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Spectral ellipsometry study in the range of electronic excitations and band structure of [(CH3)2CHNH3]4Cd3Cl10 crystals
Materials Chemistry and Physics 139 (2013) 770e774
Contents lists available at SciVerse ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Spectral ellipsometry study in the range of electronic excitations and band structure of [(CH3)2CHNH3]4Cd3Cl10 crystals B. Andriyevsky a, *, K. Dorywalski a, M. Jaskólski a, Z. Czapla b, c, A. Patryn a, N. Esser d Faculty of Electronics and Computer Sciences, Koszalin University of Technology, Sniadeckich Str. 2, PL-75-453 Koszalin, Poland Department of Physics, Opole University of Technology, Ozimska Str. 75, PL-45-271 Opole, Poland c Institute of Experimental Physics, Wroclaw University, M. Born Sq. 9, PL-50-204 Wroclaw, Poland d Leibniz-Institut für Analytische Wissenschaften-ISAS-e.V., Department Berlin, Albert-Einstein-Str.9, 12489 Berlin, Germany a
b
h i g h l i g h t s < Spectral ellipsometry in the VUV range is used for study of (IPA)4Cd3Cl10 crystals. < Band structure of (IPA)4Cd3Cl10 crystal has been calculated for the first time. < Origin of the lowest energy spectral band of dielectric function is determined. < Width of temperature dependency of dielectric permittivity is large (near 50 K). < Maximum of temperature dependency of dielectric permittivity is small (near 2%).
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 August 2012 Received in revised form 14 January 2013 Accepted 12 February 2013
Optical dielectric functions ε(E) of the (IPA)4Cd3Cl10 crystal were measured in the spectral range of fundamental electronic excitations 3.5e10 eV and in the temperature range of 310e400 K containing the phase transition point between the orthorhombic phases Cmce and Pbca. Measurements were performed by spectroscopic ellipsometry with using of synchrotron radiation. Electronic band structure, density of states and dielectric functions ε(E) of (IPA)4Cd3Cl10 were calculated and analyzed on the basis of the density functional theory. Top valence and bottom conduction bands were found to be formed mainly by the cadmiumechlorine complexes of the crystals. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: Insulators Optical properties Phase transitions Band-structure
1. Introduction Halogenocadmate(II) compounds may exist in a variety of structural architectures owing to the chemical flexibility of these compounds, which may accommodate different organic counterions as well as inorganic components. This permits to create different crystal structures on the basis of the counterparts mentioned and thus to optimize their physical properties [1,2]. One of such compounds, the crystal tetra(isopropylammonium) decachlorotricadmate(II), [(CH3)2CHNH3]4Cd3Cl10, is characterized by three temperature stimulated phase transitions at 353, 294 and 259 K, that was found by calorimetry, X-ray diffraction, dielectric
* Corresponding author. Tel.: þ48 943478690; fax: þ48 943433479. E-mail addresses: [email protected], bandriyevsky@ gmail.com (B. Andriyevsky). 0254-0584/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2013.02.030
and dilatometric studies [3,4]. The crystal comprises twodimensional cadmium(II) halide network of ½CD3 Cl10 n 4 in the ac-plane, that probably causes its cleavage perpendicularly to the baxis (Fig. 1) implying the presence of strong enough chemical bonds in the ac-plane. Layered structure of the crystal implies weak chemical bonds between ½CD3 Cl10 n 4 and isopropylammonium (IPA) groups. This in turn permits larger flexibility of the isopropylammonium groups spatial positions and orientations, which is in agreement with existence of four structural phases in the (IPA)4Cd3Cl10 crystal [3]. In the present work, results of theoretical and experimental study of the electronic properties of the (IPA)4Cd3Cl10 crystal are obtained for the first time. Electronic band structure and related properties of (IPA)4Cd3Cl10 are calculated for the phase II of the spatial symmetry group Pbca (no. 61). Experimental spectra of the effective dielectric permittivity <ε>(E) of the crystal are measured in the photon energy range of 3.5e10 eV and for different
B. Andriyevsky et al. / Materials Chemistry and Physics 139 (2013) 770e774
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number of atoms (N ¼ 276) in the unit cell of (IPA)4Cd3Cl10 crystal demands large computational resources. 3. Results and discussion
Fig. 1. View of [(CH3)2CHNH3]4Cd3Cl10 crystal structure in bc-plane (b is horizontal) for orthorhombic group of symmetry Pbca: Cd e magenta, Cl e green, N e blue, C e gray, H e white (picture is drawn using the cif-file of [3]). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
temperatures in the range of 310e400 K, comprising the phases I and II. 2. Methods of investigations
Three principal groups of spectral bands may be selected in the photon energy range 3.5e10 eV of fundamental absorption in the dielectric function <ε2>(E) of (IPA)4Cd3Cl10 at room temperature. These bands are centered at 4.9, 6.4, and 8.4 eV (Fig. 2a). Clear fine structure of the function <ε2>(E) consisting of at least 5 separate maxima is observed for the first spectral group centered at 4.9 eV, (Fig. 2a and b). These maxima (4.694, 4.886, 4.992, 5.066, 5.123 eV for the temperature 398 K) resemble molecular spectra resulted from the corresponding electron-vibration energy structure. However, the energy differences between neighboring maxima obtained, 0.192, 0.106, 0.074, 0.057 eV, are too large to be caused by repetitions of one vibration frequency. On the other hand, this series resembles spectra of electronic excitation for the hydrogen like atoms. Our attempts of analytical description using the relation, E ¼ P1 P2/n2, for the maxima positions E, where P1 and P2 are constants, and n ¼ 1, 2, ., 5 were however unsuccessful. This relation approximates the experimental five element series mentioned satisfactorily only in the case when n ¼ 5, 6, ., 9. Due to the relatively small density of (IPA)4Cd3Cl10 crystal (r ¼ 1.96 g cm3), one can suggest also the relatively weak chemical bonding of the ionic type between IPAþ and CD3 Cl10 4 molecular-like groups. This in turn implies the local character of electronic states and the
2.1. Experimental method Spectroscopic ellipsometry was used for measurements of the dielectric permittivity ε of the crystal as function of the photon energy E in the range of electronic excitations 3.5e10 eV. Measurements were performed using the vacuum ultraviolet (VUV) rotating-analyzer ellipsometer attached to the 3m-NIM monochromator of Berlin electron storage ring for synchrotron radiation BESSY II. The setup is equipped with cooling and heating systems, which allows the ellipsometric measurements to be performed in the range of 10 Ke500 K. More details of the experimental setup can be found elsewhere [5]. Experimental results obtained were presented in terms of the complex effective dielectric permittivity of crystal, <ε> ¼ <ε1> þ i<ε2> [6], as functions of the photon energy E and temperature T. In the present work, temperature measurements were performed in the range of 310e400 K. 2.2. Method of theoretical study For theoretical study of the crystal, the density functional theory based ab initio calculations were performed using the plane wave pseudopotential code Quantum ESPRESSO [7] (version 5.0). The PerdeweZunger (pz) LDA exchangeecorrelation functional was used for the calculations [8]. The core electrons of the constituent atoms of (IPA)4Cd3Cl10 were handled using the scalar nonlocal norm-conserving (nc) pseudopotentials of the TroulliereMartins type, Cd.pz-n-nc.UPF, Cl.pz-n-nc.UPF, N.pz-nc.UPF, C.pz-nc.UPF and H.pz-n-nc.UPF, generated using the “atomic” code by A. Dal Corso (Quantum ESPRESSO distribution). Some of the pseudopotentials used, Cd.pz-n-nc.UPF, Cl.pz-n-nc.UPF, and H.pz-n-nc.UPF, are with nonlinear core-correction (n). The cutoff energy was chosen at 410 eV. 29 k-points in the irreducible part of the Brillouin zone were used for the calculation of band structure (BS), 36 kpoints were used for the calculation of density of states (DOS), and only the G-point was used for the calculation of the dielectric function ε2(E). The last limitation is necessary, because the large
Fig. 2. Real (ε1) and imaginary (ε2) parts of effective dielectric function of (IPA)4Cd3Cl10 in the ranges of 4.4e10.0 eV (a) and 3.5e5.2 eV (b), at the temperatures 312 K (a) and 398 K (b). jεj is an absolute value of the complex dielectric permittivity jεj ¼ (ε21 þ ε22)1/2.
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molecular-like peculiarities in the spectra of electronic excitations of (IPA)4Cd3Cl10. In the present work, the temperature measurements of (IPA)4Cd3Cl10 were performed in the range comprising the phase transition point TIe-II ¼ 353 K [3]. It was found that quasi monotonous temperature dependencies of ε1(T) and ε2(T) for (IPA)4Cd3Cl10 are characteristic in the range of 310e400 K (Fig. 3a). On this background, only small anomalies of ε1(T) and ε2(T) occur in the temperature range of phase transition. The temperature dependency of absolute dielectric permittivity j<ε>j(T) reveals broad maximum in the range of 330e380 K, the relative value of which is however small, (Dε/ε)max z 2% (Fig. 3b). This peculiarity indicates that precursor processes seen in the electronic subsystem of (IPA)4Cd3Cl10 start probably in temperatures far from the phase transition point TIeII ¼ 353 K. The result obtained demonstrates that analysis of the temperature dependence of absolute value of permittivity, jεj ¼ (ε21 þ ε22)1/2, which is a result of corresponding measurements of two independent ellipsometric parameters J and D, may supply significant information on the crystal studied. Electronic band structure of (IPA)4Cd3Cl10 was calculated for the orthorhombic Pbca space group of symmetry corresponding to the phase II of the crystal [3]. Similar calculations for the phase I of the crystal using the symmetry operations of the corresponding orthorhombic group Cmce are impossible due to the fractional occupations of several atomic positions, which imply chemical disorder [3]. Band structure of the crystal (Fig. 4) is characterized by
Fig. 3. Temperature dependencies at cooling run of the real <ε1>(T) and imaginary <ε2>(T) parts (a) and absolute value j<ε>j ¼ (<ε1>2 þ <ε2>2)1/2 (b) of effective dielectric permittivity of (IPA)4Cd3Cl10 for the photon energy E ¼ 8.0 eV.
Fig. 4. Band structure of (IPA)4Cd3Cl10 for Pbca group of symmetry.
the flat valence bands in the range of 3 to 0 eV, that is in agreement with the relatively small density of the crystal mentioned before (r ¼ 1.96 g cm3). Flat valence bands indicate for the large degree of electronic states localization and correspondingly for the low degree of its hybridization. The first group of conduction bands in between 3 and 5 eV is separated by approximately 0.5 eV from the upper conduction bands. Clear dispersion of the wave vector dependence of energy E(k) takes place for these bands. The band gap Eg of (IPA)4Cd3Cl10 in the Pbca space group was found to be direct, GeG (Fig. 4) and its magnitude agrees in general with the position of first spectral band of fundamental electronic absorption of the crystal (Fig. 2). Flat bands of (IPA)4Cd3Cl10 (Fig. 4) result in the sharp density of states (DOS) of the crystal almost in the whole energy range presented (Fig. 5). The total densities of states of the crystal for two space groups Pbca (phase II) and P212121 (phase III) were found to be similar (Fig. 5). More information on the origin of electronic bands may be obtained from the site and the orbital momentum projected densities of states (Fig. 6a, b and c). The top part of valence band in the range of 1.5 to 0 eV is formed almost exclusively by the p-states of chlorine (Fig. 6b). Here, only small additions of p-states of carbon and nitrogen and s-states of hydrogen (Fig. 6a) take place. Larger site and orbital momentum hybridization is seen for the deeper electronic states. The localized d-states of
Fig. 5. Total density of electronic states of (IPA)4Cd3Cl10 calculated for two groups of symmetry: Pbca (solid line) and P212121 (dash-dot line).
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Fig. 7. Dielectric functions ε2(E) of (IPA)4Cd3Cl10: calculated for Pbca group of symmetry (lines) for 100 (a) and 50 (b) conduction bands, and measured experimentally at the temperature 312 K (squares).
Fig. 6. Site projected densities of electronic s- (a), p- (b) and d-states (c) of (IPA)4Cd3Cl10 calculated for Pbca group of symmetry.
cadmium are located only in the narrow part of the valence DOS in between 6.5 eV and 5 eV (Fig. 6c). The conduction bands of (IPA)4Cd3Cl10 are obviously more delocalized (Fig. 4) and more hybridized (Fig. 6). The bottom conduction bands in the range of 3.0e4.5 eV originate mainly from sstates of cadmium (near 60%) and p-states of chlorine (near 40%). A degree of the electronic state hybridization for the higher conduction bands, E > 5.0 eV, is larger. The calculated and experimentally obtained dielectric functions ε2(E) of (IPA)4Cd3Cl10 are presented in Fig. 7a and b. In view of the
analysis of DOS performed above, the first experimental spectral band of ε2(E) in the range of 4.3e5.5 eV is created by the electronic transitions from the valence p-states of chlorine in the range of 1.5 to 0 eV into the conduction partly hybridized bands of cadmium and chlorine in the range of 3.0e4.5 eV. Structure of the calculated ε2(E) functions was found to be dependent on the number of the conduction bands used (Fig. 7a and b). In the case of smaller conduction bands used for the calculation (50), one can admit better coincidence of the calculated and experimental dielectric functions ε2(E) (Fig. 7b). Generally, limitations of the one electron approximation used for the calculation of the conduction band states of crystals and leading to the insufficient coincidence of the calculated and experimental ε2(E) functions are known. In the present case of big crystal unit cell, numerous constituent atoms and electronic bands, the use of the one electron approximation leads probably to the larger discrepancy of the calculated and experimental dielectric functions. 4. Conclusions Experimental dielectric functions ε(E) of the (IPA)4Cd3Cl10 crystal consist of three clear bands with maxima at 4.9, 6.4, and 8.3 eV. The first spectral band is formed mainly by the electronic excitations of the anionic cadmiumechlorine complexes. The excited energy states of the corresponding optical transitions are characterized however by the clear wave vector dispersion of a crystal-like character.
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The temperature dependency of the absolute dielectric permittivity j<ε>j(T) measured at the photon energy E ¼ 8.0 eV in the vicinity of the phases transition temperature TIeII ¼ 353 K reveals broad maximum of the 330 Ke380 K width. This indicates for the precursor processes seen in the electronic subsystem of (IPA)4Cd3Cl10 and starting probably at temperatures far from the phase transition point TIeII. The temperature increase of the absolute electronic dielectric permittivity in maximum of the dependency j<ε>j(T) is relatively small, (Dε/ε)max z 2%. Acknowledgment This work was supported by the European Community e Research Infrastructure Action under the FP6 “Structuring the European Research Area” Programme through the Integrated Infrastructure Initiative “Integrating Activity on Synchrotron and Free Electron Laser Science” under the contract R II 3-CT2004-506008 (1). The calculations were performed in the
supercomputer centre ICM of Warsaw University in the framework of the project G26-3. References [1] Ch.E. Costin-Hogan, E. Chen, Ch.-L. Hughes, A. Pickett, R. Valencia, N.P. Rath, A. Beaty, CrystEngComm 10 (2008) 1910. [2] A. Thorn, R. Willett, B. Twamley, Cryst. Growth Des. 5 (2005) 673. [3] A. Gagor, A. Waskowska, Z. Czapla, S. Dacko, Acta Crystallogr. B67 (2011) 122. [4] B. Staskiewicz, S. Dacko, Z. Czapla, Curr. Appl. Phys. 12 (2012) 413. [5] C. Cobet, R. Goldhahn, W. Richter, N. Esser, Phys. Status Solidi B 246 (2009) 1440. [6] H. Fujiwara, Spectroscopic Ellipsometry, Principles and Applications, John Wiley & Sons Ltd, 2007, p. 190. [7] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. Fabris, G. Fratesi, S. de Gironcoli, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, J. Phys. Condens. Matter 21 (2009) 395502. http:// www.quantum-espresso.org. [8] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048.
Contents lists available at SciVerse ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Spectral ellipsometry study in the range of electronic excitations and band structure of [(CH3)2CHNH3]4Cd3Cl10 crystals B. Andriyevsky a, *, K. Dorywalski a, M. Jaskólski a, Z. Czapla b, c, A. Patryn a, N. Esser d Faculty of Electronics and Computer Sciences, Koszalin University of Technology, Sniadeckich Str. 2, PL-75-453 Koszalin, Poland Department of Physics, Opole University of Technology, Ozimska Str. 75, PL-45-271 Opole, Poland c Institute of Experimental Physics, Wroclaw University, M. Born Sq. 9, PL-50-204 Wroclaw, Poland d Leibniz-Institut für Analytische Wissenschaften-ISAS-e.V., Department Berlin, Albert-Einstein-Str.9, 12489 Berlin, Germany a
b
h i g h l i g h t s < Spectral ellipsometry in the VUV range is used for study of (IPA)4Cd3Cl10 crystals. < Band structure of (IPA)4Cd3Cl10 crystal has been calculated for the first time. < Origin of the lowest energy spectral band of dielectric function is determined. < Width of temperature dependency of dielectric permittivity is large (near 50 K). < Maximum of temperature dependency of dielectric permittivity is small (near 2%).
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 August 2012 Received in revised form 14 January 2013 Accepted 12 February 2013
Optical dielectric functions ε(E) of the (IPA)4Cd3Cl10 crystal were measured in the spectral range of fundamental electronic excitations 3.5e10 eV and in the temperature range of 310e400 K containing the phase transition point between the orthorhombic phases Cmce and Pbca. Measurements were performed by spectroscopic ellipsometry with using of synchrotron radiation. Electronic band structure, density of states and dielectric functions ε(E) of (IPA)4Cd3Cl10 were calculated and analyzed on the basis of the density functional theory. Top valence and bottom conduction bands were found to be formed mainly by the cadmiumechlorine complexes of the crystals. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: Insulators Optical properties Phase transitions Band-structure
1. Introduction Halogenocadmate(II) compounds may exist in a variety of structural architectures owing to the chemical flexibility of these compounds, which may accommodate different organic counterions as well as inorganic components. This permits to create different crystal structures on the basis of the counterparts mentioned and thus to optimize their physical properties [1,2]. One of such compounds, the crystal tetra(isopropylammonium) decachlorotricadmate(II), [(CH3)2CHNH3]4Cd3Cl10, is characterized by three temperature stimulated phase transitions at 353, 294 and 259 K, that was found by calorimetry, X-ray diffraction, dielectric
* Corresponding author. Tel.: þ48 943478690; fax: þ48 943433479. E-mail addresses: [email protected], bandriyevsky@ gmail.com (B. Andriyevsky). 0254-0584/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2013.02.030
and dilatometric studies [3,4]. The crystal comprises twodimensional cadmium(II) halide network of ½CD3 Cl10 n 4 in the ac-plane, that probably causes its cleavage perpendicularly to the baxis (Fig. 1) implying the presence of strong enough chemical bonds in the ac-plane. Layered structure of the crystal implies weak chemical bonds between ½CD3 Cl10 n 4 and isopropylammonium (IPA) groups. This in turn permits larger flexibility of the isopropylammonium groups spatial positions and orientations, which is in agreement with existence of four structural phases in the (IPA)4Cd3Cl10 crystal [3]. In the present work, results of theoretical and experimental study of the electronic properties of the (IPA)4Cd3Cl10 crystal are obtained for the first time. Electronic band structure and related properties of (IPA)4Cd3Cl10 are calculated for the phase II of the spatial symmetry group Pbca (no. 61). Experimental spectra of the effective dielectric permittivity <ε>(E) of the crystal are measured in the photon energy range of 3.5e10 eV and for different
B. Andriyevsky et al. / Materials Chemistry and Physics 139 (2013) 770e774
771
number of atoms (N ¼ 276) in the unit cell of (IPA)4Cd3Cl10 crystal demands large computational resources. 3. Results and discussion
Fig. 1. View of [(CH3)2CHNH3]4Cd3Cl10 crystal structure in bc-plane (b is horizontal) for orthorhombic group of symmetry Pbca: Cd e magenta, Cl e green, N e blue, C e gray, H e white (picture is drawn using the cif-file of [3]). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
temperatures in the range of 310e400 K, comprising the phases I and II. 2. Methods of investigations
Three principal groups of spectral bands may be selected in the photon energy range 3.5e10 eV of fundamental absorption in the dielectric function <ε2>(E) of (IPA)4Cd3Cl10 at room temperature. These bands are centered at 4.9, 6.4, and 8.4 eV (Fig. 2a). Clear fine structure of the function <ε2>(E) consisting of at least 5 separate maxima is observed for the first spectral group centered at 4.9 eV, (Fig. 2a and b). These maxima (4.694, 4.886, 4.992, 5.066, 5.123 eV for the temperature 398 K) resemble molecular spectra resulted from the corresponding electron-vibration energy structure. However, the energy differences between neighboring maxima obtained, 0.192, 0.106, 0.074, 0.057 eV, are too large to be caused by repetitions of one vibration frequency. On the other hand, this series resembles spectra of electronic excitation for the hydrogen like atoms. Our attempts of analytical description using the relation, E ¼ P1 P2/n2, for the maxima positions E, where P1 and P2 are constants, and n ¼ 1, 2, ., 5 were however unsuccessful. This relation approximates the experimental five element series mentioned satisfactorily only in the case when n ¼ 5, 6, ., 9. Due to the relatively small density of (IPA)4Cd3Cl10 crystal (r ¼ 1.96 g cm3), one can suggest also the relatively weak chemical bonding of the ionic type between IPAþ and CD3 Cl10 4 molecular-like groups. This in turn implies the local character of electronic states and the
2.1. Experimental method Spectroscopic ellipsometry was used for measurements of the dielectric permittivity ε of the crystal as function of the photon energy E in the range of electronic excitations 3.5e10 eV. Measurements were performed using the vacuum ultraviolet (VUV) rotating-analyzer ellipsometer attached to the 3m-NIM monochromator of Berlin electron storage ring for synchrotron radiation BESSY II. The setup is equipped with cooling and heating systems, which allows the ellipsometric measurements to be performed in the range of 10 Ke500 K. More details of the experimental setup can be found elsewhere [5]. Experimental results obtained were presented in terms of the complex effective dielectric permittivity of crystal, <ε> ¼ <ε1> þ i<ε2> [6], as functions of the photon energy E and temperature T. In the present work, temperature measurements were performed in the range of 310e400 K. 2.2. Method of theoretical study For theoretical study of the crystal, the density functional theory based ab initio calculations were performed using the plane wave pseudopotential code Quantum ESPRESSO [7] (version 5.0). The PerdeweZunger (pz) LDA exchangeecorrelation functional was used for the calculations [8]. The core electrons of the constituent atoms of (IPA)4Cd3Cl10 were handled using the scalar nonlocal norm-conserving (nc) pseudopotentials of the TroulliereMartins type, Cd.pz-n-nc.UPF, Cl.pz-n-nc.UPF, N.pz-nc.UPF, C.pz-nc.UPF and H.pz-n-nc.UPF, generated using the “atomic” code by A. Dal Corso (Quantum ESPRESSO distribution). Some of the pseudopotentials used, Cd.pz-n-nc.UPF, Cl.pz-n-nc.UPF, and H.pz-n-nc.UPF, are with nonlinear core-correction (n). The cutoff energy was chosen at 410 eV. 29 k-points in the irreducible part of the Brillouin zone were used for the calculation of band structure (BS), 36 kpoints were used for the calculation of density of states (DOS), and only the G-point was used for the calculation of the dielectric function ε2(E). The last limitation is necessary, because the large
Fig. 2. Real (ε1) and imaginary (ε2) parts of effective dielectric function of (IPA)4Cd3Cl10 in the ranges of 4.4e10.0 eV (a) and 3.5e5.2 eV (b), at the temperatures 312 K (a) and 398 K (b). jεj is an absolute value of the complex dielectric permittivity jεj ¼ (ε21 þ ε22)1/2.
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molecular-like peculiarities in the spectra of electronic excitations of (IPA)4Cd3Cl10. In the present work, the temperature measurements of (IPA)4Cd3Cl10 were performed in the range comprising the phase transition point TIe-II ¼ 353 K [3]. It was found that quasi monotonous temperature dependencies of ε1(T) and ε2(T) for (IPA)4Cd3Cl10 are characteristic in the range of 310e400 K (Fig. 3a). On this background, only small anomalies of ε1(T) and ε2(T) occur in the temperature range of phase transition. The temperature dependency of absolute dielectric permittivity j<ε>j(T) reveals broad maximum in the range of 330e380 K, the relative value of which is however small, (Dε/ε)max z 2% (Fig. 3b). This peculiarity indicates that precursor processes seen in the electronic subsystem of (IPA)4Cd3Cl10 start probably in temperatures far from the phase transition point TIeII ¼ 353 K. The result obtained demonstrates that analysis of the temperature dependence of absolute value of permittivity, jεj ¼ (ε21 þ ε22)1/2, which is a result of corresponding measurements of two independent ellipsometric parameters J and D, may supply significant information on the crystal studied. Electronic band structure of (IPA)4Cd3Cl10 was calculated for the orthorhombic Pbca space group of symmetry corresponding to the phase II of the crystal [3]. Similar calculations for the phase I of the crystal using the symmetry operations of the corresponding orthorhombic group Cmce are impossible due to the fractional occupations of several atomic positions, which imply chemical disorder [3]. Band structure of the crystal (Fig. 4) is characterized by
Fig. 3. Temperature dependencies at cooling run of the real <ε1>(T) and imaginary <ε2>(T) parts (a) and absolute value j<ε>j ¼ (<ε1>2 þ <ε2>2)1/2 (b) of effective dielectric permittivity of (IPA)4Cd3Cl10 for the photon energy E ¼ 8.0 eV.
Fig. 4. Band structure of (IPA)4Cd3Cl10 for Pbca group of symmetry.
the flat valence bands in the range of 3 to 0 eV, that is in agreement with the relatively small density of the crystal mentioned before (r ¼ 1.96 g cm3). Flat valence bands indicate for the large degree of electronic states localization and correspondingly for the low degree of its hybridization. The first group of conduction bands in between 3 and 5 eV is separated by approximately 0.5 eV from the upper conduction bands. Clear dispersion of the wave vector dependence of energy E(k) takes place for these bands. The band gap Eg of (IPA)4Cd3Cl10 in the Pbca space group was found to be direct, GeG (Fig. 4) and its magnitude agrees in general with the position of first spectral band of fundamental electronic absorption of the crystal (Fig. 2). Flat bands of (IPA)4Cd3Cl10 (Fig. 4) result in the sharp density of states (DOS) of the crystal almost in the whole energy range presented (Fig. 5). The total densities of states of the crystal for two space groups Pbca (phase II) and P212121 (phase III) were found to be similar (Fig. 5). More information on the origin of electronic bands may be obtained from the site and the orbital momentum projected densities of states (Fig. 6a, b and c). The top part of valence band in the range of 1.5 to 0 eV is formed almost exclusively by the p-states of chlorine (Fig. 6b). Here, only small additions of p-states of carbon and nitrogen and s-states of hydrogen (Fig. 6a) take place. Larger site and orbital momentum hybridization is seen for the deeper electronic states. The localized d-states of
Fig. 5. Total density of electronic states of (IPA)4Cd3Cl10 calculated for two groups of symmetry: Pbca (solid line) and P212121 (dash-dot line).
B. Andriyevsky et al. / Materials Chemistry and Physics 139 (2013) 770e774
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Fig. 7. Dielectric functions ε2(E) of (IPA)4Cd3Cl10: calculated for Pbca group of symmetry (lines) for 100 (a) and 50 (b) conduction bands, and measured experimentally at the temperature 312 K (squares).
Fig. 6. Site projected densities of electronic s- (a), p- (b) and d-states (c) of (IPA)4Cd3Cl10 calculated for Pbca group of symmetry.
cadmium are located only in the narrow part of the valence DOS in between 6.5 eV and 5 eV (Fig. 6c). The conduction bands of (IPA)4Cd3Cl10 are obviously more delocalized (Fig. 4) and more hybridized (Fig. 6). The bottom conduction bands in the range of 3.0e4.5 eV originate mainly from sstates of cadmium (near 60%) and p-states of chlorine (near 40%). A degree of the electronic state hybridization for the higher conduction bands, E > 5.0 eV, is larger. The calculated and experimentally obtained dielectric functions ε2(E) of (IPA)4Cd3Cl10 are presented in Fig. 7a and b. In view of the
analysis of DOS performed above, the first experimental spectral band of ε2(E) in the range of 4.3e5.5 eV is created by the electronic transitions from the valence p-states of chlorine in the range of 1.5 to 0 eV into the conduction partly hybridized bands of cadmium and chlorine in the range of 3.0e4.5 eV. Structure of the calculated ε2(E) functions was found to be dependent on the number of the conduction bands used (Fig. 7a and b). In the case of smaller conduction bands used for the calculation (50), one can admit better coincidence of the calculated and experimental dielectric functions ε2(E) (Fig. 7b). Generally, limitations of the one electron approximation used for the calculation of the conduction band states of crystals and leading to the insufficient coincidence of the calculated and experimental ε2(E) functions are known. In the present case of big crystal unit cell, numerous constituent atoms and electronic bands, the use of the one electron approximation leads probably to the larger discrepancy of the calculated and experimental dielectric functions. 4. Conclusions Experimental dielectric functions ε(E) of the (IPA)4Cd3Cl10 crystal consist of three clear bands with maxima at 4.9, 6.4, and 8.3 eV. The first spectral band is formed mainly by the electronic excitations of the anionic cadmiumechlorine complexes. The excited energy states of the corresponding optical transitions are characterized however by the clear wave vector dispersion of a crystal-like character.
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The temperature dependency of the absolute dielectric permittivity j<ε>j(T) measured at the photon energy E ¼ 8.0 eV in the vicinity of the phases transition temperature TIeII ¼ 353 K reveals broad maximum of the 330 Ke380 K width. This indicates for the precursor processes seen in the electronic subsystem of (IPA)4Cd3Cl10 and starting probably at temperatures far from the phase transition point TIeII. The temperature increase of the absolute electronic dielectric permittivity in maximum of the dependency j<ε>j(T) is relatively small, (Dε/ε)max z 2%. Acknowledgment This work was supported by the European Community e Research Infrastructure Action under the FP6 “Structuring the European Research Area” Programme through the Integrated Infrastructure Initiative “Integrating Activity on Synchrotron and Free Electron Laser Science” under the contract R II 3-CT2004-506008 (1). The calculations were performed in the
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