 150ZrN (B1)a Experiment 471 88 138TaN (B1)b Experiment 783 167 20ZrN (B1)c Theory 304 114 51.1

LaN(B2) Present 315 164 81

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uacf

A

υ

a

Y

wioiG

robtained for the similar structural symmetry.

Debye temperature (ΘD) is a fundamental physical propertyand is used to distinguish between high- and low-temperatureregions for a solid. If T > ΘD, we expect all modes to have energy

Table 3The calculated Zener anisotropy factor (A), Poisson ratio (ν), Young’s modulus(Y), and Shear modulus (C′) for LaN in B1 and B2 structures

ig. 4. Calculated band structures and DOS (a) B1 and (b) B2 phases of LaN.

quilibrium lattice constant. The band structure calculations foraN are rare, and the results are not quite clear. As is stated bytampfl et al. [4], the LaN in B1 structure has eight electronser atom pair, and only bonding states are filled. It can be seenrom the Fig. 4 that no band gap exists for LaN, and it exhibitsearly semi-metallic character. This result is in agreement withhe LDA calculations by Stampfl et al. [4], but they have alsoredicted a small band gap (0.75 eV) based on the screened-xchange (sX) LDA calculations. The total electronic densityf states (DOS) corresponding to the present band structures is,lso, depicted in Fig. 4, and the disappearing of the energy gapn DOS conforms the metallic nature of LaN.

.2. Elastic properties

The elastic constants of solids provide a link between theechanical and dynamical behaviors of crystals, and give impor-

ant information concerning the nature of the forces operatingn solids. In particular, they provide information on the stabilitynd stiffness of materials, and their ab-initio calculation requiresrecise methods. For obtaining the elastic constants from theirnown crystal structures a popular approach [19–21], which isased on the analysis of changes in calculated stress valuesesulting from changes in the strain, is used. The present val-es of elastic constants for both phases for LaN are given inable 2. Unfortunately, there are no other theoretical or exper-

mental results for comparing with the present work. However,t can be seen from the same Table 2 that they are much smaller

han those found for some other 5d transition metal nitrides, suchs HfN [22] and TaN [23], and ZrN [22,24] for B1 structure. Sim-lar deviation also exists for ZrN in Table between theory andxperiment for C11 in B1 phase. The reason of these deviations is

M

LL

a Ref. [22].b Ref. [23].c Ref. [24].

ot so clear; the computational methods and, especially, the var-ous atomic bonding mechanisms operating between cations andnions affect the bulk modulus and elastic constants [25]. Sincehe bulk modulus is inversely proportional to the bond length, themaller atomic size and shorten bond length can cause the bulkodulus to be larger, and consequently, the elastic constants.he traditional mechanical stability conditions in cubic crystalsn the elastic constants are known as C11 − C12 > 0, C11 > 0,44 > 0, C11 + 2C12 > 0, and C12 < B < C11. The elastic constants

n Table 2 satisfy these stability criteria, and hence, we can sayhat the both phases are elastically stable.

The Zener anisotropy factor A, Poisson ratio ν, Young’s mod-lus Y, and Shear modulus (C′ = (C11 − C12 + 2C44)/4), whichre the important elastic properties for applications, are alsoalculated in terms of the computed data (see Table 3) using theollowing relations [26]:

= 2C44

C11 − C12, (1)

= 1

2

[B − (2/3)G

B + (1/3)G

], (2)

nd

= 9GB

G + 3B(3)

here G = (GV + GR)/2 is the isotropic shear modulus, GVs Voigt’s shear modulus corresponding to the upper boundf G values, and GR is Reuss’s shear modulus correspond-ng to the lower bound of G values, and can be written as

V = (C11 − C12 + 3C44)/5, and 5/GR = 4/(C11 − C12) + 3/C44.The present values for Anisotropy factor (A) and the Poisson

atio given in Table 3 are reasonable, and they are close to those

aterial A ν Y (GPa) C′ (GPa)

aN (B1) 1.100 0.2505 170.88 64.464aN (B2) 1.0728 0.3722 216.13 75.446

Y.O. Ciftci et al. / Materials Chemistry a

Table 4The longitudinal, transverse, average elastic wave velocities, and Debye tem-perature for LaN in B1 and B2 structure

Material υl (m/s) υt (m/s) υm (m/s) θD (K)

LaN (B1) Present 5532.161 3170.372 3521.986 395LaNa Theory 300NbN (B1)b Theory 510L

kfmt

Θ

wg

υ

wvt

υ

a

υ

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4

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A

U

R

[[[[[

[[

[

[

[[[[

[

[[[

[

[

New York, 1996.[29] E. Schreiber, O.L. Anderson, N. Soga, Elastic Constants and their Mea-

aN (B2) Present 6314.678 2848.574 3212.39 405.92

a Ref. [29].b Ref. [30].

BT, and if T < ΘD, one expects high-frequency modes to berozen [27]. In the present case, Debye temperature (ΘD) is esti-ated by using the calculated elastic constant data, in terms of

he following classical relations [28]:

D = h

k

[3n

4π

(NAρ

M

)]1/3

υm (4)

here υm is the average wave velocity, and is approximatelyiven by

m =[

1

3

(2

υ3t

+ 1

υ3l

)]−1/3

(5)

here υl and υt, are the longitudinal and transverse elastic waveelocities, respectively, which are obtained from Navier’s equa-ions [29]:

l =√

3B + 4G

3ρ(6)

nd

t =√

G

ρ. (7)

The calculated average longitudinal and transverse elasticave velocities and Debye temperature for LaN are given inable 4. The Debye temperature is found to be 395 K (seeable 4) for LaN in B1 phase at zero pressure, and this value

s much higher than those of in Ref. [30]. The same value isredicted as 405 K for B2 phase. The present value of Debyeemperature for B2 phase is close to those obtained for NbN:10 K [31]. In this formulation, the Debye temperature is directlyelated to elastic constants via average wave velocity, and theecreasing elastic constants cause to increase in Debye temper-ture in our case.

. Summary and conclusion

The first-principles pseudopotential calculations have per-ormed on the less known properties of LaN. Our present keyesults are on the structural, mechanical, thermo dynamical, andlectronic properties for LaN. The calculated lattice constant,

hich is only available experimentally, is in excellent agree-ent with the experimental value, and more consistent than the

ther theoretical value. The present value of the bulk modu-us is lower than those from other theoretical calculation. The

[[

nd Physics 108 (2008) 120–123 123

lastic constants and the related quantities have comparable val-es with the some other transition metal nitrides. The computedand structures for LaN, which are not detailed, show metallicharacter. We hope that some our results, estimated for the firstime in this work, will be tested in future experimentally andheoretically.

cknowledgement

This work is supported by Gazi University Research Projectnit under Project No. 05/2007/23.

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