Structural Tunability Controlled by Uniaxial Strength in a Hybrid

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Structural Tunability Controlled by Uniaxial Strength in a Hybrid Perovskite Viswanathan Mohandoss J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11194 • Publication Date (Web): 26 Feb 2019 Downloaded from http://pubs.acs.org on February 26, 2019

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The Journal of Physical Chemistry

Structural Tunability Controlled by Uniaxial Strength in a Hybrid Perovskite M. Viswanathan∗ School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, United Kingdom. E-mail: [email protected];[email protected]

Abstract High-pressure studies based on neutron diffraction reveal uniaxial strength in the hybrid ABX3 -type metal guanidinium formates regardless of its symmetry across the phase transition. This interesting phenomenon is associated with the orientation of the guanidinium-guest which regulates the cooperation between hydrogen bonding and octahedral tilting. This key understanding of the physical mechanism behind the phase change attests to the importance of this phenomenon in the design and development of hybrid perovskites, by accomplishing befitting guest-host interactions.

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Introduction Metal-organic frameworks (MOFs) are a hybrid class of materials constituting both organic and inorganic components. Their unique properties arise from the organic-inorganic duality, 1 yielding enormous possibilities to create new materials by altering the inorganic/organic component ratio. 2 In hybrid perovskites, unlike their inorganic analogues, the A-site cations held within the ReO3 -type cavity have a distinctive shape and a corresponding spread of hydrogen-bonds connected to the anionic host. This results in a more complex and diverse construction of the internal structure. Interactions between the linker and the metal ion directly regulate the stability of the framework. 3 Therefore these materials can be tailored by carefully changing the components to establish desirable properties. 4 A series of C(NH2 )3 MeII (HCOO)3 (Me = Mn, Fe, Co, Ni, Cu and Zn), which basically are metal-organic frameworks, exhibit ABX3 topology and were reported by Hu et al. 5 They feature structural similarity as perovskites, wherein the guanidinium cation [C(NH2 )3 ]+ is positioned in the A-site. While members of this series i.e. metal guanidium formates (MeGFs) crystallise in orthorhombic symmetry (Pnna/Pna21 ), a Cd based-member was reported to exist in rhombohedral symmetry (R3c). 6 The reason for the Cd-member to differ from those with an orthorhombic ground state can be interpreted as an effect of ‘chemical pressure’ induced by the larger Cd2+ ion. 7 In general, investigations based on diffraction across high-pressure phase transitions in the ABX3 -type MOFs are rare. 8,9 Advantages of neutron diffraction to study such materials have recently been highlighted. 10 Considering such advantages, the inaugural high-pressure neutron diffraction studies, uncover phase transitions in MeGFs. 7,11 The corresponding phase transition in Mn/Co guanidinium formates i.e. Pnna to R3c, interestingly disregards a group–subgroup association. With the transformation to the R3c phase, the correlation between external stimuli (pressure) and chemical pressure are corroborated in the ABX3 -type MOFs. Though such observations are interesting, the physical phenomena behind the phase transition and the influence of pressure in ABX3 -type MOFs are not completely understood. 2

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The Journal of Physical Chemistry

In supramolecules, pressure affects the rearrangement of hydrogen-bonded networks by the translation/rotation of the moiety, eventually leading to a phase transition. Experimental studies on hybrid materials under the influence of pressure uncover interesting observations such as the disappearance of the in-plane lattice distortion in layered (C2 H5 NH3 )2 CuCl4 , 12 amorphization of MOF-5 at unusually low pressure, 13 pressure-induced conductivity and piezochromism in 2,2’–(ethylenedioxy)bis(ethylammonium))[CuCl4 ], 14 and the pressure effects on the inductive loop and photoresponsivity in CH(NH2 )2 PbBr3 . 15 Guanidinium: [C(ND2 )3 ]+ is a planar organic chemical unit, with a high symmetry D 3h , in free space. 16 A single guanidinium cation houses six hydrogen-bond donor atoms (N–H). As a rigid covalent unit, both the formate and guanidinium moieties independently retain their structural integrity, as realised from high-pressure studies. 17–20 In isostructural frameworks with octahedral coordination, the mechanical stability increases with greater ligand field stabilisation energy (LFSE). 21 With Mn2+ and Co2+ attributing to a large difference in the stabilisation energy, 22,23 i.e. Co2+ (d 7 : 71.5 kJ mol−1 ) > Mn2+ (d 5 : 0 kJ mol−1 ), resulting in a dissimilar resistance offered by the octahedra against distortion, the uniaxial strength and its association with guanidinium is examined in MnGF and CoGF. In terms of hydrogen bonding, qualitatively, the number of hydrogen-bonding interactions are linked to the mechanical properties 24 and that the hydrogen bonds in metal formate perovskites are more than four times stronger than those in halide perovskites. 25 It is also noteworthy that octahedral tilting is one of the influencing factors for phase transitions in perovskites. 26,27

Experimental Bulk samples of fully-deuterated CoGF/MnGF were synthesised by dissolving dehydrated CoCl2 /MnCl2 ·H2 O, C(ND2 )3 Cl2 , K2 CO3 and DCOOD in D2 O. This synthesis is a slight modification of the method suggested by Hu et al. 5 and was implemented due to the unavailability of the deuterated analogue of [C(ND2 )3 ]2 CO3 . The sample was contained in TiZr

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alloy gasket (Ti:Zr = 67.6:32.4 %), a null coherent scattering alloy. The samples were dried in a vacuum furnace prior to its loading into the gasket. For a uniform pressure transmittance, perdeuterated methanol-ethanol in 4:1 volume ratio, was used as the hydrostatic pressure transmitter. To probe the pressure held within the gasket, a small amount of Pb was used as a pressure reference. The cell-volume of Pb reveals the pressure using the P-T equation of state. Therefore, Pb is included as a second phase in the refinement. 28 Ceramic anvils made from zirconia toughened alumina (ZTA) were used in these experiments as they feature a benefit of better neutron transparency in comparison with WC. ZrO2 and Al2 O3 are also included in the refinement as additional phases. The high-pressure diffraction experiments at 298 K, were performed with the PEARL diffractometer 29 at the ISIS Pulsed Neutron and Muon Source, UK. Rietveld refinements were done using GSAS, 30 wherein soft restraints were applied within the formate and guanidinium moiety, as explained in ref. 10 resulting in meaningful structural features.

Results and discussion In this work, using high-pressure neutron powder diffraction, we show that the orientation of [C(ND2 )3 ]+ and its in-plane hydrogen-bonding influences the mechanical response across the phase transitions in MeGFs, regulating the guest-host interactions via the cooperation between hydrogen bonding and octahedral tilting. A comparative assessment is done, between (i) the same material in different phases, and (ii) the same phase in the differing materials. The pressure dependence of lattice parameters exhibits a linear behaviour of compression in both Pnna and R3c phases of Mn/CoGF. Figure 1 shows the relative change in the lattice parameters for pre- and post-phase transition, for both MnGF and CoGF (also see ESI). For the Pnna phase, the unit-cell undergoes a lattice compression along a and b-axes, while the c-axis shows a little variation, a scenario arising as a result of ‘uniaxial compressive strength’. Similar features are realised in the R3c phase with a stiff a-axis exhibiting uniaxial strength.

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(c)

(a) MnGF

-0.8

-1.6

-1.6

-2.4

-2.4

-4.0 0.0

a b c

0.3

Pnna

0.6

a c

0.9

1.2

-3.2

R3c

2.4

2.7

-0.0178(2) GPa-1

0.0

0.0

2.02

-0.8

2.00

l/l (%)

-0.8 -1.6

-1.6

-2.4

-2.4

0.0

b/c a/c MnGF CoGF

0.3

0.6 0.9 1.2 1.5 Pressure (GPa)

1.8

2.1

(d)

0.0

-4.0

-0.0249(5) GPa-1

0.90

3.0

(b) CoGF

-3.2

-0.0145(3) GPa-1

1.28

0.92

-4.0

1.8 2.1 1.5 Pressure (GPa)

(MnGF) > |dy/dP|(CoGF) -0.0202(5) GPa-1 |dy/dP| Pnna

1.30

0.94

a b c

0.4

Pnna

0.8

1.2

a c

1.6

y = c/a

-3.2

1.32

y = l/l'

-0.8

l/l (%)

l/l (%)

1.34

0.0

0.0

l/l (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3.6

4.0

4.4

1.98 1.96

-3.2

-1 1.94 -0.0512(15) GPa

-4.0

1.92

R3c

2.0 2.4 2.8 3.2 Pressure (GPa)

|dy/dP|(MnGF) > |dy/dP|(CoGF) R3c

4.8

1.5

-0.0297(9) GPa-1

MnGF CoGF

2.0

2.5

3.0 3.5 4.0 Pressure (GPa)

4.5

5.0

Figure 1: Pressure dependence of the change in lattice parameters for (a) MnGF, (b) CoGF; and the ratio of the pliable and stiff lattice parameter, y, for Mn/CoGF in (c) Pnna and (d) R3c phase.

Table 1: Coefficient of linear compression of the lattice parameters, struts and hinges of MnGF and CoGF. Details of Pnna and R3c respectively are shown. **Unable to obtain the values of K θ4 for these data sets. Sample in Pnna phase MnGF (0 – 1.12 GPa) CoGF (0 – 1.19 GPa)

Ka Kb Kc K rb K rac K θ1 K θ4 −1 −1 −1 −1 −1 −1 −1 (TPa ) (TPa ) (TPa ) (TPa ) (TPa ) (TPa ) (TPa ) 26.6(6)

15.4(3)

0.11(8)

16.2(6)

12.4(3)

17.7(3)

**

20.7(4)

12.5(2)

0.96(10) 11.4(9)

10.1(2)

13.2(2)

**

12.1(5) 9.58(16) 12.8(2)

**

19.8(3) 11.77(21) 0.80(5) CoGF (0.01 – 1.86 GPa)

Sample in R3c phase

Ka Kc Kr K θ1 −1 −1 −1 −1 (TPa ) (TPa ) (TPa ) (TPa )

MnGF (1.61 – 3.0 GPa)

2.4(2)

29.1(5)

8.8(5)

10.2(7)

CoGF (2.65 – 4.83 GPa)

3.3(3)

18.2(3) 6.95(17) 5.90(17)

The ratio of the pliable and stiff lattice parameter, y, for both the low- and high-pressure phases are shown in Figure 1 (c) and (d) respectively. The rate at which the ratio declines with pressure is linear, and is in conformity with the changes in volume for both phases of both the samples. The comparative observations confirm the higher rigidity of CoGF, (MnGF)

i.e. |dy/d P|

(CoGF)

> |dy/d P|

, in both the phases. Such an exhibition of very low 5

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compressibility in one of the directions, by up to ∼25 times, is a fascinating scenario. Nature provides room for such an occurrence of ‘uniaxial’ resistance to compression, regardless of the ‘B-site metal-ion’ both in the ‘low and high-symmetric’ structures. Such instances occur in supramolecules, wherein the directionality of interactions and/or the presence of hingeing mechanism are held accountable for the anisotropic behaviour.

Figure 2: (a) Volumetric compressibility of Mn/CoGF in both the phases. Also shown are the absolute changes and the volume compressibility; (b) relative change in the volume of Mn/CoGF. The coefficients of linear compressibility, K l , for all the cases are listed in Table 1. A comparison of ∆l /l (P ) within a nearly identical pressure window reveals MnGF suffers from a higher degree of compressibility in comparison with CoGF. Regarding the orthorhombic phase, MnGF demonstrates a higher compressibility along the a and b-axes. This is understood based on the LFSE of Mn2+ being less than Co2+ . The changes in the c-axis are very MnGF

small for both MnGF and CoGF, i.e., qualitatively K c

CoGF

and K c

are quite similar. In

the high-pressure phase (R3c), the c-axis of MnGF is more compressible than that of CoGF MnGF

i.e. K c

CoGF

> Kc

, while the values for K a are too close to differentiate between them.

Within the same structure, irrespective of whether in the Pnna or R3c space groups, CoGF is stiffer than its Mn analogue. Considering the same material, the rhombohedral unit-cell is stiffer than the orthorhombic unit-cell. This is reflected in the volumetric compressibility of Mn/CoGF as shown in Figure 2. It has been proposed that the mechanical response of MOFs can be predicted in terms of 6

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R3c

0.9

1.2 1.5 1.8 Pressure (GPa)

2.1

2.4

/ (%)

 (degrees)

 (degrees)

0.0

-0.4

-0.4

-0.8

-0.8

-1.2

-1.2 -1.6 0.0

2.7

2.4 2.4 94 1 82.5 92 1 1.8  1.8 CoGF 90 1.2 1.2 82.0 88 0.6 0.6 86 81.5 84 0.0 0.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0 0.4 0.8 1.2 1.6 2.0 Pressure (GPa) -0.6 -0.6 Pressure (GPa) -1.2 -1.2 Pnna R3c -1.8 -1.8 -2.4 -2.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 Pressure (GPa)

r

r/r (%)

1.5 1.8 2.1 2.4 2.7 Pressure (GPa)

0.3 0.6 0.9 1.2 Pressure (GPa)

rb rac

MnGF

0.0

Pnna

0.3

0.0

0.6

CoGF

-0.4

R3c

0.9

1.2 1.5 1.8 Pressure (GPa)

2.1

rb rac

-1.6 2.4

2.7

r

0.0 -0.4

r/r (%)

82.0

(b)

r/r (%)

82.5

1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0

/ (%)

/ (%)

1

83.0

r/r (%)

 

 (degrees)

(a) 1.5 94 92 MnGF 1.0 90 0.5 88 86 0.0 84 0.0 -0.5 -1.0 -1.5 Pnna -2.0 0.0 0.3 0.6

/ (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

 (degrees)

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-0.8

-0.8

-1.2

-1.2

-1.6 -2.0

-1.6 Pnna

R3c

-2.0

-2.4 -2.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 Pressure (GPa)

Figure 3: Relative change in (a) the hingeing angle and (b) M· · · M struts with pressure for Mn/CoGF in both the phases. the behaviour of the rudimentary building units: flexing struts (r ) and hinges (θ). 31 It has been shown that MeGFs constitute of four subordinate units (2 struts, 2 hinges) of the Pnna structure. 10 The situation is simplified to two subordinate units (1 strut, 1 hinge) in the R3c unit cell, as a result of an increase in the symmetry. The coefficient of compressibility of the struts and hinges are listed in Table 1 and are derived from the relative change in the hingeing angle and strut length, respectively, for both Mn/CoGF in both phases as shown in Figure 3. The order of compressibility for the low-pressure Pnna phase, K θ1 > K rb > K rac , demonstrates hingeing is the dominant factor similar to the thermal expansion scenario. For the high-pressure R3c phase, the values of K θ1 and K r are very similar i.e. both framework hingeing and deformation appear to have a nearly equal contribution. It is noteworthy that MnGF demonstrates higher compressibility of the struts and hinges than those in CoGF. This ascertains that CoO6 octahedra exhibits more resistance to deformation than its MnO6 analogue. The metal-oxygen octahedra, an integral part of the anionic host, is linked to the [C(NH2 )3 ]+ guest via hydrogen bonds. Figure 4(a, a’) shows the relaxation process of the octahedral tilting accompanied by a reduction in the number of degrees of freedom. As a result, the ‘low-magnitude tilt’ transforms into a repetition of the other tilt angle. Such an effect influ7

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0.5

1.0

1.5

2.0

2.5

3.0

-

(b) Pnna

(b’) R3c

Pnna R3c

2θX

2θX

MnGF

2Torsion (degrees)

2θX

2θY O1-O1-O1-O1 O3-O2-O2-O3

2θTorsion 2θX ≠ 2θY

O1-O1-O1-O1

O3-O2-O3-O2

(c) MnGF

-

(c’) CoGF

39

Pnna R3c

y = a + b*x

Equation

52.08398

Slope

2.38043

Residual Sum of Squares

4.58917

Pearson's r

0.93934

33

Adj. R-Square Equation

41.20621

Slope

1.94977

27

Residual Sum of Squares

7.60299

Pearson's r

0.94753 0.89781

R-Square(COD)

0.88504

Adj. R-Square

24

y = a + b*x

Equation

?$OP:A=1

Plot

Instrumental

Intercept

1.74104 ± 0.07181

Slope

-0.43058 ± 0.06387

Residual Sum of Squares

4.9

0.5

{

Pnna R3c

33

N1-N1-O1-O1 N1-N2-O2-O3 N1-N1-O1-O1

30 27 24 21

14.57344 -0.92212

Pearson's r

4.2

36

Instrumental

Weight Intercept

Weight

1.4 2.1 2.8 3.5 Pressure (GPa)

39

N1-N2-O2-O3 N1-N1-O1-O1

B

Plot

21 0.7

N1-N1-O1-O1

0.86765 y = a + b*x

30

R-Square(COD)

R3c

0.88236

R-Square(COD)

Adj. R-Square

Pnna

Instrumental

Weight Intercept

36

18 0.0

{

A

Plot

CoGF

2N-N-O-O (degrees)

0.0 66 63 60 57 54 51 48 45 42 39 4 3 2 1 0 (a’) 66 63 60 57 54 51 48 45 42 39 4 3 2 1 0 0.0

2N-N-O-O (degrees)

(a)

2Torsion (degrees)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.8503

1.0 1.5 2.0 Pressure (GPa)

0.83159

2.5

3.0

18 0.0

0.7

1.4

2.1 2.8 3.5 Pressure (GPa)

4.2

4.9

Figure 4: (a) MnGF and (a’) CoGF, displaying the relaxation of octahedral tilts with an increase in pressure. The relaxation process is accompanied by a reduction in the number of degrees of freedom in tilting as a result of a phase transformation to a higher-symmetry. The formato-guanidinium torsion angles, for (b) Pnna and (b’) R3c: a resultant of octahedral tilting. Relaxation effects of the same for (c) MnGF and (c’) CoGF, across the phase transition. The rhombohedral structure experiencing a single formato-guanidinium torsion. Note on a, a’: The green and red symbols represent the same tilt measured along a different path. The black symbols represent the second tilt: when measured in a different path their values (with increasing pressure) are 4.7 to 3.4o (MnGF) and 3.17 to 1.89o (CoGF).

ences the guest-host interaction via the ‘formato-guanidinium torsional angle’. Figure 4(b) shows the two different torsional angles in the Pnna phase linking to (i) the symmetrically equivalent O· · · D bonds (highlighted in blue), (ii) symmetrically inequivalent O· · · D bonds (red and grey), whilst for R3c there is just one (see Figure 4b’). The torsion angles, when measured via D/H, results in an inconsistency especially in the Pnna phase, as they slightly come out of the plane. Yet, as guanidinium has a planar construct, and with the internal arrangement it possesses, ideally the torsional angles should be identical, regardless of the path taken via N or D, i.e. θO-O-N-N =θO-O-D-D . Figure 4(c, c’) shows Pnna has two distinct values, transforming to a single identity in R3c. Figure 5 shows a comparison between the environment of guanidinium in MnGF, in the structure while at the ‘highest pressure possessing lower-symmetry’ and the ‘lowest pressure possessing the higher-symmetry’ phase. The high-symmetry structure hosts a much simpler 8

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The Journal of Physical Chemistry

Pnna (1.13 GPa)

MnGF

(a)

R3c (1.61 GPa)

2θ ~ 1.8o

2θ ~ 48.7

o

∆(2θ) ~ 46.9o

(b)

o

~ 99

Figure 5: (a) MnGF depicting the difference in the octahedra tilt in both the phases; (b) the difference in the stacking of guanidinium in both phases. guest-host interaction with a single length hydrogen bond. The highlighted atoms in Pnna o

show a minimum level of torsion, 2θ ≈ 1.8 , while the equivalent scenario in R3c, with o

o

2θ ≈ 48.7 , results in a difference, ∆(2θ)≈ 46.9 . This effectively translates, to an alteration o

on the relative orientation, between the octahedra and guanidinium, by around 45 . In the orthorhombic unit-cell, the molecular plane of the guanidinium cation is nearly perpendicular to the diagonal of the formate cage. Thus, the stacking of guanidinium by itself is close to being normal to one another in a zigzag arrangement along the b-axis, as shown in Figure 5(b). Such a zigzag inter-guanidinium stacking is completely transformed in the rhombohedral unit-cell, due to the alteration caused by the interplay of the hydrogen bonding and octahedral tilting. Interestingly, the pliable planes in both the phases, i.e. (001) of orthorhombic and (110)

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(a)

(b)

Figure 6: (a) Planar guanidinium attached to metal-formate host in MnGF: The tilting of octahedra is promoted with an applied pressure. (b) The concurrent rotation of formates along with octahedral tilting composes the relaxation process, which is favourable rather than the crushing of guanidinium/N–D· · · O bonds: leading to a stiff c-axis. While the sketch shown here is for the Pnna phase, the principle is similar for the R3c. of rhombohedral, are perpendicular to the guanidinium cation which is connected to the formato-oxygens via hydrogen bonds: a crucial factor in understanding the uniaxial stiffness. These hydrogen bonds lie in the plane perpendicular to the ‘compressive ab-plane’ in Pnna [(001) in the case of R3c]. Whilst, it is these guest-host hydrogen bonds that restrict compression, the axes ‘free from formato-guanidinium connectivity’ exhibits increased compressibility. When the intrinsic rigidity of the molecular moieties, is stronger than the intermolecular struts and hinges, it is the relatively softer components that are affected. In this case, both guanidinium and formate being stiff molecular moieties, the parameters that can potentially yield to a stimulus are, the metal-formate struts, octahedral tilting and the N–D· · · O bonds. The latter exhibits rigidity in the investigated pressure window, i.e. the ∆d N···O ≈ 0.05 to 0.1 ˚ A, across the phase transition. Such an evidence of rigid hydrogen bonding is supportive of the studies based on NMR. 25 Hence, the application of pressure facilitates the tilting of the octahedra which concurrently influences the rotation of formates, as illustrated in Figure 6. These hydrogen bonds resist the load by redirecting it to the metal-formate cage. 10

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Therefore, the plane that constitutes the N–H· · · O bonds is stiffer, while the perpendicular directions are ‘free from formato-guanidinium connectivity’ and hence are compressible, at the expense of voids. It is this collective participation, which takes the load. Perhaps, at extreme pressures, the N–H· · · O bonds and/or guanidinium might collapse leading to a different scenario.

Conclusion In summary, regardless of the symmetry, uniaxial stiffness is realised in metal guanidinium formates. Such a characteristic feature is influenced by the native rigidity of the guanidinium moiety and the guest-host interactions that resist compression parallel to the planarguanidinium cation. The inherent uniaxial strength leads to cooperation between the hydrogen bonding and octahedral tilting promoting phase transitions. The complexity behind the phase transition reveals the interplay between the guest and the host-framework. The same principles based on ‘chemical pressure’ held within the unit-cell, can be implemented via crystal engineering. Our findings establish comprehensive insights into MeGFs wherein the uniaxial stiffness influenced by the orientation of the guest, impacts the guest-host connectivity which controls the structural tunability. This physical mechanism behind the phase transformation, is a valuable addition to the concepts of crystal engineering that provides a promising platform for the advancement of hybrid perovskites.

Acknowledgement The author is thankful to (a) STFC for providing neutron beamtime at ISIS Pulsed Neutron and Muon Source, UK; (b) Dr C L Bull and Dr M G Tucker for help with data collection; (c) Professor William Gillin and Professor Mike Watkinson for discussions on the manuscript and their overall advice on academic matters and acknowledges QMUL for funding through the College Doctoral Training Award. 11

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Supporting Information Available Plots, description of hinges in the high-symmetric phase.

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