Negative Compressibility of Single Selenium Chain Confined in Zeolite Pore

Pressure induced structural and electronic transitions of Se helical chains confined inside nano-channels are studied. Raman scattering and optical absorption experiments show strong evidence of band gap reduction under high pressure. Ab initio calculations reveal that under hydrostatic compression, the Se chains should elongate and the change in morphology leads to a softening of phonons and narrowing of band gaps, and these signatures are observed in experiments. Our investigation demonstrates a negative compressibility in one dimension.

Selenium is a group VI non-metallic element with a band gap of about 2 eV at ambient pressure. To realize metallization for bulk selenium with a concomitant structural phase transition, a large pressure up to tens of GPa is necessary 1-3 . Such phase transition phenomena of polycrystalline selenium have been observed at very high pressures by in situ Raman and X-ray diffraction. The metallization 4 and anomalous liner expansion coefficient under 20 GPa pressure 5 have been examined for crystalline selenium using density functional calculations. Here, we investigate the property of a single Se chain under pressure and we demonstrate that a much lower pressure is sufficient to induce detectable changes in the properties of a confined Se chains inside nano-channels. The pressure induced structural and electronic changes of Selenium chains confined in zeolite channels are studied using Raman spectroscopy and optical absorption spectra, and the results hint at a trend towards metallization as we increase the pressure. Such changes are interpreted using density functional theory (DFT) calculations. The calculations focus on understanding the hydrostatic pressures effect applied on the single trigonal helical 3 chain structures. The first-principles calculation results are in excellent agreement with the experimental findings.
Our zeolite template AlPO 4 -5 crystals (IUPAC code AFI; molecular formula Al 12 P 12 O 48 ) are synthesized using a hydrothermal method 6 . The crystalline framework with parallel one-dimensional channels is formed by alternating tetrahedra of [AlO 4 ]and [PO 4 ] + units (space group: P6/mcc). The inner diameter of the channel is 7.3 Å, and the separation distance between two neighboring channels is 13.7 Å. The selenium species are incorporated into the AlPO 4 -5 crystal channels by vapor phase diffusion method as described previously [7][8][9] . Earlier X-ray absorption spectroscopy study on the Se-Se distances has confirmed that single chains of Se are indeed being confined in the assembling template 10 .
Visible light Raman spectra of our isolated selenium chains are shown in figure 1. The response of a pure Zeolite sample is much weaker than that with selenium inside its channels, and thus can be neglected. We have previously studied the six optical phonon modes Г (optic) =A 1 +A 2 +2E 1 +2E 2 , shown partially in figure 1. The highest peak (257cm -1 ) with single frequency A 1 is the symmetric chain radial expansion mode, rather similar to radial breathing mode in carbon nanotubes. The mode A 2 is chain rotation mode and Raman-inactive. Both E modes are doubly-degenerate, while one of them is peaked at 233 cm -1 and the other is well below our present Raman frequency. These modes have ZZ configuration, in which both the excitation and the scattering light are parallel to the chain direction. We can also identify a peak for molecular Se at 267cm -1 , which appear in 4 both ZZ and YY (both excitation and the scattering light are perpendicular to the chain axis) configurations. This peak is attributed to the crown-shaped Se8 ring structure 11,12 .
As we increase the pressure, the most significant change is that the low-frequency tail rises up while the high-frequency signal suppresses down. Such kind of red-shift of oscillator strength has been discussed before by others on the basis of chain-chain interaction 13 . There is no inter-chain coupling in our structure, and thus our observed pressure-induced frequency magnitude change has a different origin. As pressure up to 6.42 GPa is being applied in the channels through a pressure-transmitting liquid solution (ethanol to methanol 1:4 in volume percentage), we may think that the observed changes are due to a longitudinal compression of the individual Se chains. Quite on the contrary, we found the surprising result that the Se chains are elongated, as we will establish in the following discussions. In short, both the Se-Se bond length and angle are increased by the pressure. This structural change gives rise to the softening of vibration modes.
As mentioned, cyclic Se molecules such as rhombohedral Se6 or α -monoclinic Se8 rings could also exist in the channels, since the defects in the zeolite crystal might possibly accommodate these stable molecular structures. Electronically the ring clusters show a similar semiconducting band gap as the trigonal chain. Bulk Se chain and ring structures under high pressure have also been investigated by X-ray and Raman spectroscopy measurements. The Raman frequencies showed a similar pressure-induced softening 14 .
However we want to emphasize again that previously it was interpreted in terms of an interference effect between inter-and intra-molecular bonds in the molecular crystals 13 .
In the bulk material, the intra-chain Se-Se covalent bonds are much stronger than the 5 inter-chain Van der Waals interactions. The applied pressure would pack the chains denser and thus increase chain-chain coupling rapidly. In our experiment, we have eliminated this mechanism since we are dealing with single selenium spiral chains and inter-chain coupling does not enter into the picture here.
An isolated single trigonal Se helical chain is energetically more favorable compared with a linear or zigzag chain 15 . This reflects the fact that bulk Se crystal can be viewed as an array of such helices with weak inter-chain couplings. However, a trigonal Se helix is a semiconductor while both of the hypothetical linear or zigzag chains are metallic (coordination number equals 2 in all cases).
To model the hydrostatic pressure applied on the Se chain in the confined channels, we have studied various compressed and decompressed chains. We do not consider Al, P and O atoms on the wall of AFI channels, simply assuming that Se chains are unaffected by weak interaction with these host atoms. Furthermore, the incommensurate periodicity and huge computation expense definitely prevent us from including the channel template material. In our simulation the compression and decompression are done along the chain axis, while the symmetry remains unchanged. Interestingly the compressed chains give no significant band gap modification. On the other hand, the decompressed chains turn out to have gradually narrowing band gaps. What we observed experimentally is that band gap indeed decreases as the applied pressure increases. Figure 2 shows the optical absorption peaks along different polarizations of the incident light. The polarized optical absorption spectroscopy shows a marked anisotropy, where E||c (polarized along the 6 channel direction) absorption is generally much higher than E ⊥ c (polarized perpendicular to the channel direction). Such anisotropy is the typical absorption spectra of elongated objects, for if the objects are in form of clusters or rings, the dependence on polarization should be weak. This thus provides strong evidence that the Se atoms are in the form of long chains inside the channels.
As we increase the pressure, the absorption shifts conspicuously to the lower energy region for E||c, while there is a very small shift towards higher frequency for E ⊥ c.  This result suggests that the trigonal chain's length increases counter-intuitively with increasing the hydrostatic pressure. We are able to understand this effect in the following discussions. Trigonal chalcogen phases (Se and Te) are known to have unusual negative linear compressibility 16 among some other rare materials. That means the spiral selenium chain diameter contracts and the chain length expands under pressure. Figure 3a shows a total-energy map of Se chain as a function of helical radius r and length lattice constant c.
Using DFT method, we first obtain the equilibrium structure of the helical Se chain located in the center of the plot. Contraction or expansion in all three dimensions gives very high energies in the landscape, and so the anisotropic deformation is favorable under pressure. Away from equilibrium, the Se chain can minimize deformation energy either by elongating in length and at the same time contracting in radius, or it can shorten in length and expand in radius simultaneously. We will show in the following that the chain will choose to elongate in length and shrink in radius in order to be compatible with the hydrostatic external pressure. Once the structural parameters are different from their equilibrium values, there are finite energy gradients along structural coordinates (i.e. ), and when properly normalized by an area, these gradients correspond to a pressure. If we want to deform the Se chain to the non-equilibrium position, a corresponding external pressure tensor has to be applied to the chain. As the experiment applies hydrostatic pressure, the boundary condition is to have equal pressure along radial and longitudinal directions where 0 0.976 r = Å and 0 4.962 c = Å are the chain radius and length under zero pressure. ∂ can be regarded as the pressure along the radial and tangential direction that would be needed to maintain the chain deformation.
The pressure vector components We now discuss the effect of elongation on phonon frequencies. We expect that when the chains are elongated, the weakening of neighboring atomic interaction should lead to reduced phonon frequencies. Such softening effects of tensile strain response are well known in quasi-one-dimensional systems such as carbon nanotubes 17 . Our numerical results indeed found that helical Se chains behave in a similar manner. Figure 4 shows the calculated phonon frequencies as a function of c δ . For each value of c δ , we relax the atoms to their zero force position and we compute the zone-center phonon frequencies by computing and diagonalizing the force matrix. We also computed the phonon frequencies of an isolated Se8 atomic ring (fully relaxed, see inset for atomic geometry) and results are plotted in Fig. 4 for comparison. We first note that the highest two Raman active modes of the equilibrium ( 0) c δ = Se chain are slightly below the highest frequency mode of the 8-atom Se ring. This qualitatively compares very well with the experimental results shown in Fig. 1c. When the c δ is changed, there is a decrease (increase) of phonon frequencies as the chain is elongated (shortened). We note that in Fig. 1b for the measured Raman spectra under high pressure, there is an overall reduction of signal intensity, but the signal strength is skewed towards the low frequency side of the spectra.
We cannot say for sure whether it is a signature of the softening of the Se chain, but it is perhaps fair to say that the results are not inconsistent with the LDA predicted softening The volume compression actually results in contraction of chain radius, longer Se-Se bond length and larger bond angle. This extraordinary picture makes all the experimental and theoretical data fully consistent. Brief mention should be made of the marked directional negative compressibility, which might not be strange in a class of compounds and biological systems 18 . But to the best of our knowledge the single element Se chains response to pressure has not been studied.
In conclusion, we investigated the properties of Se atomic chains under pressure inside one-dimensional nano-channels. We found that inside the nano-channels, just a moderate external pressure can induce quite conspicuous change in structural, electronic, optical and vibrational properties. The confined geometry allows us to investigate the effect of pressure on a single chain. Density functional calculations show that the Se chain should be elongated under pressure, and as a consequence, the band gap should narrow and phonon frequencies should become softer, as observed experimentally. We presented a means of quantum control realized by the application of hydrostatic pressure. This remarkable property may find applications in the deep ocean telecom systems and sensitive pressure sensors.