Intrinsic Zero-Linear and Zero-Area Compressibility over an Ultra-Wide Pressure Range within a “Gear-Spring” Structure

Materials with zero-linear compression (ZLC) and zero-area compression (ZAC) hold great promises for specic applications retaining constant in specic directions or planes under external impaction. Up to now, no more than ten ZLC/ZAC materials have been reported, most of which are of very limited working pressure ranges (< 10 GPa). Herein, we report the observation of concurrent ZLC and ZAC in Li 2 Ti(IO 3 ) 6 with a “Gear-Spring” type structure over an ultra-wide pressure range (0 ~ 40 GPa). Structure analysis reveals that the rotatable metal coordination polyhedra (gears) and extremely compressible metal chains (springs) work together to form an exquisite mechanical unloading device with intrinsic ZLC and ZAC behavior. Moreover, Li 2 Ti(IO 3 ) 6 sets a record-wide ZLC/ZAC working pressure range (up to 40 GPa) among anisotropic compression materials. The demonstration of intrinsic and long-lasting ZLC/ZAC with a “Gear-Spring” mechanism paves the way to shock-resistant precision optics applied under extreme conditions.


Introduction
Substances normally contract under external hydrostatic pressure, just as they expand with heat and contract with cold. 1,2 From the perspective of thermodynamics, it is impossible for a given material exhibiting negative volume compressibility. 3 Nevertheless, there are several types of materials possessing negative compressibility in speci c crystalline directions or planes, while the overall cell volume keeps decreasing under compression. [4][5][6] In the past decades, materials with negative linear compressibility (NLC) and negative area compressibility (NAC) have been widely explored with speci c mechanisms, such as "wine-rack", honeycomb networks, and Lifshitz model. [7][8][9] In general, zero linear compressibility (ZLC) and zero area compressibility (ZAC) can be easily achieved by nding a balance between negative and positive compressibility, and the linear and area compressibility of diamond and Os are used as standard to classify a ZLC or ZAC material. [10][11][12][13] ZLC and ZAC materials are ideal candidates for precision instruments applied under extreme environments, such as submarine ber-optic communication and shock-resistant optical windows. 1,14,15 Surprisingly, material with ZLC or ZAC has been rarely discovered compared with those of NLC and NAC property. 9,10,[16][17][18][19] Meanwhile, there lacks clear structure-property mechanism for the rational design of ZLC/ZAC materials.
In the decade's exploration of materials with abnormal compressibility, remarkable ndings have been concentrated in two types of materials: metal-organic frameworks (MOFs) and all-inorganic frameworks. 4 The most important strategy to achieve materials with abnormal compressibility is to establish clear and instructive structure-property relationship. The diverse organic units endow MOFs the ability to exhibit exible mechanical responses under compression, [20][21][22][23] including both large NLC and near-ZLC. The "wine racks" structure model is the most popular mechanism describing the NLC and near-ZLC behaviors in MOFs. Particularly, "molecular gears and torsion springs" structure model is proposed to describe the NLC and extreme compressibility of LnFe(CN) 6 (Ln = Ho, Lu or Y), which bene t from the LnN 6 torsion springs and the rigid Fe(CN) 6 gears. 24 However, MOFs are soft and usually show above-mentioned abnormal compressibility within a very narrow pressure range, typically no more than 10 GPa, which greatly limits their potential applications. Comparatively, all-inorganic frameworks such borates possessing covalentlybonded frameworks are less compressible. Although up to now the highest pressure of ZLC is 8 GPa in (Ca,Sr)B 2 O 4 , from the viewpoint of structural chemistry, they are still good candidates with abnormal compressibility in a relatively wide pressure range. 4 In addition, all-inorganic frameworks can have good chemical/physical stability and excellent optical performances, which makes them potential for nextgeneration shock-resistant optical windows and ber communications. Unfortunately, there lacks clear mechanism for the rational design of all-inorganic frameworks with abnormal compressibility. An exception is the recently reported "Lu-Ban Stool"-like model for (Ca,Sr)B 2 O 4 , in which the subtle counterbalance originated from the expansion and contraction effect between the rotation of the [BO 3 ] "planks" and the shrinkage of Ca-O "legs" attributes to an excellent ZLC property. 10 We are aiming at exploring all-inorganic optical materials with both excellent ZLC/ZAC properties and good chemical/physical stabilities by structure design strategy. Numerous known inorganic compounds in the ICSD database have been screened to look for framework-like structures, among which a unique family of transition metal iodates with metal-metal bonding and chains are identi ed potential for ZLC/ZAC behavior. Herein, we report the anomalous mechanical responses of Li 2 Ti(IO 3 ) 6 to external pressure as a representative of inorganic framework structure. The anisotropic compressibility of Li 2 Ti(IO 3 ) 6 was examined by using in-situ X-ray diffraction (XRD), Raman spectra, and rst-principles calculations. A "Gear-Spring" mechanism was proposed responsible for the emerging intrinsic ZLC/ZAC properties, which sheds light on the future structure design of all-inorganic materials with anomalous compressibility.
No obvious structural phase transition is observed under compression up to 40.2 GPa since there is only peak shift instead of new peak emerging or disappear, and the pressure effect on the crystal structure is reversible (Fig. S3). Different Bragg peaks exhibit obviously distinct shift behaviors under compression, implying an extremely anisotropic compressibility along different crystallographic axes. Among them, the (hk0) peaks such as (2 0) and (300) basically keep their 2θ values unchanged, indicating an incompressibility or minimal compressibility along the a and b axes. Speci cally, the (hk0) peaks shift slightly to lower 2θ angle rst in the 0~8 GPa range (i), and then slightly to higher 2θ angle in the 8~19 GPa (ii), and nally to lower 2θ angle again above 19 GPa (iii) (Fig. S4). By contrast, the (hkl) peaks such as (2 1) Table S1 displays the re ned cell parameters of Li 2 Ti(IO 3 ) 6 as functions of applied pressure.
The extremely anisotropic compression behavior is evident. The evolution of the a axis has gone through three pressure regions in accordance with the peak shift of the (hk0) planes. Notably, the overall change of the a axis (Δa) in the 0~40.2 GPa region is as low as 0.97%, a low enough value to be regarded as ZLC. Due to the hexagonal symmetry of space group P6 3 with a = b, the ab plane exhibits similar compression behavior with individual a and b axes, i.e. the overall area change of the ab plane (Δs) in the 0~40.2 GPa is as low as 1.95%, which is also a low enough value to be ZAC. Comparatively, c axis exhibits tremendous compressibility with Δc = 28.69% at 40.2 GPa, and a normal V-P curve is obtained in the whole pressure range.  6 . The linear compressibility (K l ) has been de ned as −dl/ldp to evaluate the strength of mechanical response to external pressure of a given material. 4 Fig. 1d represents the pressure-dependent linear compressibilities (K a/b and K c ) of Li 2 Ti(IO 3 ) 6 , derived using the online PASCal package 30 and within three above-discussed pressure ranges (i, ii, iii). It is interesting to see that The online PASCal package is found only applicable to those cases with either a positive or a negative K l .
To calculate the total K l for our case with both positive and negative linear compressibilities in a pressure range, we simply use the most primitive formulas (K l = -Δl/lΔp and K s = -Δs/sΔp) to evaluate the linear and area compressibilities, where l represents the length of the starting unit cell, s represents the area of the initial crystal plane, Δl, Δs and Δp represents the changes of linear, area and pressure, respectively.
The recalculated K a and K s in the pressure range of 0~40.2 GPa are provided in Fig. S6, and the compressive properties of representative ZLC/ZAC materials including the superhard diamond and Os as references are concluded in Table 1.
First of all, Li 2 Ti(IO 3 ) 6 possesses relatively small K l (0.24 TPa -1 ) and K s (0.48 TPa -1 ) within these materials including diamond (K l = 0.62 TPa -1 , K s = 1.23 TPa -1 ) and Os metal (K l = 0.54/0.60 TPa -1 , K s = 1.02 TPa -1 ), making it worthy of ZLC and ZAC material. Remarkably, inorganic ceramics or crystalline materials with both ZAC property and transparency in important wavelengths are rather rarely reported up to now, which holds great promise for practical shock-resistant optical usages. Secondly, Li 2 Ti(IO 3 ) 6 exhibits ZLC and ZAC in an ulta-wide pressure range, i.e. 0~40.2 GPa, compared with ZLC/ZAC MOFs and metal borates. 40.2 GPa may not be the highest pressure value for Li 2 Ti(IO 3 ) 6 to survive, nevertheless, this value still refreshes the world record of ZLC/ZAC material (except diamond and Os). At last, as we know, there are several structural mechanisms for previously discovered ZLC/ZAC materials, such as "Wine-rack" for MOFs, "Lu-Ban Stool"/"Corragated graphite"/"Lifshitz" for some borates, and superhard for diamond and Os, respectively. However, Li 2 Ti(IO 3 ) 6 does not belong to any of the above-mentioned mechanisms.
Intrinsic ZLC/ZAC in "Gear-Spring" structures. The crystal structure of Li 2 Ti(IO 3 ) 6 can be vividly regarded as a "Gear-Spring" type. As shown in Fig. 2a The parameters of the "Gear-Spring" model, gear radii (r(Gear-A), r(Gear-B)), spring length (c) and rotation angles (θ(Gear-A), θ(Gear-B)) were derived from structure optimization using the experimental cell parameters of Li 2 Ti(IO 3 ) 6 under various pressures. As rigid "gears", the sizes of "Gear-A" and "Gear-B" should basically remain unchanged, which has been perfectly validated by the calculation results (Fig.  2b). In the meantime, the spring length (c) decearses rapidly along with the increasing of applied pressure, working together as real springs. It is really amazing that the two gears (A and B) can rotate synergistically either in the direction or angles (Fig. 2c)  pressure to maintain the size of Gear-A unchanged. In brief, the emerging ZLC/ZAC phenomena in Li 2 Ti(IO 3 ) 6 can be perfectly explained by the "Gear-Spring" mechanism. Materials with such a "gear" and "spring" cooperation structure are expected to have intrinsic ZLC/ZAC properties, and also in an ultra-wide pressure range.
The local structure evolution of Li 2 Ti(IO 3 ) 6 during ZLC/ZAC processes are probed by in-situ high-pressure Raman spectra (Fig. S7).

Conclusion
In summary, we report intrinsic ZLC and ZAC properties in an all-inorganic iodate material Li 2 Ti(IO 3 ) 6 . The ultra-wide working pressure range (0~40.2 GPa) of Li 2 Ti(IO 3 ) 6 sets a new record for arti cial ZLC or ZAC materials (except diamond and Os). Based on structure analyses, we proposed a novel "Gear-Spring" mechanism that can describe and explain the anomolous compression behavior of Li 2 Ti(IO 3 ) 6 perfectly.
We are con dent to predict anomolous compression properties (including intrinsic ZLC and ZAC) in compounds with such a "Gear-Spring" structure. Moreover, Li 2 Ti(IO 3 ) 6 maintains its nonlinear optical functionality along with ZLC/ZAC behavior to high pressure, which makes it promising for special optical devices under extreme environments. High-pressure generation. A symmetric diamond-anvil-cell (DAC) was used to produce high pressure. T301 steel gaskets were pressed to the thickness of about 35 μm, and then 180 μm holes were drilled as the sample chambers. Compact sample and a ruby ball were thrown into the sample chamber. Silicone oil was employed as the pressure medium. The pressure was calibrated based on the uorescence peak of ruby ball. 31 High-pressure XRD measurement. In-situ high-pressure XRD experiments were recorded at the 4W2 High Pressure Station in Beijing Synchrotron Radiation Facility (BSRF) with a beam wavelength of 0.6199 Å at room temperature. A Mar345 image plate was used to record the in-situ high-pressure XRD patterns, and CeO 2 was chosen as the calibration standard. DIOPTAS software was used to execute the data reduction. 32 Cell parameters under different pressures were re ned by Rietveld method using the FULLPROF software. 33 The compressibility was calculated by the empirical function l = l 0 + λ (p -p c ) υ via the online program PASCal (http://pascal.chem.ox.ac.uk/). 30 High-pressure Raman measurement. In-situ high-pressure Raman spectra were recorded on a Renishaw Raman microscope using a 532 nm laser. The system was calibrated by the Raman signal of Si, and spectra were collected in the range of 100-1100 cm -1 .

Methods
High-pressure SHG measurement. In-situ high-pressure SHG experiment was measured in a homedesigned optical system. A ber laser (NPI LASERCo., Ltd, 1064 nm, 20MHz, 15 ps) was used as the exciting light source, and the laser spot was focused to 40 μm. A photomultiplier tube (Thorlabs, Inc., PMT1000) was employed to collect the SHG signal. The high-pressure SHG measurement is based on the ambient powder SHG measurement extended by Kurtz and Perry. 34 First-principles calculation. The rst-principles calculation was performed using the CASTEP package. 35 Structure optimization at various pressure points was performed adopting the experimental cell sizes with all the atomic positions relaxed.

Data availability
The data that support the ndings of this study are available in the Supplementary Information (experimental data and characterization data). All raw data and analysis les used in the study are available upon request from the authors.

Supplementary Files
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