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High-pressure behavior of red mercuric iodide: in situ X-ray diffraction and optical absorption studies
Solid State Communications 131 (2004) 473–478 www.elsevier.com/locate/ssc
High-pressure behavior of red mercuric iodide: in situ X-ray diffraction and optical absorption studies Sukanta Karmakar*, Surinder M. Sharma Synchrotron Radiation Section, Bhabha Atomic Research Centre, Mumbai 400085, India Received 21 November 2003; received in revised form 25 March 2004; accepted 7 May 2004 by A.K. Sood Available online 25 May 2004
Abstract We have investigated the behavior of red mercuric iodide (a-HgI2) under high pressures using in situ X-ray diffraction and optical absorption techniques. Our experimental results indicate that the tetragonal ! orthorhombic phase transformation, observed at 1.4 GPa, is accompanied by an abrupt increase in the band gap while the nature of the gap does not change. However, across the orthorhombic ! hexagonal phase transformation, observed at , 7.2 GPa, the gap decreases discontinuously and changes from direct to indirect type. These studies suggest that HgI2 may metallize at ,40 GPa, if not prevented by any other structural change. q 2004 Elsevier Ltd. All rights reserved. PACS: 61.50.ks; 78.40.Fy; 61.10.Nz; 71.30. þ h Keywords: A. Mercuric iodide; C. X-ray diffraction; D. Optical absorption; E. High pressure
1. Introduction Mercuric iodide HgI2 is an important material due to its use in opto-electronic devices and g-ray detectors [1,2]. Under ambient condition, the red colored HgI2 is a photonic band gap semiconductor and crystallizes in a layered tetragonal structure (space group P42 =nmc; Z ¼ 2) [3]. As shown in Fig. 1, in a layer each mercury atom is tetrahedrally coordinated with iodine atoms and these tetrahedra are corner-linked to each other. Inter-layer interaction is weak and is of van der Waals type. Several studies have been carried out to investigate the behavior of a-HgI2 under different thermodynamic conditions [3– 7]. Xray diffraction [3] as well as Raman scattering [4] studies show that tetragonal red a-HgI2 transforms to the yellow orthorhombic HgBr2 phase above 400 K. Reflection and absorption studies show that in the tetragonal phase band gap undergoes redshift with the increasing temperature [5]. Under pressure, Bridgman had shown that red mercuric * Corresponding author. Tel.: þ91-222-559-1312; fax: þ 91-2225505-151. E-mail address: [email protected] (S. Karmakar). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2004.05.005
iodide undergoes a transition to a yellow form at ,1.3 GPa [6]. Subsequent high pressure X-ray diffraction studies by Mikler [7] showed that the yellow phase found by Bridgman is orthorhombic, which at still higher pressures (, 7.5 GPa) transforms to a hexagonal phase (8H polytype of CdI2 structure [8], space group P 3c1). Khilji et al. [4], with the help of Raman scattering, determined the phase diagram of HgI2 up to 570 K and 1.5 GPa. However, no systematic data is available on the pressure induced electronic changes in this material. To simultaneously obtain the pressure induced structural and electronic structure information, we have now carried out optical absorption and powder X-ray diffraction studies up to 12 and 15 GPa, respectively.
2. Experimental Single crystals of red a-HgI2 were grown by slow evaporation of solution of HgI2 (reagent grade, Merck) in acetone. It is known that, for these conditions, crystals grow such that these are thin along c-axis—due to a smaller growth rate along (001) direction [9].
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Fig. 1. (a) Layered structure of a-mercuric iodide showing covalently bonded planes of thickness cl separated by a soft van der Waals gap of thickness cw ; Illustration of the (b) orthorhombic HgI2 structure showing sixfold coordination of Hg atom in the layers, (c) 8H polytype hexagonal structure having sevenfold coordination of Hg atom.
To carry out optical absorption measurements, a single crystal of , 30 mm thickness and lateral dimensions of , 100 mm was mounted in a hole of , 180 mm diameter of a steel gasket (pre-indented to 80 mm thickness) of a diamond anvil cell (DAC). A small ruby chip (, 10 mm diameter) also mounted in the gasket hole provides pressure measurements [10]. As HgI2 is soluble in the commonly used methanol:ethanol mixture, silicone oil was used as pressure transmitting medium. The measured lineshape and separation of ruby R1-R2 lines suggest that non-hydrostatic stresses are small up to ,12 GPa in these experiments [11]. A schematic of the light absorption set up used in the present measurements is shown in Fig. 2. Xe arc lamp of 150 W, operated with a feedback stabilized power supply, is used as the light source. The unpolarized light, monochromatized by a 12 m Chromex monochromator (using 1200 grooves/mm grating, blazed at 520 nm) and intercepted by a chopper (at 10 Hz frequency), is passed through a field stop and is focused with the help of a 15 £ reflecting objective onto the sample. At the sample, the spot size is found to be approximately 10 – 20 mm in diameter. A small
lens assembly, attached at the back of the diamond anvil cell, collects the transmitted beam and focuses onto a GaAs photomultiplier. The photomultiplier signal is then preamplified and analyzed by a lock-in-amplifier. Transmittance was monitored through the comparison of the sample-in sample-out intensities, as in all such studies [12]. The first order tetragonal to orthorhombic phase transition in red HgI2, occurring at 1.3 GPa, can also be observed visually as it shows up as a sudden color change of the red crystal changes to yellow (Fig. 3). To further confirm the nature of the band gap at various phases, high pressure photo-luminescence (PL) measurements were also carried out on the same batch of single crystal HgI2 using Nd:YAG diode pumped solid state laser ðl ¼ 532 nmÞ up to 1.3 GPa and Ar ion laser ðl ¼ 458 nmÞ above 1.3 GPa. Laser power was kept at minimum so as to minimize the heating of the crystal. High pressure angle dispersive X-ray diffraction studies were carried out using monochromatic (graphite mono from a rotating chromator) Mo Ka X-rays ðl ¼ 0:71069 AÞ anode X-ray generator and an imaging plate detector. For these studies, a few crystals were powdered and this powdered sample was loaded in a Mao-Bell kind DAC along with a ruby chip. As in absorption studies, silicone oil was used as a pressure transmitting fluid. The incident X-ray beam was collimated to a diameter of 100 mm and the distance between the sample and the imaging plate was kept approximately 120 mm. At each pressure the data was collected for approximately 8 h. The two-dimensional diffraction rings recorded on the imaging plate were integrated to get one-dimensional diffraction profiles using FIT2D software [13]. Structural parameters at various pressures were obtained using the GSAS refinement programs [14].
3. Results and discussion 3.1. Light absorption For light absorption studies, the frequency dependant absorption coefficient aðnÞ is obtained by employing the formula I ðnÞ 2 ac aðnÞ ¼ d1 ln 0 ð1Þ IðnÞ where I0 ðnÞ and IðnÞ are the intensities of light transmitted through the pressure transmitter and the crystal, respectively [12]. Sample thickness ðdÞ under pressure is determined from the observed linear compressibility of the material along c-axis from the X-ray diffraction experiments. The constant ac accounts for reflection losses at various interfaces and was adjusted to yield zero absorption below the band gap. Weak absorption tails at the edges can be attributed to defect states. Fig. 4 shows the absorption coefficients at various pressures. Absorption edges are
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Fig. 2. Schematic representation of high pressure optical absorption set up.
calculated by two methods from the energy dependent absorption coefficients. The first is by fitting to the following equations [15] A ðhn 2 Eg Þ1=2 for direct gap hn B aðnÞ ¼ ðhn 2 Eg Þ2 for indirect gap hn
aðnÞ ¼
ð2aÞ ð2bÞ
In the second method, band gap has been determined by taking the energy derivatives of the absorption coefficient, i.e. d2 a=dE2 ¼ 0 at E ¼ Eg (for direct gap) and da=dE ¼ 0 at E ¼ Eg (for indirect gap) [15]. Both the methods give consistent values of the band gaps. At ambient conditions, both the methods show the direct gap nature of the electronic structure of the tetragonal phase, in agreement with recent band structure calculations [16]. For tetragonal phase, the observed pressure induced variation of the band
Fig. 3. Microphotographs of HgI2 single crystal in the gasketed diamond anvil cell taken at different pressures. The circular spot in (a) indicates the typical size of the monochromatic beam focused on to the sample. At 1.3 GPa initially red crystal turns yellow.
Fig. 4. Absorption coefficient aðnÞ at different pressures across all the three phases. (‘d’ indicates direct gap and ‘ind’ indicates indirect gap, ‘rel’ represents the absorption behavior on release of pressure).
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gap energy Eg can be written as Eg ¼ 2:1257 2 0:0524P 2 0:021P2
ð3Þ
The observed energy gap at ambient condition agrees well with the earlier reported values (2.14 eV [1]). At 1.4 GPa band gap is observed to increase suddenly by 0.4 eV, indicating an electronic transition in this compound. Further the change in color across the first phase transition at , 1.4 GPa, as shown in Fig. 3, is consistent with an increase in the band gap from 2.05 to ,2.46 eV. Our analysis of the data of the absorption profiles ðaðnÞÞ; show that the new phase also has a direct gap. In this phase, the band gap decreases almost linearly at a faster rate (0.1 eV/GPa) than the initial tetragonal phase. At 7.0 GPa the shape of the absorption profile changes and shows a sudden decrease in band gap by 0.3 eV. In this phase, this gap closes at the rate 0.055 eV/GPa. Upon release of pressure, the form of absorption profiles remains similar up to 1.3 GPa, below which it transforms back to the initial form, i.e. similar to that at ambient conditions (Fig. 4(d)). Fig. 5 shows the pressure-induced variations in the energy gaps on increase and decrease in the pressure. Extrapolation of the observed pressure dependence of the band gap suggests that this material will become metallic at , 40 ^ 6 GPa, if no more phase transformations take place at higher pressures. HgI2 is known to show luminescence from several kinds of excitonic states [17]. In our PL measurements, at ambient
Fig. 5. Pressure dependence of the energy gap in HgI2. Band gap changes suddenly at 1.4 GPa due to direct – direct transition followed by another direct–indirect transition at ,7.0 GPa. Upon release of pressure, the observed changes in the gap do not retrace the changes observed on pressure increase. Circles indicate the gap determined from Eqs. 2(a) and 2(b) and triangles from the derivatives. Open squares indicate the results deduced from the photo-luminescence experiments (see text). Inset shows the variation of the photo-luminescence intensity with pressure.
conditions, we find a near band gap excitonic band at , 627 nm. Excitonic band energy (, 1.98 eV), when compared to the absorption measurements is almost 150 meV less than the band gap energy (, 2.13 eV). Beyond 1.3 GPa, this peak vanishes and the PL spectra of the yellow phase shows an excitonic band at , 559 nm (2.22 eV), i.e. , 180 meV less than the band gap in this phase. Even if we assume that the excitonic band energy to be pressure independent, pressure dependence of the deduced band gap differs systematically from the results of absorption measurements. For comparative value these are also shown in Fig. 5. However, PL intensity of 559 nm band falls sharply beyond 7.0 GPa (inset of Fig. 5) confirming the direct – indirect type of change in the band gap across this pressure. 3.2. X-ray diffraction The diffraction patterns of HgI2 at various pressures are shown in Fig. 6. The observed changes in the diffraction patterns show that the tetragonal HgI2 undergoes a phase transition to an orthorhombic structure beyond 1.4 GPa. This phase persists up to 7.2 GPa, beyond which it transforms into a hexagonal structure (8H polytype of CdI2 structure). These results are in agreement with earlier results [6,7]. Upon release of pressure hexagonal phase
Fig. 6. X-ray diffraction profiles at (a) ambient, (b) 0.4 GPa, (b) 1.9 GPa, (c) 7.2 GPa, and (d) 0.9 GPa (R) released from 15 GPa. The observed diffraction profiles are represented by þ and Le-Bail fitted curve with solid lines. Diffraction peaks from the steel gasket are marked as p .
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c-axis compressibility for all the phases has been determined from the one-dimensional analogue of Murnaghan 0 equation of state [18], viz. c=c0 ¼ ½ðb0 =bÞP þ 121=b (see inset Fig. 7). For modulii along c-axis we use the notation bk and b0k and for along a-axis these are represented by b’ and b0’ : Pressure – volume data (Fig. 7) were fitted to Birch– Murnaghan equation of state to determine the bulk modulus ðBÞ and its pressure derivatives ðB0 Þ for all the three phases. Table 1 summarizes the basic crystallographic and bulk modulii data of various phases as deduced from our studies. For HgI2 the ratio of parallel and perpendicular linear modulii is similar to that of GaSe and hence one can treat the initial structure of HgI2 as layered and can determine the anisotropic compressibility as in Ref. [19], i.e. ð4Þ
dl=l ¼ 2dP=bl
Fig. 7. Observed variation of volume/(formula unit) for the tetragonal, orthorhombic and hexagonal phases with pressure. The solid lines are fit to Birch– Murnaghan equation of state. Open triangles are the data points while releasing the pressure from 15 to 3 GPa. Open diamond symbol represents the volume just after the reverse transformation to the tetragonal phase. Inset, variation of cell dimension along c-axis with pressure for all the three phases. The solid lines are fit to one-dimensional Murnagahan equation of state. Open symbols are for the pressure release run.
continues to exist even up to 3 GPa, showing large hysteresis for the second phase transition. The orthorhombic phase is found to co-exist (however, in the Le-Bail analysis abundance cannot be estimated) at this pressure. The orthorhombic phase is found to co-exist with the tetragonal phase at 0.9 GPa, implying the hysteresis of the first transition also. Cell parameters of all the phases have been determined by Le-Bail type of profile fitting. Typical fit parameters are x2 , 1:0; RðpÞ , 2%; RðwpÞ , 3%: The
The layered nature implies that for the compressibility along c-axis, the compression depends on the relative strengths of covalent and van der Waals forces. For this we can view HgI2 layers as composed of stiff and soft parts, viz. the Hg – I layer thickness cl and the I – I inter-layer separation cw (Fig. 1(a)). At ambient conditions, ˚ , cl0 ¼ 3:49 A ˚ , cw0 ¼ 2:73 A ˚ [3]. Assuming c0 ¼ 6:22 A the isotropic compressibility within the Hg– I layers, the relative change in cl under pressure is determined by the relative change in the a-axis. Using Eq. (4), we get cl ðPÞ ¼ 3:49 expð2P=210:7Þ: The macroscopic compressibility xc along c-axis is related to covalent bond compressibility xl ; van der Waals compressibility xw and cl and cw by the formula [19] cxc ¼ cl xl þ cw xw
ð5Þ
In addition we can use following relations c ¼ cl þ cw
ð6Þ
1=xl ¼ bl ¼ ba 1=xw ¼ bw ¼ bw0 þ b0w0 P þ b00w0 P2
Table 1 Crystallographic parameters and modulii of the three phases of HgI2 Tetragonal
Orthorhombic
Hexagonal
˚) a (A ˚) b (A ˚) c (A Space group Formula unit Fractional coordinates
4.371(8) 4.371(8) 12.42(2) P42 =nmca 2 Hg 34 14 34 a I 14 14 0:389
Bulk modulus B and B0 (GPa) Linear modulus bk along c-axis and b0k (GPa) Linear modulus b’ along a-axis and b0’ (GPa)
33.9 ^ 1, 8.6 ^ 2 52.4 ^ 1, 10 ^ 2 210.7 ^ 4, 11 ^ 2
4.64(1) 7.16(1) 13.19(4) Cmc21 a 4 Hg 0 0:343 0:999c I1 0 0:053 0:125 I2 0 0:380 0:401 74.2 ^ 3, 10 ^ 1.5 134 ^ 5, 4.6 ^ 1.8
3.98(2) 3.98(2) 22.80(7) (8H)b (ABCABACBA) P 3c1 4 Hg 0 0 0c I1 13 23 0:007 I2 23 13 0:016 70.4 ^ 11.2, 7.7 ^ 3.5 114 ^ 7.7, 10.6 ^ 2
a b c
See Ref. [3]. See Ref. [7]. See Ref. [21].
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where bl and bw are the layer and inter-layer bulk modulii, respectively, and bw0 ; b0w0 ; b00w0 are the zero pressure bulk modulus and its first and second order pressure derivatives at zero pressures. Assuming that 1=xc ¼ bk þ b0k P; i.e. linear pressure dependence of the compressibility along caxis, and using Eqs. (5) and (6) at low pressures, we get bw0 ¼ 26:9 GPa, b0w0 ¼ 5:6; b00w0 ¼ 0:19 GPa21. Here, unlike in GaSe, b0w0 is close to the value of van der Waals media for which it is expected to be 7, implying that here the inter-layer space is more like van der Waals gap. Similar analysis cannot be extended to the high pressure phases. For orthorhombic phase, the Raman spectra show that in this phase, the inter-layer interaction is significantly increased. At still higher pressures, it is likely to be even more.
5. Conclusion In conclusion we note that (1) X-ray diffraction studies confirm that HgI2 undergoes tetragonal ! orthorhombic ! hexagonal phase transitions at 1.4 and 7.2 GPa, respectively. (2) The band gap is direct in the tetragonal and orthorhombic phases and indirect in the hexagonal phase. (3) In the tetragonal phase, intra-layer covalent bond deformation potential is much stronger than the van der Waals bond deformation potential and these are of opposite sign. (4) The observed pressure dependence of the band gap suggests that, in the absence of any more phase transformations, HgI2 may metallize at , 40 ^ 6 GPa. Acknowledgements
4. Deformational potentials For semiconductors, the variations in the gaps, as observed from the experiments, can be cast in terms of deformation potentials, which in turn can be tested against any theoretical calculations. However, though no such calculations are available for HgI2, we deduced these parameters here to facilitate comparison with any future calculations. For a linear strain one can write the deformation potential tensor Ek as [20] Ek ¼ dEg =ðdl=lÞ ¼ 2bl ðdEg =dPÞ
ð7Þ
For the tetragonal phase, using the linear modulii determined above (along c-axis and in the ab plane) and the pressure dependence of the band gap, we can deduce the following deformation potentials Ek ¼ 2:746 eV along the c-axis
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
E’ ¼ 14:72 eV in the ab-plane The observed pressure dependence of variation of Eg is primarily due to the changes in the interaction potentials. However, as we discussed above, for the tetragonal layered structure one can treat that the deformation potential has two parts, one due to intra-layer variations and another due to the inter-layer changes. So, we can describe the changes in the band gap as separable in two types of contributions, viz. Ec (covalent) and W (van der Waals), respectively, i.e. Eg ðPÞ ¼ Eg ð0Þ þ ½dEc =dcl Dcl ðPÞ þ ½dW=dcw Dcw ðPÞ
We would like to thank Prof. K. Syassen of Max-Plank Institute, Stuttgart for his suggestions regarding our high pressure optical absorption set up. We also like to thank Dr S.K. Sikka for many useful discussions and suggestions about this work.
[11] [12] [13] [14]
[15]
ð8Þ
From the pressure dependence of cl and cw ; given above, and by fitting to our experimental Eg ðPÞ we get
[16] [17]
for the covalent Hg – I bonded layer dEc =dcl ¼ 15:85 eV=A
[18] [19]
for the inter-layer interaction dW=dcw ¼ 22:21 eV=A
[20]
Qualitatively, the higher value of the planer deformation potential in the ab plane compared to that along c-axis can be interpreted as due to the stronger intra-layer interaction.
[21]
R.H. Bube, Phys. Rev. 106 (1957) 703. M. Piechotka, Mater. Sci. Eng. 18 (1997) 1. G.A. Jeffery, M. Vlasse, Inorg. Chem. 6 (1967) 396. M.Y. Khilji, W.F. Sherman, A. Stastmuller, G.R. Wilkinson, J. Raman Spectrosc. 11 (1981) 238. A. Burger, D. Nason, J. Appl. Phys. 71 (1992) 2717. P.S. Bridgman, Proc. Am. Acad. Arts Sci. 51 (1915) 55. H. Mikler, Monatsh. Chemie 103 (1972) 110. C.W.F.T. Pistorius, Prog. Solid State Chem. 11 (1976) 1. A. Anedda, E. Grilli, M. Guzzi, F. Raga, A. Serpi, Solid State Commun. 39 (1981) 1121. R.A. Forman, G.J. Piermarini, J.D. Barnett, S. Block, Science 176 (1972) 284. S.M. Sharma, Y.M. Gupta, Phys. Rev. B 43 (1991) 879. A.R. Goni, A. Cantarevo, U. Schwartz, K. Syassen, A. Chevy, Phys. Rev. B 45 (1992) 4221. A.P. Hammersley, S.O. Svensson, M. Hanfland, A.N. Fitch, D. Hauserman, High Pressure Res. 14 (1996) 235. A.C. Larson, R.B. Von Dreele, GSAS: general structure analysis system, Los Alamos National Laboratory LAUR Publication, 1998C. A.R. Goni, K. Syassen, in: T. Suski, W. Paul (Eds.), Semiconductors and Semimetals, vol. 54, Academic Press, New York, 1998, pp. 247 –425. Y.C. Chang, R.B. James, Phys. Rev. B 46 (1992) 15040. I.Kh. Akopyan, B.V. Bondarenko, O.N. Volkova, B.V. Novikov, T.A. Pavlova, Phys. Solid State 39 (1997) 58. F.D. Murnaghan, Proc. Natl Acad. Sci. USA 30 (1944) 244. M. Gauthier, A. Polian, J.M. Besson, A. Chevy, Phys. Rev B 40 (1989) 3837. J.M. Ziman, Principles of the Theory of Solids, Cambridge University Press, Cambridge, 1972. The fractional coordinates for the orthorhombic and hexagonal phases were refined at 1.9 and 7.2 GPa, respectively, from the initial coordinates taken from Refs. [3,7].
High-pressure behavior of red mercuric iodide: in situ X-ray diffraction and optical absorption studies Sukanta Karmakar*, Surinder M. Sharma Synchrotron Radiation Section, Bhabha Atomic Research Centre, Mumbai 400085, India Received 21 November 2003; received in revised form 25 March 2004; accepted 7 May 2004 by A.K. Sood Available online 25 May 2004
Abstract We have investigated the behavior of red mercuric iodide (a-HgI2) under high pressures using in situ X-ray diffraction and optical absorption techniques. Our experimental results indicate that the tetragonal ! orthorhombic phase transformation, observed at 1.4 GPa, is accompanied by an abrupt increase in the band gap while the nature of the gap does not change. However, across the orthorhombic ! hexagonal phase transformation, observed at , 7.2 GPa, the gap decreases discontinuously and changes from direct to indirect type. These studies suggest that HgI2 may metallize at ,40 GPa, if not prevented by any other structural change. q 2004 Elsevier Ltd. All rights reserved. PACS: 61.50.ks; 78.40.Fy; 61.10.Nz; 71.30. þ h Keywords: A. Mercuric iodide; C. X-ray diffraction; D. Optical absorption; E. High pressure
1. Introduction Mercuric iodide HgI2 is an important material due to its use in opto-electronic devices and g-ray detectors [1,2]. Under ambient condition, the red colored HgI2 is a photonic band gap semiconductor and crystallizes in a layered tetragonal structure (space group P42 =nmc; Z ¼ 2) [3]. As shown in Fig. 1, in a layer each mercury atom is tetrahedrally coordinated with iodine atoms and these tetrahedra are corner-linked to each other. Inter-layer interaction is weak and is of van der Waals type. Several studies have been carried out to investigate the behavior of a-HgI2 under different thermodynamic conditions [3– 7]. Xray diffraction [3] as well as Raman scattering [4] studies show that tetragonal red a-HgI2 transforms to the yellow orthorhombic HgBr2 phase above 400 K. Reflection and absorption studies show that in the tetragonal phase band gap undergoes redshift with the increasing temperature [5]. Under pressure, Bridgman had shown that red mercuric * Corresponding author. Tel.: þ91-222-559-1312; fax: þ 91-2225505-151. E-mail address: [email protected] (S. Karmakar). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2004.05.005
iodide undergoes a transition to a yellow form at ,1.3 GPa [6]. Subsequent high pressure X-ray diffraction studies by Mikler [7] showed that the yellow phase found by Bridgman is orthorhombic, which at still higher pressures (, 7.5 GPa) transforms to a hexagonal phase (8H polytype of CdI2 structure [8], space group P 3c1). Khilji et al. [4], with the help of Raman scattering, determined the phase diagram of HgI2 up to 570 K and 1.5 GPa. However, no systematic data is available on the pressure induced electronic changes in this material. To simultaneously obtain the pressure induced structural and electronic structure information, we have now carried out optical absorption and powder X-ray diffraction studies up to 12 and 15 GPa, respectively.
2. Experimental Single crystals of red a-HgI2 were grown by slow evaporation of solution of HgI2 (reagent grade, Merck) in acetone. It is known that, for these conditions, crystals grow such that these are thin along c-axis—due to a smaller growth rate along (001) direction [9].
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Fig. 1. (a) Layered structure of a-mercuric iodide showing covalently bonded planes of thickness cl separated by a soft van der Waals gap of thickness cw ; Illustration of the (b) orthorhombic HgI2 structure showing sixfold coordination of Hg atom in the layers, (c) 8H polytype hexagonal structure having sevenfold coordination of Hg atom.
To carry out optical absorption measurements, a single crystal of , 30 mm thickness and lateral dimensions of , 100 mm was mounted in a hole of , 180 mm diameter of a steel gasket (pre-indented to 80 mm thickness) of a diamond anvil cell (DAC). A small ruby chip (, 10 mm diameter) also mounted in the gasket hole provides pressure measurements [10]. As HgI2 is soluble in the commonly used methanol:ethanol mixture, silicone oil was used as pressure transmitting medium. The measured lineshape and separation of ruby R1-R2 lines suggest that non-hydrostatic stresses are small up to ,12 GPa in these experiments [11]. A schematic of the light absorption set up used in the present measurements is shown in Fig. 2. Xe arc lamp of 150 W, operated with a feedback stabilized power supply, is used as the light source. The unpolarized light, monochromatized by a 12 m Chromex monochromator (using 1200 grooves/mm grating, blazed at 520 nm) and intercepted by a chopper (at 10 Hz frequency), is passed through a field stop and is focused with the help of a 15 £ reflecting objective onto the sample. At the sample, the spot size is found to be approximately 10 – 20 mm in diameter. A small
lens assembly, attached at the back of the diamond anvil cell, collects the transmitted beam and focuses onto a GaAs photomultiplier. The photomultiplier signal is then preamplified and analyzed by a lock-in-amplifier. Transmittance was monitored through the comparison of the sample-in sample-out intensities, as in all such studies [12]. The first order tetragonal to orthorhombic phase transition in red HgI2, occurring at 1.3 GPa, can also be observed visually as it shows up as a sudden color change of the red crystal changes to yellow (Fig. 3). To further confirm the nature of the band gap at various phases, high pressure photo-luminescence (PL) measurements were also carried out on the same batch of single crystal HgI2 using Nd:YAG diode pumped solid state laser ðl ¼ 532 nmÞ up to 1.3 GPa and Ar ion laser ðl ¼ 458 nmÞ above 1.3 GPa. Laser power was kept at minimum so as to minimize the heating of the crystal. High pressure angle dispersive X-ray diffraction studies were carried out using monochromatic (graphite mono from a rotating chromator) Mo Ka X-rays ðl ¼ 0:71069 AÞ anode X-ray generator and an imaging plate detector. For these studies, a few crystals were powdered and this powdered sample was loaded in a Mao-Bell kind DAC along with a ruby chip. As in absorption studies, silicone oil was used as a pressure transmitting fluid. The incident X-ray beam was collimated to a diameter of 100 mm and the distance between the sample and the imaging plate was kept approximately 120 mm. At each pressure the data was collected for approximately 8 h. The two-dimensional diffraction rings recorded on the imaging plate were integrated to get one-dimensional diffraction profiles using FIT2D software [13]. Structural parameters at various pressures were obtained using the GSAS refinement programs [14].
3. Results and discussion 3.1. Light absorption For light absorption studies, the frequency dependant absorption coefficient aðnÞ is obtained by employing the formula I ðnÞ 2 ac aðnÞ ¼ d1 ln 0 ð1Þ IðnÞ where I0 ðnÞ and IðnÞ are the intensities of light transmitted through the pressure transmitter and the crystal, respectively [12]. Sample thickness ðdÞ under pressure is determined from the observed linear compressibility of the material along c-axis from the X-ray diffraction experiments. The constant ac accounts for reflection losses at various interfaces and was adjusted to yield zero absorption below the band gap. Weak absorption tails at the edges can be attributed to defect states. Fig. 4 shows the absorption coefficients at various pressures. Absorption edges are
S. Karmakar, S.M. Sharma / Solid State Communications 131 (2004) 473–478
475
Fig. 2. Schematic representation of high pressure optical absorption set up.
calculated by two methods from the energy dependent absorption coefficients. The first is by fitting to the following equations [15] A ðhn 2 Eg Þ1=2 for direct gap hn B aðnÞ ¼ ðhn 2 Eg Þ2 for indirect gap hn
aðnÞ ¼
ð2aÞ ð2bÞ
In the second method, band gap has been determined by taking the energy derivatives of the absorption coefficient, i.e. d2 a=dE2 ¼ 0 at E ¼ Eg (for direct gap) and da=dE ¼ 0 at E ¼ Eg (for indirect gap) [15]. Both the methods give consistent values of the band gaps. At ambient conditions, both the methods show the direct gap nature of the electronic structure of the tetragonal phase, in agreement with recent band structure calculations [16]. For tetragonal phase, the observed pressure induced variation of the band
Fig. 3. Microphotographs of HgI2 single crystal in the gasketed diamond anvil cell taken at different pressures. The circular spot in (a) indicates the typical size of the monochromatic beam focused on to the sample. At 1.3 GPa initially red crystal turns yellow.
Fig. 4. Absorption coefficient aðnÞ at different pressures across all the three phases. (‘d’ indicates direct gap and ‘ind’ indicates indirect gap, ‘rel’ represents the absorption behavior on release of pressure).
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gap energy Eg can be written as Eg ¼ 2:1257 2 0:0524P 2 0:021P2
ð3Þ
The observed energy gap at ambient condition agrees well with the earlier reported values (2.14 eV [1]). At 1.4 GPa band gap is observed to increase suddenly by 0.4 eV, indicating an electronic transition in this compound. Further the change in color across the first phase transition at , 1.4 GPa, as shown in Fig. 3, is consistent with an increase in the band gap from 2.05 to ,2.46 eV. Our analysis of the data of the absorption profiles ðaðnÞÞ; show that the new phase also has a direct gap. In this phase, the band gap decreases almost linearly at a faster rate (0.1 eV/GPa) than the initial tetragonal phase. At 7.0 GPa the shape of the absorption profile changes and shows a sudden decrease in band gap by 0.3 eV. In this phase, this gap closes at the rate 0.055 eV/GPa. Upon release of pressure, the form of absorption profiles remains similar up to 1.3 GPa, below which it transforms back to the initial form, i.e. similar to that at ambient conditions (Fig. 4(d)). Fig. 5 shows the pressure-induced variations in the energy gaps on increase and decrease in the pressure. Extrapolation of the observed pressure dependence of the band gap suggests that this material will become metallic at , 40 ^ 6 GPa, if no more phase transformations take place at higher pressures. HgI2 is known to show luminescence from several kinds of excitonic states [17]. In our PL measurements, at ambient
Fig. 5. Pressure dependence of the energy gap in HgI2. Band gap changes suddenly at 1.4 GPa due to direct – direct transition followed by another direct–indirect transition at ,7.0 GPa. Upon release of pressure, the observed changes in the gap do not retrace the changes observed on pressure increase. Circles indicate the gap determined from Eqs. 2(a) and 2(b) and triangles from the derivatives. Open squares indicate the results deduced from the photo-luminescence experiments (see text). Inset shows the variation of the photo-luminescence intensity with pressure.
conditions, we find a near band gap excitonic band at , 627 nm. Excitonic band energy (, 1.98 eV), when compared to the absorption measurements is almost 150 meV less than the band gap energy (, 2.13 eV). Beyond 1.3 GPa, this peak vanishes and the PL spectra of the yellow phase shows an excitonic band at , 559 nm (2.22 eV), i.e. , 180 meV less than the band gap in this phase. Even if we assume that the excitonic band energy to be pressure independent, pressure dependence of the deduced band gap differs systematically from the results of absorption measurements. For comparative value these are also shown in Fig. 5. However, PL intensity of 559 nm band falls sharply beyond 7.0 GPa (inset of Fig. 5) confirming the direct – indirect type of change in the band gap across this pressure. 3.2. X-ray diffraction The diffraction patterns of HgI2 at various pressures are shown in Fig. 6. The observed changes in the diffraction patterns show that the tetragonal HgI2 undergoes a phase transition to an orthorhombic structure beyond 1.4 GPa. This phase persists up to 7.2 GPa, beyond which it transforms into a hexagonal structure (8H polytype of CdI2 structure). These results are in agreement with earlier results [6,7]. Upon release of pressure hexagonal phase
Fig. 6. X-ray diffraction profiles at (a) ambient, (b) 0.4 GPa, (b) 1.9 GPa, (c) 7.2 GPa, and (d) 0.9 GPa (R) released from 15 GPa. The observed diffraction profiles are represented by þ and Le-Bail fitted curve with solid lines. Diffraction peaks from the steel gasket are marked as p .
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c-axis compressibility for all the phases has been determined from the one-dimensional analogue of Murnaghan 0 equation of state [18], viz. c=c0 ¼ ½ðb0 =bÞP þ 121=b (see inset Fig. 7). For modulii along c-axis we use the notation bk and b0k and for along a-axis these are represented by b’ and b0’ : Pressure – volume data (Fig. 7) were fitted to Birch– Murnaghan equation of state to determine the bulk modulus ðBÞ and its pressure derivatives ðB0 Þ for all the three phases. Table 1 summarizes the basic crystallographic and bulk modulii data of various phases as deduced from our studies. For HgI2 the ratio of parallel and perpendicular linear modulii is similar to that of GaSe and hence one can treat the initial structure of HgI2 as layered and can determine the anisotropic compressibility as in Ref. [19], i.e. ð4Þ
dl=l ¼ 2dP=bl
Fig. 7. Observed variation of volume/(formula unit) for the tetragonal, orthorhombic and hexagonal phases with pressure. The solid lines are fit to Birch– Murnaghan equation of state. Open triangles are the data points while releasing the pressure from 15 to 3 GPa. Open diamond symbol represents the volume just after the reverse transformation to the tetragonal phase. Inset, variation of cell dimension along c-axis with pressure for all the three phases. The solid lines are fit to one-dimensional Murnagahan equation of state. Open symbols are for the pressure release run.
continues to exist even up to 3 GPa, showing large hysteresis for the second phase transition. The orthorhombic phase is found to co-exist (however, in the Le-Bail analysis abundance cannot be estimated) at this pressure. The orthorhombic phase is found to co-exist with the tetragonal phase at 0.9 GPa, implying the hysteresis of the first transition also. Cell parameters of all the phases have been determined by Le-Bail type of profile fitting. Typical fit parameters are x2 , 1:0; RðpÞ , 2%; RðwpÞ , 3%: The
The layered nature implies that for the compressibility along c-axis, the compression depends on the relative strengths of covalent and van der Waals forces. For this we can view HgI2 layers as composed of stiff and soft parts, viz. the Hg – I layer thickness cl and the I – I inter-layer separation cw (Fig. 1(a)). At ambient conditions, ˚ , cl0 ¼ 3:49 A ˚ , cw0 ¼ 2:73 A ˚ [3]. Assuming c0 ¼ 6:22 A the isotropic compressibility within the Hg– I layers, the relative change in cl under pressure is determined by the relative change in the a-axis. Using Eq. (4), we get cl ðPÞ ¼ 3:49 expð2P=210:7Þ: The macroscopic compressibility xc along c-axis is related to covalent bond compressibility xl ; van der Waals compressibility xw and cl and cw by the formula [19] cxc ¼ cl xl þ cw xw
ð5Þ
In addition we can use following relations c ¼ cl þ cw
ð6Þ
1=xl ¼ bl ¼ ba 1=xw ¼ bw ¼ bw0 þ b0w0 P þ b00w0 P2
Table 1 Crystallographic parameters and modulii of the three phases of HgI2 Tetragonal
Orthorhombic
Hexagonal
˚) a (A ˚) b (A ˚) c (A Space group Formula unit Fractional coordinates
4.371(8) 4.371(8) 12.42(2) P42 =nmca 2 Hg 34 14 34 a I 14 14 0:389
Bulk modulus B and B0 (GPa) Linear modulus bk along c-axis and b0k (GPa) Linear modulus b’ along a-axis and b0’ (GPa)
33.9 ^ 1, 8.6 ^ 2 52.4 ^ 1, 10 ^ 2 210.7 ^ 4, 11 ^ 2
4.64(1) 7.16(1) 13.19(4) Cmc21 a 4 Hg 0 0:343 0:999c I1 0 0:053 0:125 I2 0 0:380 0:401 74.2 ^ 3, 10 ^ 1.5 134 ^ 5, 4.6 ^ 1.8
3.98(2) 3.98(2) 22.80(7) (8H)b (ABCABACBA) P 3c1 4 Hg 0 0 0c I1 13 23 0:007 I2 23 13 0:016 70.4 ^ 11.2, 7.7 ^ 3.5 114 ^ 7.7, 10.6 ^ 2
a b c
See Ref. [3]. See Ref. [7]. See Ref. [21].
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where bl and bw are the layer and inter-layer bulk modulii, respectively, and bw0 ; b0w0 ; b00w0 are the zero pressure bulk modulus and its first and second order pressure derivatives at zero pressures. Assuming that 1=xc ¼ bk þ b0k P; i.e. linear pressure dependence of the compressibility along caxis, and using Eqs. (5) and (6) at low pressures, we get bw0 ¼ 26:9 GPa, b0w0 ¼ 5:6; b00w0 ¼ 0:19 GPa21. Here, unlike in GaSe, b0w0 is close to the value of van der Waals media for which it is expected to be 7, implying that here the inter-layer space is more like van der Waals gap. Similar analysis cannot be extended to the high pressure phases. For orthorhombic phase, the Raman spectra show that in this phase, the inter-layer interaction is significantly increased. At still higher pressures, it is likely to be even more.
5. Conclusion In conclusion we note that (1) X-ray diffraction studies confirm that HgI2 undergoes tetragonal ! orthorhombic ! hexagonal phase transitions at 1.4 and 7.2 GPa, respectively. (2) The band gap is direct in the tetragonal and orthorhombic phases and indirect in the hexagonal phase. (3) In the tetragonal phase, intra-layer covalent bond deformation potential is much stronger than the van der Waals bond deformation potential and these are of opposite sign. (4) The observed pressure dependence of the band gap suggests that, in the absence of any more phase transformations, HgI2 may metallize at , 40 ^ 6 GPa. Acknowledgements
4. Deformational potentials For semiconductors, the variations in the gaps, as observed from the experiments, can be cast in terms of deformation potentials, which in turn can be tested against any theoretical calculations. However, though no such calculations are available for HgI2, we deduced these parameters here to facilitate comparison with any future calculations. For a linear strain one can write the deformation potential tensor Ek as [20] Ek ¼ dEg =ðdl=lÞ ¼ 2bl ðdEg =dPÞ
ð7Þ
For the tetragonal phase, using the linear modulii determined above (along c-axis and in the ab plane) and the pressure dependence of the band gap, we can deduce the following deformation potentials Ek ¼ 2:746 eV along the c-axis
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
E’ ¼ 14:72 eV in the ab-plane The observed pressure dependence of variation of Eg is primarily due to the changes in the interaction potentials. However, as we discussed above, for the tetragonal layered structure one can treat that the deformation potential has two parts, one due to intra-layer variations and another due to the inter-layer changes. So, we can describe the changes in the band gap as separable in two types of contributions, viz. Ec (covalent) and W (van der Waals), respectively, i.e. Eg ðPÞ ¼ Eg ð0Þ þ ½dEc =dcl Dcl ðPÞ þ ½dW=dcw Dcw ðPÞ
We would like to thank Prof. K. Syassen of Max-Plank Institute, Stuttgart for his suggestions regarding our high pressure optical absorption set up. We also like to thank Dr S.K. Sikka for many useful discussions and suggestions about this work.
[11] [12] [13] [14]
[15]
ð8Þ
From the pressure dependence of cl and cw ; given above, and by fitting to our experimental Eg ðPÞ we get
[16] [17]
for the covalent Hg – I bonded layer dEc =dcl ¼ 15:85 eV=A
[18] [19]
for the inter-layer interaction dW=dcw ¼ 22:21 eV=A
[20]
Qualitatively, the higher value of the planer deformation potential in the ab plane compared to that along c-axis can be interpreted as due to the stronger intra-layer interaction.
[21]
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