Communication pubs.acs.org/JACS
Cite This: J. Am. Chem. Soc. 2017, 139, 15648-15651
Large Negative Linear Compressibility in InH(BDC)2 from Framework Hinging Qingxin Zeng, Kai Wang,* and Bo Zou* State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun 130012, China S Supporting Information *
methanol monohydrate (Ka = −3.8 TPa−1),4 YFe(CN)6 (Kc = −12.7 TPa−1),14 and other materials listed in Table S1 (Supporting Information).6,7,15−23 Seeking materials with a large value or wide pressure range of NLC effecta coexistence of the two parameters is of course the most desired, however, such materials still remain to be discovered (if indeed they exist at all)has become the top urgent issues in NLC researches in the recent years.12,24−27 Ag3[Co(CN)6]-I and Zn[Au(CN)2]2-I are the only two materials that exhibit NLC larger than −30 TPa−1.3,27 However, the strong toxicity of CN− group and the high cost of the noble metal components heavily lower their practical application values. Hence it is of crucial importance to seek for other safer and cheaper extreme NLC materials. In this work, by performing angle-dispersive X-ray powder diffraction (ADXRD) experiments at Shanghai Synchrotron Radiation Facility (SSRF),28 we show that a β-quartz-like metal−organic framework, InH(BDC)2 (BDC = 1,4-benzenedicarboxylate), exhibits an extreme NLC effect along the c-axis (Kc = −62.4 TPa−1) in the pressure range of 0−0.53 GPa due to framework hinging. What is more, it is highly significant that InH(BDC)2 is synthesized by green solvothermal methods using economical and nontoxic components compared to Au+/Ag+, and CN−containing materials that dominated the fields of extreme NLC materials.29,30 Under ambient conditions, InH(BDC)2 crystallizes in the hexagonal structure with space group P6422. One unit-cell contains three formula units, and all the indium atoms in the crystal structure are equivalent, positioning the coordinate of (0.5, 0, 0). Each indium atom connects to four other indium atoms by linear terephthalate ligands to form a pseudotetrahedron unit, as shown in Figure 1a. As a whole, the pseudotetrahedron indium centers are linked via “arm-like” linear BDC2− anions to form 2-fold interpenetrated β-quartz nets, as shown in Figure 1b. InH(BDC)2 was chosen to be studied here because that the previous study on its abnormal mechanical response to variable temperature showed that it displayed large negative thermal expansion (NTE) along the caxis (αc = −35 MK−1) due to its highly flexible β-quartz-like frameworks.31 Although there is no thermodynamic requirement that NLC and NTE must coexist, it does seem likely that a general correspondence will be observed for noncubic framework materials,3 such as the MIL-53 family,25,32 silver(I) 2-methylimidazolate,15 Ag3[Co(CN)6],3,33,34 and KMn[Ag(CN)2]3.6,35 Hence we expected that InH(BDC)2 would
ABSTRACT: Materials with negative linear compressibility (NLC) counterintuitively expand along one specific direction coupled to the volume reduction when compressed uniformly. NLC with a large value is desired for compression and materials science. However, NLC is generally smaller than −20 TPa−1. High-pressure X-ray diffraction experiments reveal that the β-quartz-like InH(BDC)2 generates an extreme NLC (−62.4 TPa−1) by framework hinging. InH(BDC)2 is much safer and lower-cost than Au+/Ag+ and CN−-containing materials that dominated the fields of large NLC. This work reconfirms that a negative thermal expansion flexible framework could likely exhibit large NLC. Moreover, a large NLC could be anticipated to arise from β-quartz-like or related frameworks composed of rigid linear ligands and flexible framework angles.
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andated by the fundamental thermodynamic principle, the unit-cell volume of a material crystal always continuously decreases when an increasing hydrostatic pressure is applied in the absence of the phase transition.1 However, a counterintuitive expansion along one specific direction coupled to the volume reduction is not thermodynamically forbidden, known as negative linear compressibility (NLC).2−4 NLC is a remarkably anomalous and rare phenomenon because the vast majority of materials reduce their volume by contracting along all the three unit-cell axes when uniformly compressed.5−7 With the anomalous mechanical response, NLC materials have a broaden potential applications in fields, such as highly sensitive pressure sensors,2 artificial muscles used in “smart” body armor,8−10 and optical fibers with high shock resistance.3,11 The quantity of compressibility is conventionally defined as the isothermally relative change rate of dimension with pressure, Ki = −(1/i)(∂i/∂p)T, where i can be assigned as V (volume), A (area), and l (length) for volume, area and linear compressibility, respectively.2 From the definition, the linear compressibilities have a relationship with the volume compressibility: KV = Kl1 + Kl2 + Kl3, where l1, l2 and l3 are three orthogonal principal axes in the unit-cell.12 NLC occurs only when the sum of the linear compressibility of the other two axes in the orthogonal directions exceeds the volume compressibility. Hence NLC is generally smaller in value than PLC (positive linear compressibility).3 The PLC for crystalline materials typically vary in value from 5 to 50 TPa−1.13 In contrast, the majority of NLC materials exhibit a negative compressibility coefficient smaller than −20 TPa−1, such as © 2017 American Chemical Society
Received: September 27, 2017 Published: October 25, 2017 15648
DOI: 10.1021/jacs.7b10292 J. Am. Chem. Soc. 2017, 139, 15648−15651
Communication
Journal of the American Chemical Society
Figure 1. Framework structure of InH(BDC)2. (a) A pseudotetrahedron unit composed by four In-BDC-In linear linkers. (b) The c-axisoriented extended 2-fold interpenetrated β-quartz nets in InH(BDC)2 crystal. The two sets of β-quartz nets are represented by different colors. H atoms are omitted for clarity.
expand along its NTE direction (the c-axis) while reducing its volume under increasing pressure. The pressure-dependent structural variations of InH(BDC)2 were investigated in the pressure range of 0−1.06 GPa by means of in situ high-pressure ADXRD measurements. Figures S1 and S2 (SI) show the collected ADXRD data at elevated pressures. The absence of the phase transition during the compression process can be indicated by the persistence of diffraction patterns (Figure S1, Supporting Information). As the pressure increased from 0 to 0.53 GPa, the Bragg peak of (102) shifted evidently to lower angles (Figure S2a, Supporting Information), implying that the d-spacing of (102) abnormally increased upon compression. The other peaks shifted toward high-angle direction or kept nearly unshifted (the Bragg peak of (112)) as a result of d-spacing shortening or unchanging under compression. The lattice parameters were extracted from Pawley refinements of diffraction data based on the initial structure symmetry model, P6422, at ambient pressures (Figure S3, Supporting Information). As shown in Figure S4 (SI), the continuous evolution of unit-cell volume over the whole process of compression demonstrates the absence of the phase transition. The variations of the lattice parameters a (≡b) and c with pressure are plotted as Figure S2b (SI). It is evident that the c-axis expands with increasing pressure coupled to the contractions along the a and b axes at pressures below 0.53 GPa. As the c-axis expanded at pressures just below 0.53 GPa, the NLC effect was hence studied over the pressure range of 0− 0.53 GPa. Figure 2a shows the change rate of the lattice parameters a and c as a function of hydrostatic pressure. The caxis elongated about 3.7% over the pressure range of 0−0.53 GPa, implying a large NLC value. The compressibility coefficients of the three unit-cell axes calculated using PASCal program36 are Ka = Kb = 102.4 TPa−1, Kc = −62.4 TPa−1, respectively. This distinctly shows NLC along the c-axis and PLC along the ab plane, see in Figure 2c. The variation of the compressibility of the unit-cell axes with pressure is depicted as Figure 2b. As can be seen in Table S1 (SI), compared to other NLC materials, the value of NLC along the c-axis, − 62.4 TPa−1, is the second largest among all the NLC materials that have ever been found. Ag3[Co(CN)6]-I is the most extreme NLC material with a NLC value of −76 TPa−1, however, the stress-induced abnormal extreme expansion soon (just at 0.19 GPa) leads to a phase transition with a significant volume
Figure 2. (a) Change rate of the lattice parameters a and c as a function of hydrostatic pressure from 0 to 0.53 GPa. (b) Evolution of compressibility of the unit-cell axis as a function of pressure. (c) The compressibility indicatrix of InH(BDC)2. The blue (red) portion represents NLC (PLC) effect.
collapse (16.25% reduction in volume), after which the NLC value decreases to −5.3 TPa−1.3 The NLC mechanism can be rationalized by the special geometrical relationships in the β-quartz framework topology.27 At ambient conditions, owing to the special coordinates of In atoms (see details in Figure S4, Supporting Information), the lattice parameters are related to the two main parameters in βquartz topology, r and θ, with the relationships: 2c = 3r ·cos(θ /2)
(1)
a = b = 2r ·sin(θ /2)
(2)
where r is the length of In−BDC−In linker; and θ is the angle of In1a− In1−In1b, coordinates for In1, In1a and In1b are (1/ 2, 1, 0), (1/2, 1/2, 2/3) and (1/2, 3/2, 2/3), respectively, as shown in Figure 3a.
Figure 3. (a) Schematic representations of the β-quartz-like topology of InH(BDC)2 in an extended unit-cell. Only a part of In atoms are shown and other atoms are omitted for clarity. (b) Variations of In− BDC−In linker distance r and corresponding framework angle θ (In1a−In1−In1b) with increasing pressure. (c) Variations of compressibility of sin(θ/2) and cos(θ/2) with increasing pressure. 15649
DOI: 10.1021/jacs.7b10292 J. Am. Chem. Soc. 2017, 139, 15648−15651
Communication
Journal of the American Chemical Society
anticipate extreme NLC effects from similar topologies with a linear ligand that is as rigid as possible and a framework angle that is as flexible as possible to guarantee a small Kr and a large Kθ, respectively. Notably, the NLC mechanism is intrinsically the same to the previously reported NTE mechanism, in which case the flexible frameworks hinged to close the In1a−In1− In1b angle upon cooling, giving rise to NTE along the same direction to NLC, namely, the c-axis.31 However, at pressures higher than 0.53 GPa, the dominating factor that affects the behavior of the c-axis switches into r from θ because the change rate of |r| exceeds that of cos(θ/2), see in Figure S7 (SI). Consequently, the compressibility of the c-axis transforms from NLC to PLC at higher pressures. Analogous cases are quite common in the broad family of NLC materials.15,17,23,25,37 In conclusion, a cheaper and safer β-quartz-like metal− organic frameworks material, InH(BDC)2, was found to show the most extreme NLC effect along its NTE direction (the caxis). In situ high-pressure ADXRD revealed that the NLC behavior can be ascribed to a mechanism of β-quartz framework hinging. This work puts forward a much more suitable NLC candidate for applications than most other NLC materials in magnitude of NLC effect. Meanwhile, it also demonstrates that a NTE flexible framework could also likely show a NLC phenomenon. Moreover, on the basis of the β-quartz-like topology of the two strongest NLC materials InH(BDC)2 and Zn[Au(CN)2]2, the rational anticipation of abnormal mechanical response is that an extreme NLC effect can arise from βquartz-like or related frameworks (such as the wine-rack-like, honeycomb-like and scissors-like) with a linear ligand that is as rigid as possible and a framework node that is as flexible as possible to obtain a small Kr and a large Kθ, respectively, which is of crucial important for the further designing extreme NC materials.
In the absence of phase transitions, due to the special coordinate (0.5, 0, 0) that In atom positioned and the high symmetry of the hexagonal space group,31 the symmetrically equivalent In atoms in crystal are kept fixed to the unit-cell lattice during compression. Hence, the accurate positions of the In atoms could be obtained on the basis of the refined lattice parameters. The relationships at ambient conditions shown in 1 also apply to structures at high pressure because the r and θ are determined only by the pressure-independent coordinate of In atom (Figure S5, Supporting Information), meanwhile, the Raman spectra showed no unexpected deformations of linear BDC2− linker (Figure S6, Supporting Information). Hence, the values of r and θ can be directly derived from the lattice parameters using 1. The change rates of r and θ derived from lattice parameters are shown in Figure 3b. It is evident that both r and θ decrease upon compression, that is, the length of metal−ligand−metal (In−BDC−In) linker decreases and the hinge angle of linker−node−linker (In1a−In1−In1b) closes as a result of increasing pressure. From the definition of compressibility and 1, we have (details can be seen in SI) Kc = K r + K
cos(θ /2)
(3)
Ka = K r + K
sin(θ /2)
(4)
It indicates from eq 3 and 4 that the compressibility of unitcell axes can be intrinsically revealed using the compressibility of r and θ. As the change in r is negligible over the pressure range of 0−0.53 GPa (Kr is hence approximate to 0), the mechanical responses of the unit-cell axes upon elevating pressure are dominated by the behavior of θ, see in SI. Kcos(θ/2) and Ksin(θ/2) are calculated based on Ki = −(1/i)(∂i/∂p)T and plotted in Figure 3c. As pressure rises from 0 to 0.53 GPa, the closing motion of θ (
