DOI: 10.1002/asia.201301040
Ferroelectric Transition in the Inorganic Supramolecular Complex
(Hg
6P
4) ACHTUNGTRENNUNG (CuCl
3)
2Xiao-Ming Jiang,
[a]Zhi-Bo Yan,
[a]Dan Liu,
[a]Jing-Xue Wang,
[a]Mei-Feng Liu,
[a]Guo-Cong Guo,
[b]Biao-Bing Jin,
[a]Xiao-Guang Li,
[c]and Jun-Ming Liu*
[a]Ferroelectric materials, which enable the electric switch- ing of electric polarization, are of current interest and great importance due to their ferroelectric, piezoelectric, pyro- electric, and nonlinear optical properties, and usages in data storage, energy harvesting, and optical signal processing.[1]
Since the discovery of the first ferroelectric Rochelle salt in 1921,[2]intensive research in this field has led to many ferro- electric compounds. Inorganic oxides, sulfides, and halides, especially perovskite and perovskite-like oxides (BaTiO3,[3a]
PbACHTUNGTRENNUNG(ZrxTi1x)O3,[3b] etc.)[3]are important classes of ferroelec-
trics because of their large spontaneous polarization and high phase-transition temperature. Several other ferroelec- tric classes have also received much attention recently, that is, organic–inorganic hybrids,[4] organic compounds,[5] liquid crystals,[6] and polymers.[7] Some of these materials have been found to possess ferroelectric properties comparable to those of inorganic oxides, in addition to some other advan- tages like mechanical flexibility, ease of processing, and sus- tainability.[8]Therefore, the search for new ferroelectric ma- terials has become a key area of research in ferroelectric sci- ence.[9]
The design and synthesis of supramolecular complexes (SCs) are considerably active fields of crystal engineering and materials science.[10]SCs are aggregates of well-defined composition and structure consisting of two or more differ- ent building blocks, in which species of different structures and functions can be assembled into mixed framework com- pounds that are likely to exhibit diverse structures, im-
proved properties, and unique functions that cannot be ob- tained from pure building blocks. Weak host–guest interac- tion is one of the most characteristic features of SCs, which has recently attracted great attention because of its high po- tential for the design of new functional materials.[11] The host–guest interaction is so weak that the guest molecules or ions are loosely confined in the host framework and may ex- hibit a dynamic disorder at high temperature but become or- dered below a particular temperature Tc, leading to a long- range order with electric polarization (i.e., ferroelectricity).
Hydrogen bonds, which represent a typical weak interaction, display a directional alignment and lead to ferroelectric transitions in some organic SCs,[12]Rochelle salt,[2]potassium dihydrogen phosphate (KDP),[13]triglycine sulfate (TGS),[14]
and so on.[15]Weak electrostatic supramolecular interactions (SIs) between hosts and guests, which have been identified in numerous inorganic SCs,[16]constitute another important type of weak interaction and may also lead to ferroelectrici- ty, However, to the best of our knowledge, so far no inor- ganic ferroelectric SC has been found.
In this communication, we report the new inorganic SC
(Hg6P4)ACHTUNGTRENNUNG(CuCl3)2(1), which features a ferroelectric transition
at about 37 K, as indicated by the temperature dependence of the dielectric constant and specific heat measurements.
Its spontaneous polarization in the polycrystalline form was probed using the high-precision pyroelectric current method. To gain further insights into the structural origin of the ferroelectric transition, variable-temperature powder X- ray diffraction (XRD) measurements were performed and the Terahertz time-domain spectroscopy (THz-TDS) tech- nique was adopted to detect vibration modes of SIs in1. A low-temperature ferroelectric phase was predicted based on symmetry analysis and first-principles calculations.
Compound 1 was synthesized by solid-state reactions in sealed Pyrex tubes. Its purity and crystallinity were con- firmed by a powder XRD study (Figure S1, Supporting In- formation) and its exact composition was established from the X-ray structure determination (Tables S1–S3, Supporting Information).[17 ]The compound is stable in the presence of air and water. Semi-quantitative microscopy analysis using energy-dispersive X-ray spectroscopy (EDS) was performed to confirm the presence of Hg, Cu, P, and Cl in the approxi- mate molar ratio 3.0:1.0:2.0:2.9, which is in good agreement with the chemical formula of1, and no other elements were detected.
[a] Dr. X.-M. Jiang, Dr. Z.-B. Yan, Dr. D. Liu, Dr. J.-X. Wang, Dr. M.-F. Liu, Prof. B.-B. Jin, Prof. J.-M. Liu
Laboratory of Solid State Microstructures Nanjing University
Nanjing 210093 (China) E-mail: [email protected] [b] Prof. G.-C. Guo
State Key Laboratory of Structural Chemistry Fujian Institute of Research on the Structure of Matter Chinese Academy of Sciences
Fuzhou 350002 (China) [c] Prof. X.-G. Li
Hefei National Laboratory for Physical Sciences at Microscale University of Science and Technology of China
Hefei 230026 (China)
Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/asia.201301040.
The crystal structure of1at about 300 K is composed of a three-dimensional (3-D) 13ACHTUNGTRENNUNG(Hg6P4)4+ host cationic frame- work with cavities embedded with 1-D infinite 11ACHTUNGTRENNUNG(CuCl3)2 anionic guests (Figure 1). Two phosphorus atoms, each tetra- hedrally coordinated by one phosphorus atom and three mercury atoms, join into pairs through a PP bond. Each
pair is surrounded by six mercury atoms, forming a Hg6P2 octahedron, which share all corners with each other to form a 3-D perovskite-like 13ACHTUNGTRENNUNG(Hg6P4)4+ host octahedral network.
The 11ACHTUNGTRENNUNG(CuCl3)2 anionic guest is formed by corner-sharing
CuCl4 tetrahedra, which each share two of its vertices with each other to form anionic chiral chains.
The HgP and PP bond lengths in the cationic moiety in 1 range from 2.409(4) to 2.434(4) and 2.172(7) to 2.190(5) , respectively, which lie in the normal ranges for HgP and PP bond lengths, in known mercury pnictide halides,[16a,b]respectively. The CuCl bond lengths (2.193(5)–
2.681(6) ) in the anionic guests of 1 are close to those found in literature.[16c]
The distances between the cationic host and anionic guests in1are significantly longer than the expected values for covalent bonding, thus suggesting typical SIs between them.[10] The shortest interatomic distance between the Cl atoms of the guest anions and the Hg atoms in the host framework is 2.857(4) , which is much longer than the HgCl covalent bond length but shorter than the sum of the van der Waals radii of Hg and Cl atoms. This indicates weak electrostatic SIs between the cationic and anionic moieties of 1, as found in many other inorganic SCs.[16d–f]The struc- ture of1was also established by X-ray structure determina- tion at about 120 K in addition to that at about 300 K. It can be seen from the atomic coordinates and temperature fac- tors of the atoms in 1at about 300 K and 120 K (Tables S2 and S3, respectively, Supporting Information) that the tem- perature factors of all Cu atoms are significantly larger than those of host atoms at both temperatures and that the Cu2 position is obviously split into Cu2 and Cu3 positions at the lower temperature (Figure 2). The temperature factors of all
Cl atoms at about 120 K are several times larger than those of the host atoms while they are comparable to each other at about 300 K. The obvious differences between the guest disorders at the two temperatures indicates a dynamic disor- der of the guest moiety of 1, which can be ascribed to the weak electrostatic SIs between the host and guests.
The TGA curve indicates that 1 is stable up to about 2508C (Figure S2, Supporting Information). The diffuse re- flectance spectrum reveals the presence of an optical gap of 2.10 eV (Figures S4 and S5, Supporting Information), which is consistent with its red color. The IR spectrum shows no obvious absorption in the range of 4000–400 cm1 (Fig- ure S3, Supporting Information), which supports the idea that the compound may be potentially used as a window material for laser delivery media and infrared transmission for optical fiber applications in telecommunication.[18]
The dynamic disorder of the guest moiety of1prompted us to measure its phase-transition properties. Measurements of the temperature (T) dependence of the dielectric permit- tivity e with frequencies from 1 kHz to 1 MHz were per- formed in the heating mode. The real component ofe(Fig- ure 3 b) has broad anomalous maxima around 37 K. Mean- while, the specific heat Cp (Figure 3 a) was also measured for a single crystal and an obvious peak that marks the phase transition was found around the same temperature.
In order to check whether the phase transition is a ferro- electric–paraelectric transition or not, the spontaneous po- larization (P) as a function ofTfor the powder sample was measured using the high-resolution pyroelectric current (I) method in combination with a careful exclusion of other possible contributions, considering thatIis much more sen- sitive than polarization in response to variations in structure and background.[19] Several identical I measurements were performed at different heating rates (2–6 K min1). It can be seen from Figure 3 c that the measured peaks for Iand val- leys/kinks at the three heating rates appear exactly at the same temperature, thus demonstrating that the measured signals originate from the pyroelectricity.[20] The spontane- ous polarizationP, as evaluated by integratingIas a function ofT, is plotted in Figure 3 d as a function ofT, and is found to be about 114mC m2. On the other hand, the polarity ofI andPcan be determined by the sign of poling electric fields (E), confirming that the ferroelectric domain in 1 can be switched by varying E along different directions. The fact Figure 1. Building units of the host (a, Hg6P2octahedron) and guest (b,
CuCl4tetrahedron) of1, and its supramolecular architecture (c). Two of four Cl atoms coordinated to Cu atoms are omitted for clarity and gray octahedra represent Hg6P2units.
Figure 2. Disorder of the anionic guests interpenetrated with the cationic host framework at about 120 K. All atoms are drawn as 50 % thermal el- lipsoids. Gray octahedra represent Hg6P2units.
that the polarizations obtained from three different heating rates and positive and negative E agreed with each other fur- ther ensured that no factor other than the pyroelectric cur- rent contributed. In addition, a minor dielectric abnormality at about 10 K was found on the e curve of 1 (Figure 3 b), which corresponds to the larg- estIpeak in Figure 3 c. Gener- ally, the polarization of a single crystal is about 10 times that of a powder sample because of random averaging of the crystal orien- tation during the pyroelectric current measurement;[21] thus, compound1 possesses a spon- taneous polarization of about 1140mC m2 in the single-crys- tal form, which is comparable to those of the organic SC 4- methoxyanilinium tetrafluo- roborate-18-crown-6 (0.54 mC cm2at about 109 K),[22]hy- drogen-bonded Rochelle salt (0.2mC cm2), and lithium am- monium tartrate (0.20 mC cm2).
To gain further insights into the structural origin of the fer- roelectric transition, variable- temperature powder XRD measurements were per- formed. As shown in Figure 4 a and 4 b, the XRD patterns of (0,2,2), (0,0,4), and (6,-2,2) Bragg peaks from 10 to 52 K show an abrupt shift to higher Bragg angles (q) and an inten- sity enhancement at about 35 K, which is close to the transition temperature (Tc~ 37 K) determined by the die- lectric and specific heat meas- urements. The main Bragg peaks in the 2q range of 10–
708 at these temperatures can be properly indexed with the same symmetry system of 1(monoclinic) at about 300 K.
The temperature dependence of the lattice constants, a, b, c, and b, in the paraelectric and ferroelectric phases are shown
Figure 3. Plots of the specific heat (Cp) for a single crystal of1(a), the real component of the dielectric permit- tivity (e) of1at different frequencies (b), the pyroelectric current (I) at different heating rates and with posi- tive and negative poling electric fields of8.0 kV cm(c), and the spontaneous polarization (P) as a function of temperature (d).
Figure 4. Temperature dependence of XRD patterns around (0, 2, 2) (a), (6,2, 2), and (0, 0, 4) Bragg peaks (b), and of the cell parameters (a,b,candb) of1(c–f).
in Figure 4 c–f, and it is found that the lengths of cell axes have obvious changes at about 35 K, whilebis nearly con- stant, thus indicating that the ferroelectric transition of1is accompanied by a structural phase transition.
Ferroelectric transitions can be classified into disorder–
order type and displacing type, and both types can coexist in the same ferroelectric transition.[23]It is suggested that the ferroelectricity of 1 is mainly due to the disorder-to-order transition of the guest moiety in1, with the breaking of the C2/c symmetry of the high-temperature paraelectric phase based on the structural studies. The dynamic disorder of anionic guest in1 at the paraelectric phase manifests itself in two ways (Figure 2), that is, large temperature factors and obvious position splitting. Similar phenomena can be found in many organic ferroelectric SCs[24, 4d, 15a,c]in which the disor- dered molecules or ions play a key role in their ferroelectric transitions. The oxidation state of all Cu atoms in 1is +1;
as Cu+ is nonmagnetic, the origin of the ferroelectric transi- tion in1is not a spin order, which is the important driving force for ferroelectric polarization in multiferroics.[21]Hence, 1is a proper ferroelectric compound as a result of a structur- al phase transition.
Hydrogen bonding is the typical weak interaction that leads to disordered molecules or ions and plays a significant role in the ferroelectric transitions of many known ferroelec- trics, such as Rochelle salt, KDP, TGS, organic SCs, and so
on.[2, 12–15]By contrast, the ferroelectric compound 1exhibits
SIs (i.e., another type of weak interaction), according to the above structural studies. To determine the existence of SIs in 1 experimentally, terahertz time-domain spectroscopy (THz-TDS) was used to detect the vibration modes of the SI in 1. THz-TDS, which directly measures the THz waves temporal electric field, can give the amplitude and phase of the THz wave pulse simultaneously and has been developed as a powerful noncontact and nondestructive tool for char- acterizing the parameters of materials in the THz region.[25]
The vibration modes of SI can be detected by THz-TDS based on the facts that they have a similar energy scale (1 THz~33.33 cm1) and THz absorption peaks are attribut- ed to weak intermolecular and lattice phonon vibrations which, however, cannot be precisely detected by other com- monly used techniques such as IR, UV, and Raman spec- troscopy.
The THz transmission spectra of 1 over temperatures ranging from 11 K to 300 K are shown in Figure 5. Three wide absorption peaks located at about 0.3, 0.75, and 1.1 THz are found in the spectra below about 100 K, and they can be attributed to numerous weak SIs in1. However, the peak at 1.1 THz disappears above 100 K, which is consis- tent with aforementioned subtle difference in the guest dis- order between the structures of1at about 300 K and 120 K (Tables S2 and S3, Supporting Information). The disappear- ance of the absorption peak at 1.1 THz above about 100 K further confirms that the anionic guests are truly dynamical- ly disordered, so that the positional disorder leads eventual- ly to a disorder-to-order phase transition at Tc. Although the absorption peak at 0.75 THz continuously shifts to lower
frequencies as the temperature is decreased from about 300 K to 11 K, no significant change of either absorption fre- quencies or intensities of the three THz absorption peaks was found near the Tc (~37 K). This may be because the ferroelectric transition is mainly ascribed to Cu atoms of the guests while the SIs mainly exist between the Cl atoms of the guests and the Hg atoms of the host. As can be seen from the structure of 1, the shortest ClHg distance is 2.857(4) , while that of CuHg is 3.733(2) .
The temperature dependence of THz absorption peaks as well as the structural studies indicate that weak electrostatic SIs in 1lead to the dynamic disorder of guest ions and fur- ther to the ferroelectric transition. This is strikingly different from many other ferroelectrics in which hydrogen bonds play a significant role. The findings of our study thus open up a new avenue to explore novel ferroelectric materials in inorganic SCs.
Although it has not yet been possible to solve the exact structure of the low-temperature phase because of the lack of single-crystal diffraction data at low temperatures, the fer- roelectric phase structure can be predicted based on the symmetry analysis with the help of Bilbao Crystallographic Server[26] and first-principles calculations using the Vienna ab-initio simulation package (VASP).[27] It is reasonable to propose that the ferroelectric transition of 1 preserves the primitive unit cell of the paraelectric phase (namely, klas- sengleich indexik=1) and that the possible symmetry break is restricted to only isotropy subgroups, that is, the space group of the ferroelectric phase can be reached through a phase transition with a single active irreducible represen- tation of the space group of the paraelectric phase, as de- manded by the Landau postulate. Four subgroups of the space group C2/cof 1at the paraelectric phase for a given k-index of 1 are shown in Figure S7 in the Supporting Infor- mation. OnlyCc,C2,andP1are polar groups, which are in- dispensable for ferroelectricity, and P1 is not the maximal subgroup ofC2/c(Figure S9, Supporting Information). Thus, the two maximal polar subgroups,CcandC2, corresponding to the active irreducible representations Buand Au of C2/
Figure 5. THz transmission spectra of1at different temperatures.
c(Figure S8, Supporting Information), respectively, are pos- sible for the ferroelectric phase of 1. Only the maximal polar subgroups are chosen for the ferroelectric phase due to energetic reasons to ensure the formation of a minimum number of domain walls.
The two postulated structures of Cc and C2, derived by the paraelectric structure of1with symmetry breaking of 2 and m, respectively, were used for geometry optimization calculations, in which the symmetries were maintained, and a comparison of their energies was made. It was found from the energy calculations that the ground state energy of the C2 structure (37 953.0306 eV/primitive unit cell) is lower than that of Cc structure (37 952.9993 eV/primitive unit cell) after geometry optimization. Thus, the space group of the ferroelectric phase is likely to beC2.
In summary, an inorganic supramolecular complex,
(Hg6P4)ACHTUNGTRENNUNG(CuCl3)2, with a 3-D perovskite-like cationic host
framework (Hg6P4)4+, with cavities embedded with 1-D in- finite11ACHTUNGTRENNUNG(CuCl3)2guest anions and weak electrostatic supra- molecular interactions between them, has been prepared by a solid-state reaction. The complex features a ferroelectric transition at about 37 K as determined by the temperature dependence of the dielectric constant and specific heat measurements and possesses a spontaneous polarization of about 114mC m2in the polycrystalline form (~1140mC m2 in the single-crystal form), as obtained from high-precision pyroelectric current measurements. The variable-tempera- ture powder XRD measurements indicate that the ferroelec- tric transition of 1 is accompanied by a structural phase transition. Terahertz time-domain spectroscopy and structur- al studies show that weak electrostatic supramolecular inter- actions in1lead to the dynamic disorder of ions and ferro- electric transitions, thereby indicating that this inorganic supramolecular system is a promising ferroelectric.
Experimental Section
Reagents and Syntheses
All starting materials of analytical grade were purchased from Aladdin Industrial Corporation and used as received without further purification.
Single crystals of1were obtained by a solid-state reaction. Compound 1 was crystallized from Hg2Cl2 (3.0 mmol, 1416.6 mg, 99.5 %), Cu (2.0 mmol, 127 mg, 99.99 %), and red phosphorus P (4.0 mmol, 124 mg, 99.99 %). The starting materials were ground into fine powders in an agate mortar and pressed into a pellet, which was transferred into a Pyrex tube. The tube was evacuated to 1 104Torr, flame-sealed, and then placed into a computer-controlled furnace. The tube was heated from room temperature to 2508C at a rate of 508C h1, kept at 2508C for 1 day, then heated to 4508C at 208C h1and kept at that temperature for 3 days. Subsequently, it was slowly cooled to 508C at a rate of 2.58C h1. Red crystals of1(1480 mg, 90 %) were obtained (Figure S10; Supporting Information). Small mercury drops were present as minor impurity in the product, which could easily be removed mechanically. Pure crystals of 1for physical property measurements were handpicked under a micro- scope and their purity was confirmed by powder XRD measurements (Figure S1, Supporting Information) (Caution! Hg2Cl2 is toxic and ex- treme care must be exercised; some toxic gases may be released when the Pyrex tubes are opened).
Crystal Structure Determination
Single crystals of 1with suitable dimensions were mounted on a glass fiber for single-crystal X-ray diffraction analysis. The measurements were performed on a Rigaku Saturn CCD diffractometer equipped with graph- ite-monochromated MoKa radiation (l=0.71073 ) at about 300 and 120 K, respectively. The intensity data sets of several crystals were col- lected at both temperatures. Thewscan technique was used during the collection of diffraction data and they were reduced using the Crystal- Clear software. The structure of1was solved by direct methods and re- fined by full-matrix least-squares techniques onF2.All calculations were performed with the Siemens SHELXL version 5 package of the crystallo- graphic software. The formula is based on taking collectively into account crystallographically refined compositions and requirements of charge neutrality. Relevant crystallographic data and details of the experimental conditions for1are summarized in Table S1 in the Supporting Informa- tion. Atomic coordinates of1at about 300 and 120 K are reported in Ta- bles S2 and S3, respectively, in the Supporting Information. All the data sets of different crystals of1give consistent atomic coordinates and tem- perature factors (Notes:The alerts of levelAin the checkcif file are be- cause of the positional disorder of guest anions in the crystal structure, which have been fully discussed in the text).
Powder XRD, Thermogravimetric Analysis (TGA), EDS, IR and UV/Vis/
NIR Diffuse Reflectance Spectroscopy Measurements
The powder XRD pattern (Figure S1, Supporting information) was col- lected with a Rigaku DMAX 2500 diffractometer at 40 kV and 100 mA for CuKaradiation (l=1.5406 ) with a scan speed of 58C min1at room temperature. The simulated pattern was produced using the Mercury pro- gram and single-crystal reflection data. The variable-temperature powder XRD measurements were performed using a MXPAHF 18 kW rotating anode X-ray diffractometer equipped with CuKaradiation and a variable- temperature apparatus. TGA study of1(Figure S2, Supporting Informa- tion) was carried out with a NETZSCH STA 449C instrument under a ni- trogen atmosphere. The sample and reference were held in Al2O3cruci- bles, heated at a rate of 108C min1 from room temperature to 8008C.
Semi-quantitative microscopy analyses using energy-dispersive X-ray spectroscopy (EDS) were performed on a JSM6700F scanning electron microscope (SEM) using several single crystals of1. The diffuse reflec- tance spectrum (Figure S4, Supporting Information) was recorded at room temperature on a computer-controlled Lambda 900 UV/Vis/NIR spectrometer equipped with an integrating sphere in the wavelength range of 300–2000 nm. A BaSO4plate was used as a reference, on which the finely ground powder of1was coated. The absorption spectrum (Fig- ure S5, Supporting Information) was calculated from the reflection spec- trum using the Kubelka–Munk function.[28]The IR spectrum (Figure S3, Supporting Information) was recorded by using a Nicolet Magana 750 FT-IR spectrophotometer in the range of 4000–400 cm1. The powder sample was pressed into pellets with KBr.
Specific Heat (Cp) Measurements
The specific heatCp was measured on a single crystal of about 1.0 0.5 0.5 mm3using the Physical Properties Measurement System (PPMS) in the standard procedure.
Pyroelectric Current (I) Measurements
A thin disk of 0.25 mm in thickness was prepared by pressing a powder sample of1at about 1.0 GPa. The top and bottom surfaces were poled and sandwich-coated with Au layers as two electrodes using an ion sput- tering coater. The measurement was performed using a Keithley 6514A electrometer connected to the PPMS, whose precision can reach up to 1015A. In detail, the sample was submitted to the PPMS and cooled down to about 60 K. A positive poling electric field of 8 kV cm1 was then applied to the sample until the sample reached about 2 K, at which the sample was short-circuited for 60 min in order to release any charges accumulated on the sample surfaces and inside the sample. The sample was then heated slowly at a specific heating rate, during which the pyro- electric current (I) was collected. Identical measurements were per- formed with different heating rates ranging from 2 to 6 K min1, and the
collected data were compared to ensure no contribution other than the pyroelectric current. Other contributions to the pyroelectric current, such as thermal activation, will lead to an obvious temperature shift of the py- roelectric current peaks. The validity of this procedure was demonstrated in other works.[19a, 20] The pyroelectric current at the heating rate of 6 K min1 was also measured under a negative poling electric field of 8 kV cm1. It is worth noting here that in order to obtain the true spon- taneous polarization of ferroelectric materials, the poling electric field should be large enough, which can be achieved by decreasing the thick- ness of the disk sample and increasing the magnitude of the voltage ap- plied to the sample.
Dielectric Susceptibility (e)
The dielectric susceptibilityewas determined at various frequencies as a function of temperature (T) on the thin disk sample as used in the py- roelectric current measurements, and the data were collected in the heat- ing mode using a HP4294A impedance analyzer connected with PPMS.
Terahertz Characterization
Terahertz (THz) spectra were obtained using the Terahertz time-domain spectroscopy (THz-TDS) technique (Figure S6).[25h,i]A mode-locked Ti:- sapphire laser (Coherent Company) was used to produce optical pulses with a time width less than 100 fs and a wave-length of 800 nm at a repeti- tion rate of 82 MHz. The THz pulses were generated and detected using two GaAs photoconductive antennas, respectively. The sample holder and the THz beams were placed in a closed box purged with dry N2gas to maintain the relative humidity below 4 %. Using a lock-in detection scheme, a signal-to-noise ratio of 105 was achieved. In these measure- ments, the temporal profiles of the THz pulse in the absence and pres- ence of sample were measured. Subsequently, the transmission spectrum H(w)of the sample was obtained, which is the ratio of Fourier transforms on the two temporal profiles.
Computational Procedures
Geometry optimizations in which the symmetry was maintained and energy calculations were performed based on the projected augmented wave (PAW)[29]pseudopotentials using the Vienna ab initio simulation package (VASP).[27]The valence states include 3s23p3, 3s23p5, 5d106s2, and 3d104s1for P, Cl, Hg, and Cu, respectively. The electron–electron interac- tion is described using the local-density approximation (LDA) method.
The number of plane waves included in the basis was determined by using a cutoff energy of 400 eV, and the numerical integration of the Bril- louin zone was performed using a 3 3 2 Monkhorst Packk-point sam- pling.
Acknowledgements
We gratefully acknowledge financial support by the National 973 Projects of China (Grants No. 2011CB922101 and No. 2009CB623303), the Natu- ral Science Foundation of China (Grants No. 11234005 and No.
11074113), and the Priority Academic Program Development of Jiangsu Higher Education Institutions, China.
Keywords: ferroelectric · phase transitions · pyroelectric current measurements · supramolecular chemistry · terahertz time-domain spectroscopy
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Received: August 4, 2013 Published online: September 4, 2013
