Modelling of the electronic and ferroelectric properties

Accepted Manuscript Modelling of the electronic and ferroelectric properties of trichloroacetamide using Monte Carlo and first-principles calculations Yaxuan Cai, Shijun Luo, Zhao Wang, Juan Xiong, Haoshuang Gu PII:

S2352-8478(16)30103-4

DOI:

10.1016/j.jmat.2016.12.005

Reference:

JMAT 90

To appear in:

Journal of Materiomics

Received Date: 27 September 2016 Revised Date:

24 November 2016

Accepted Date: 21 December 2016

Please cite this article as: Cai Y, Luo S, Wang Z, Xiong J, Gu H, Modelling of the electronic and ferroelectric properties of trichloroacetamide using Monte Carlo and first-principles calculations, Journal of Materiomics (2017), doi: 10.1016/j.jmat.2016.12.005. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Modelling of the electronic and ferroelectric properties of trichloroacetamide using Monte Carlo and first-principles calculations

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Yaxuan Cai a, Shijun Luo **,b, Zhao Wang a, Juan Xiong a and HaoshuangGu *,a

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We calculated the electronic structure and the ferroelectric properties of trichloroacetamide. Its polarization originates from the charge transfer due to the strong “push-pull” effect of electron-releasing and -withdrawing groups. Its polarization reversal can be accomplished by rotating trichloromethyl group, which leads to a low coercive field. The simulated spontaneous polarization and Curie temperature of trichloroacetamide are consistent with the experimental values.

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Modelling of the electronic and ferroelectric properties of trichloroacetamide using Monte Carlo and first-principles calculations

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Yaxuan Cai a, Shijun Luo **,b, Zhao Wang a, Juan Xiong a and HaoshuangGu *,a a

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Hubei Collaborative Innovation Center for Advanced Organic Chemical Materials — Hubei Key Laboratory of Ferro & Piezoelectric Materials and Devices, Faculty of Physics & Electronic Sciences, Hubei University, Wuhan 430062, P. R. China b School of Sciences, Hubei Automotive Industries Institute, Shiyan 442002, P. R. China

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* Corresponding author: e-mail [email protected] **e-mail: [email protected]

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Abstract The electronic structure and ferroelectric mechanism of trichloroacetamide were studied using first principles calculations and density functional theory within the generalized gradient approximation. Using both Bader charge and electron deformation density, large molecular spontaneous polarization is found to originate from the charge transfer cause by the strong “push-pull” effect of electron-releasing interacting with electron-withdrawing groups. The intermolecular hydrogen bonds, N-H…O, produce dipole moments in adjacent molecules to be aligned with each other. They also reduce the potential energy of the molecular chain threaded by hydrogen bonds. Due to the symmetric crystalline properties, however, the polarization of trichloroacetamide is mostly compensated and therefore small. Using the Berry Phase method, the spontaneous polarization of trichloroacetamide was simulated, and good agreement with the experimental values was found. Considering the polarization characteristics of trichloroacetamide, we constructed a one-dimensional ferroelectric Hamiltonian model to calculate the ferroelectric properties of TCAA. Using the Hamiltonian model, the thermal properties and ferroelectricity of trichloroacetamide were studied using the Monte Carlo method, and the Tc value was calculated. Keywords first-principles study, Monte Carlo, trichloroacetamide, TCAA, organic ferroelectrics

1. Introduction In the past decades, organic ferroelectric materials have attracted increasing attention because of their large number of potential applications, especially with respect to bionic devices [1-4]. Single-component organic ferroelectrics with low-molecular-

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mass usually have many benefits, including low toxicity, mechanically flexibility, and environmental friendliness. These highly desirable properties makes them promising candidates for the commercial fabrication of flexible and lightweight functional ferroelectric devices using conventional processing techniques like spin-coating, spraycoating, inkjet printing, and vapor-phase deposition [1, 5]. So far, very few singlecomponent low-molecular-mass organic ferroelectric molecules have been discovered [1]. The rareness of organic ferroelectric molecules hinders the development of organic ferroelectrics both theoretically and experimentally. Although most of the organic compounds in the Cambridge Structure Database have been studied already to predict and find organic ferroelectric molecules, only one organic molecule with poor ferroelectric properties, cyclohexane-1,1’-diacetic acid, was found [6]. Despite being an anti-ferroelectric, the polarization mechanism of the proton transfer of this squaric acid [7] is particularly interesting with regard to its homologous series of organic compounds [1]. Croconic acid (4, 5-dihydroxy-4-cyclopentene-1, 2, 3-trione, H2C5O5) was first reported as a proton-transfer type single-component organic ferroelectric [8], for which the large polarization is generated by charge transfer (CT) via the hydrogen bonds. Collective site-to-site transfer of protons dramatically reduces the polarizationflip energy, which facilitates flipping of the polarization [9]. Trichloroacetamide (TCAA) is another single-component low-molecular-mass organic ferroelectric at room temperature [10-12]. As shown in Fig. 1(c), there are two carbon atoms in each TCAA molecule. One is bonded to an oxygen atom and an amino (NH2) group, and the other one links three chlorine atoms forming trichloromethyl (CCl3). However, unlike the other order-disorder type ferroelectric materials, TCAA has two slightly different molecules in its ferroelectric (FE) phase that originate from the differently oriented trichloromethyl (CCl3) [10]. Because of the different orientations of trichloromethyl (CCl3), there are two different molecules in the FE phase (62 % and 38 %), and three different molecules in the paraelectric (PE) phase (51.8 %, 27.6 %, and 20.6 %). The ferroelectric TCAA with its high Curie temperature of 355 K and small polarization of 0.2 µC cm-2, shows polarization reversal in an electric field as low as 7.5 kV cm-1. It shows an even smaller coercive field (4 kVcm-1) than other ferroelectric materials like croconic acid, which has a small coercive field of 11 kV cm-1 [11, 12]. There are few theoretical studies of its ferroelectric mechanism that determine its properties and device applications. In this paper, we investigate the ferroelectric and thermal properties of TCAA with respect to its molecular and electronic structure. We found that TCAA undergoes a polarization reversal though the rotation of certain groups. This reversal mechanism can significantly reduce the coercive field. The outcomes of this study may provide new ways to find potential single-component organic ferroelectrics of the group-rotation type, which have a low coercive field and good switch performance.

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This paper is organized into three sections. In the theoretical methods section, we provide the details of our calculation. In the results and discussion section, the density of states (DOS), electron density, deformation charge density and Bader charge of TCAA are calculated to simulate polarization using first principle calculations and the Berry phase method. A Hamiltonian-model-based structure of TCAA was built, according to our first principle calculation results. The Curie temperature was obtained using the Monte by Carlo method. Its value is consistent with earlier research [9]. A summary is given in the fourth section.

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2. Theoretical methods

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TCAA has several structures both in the PE and FE phase. For simplification, we only present the detailed study of one FE structure with 62 % occupancy and one PE structure with 51.8 % occupancy. The TCAA crystal in the FE structure, which is plotted in Fig. 1, is an orthorhombic phase with space group P21 without an inversion center. We calculated the DOS, charge density, and deformation charge density of TCAA using the Vienna ab-initio Simulation Package (VASP). The first principles calculations were performed using density functional theory (DFT) with a generalized gradient approximation (GGA). For the self-consistent calculations, the Γ-centered Monkhorst-Pack scheme was used to generate the K points in the Brillouin zone [13]. A plane-wave cut-off of 550 eV and a k-point grid of 7 × 13 × 7 were used in our calculation. The convergence criterion for the total energy was 10−4 eV, and the force convergence criterion was assumed to be 0.01 eV/Å for the optimization of the lattice parameters. Based on the experimental data (collected from X-ray diffraction in the Cambridge Crystallographic Data Centre) of a =10.4368 Å, b =5.80040 Å, and c =10.1922 Å [10], the optimized lattice parameters are a =10.7708 Å, b = 5.9860 Å, and c =10.5184 Å. The deviation of the optimized lattice parameters a, b, and c from the experimental values is about 3.2 %.

Fig. 1. Crystal of the FE structure of TCAA viewed along the b-axis (a) and c-axis (b). Molecule of TCAA and the schematic diagram of the dipole moment components (c).

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3. Results and Discussion 3.1. Ferroelectric mechanism The total density of states (DOS) and the partial density of states (PDOS) of the TCAA FE phase are shown in Fig. 2. The calculated indirect band gap is 4.25 eV. The valence bands mainly consist of the 1s orbital of H, 2p orbitals of N, O, C and Cl, while the bottom of the conduction band contains 2p orbitals of N, O, C and Cl. The three chlorine atoms have nearly the same PDOS, which indicates the presence of a π conjugation bond among the three chlorine groups. As shown in Fig. 2, both hydrogen and nitrogen atoms have similar PDOS peaks in the valence band, and the hydrogen atoms have hardly any PDOSs at the bottom of the conduction band. This indicates an ionic bond characteristic between the hydrogen and nitrogen atoms as well as the stronger covalent bond components in the N-C and O-C bonds.

Fig. 2. DOS and PDOS of TCAA.

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Fig. 3. Charge density and deformation charge density of TCAA. Electron density maps of TCAA with contour levels for 0.3 eÅ-3(a, b). Deformation density maps of TCAA with contour levels for 0.1 eÅ-3 (c) and 0.05 eÅ-3 (d), respectively. Green lines are positive, red lines are negative, and black dashed lines are zero.

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The deformation density maps show the difference between the electron density of the molecule and the electron density of the independent atom model (IAM): ρ−ρΙΑΜ [14]. The electron deformation density illustrates the nature, and the electron density maps are projected to the plane determined by C1, C2 and N atoms, as shown in Fig. 3(c) and (a). The electron density and the electron deformation density range from 0 eÅ-3 to 5.8 eÅ-3 and from -0.2 eÅ-3 to 0.9 eÅ-3, respectively. Fig. 3(c) shows that, in the amino group, the valence electrons of hydrogen atoms are clearly polarized towards the nitrogen atoms, and the partly exposed hydrogen nucleus attracts the valence electrons from the oxygen atoms of the adjacent molecule. This indicates that there are hydrogen bonds, N-H…O, between two adjacent molecules. In TCAA, each molecule is connected with two adjacent molecules by two intermolecular hydrogen bonds, N-H…O. In order to show the electronic structure of the three chlorine atoms clearly, we plotted the electron density and the deformation density maps projected to the plane determined by the three chlorine atoms – see Fig. 3(b) and (d). The electron density

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contour levels in Fig. 3(b) show that the electrons of three chlorine atoms form a large π bond. The electron-withdrawing groups “CCl3, O” with their high electron affinity attract electrons from the electron-releasing group “CNH2”. We also calculated the Bader charge [15] for each atom in the molecule to analyze the charge transfer – see Table 1. The charges of the electron-withdrawing groups “CCl3”, “O” and the electron-releasing group “CNH2” are about +0.09 electrons, +1.15 electrons, and -1.24 electrons, respectively. This indicates that 1.24 electrons transfer from the electronreleasing group “CNH2” to the electron-withdraw groups “CCl3, O”. The intermolecular hydrogen bonds, N-H…O, align the dipole moments of the adjacent neighbor molecules to be parallel.

 2 .3 0 .0 0 .0   0 .0 2 .3 0 .0   .  0.0 0.0 2.5 

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We calculated about 1.1×10-29 Cm for the molecular dipole moment of the FE phase. Provided the dipole moments can accumulate inside each unit cell, TCAA can become a good organic ferroelectric with a polarization of about 7.5 µC cm-2. Then, we calculated the polarization of TCAA using the Berry phase method [16-17]. Since the PE structure of TCAA is present in the experiment, it can serve as zero polarization reference with high centric symmetry in our calculation. According to our calculation, the spontaneous polarization is 0.20 µCcm-2 along the b-axis for the 62 % FE structure, and 0.18 µC cm-2 for the 38 % FE structure. Taking into account the proportion of the two structures, the polarization of the TCAA is 0.19 µC cm-2, which agrees well with the experimental value (0.2 µC cm-2) [11]. We calculated the dielectric tensor for TCAA as

r

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Since the induced dielectric polarization density P is related to the dielectric constant r r r ε r and the electric field E by P = ε 0 (ε r − 1) E , a high dielectric constant in a ferroelectric material usually indicates excellent polarization property. Organic ferroelectrics with low dielectric constants are classified as improper ferroelectrics [1]. The small dielectric tensor values for TCAA also suggest that TCAA does not have very good ferroelectric properties. Table 1. Bader charge for different atoms in TCAA. Atom H1 H2 C1 Bader charge 0.50 0.47 2.50 N O Cl1 Cl2 6.30 7.15 7.13 7.14

C2 3.67 Cl3 7.15

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Using the deformation density maps of TCAA (Fig.3.) and the Bader charge for each atom (Table 1), we can determine the total molecular dipole moment using the dipole moment components - see Fig. 1. (c):

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(1)

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r r r r r r r r r P = P1 +P2 +P3 +P3 +P4 +P5 +P6 +P7 r

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Here, P1 and P2 are the dipoles of two hydrogen atoms and the nitrogen atom, rer spectively. Furthermore, P3 is the dipole of nitrogen atom and the group of carbon atr r r r oms, P4 is the dipole of the oxygen atom and the group of carbon atoms, P5 , P6 and P7 are the dipoles of each of the three chlorine atoms and the group of carbon atoms, respectively. r The four dipole moments P1 in one cell add up to be close to zero in total. The same r r r r r is true for P2 , P3 , and P4 . The situation is different for P5 . However, the four P5 in one cell are not compensated along the b-axis because all point in the same direction (the r r b-axis). The same applies for the dipole moments P6 and P7 . In other words, these three dipole moments associated with chlorine atoms are the main source of cell polarization in TACC.

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3.2. Polarization reversal and ferroelectric phase transition As mentioned above, the polarization of the TCAA originates from the π conjugated Cl3 group. Polarization reversal is very important for ferroelectric materials, and it is hard to obtain because of severe steric limitations due to the molecular anisotropy. The π conjugated Cl3 group of TCAA is far away from other atoms (except for the carbon atom in the same trichloromethyl group) and not bonded with other atoms. A rotation of trichloromethyl can easily occur, which can reverse the molecular polarization. When the group of three chlorine atoms rotates 60 º around the perpendicular line through the center of the triangle of the Cl3 group (and vertical to the plane defined by the Cl3 group) the polarization of the TCAA reverses – see Fig. 4 . Similarly, the oxygen atom and the amino group together rotate 180 º around the carbon atom they link to. However, according to the previous analysis, the rotation of the oxygen atom and amino-group does not affect the overall polarization. The ferroelectric phase transition of TCAA is also attributed to a rotation of the three chlorine atom groups [10]. In a unit cell of TCAA, TCAA is in the PE phase if two molecules are in a positive and the other two molecules are in a negative polar configuration.

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Fig. 4. Schematics of the polarization reversal and phase transition of TCAA.

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This polarization reversal mechanism is significantly different from the mechanism for proton transfer in organic ferroelectrics such as croconic acid [9]. In the organic ferroelectrics of the proton-transfer type, the proton of the hydrogen bond transfers to produce the polarization reversal. In TCAA, the hydrogen bond N-H…O only strengthens the intermolecular interaction, and generates molecular dipole moments in the same direction. The hydrogen bond does not play a direct role in the polarization reversal. We calculated the bond length for O…H, H-N, and the distance between carbon and nitrogen, as 2.15 Å, 0.86 Å, and 2.92 Å, respectively. We obtained a bond angle ( OHN) of 149 º, which is greater than 130 º. These results are compared with the criterion of hydrogen bonds as reported by Jeffrey [18]. We find that the intermolecular hydrogen bond in TCAA is a moderate hydrogen bond. Since the hydrogen bond in TCAA does not correlate well with the polarization reversal, the moderately strong hydrogen bond can introduce a relative high polarization, and help generate a high Curie temperature in ferroelectrics. As a result, for organic ferroelectrics with rotating electron-withdrawing groups to produce polarization reversal, moderately strong hydrogen bonds are required. The structure of the electric dipole moment for TCAA is very complex. Generally, the arrangement of the molecular electric dipole moments can be regarded as electric dipole chains. Only considering the nearest neighbor interaction of the electric dipole moments of the molecules, the Hamiltonian of ferroelectric can be written as H = −∑ KPP i j − ∑ EPi i, j

(2).

i

Here, Pi and Pj are electric dipole moments of the i-th and j-th dipoles, E is the external electric field, and K denotes the coupling coefficient between the two adjacent dipoles. Our objective is to simulate the phase transition temperature, so we let the external electric field be zero. We use the parameter x =1, 0 and -1 to represent the positive, centric, and negative polar configuration, respectively. The electric dipole moment is assumed to be approximately proportional to the parameter x. As a result, the Hamil-

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tonian can be formulated similarly:

χ=

p2 − p kBT

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H = − kxi x j (3). In each unit cell of TCAA, there are four molecules, and each molecule has two hydrogen bonds linking other molecules. The energy barrier is ∆E = 0.82eV between the centric structure of paraelectric phase and the polar structure of ferroelectric phase in the unit cell. The coefficient can be obtained using k = ∆E / (4 × 2) = 0.10eV . In the present simulations, we use periodic boundary condition to erase the influence of the boundary effect upon the simulated calculations. The parameter x takes new value with the aid of Metropolis importance sampling [19], and the accepting probability of the new position can be written as 1 ∆E < 0  p= (4), exp(−∆E / k BT ) ∆E ≥ 0 where ∆E denotes the energy difference between the new and old states of the system, T is the temperature and kB is the Boltzmann constant. Using a Markov process, the system could reach an equilibrium state. The present calculations show that, after significantly fewer than 200,000 Monte Carlo steps, the system with 2000 unit cells has reached equilibrium. Hence, the first 200,000 Monte Carlo (MC) steps were abandoned, and the statistical mean of the last 100,000 MC steps was calculated using the formula:

(5).

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Here, χ is the polarizability of the system, and p is the polarization.

Fig. 5. The polarizability curves as a function of temperature.

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The temperature dependence of the polarizability using MC simulations is shown in Fig. 5. The polarizability peaks at T=403 K, which corresponds to the Curie temperature (Tc). This result, based on the one-dimensional ferroelectric Hamiltonian model to describe the dipole-dipole interaction with hydrogen bonds, is consistent with the experimental result (Tc=355K) [10]. 4. Summary

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We have investigated both the electronic structure and the ferroelectric properties of TCAA using first-principles calculations. Based on the analysis of the electronic and molecular structure, the polarization appears to originate from the charge transfer due to the strong “push-pull” effect of electron-releasing and -withdrawing groups. The intermolecular hydrogen bond favors the molecular dipole moments in the same direction. The trichloromethyl group can rotate when an external electric field is applied, and polarization reversal can be accomplished by rotating it. Using the Berry Phase method, spontaneous polarization of TCAA was calculated using the wave functions, and the calculated values are in good agreement with the experimental data. It is found that, despite the large molecule dipole moment of TCAA, the opposing orientations of molecules in a crystal compensate most of the dipole moments. Using the dipoledipole interaction model to include hydrogen bonds using the Monte Carlo method, the obtained Curie temperature is consistent with the experimental result. 5. Acknowledgements

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References

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Research supported by the National Science Foundation of China (NSFC) (Grant Nos. 11474088, 11504099 and 11274103), Natural Science Foundation of Hubei Provincial Department of Education (Grant No. Q20141005) and the Applied Basic Research Programs of Wuhan City (Grant No. 2014010101010006).

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single-component molecular crystal. Nature 2010;463(7282):789-792. [9] Cai Y, Luo S, Zhu Z, et al. Ferroelectric mechanism of croconic acid: A first-principles and Monte Carlo study. The Journal of chemical physics 2013;139(4):044702. [10] Saito K, Yamamura Y, Kikuchi N, et al. Polarization reversal by intramolecular disordering in organic ferroelectrics: trichloroacetamide. CrystEngComm 2011;13(7):2693-2698. [11] Akishige Y, Kamishina Y. Weak ferroelectricity on organic crystal trichloroacetamide. Journal of the Physical Society of Japan 2001;70(10):3124-3128. [12] Kamishina Y, Akishige Y, Hashimoto M. Ferroelectric activity on organic crystal trichloroacetamide. Journal of the Physical Society of Japan 1991;60(7):2147-2150. [13] Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations. Physical review B 1976;13(12):5188. [14] Cole J M, Goeta A E, Howard J A K, et al. X-ray and neutron diffraction studies of the nonlinear optical compounds MBANP and MBADNP at 20 K: charge-density and hydrogen-bonding analyses. Acta Crystallographica Section B: Structural Science 2002;58(4):690-700. [15] Bader R F W. Atoms in molecules. John Wiley & Sons, Ltd: 1990. [16] King-Smith R D, Vanderbilt D. Theory of polarization of crystalline solids. Physical Review B 1993;47(3):1651. [17] Vanderbilt D, King-Smith R D. Electric polarization as a bulk quantity and its relation to surface charge. Physical Review B 1993;48(7):4442. [18] Jeffrey G A, Jeffrey G A. An introduction to hydrogen bonding. New York: Oxford university press; 1997. [19] Metropolis N, Rosenbluth A W, Rosenbluth M N, et al. Equation of state calculations by fast computing machines. The journal of chemical physics 1953;21(6):1087-1092.

ACCEPTED MANUSCRIPT Yaxuan Cai received her master degree in Sun Yat-sen University. Currently. She is currently pursing doctor degree in Faculty of Physics and Electronic Sciences in Hubei University. Her research

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topic is first-principles and Monte Carlo study on materials.

Shijun Luo received his Ph.D. from Huazhong University of Science and Technology. Currently, he is a professor in

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School of Sciences of Hubei Automotive Industries Institute. include

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first-principles calculation and magnetic materials.

Zhao Wang received his Ph.D. in Faculty of Physics and Electronic Sciences from Hubei University. Currently, he is an associate professor in Faculty of Physics and Electronic Sciences of Hubei

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University. His research interests focus on gas sensors, energy harvester and microfluidic sensor based on piezoelectric materials.

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Juan Xiong received her Ph.D. in Faculty of Physics and Electronic Sciences from Hubei University. Currently, she is an associate professor in Faculty of Physics and Electronic Sciences

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of Hubei University. Her research interests focus on piezoelectric film and the devices, solar energy cell and photocatalyst.

Haoshuang Gu received his Ph.D. from Huazhong University of Science and Technology. Currently, he is a professor in Faculty of Physics and Electronic Sciences of Hubei University. His research interests include the low dimensional semiconductor and ferroelectric nanomaterials, micro sensors, energy harvester and

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biomaterials.