Unexpected Piezoresistive Effect, Room‐Temperature Ferromagnetism, and Thermal Stability of 2D β‐CuI Crystals in Reduced Graphene Oxide Membrane

2D materials are promising nanomaterials for future applications due to their predominant quantum effects and unique properties in optics, electrics, magnetics, and mechanics. However, explorations in unique properties and potential applications of novel 2D materials have been hampered by synthesis and their stability under ambient conditions. Recently, in the graphene, 2D β‐CuI is observed experimentally under ambient conditions. Here, it is shown that this 2D β‐CuI@graphene possesses unexpected piezoresistive effect and room‐temperature ferromagnetism. Moreover, this 2D β‐CuI crystal is likely to be stable in a wide range of temperature, that is, below 900 K. Theoretical studies reveal that the unexpected piezoresistive effect is mainly attributable to the convergence of the electrons on Cu and I atoms to the Fermi level with increasing strain. There is a magnetic moment that is ≈0.97 μB on the edge of β‐CuI nanocrystal created by an iodine vacancy, which is considered the origin of such strong room‐temperature ferromagnetism. Clearly, the 2D β‐CuI@graphene provides a promising nanomaterial in the nano‐sensors with low power consumption pressure and magnetic nano‐devices with a size down to atomic scale. The discovery in the present work will evoke various new 2D nanomaterials with novel properties in nanotechnology, biotechnology, sensor materials, and technologies.


Introduction
2D materials exhibit many peculiar properties due to the confinement of carrier migration and heat diffusion in 2D planes, [1] which have shown potential in electric, [2] magnetic, [3,4] optical, [5] chemical, and biomedical applications. [6,7] Studying the synthesis of novel 2D materials and exploring their new physical and chemical properties in the 2D limit are essential both for new potentials and for understanding the origin of their promising properties. However, compared with thousands of 2D materials that can be potentially obtained in theory, [8] only a few dozen 2D materials have been successfully achieved experimentally, [9][10][11] due to the fact that most of 2D materials are extremely unstable under ambient conditions. [12] Recently, in the graphene, the 2D β-CuI crystal was synthesized under ambient conditions, whose atomic structure was observed experimentally, [13] although it was theoretically predicted to 2D materials are promising nanomaterials for future applications due to their predominant quantum effects and unique properties in optics, electrics, magnetics, and mechanics. However, explorations in unique properties and potential applications of novel 2D materials have been hampered by synthesis and their stability under ambient conditions. Recently, in the graphene, 2D β-CuI is observed experimentally under ambient conditions. Here, it is shown that this 2D β-CuI@graphene possesses unexpected piezoresistive effect and room-temperature ferromagnetism. Moreover, this 2D β-CuI crystal is likely to be stable in a wide range of temperature, that is, below 900 K. Theoretical studies reveal that the unexpected piezoresistive effect is mainly attributable to the convergence of the electrons on Cu and I atoms to the Fermi level with increasing strain. There is a magnetic moment that is ≈0.97 μ B on the edge of β-CuI nanocrystal created by an iodine vacancy, which is considered the origin of such strong roomtemperature ferromagnetism. Clearly, the 2D β-CuI@graphene provides a promising nanomaterial in the nano-sensors with low power consumption pressure and magnetic nano-devices with a size down to atomic scale. The discovery in the present work will evoke various new 2D nanomaterials with novel properties in nanotechnology, biotechnology, sensor materials, and technologies.
be stable only in an extremely narrow temperature range of 645-675 K. [14] Recently, 2D Na 2 Cl and Na 3 Cl crystals with abnormal stoichiometries on reduced graphene oxide (rGO) membranes under ambient conditions were reported. [11] The discovery of novel 2D materials and their unique properties, which are evoked by 2D graphene-based materials (e.g., graphene or rGO membranes) with stable and restricted spatial π-conjugated systems, represents a step forward in the understanding of 2D materials and interface interaction. Successively, novel 2D CaCl crystals with monovalent calcium ions, [10] graphitic-like hexagonal phase of alkali halides, [15] and single layer of β-CuI crystals under ambient conditions [13] have been synthesized and explored based on 2D graphene-based materials. Moreover, the novel 2D CaCl crystals exhibit metallicity, room-temperature ferromagnetism, heterojunction, and piezoelectricity-like property. [10] Clearly, on the graphene, not only are there novel 2D structures, but these new structures usually exhibit distinguish properties.
Here, we report unexpected piezoresistive effect and roomtemperature ferromagnetism of the 2D β-CuI crystal in rGO membrane. In particular, this piezoresistive effect has been found for the first time on novel crystals in graphene, indicating that these new crystals in graphene have a great promising application. In addition, this 2D β-CuI crystal has abnormal thermodynamic quantities relative to that of normal CuI, and is stable within a wide range of temperature, that is, below 900 K.

Synthesis and Characterizations of 2D β-CuI Crystals
2D β-CuI crystals were synthesized by an improving wet chemical method (see Experimental Section). Based on analysis of X-ray photoelectron spectrum (XPS) and scanning electron microscope (SEM), the mass content of Cu atoms in the Cu-I@rGO membrane was ≈2.94% (See Figure 1f and Figures S1 and S2, Supporting Information). Transmission electron microscopy (TEM) image shows two stable polycrystal diffraction patterns (Figure 1b) within random ultra-thin areas, Figure 1. 2D β-CuI crystals in rGO membrane under ambient conditions. a) Stable crystal structure of β-CuI encapsulated between graphene layers from DFT calculations. b) Low-resolution TEM image of the Cu-I@rGO membranes. The selected area diffraction (SAED) pattern of the Cu-I@rGO is shown in the inset. The ( 1100) reflections of the graphene sheets and the β-CuI crystals are indicated by the emerald and red lines, respectively. c) High-resolution TEM of β-CuI nanocrystals in rGO membrane. Nanocrystals are marked with yellow dashed lines. d) FFT of the entire bright-field image ( Figure S3, Supporting Information). It is shown in the inset that the orientations of the β-CuI crystals match closely with the encapsulating graphene lattice directions with a 30° rotational translation. e) X-ray diffraction (XRD) spectra of Cu-I@rGO membranes, rGO membranes, and background (sample stage); theoretical spectra of β-CuI@rGO through VESTA; [17] and the standard PDF cards of the β-CuI, PDF# 45-1316. f) X-ray photoelectron spectra (XPS) of Cu-I@rGO membranes. www.advelectronicmat.de which correspond to the (1100) reflections of the β-CuI and graphene crystals, respectively. The smaller diffraction ring indicates that the multiple-orientation β-CuI crystals widely distribute in the rGO membranes. From the high-resolution TEM images (Figure 1c and Figure S3, Supporting Information), we observed single-orientated crystal of β-CuI, which has an in-plane lattice spacing of ≈3.63 Å. Fast Fourier transform (FFT) [16] of the high-resolution image shows that the CuI crystal yielded a hexagonal lattice with six first-order maxima points (β-CuI) at ≈2.75 nm −1 , consistent with the (1100) reflections in Figure 1b. This structure of β-CuI exhibits P-3m1 symmetry (space group: 164), with a lattice constant of ≈4.19 Å. In addition, the orientations of the β-CuI crystals match closely with the encapsulating graphene lattice directions with a 30° rotational translation as shown in Figure 1d, indicating that there is a perfect lattice match between the 2D β-CuI crystals and the graphene crystals. Moreover, the FFT comparison between the β-CuI region and the rGO background region on high-resolution images indicates that the second-order diffraction point of single crystal β-CuI is located on the first-order polycrystalline diffraction ring of graphene, as shown in Figure S4, Supporting Information.
After the 434 K drying process in air, these 2D β-CuI crystals still extensively existed in rGO membranes and were directly observed by TEM at 200 kV high-tension (see Figure S12, Supporting Information), indicating that the stability of the 2D β-CuI crystals was inextricably linked with the perfect lattice match of it and graphene crystals. Moreover, we performed X-ray absorption spectroscopy (XAS) measurements to illustrate particular CuI bonding in Cu-I@rGO membrane. The Cu L 3 XAS spectrum of the Cu-I@rGO clearly shows the characteristic features of CuI, a main absorption at around 936 eV and a shoulder close to 935 eV (as shown in Figure S5, Supporting Information). The results of our multiple tests are consistent with those in ref. [13] which allows us to clearly identify the CuI compound. Although CuO (≈931 eV) and Cu 2 O (≈933 eV) peaks appear on Cu L 3 XAS spectrum of the Cu-I@rGO, there are no polycrystalline diffraction rings or spots of other crystals except polycrystalline diffraction rings of graphene and β-CuI on sample. This indicates that there is no oxide of copper in the sample, or that the content of oxide of copper is extremely low relative to CuI.
The structure of the β-CuI crystals was further analyzed using X-ray diffraction (XRD). As shown in Figure 1e, compared with pristine rGO membrane, three Bragg peaks of the Cu-I@rGO membrane were clearly enhanced at 8.9°, 24.0°, and 49.4°, respectively. Especially for the Bragg peak at 24.0°, it not only corresponds to the interlayer spacing (≈3.7 Å) of rGO membranes, [18] but also is close to the value of 2θ for the (002 and 010) crystal plane of β-phase CuI, according to our CP2K [19] and VESTA [17] simulation results (see Experimental Section) as well as the standard PDF cards of the β-CuI crystals. Simultaneously, the Bragg peak at 49.4° of the Cu-I@rGO was also close to the value of 2θ of secondary diffraction peak for (002 and 010) crystal plane of β-phase CuI crystal. While for the Bragg peak at 8.9°, it corresponds to the spacing of ≈10.01 Å for rGO membrane with encapsulated 2D β-CuI crystals of single layer (2D β-CuI crystals). Thus, it confirmed statistically the extensive existence of β-CuI crystals in rGO membrane based on such a large increase in the peak intensities of 8.9°.

Thermal Stability of β-CuI@graphene
The normal β-CuI is known to be stable at an extremely narrow temperature range of 645-675 K. [14] However, the 2D β-CuI confined between layers of graphene in this work can be stable at room temperature. In order to explore the effect of high temperature on its crystal structure, the Cu-I@rGO membranes were analyzed by TEM after they were heated at various temperatures (500, 700, and 900 K) for 2 h under argon environment. There was still a large amount of β-CuI in the rGO membranes even treated by 900 K, showing that the heat treatment at 900 K did not destroy the crystal structure of β-CuI in rGO membrane, as shown in Figure 2a,b. In fact, the normal CuI has different crystal structures from room temperature to the melting point, namely α-CuI structure, β-CuI phase, and γ-CuI phase. [20] It also presents superionic and liquid disordered phases at high temperature. [20] Therefore, the normal CuI is often considered as a model system for studying phase transitions.
To better understand the structure and phase transitions of the β-CuI@graphene at high temperature, we have performed extensive ab initio molecular dynamics (AIMD) simulations at the temperature range of 300-900 K. As shown in Figure 2c, the layer spacing of graphene in the 2D β-CuI@graphene stabilized at the range of 11-12 Å and showed a weak increase with increasing temperature at the range of 300-900 K, indicating that the sandwich structure of graphene/β-CuI/graphene is stable. In addition, radius distribution functions between Cu and I are shown in Figure 2d, an appreciable probability density is observed between the first two peaks with the increase of temperature, implying the ease of Cu diffusion. Especially at 900 K, there is only one coordination peak between Cu and Cu in Figure 2d, which indicates the presence of a large degree of increasing disorder in the Cu atom distribution, with a diffusion as liquid-like Cu-Ion.
Superionic CuI is usually classified as one of three phases in terms of the diffusion coefficient of the Cu and I atoms. [20] The three phases of CuI are defined as follows: the solid phase (D Cu = 0 and D I = 0), the superionic phase (D Cu > 0 and D I = 0), and the fluid phase (D Cu > 0 and D I > 0). Diffusion coefficients (D) were calculated for the Cu and I atoms from their mean-square displacements (MSDs) in Figure 2e,f (details in Table S1, Supporting Information). Surprisingly, the β-CuI in the 2D β-CuI@graphene presents a solid phase at 300 and 500 K, a superionic phase at 700 and 900 K, which indicates that it has abnormal thermodynamic quantities relative to that of the normal CuI. Furthermore, the superionic state of the β-CuI at 900 K is not consistent with previous findings that the normal CuI appears as a liquid phase. [20] Thus, there is a possible state different from this 2D β-CuI crystal at higher temperature, and there is a phase transition from this state to the 2D β-CuI crystal during the annealing from a higher temperature to the room temperature. These finds showed that graphene plays an important role in the high temperature stability and the reversible phase transition of the β-CuI in β-CuI@graphene. www.advelectronicmat.de

Piezoresistive Effect
The pressure-sensing based on piezoresistive effect attracts more attention from scientists and technicians in the development of electronic skins and novel wearable devices of health monitoring. [21,22] Tremendous effort is devoted toward improving their stability and sensitivity. We note that the β-phase of CuI crystal was previously only stable at an extremely narrow temperature range of 645-675 K. [14] The crystals that are extremely unstable under ambient conditions potentially exhibit sensitivity to the environment, such as compressive strain.
In order to investigate the piezoresistive effect of 2D β-CuI@graphene, the Cu-I@rGO membrane was cut into a rectangle of 3.0 cm × 1.0 cm to fabricate a device of pressure sensor, as depicted in Figure 3a and Figure S6b, Supporting Information (details in Experimental Section and Supporting Information). First, the electrical resistivity of Cu-I@rGO and rGO membrane was experimentally measured. Cu-I@rGO membrane has better conductivity than rGO membrane (see Figure S7, Supporting Information). Next, a periodic mechanical pressure was performed on the device through a self-made actuator. The dynamic current response to pressure was monitored by a synchronous I-t measurement system in the electrochemical workstation (DH7000, China). As shown in Figure 3b, the dynamic current changed sensitively under actions of on/off cycles of compressive strain caused by a low pressure of 27.8 Pa, where ΔI represents the current change before and after applying pressure at a voltage of 1.0 V, and I 0 represents the initial current without pressure. The electric current change was highly reversible in Figure 3b, which exhibited good stability of Cu-I@rGO device. In contrast, the pristine rGO membrane device had a negligible electric current response. By enlarging the detail of the electric current response of Cu-I@rGO device as shown in Figure 3c, its response time (rise time) and recovery time (fall time) were about 78 and 90 ms under the low pressure. Furthermore, under applied pressures ranging from 16.7 to 74.0 Pa, the electric current changes and response-recovery time in the device were observed (Figure 3d), which showed similar fast and enhanced responses. It is superior to most of advanced strain sensors, such as the latest highly sensitive strain sensors with response time and recovery time of ≈490 and ≈500 ms. [23] In order to further demonstrate the performance of the Cu-I@rGO, we derived the pressure sensitivity S p , defined as (ΔR/R 0 )/P, where ΔR/R 0 is the resistance variation and P is the applied pressure. A good linear relationship between ΔR/R 0 and P is shown in Figure 3e, and its correlation coefficient was 0.96. From the linear fitting, at the low-pressure range from 16.7 to 74.0 Pa, the pressure sensitivity S p is ≈0.184 kPa −1 , which is higher than that of piezoresistive devices based on graphene, such as pressure sensors based on graphene www.advelectronicmat.de hybrid (0.032 kPa −1 ) [24] and plasma-doping of graphene sheet (0.045 kPa −1 ). [25] In addition, under a low applied voltage [26] (such as 0.01 V in Figure 3e), the dynamic current still changed sensitively under actions of on/off cycles of compressive strain at 47.6 Pa. These results indicated an excellent piezoresistive performance of β-CuI@rGO, showing the potential applications of the novel 2D crystals in design of a low power consumption, atomic size, and ultra-fast response nano-pressure sensor.
To clearly understand the conformation mechanism of the 2D β-CuI@graphene, we first constructed four possible models that β-CuI single layers were sandwiched between two graphene sheets (β-CuI@graphene) based on our TEM and XRD results. Their optimized structures and corresponding total energies were obtained by DFT calculations, as shown in Figure S8 and Table S2, Supporting Information. The most stable model of the β-CuI@graphene with the lowest-energy is the structure with an AA stacking of graphene sheets, and has a lattice constant of ≈4.27 Å, which is consistent with our TEM results.
In order to quantitatively investigate the deformation behavior, the relative strain ΔS on the model is defined as ΔS = ∆h h , in which h is the height of β-CuI@graphene. Although we set the strain from 1% to 10%, the sandwiched structures with different relative strain (ΔS) were also optimized and maintained very well during the compression process. The single layer of β-CuI crystal adapts to the decrease in z-direction mainly through the change in bond angles (≈7.0%), while the bond length (d CuI ) remains relative stable (≈2.5%) at the compression of 10% (see Figure 4b). Around the Fermi level, the energy band structures of β-CuI@graphene gradually broaden with increasing strains (Figure 4c), which was derived by DFT calculations. It implies that more electrons converge to this vicinity. These electrons converged to the Fermi level are mainly contributed by Cu and I atoms, as shown in Figure 4d. Such aggregation of these electrons effectively improves the electrical conductivity, resulting in a significant increase of the relative electrical conductivity in z-direction during whole considered chemical potential range at 300 K (Figure 4e). When the strain reached 5%, the electrical conductivity σ was about five times the electrical conductivity of pristine model σ 0 at a small chemical potential of nearby 0 eV (see Figure S9b, Supporting Information). To better compare with the experimental results, the resistivity variation Δρ/ρ 0 versus strain was calculated at a chemical potential of 20 meV and 300 K (Figure 4f). The Δρ/ρ 0 decreases with increasing strains, with a good linear relationship with strains at a low strain range, which agrees well with the experiment results (Figure 3e). Our theoretical results indicate that the single layer of β-CuI@graphene has the corresponding electrical conductivity, good stability, and flexibility during the compression process, suggesting an outstanding piezoresistive effect.

Room-Temperature Ferromagnetism
An unexpected room-temperature ferromagnetism of the Cu-I@rGO membrane was also observed experimentally. Figure 5a,b shows that the saturation magnetization (M s ) of the Cu-I@rGO membranes was ≈0.095 emu g −1 at 300 K, whereas the M s of the pristine rGO membrane was ≈0.027 emu g −1 , showing a ≈350% enhancement in magnetism. Taking into account the mass content of only ≈2.94 wt% for Cu atoms in the rGO membrane (as shown Figure S2, Supporting Information), an estimated M s for β-CuI crystals (excluded the contribution from the pristine rGO membranes) reached up to ≈0.77 emu g −1 , with a corresponding averaged magnetic moment of ≈0.026 µ B per one CuI molecule, demonstrating its room-temperature ferromagnetism.
The existence of such room-temperature ferromagnetism of the β-CuI crystals is surprising, as there is no report on magnetic properties in the existing CuI crystals due to the absence of net spin polarization. It was also confirmed by our DFT calculations on the β-CuI@graphene model with periodic configuration ( Figure S10, Supporting Information). However, from our high-resolution TEM images (Figure 1c), there are many 2D β-CuI nanocrystals with a lateral size of several nanometers. These nanocrystals are naturally rich in defects at the edge, which is the potential origin of the ferromagnetism. [10,27,28] We constructed two atomic models of β-CuI nanocrystal (a diameter of ≈3 nm) with and without atomic vacancy. For the optimized structure without vacancy (Figure 5c), the Cu atoms on the edge approaches the center so that all the atoms in the system still obey the "octet rule," where each Cu atom is bonded to three I atoms with valence electron configuration of 3d 10 and each I atom bonded to three Cu atoms. Therefore, the β-CuI nanocrystal has a nonmagnetic ground state (M tot = 0 μ B ). Considering that the edge of the nanocrystal is terminated with I atoms after the reconstruction, vacancies of I atoms at the edge are likely to form during the growth or postgrowth processes. Therefore, the nanocrystal with an I vacancy was built by removing one I atom on the edge (Figure 5d). Interestingly, the Cu atoms near this vacancy spontaneously reconstructed with the neighboring I atoms to form I-Cu-I, which breaks the "octet rule" and introduces new spin centers into the system, resulting in an intrinsic magnetic ground state with spin moment M tot = 0.97 μ B . Taking into account the averaged magnetic moment of ≈0.026 µ B in our experiments, an estimated probability of this vacancy of I atom in nanocrystals is ≈2.68%, that is, a nanocrystal composed of ≈40 Cu-I molecules has one magnetic vacancy. Based on above discussion, the size of β-CuI nanocrystal with one magnetic vacancy is consistent with the size of 2D β-CuI crystals with diameter of 3-10 nm in TEM images (see Figure 1c). The existence of magnetic moment on the edge of β-CuI nanocrystal created by vacancy indicates that it could be a potential candidate for next generation spintronics devices. [29]

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Finally, β-CuI likely is randomly distributed in the rGO membrane, according to the preparation method that Cu +2 distributed in the graphene oxide (GO) membrane through vacuum filtration were reduced by HI to form β-CuI. Moreover, the piezoresistive effect and room-temperature ferromagnetism of Cu-I@rGO based on β-CuI should be affected by the content and distribution of β-CuI. The results of TEM and XAS spectra also indicated that the distribution of β-CuI in rGO membrane is not uniform, and the crystal size is at the nanometer level. At the present, the distribution and the content of β-CuI within the same layer and between layers in rGO membrane still need to be further explored. Therefore, a lot of work needs to be completed in the future to control the piezoresistive effect and room-temperature ferromagnetism of β-CuI@rGO by controlling content and size of β-CuI.

Conclusions
In this work, we experimentally observed unexpected piezoresistive effect and room-temperature ferromagnetism of 2D β-CuI in rGO membrane. Furthermore, the pressure sensor based on the 2D β-CuI in rGO membrane exhibited a sensitivity as high as ≈0.184 kPa −1 within the low-pressure range from 16.7 to 74.0 Pa, short response time (78 ms), and ultralow operating voltage (0.01 V). Theoretical studies reveal that the mechanism of piezoresistive effect of the 2D β-CuI in graphene suggests that the short response-recovery time of piezoresistive effect is inextricably linked with sensitive electronic structure and flexibility of 2D single layer nanocrystals. The spin polarized calculation reveals that the strong ferromagnetism is mainly due to the iodine vacancies at the edge of crystals, on which there has a large magnetic moment of 0.97 μ B . In addition, the 2D β-CuI crystals can be extensive and stable under ambient conditions, which are evoked by the stable and restricted spatial π-conjugated systems of graphene layers.
This 2D β-CuI in the Cu-I@rGO probably keeps stable in the temperature range below 900 K. The TEM works at the room temperature, and the Cu-I@rGO sample was observed by TEM after annealing from 900 K to room temperature. Thus, there is a possible state different from this 2D β-CuI crystal at higher temperature, and there is a phase transition from this state to 2D β-CuI crystal during the annealing from a higher temperature to the room temperature. Interestingly, AIMD simulations show that the β-CuI presents a superionic phase at 700 and 900 K, which is also different from the previous theoretical prediction.
Clearly, the 2D β-CuI crystal in rGO membrane provides a promising nanomaterial in the nano-sensors with low power consumption and magnetic nano-devices with a size down to atomic scale. These properties and behaviors of the 2D β-CuI crystals will also highly expand the applications for the graphene encapsulation. Moreover, the discovery in the present work will evoke various new 2D nanomaterials with novel properties in nanotechnology, biotechnology, sensor materials, and technologies.

Experimental Section
Preparation of Cu-I@rGO Membranes: The 2D β-CuI between restricted graphene layers were synthesized by a modified wet chemical method described in the previous report. [13] The GO sheets dispersed in water were prepared from graphite powder via a modified Hummers' method. [18] 5 mg mL −1 of raw GO solution was diluted to 0.75 mg mL −1 , and then 10 mL diluted GO solution was vacuum filtered and a GO membrane was formed on a polycarbonate membrane with Magnetization hysteresis loops of the rGO membranes and the Cu-I@rGO membranes were measured at 300 K. The inset shows a low-field zoom of the curves from the main panel where excess moments and coercive force are seen clearly. The magnetic field is set to be perpendicular to the sample surface. b) The M s with error bar of the Cu-I@rGO membranes and the pristine rGO membrane at 300 K. c) Atomic configuration of β-CuI nanocrystal (left) and its spin density plot after optimization of structure (right). d) Atomic configuration of β-CuI nanocrystal with one iodine vacancy on the edge of the nanocrystal (left) and its spin density plot after optimization of structure (right). Initial structure for I vacancy on the edge was created by removing the I atom in the red circle. The spin density plots the spin up density subtracted by the spin down one with an iso-surface of 0.00017 atomic units.

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pore diameter of 0.8 µm. Then, 2 mL cooled solution of CuCl 2 at a concentration of 0.075 mol L −1 was added. When the salt solution was drained, 1 mL of HI solution was added to reduce the GO membrane for 12 h, and then a large amount of ethanol was added to rinse. Finally, the film was peeled off from the polycarbonate film and dried at 343 K for 12 h. Based on XRD results that Bragg peak of the Cu-I@rGO membrane was clearly enhanced at 8.9° as shown in Figure S11d, Supporting Information, the content of 2D β-CuI crystal could increase significantly by reducing the GO concentration. Further drying at 434 K, there was no effect on the structure of the β-CuI crystals, as shown in Figure S12, Supporting Information. Details of the reagents and materials involved were as follows: cupric chloride dihydrate (Aladdin, 99.999% metals basis), hydriodic acid (Acros Organics, aqueous solution, 57 c), polycarbonate membrane (Millipore, pore diameter 0.8 µm).
Characterizations: XRD spectra of pristine rGO membranes and Cu-I@rGO membranes were measured by a Bruker D8 Advance X-ray diffractometer equipped with a Cu anode X-ray tube. High-resolution TEM micrographs and selected-area electron diffraction (SAED) images were acquired at room temperature by the FEI F200C TEM operating at 200 kV. SAED images were taken with a ≈350 nm diameter selected-area aperture. The exposure time was varied between 0.5 and 2 s and binning 2 was adopted for acquiring the images. All the high-resolution images were only taken once since the structural features of the crystals were not observable in the images after the second electron radiation, indicating the structures of the β-CuI crystals were severely damaged after the first electron radiation. XPS analysis was performed with a Thermo Scientific K-Alpha X-ray photoelectron spectrometer. The magnetic properties of the dried Cu-I@rGO membranes and pristine rGO membranes with respect to temperature and field were measured using a quantum design SQUID/MPMS (MPMS3) magnetometer. SEM (Thermo Fisher Scientific, Phenom Pharos; Hitachi, SU8010) was used to analyze the topography, elements, and thickness of samples. XAS measurements of Cu-I@rGO membranes were performed using the BL08U1A beamline at the Shanghai Synchrotron Radiation Facility.
Electrical Measurements: The Cu-I@rGO membrane prepared by extraction filtration and pure rGO membrane were cut into a rectangle of 3.0 cm × 1.0 cm, and they were connected by two Cu foil electrodes using silver conductive paint and fixed by two flexible plastic plates (as shown in Figure S6b, Supporting Information). The electrical signals of the assembled sensors were recorded by an electrochemical workstation (DH7000, China) under the mode of i-t with a constant voltage of 1, 0.2, or 0.01 V.
The electrical conductivity of Cu-I@rGO membranes and rGO membranes measured by using electrochemical workstation with two electrodes connecting with the up and down surfaces (1 cm × 1 cm) of the dried rGO and Cu-I@rGO membranes, respectively. The average and standard deviation of electrical resistivity were calculated from current-voltage curves.
The electrical resistivity ρ was approximately calculated as: where R was the electrical resistance, S was the contact area of copper electrode (1 cm × 1 cm), and L was thickness of membrane between two copper electrodes (6 µm). Theoretical Computation Methods: Main first principles calculations based on DFT were performed with the Vienna ab initio Simulation Package code. [30] The projector augmented wave pseudopotentials were applied. In order to investigate the structural properties, the generalized gradient approximation of the Perdew-Burke-Ernzerhof (PBE) [31] was used to treat the exchange-correlation interaction between electrons. A plane-wave basis set with a kinetic-energy cut-off of 520 eV was used to expand the wave function of valence electrons (2s 2 p 2 for C, 5s 2 p 5 for I, and 3d 10 4s 1 for Cu). A 15 Å vacuum space between sheets was set to prevent the interaction between two layers. The structural relaxations were performed by computing the Hellmann-Feynman forces within total energy and force convergences of 10 −5 eV and 10 −3 eV Å −1 , respectively. The van der Waals interactions were introduced in the calculating, which was described by a correction through the Grimme's zero damping D-3 method. [32] Gamma-centered Monkhorst-Pack grids of 12 × 12 × 1 was used for the model.
Before the XRD spectrum of β-CuI@graphene was simulated, its structure optimization loaded with an external pressure of 1 bar had been carried out using the freely available program package CP2K/ Quickstep. [33] The density functional implementation in Quickstep was based on a hybrid Gaussian plane wave scheme. Orbitals were described by an atom centered Gaussian-type basis set, and a plane wave basis set with a cutoff set to 420 Ry was used to re-expand the electron density in the reciprocal space. PBE functional with Grimme's dispersion correction was used. The core electrons were represented by analytic Goedecker-Teter-Hutter (GTH) pseudopotentials. [34] For valence electrons (2s, 2p for C, 3d, 4s for Cu, and 5s, 5p for I), the Gaussian basis sets were double-ζ basis functions with one set of polarization functions (DZVP-MOLOPT-SR-GTH). [35] All Born−Oppenheimer molecular dynamics simulations were carried out with CP2K simulation package for more than 30 ps at a time step of 1 fs, which was performed on super cell of β-CuI@graphene, as shown in Figure S13, Supporting Information. At the start of the AIMD simulations, the 2D β-CuI@graphene samples were assigned an initial temperature of 300 K according to a Boltzmann distribution. The samples were then heated up to the desired temperature by annealing velocities (1.001). For all the MD trajectories, the initial 5 ps (5000 steps) was regarded as the equilibration period. Canonical (NVT) ensemble and Nose-Hoover thermostats were set to 300, 500, 700, and 900 K, respectively. Note that due to the large size of the supercells, only Γ point was used in all calculations, and an energy convergence of 3 × 10 −6 eV was chosen. The diffusion coefficient (D) and average MSD were defined as: where N was the total number of Cu or I ions in the system and d equaled the dimension of the lattice on which diffusion takes place. ( ) r t i was the displacement of the i-th Cu or I ion at time t. The average MSD was also an ensemble average over time t 0 . Therefore, D was obtained by MSD's linear slope divided by 2d (here d = 3). Electronic Property of the β-CuI@graphene: The electronic properties of the β-CuI@graphene were studied by calculating its band structure and density of states. As shown in Figure S14a, Supporting Information, the model exhibited distinct metallic property. To explore the interaction of CuI with graphene, the difference in charge density (Δρ) was also calculated, which was defined as: where ρ total , ρ CaCl , and ρ graphene were the density of the whole system, β-CuI module, and graphene layers, respectively. As shown in Figure S14c, Supporting Information, the calculated result showed that there was a significant charge transfer between I atoms and graphene, indicating significant ions-π interaction between I atoms and the aromatic rings in graphene. Piezoresistive Effect of the β-CuI@graphene: To simulate the strain perpendicular to the β-CuI@graphene plane induced by external stress during compressing process, the graphene layer was moved along the z-direction from its original equilibrium position. As shown in Figure 4a, the relative strain ΔS could be defined as: where Δh was the displacement of graphene layer in z-direction from its original equilibrium position, and h was the thickness of the model calculated as the distance between two graphene planes.
To evaluate the stability of the β-CuI@graphene under different strains, the cohesive energy was calculated, which was derived from the equation: where E (C) , E (Cu) , E (I) , and E (total) were the energies of a C atom, a Cu atom, an I atom, and one β-CuI@graphene unit, respectively. The negative cohesive energy of β-CuI@ graphene indicated that the structure was stable (see Figure S9a, Supporting Information). After obtaining the E-k relation from DFT calculations under strains, the relative electrical conductivity σ/τ at chemical potential μ was calculated by using the BoltzTraP code based on Boltzmann transport theory. [36] The constant relaxation time approximation was used in this code. [37] The electrical resistivity ρ was calculated by ρ = 1/σ, and the resistivity variation was defined as (ρ − ρ 0 )/ρ 0 , where ρ 0 was the resistivity of pristine model without strain. Figure S9b, Supporting Information, shows chemical potential μ dependence of electrical conductivity ratio σ/σ 0 at 300 K. The electrical conductivity ratio σ/σ 0 increased dramatically with the increasing strains during whole range of chemical potential. On the contrary, the electrical resistivity decreased sharply with increasing strains, demonstrating the outstanding piezoresistive effect in β-CuI@rGO.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.