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Ferroelectric metal organic framework (MOF)
Inorganic Chemistry Communications 13 (2010) 1590–1598
Contents lists available at ScienceDirect
Inorganic Chemistry Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i n o c h e
Mini review
Ferroelectric metal organic framework (MOF) Min Guo, Hong-Ling Cai, Ren-Gen Xiong ⁎ Ordered Matter Science Research Center, Southeast University, Nanjing, Jiangning, 211189, PR China
a r t i c l e
i n f o
Article history: Received 18 July 2010 Accepted 3 September 2010 Available online 16 September 2010 Keywords: Multiferroic Ferroelectric MOF Perovskite-type
a b s t r a c t Multiferroic metal organic frameworks (MOFs) with magnetic ordering and ferroelectric ordering coexisting have recently drawn considerable interest for their amazing applications in the field of magnetoelectric multifunctional materials. Based on the Landau theory and related characterizations, this comment in detail discusses the second-order ferroelectric phase transition of ABO3 perovskite-type MOFs, including Curie– Weiss constants, symmetry breaking, spontaneous polarization, dielectric hysteresis loop, and so on. Eventually, the author gives a prospect about the development of ferroelectric MOFs. This mini-account will be of guiding significance for the design and synthesis of metal organic framework functional materials with specific multiferroic properties. © 2010 Elsevier B.V. All rights reserved.
Contents Introduction . . . . . . . . . . . . . . . . . . The first antiferroelectric MOF, Cu(HCOO)2 ∙ 4H2O Porous MOFs with movable polar guests . . . . . MOFs with ABO3 perovskite-type frameworks. . . Experimental . . . . . . . . . . . . . . . . . . Results and discussion. . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . Prospects . . . . . . . . . . . . . . . . . . . . Acknowledgement . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . .
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Introduction
The first antiferroelectric MOF, Cu(HCOO)2 ∙ 4H2O
Metal organic framework (MOF) containing guest molecules has become one of the most important candidates of developing multiferroic functional materials because of its manually coupled controllable ferroelectric properties derived from the involving guest or solvent molecule ordering, and magnetic properties derived from the transition metal ion spin ordering in the host lattices. These materials have drawn particular interest because of promising applications in sensing, data communication, spin-crossover, and signal processing. Ferroelectric phenomenon is usually associated with the occurrence of the phase transition. Dielectric anomaly combined with the DSC (differential scanning calorimetry) results is a convincing strategy to confirm the phase transition.
At the end of the 1960s, Okada and Sugie reported the first the antiferroelectric MOF (metal organic framework), Cu(HCOO)2 · 4H2O, with formic acid as building blocks and protonated organic amines as templates (Fig. 1a) [1]. Temperature dependence of dielectric constants shows a behavior of the first-order transition at about 235 K (Fig. 1b), which is shifted to a higher temperature of 245 K by deuterium substitution of the hydrogen in H2O. Typical double hysteresis loop measured at 227 K is observed suggesting an antiferroelectric transition. Nevertheless, an additional phase transition was found at 227 K from the pyroelectric current measurement (Fig. 2a) by Suzuki and Okada. As shown in the dielectric loops measured at varying temperature in Fig. 2b, the newly found phase below 227 K is considered to be an approximately ferroelectric phase. This work has aroused the chemists' research interest on the exploration of ferroelectric MOF materials.
⁎ Corresponding author. E-mail address: [email protected] (R.-G. Xiong). 1387-7003/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.inoche.2010.09.005
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Fig. 1. (a) Crystal structure of Cu(HCOO)2 · 4H2O. (b) Temperature dependence of dielectric constants of Cu(HCOO)2 · 4H2O (blue) and Cu(HCOO)2 · 4D2O (red).
Porous MOFs with movable polar guests Kobayashi has reported three porous MOFs containing movable polar guest or solvent molecules, [Mn3(HCOO)6](H2O)(CH3OH) [2a] (Fig. 3), [Mn3(HCOO)6](C2H5OH) [2b] (Fig. 4), and [La2Cu3{NH(CH2COO)2}6] (H2O)n [2c] (Fig. 5). With regard to them, the phase transitions are induced by the ordering or freezing of the polar guest molecules. The dielectric constants of the systems are closely related to different positional freedoms and molecular dipole moments of the guest molecules. In another way, there might happen ferromagnetic transitions derived from the M2+ (M=magnetic metals) spin ordering incorporated in the host lattice based on the Goodenough–Kanamori rule. [Mn3 (HCOO)6](H2O)(CH3OH) and [Mn3(HCOO)6](C2H5OH) are two structural related compounds with the same host framework and different guest molecules, and give different anomalies at about 150 K with εr =20 and 165 K with εr = 45, respectively (Figs. 3 and 4). In addition, there happens a ferromagnetic phase transition in [Mn3(HCOO)6](C2H5OH) at Tc =8.5 K (Fig. 4b). As seen in Fig. 5, the εr of [La2Cu3{NH(CH2COO)2}6] (D2O)n shows two anomalies at around 190 K and 280 K, which are approximately 10 K and 25 K higher than that of [La2Cu3{NH (CH2COO)2}6](H2O)n, suggesting a prominent deuteration effect. MOFs with ABO3 perovskite-type frameworks Cheetham and others have systematically investigated a series of metal organic frameworks with ABO3 perovskite-type topologies,
[(CH3)2NH2][M(HOOC)3] (DMMF), where A = H2NMe2, B = M (M is divalent metal elements, Zn2+, Mn2+, Fe2+, Co2+, Ni2+), and O = HCOO [3]. The common framework of ABO3 perovskite is depicted in Fig. 6a. The dielectric constant measurements indicate that antiferroelectric behavior occurs in the range of 160–185 K (DMZnF, 160 K, DMMnF, 185 K, DMFeF, 160 K, DMCoF, 165 K, DmNiF, 180 K ), which might originate from the order–disorder type electric ordering of the organic molecules. Furthermore, as seen in Fig. 7, the specific heat result of DMMnF not only points to the second-order phase transition, but also gives calculated value of ΔS suggesting that the transition is more complex than a simple 3-fold order–disorder model. In the beginning of this year, detailed observation on the mechanism of the phase transition of [(CH3)2NH2][Mn(HCOO)3] has been carried on by Senaris-Rodriguez, proposing a transition of more complex than that of a simple homogeneous 3-fold order–disorder model. [4] The dielectric anomaly combining with the DSC result approves of the happening of the phase transition. Interestingly, when Zn2+ is replaced by a transition metal ion (Mn2+, Fe2+, Co2+, and Ni2+), the corresponding compounds became magnetically ordered leading to multifunctional materials with coupled ferroelectric order and weakly magnetic order. [3b] Recently, Zhang and Xiong have also newly reported an ABO3 perovskite-type MOF inclusion, (HIm)2[KFe(CN)6] (Him = imidazolim cation) [5]. An order–disorder mechanism is found in the structural transformations owing to the motions of the cationic guests of polar Him under different temperatures. The dielectric constant curve gave exceptional two-step phase transitions at 187 K and 158 K, representing a promising switchable molecular dielectrics (Fig. 8). Study on such materials will be a great guide for understanding structural phase transitions and searching for new electric ordering materials. Unfortunately, although much attention has been focused on the dielectric investigation of ABO3 perovskite-type compounds, no one has detected one standard dielectric hysteresis loop. Wang and Gao in Peking University are the first to break through this limit, a new MOF, [NH4][Zn(HCOO)3] possessing perfect ferroelectric hysteresis loop has been successfully prepared. [6a] Experimental
Fig. 2. (a) Pyroelectric currents vs. temperature measured on the heating process of Cu (HCOO)2 · 4H2O (CFTH) and Cu(HCOO)2 · 4D2O (CFTD). Tc is the phase transition temperature. (b) Double hysteresis loop at 223 K. (c) Detail of the central portion of (b). Dielectric loops at 233 K (c), at 233 K (d), at 233 K (e), and at 233 K (f).
The single crystals of [NH4][Zn(HCOO)3] was obtained by reaction of ammonium formate, formic acid, and Zn(ClO4) · 6H2O in methanol [6a]. The selected crystallographic data and views of the structures of [NH4][Zn(HCOO)3] at 290 K and 110 K were given in Table 1 and Fig. 9. By changing the size of the guest molecule with the smaller NH+ 4 group instead of [H2NMe2]+, there induces a stronger driving force between ordered and disordered structures. As a consequence, a measurable dielectric hysteresis loop has been obtained, which is the clear evidence for a typical ferroelectric behavior. The spontaneous
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Fig. 3. [Mn3(HCOO)6](H2O)(CH3OH). (a) Crystal structure at room temperature. The MnO6 is represented as a purple octahedron, and the purple HCOO ligand is represented as a light blue triangle. (b) Temperature dependence of the dielectric constants of the a-cut single crystal (blue). The dielectric constants of [Mn3(HCOO)6] without guest molecules are also presented (black).
Fig. 4. [Mn3(HCOO)6])(C2H5OH). (a) Temperature dependence of the dielectric constants of the a-cut single crystal (red). The blue line represents the εr of the a-cut single crystal of deuterated [Mn3(HCOO)6])(C2H5OD). (b) Temperature dependence of the magnetization of [Mn3(HCOO)6])(C2H5OH) at H = 5 Oe.
polarization value reaches to 1.0 μC cm−2, much higher than that of Rochelle salt (Ps = 0.25 μC cm−2), as shown in Fig. 10. It is a landmark work and firstly knocks the door of multiferroic MOFs of technological important open because many transition metal ions MOF have displayed good dielectric hysteresis loops. [6b]
Results and discussion In the vicinity of the phase transition point, the phase transition occurrences are accompanied with the physical property anomaly. According to the Curie–Weiss law, the temperature dependent
Fig. 5. [La2Cu3{NH(CH2COO)2}6](H2O)n, (n ≈ 9) (a) Crystal structure at room temperature. The red balls represent guest water molecules resided in the channel. (b) Temperature dependence of the dielectric constants of the c-cut single crystal (red). The blue line represents the εr of the a-cut single crystal of deuterated [La2Cu3{NH(CH2COO)2}6](D2O)n. The horizontal lines indicate the corresponding εr of the guest free crystals.
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Fig. 6. [(CH3)2NH2][Zn(HOOC)3]. (a) Crystal structure at room temperature. (b) Temperature dependence of the dielectric constants of the single-crystal sample, with a hysteresis of about 10 K.
Fig. 7. [(CH3)2NH2][Mn(HOOC)3]. (a) Temperature dependence of the dielectric constants of the single-crystal sample at 1 kHz, using an amplitude of 1 V. The measurements were done with no magnetic field and with that of 5 T. A clear hysteresis of about 10 K was found. (b) Temperature dependence of heat capacity.
dielectric constant obeys εc-axis = ε∞ + C / (T − Tc), thus there will be an abrupt permittivity near the phase transition temperature. Since the size of the single-crystal sample is usually not big enough to perform the anisotropic dielectric constant, its powder dielectric permittivity is a convenient and fast method to manifest a phase transition. In preparation of the electrode, the powder sample is pressed as a pellet like the KBr pellet in the IR measurement. The electric domain covered under the electric conductive adhesive undergoes different mechanic–electric coupling effects, resulting to a wider dielectric anomaly peak compared to that of the single-crystal sample. Nevertheless, it's sufficient to determine the appearance of the phase transition with
such broad peak measured under a high frequency (usually 1 MHz) [7]. The structure of [NH4][Zn(HCOO)3] belongs to the ABO3 perovskite-type family. It features a three-dimensional chiral anionic [Zn 9 6 (HCOO)− 3 ] framework having a rare (4 ·6 ) topology. It can be considered to be built by interpenetration of three sets of twodimensional cubic nets resulting to hexagonal channels with NH+ 4 cations located in them. The temperature dependences of dielectric constants of single-crystal and powdered [NH4][Zn(HCOO)3] are shown in Figs. 10 and 11. At 191 K, there is a measurable dielectric anomaly with a peak value change of about two orders of magnitude.
Fig. 8. (HIm)2[KFe(CN)6]. (a) Crystal structure at room temperature. (b) Anisotropic dielectric constants measured at 1 MHz. (c) Temperature dependence of the molar heat capacity.
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Table 1 Selected crystallographic data for [NH4][Zn(HCOO)3] at 290 and 110 K. Formula fw T, K Crystal system Space group a, Å b, Å c, Å α, ° β, ° γ, °
C3H7NO6Zn 218.47 290 hexagonal P6322 7.3084(2) 7.3084(2) 8.1705(3) 90 90 120
110 hexagonal P63 12.5919(3) 12.5919(3) 8.2015(2) 90 90 120
Fig. 11. Temperature dependence of the dielectric constants of powdered (or polycrystalline) [NH4][Zn(HCOO)3].
Such a dramatic increase of dielectric constant implies a promising ferroelectric phase transition and also shows that the disordered cation ammonium becomes the more ordered one indicating the occurrence of symmetry breaking from high symmetry (more disordered status) to low symmetry. This result is then supported by the DSC and specific heat measurements, which both display thermal anomalies at phase transition temperature point. The fitted Curie–Weiss constant C of 5.39 × 103 K is comparable to that of NaNO2 (C = 5.0 × 103 K), which suggests a typical order–disorder type ferroelectric phase transition. According to the entropy change ΔS = RlnN, it gives N N 1 (N = 1.3) to further confirm that there happens the order–disorder phase transition. The structure determination resolved under different temperatures also shows that, as cooling down, the symmetries change from
the high-symmetry space group P6322, point group D6 with 12 symmetry elements (E, 2C6, 2C3, C2, 3C2′, 3C2′′) under a high temperature to the low-symmetry space group P63, point group C6 with 6 symmetry elements (E, 2C6, 2C3, C2) under a low temperature. According to the Landau phase transition theory, it's obvious that symmetry breaking transition has happened and the symmetry elements are reduced by half, which is associated with a typical second-order transition. Furthermore, it belongs to uniaxial ferroelectric phase transition along the polar 6 axis. The 18 cases of uniaxial ferroelectric transition are depicted in Scheme 1. (Top, Aizu notations).
Fig. 9. The structure of [NH4][Zn(HCOO)3] at different temperatures. (a) 290 K, the NH4 group is disordered to be a polyhedron. (b) 110 K, the NH4 is ordered to be a typical tetrahedron.
Fig. 10. (a) Temperature dependence of the dielectric constants and (b) the dielectric hysteresis loop of [NH4][Zn(HCOO)3].
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Scheme 1. 18 uniaxial ferroelectric phase transitions (top, Aizu expressions).
The space group change from P6322 to P63 during the phase transition process is depicted in Fig. 12. The twofold axis and twofold screw axis along the ab plane in P6322 disappear, and the sixfold axis, threefold axis, and twofold screw axis along the c-axis remained unchanged leading to the final low temperature space group of P63. It's noted that, the number of the symmetry operations in P6322 decreases from 12 to 6 in P63 by half, in perfect agreement with the symmetry breaking analysis from the 32 point group in a macroscopic view-point. The detailed symmetry operation changes are given below (as shown in Scheme 2.), suggesting that the symmetry operation number decrease in a microscopic view-point is exactly with that of symmetry breaking. According to the Curie symmetry principle, the space group with a broken symmetry of a low temperature phase is a subgroup of the high symmetry of a high temperature phase (primary phase). For example, in this case, P63 is a subgroup of P6322 (the subgroups of P6322 contain four space groups of P6311, P321, P312, and C2221).
Therefore, the qualitatively derived Gibbs free energy expression of this phase transition based on the Landau theory is 1 2 2 2 A Px + Py + Pz + BP x P y P z 2 1 4 1 2 2 4 4 2 2 2 2 C Px + Py + Pz + D Px Py + Px Pz + Py Pz 4 2 1 3 1 6 3 3 6 6 E Px P y P z + Py P x P z + Pz P x P y + F Px + Py + Pz 3 6 1 4 2 4 2 4 2 4 2 4 2 4 2 H Px Py + Px Pz + Py Px + Py Pz + Pz Px + Pz Py 4 1 2 2 2 KP P P + ⋯ 2 x y z
G = G0 + + + + +
ð1Þ
Here, Px, Py, and Pz are the polarization vectors P along three crystallographic axis directions. From the Aizu notation of 622F6, we
Fig. 12. The transformation of the space group of [NH4][Zn(HCOO)3] from the ferroelectric phase (high temperature phase) to the paraelectric phase (low temperature phase).
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Scheme 2. The changes of symmetry operations from P6322 to P63.
get that the polar axis is along the z axis, then Px = Py = 0. Hence, the above free energy expression can be reduced to G = G0 +
1 2 1 4 1 6 AP + CPz + FPz + ⋯ 2 z 4 6
ð2Þ
where, A is linear relative with the temperature factor T, giving A = αo (T − Tc). Tc is the phase transition temperature. If we assume that the sign of the coefficient is positive, we can make diagrams of the Gibbs free energy G evolving with the varying of polarization Pz. (Fig. 10). Noting that electric displacement: D = εoE + P. As seen in Fig. 13, if T b Tc, there are two G maxima corresponding to two equal and mutually inversed spontaneous polarizations, which means that the system is in a ferroelectric state. If T N Tc, G has only a minimum at Pz = 0, which means that the system is in a paraelectric state. The paraelectric–ferroelectric phase transition happens at T = Tc. We know that the necessary condition for the occurrence of the dielectric hysteresis curve is that the E (Pz) curve simultaneously possesses a maximum and a minimum, and then it should meet Eq. (3). ∂E 2 4 = α0 T−T c + 3CPz + 6FPz = 0 ∂P z
ð3Þ
It's noted that, for second-order ferroelectric phase transition, the sign coefficients of αo, C, and F are all positive. Thus, the above expression is only established when T b Tc. The Pz vs. E curve can be obtained from the relationship between potential E and Pz, as seen in Eq. (4). E=
∂G1 3 5 = α0 T−T c P z + CPz + FPz ∂P z
ð4Þ
For this expression, there are there solutions depending upon the signs of (T − Tc), which is depicted in Fig. 14. At T N Tc or T = Tc, the
Fig. 14. The Pz(E) diagrams of the second-order ferroelectric phase transition at T b Tc (a), T = Tc (b), and T N Tc (c), while the pathway along BCFB′C′F′B forms a dielectric hysteresis loop.
Pz(E) should be a single-valued function, although the corresponding curves are not straight lines. Nevertheless, when T b Tc, Pz(E) is a multivalued function. The slope of the FOF′ curve is negative, indicating an instable state. The actual Pz–E relationship should be showed as linear FB′ and linear F′B. Therefore, when the potential changes in a cycle, the Pz(E) curve forms a loop, that's the dielectric hysteresis curve of ferroelectrics. On the other hand, noting that ∂G / ∂Pz = Ez, ∂Ez / ∂Pz = ε−1 c , the Eq. (4) can be written as ε−1 c = a(T − Tc) after differentiating Ez with respect to Pz ,which is the well-known Curie–Weiss law, ignoring the influence of biasing the electric field part (+ 3CPz2 + 5FPz4 + ··· ). Another strategy to distinguish the first-order phase transition with the second-order phase transition is from the remanent polarization vs. the temperature plot. As seen in Fig. 15, in approaching to the phase transition temperature Tc (=192 K), the remanent polarization Pr evolves continuously as a function of the temperature, rather than by an abrupt way, which gives that this phase transition is apt to be a second-order ferroelectric phase transition (with Pr as the order parameter). The curve of the pyroelectric coefficient as a function of the temperature also suggests the second-order phase transition. Furthermore, we can obtain the relationship between pyroelectric coefficient and Curie constant. It is assumed that in dielectrics the elastic Gibbs free energy G1 is the characteristic function, since stress and electric field are both one dimensional, we could write: dG1 = −SdT + xdX + EdD:
ð5Þ
Fig. 13. Gibbs free energy as a function of polarization Pz (order parameter) for the second-order phase transition. T b Tc is for a stable ferroelectric phase, and T N Tc is for a stable paraelectric phase.
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Fig. 16. Temperature dependence of the molecular polarizability of [NH4][Zn(HCOO)3], with a peak at about 191 K, which is agreed with the dielectric constant result. Fig. 15. Remanent polarization and pyroelectric coefficient as a function of temperature of [NH4][Zn(HCOO)3], indicating a probably second-order phase transition.
Differentiate both sides of Eq. (5) with respect to D: ∂G1 ∂2 G1 1 = : = E; ε ∂D ∂D2
ð6Þ
Around the phase transition temperature, G1 is given in even powers of D, differentiate it with respect to D, we can get ∂G1 3 5 = αD + βD + γD : ∂D
ð7Þ
It could also be written as E = α0 ðT−T0 ÞD + φðDÞ:
ð8Þ
Here φ(D) is the higher-order terms of D, α0 = 1/ (ε0C), C is the Curie constant. From this equation, it comes to ∂E = α0 D: ∂T
ð9Þ
Around the Curie point, taking into account that if E = 0, D = Ps, we then have 0 = α0 ðT−T0 ÞPs + φðPs Þ
ð10Þ
The above provides the relationship among pyroelectric coefficient, Curie constant, spontaneous polarization and permittivity. From Eq. (15), around the Curie point, the Curie constant can be obtained from the measurement of the pyroelectric coefficient and vice versa (also see Fig. 15). The examples in reference [8] show that the calculated values are consistent with the results from experiments. Although the Landau phenomenological theory has been very useful in describing the essence of ferroelectricity through the correlation of the free energy of a ferroelectric crystal G, as a function of polarization P, an atomic model theory is needed to link the macroscopic parameters with the microscopic structures. Slater's local field theory provides the connection by computing the exact local Lorentz field. Meanwhile, the Clausius–Mosotti formula bridges the dielectric constant with the molecular polarizability that is the macroscopic electric properties with the microscopic molecule dipole moments [9]. Fig. 16 gives the temperature dependence of molecular polarizability (α) of [NH4][Zn(HCOO)3], deduced from the relationship between dielectric permittivity and molecular polarizability, as shown in Eq. (16). Thus, the strategy will shed light on the probability of orient designs of ferroelectric materials with particular applications associated with their molecular structure. α P ε0 ν ε=1+ =1+ ε0 E 1− 1−α 3ε ν
ð16Þ
0
where εo and ν represent dielectric constant and molecular volume, respectively.
or ∂G1 ∂D
j
= α0 ðT−T0 ÞPs + φðPs Þ = 0
D = PS
ð11Þ
and d ∂G1 dT ∂D
j
= D = PS
∂2 G1 ∂D2
j
dD ∂2 G1 + ∂T∂D D = PS dT
j
= 0: D = PS
ð12Þ
From Eqs. (6) and (9), one finds that ∂2 G1 ∂T∂D
j
= D = PS
∂E ∂T
j
D = PS
= α0 PS :
ð13Þ
Consequently, Eq. (11) can be expressed as p + α0 PS = 0; ε
ð14Þ
where p = dD / dT is the pyroelectric coefficient, thus p P = s: εr C
ð15Þ
Conclusions As expected, through changing ABO3 perovskite-type structure types, such as replacing Zn with the other transition metal atoms, they might not only display detectable good dielectric hysteresis loop, but also additional magnetic ordering, which will expand the applications of MOFs as the promising multiferroic materials. Although the remanent polarization is small compared with that of typical BaTiO3, it might be improved by varying the components of ABO3 perovskite-type analogues. For example, substitution of the O group with fluorine-contained organic ligand will enhance the possibility of polarization and raise the phase transition temperature leading to a ferroelectric material usable within the whole temperature scope below its melting point. Note that its precondition is to use chiral ligand with a low symmetry. Thereafter they can be kept in a ferroelectric state before or after the phase transition, or the phase transition temperature is higher than the ambient temperature, or the symmetry at most happens 2F1 Aizu ferroelectric symmetry breaking. Furthermore, guest molecules with free radicals or magnetic–electric coupling abilities may increase the phase transition temperature to break the current ultra-low temperature magnetic orientation
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phenomena to make ferroelectric materials to be of technological application. It's still necessary to further use macroscopic thermodynamics, that is, the Landau phase transition theory to explain the qualitative relationship between structures and properties, use the micro-softmode theory and first principles to fit the phase transition temperature. Meanwhile, deuterated effect and dielectric relaxation are also two important approaches to understand the phase transition behavior. In addition, it should also be concerned about the research of coexistence of magnetic domain and ferroelectric domain to make the multiferroic MOF a usable device.
[3]
[4] [5] [6] [7]
Prospects Finally, it's noted that the ferroelectric phenomenon has been involved in interdisciplinary fields of chemistry, physics, electronics, materials, crystallography, and mechanics. Compared to traditional limited pure inorganic ferroelectrics, MOF ferroelectrics might be numerous and more flexible, and can be tailored and controlled according to people's desire to become real multiferroic materials of technique importance. Modern phase transition measurements and evaluation strategies are the premises of the development of MOF functional materials. In the near future, it's to believe that the aim to explore more MOFs with dramatically ferroelectric and multiferroic properties could be achieved. At the same time, the doping ferroelectric MOF or molecule-based materials into organic or inorganic polymeric materials such as F (atom)-substituted polymer and cement will be practical applications. Acknowledgement This work was financially supported by the National Natural Science Foundation of China (No: 90922005 and No: 20931002) and the 973 project (Grant 2009CB623200) as well as JiangSu NSF (BK2008029). References [1] K. Okada, H. Sugie, J. Phys. Soc. Jpn. 25 (1968) 1128. [2] (a) H.B. Cui, K. Takahashi, Y. Okano, Z.M. Wang, H. Kobayshi, A. Kobayashi, Angew. Chem. Int. Ed. 44 (2005) 6508;
[8] [9]
(b) H.B. Cui, Z.M. Wang, K. Takahashi, Y. Okano, H. Kobayshi, A. Kobayashi, J. Am. Chem. Soc. 128 (2006) 15074; (c) H.B. Cui, B. Zhou, L.S. Long, Y. Okano, H. Kobayashi, A. Kobayashi, Angew. Chem. Int. Ed. 47 (2008) 3376. (a) P. Jain, N.S. Dalal, B.H. Toby, H.W. Kroto, A.K. Cheetham, J. Am. Chem. Soc. 130 (2008) 10450; (b) P. Jain, V. Ramachandran, R.J. Clark, H.D. Zhou, B.H. Toby, N.S. Dalal, H.W. Kroto, A.K. Cheetham, J. Am. Chem. Soc. 131 (2009) 13625. M. Sánchez-Andújar, S. Presedo, S. Yáñez-Vilar, S. Castro-García, J. Shamir, M.A. Señarís-Rodríguez, Inorg. Chem. 49 (2010) 1510. W. Zhan, Y. Cai, R.G. Xiong, H. Yoshikawa, K. Awaga, Angew, Chem. Int. Ed. 49 (2010) 6608. (a) G.C. Xu, X.M. Ma, L. Zhang, Z.M. Wang, S. Gao, J. Am. Chem. Soc. 132 (2010) 9588; (b) G. Rogez, N. Viart, M. Drillon, Angew. Chem. Int. Ed. 49 (2010) 1921. (a) W. Zhang, L.Z. Chen, R.G. Xiong, T. Nakamura, S.P.D. Huang, J. Am. Chem. Soc. 131 (2009) 12544; (b) H.Y. Ye, D.W. Fu, Y. Zhang, W. Zhang, R.G. Xiong, S.P.D. Huang, J. Am. Chem. Soc. 131 (2009) 42; (c) H.Y. Ye, L.Z. Chen, R.G. Xiong, Acta Crystllogr. Sec. B-Struc. Sci. 66 (2010) 387; (d) W. Zhang, H.Y. Ye, H.L. Cai, J.Z. Ge, R.G. Xiong, S.P.D. Huang, J. Am. Chem. Soc. 132 (2010) 7300; (e) H.Y. Ye, H.L. Cai, J.Z. Ge, R.G. Xiong, J. Appl. Cryst. 43 (2010) 1031. S.T. Liu, J.D. Zook, Ferroelectrics 7 (1974) 171. (a) J.C. Slater, Phys. Rev. 78 (1950) 748; (b) T. Lee, I.A. Aksay, Cryst. Growth & Design 1 (2001) 401.
Min Guo received her Bachelor's degree in 2003 from the Department of Chemistry in Jilin University, Changchun, and her Doctor's degree from State Key Lab of Inorganic Synthesis and Preparative Chemistry in 2008 in the same school. She is currently pursuing her Postdoctor's research in Ordered Matter Science Research Center in Southeast University, Nanjing, supervised by Prof. Rengen Xiong Her research work is focused on the synthesis and characterization of molecule-based ferroelectric materials.
Rengen Xiong received his PhD in 1994 from the University of Logistical Engineering. He has been a professor firstly at the Coordination Chemistry Institute at Nanjing University from 1998 to 2006. Up to now, he has been appointed as the head of the Ordered Matter Science Research Center in Southeast University. His research interests mainly cover the exploration of molecule-based ferroelectric materials.
Contents lists available at ScienceDirect
Inorganic Chemistry Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i n o c h e
Mini review
Ferroelectric metal organic framework (MOF) Min Guo, Hong-Ling Cai, Ren-Gen Xiong ⁎ Ordered Matter Science Research Center, Southeast University, Nanjing, Jiangning, 211189, PR China
a r t i c l e
i n f o
Article history: Received 18 July 2010 Accepted 3 September 2010 Available online 16 September 2010 Keywords: Multiferroic Ferroelectric MOF Perovskite-type
a b s t r a c t Multiferroic metal organic frameworks (MOFs) with magnetic ordering and ferroelectric ordering coexisting have recently drawn considerable interest for their amazing applications in the field of magnetoelectric multifunctional materials. Based on the Landau theory and related characterizations, this comment in detail discusses the second-order ferroelectric phase transition of ABO3 perovskite-type MOFs, including Curie– Weiss constants, symmetry breaking, spontaneous polarization, dielectric hysteresis loop, and so on. Eventually, the author gives a prospect about the development of ferroelectric MOFs. This mini-account will be of guiding significance for the design and synthesis of metal organic framework functional materials with specific multiferroic properties. © 2010 Elsevier B.V. All rights reserved.
Contents Introduction . . . . . . . . . . . . . . . . . . The first antiferroelectric MOF, Cu(HCOO)2 ∙ 4H2O Porous MOFs with movable polar guests . . . . . MOFs with ABO3 perovskite-type frameworks. . . Experimental . . . . . . . . . . . . . . . . . . Results and discussion. . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . Prospects . . . . . . . . . . . . . . . . . . . . Acknowledgement . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . .
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Introduction
The first antiferroelectric MOF, Cu(HCOO)2 ∙ 4H2O
Metal organic framework (MOF) containing guest molecules has become one of the most important candidates of developing multiferroic functional materials because of its manually coupled controllable ferroelectric properties derived from the involving guest or solvent molecule ordering, and magnetic properties derived from the transition metal ion spin ordering in the host lattices. These materials have drawn particular interest because of promising applications in sensing, data communication, spin-crossover, and signal processing. Ferroelectric phenomenon is usually associated with the occurrence of the phase transition. Dielectric anomaly combined with the DSC (differential scanning calorimetry) results is a convincing strategy to confirm the phase transition.
At the end of the 1960s, Okada and Sugie reported the first the antiferroelectric MOF (metal organic framework), Cu(HCOO)2 · 4H2O, with formic acid as building blocks and protonated organic amines as templates (Fig. 1a) [1]. Temperature dependence of dielectric constants shows a behavior of the first-order transition at about 235 K (Fig. 1b), which is shifted to a higher temperature of 245 K by deuterium substitution of the hydrogen in H2O. Typical double hysteresis loop measured at 227 K is observed suggesting an antiferroelectric transition. Nevertheless, an additional phase transition was found at 227 K from the pyroelectric current measurement (Fig. 2a) by Suzuki and Okada. As shown in the dielectric loops measured at varying temperature in Fig. 2b, the newly found phase below 227 K is considered to be an approximately ferroelectric phase. This work has aroused the chemists' research interest on the exploration of ferroelectric MOF materials.
⁎ Corresponding author. E-mail address: [email protected] (R.-G. Xiong). 1387-7003/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.inoche.2010.09.005
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Fig. 1. (a) Crystal structure of Cu(HCOO)2 · 4H2O. (b) Temperature dependence of dielectric constants of Cu(HCOO)2 · 4H2O (blue) and Cu(HCOO)2 · 4D2O (red).
Porous MOFs with movable polar guests Kobayashi has reported three porous MOFs containing movable polar guest or solvent molecules, [Mn3(HCOO)6](H2O)(CH3OH) [2a] (Fig. 3), [Mn3(HCOO)6](C2H5OH) [2b] (Fig. 4), and [La2Cu3{NH(CH2COO)2}6] (H2O)n [2c] (Fig. 5). With regard to them, the phase transitions are induced by the ordering or freezing of the polar guest molecules. The dielectric constants of the systems are closely related to different positional freedoms and molecular dipole moments of the guest molecules. In another way, there might happen ferromagnetic transitions derived from the M2+ (M=magnetic metals) spin ordering incorporated in the host lattice based on the Goodenough–Kanamori rule. [Mn3 (HCOO)6](H2O)(CH3OH) and [Mn3(HCOO)6](C2H5OH) are two structural related compounds with the same host framework and different guest molecules, and give different anomalies at about 150 K with εr =20 and 165 K with εr = 45, respectively (Figs. 3 and 4). In addition, there happens a ferromagnetic phase transition in [Mn3(HCOO)6](C2H5OH) at Tc =8.5 K (Fig. 4b). As seen in Fig. 5, the εr of [La2Cu3{NH(CH2COO)2}6] (D2O)n shows two anomalies at around 190 K and 280 K, which are approximately 10 K and 25 K higher than that of [La2Cu3{NH (CH2COO)2}6](H2O)n, suggesting a prominent deuteration effect. MOFs with ABO3 perovskite-type frameworks Cheetham and others have systematically investigated a series of metal organic frameworks with ABO3 perovskite-type topologies,
[(CH3)2NH2][M(HOOC)3] (DMMF), where A = H2NMe2, B = M (M is divalent metal elements, Zn2+, Mn2+, Fe2+, Co2+, Ni2+), and O = HCOO [3]. The common framework of ABO3 perovskite is depicted in Fig. 6a. The dielectric constant measurements indicate that antiferroelectric behavior occurs in the range of 160–185 K (DMZnF, 160 K, DMMnF, 185 K, DMFeF, 160 K, DMCoF, 165 K, DmNiF, 180 K ), which might originate from the order–disorder type electric ordering of the organic molecules. Furthermore, as seen in Fig. 7, the specific heat result of DMMnF not only points to the second-order phase transition, but also gives calculated value of ΔS suggesting that the transition is more complex than a simple 3-fold order–disorder model. In the beginning of this year, detailed observation on the mechanism of the phase transition of [(CH3)2NH2][Mn(HCOO)3] has been carried on by Senaris-Rodriguez, proposing a transition of more complex than that of a simple homogeneous 3-fold order–disorder model. [4] The dielectric anomaly combining with the DSC result approves of the happening of the phase transition. Interestingly, when Zn2+ is replaced by a transition metal ion (Mn2+, Fe2+, Co2+, and Ni2+), the corresponding compounds became magnetically ordered leading to multifunctional materials with coupled ferroelectric order and weakly magnetic order. [3b] Recently, Zhang and Xiong have also newly reported an ABO3 perovskite-type MOF inclusion, (HIm)2[KFe(CN)6] (Him = imidazolim cation) [5]. An order–disorder mechanism is found in the structural transformations owing to the motions of the cationic guests of polar Him under different temperatures. The dielectric constant curve gave exceptional two-step phase transitions at 187 K and 158 K, representing a promising switchable molecular dielectrics (Fig. 8). Study on such materials will be a great guide for understanding structural phase transitions and searching for new electric ordering materials. Unfortunately, although much attention has been focused on the dielectric investigation of ABO3 perovskite-type compounds, no one has detected one standard dielectric hysteresis loop. Wang and Gao in Peking University are the first to break through this limit, a new MOF, [NH4][Zn(HCOO)3] possessing perfect ferroelectric hysteresis loop has been successfully prepared. [6a] Experimental
Fig. 2. (a) Pyroelectric currents vs. temperature measured on the heating process of Cu (HCOO)2 · 4H2O (CFTH) and Cu(HCOO)2 · 4D2O (CFTD). Tc is the phase transition temperature. (b) Double hysteresis loop at 223 K. (c) Detail of the central portion of (b). Dielectric loops at 233 K (c), at 233 K (d), at 233 K (e), and at 233 K (f).
The single crystals of [NH4][Zn(HCOO)3] was obtained by reaction of ammonium formate, formic acid, and Zn(ClO4) · 6H2O in methanol [6a]. The selected crystallographic data and views of the structures of [NH4][Zn(HCOO)3] at 290 K and 110 K were given in Table 1 and Fig. 9. By changing the size of the guest molecule with the smaller NH+ 4 group instead of [H2NMe2]+, there induces a stronger driving force between ordered and disordered structures. As a consequence, a measurable dielectric hysteresis loop has been obtained, which is the clear evidence for a typical ferroelectric behavior. The spontaneous
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Fig. 3. [Mn3(HCOO)6](H2O)(CH3OH). (a) Crystal structure at room temperature. The MnO6 is represented as a purple octahedron, and the purple HCOO ligand is represented as a light blue triangle. (b) Temperature dependence of the dielectric constants of the a-cut single crystal (blue). The dielectric constants of [Mn3(HCOO)6] without guest molecules are also presented (black).
Fig. 4. [Mn3(HCOO)6])(C2H5OH). (a) Temperature dependence of the dielectric constants of the a-cut single crystal (red). The blue line represents the εr of the a-cut single crystal of deuterated [Mn3(HCOO)6])(C2H5OD). (b) Temperature dependence of the magnetization of [Mn3(HCOO)6])(C2H5OH) at H = 5 Oe.
polarization value reaches to 1.0 μC cm−2, much higher than that of Rochelle salt (Ps = 0.25 μC cm−2), as shown in Fig. 10. It is a landmark work and firstly knocks the door of multiferroic MOFs of technological important open because many transition metal ions MOF have displayed good dielectric hysteresis loops. [6b]
Results and discussion In the vicinity of the phase transition point, the phase transition occurrences are accompanied with the physical property anomaly. According to the Curie–Weiss law, the temperature dependent
Fig. 5. [La2Cu3{NH(CH2COO)2}6](H2O)n, (n ≈ 9) (a) Crystal structure at room temperature. The red balls represent guest water molecules resided in the channel. (b) Temperature dependence of the dielectric constants of the c-cut single crystal (red). The blue line represents the εr of the a-cut single crystal of deuterated [La2Cu3{NH(CH2COO)2}6](D2O)n. The horizontal lines indicate the corresponding εr of the guest free crystals.
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Fig. 6. [(CH3)2NH2][Zn(HOOC)3]. (a) Crystal structure at room temperature. (b) Temperature dependence of the dielectric constants of the single-crystal sample, with a hysteresis of about 10 K.
Fig. 7. [(CH3)2NH2][Mn(HOOC)3]. (a) Temperature dependence of the dielectric constants of the single-crystal sample at 1 kHz, using an amplitude of 1 V. The measurements were done with no magnetic field and with that of 5 T. A clear hysteresis of about 10 K was found. (b) Temperature dependence of heat capacity.
dielectric constant obeys εc-axis = ε∞ + C / (T − Tc), thus there will be an abrupt permittivity near the phase transition temperature. Since the size of the single-crystal sample is usually not big enough to perform the anisotropic dielectric constant, its powder dielectric permittivity is a convenient and fast method to manifest a phase transition. In preparation of the electrode, the powder sample is pressed as a pellet like the KBr pellet in the IR measurement. The electric domain covered under the electric conductive adhesive undergoes different mechanic–electric coupling effects, resulting to a wider dielectric anomaly peak compared to that of the single-crystal sample. Nevertheless, it's sufficient to determine the appearance of the phase transition with
such broad peak measured under a high frequency (usually 1 MHz) [7]. The structure of [NH4][Zn(HCOO)3] belongs to the ABO3 perovskite-type family. It features a three-dimensional chiral anionic [Zn 9 6 (HCOO)− 3 ] framework having a rare (4 ·6 ) topology. It can be considered to be built by interpenetration of three sets of twodimensional cubic nets resulting to hexagonal channels with NH+ 4 cations located in them. The temperature dependences of dielectric constants of single-crystal and powdered [NH4][Zn(HCOO)3] are shown in Figs. 10 and 11. At 191 K, there is a measurable dielectric anomaly with a peak value change of about two orders of magnitude.
Fig. 8. (HIm)2[KFe(CN)6]. (a) Crystal structure at room temperature. (b) Anisotropic dielectric constants measured at 1 MHz. (c) Temperature dependence of the molar heat capacity.
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Table 1 Selected crystallographic data for [NH4][Zn(HCOO)3] at 290 and 110 K. Formula fw T, K Crystal system Space group a, Å b, Å c, Å α, ° β, ° γ, °
C3H7NO6Zn 218.47 290 hexagonal P6322 7.3084(2) 7.3084(2) 8.1705(3) 90 90 120
110 hexagonal P63 12.5919(3) 12.5919(3) 8.2015(2) 90 90 120
Fig. 11. Temperature dependence of the dielectric constants of powdered (or polycrystalline) [NH4][Zn(HCOO)3].
Such a dramatic increase of dielectric constant implies a promising ferroelectric phase transition and also shows that the disordered cation ammonium becomes the more ordered one indicating the occurrence of symmetry breaking from high symmetry (more disordered status) to low symmetry. This result is then supported by the DSC and specific heat measurements, which both display thermal anomalies at phase transition temperature point. The fitted Curie–Weiss constant C of 5.39 × 103 K is comparable to that of NaNO2 (C = 5.0 × 103 K), which suggests a typical order–disorder type ferroelectric phase transition. According to the entropy change ΔS = RlnN, it gives N N 1 (N = 1.3) to further confirm that there happens the order–disorder phase transition. The structure determination resolved under different temperatures also shows that, as cooling down, the symmetries change from
the high-symmetry space group P6322, point group D6 with 12 symmetry elements (E, 2C6, 2C3, C2, 3C2′, 3C2′′) under a high temperature to the low-symmetry space group P63, point group C6 with 6 symmetry elements (E, 2C6, 2C3, C2) under a low temperature. According to the Landau phase transition theory, it's obvious that symmetry breaking transition has happened and the symmetry elements are reduced by half, which is associated with a typical second-order transition. Furthermore, it belongs to uniaxial ferroelectric phase transition along the polar 6 axis. The 18 cases of uniaxial ferroelectric transition are depicted in Scheme 1. (Top, Aizu notations).
Fig. 9. The structure of [NH4][Zn(HCOO)3] at different temperatures. (a) 290 K, the NH4 group is disordered to be a polyhedron. (b) 110 K, the NH4 is ordered to be a typical tetrahedron.
Fig. 10. (a) Temperature dependence of the dielectric constants and (b) the dielectric hysteresis loop of [NH4][Zn(HCOO)3].
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Scheme 1. 18 uniaxial ferroelectric phase transitions (top, Aizu expressions).
The space group change from P6322 to P63 during the phase transition process is depicted in Fig. 12. The twofold axis and twofold screw axis along the ab plane in P6322 disappear, and the sixfold axis, threefold axis, and twofold screw axis along the c-axis remained unchanged leading to the final low temperature space group of P63. It's noted that, the number of the symmetry operations in P6322 decreases from 12 to 6 in P63 by half, in perfect agreement with the symmetry breaking analysis from the 32 point group in a macroscopic view-point. The detailed symmetry operation changes are given below (as shown in Scheme 2.), suggesting that the symmetry operation number decrease in a microscopic view-point is exactly with that of symmetry breaking. According to the Curie symmetry principle, the space group with a broken symmetry of a low temperature phase is a subgroup of the high symmetry of a high temperature phase (primary phase). For example, in this case, P63 is a subgroup of P6322 (the subgroups of P6322 contain four space groups of P6311, P321, P312, and C2221).
Therefore, the qualitatively derived Gibbs free energy expression of this phase transition based on the Landau theory is 1 2 2 2 A Px + Py + Pz + BP x P y P z 2 1 4 1 2 2 4 4 2 2 2 2 C Px + Py + Pz + D Px Py + Px Pz + Py Pz 4 2 1 3 1 6 3 3 6 6 E Px P y P z + Py P x P z + Pz P x P y + F Px + Py + Pz 3 6 1 4 2 4 2 4 2 4 2 4 2 4 2 H Px Py + Px Pz + Py Px + Py Pz + Pz Px + Pz Py 4 1 2 2 2 KP P P + ⋯ 2 x y z
G = G0 + + + + +
ð1Þ
Here, Px, Py, and Pz are the polarization vectors P along three crystallographic axis directions. From the Aizu notation of 622F6, we
Fig. 12. The transformation of the space group of [NH4][Zn(HCOO)3] from the ferroelectric phase (high temperature phase) to the paraelectric phase (low temperature phase).
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Scheme 2. The changes of symmetry operations from P6322 to P63.
get that the polar axis is along the z axis, then Px = Py = 0. Hence, the above free energy expression can be reduced to G = G0 +
1 2 1 4 1 6 AP + CPz + FPz + ⋯ 2 z 4 6
ð2Þ
where, A is linear relative with the temperature factor T, giving A = αo (T − Tc). Tc is the phase transition temperature. If we assume that the sign of the coefficient is positive, we can make diagrams of the Gibbs free energy G evolving with the varying of polarization Pz. (Fig. 10). Noting that electric displacement: D = εoE + P. As seen in Fig. 13, if T b Tc, there are two G maxima corresponding to two equal and mutually inversed spontaneous polarizations, which means that the system is in a ferroelectric state. If T N Tc, G has only a minimum at Pz = 0, which means that the system is in a paraelectric state. The paraelectric–ferroelectric phase transition happens at T = Tc. We know that the necessary condition for the occurrence of the dielectric hysteresis curve is that the E (Pz) curve simultaneously possesses a maximum and a minimum, and then it should meet Eq. (3). ∂E 2 4 = α0 T−T c + 3CPz + 6FPz = 0 ∂P z
ð3Þ
It's noted that, for second-order ferroelectric phase transition, the sign coefficients of αo, C, and F are all positive. Thus, the above expression is only established when T b Tc. The Pz vs. E curve can be obtained from the relationship between potential E and Pz, as seen in Eq. (4). E=
∂G1 3 5 = α0 T−T c P z + CPz + FPz ∂P z
ð4Þ
For this expression, there are there solutions depending upon the signs of (T − Tc), which is depicted in Fig. 14. At T N Tc or T = Tc, the
Fig. 14. The Pz(E) diagrams of the second-order ferroelectric phase transition at T b Tc (a), T = Tc (b), and T N Tc (c), while the pathway along BCFB′C′F′B forms a dielectric hysteresis loop.
Pz(E) should be a single-valued function, although the corresponding curves are not straight lines. Nevertheless, when T b Tc, Pz(E) is a multivalued function. The slope of the FOF′ curve is negative, indicating an instable state. The actual Pz–E relationship should be showed as linear FB′ and linear F′B. Therefore, when the potential changes in a cycle, the Pz(E) curve forms a loop, that's the dielectric hysteresis curve of ferroelectrics. On the other hand, noting that ∂G / ∂Pz = Ez, ∂Ez / ∂Pz = ε−1 c , the Eq. (4) can be written as ε−1 c = a(T − Tc) after differentiating Ez with respect to Pz ,which is the well-known Curie–Weiss law, ignoring the influence of biasing the electric field part (+ 3CPz2 + 5FPz4 + ··· ). Another strategy to distinguish the first-order phase transition with the second-order phase transition is from the remanent polarization vs. the temperature plot. As seen in Fig. 15, in approaching to the phase transition temperature Tc (=192 K), the remanent polarization Pr evolves continuously as a function of the temperature, rather than by an abrupt way, which gives that this phase transition is apt to be a second-order ferroelectric phase transition (with Pr as the order parameter). The curve of the pyroelectric coefficient as a function of the temperature also suggests the second-order phase transition. Furthermore, we can obtain the relationship between pyroelectric coefficient and Curie constant. It is assumed that in dielectrics the elastic Gibbs free energy G1 is the characteristic function, since stress and electric field are both one dimensional, we could write: dG1 = −SdT + xdX + EdD:
ð5Þ
Fig. 13. Gibbs free energy as a function of polarization Pz (order parameter) for the second-order phase transition. T b Tc is for a stable ferroelectric phase, and T N Tc is for a stable paraelectric phase.
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Fig. 16. Temperature dependence of the molecular polarizability of [NH4][Zn(HCOO)3], with a peak at about 191 K, which is agreed with the dielectric constant result. Fig. 15. Remanent polarization and pyroelectric coefficient as a function of temperature of [NH4][Zn(HCOO)3], indicating a probably second-order phase transition.
Differentiate both sides of Eq. (5) with respect to D: ∂G1 ∂2 G1 1 = : = E; ε ∂D ∂D2
ð6Þ
Around the phase transition temperature, G1 is given in even powers of D, differentiate it with respect to D, we can get ∂G1 3 5 = αD + βD + γD : ∂D
ð7Þ
It could also be written as E = α0 ðT−T0 ÞD + φðDÞ:
ð8Þ
Here φ(D) is the higher-order terms of D, α0 = 1/ (ε0C), C is the Curie constant. From this equation, it comes to ∂E = α0 D: ∂T
ð9Þ
Around the Curie point, taking into account that if E = 0, D = Ps, we then have 0 = α0 ðT−T0 ÞPs + φðPs Þ
ð10Þ
The above provides the relationship among pyroelectric coefficient, Curie constant, spontaneous polarization and permittivity. From Eq. (15), around the Curie point, the Curie constant can be obtained from the measurement of the pyroelectric coefficient and vice versa (also see Fig. 15). The examples in reference [8] show that the calculated values are consistent with the results from experiments. Although the Landau phenomenological theory has been very useful in describing the essence of ferroelectricity through the correlation of the free energy of a ferroelectric crystal G, as a function of polarization P, an atomic model theory is needed to link the macroscopic parameters with the microscopic structures. Slater's local field theory provides the connection by computing the exact local Lorentz field. Meanwhile, the Clausius–Mosotti formula bridges the dielectric constant with the molecular polarizability that is the macroscopic electric properties with the microscopic molecule dipole moments [9]. Fig. 16 gives the temperature dependence of molecular polarizability (α) of [NH4][Zn(HCOO)3], deduced from the relationship between dielectric permittivity and molecular polarizability, as shown in Eq. (16). Thus, the strategy will shed light on the probability of orient designs of ferroelectric materials with particular applications associated with their molecular structure. α P ε0 ν ε=1+ =1+ ε0 E 1− 1−α 3ε ν
ð16Þ
0
where εo and ν represent dielectric constant and molecular volume, respectively.
or ∂G1 ∂D
j
= α0 ðT−T0 ÞPs + φðPs Þ = 0
D = PS
ð11Þ
and d ∂G1 dT ∂D
j
= D = PS
∂2 G1 ∂D2
j
dD ∂2 G1 + ∂T∂D D = PS dT
j
= 0: D = PS
ð12Þ
From Eqs. (6) and (9), one finds that ∂2 G1 ∂T∂D
j
= D = PS
∂E ∂T
j
D = PS
= α0 PS :
ð13Þ
Consequently, Eq. (11) can be expressed as p + α0 PS = 0; ε
ð14Þ
where p = dD / dT is the pyroelectric coefficient, thus p P = s: εr C
ð15Þ
Conclusions As expected, through changing ABO3 perovskite-type structure types, such as replacing Zn with the other transition metal atoms, they might not only display detectable good dielectric hysteresis loop, but also additional magnetic ordering, which will expand the applications of MOFs as the promising multiferroic materials. Although the remanent polarization is small compared with that of typical BaTiO3, it might be improved by varying the components of ABO3 perovskite-type analogues. For example, substitution of the O group with fluorine-contained organic ligand will enhance the possibility of polarization and raise the phase transition temperature leading to a ferroelectric material usable within the whole temperature scope below its melting point. Note that its precondition is to use chiral ligand with a low symmetry. Thereafter they can be kept in a ferroelectric state before or after the phase transition, or the phase transition temperature is higher than the ambient temperature, or the symmetry at most happens 2F1 Aizu ferroelectric symmetry breaking. Furthermore, guest molecules with free radicals or magnetic–electric coupling abilities may increase the phase transition temperature to break the current ultra-low temperature magnetic orientation
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phenomena to make ferroelectric materials to be of technological application. It's still necessary to further use macroscopic thermodynamics, that is, the Landau phase transition theory to explain the qualitative relationship between structures and properties, use the micro-softmode theory and first principles to fit the phase transition temperature. Meanwhile, deuterated effect and dielectric relaxation are also two important approaches to understand the phase transition behavior. In addition, it should also be concerned about the research of coexistence of magnetic domain and ferroelectric domain to make the multiferroic MOF a usable device.
[3]
[4] [5] [6] [7]
Prospects Finally, it's noted that the ferroelectric phenomenon has been involved in interdisciplinary fields of chemistry, physics, electronics, materials, crystallography, and mechanics. Compared to traditional limited pure inorganic ferroelectrics, MOF ferroelectrics might be numerous and more flexible, and can be tailored and controlled according to people's desire to become real multiferroic materials of technique importance. Modern phase transition measurements and evaluation strategies are the premises of the development of MOF functional materials. In the near future, it's to believe that the aim to explore more MOFs with dramatically ferroelectric and multiferroic properties could be achieved. At the same time, the doping ferroelectric MOF or molecule-based materials into organic or inorganic polymeric materials such as F (atom)-substituted polymer and cement will be practical applications. Acknowledgement This work was financially supported by the National Natural Science Foundation of China (No: 90922005 and No: 20931002) and the 973 project (Grant 2009CB623200) as well as JiangSu NSF (BK2008029). References [1] K. Okada, H. Sugie, J. Phys. Soc. Jpn. 25 (1968) 1128. [2] (a) H.B. Cui, K. Takahashi, Y. Okano, Z.M. Wang, H. Kobayshi, A. Kobayashi, Angew. Chem. Int. Ed. 44 (2005) 6508;
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(b) H.B. Cui, Z.M. Wang, K. Takahashi, Y. Okano, H. Kobayshi, A. Kobayashi, J. Am. Chem. Soc. 128 (2006) 15074; (c) H.B. Cui, B. Zhou, L.S. Long, Y. Okano, H. Kobayashi, A. Kobayashi, Angew. Chem. Int. Ed. 47 (2008) 3376. (a) P. Jain, N.S. Dalal, B.H. Toby, H.W. Kroto, A.K. Cheetham, J. Am. Chem. Soc. 130 (2008) 10450; (b) P. Jain, V. Ramachandran, R.J. Clark, H.D. Zhou, B.H. Toby, N.S. Dalal, H.W. Kroto, A.K. Cheetham, J. Am. Chem. Soc. 131 (2009) 13625. M. Sánchez-Andújar, S. Presedo, S. Yáñez-Vilar, S. Castro-García, J. Shamir, M.A. Señarís-Rodríguez, Inorg. Chem. 49 (2010) 1510. W. Zhan, Y. Cai, R.G. Xiong, H. Yoshikawa, K. Awaga, Angew, Chem. Int. Ed. 49 (2010) 6608. (a) G.C. Xu, X.M. Ma, L. Zhang, Z.M. Wang, S. Gao, J. Am. Chem. Soc. 132 (2010) 9588; (b) G. Rogez, N. Viart, M. Drillon, Angew. Chem. Int. Ed. 49 (2010) 1921. (a) W. Zhang, L.Z. Chen, R.G. Xiong, T. Nakamura, S.P.D. Huang, J. Am. Chem. Soc. 131 (2009) 12544; (b) H.Y. Ye, D.W. Fu, Y. Zhang, W. Zhang, R.G. Xiong, S.P.D. Huang, J. Am. Chem. Soc. 131 (2009) 42; (c) H.Y. Ye, L.Z. Chen, R.G. Xiong, Acta Crystllogr. Sec. B-Struc. Sci. 66 (2010) 387; (d) W. Zhang, H.Y. Ye, H.L. Cai, J.Z. Ge, R.G. Xiong, S.P.D. Huang, J. Am. Chem. Soc. 132 (2010) 7300; (e) H.Y. Ye, H.L. Cai, J.Z. Ge, R.G. Xiong, J. Appl. Cryst. 43 (2010) 1031. S.T. Liu, J.D. Zook, Ferroelectrics 7 (1974) 171. (a) J.C. Slater, Phys. Rev. 78 (1950) 748; (b) T. Lee, I.A. Aksay, Cryst. Growth & Design 1 (2001) 401.
Min Guo received her Bachelor's degree in 2003 from the Department of Chemistry in Jilin University, Changchun, and her Doctor's degree from State Key Lab of Inorganic Synthesis and Preparative Chemistry in 2008 in the same school. She is currently pursuing her Postdoctor's research in Ordered Matter Science Research Center in Southeast University, Nanjing, supervised by Prof. Rengen Xiong Her research work is focused on the synthesis and characterization of molecule-based ferroelectric materials.
Rengen Xiong received his PhD in 1994 from the University of Logistical Engineering. He has been a professor firstly at the Coordination Chemistry Institute at Nanjing University from 1998 to 2006. Up to now, he has been appointed as the head of the Ordered Matter Science Research Center in Southeast University. His research interests mainly cover the exploration of molecule-based ferroelectric materials.