Negative Linear Compressibility Due to Layer Sliding in a Layered

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Negative Linear Compressibility Due to Layer Sliding in a Layered MOF Qingxin Zeng, Kai Wang, Yuancun Qiao, Xiaodong Li, and Bo Zou J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b00121 • Publication Date (Web): 15 Mar 2017 Downloaded from http://pubs.acs.org on March 17, 2017

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The Journal of Physical Chemistry Letters

Negative Linear Compressibility Due to Layer Sliding in a Layered MOF Qingxin Zeng,a Kai Wang,a Yuancun Qiao,a Xiaodong Li,b and Bo Zoua,* a

State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China

b

Beijing Synchrotron Radiation Laboratory, Institute of High Energy Physics, Chinese Academy

of Sciences, Beijing 100039, China AUTHOR INFORMATION Corresponding Author * To whom correspondence should be addressed. Bo Zou, E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT Negative linear compressibility (NLC) is a rare and counterintuitive phenomenon because materials with this property would expand along one specific direction when uniformly compressed. NLC materials have a broad range of potential applications in designing pressure sensors, artificial muscles and so on. Designing and searching for systems with NLC is desired and crucial for material and compression science. Herein, with the help of high-pressure X-ray diffraction measurements and density functional theory calculations, we find that the 2D layered Co(SCN)2(pyrazine)2 exhibits NLC with a new mechanism—layer sliding. When compressed, the ab planes slide along the a axis, leading to the decrease of lattice parameter β, which results in the NLC effect along principal axis X3 (≈ -0.84a - 0.55c). The layer sliding mechanism opens exciting opportunities for seeking, designing and synthesizing new classes of materials with anomalous mechanical properties in monoclinic layered or other related systems.

TOC GRAPHICS

KEYWORDS negative linear compressibility, layer sliding, high-pressure chemistry, anomalous mechanics, density functional theory calculations


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Apart from the majority of materials that shrink isotropically under uniform stress conditions, a limited number of materials counterintuitively expand along a specific direction coupled to volume reduction on increasing hydrostatic pressure, the so-called negative linear compressibility (NLC).1-3 Among the whole innumerable kinds of known materials, NLC is rare because it could only be found in two to three dozen candidates.2-10 Despite its rarity, with its unusual and highly attractive mechanical response, NLC materials have extensive application prospects in fields, such as optical devices used in high-pressure deep-sea environments, ultrasensitive pressure detectors for sonar and aircraft altitude measurements, and artificial muscles and next-generation body armor with high shock resistance.2, 11-13 Studies on NLC materials have rapidly developed over the past decade since the largest value of NLC (-75 TPa-1) in Ag3[Co(CN)6] was discovered by Goodwin et al. (2008).3-4 In a recent review, Goodwin et al. grouped the known materials exhibiting NLC into four classes according to their mechanisms.5 (1) Ferroelastic phase transition. For example, Zn(CN)2 takes an improper ferroelastic phase transition from a cubic structure into an orthorhombic structure at 1.52 GPa. Such a symmetry-breaking phase transition results in NLC along the a axis up to approximately 5 GPa.14 Analogous situations can be found in PtS9, and TeO25. (2) Polyhedral tilting. For example, UTSA-16 shows NLC along the tetragonal c axis due to the tilting of Co4O4 units coupled with the distortions within the cobalt(II) tetrahedra.15 The mechanism is also the subject of a recent research on LnFe(CN)6, in which case, NLC arises due to the tilting and rotating of LnN6 and Fe(CN)6 polyhedrons.16 (3) Helices. For example, trigonal polymorphs of Se and Te. The two simple elemental inorganic are consist of an array of trigonal helices packed on a triangular lattice. They expand along the c axis via a combined effect of inter-helix bonds shrinking and intra-helix bond angle increasing under high pressure.17 (4) Framework hinging of


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molecular topologies. Materials with this mechanism expand along one lattice direction coupled to a densification in the vertical direction,5 such as wine-rack,6-8, 18-23 honeycomb,1, 3, 24-25 scissorlike,26-28 and butterfly wing,29 which are essentially related to each other in geometry. With the combination restrictions of rareness of NLC material types and undeveloped technology in materials engineering, discussing the extensive applications of NLC materials is premature. However, the discovery of more NLC materials means an earlier realization of applications of this kind of materials to some extent. Exploring materials with NLC is becoming increasingly important and attractive. However, it still need to make more efforts on discovering new materials with NLC or probing the properties more deeply. New NLC mechanisms are required to seek more interesting NLC materials. In this work, we put forward a new NLC mechanism, layer sliding, in a layered metal-organic framework (MOF), Co(SCN)2(pyrazine)2 (Co(SCN)(pyz)), by performing high-pressure angle-dispersive X-ray powder diffraction (ADXRD) experiments and density functional theory (DFT) calculations. This work is the first report for such an unusual NLC mechanism. Co(SCN)(pyz) was first synthesized by Jacobson et al. and crystallized in the monoclinic structure, space group C2/m,30 with 2D layered networks at ambient condition, as shown in Figure 1a. In one unit cell, there are two formula units and all the Co atoms are equivalent. For each layer of the ab planes, each Co atom acts as a wine-rack knot that coordinates to four nitrogen atoms that respectively belong to four dependent pyrazine ligands, as shown in Figure 1b. Out of the wine-rack plane, two arm-like SCN ligands connect to the same Co atom through N−Co coordination bonds. Without bonds connecting to neighboring layers, all layers are independent of each other, which suggests a relatively large interlayer compressibility.


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Figure 1. (a) Crystal structure of Co(SCN)(pyz), viewed along b axis at ambient pressure. (b) Monolayer structure of Co(SCN)(pyz) viewed perpendicular to the ab plane. The hydrogen atoms are omitted for clarity. In situ high-pressure ADXRD study was performed to monitor the pressure-induced structural changes in the crystals of Co(SCN)(pyz) from ambient pressure to 1.95 GPa. The collected ADXRD data at different pressures are shown in Figure S1 (Supporting Information (SI)). Along with the pressure increased to 1.0 GPa, all diffraction peaks shifted to higher angles except for the particular slight shift toward lower-angle of the (200) peak, which indicates an increase of length in the d(200) spacing, as shown in Figure 2a. However, the Bragg peak of (200) was too weak and vanished into the diffraction background at pressures above 1.0 GPa (Figure S1, SI). The diffraction patterns remained unchanged during the entire compression process, implying the absence of phase transition. Hence all diffraction data could be identified to a cell model that is isostructural to the ambient phase structure, namely, the C2/m space group. The lattice parameters were extracted from the powder diffraction data using Pawley refinement. The refinement of selected ADXRD patterns collected at elevated pressures is shown in Figure S2 (SI). The variations of unit cell volume and lattice parameters with pressure are shown in Figure 2b. The continuous variations of a, b, c, β, and V indicate the stability of the unit cell structure at pressures below 1.95 GPa.


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Figure 2. (a) High-pressure diffraction patterns of Bragg peak (200) up to 1.0 GPa. The original diffraction data are plotted as scatter dots and fitted into solid lines using Gaussian functions. (b) Experimental evolution of changes of lattice parameters a, b, c, β, and unit cell volume as a function of hydrostatic pressure. We used the online program PASCal to rebuild three orthogonal principal axes of the strain tensor based on the original unit cell axes in Co(SCN)(pyz) because it crystallizes in the monoclinic crystal system with three non-orthogonal unit cell axes.31 The three principal axes were constructed as: X1 was parallel to c; X2 was parallel to the rotation axis b; X3 = X1 × X2, was parallel to -0.84a - 0.55c. The compressibility coefficients of the three rebuilt principal axes were calculated by PASCal based on the relationship (Kl = (∂(lnl)/∂p)T) to investigate the NLC property behind the low-angle shifting of (200) peak. Over the pressure range of 0 ~ 1.0 GPa, the compressibility coefficients along the three principal axes X1 (= c), X2 (≡ b), and X3 (≈ − 0.84a − 0.55c) were 49.74, 8.83 and -1.99 TPa-1, respectively. This distinctly showed a NLC behavior along the X3 direction. The NLC value of Co(SCN)(pyz) is comparable with the values of [NH4][Zn(HCOO)3] and methanol monohydrate.24–25 The volumetric compressibility coefficient was 68.43 TPa-1. The ratios of the compressibilities of the principal axes to the volume


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compressibilities are K1/KV = 0.73, K2/KV = 0.13, and K3/KV = −0.03, respectively. Co(SCN)(pyz) is notably highly anisotropic because the expected ratio of Ki/KV for isotropic materials is 0.33.24 Figure 3 shows the change rate of length and the evolution of compressibility coefficients of the three principal axes with increasing pressure. As shown in Figure 3a, X3 lengthened slightly by approximately 0.3% upon compression to 1.0 GPa while X1 drastically shrunk by approximately 6.0%. The different length variations of X1 and X3 were consistent with the sharp contrast in the values of K1 (compressibility of X1) and K3 (a negative one,) over the pressure range, as shown in Figure 3b.

Figure 3. (a) Pressure dependent variations of relative lengths of the principal axes. Experimental data are shown as symbols and fitted to solid lines using an empirical fit l = l0 + λ (p - pc)υ.31 (b) Evolution of linear compressibilities as a function of hydrostatic pressure over the pressure range of 0 – 1.0 GPa, obtained from PASCal.31 For this particular structure, the compressibilities of the three principal axes are given by the following equations (the equations deduction are presented in Supporting Information): K1 = Kc = Kd(001)/sin β

(1)

K2 = Kb

(2)


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K3 = Kd(100) = Ka·sin β

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(3)

Upon compression to 1.95 GPa, d(001) shrunk rapidly (approximately 3.0% per GPa, as shown in Figure S3b, SI) due to the absence of strong interlayer interactions. Meanwhile, the lattice parameter β decreased (Figure 2b). The shrinkage of the c axis was enhanced by the combination of the two preceding factors, resulting in a colossal positive compressibility of X1. Figure 1b shows that all the four sides of one wine-rack framework unit in the ab planes were monotonous rigid pyrazine ligands and the two kinds of adjacent angles are 91.92° and 88.08°,29 approximating right angles. That means that wine-rack frameworks are square in geometry and isotropic and rigid in structure topology. While the pressure increased, the a and b axes isotropically shrunk slightly, by only 0.8% per GPa. Hence, the compressibility of X2 was relatively small. As for the X3 direction, we discuss the pressure-induced variation of d(100) instead. Although a and β decreased when pressure increased from 1 atm to the limit of our experiment (1.95 GPa), the corresponding value of sin β increased for β > 90°. Therefore, the decreases of lattice parameters a and β conversely contribute to the length variation of d(100), as indicated in Equation (3). As pressure increases from P to P', we obtain the following relationships: d(100) = a·sin β. d'(100) = a'·sin β'. sin β'/ sin β – a/a' > 0 must be present to make d'(100) greater than d(100) where sin β'/ sin β shows the increased portion of d(100) generated from angle β closing, which is the blue line in Figure 4a, while the red line in Figure 4a represents –a/a', which represent the reduced portion of d(100) caused by the a axis shrinking. The sum of the blue and red lines is plotted as the black line. The increment rate is larger than the decrement rate at pressures lower than 1.0 GPa because


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the black line is above 0 in that pressure range. Therefore, d(100) (also X3) exhibits NLC behaviors at pressures below 1.0 GPa. However, when pressure is higher than 1.0 GPa, the value of the black line becomes negative, thereby indicating that the compressibility of d(100) (X3) transforms from negative to positive (Figure 4a, Table S1, SI). Essentially, the decrease of β is due to the layer sliding of the ab planes. As shown in Figure 4b, the right layer is treated as fixed. In addition to the contraction in the interlayer distance, the left layer relatively slides along the a axis from the left solid line to the dashed line as the pressure increases, resulting in a diminution of Co1···Co1···Co1A* angle from β to β', that is, the included obtuse angle of a and c axes.

Figure 4. (a) Two inverse factors collectively affecting the pressure-induced variation of d(100): blue line: sin β'/sin β; red line: – a/a', where β' and a' (β and a) are lattice parameters belonging to the unit cell at a higher (lower) pressure. The black line is the sum of the two factors. The length of d(100) increases (decreases) when the black line is above (below) 0. (b) Crystal structural evolution of Co(SCN)(pyz) under high pressure, viewed along the b axis. Upon compressing, the left layer relatively slides along a axis, resulting in a closing effect of angle Co1···Co1···Co1A* (symmetry operations for the three Co atoms are (x, y, z+1), (x, y, z) and (x+1, y, z), respectively), that is, the lattice parameter β. The diminution of β is exaggerated for illustrative purpose. Color scheme: Co, dark blue. Other atoms are omitted for clarity.


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DFT calculations were carried out with Co(SCN)(pyz) from 0 to 2.0 GPa to investigate the slippage of ab planes in Co(SCN)(pyz). Analysis on the computed data showed the pressure range for NLC behavior was 0-0.9 GPa (see in Table S4, SI), which is slightly smaller than the experimental observation. Such a difference can arise in DFT calculations when an empirical correction is not used to account for van der Waals forces. The absence of kinetic effects in the calculations and limitations in pseudopotential-DFT approaches can also lead to a difference between experiments and computations. Identical to the ADXRD experimental data, the computational results also showed a layer sliding of the ab planes due to the weak interlayer interactions. The most notable interaction is presumably the NCS···SCN interaction (S⋯S distance is 3.41 Å at 0 GPa), in which the two SCN groups were belong to the first and the third layers of the ab planes, as shown in Figure S6 (SI). The performed Mulliken charge distribution of Co(SCN)(pyz) showed that the SCN ligand was partially negative (S1, −0.18; C1, −0.03; N2, −0.51; Figure S7, SI), which suggests a repulsive interaction of NCS⋯SCN. As the external pressure elevated, the compression of the interlayer spacing of the ab planes shortened the NCS···SCN distance. The N···N distance (d1) hence decreases ca. 0.18 Å over the pressure range 0–0.9 GPa, see in Figure 5. The decrease of d1 strengthens the repulsive interaction of NCS···SCN. Meanwhile, the projection of N···N distance in a axis direction increased as a result of the repulsive interaction of NCS···SCN (Figure 5 and Figure S8a (SI)). The separation of NCS···SCN in [100] direction effected on the ab planes through N2−Co1 bond (N2 was from NCS ligand). As shown in Figure S8b (SI), over the pressure range of 0−0.9 GPa, the angle of N2−Co1···Co1A* increased by only 0.4°, which indicated that there was no distortion of the octahedral coordination geometry of the Co metal nodes. Hence, the NCS···SCN repulsion finally drove the slippage of the ab planes along the a


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axis. The high-temperature dynamics calculations performed with the Forcite tools in Materials Studio at 0 and 0.9 GPa at 300 K showed the rigidity of the octahedral coordination geometry of the Co as the N2-Co-N1 angles changed slightly when the temperature and pressure increased (Figure S9 depicts the statistical average of N2-Co-N1 angles; Figure S10 depicts the computed evolutions of the four angles of N2-Co-N1 as a function of simulation time from 0 to 100ps with a step of 10ps.). The layer sliding mechanism is hence independent of temperature.

Figure 5. Computed evolution of N···N distance (d1, black) and its projection in [100] direction (d2, red) as a function of pressure. The solid lines are obtained from an empirical fit l = l0 + λ(p − pc)υ based on the computational data (shown as black squares and red dots, respectively).31 The decrease of β caused by layer sliding precisely resulted in the NLC along X3 in crystal Co(SCN)(pyz) from experimental and DFT computational perspectives. The NLC effect was weakened by the shrinking of the a axis to a certain degree, and even thoroughly counteracted and inverted to positive linear compressibility at pressures higher than 1.0 GPa (Table S1, SI). Figure 6 shows the mechanism of NLC effect at pressures below 1.0 GPa. The left rhomboid delineated with black lines represents the unit cell structure at a low pressure. The right one delineated using blue lines signifies a model structure under higher pressures. The latter has compressed unit cell axes and a smaller angle β than the former, meanwhile its b and c axes are


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respectively parallel to the black one. Although the low-pressure structure has longer lattice axes than the high-pressure structure, the length of d(100) is evidently longer in the latter than in the former structure. Moreover, because d(200) and d(100) has the relationship: 2d(200) = d(100), both can consistently change with X3. Thus, the diffraction patterns of (200) peak illustrated in Figure 2a shift to lower angles at pressures below 1.0 GPa.

Figure 6. Compression mechanism in Co(SCN)(pyz). The left (right) rhomboid represents a low (high) pressure unit cell of Co(SCN)(pyz). The crystal of Co(SCN)(pyz) expands along d(100) upon compression as a result of angle β closing. The diminution of β is exaggerated for illustrative purpose. The hydrogen atoms and SCN ligands are omitted for clarity. In conclusion, a MOF material Co(SCN)2(pyrazine)2, that crystalizes in 2D layered networks, was found to demonstrate the NLC phenomenon along the principal axis X3 (≈ −0.84a − 0.55c). In situ high-pressure powder XRD and DFT calculations revealed that the pressure-induced layer sliding of the ab planes results in the NLC effect along X3(= c). The NLC effect is weakened by the shrinking of a axis and is eventually eliminated with the increasing pressure above 1.0 GPa. Layer sliding is a new rational mechanism that can lead to the exceptional NLC phenomenon, which has a broad range of potential applications in designing pressure sensors, artificial muscles, and so on. This enlightening discovery explores an exciting new field for seeking, designing and synthesizing new classes of materials with NLC property in layered monoclinic or


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related systems, which would be of significant benefit to realization of the application of NLC materials in the future. Experimental methods Sample preparation. Co(SCN)2(pyrazine)2 was synthesized by liquid-liquid diffusion at room temperature according to the previously reported work.30 10 mL water containing 2.5 mmol Co(NCS)2 (0.434 g) was loaded into a glass vial. Onto this solution 15ml acetone solution containing 5.0 mmol pyrazine (0.405 g) was added. After slowly diffusing, the mixture was kept undisturbed. After 1 week, orange block crystals of Co(SCN)(pyz) were collected, washed with acetone and dried in air at room temperature. High-Pressure generation. The high-pressure experiments were performed using a symmetric diamond anvil cell (DAC). Powder sample was loaded into a 0.15 mm sized hole drilled in a T301 steel gasket, which was preindented to a thickness of 0.04 mm. A ruby ball was placed into the sample chamber to gauge the in situ pressure according to the R1 ruby fluorescence method.32 Silicon oil was used as the pressure-transmitting medium. All of the experiments were performed at room temperature to ensure a consistent temperature condition. ADXRD measurements. In situ high-pressure powder angle-dispersive X-ray diffraction (ADXRD) experiments with a wavelength of 0.6199 Å beam were performed at the 4W2 High Pressure Station in Beijing Synchrotron Radiation Facility. CeO2 was used as the standard sample to do the calibration. For each pressure, Mar-345 CCD detector was used to collect the 2D images of ADXRD patterns, which were then integrated using the FIT2D program. The program of Materials Studio was used for further analyzing the ADXRD data to carry out lattice parameters. The compressibilities were obtained using the empirical form l = l0 + λ (p - pc)υ by the free online program PASCal from http://pascal.chem.ox.ac.uk/.31


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Computational Methodology. Ab initio calculations were performed with the pseudopotential plane-wave methods based on density functional theory implemented in the CASTEP package at the GGA-DFT level with the PBE exchange correlation functional.33, 34 PBE-D2 is applied as dispersion corrections.35 The 1x1x1 unit cell of the reported ambient structure of Co(SCN)(pyz) with 2 formula units in a unit cell was used as a structural model. The plane-wave cutoff energy and Monkhorst-Pack grid for the electronic Brillouin zone integration were 1000eV and 2x2x2, respectively. The self-consistent field (SCF) tolerance was set as 5.0 × 10-7 eV/atom. The optimization is stopped when stress and forces on the atoms were less than 0.02 GPa and 0.01 eV/Å, respectively. The spin state of Co atoms is calculated using CASTEP, and the Mulliken spin density populations indicate the two Co atoms in a unit cell are high-spin state (S=3) with a spin moment of 2.59 µB0 both at 0 and 0.9 GPa. The room temperature structure simulations were performed on 0 GPa and 0.9 GPa, respectively, using the Forcite Dynamics tools in Materials Studio. Relatively large 3x3x4 simulation supercell comprised of 1944 atoms was used. The Universal force-field at ultrafine quality was employed, while the van der Waals forces were controlled by Ewald summation. The simulations were run under isothermal-isobaric molecular dynamic simulations (MD-NPT) at 300 K. Temperature was controlled by the Nose thermostat (Q ratio = 0.01). The pressure was maintained with the Berendsen barostat (decay constant 0.1 ps). Each simulation was run for 100 ps with a 1 fs time step for a total of 100000 steps. ASSOCIATED CONTENT Supporting Information. XRD patterns, refinements, compressibilities, DFT results and NLC mechanisms. AUTHOR INFORMATION


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*To whom correspondence should be addressed. E-mail: [email protected]. Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work is supported by the National Science Foundation of China (NSFC) (Nos. 21673100, 91227202), Changbai Mountain Scholars Program (No. 2013007), and program for innovative research team (in science and technology) in university of Jilin Province. ADXRD measurements were performed at 4W2 HP-Station, Beijing Synchrotron Radiation Facility (BSRF), which is supported by Chinese Academy of Sciences (Grant KJCX2-SW-N20, KJCX2-SW-N03). REFERENCES (1) Cairns, A. B.; Catafesta, J.; Levelut, C.; Rouquette, J.; van der Lee, A.; Peters, L.; Thompson, A. L.; Dmitriev, V.; Haines, J.; Goodwin, A. L. Giant negative linear compressibility in zinc dicyanoaurate. Nat. Mater. 2013, 12, 212-216. (2) Baughman, R. H.; Stafstrom, S.; Cui, C.; Dantas, S. O. Materials with negative compressibilities in one or more dimensions. Science 1998, 279, 1522-1524. (3) Goodwin, A. L.; Keen, D. A.; Tucker, M. G. Large negative linear compressibility of Ag3[Co(CN)6]. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 18708-18713. (4) Goodwin, A. L.; Calleja, M.; Conterio, M. J.; Dove, M. T.; Evans, J. S.; Keen, D. A.; Peters, L.; Tucker, M. G. Colossal positive and negative thermal expansion in the framework material Ag3[Co(CN)6]. Science 2008, 319, 794-797.


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Cd(imidazolate)2. J. Am. Chem. Soc. 2013, 135, 7610-7620. (15) Binns, J.; Kamenev, K. V.; Marriott, K. E.; McIntyre, G. J.; Moggach, S. A.; Murrie, M.; Parsons, S. A non-topological mechanism for negative linear compressibility. Chem. Commun. 2016, 52, 7486-7489. (16) Duyker, S. G.; Peterson, V. K.; Kearley, G. J.; Studer, A. J.; Kepert, C. J. Extreme compressibility in LnFe(CN)6 coordination framework materials via molecular gears and torsion springs. Nat. Chem. 2016, 8, 270-275. (17) Keller, R.; Holzapfel, W. B.; Schulz, H. Effect of pressure on the atom positions in Se and Te. Phys. Rev. B 1977, 16, 4404-4412. (18) Cairns, A. B.; Thompson, A. L.; Tucker, M. G.; Haines, J.; Goodwin, A. L. Rational design of materials with extreme negative compressibility: selective soft-mode frustration in KMn[Ag(CN)2]3. J. Am. Chem. Soc. 2011, 134, 4454-4456. (19) Lekin, K.; Phan, H.; Winter, S. M.; Wong, J. W.; Leitch, A. A.; Laniel, D.; Yong, W.; Secco, R. A.; Tse, J. S.; Desgreniers, S.; Dube, P. A.; Shatruk, M.; Oakley, R. T. Heat,


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Figure 1. (a) Crystal structure of Co(SCN)(pyz), viewed along b axis at ambient pressure. (b) Monolayer structure of Co(SCN)(pyz) viewed perpendicular to the ab plane. The Hydrogen atoms are omitted for clarity. 85x26mm (300 x 300 DPI)



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Figure 2. (a) High-pressure diffraction patterns of Bragg peak (200) up to 1.0 GPa. The original diffraction data are plotted as scatter dots and fitted into solid lines using Gaussian functions. (b) Experimental evolution of changes of lattice parameters a, b, c, β, and unit cell volume as a function of hydrostatic pressure. 85x60mm (300 x 300 DPI)


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Figure 3. (a) Pressure dependent variations of relative lengths of the principal axes, experimental data are shown as symbols and fitted to solid lines using an empirical fit l = l0 + λ (p - pc)υ.31 (b) Experimental evolution of linear compressibilities as a function of hydrostatic pressure over the pressure range of 0-1.0 GPa, obtained from PASCal.31 85x59mm (300 x 300 DPI)



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Figure 4. (a) Two inverse factors collectively affecting the pressure-induced variation of d(100): blue line: sin β'/sin β; red line: – a/a', where β' and a' are lattice parameters belonging to one higher-pressure unit cell than which β and a belong to. The black line is the sum of the two factors. The length of d(100) increases (decreases) when the black line is above (below) 0. (b) Crystal structural evolution of Co(SCN)(pyz) under high pressure, viewed along the b axis. Upon compressing, the left layer relatively slides along a axis, resulting in a closing effect of angle Co1···Co1···Co1A* (symmetry operations for the three Co atoms are (x, y, z+1), (x, y, z) and (x+1, y, z), respectively), namely, the lattice parameter β. The diminution of β is exaggerated for illustrative purpose. Color scheme: Co, dark blue. Other atoms are omitted for clarity. 85x40mm (300 x 300 DPI)


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Figure 5. Computed evolution of N···N distance (d1, black) and its projection in [100] direction (d2, red) as a function of pressure. The solid lines are obtained from an empirical fit l = l0 + λ (p - pc)υ based on the computational data (shown as black squares and red dots, respectively). 31 89x54mm (300 x 300 DPI)



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Figure 6. Compression mechanism in Co(SCN)(pyz). The left (right) rhomboid represents a low (high) pressure unit cell of Co(SCN)(pyz). The crystal of Co(SCN)(pyz) expands along d(100) upon compression as a result of angle β closing. The diminution of β is exaggerated for illustrative purpose. The hydrogen atoms and SCN ligands are omitted for clarity. 81x32mm (300 x 300 DPI)


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Negative Linear Compressibility Due to Layer Sliding in a Layered

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