Anomalous mechanical materials squeezing three-dimensional volume compressibility into one dimension

Anomalous mechanical materials, with counterintuitive stress-strain responding behaviors, have emerged as novel type of functional materials with highly enhanced performances. Here we demonstrate that the materials with coexisting negative, zero and positive linear compressibilities can squeeze three-dimensional volume compressibility into one dimension, and provide a general and effective way to precisely stabilize the transmission processes under high pressure. We propose a “corrugated-graphite-like” structural model and discover lithium metaborate (LiBO2) to be the first material with such a mechanical behavior. The capability to keep the flux density stability under pressure in LiBO2 is at least two orders higher than that in conventional materials. Our study opens a way to the design and search of ultrastable transmission materials under extreme conditions.


Section S1 Matching condition between linear compressibility and volume compressibility
If there exists a matching direction (θ, φ) along which the linear and volume compressibilities coincide in a material, then the following condition must be satisfied: where (θ,φ) is determined by the spatial ellipsoid with the principal axes of α X , α Y , and α Z , and varies in the range [minimum( X , Y , Z ), maximum( X , Y , Z )]. Clearly, for a normal mechanical system where all three principal axes are PLC, (θ,φ) is always smaller than  X + Y + Z . The equation (1) cannot be fulfilled and the matching direction cannot be found.
Moreover, the matching conditions for the anomalous linear compressibilities are shown as follows: (i) if only a NLC axis is introduced into the normal mechanical system, say,  X < 0, then the range of (θ,φ) value now is changed to the direction (θ, φ) for (θ,φ) =  V can be found. However, the absolute value of the NLC component is smaller than that of either PLC component in majority of NLC materials, and thus this matching condition is seldom satisfied in practice. Although this matching condition could be achieved if NLC occurs in two-dimension, its practical application would be hindered by the weak angle tenability owing to the low anisotropy within the two-dimensional negative compressibility plane.
(ii) if only a ZLC axis is introduced into the normal mechanical system, say,  X = 0, Equation (1) cannot be fulfilled and the matching direction cannot exist. For the zero area (or volume) compressibility materials this matching condition cannot be satisfied as well, since the compressibility coefficient for no material is exactly equal to zero, even for diamond (0.75/TPa) and osmium (0.72/TPa), the most incompressible materials in nature.
(iii) if a ZLC axis is independently introduced into the NLC system, then minimum( Y , Z ) ~ 0, and the equation (2) can always be satisfied. This means that the matching direction can be always found in the mechanical system coexisting with NLC, ZLC and PLC.    Raman and b. infared spectra. The measured and calculated spectra are in good agreement, and almost all main peaks in the experimental spectra can be assigned in the simulated spectra, demonstrating that no defects and adsorbed species exist in the sample.      Table S5. Positive and negative linear compressibilities are represented by red and blue surfaces, and volume compressibility is represented by green sphere, respectively. Clearly, for all materials no intersecting line exists between the volume and linear compressibility surfaces, indicating that they cannot squeeze the three-dimensional volume compressibility into one dimension.

Table S5
| Linear compressibilities (α l ) and volume compressibility (α V ) in LiBO 2 , Ag 3 Co(CN) 6 , diamond, graphite, copper, and quartz, as well as the relative fluctuation of flux density and optimal transmission direction in these materials as they move from sea level to the Mariana Trench. The minimum relative fluctuation of flux density is defined as the product of the compressibility of transmission cross-section and the pressure at Mariana Trench (0.11GPa) along the optimal direction among the integer angles (in degree) closest to the exact matching direction between volume and linear compressibilities. All the linear compressibility values at the integer angles closest to the matching curve in LiBO 2 are listed in Table S6. For other materials the optimal transmission direction is along the largest PLC axis, since its compressibility value has the smallest difference with the volume compressibility.