Abstract
The electron momentum density distribution and phase transition in ZnS are reported in this paper. The calculations are performed on the basis of density functional theory (DFT) based on the linear combination of atomic orbitals (LCAO) method. To compare the theoretical Compton profile, the measurement on polycrystalline ZnS has been made using a Compton spectrometer employing 59.54 keV gamma rays. The spherically averaged theoretical Compton profile is in agreement with the measurement. On the basis of equal valence-electron-density Compton profiles, it is found that ZnS is less covalent as compared to ZnSe. The present study suggests zincblende (ZB) to rocksalt (RS) phase transition at 13.7 GPa. The calculated transition pressure is found in good agreement with the previous investigations.
1. Introduction
Zinc sulfide (ZnS) is an important member of the II–VI group due to its wide range of technological applications [1–4]. ZnS is a wide band gap (3.6 eV) material used in the optoelectronic devices such as optical memories and visual displays. It has two different crystal structures (zincblende and wurtzite), both of which exhibit direct band gaps. It is believed that ZnS transforms from the zincblende (ZB) or wurtzite (WZ) structure to the rocksalt (RS) structure and then to the β-Sn phase.
The electronic, optical, and structural properties of ZnS have been reported earlier by the number of research groups [5–36]. Liu and Chan [5] have performed density functional calculations within local density approximation (LDA) to explore the electronic properties of ZB ZnS with various impurities and defects. Khenata et al. [6] also have investigated the electronic properties of zinc monochalcogenides including ZnS using full-potential linear augmented plane-wave method plus local orbitals (FP-LAPW + lo) within LDA. Goswami et al. [7] have reported the electronic properties of low dimensional ZnS using density functional tight binding (DFTB) method in ZB and WZ modifications. Erbarut [8] have reported the electronic spectra of vacancies and their various charge states in cubic ZnS using Green’s function approach within the localized orbital method. Benmakhlouf et al. [9] have predicted the pressure dependency on the electronic structure of ZnS using pseudopotential scheme. They observed that ZnS was found to exhibit direct and indirect band gaps under pressure. The band structure of ZnS has been investigated by Jaffe et al. [10] using an all-electron Hartree-Fock (HF) method including correlation corrections and evaluated the role of Zn 3d-band states in the electronic and optical properties of the material. The pressure dependence of the band gap in the ZB phase of ZnS has been investigated by Ves et al. [11] using linear-muffin-tin-orbital (LMTO) method within atomic-sphere-approximation (ASA). They found good agreement with the optical-absorption measurements. The structural properties of cubic ZnS have been investigated by Martins et al. [12] using plane wave pseudopotential (PW-PP) method and compared with an all electron LAPW method. Jaffe et al. [13] have reported ZB→RS transition in ZnS at 16.1 GPa using ab initio calculations based on HF-LCAO method. The phase transition and structural properties of ZnS in ZB, RS, β-Sn, and cinnabar (Cin) phases have been investigated by Nazzal and Qteish [14] using pseudopotential and local density approach. Qteish et al. [15] have investigated the phase transformation in ZnS under high pressure using first-principles pseudopotential and full-potential linear muffin-tin orbital (FP-LMTO) methods. They found that there is no stable intermediate Cin phase of ZnS under pressure. Catti [16] has performed ab initio calculations to study the atomic pathway of the ZB to RS transition in ZnS using LCAO method within hybrid and LDA functionals. Using the tight-binding linear muffin-tin orbital (TB-LMTO) method, Gangadharan et al. [17] observed the ZB→RS phase transition at 15.5 GPa. Miao and Lambrecht [18] have reported the structural phase transition at 14.5 GPa in ZnS using the pseudopotentials and a plane-wave basis. The phase transition ZB→RS in ZnS has been investigated by Chen et al. [19] using the plane-wave pseudopotential (PW-PP) density functional theory. The structural phase transformation of ZnS under high pressure has also been investigated by Gupta et al. [20] using the first-principle PW-PP and FP-LAPW methods. Ab initio calculations of the electronic, linear, and nonlinear optical properties of zinc chalcogenides including ZnS and ZnSe have been investigated by Reshak and Auluck [21] using the full potential linear augmented plane wave (FP-LAPW) method. A number of studies are available in the literature on momentum densities of zincblende compounds, namely, AlAs, CdSe, BeS, BeSe, BeTe, GaSb, , and BN [22–27].
Experimentally, pressure-induced phase transition in some II–VI compounds including ZnS has been investigated by Samara and Drickamer [28]. Piermarini and Block [29] have observed ZB→RS transition at 15.0 GPa using the ruby fluorescence line-shift based on the Decker equation of state (EOS). Pressure-induced structural changes in ZnS have been investigated by Zhou et al. [30] and Desgreniers et al. [31] using X-ray diffraction measurements. Using the energy dispersive X-ray diffraction technique, Pan et al. [32] have investigated the transition pressure of 11.5 GPa for the WZ→ZB and 16 GPa for the ZB→RS transitions.
Despite these studies, the ground state properties, that is, directional and spherically averaged Compton profiles of ZnS, have received little attention. It is well known that the Compton scattering is particularly sensitive to the momentum distribution of loosely bound electrons and therefore provides an interesting way to probe the electronic structure of materials [37, 38]. Measurements of line shape yield the Compton profile, , which is the one-dimensional projection of the electron momentum density along the scattering vector. Within impulse approximation, where is the electron momentum density and is the electron momentum component parallel to the photon scattering vector [37–39]. Looking at the technological importance of zincblende ZnS and success of ab-initio methods has motivated us to explore the electron momentum density and structural phase transition in the compound.
2. Experimental Details
The 241Am gamma-ray Compton spectrometer described by Sharma et al. [40] has been employed for the Compton profile measurement of ZnS. The sample having purity 99.99% was procured from Alfa Aesar, Johnson Matthey Co., USA. The ZnS sample of effective density 1.3606 gm/cm3 was prepared from polycrystalline powder having thickness 3.2 mm. The sample was held vertical by affixing on the back of the lead covered brass slab with a hole of diameter 18.10 mm. The incident gamma rays of 59.54 keV from 5Ci annular 241Am source were scattered at an angle 166° ± 3.0° from the sample. The scattered radiation was analyzed using an HPGe detector (Canberra model, GL0110S) providing overall momentum resolution 0.6 a.u. The chamber was evacuated to about 1.33 Pa to reduce the contribution of air scattering. The spectra were recorded with a multichannel analyzer (MCA) with 4096 channels. The channel width was ~20 eV corresponding to 0.03 a.u. of momentum. The 2.75 × 104 counts were collected at the Compton peak, and the stability of the system was checked by using a weak 241Am source.
The raw Compton data were corrected for several systematic corrections like background, instrumental resolution, absorption, cross section and multiple scattering, and so forth, using computer code of the Warwick group [41, 42]. We observed 4.7% contribution of multiple scattering in the momentum region −10 a.u. to +10 a.u. Finally, the corrected experimental data were normalized to 20.24 electrons in the range 0 to +7 a.u. being the area of free atom Compton profile [43]. In the present experimental setup, the electrons of Zn contribute up to 2.2 a.u. only.
3. Theoretical Details
We employed first-principles LCAO method embodied in the CRYSTAL06 code [44] to explore the momentum density and phase transition in zincblende ZnS. In LCAO method each crystalline orbital is a linear combination of Bloch functions defined in terms of local functions , normally referred to as atomic orbitals. The local functions are expressed as linear combination of certain number of individually normalized Gaussian-type functions. For Zn and S, the local functions were constructed from the Gaussian type functions [45]. The Kohn-Sham Hamiltonian was constructed following the prescription of Dovesi et al. [44] while considering the exchange functional of Becke [46] and the Perdew-Burke-Ernzerhof (PBE) correlation functional [47, 48]. The self-consistent calculations were performed considering 145 points in the irreducible Brillouin zone with tight tolerances. To achieve self-consistency 50 percent mixing of successive cycles was considered, and the self-consistency was achieved within 13 cycles.
4. Results and Discussion
In Table 1 we compare the experimental Compton profile for ZnS with the earlier measurement [33]. Also given here is the unconvoluted spherically averaged theoretical Compton profile computed from DFT-PBE scheme. The present measurement on ZnS is in good agreement with earlier data [33]. In order to compare the theoretical values with the present experiment, the theoretical values were convoluted with the Gaussian function and normalized to 20.24 electrons from 0 to +7 a.u. To examine the agreement between theory and experiment, we plot in Figure 1 the difference profile deduced from the convoluted theoretical profile and the experiment. From Figure 1, it reveals that the electron momentum density based on the DFT-PBE calculations mostly overestimates the measurement in the momentum range a.u. Thereafter the trend is reversed. The maximum difference shown by the DFT-PBE with experimental is about 3.7%. It is also seen that the differences are small in the high momentum region. It is expected because this is the region of core electrons which are unaffected in solid formation. From Figure 1, it can be inferred that DFT-PBE values are in overall good agreement with the experiment, but there are some residual differences especially in the low momentum region. This may possibly be due to the direct involvement of -band electrons of Zn in determination of ground state properties of ZnS. The larger disagreement in the low momentum region also indicates that Lam and Platzman (LP) correction [49] may be useful in bringing the theory closer to the experiment below the Fermi momentum. Further, more accurate -band basis sets may probably be helpful to estimate the momentum density accurately.
To examine the directional features theoretically, we consider the directional Compton profiles of ZnS along [100], [110], and [111] directions. We present the anisotropies derived from unconvoluted theory (DFT-PBE) in Figure 2. From Figure 2, it is visible that the anisotropies [100]–[110] and [100]–[111] are positive in nature at a.u. The maximum anisotropy is seen between [100] and [110] directions at a.u. The figure also depicts that anisotropies are not observable in the high momentum region. The isotropic contribution due to core electrons dominates in determining the electron momentum density in this region and therefore anisotropies diminish. Measurements on single crystalline samples would be helpful to examine the directional features of bonding through anisotropies.
To compare the nature of bonding in isovalent and isostructural zincblende ZnS and ZnSe, we have generated experimental equal valence electron density (EVED) profiles. In Figure 3, we plot the experimental EVED profiles of the two compounds deduced from experimental valence (experiment-convoluted core). For ZnSe, data is taken from our own earlier measurement [50]. The EVED profiles were derived by normalizing valence electron profiles to 4.0 electrons and scaling the resulting profiles by the Fermi momentum (). For ZnS and ZnSe, turned out to be 0.958 and 0.917 a.u., respectively, using the expression , where is the valence electron density. A number of researchers have shown that this scheme offers a way to understand the nature of bonding in solids [51–56]. Figure 3 depicts that the EVED profile corresponding to ZnSe is larger around the low momentum region compared to ZnS. As the larger value around low momentum is attributed to larger covalent character, it points out that ZnS is less covalent and hence more ionic than ZnSe. In contrast, J. C. Phillips [57] arrived at the opposite conclusion; that is, ZnSe shows larger ionic character as compared to ZnS.
To determine the structural parameters for the two structures, the total energy was calculated. Using the Birch Murnaghan equation of state (EOS) [58, 59], we obtained the energy-volume dependences . The total energy against volume curves for ZB (B3) and RS (B1) phases of ZnS is plotted in Figure 4. The energy states of B3 phase are below the B1 phase. It indicates the stability of the B3 phase. In Figure 4, the symbol represents our computed values and the curves represent fitting results to the following Birch-Murnaghan equation of state (EOS) [58, 59]: where is the minimum energy, is the corresponding volume, and is the bulk modulus at zero pressure and . The lattice constant , bulk modulus , and its pressure derivative at zero pressure for both phases are calculated by fitting the above equation. These results are summarized in Table 2.
Now we discuss the structural transition B3 → B1 in ZnS. The transition pressure () is obtained from the enthalpy calculations. Here, we have considered zero temperature in our calculations. At this temperature the thermodynamically stable phase is that one with the lowest enthalpy, at a given pressure. The calculated enthalpies of the two phases are plotted in Figure 5. The transition occurs when the enthalpy of the lower pressure phase coincides with some other phase at high pressure. After the point of intersection, the enthalpy of B1 becomes less than B3 phase. Hence, at low pressure the stable phase is B3 and at high pressure the stable phase is B1. The figure reveals structural transition from B3 to B1 at 13.7 GPa.
5. Conclusions
In this paper, electron momentum density distribution and phase transition in ZnS are reported. Compton profile measurement on polycrystalline ZnS supports the DFT-PBE calculation with the PBE correlation functional. The maximum anisotropy, that is, ~2.1% of , is seen between [100] and [110] directions at a.u. On the basis of EVED profiles, it is found that ZnS is less covalent compared to ZnSe. It has also been found that B3 is energetically favorable state, and B3 to B1 phase transition occurs at 13.7 GPa.
Acknowledgments
This work is financially supported by the CSIR through Project no. 03 (1205)/12/EMR-II. G. Sharma is also thankful to the Head of the Department of Pure & Applied Physics, University of Kota, for providing computational facilities.