Analytical Study of Nanomaterials Under High Pressure

Introduction

Recently the study of nanomaterials are achieving more attention due to its surprising properties such as size, shape, morphology, compressible properties, and their structural properties changed with pressure, volume, and temperature ^{1, 2}. So its extraordinary properties mechanical, thermal and electronic properties make it more relievable for developing several multi functional applications ³. Synthesized and electrochemical anodizations experimental were studied under high pressure up to 31 GPa for Anatase titanium dioxide (TiO₂) nanotubes by Raman spectroscopy and synchrotron X-ray diffraction ⁴ and study of a synchrotron X-ray diffraction presented pressure-induced changes in nanocrystalline anatase (30-40 nm) to 35 GPa ⁵.

A simple theory predicts for several nanomaterials on the effect of pressure for volume expansion ⁶ and high-pressure behavior of Ni-filled and Fe-filled MWCNTs examined up to 27 GPa and 19 GPa with help of synchrotron-based angle-dispersive X-ray diffraction ⁷. A equation of state studied for several namomaterials such as metals Ni (20 nm), α-Fe (nanotubes), Cu (80 nm) and Ag (55nm), semiconductors Ge (49 nm), Si, CdSe (rock-salt phase), MgO (20 nm) and ZnO, and carbon nanotube (CNT) in term pressure related with volume and their theoretical data agreement between experimental data ⁸. Plasma Enhanced Chemical Vapor Deposition (PECVD) and annealing technique are used in Crystal size synthesized of nanocrystal 3C-SiC (than 30 nm) ⁹. H.A. Ludwig et al., investigated X-ray experiments under high pressure up to 6 GPa at 300°K for Rb₃C₆₀ using a diamond anvil cell and angular dispersive X-ray scattering ¹⁰. 

Method of analysis

These equations of state (EOS) are determining the effect of pressure on nanomaterials, where P is a function of relative change in Volume

as several equations of states (EOS) written as follows:

Rohit Gupta EOS written as ¹¹,

Mie–Gruneisen EOS written as ¹²,

Tait EOS written as ¹³,

Murnaghan EOS written as ¹⁴,

Birch–Murnaghan EOS written as ¹⁵,

Vinet EOS written as ¹⁶,

Kholiya and Chandra EOS written as ¹⁷,

Kalita and Mariotto et al. ²⁴ examined experimental data for several nanomaterial compounds but here our interest only few material such as, TiO₂ (anatase), Ni (20 nm), CdSe (rock salt phase), AlN (Hexagonal), 3C-SiC (30 nm) and Rb₃C₆₀. The given experimental data is compared with several other EOSs such as, Rohit Gupta EOS, Mie–Gruneisen EOS, Tait EOS, Murnaghan EOS, Birch–Murnaghan EOS, Vinet EOS and Kholiya-Chandra EOS. Kholiya and Chandra ¹⁷ recently performed computational study on high-pressure compression behaviour of nanomaterials and provided good agreement with experimental data at high pressure also verified by average deviations.

Table 1: Shows values of B_0, B’_0, and B”₀ and average percentage deviations from Eq. (1).

Results and Discussions

Second order bulk modulus (B”₀) are calculated for TiO₂ (anatase), Ni (20 nm), CdSe (rock salt phase), AlN (Hexagonal), 3C-SiC (30 nm) and Rb₃C₆₀ nanomaterials and finding pressure for various points with respect to volume for several nanomaterial equation of states like, Rohit Gupta EOS, Mie–Gruneisen EOS, Tait EOS, Murnaghan EOS, Birch–Murnaghan EOS Vinet EOS and Kholiya-Chandra EOS. The data for all nanomaterials defined from three constants such as ,  and  are listed in table 1. The second order bulk modulus are calculated from equation (1). Under compressions of such nanomaterials (TiO₂ (anatase), Ni (20 nm), CdSe (rock salt phase), AlN (Hexagonal), 3C-SiC (30 nm) and Rb₃C₆₀) pressures and its validity test are calculated again from Eq. (1) and several other isothermal EOSs Eq. (2 to 7).  Microsoft Office software has been used to do the calculations.

The results obtained from these EOSs are presented in Fig. 1 to 6 in terms between pressure and

and its experimental data from ^18-23. Eq. (1) gives better agreement such as compared with the other EOSs. The obtained results compared with experimental data show in Figs. 1 to 6, these values calculated from using Eq. (1) and closer to experimental data of nanomaterials. The experimental uncertainty result provided by Sharma and Kumar [2] with experimental measured P–V data is often pressuring calibration errors; therefore, we considered Eq. (1) calculation for the compression behavior of TiO₂ (anatase), Ni (20 nm), CdSe (rock salt phase), AlN (Hexagonal), 3C-SiC (30 nm) and Rb₃C₆₀. The results are reported in Fig. 1 to 6 along with the experimental data [18-23] and these corresponding results are presented in Table 1. Significantly, the results are showing better agreement with the experimental data.

Figure 1: Several EOSs are used for calculating high-pressure behaviour for TiO₂ (Anatase). Click here to View figure

Figure 2: Several EOSs are used for calculating high-pressure behaviour for Ni (20 nm). Click here to View figure

Figure 3: Several EOSs are used for calculating high-pressure behaviour for CdSe (Rock Salt). Click here to View figure

Figure 4: Several EOSs are used for calculating high-pressure behaviour for AlN (Hexagonal). Click here to View figure

Figure 5: Several EOSs are used for calculating high-pressure behaviour for 3C-SiC (30 nm). Click here to View figure

Figure 6: Several EOSs are used for calculating high-pressure behaviour for Rb3C60. Click here to View figure

Conclusion

Second order pressure derivative of bulk modulus EOS for nanomaterials are predicted by our previous EOS study. EOSs for nanomaterials are much useful under high pressure compression behavior of nanomaterials and solids. The major advantages of these EOSs are that the experimental data is not available. Therefore the given studies for nanomaterials must be helpful under high-pressure compression behavior because at this level arrangement of experimental setup don’t easy task. The results give better deal compare with experimental data and EOSs data, it is clear from figure 1 to 6. Present work is simple and effective method to study compression behaviour of nanomaterials and solids.

Conflicts of Interest

The authors declare no competing interests. 

Funding Sources

There is no funding sources

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