Structural Optimum Design and Pre-stress Simulation of Fiber Housing for Railgun

Transition metal dichalcogenides (TMDs), as a new emerging family of graphene-like layered materials, have raised tremendous interest owing to their rich physical properties and promising potential applications^[1-5].TMDs share the same molecular structure X-M-X, where M is a transition metal atom (Mo, W, Ti and so on) and X is a chalcogenide atom (S, Se and Te).MX₂ is composed of stacked tri-atomic sheets with metal atom sandwiched between two sheets of chalcogenide atoms, and the intra bond of metal and chalcogenide is much stronger than the inter layer van der Walls force.

Among TMDs, titanium ditelluride (TiTe₂) has raised considerable interest due to its unusual electrical properties, rich intercalation chemistry and wide potential of use.1T-TiTe₂ is confirmed to be quasi-two-dimensional Fermi liquid in detail by high-resolution angle-resolved photoelectron spectroscopy (ARPES) and density-functional band calculations^[6].Anomalous electronic transport properties were found in back-gated field-effect transistors with 1T-TiTe₂ semimetal thin-film channels^[7].1T-TiTe₂ is a semimetal which has a 0.6 eV overlap of its conduction band and valence band^[8].Previous studies have predicted that TiTe₂ undergoes a series of topological phase transition under high pressure^[9].

Pressure has been proven to be a clean and powerful way to tune the structure and electronic orders of materials. Layered material In₂Se₃ undergoes a rhombohedral to cubic structural transition in 15.9-35.6 GPa and shows a decompression driven T_C (onset temperature of superconductivity) enhancement^[10].A pressure-induced Pnma to Cmcm structural transition of SnS is found at about 12.6 GPa^[11].The pressure-induced semiconducting to metallic transition has been reported in MoS₂^[12].Superconductivity has also been introduced successfully in WTe₂^[13], MoTe₂^[14] and ZrTe₅^[15].In the case of TiTe₂, the fact that Ti-3d and Te-5p electrons are very sensitive to external pressure gives us some guidance in understanding the high pressure behavior of TiTe₂.Room-temperature resistivity measurement combined with X-ray diffraction (XRD) patterns at different pressures is important to understand the high pressure properties of TiTe₂, yet there is few experimental report up to date.

Here we report our experimental result of high pressure electrical transport properties and XRD of 1T-TiTe₂ up to 43 GPa. We found that the resistivity at room temperature goes through a series of anomaly changes under high pressure. To better understand these resistivity anomalies, we performed the low-temperature resistance measurement of TiTe₂ at high pressure and observed superconductivity at about 6 GPa.T_C first increases with increasing pressure to 13 GPa, and then increases slowly from 13 GPa to 22 GPa, and keeps constant to the highest pressure 43 GPa achieved in this work. Raman spectra together with XRD patterns show a topological phase transition at around 6 GPa followed by a structure phase transition from trigonal P3m1 to monoclinic C2/m phase.

1. Methods

The single crystalline TiTe₂ sample were purchased from 2D Material company. The sample was crystalized to layered bulk form with 5 mm×5 mm in size and 1 mm in thickness. We used energy dispersive spectrum (EDS) to detect the composition of the sample and the measured atomic ratio was Ti:Te=1:2.001, which was almost the perfect stoichiometry ratio. Powder XRD was employed with Cu K_α line using a PANalytical X-Pert Pro diffractometer. The resistance data collected at room temperature were measured in a symmetric diamond anvil cell while the low-temperature data were collected using the Be-Cu diamond anvil cell. The diamond culet was 300 μm in diameter. The Be-Cu gasket was initially pre-indented to the thickness of 35 μm, and then a hole of 280 μm was drilled in it using a laser drilling system. A mixture of epoxy and cubic boron nitride (cBN) powder was pressed into the hole to form an insulating layer between the electrodes and the Be-Cu gasket. A hole of 120 μm in diameter was re-drilled in the cBN+epoxy gasket as a sample chamber. TiTe₂ sample was cut into the size of 50 μm×50 μm×10 μm. A Pt sheet in thickness of 4 μm was cut in to 200 μm×10 μm and connected to 4 corners of the sample. Silver paste was employed to glue the Pt sheet and the sample. We used silicon oil as the pressure-transmitting medium to ensure a quasi-hydrostatic condition. Several ruby balls were loaded into the sample chamber as pressure calibrant^[16].The van der Pauw four-probes method was employed to eliminate the contact resistance^[17].We performed high pressure XRD at Beamline 12.2.2 of the Advanced Light Source at Lawrence Berkeley National Laboratory. Neon was used as a pressure transmitting medium for synchrotron XRD experiments^[18].The DIOPTAS^[19] program was used for image integrations and the Le Bail method was employed to fit the XRD data using the Fullprof program^[20-21].

2. Results and Discussionss

The XRD pattern of powder sample TiTe₂ is shown in Fig. 1(a).The structure of TiTe₂ is trigonal P3m1 (shown in Fig. 1(b)), the same as reported previously^[22].

Figure  1.  (a) XRD pattern of powder TiTe₂ collected at ambient condition; (b) Trigonal P3m1 structure of TiTe₂(Yellow and blue balls represent Ti and Te atom respectively.)

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Fig. 2 shows the room-temperature resistivity data ρ(T) obtained at various pressure points between 2-43 GPa. During compression, the resistivity of TiTe₂ first decreases sharply, reaching a minimum at around 6 GPa. With further compression, the resistivity increases slightly as pressure increases to about 13 GPa, followed by a relatively fast increase up to 22 GPa. The resistivity of TiTe₂ remains relatively constant as pressure rises to about 43 GPa. In decompression, the resistivity increases with decreasing pressure till 3.2 GPa, which behaves totally differently compared with the compression result. This novel behavior of resistivity of TiTe₂ triggers our interests towards the high pressure measurement of electrical properties. To get a better insight of electronic transport properties of TiTe₂, we performed the low-temperature resistance experiment, and the results are shown in Fig. 3.

Figure  2.  Room-temperature resistivity changes with pressure(The black dots and red circles are compression anddecompression data, respectively. Inset is thesetup of this measurement.)

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Figure  3.  (a) Resistance of TiTe₂ between 2-300 K measured at various pressures; (b) Low-temperature regime of the resistivity of TiTe₂ under high pressure up to 36.8 GPa

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The compression temperature-dependent resistance data R(T) at different pressure points between 3.7-36.8 GPa with a large temperature scale (2-300 K) is shown in Fig. 3(a).The resistance data at 3.7 GPa shows a typical metallic behavior with a linear decrease in resistance as the temperature is lowered. Upon increasing pressure, we observed a drop in resistance at 7.2 GPa, implying a pressure-induced re-entrant superconductivity^[23].The onset of superconductivity presents to the highest pressure of about 36.8 GPa.

Low-temperature (2-10 K) resistivity of TiTe₂ collected at various pressure between 7.2-36.8 GPa is shown in Fig. 3(b).The onset temperature of superconductivity (T_C) at 7.2 GPa is 3.8 K, it goes through a slight increase to about 5.3 K at 13 GPa, and increases continually to 6.3 K at around 22 GPa, above which T_C remains almost constant as the pressure increases to 36.8 GPa. Below we further discuss the evolution of T_C as a function of pressure. It can be seen that T_C is divided into three regions, which agrees well with the room-temperature resistivity measurement.

In order to investigate the possible correlation between atomic structure and electrical transport property, we performed synchrotron XRD experiments under pressures up to 43.4 GPa. The collected XRD patterns are shown in Fig. 4(a).At pressure lower than about 10 GPa, the XRD patterns are refined to trigonal structure of P3m1 space group. It is the same structure as under the ambient pressure. At pressure above 10 GPa, due to the strong preferred orientation of the compressed TiTe₂ sample, the XRD patterns were refined using the Le Bail method.

Figure  4.  (a) Synchrotron XRD patterns of TiTe₂ collected at various pressures up to 43.4 GPa; (b) Representative refinement of patterns collected at 1.0 GPa and (c) 22.4 GPa

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It can be seen that the ambient crystal structure of TiTe₂ (trigonal P3m1 space group) is stable up to about 10.8 GPa. A structure phase transition from P3m1 to C2/m starts at around 13 GPa and completes at about 22 GPa. In the pressure range of 13-22 GPa the structure of TiTe₂ corresponds to a mixture phase of lower-pressure trigonal phase and high-pressure monoclinic phase, while the latter is quite stable till the highest pressure achieved in this work. During decompression, the high pressure phase can survive down to 2.4 GPa. When the pressure is further released to ambient condition, TiTe₂ returns to its trigonal structure. The normalized lattice parameters a/a₀, c/c₀, V/V₀ and the c/a ratio of TiTe₂ up to 15 GPa are plotted in Fig. 5 (in which a₀, c₀, V₀ are the lattice parameters at the first pressure point 1.0 GPa).From a/a₀ and V/V₀ we could know that there is a slightly lattice distortion at about 6 GPa.

Figure  5.  Normalized lattice parameters a/a₀, c/c₀, V/V₀ and c/a ratio of TiTe₂ (A minimum ofthe ratio can be seen at around 6 GPa)

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The c/a ratio drops to a minimum at about 6 GPa, indicating a possible topological phase transition as is reported in BiTeI^[24] and BiTeBr^[25], respectively. It is interesting to mention that in compression procedure at 13 GPa and 22 GPa the room-temperature resistivity and T_C both show anomalous changes. And in decompression, the resistivity increase slowly with decreasing pressure until 3.2 GPa, the structure phase transition correlates well with our electrical transport measurement.Fig. 6 shows the structure phase transition together with the resistivity and superconductivity phase diagram. From Fig. 6 we can see that the anomaly changes of resistivity and T_C at 13 GPa and 22 GPa are attributed to the structure phase transition. The resistivity of the high pressure trigonal phase is larger than that of the low pressure monoclinic phase. At lower pressure of about 6 GPa, the resistivity decreases to a minimum and T_C emerges at the same pressure. No structure phase transition is observed here, indicating there might be an electronic structure phase transition.

Figure  6.  Room temperature resistivity, structural and superconductivity phase diagram of TiTe₂ (The blue andred line represent Run 1 and Run 2 of superconductingphase respectively. The brown line shows the resistivityanomaly and superconductivity emergence at about 6 GPa.)

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To better explicate the resistivity drop and superconducting transition at about 6 GPa, In situ Raman spectroscopy experiments are conducted to clarify its vibration modes changes with different pressure. Raman spectroscopy is commonly used to gain the insight of lattice vibrations of crystalline and has often been used to probe two prominent vibration modes (A_1g and E_g)^[26] of layered material TiTe₂, the results are shown in Fig. 7.

Figure  7.  (a) Raman spectra of TiTe₂ up to 10 GPa (A new peak emerged at a relatively low external pressure of 0.7 GPa); (b) Raman peaks of TiTe₂ (A phonon softening can be seen from 4-10 GPa)

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In Fig. 7(a) we can see that a new Raman peak emerges at a very small external pressure and E_g mode disappears gradually and the new peak dominates the spectra, suggesting an emergence of a new phonon mode. In further compression, this evolution seems completed at around 6 GPa. Above 10 GPa, all Raman peaks broaden and lose the intensity, indicating the metallization of TiTe₂.In Fig. 7(b) we can see the softening of the E_g mode from 4 GPa to 10 GPa. From the Bardeen-Cooper-Schrieffe (BCS) and Mcmillan-Allen-Dynes theories^[27-28] we know that when the electron-phonon coupling (λ) overcomes the Coulomb repulsion, Cooper pairs is formed, resulting in the rise of superconductivity. The electron-phonon coupling formula is shown as

Where N(E_F) is the density of state at Fermi surface, D is the deformation potential, M is the effective mass of the atom and ω_ph is the phonon frequency. So the superconductivity phase transition at about 6 GPa can be understood in such way:new Raman mode and the phonon softening have increased the intensity of electron phonon coupling, which results in the occurrence of the superconductivity phase transition.

3. Conclusions

We investigated the room-temperature resistivity of TiTe₂ at high pressure up to 43 GPa, and observed the resistivity anomalies at 6, 13 and 22 GPa during compression. Low-temperature resistance measurement was employed to better understand the electrical transport properties of TiTe₂, and superconductivity was observed successfully. The superconducting transition temperature shows similar behavior as the resistivity. High pressure XRD was employed to investigate the correlation between structural properties and electrical transport properties. The structure phase transition of TiTe₂ starts at about 13 GPa and completes at about 22 GPa. The lattice parameter c/a ratio shows a possible topological electronic structure phase transition, which can explain the resistivity anomaly at around 6 GPa. This result correlates well with our electrical transport properties measurement. Raman spectra was conducted to better clarify the superconductivity phase transition and the resistivity anomaly at about 6 GPa. The emerging of new Raman peak and phonon softening in E_g mode may have increased the intensity of electron phonon coupling, which results in the occurrence of superconductivity in 1T-TiTe₂.