Spin crossover-induced colossal positive and negative thermal expansion in a nanoporous coordination framework material

External control over the mechanical function of materials is paramount in the development of nanoscale machines. Yet, exploiting changes in atomic behaviour to produce controlled scalable motion is a formidable challenge. Here, we present an ultra-flexible coordination framework material in which a cooperative electronic transition induces an extreme abrupt change in the crystal lattice conformation. This arises due to a change in the preferred coordination character of Fe(II) sites at different spin states, generating scissor-type flexing of the crystal lattice. Diluting the framework with transition-inactive Ni(II) sites disrupts long-range communication of spin state through the lattice, producing a more gradual transition and continuous lattice movement, thus generating colossal positive and negative linear thermal expansion behaviour, with coefficients of thermal expansion an order of magnitude greater than previously reported. This study has wider implications in the development of advanced responsive structures, demonstrating electronic control over mechanical motion.

for the corresponding plots of variable temperature lattice parameters and coefficients of thermal expansion.   Fig. 11 for the corresponding plots of variable temperature lattice parameters and coefficients of thermal expansion.  Fig. 12 for the corresponding plots of variable temperature lattice parameters and coefficients of thermal expansion.  : maximum thermal expansion coefficients at the spin transition for the a ( a sco ), b ( b sco ), c ( c sco ) and volume ( V sco ) dimensions; the spin transition temperature as measured by powder X-ray diffraction, determined along the c axis (T XRD ); the spin transition temperature as measured by magnetic susceptibility (T mag ); and the width of the transition determined by the peak width at half maximum of the  V plots.

Equation (1) model parameters
x  a sco / 10 −6 K −1 series arises from the contribution of both Fe(II) and Ni(II) metal centres, and the most suitable method for comparison is using the HS fraction of Fe(II),  HS .
The experimental molar magnetic susceptibility,  exp T, can be described by the relationship x = Fe(II) molar fraction). From this, the  Fe T contribution can be isolated, which is directly proportional to the HS fraction ( HS ) of Fe(II) sites, since LS Fe(II) is diamagnetic.

Supplementary Note 2. Single crystal X-ray diffraction structures
At both temperatures the single crystal exists in the orthorhombic space group Cmma.

Supplementary Note 3. Synchrotron powder X-ray diffraction
A comparison of the diffraction data for the [Fe x Ni 1−x ] series at 250 K is shown in Fig. S4 Unit cell parameters were modelled by Le Bail refinement within GSAS 9 using the EXPGUI 10 interface (see Supplementary Fig. 6 for a representative example). A histogram profile function with a pseudo-Voigt peak shape and a 10 to 16 term shifted Chebyshev background function were used. Peak profile and unit cell parameters were refined. Sequential refinements were performed using a software script, in which the starting parameters for a refinement were taken from the parameters of the previous temperature in the series.

Supplementary Note 4. Lattice parameter model of [Fe x Ni 1−x ]
The variable temperature lattice parameter data for [Fe x Ni 1−x ] were modelled using equation (1), denoted L(T), which combines a sigmoidal function with a 3 rd order polynomial: The sigmoidal function was incorporated as it was found empirically to provide an excellent fit in the region of the spin crossover transition. This function has been previously used to fit structural changes in a spin crossover material 11  The coefficients of linear and volumetric thermal expansion are proportional to the first derivative of the unit cell model formula with respect to temperature, and were calculated according to equation (2):

[Fe(bpac)(Au(CN) 2 ) 2 ]·2EtOH
As shown in Supplementary Fig. 7, the lattice parameters of [Fe] display remarkable variation over the temperature range studied. In addition to the extreme degree of lattice flexing over the spin transition, there is additional continuous lattice movement at lower temperature. Between 210 K and 100 K the coefficients of linear thermal expansion range between 85 × 10 −6 K −1 > α a > −1100 × 10 −6 K −1 along the a-axis, and 860 × 10 −6 K −1 > α b > −39 × 10 −6 K −1 along the b-axis ( Supplementary Fig. 7). This behaviour likely arises due to a temperature dependence on the distortive influences on the framework geometry, such that these influences become weaker as the temperature is decreased. Such influences could include inter-lattice and lattice-guest interactions, which would weaken as atomic vibrations undergo thermal contraction. Eventually the energetics reach a critical point, where the distortive force is too weak to counteract the geometrical strain of the more rigidly octahedral LS Fe(II), and the material undergoes the second structural transition at 170 K.

[Fe x Ni 1-x (bpac)(Au(CN) 2 ) 2 ]·2EtOH
Supplementary Figs. 9-12 display the temperature-dependence on the unit cell parameters of the Ni(II)-doped materials, [Fe x Ni 1−x ], refined from powder X-ray diffraction; the model fit to these data; and the corresponding coefficients of thermal expansion.

Magnetic Susceptibility Measurements
Magnetic properties were measured on a MPMS-XL7 Quantum Design SQUID magnetometer.
After measurement at 1 Tesla of applied magnetic field under ethanol solvent, the sample was dried and weighed to determine χ M T values.

Single Crystal X-ray Diffraction Experiments
A summary of collection and refinement details is contained in Supplementary Table 2 an Oxford Instruments nitrogen gas cryostream. The crystal was first quench-cooled in the cryostream at 100 K, then data collections were performed at 100, 190 and 240 K, below the low temperature phase transition, and below and above the spin crossover transition, respectively.