**3. Result and discussion**

#### **3.1 Lithium**

According to the aforementioned in the introduction, high pressure physics is useful in achieving a novel structure and superconductivity [12–14, 17, 33, 57–59]. Li is one of the challenging to find a novel structure [43, 60–63]. Since it is interesting that there is complex structures were discovered in alkali metal, i.e. sodium (Na) [64], potassium (K) [65–68], and rubidium (Rb) [69, 70]. Therefore, Li might be expected to possible to be a complex structure at high pressure. For the transitions sequence of Li, we found that the Im-3 m structure transformed into the Fm-3 m structure at pressure 8 GPa. Next, the Fm-3 m structure transformed into the R-3 m structure at pressure 39 GPa. With increasing pressure, the R-3 m structure transformed into the I-43d structure at pressure 44 GPa, then it transformed into C2mb at pressure 73 GPa. On further compression, the C2mb structure transformed into the C2cb structure at 80 GPa. Finally, it transformed into Cmca 120 GPa. It is interesting that there is no found the incommensurate host-guest structure at any pressure among such sequence [43, 60–63, 71].

Li was observed by optical spectroscopic through diamond anvil cells (DAC) [72]. The solution of the experimental study revealed that there is unknown phase above 50 GPa. Moreover, the characteristic of the high frequency band, i.e. Li-Li vibration, can interpret to be an incommensurate host-guest structure. The commensurate host-guest structure is defined by the different the number of the guest atoms in channels in along the c axis of the host structure, referring to the commensurate value cH/cG, also known as *γ*. At this point, it is interested to examine the unknown structure by following the Ref. [72].

As mentioned above, the unknown structure can be identified by a random search techniques. The random search technique is the high performance for the prediction of the materials. For elemental Li, the *ab initio* random structure searching (AIRSS) technique [6] is employed for determination the unknown

*Superconductivity in Materials under Extreme Conditions: An* ab-initio*… DOI: http://dx.doi.org/10.5772/intechopen.99481*

structure. The remarkable result shown that Li is predicted to be the incommensurate host-guest structure above 50 GPa. Tsuppayakorn-aek et al. [13] was pointed out that structural phase transitions of Li might be considered to be different origins in two-phase transition sequences (**Figure 1**). Interestingly, one of two transition sequences can be obtained the incommensurate host-guest structure, indicating that it is energetically stabilized above 50 GPa and Li is likely to crystallize in the incommensurate host-guest structure at high temperature.

The existence of the incommensurate host-guest structure can be considered from the ELF calculation. As a possible cause of this, one might think of there is the s-p*μ* hybridization between the host–host atoms at 150 GPa (**Figure 2**) [13]. The study useful to point out that the possibility of the incommensurate host-guest structure is stable. Moreover, the nature of chemical bonding shown that the

**Figure 1.** *The relative enthalpy of Li as a function of pressure.*

**Figure 2.**

*The electron localization function (ELF) of the host-guest structure of Li is calculated in the (001) atomic plane.*

incommensurate host-guest structure has tend to favor superconductivity at higher pressure. It is worth to note that the nature of the chemical bonding of the host–host atoms, i.e. the *μ* bonging, might be considered to be a superconducting phase.

#### **3.2 Strontium**

Structural phase transitions in alkaline earth metal under high pressure is interested among the periodic table. Nowadays, there are several works reported a transition sequences [33, 37, 40, 47, 58]. It is interesting to consider that a transition sequences of Ca and Sr. are similar. Ca shown that it exhibited stable structure at high temperature and low pressure through compression [58, 73]. The experimental observations [74] and the theoretical study [58, 73] reported that the simple cubic (sc) structure is stable at room temperature. At this point, the solution of theoretical study revealed that the sc structure is stable by performing a molecular dynamics (MD) calculation [73]. This is because the MD calculation can include a temperature via *ensemble*. However, the sc structure is considered by a lattice dynamics calculation [75], indicating that it is unstable structure. This is due to that fact that the sc structure is not a harmonic phase, but it is anharmonic phase [75]. Here, the sc structure is difficult to estimate the *Tc* by theoretical study.

In 2009, Ca was reported a novel structure at high pressure that it is the *β*-tin structure [58]. Here, it is worth to note that the transitions sequence of Ca is similar Sr. (the Fm-3 m structure transformed into the Im-3 m structure, then it transformed into the *β*-tin structure) Here, the *β*-tin structure is found that it is stable at high pressure and low temperature [58]. The *Tc* of the *β*-tin structure was estimated to be 5 K at 40 GPa. The case of Ca is interesting due to the d electrons are important for the estimated *Tc*. As a possible cause of this, one might think of the d electron is dominated near the Fermi level.

It is interesting to note that structural phase transitions in Sr. [33–37, 47]. The remarkable studies revealed that there are discrepancy between the experimental observations [34–36] and the theoretical studies [33, 37, 47]. The experimental observations were reported that the Fm-3 m structure transformed into the Im-3 m structure, then it transformed into the *β*-tin structure. Next, the *β*-tin structure transformed into the Sr-IV, finally, the Sr-IV structure transformed into the Sr-V structure. On the contrary, the theoretical studies were reported that the Fm-3 m structure transformed into the Im-3 m structure, then it transformed into the Sr-IV structure, showing that the the *β*-tin structure is not energetically favored over the Sr-IV structure.

In 2012, Sr. was predicted that there is a candidate structure [33]. The relative enthalpy of Sr. was reported that the Cmcm structure is thermodynamically favored over the Fm-3 m structure, the Im-3 m structure, and the *β*-tin structure. In addition, the Cmcm structrue was displayed that it can transform into the hcp structure as well. The Cmcm structure was investigated superconductivity, showing that the *Tc* of the Cmcm is estimated to be 4 K. The remarkable result manifested that the predicted *Tc* values are in good agreement with experiment [76, 77].

However, the discrepancy between the experimental observations and the theoretical studies were not solved yet. In 2015, the discrepancies in transition sequence between the experimental and theoretical works was explained by Tsuppayakornaek et al. [10]. Regarding transition sequence in Sr., it was investigated by the hybrid exchange-correlation functional, i.e. screened exchange local density approximation (sX-LDA) [78–80]. The stable structure of the *β*-tin was corrected by sX-LDA functional. In fact, the sX-LDA functional is important for the d electrons. At this point, it is interesting to compare the experimental observation and the theoretical study [10] by considering the energy levels in each electron

*Superconductivity in Materials under Extreme Conditions: An* ab-initio*… DOI: http://dx.doi.org/10.5772/intechopen.99481*

configuration of isolate strontium (**Figure 3**). The solution of the energy levels indicated that the sX-LDA functional is in good agreement with the experiment [81].

The remarkable result of the Ref. [10] shown that the *β*-tin structure is thermodynamically favored over the hcp structure by sX-LDA functional (**Figure 4**). The Ref. [10] manifested that the Im-3 m structure transformed into the *β*-tin structure,

**Figure 3.** *The energy level each electron configuration of isolate Sr.*

**Figure 4.** *The relative enthalpy of Sr. as a function of pressure by sX-LDA functional.*

showing that the theoretical study is in good agreement with experimental observations [34–36].

Regarding the superconductor in the *β*-tin structure is interesting. Although the *β*-tin structure is thermodynamically stable by sX-LDA functional, it is not calculated the *Tc*. This because the sX-LDA functional is not implemented for the *Tc* calculation. However, other hybrid exchange-correlation functionals, i.e. PBE0 or HSE06, are possible for investigation the stability of the *β*-tin structure, leading to find the *Tc*.

#### **3.3 Scandium**

Structural prediction at high pressure is suitable for identifying unknown structure. Scandium (Sc) is one of d-transition metal, showing that there is an unknown structure (Sc-III) at high pressure [82]. The transition sequences is found that the hcp structure transformed into the host-guest structure [83, 84]. The host-guest structure is thermodynamically stable up to 70 GPa [85]. It is interesting to note that what is the unknown structure beyond the host-guest structure above 70 GPa. In 2018, Tsuppayakorn-aek et al. [14] was identified the unknown structure by *ab initio* random structure searching (AIRSS). The predicted structure was manifested that Sc-III is the tetragonal structure with space group P41212. The P41212 structure was shown that it is thermodynamiclly stable favored over the hcp structure and the host-guest structure above 93 GPa (**Figure 5**) [14]. Also, the P41212 structure was found that it is dynamically structure at 120 GPa, as shown in (**Figure 6**). Moreover, the solution of the simulated XRD pattern [14] is in good agreement with the observed XRD pattern from the experimental study [82]. Structural phase transitions of Sc was reported that the hcp structure transformed into the host-guest structure, and then, it transformed into the P41212 structure.

Regarding superconductor of the P41212 structure, it was found to be the metallicity by considering density of state (DOS), leading to investigate the *Tc*. The P41212 structure displayed that the estimated *Tc* is 8.36 K at 110 GPa. While, the

**Figure 5.** *The relative enthalpy of Sc as a fucntion of pressure.*

*Superconductivity in Materials under Extreme Conditions: An* ab-initio*… DOI: http://dx.doi.org/10.5772/intechopen.99481*

**Figure 6.** *The phonon dispersion of the P41212 structure.*

**Figure 7.** *The* Tc *of the P41212 structure compare the Tc of Sc-III phase.*

experimental study was reported the *Tc* is 8.31 K and 111 GPa [86]. Moreover, the P41212 structure was explored the *Tc* above 130 GPa. Also, it was found that the *Tc* decreased monotonically with increasing pressure (**Figure 7**). In addition, the EPC strengths decreased with increasing pressure as well.

Tsuppayakorn-aek et al. [14] was revealed in that the *Tc* of the P41212 structure decreased with increasing pressure occurred from the mechanical of the DOS. It can be easily understood by considering the partial-density of state. They were shown that the p-electron decreased with increasing pressure. In contrast, the s electron

increased with increasing pressure. In addition, the decreasing of *Tc* value is supported by the ELF calculation. The ELF is displayed in the (110) atomic plane of the P41212 structure, showing that the characteristic of electron state. One can see that the p-electron is accumulated between Sc atoms, indicating that the nature of the chemical bonding is the weak bonding. On increasing pressure, the p-electron transferred into the s and d electrons. This implied that the decreasing of the pelectron might affect the *Tc* value.

Sc is one of the group-IIIB element was shown that structural phase transformation displayed the complex to simple transition. Also, it promoted the superconducting temperature transition to be 8.36 K at 110 GPa, which it is in good agreement with the experimental observation.

#### **3.4 Arsenic**

The group-V element is one of central interest in superconductor. It is interesting to note that arsenic (As), antimony (Sb), and bismuth (Bi) share the remarkable similarity of structural and property [87, 88]. Structural of the group-V element was reported that As-III, Sb-IV, and Bi-III are the incommensurate host-guest structure [89–92]. Also, it is worth to note that the Im-3 m structure is thermodynamically stable favored over the incommensurate structure [87, 88].

Tsuppayakorn-aek et al. [12] was explored the high-pressure phase in As. This because it is interesting to find the high-pressure phase, leading to go beyond the Im-3 m structure. The structural prediction was investigated up to 300 GPa. The predicted structure was shown that the body-centered tetragonal (bct) structure with space group I41/acd to be the stable structure at high pressure. The I41/acd structure is energetically and dynamically stable. Also, it is thermodynamically favored over the host-guest structure. The I41/acd structure displayed that it compete with the Im-3 m structure. Moreover, The I41/acd structure and the Im-3 m structure are very closed in enthalpy from 100 to 300 GPa. Also, the I41/acd structure is sub-spacegroup of the the Im-3 m structure. It is possible that the I41/ acd structure is coexistence phase with the Im-3 m structure.

Here, the I41/acd structure was discovered to be the metallicity, indicating that it is superconducting phase. As already mentioned, the I41/acd structure and the Im-3 m structure are wonderfully closed in enthalpy. It is interesting to investigate the superconducting phase of both of them. An important and a fundamental of the spectral function led to consider superconductor. In fact, the spectral function is associated with the electron–phonon coupling (EPC). The I41/acd structure was regarded in superconductor, it was found that the estimated *Tc* is 4.2 K at 150 GPa. On increasing pressure, the *Tc* of the I41/acd structure decreased with the EPC. Likewise, the *Tc* of the Im-3 m is likely to decrease, where a pressure increasing. It is worth to note that the I41/acd and Im-3 m structures are very similar in the *Tc* [12].

The remarkable results of the *Tc* value were shown that the *Tc* of the I41/acd structure has higher than the Im-3 m structure at 150 GPa. The reason can be considered by the spectral function (*α<sup>2</sup> F*) (**Figure 8**). The contribution of the *α<sup>2</sup> F* shown that the I41/acd structure is higher than those of the Im-3 m structure around middle frequency regime (6–13 THz).

Now, it is worth to note that the I41/acd structure hold the metallic state at 300 GPa. Tsuppayakorn-aek et al. [12] suggested that the I41/acd structure is not favored superconductor above 300 GPa, indicating that it is likely to transform into a normal metallic state (**Figure 9**). As a possible cause of this, one might think of phase transformation [19]. Moreover, the EPC of the I41/acd structure is very poor characterized by compression. At this point, it is possible that a novel phase might occur above 300 GPa.

*Superconductivity in Materials under Extreme Conditions: An* ab-initio*… DOI: http://dx.doi.org/10.5772/intechopen.99481*

**Figure 8.** *The spectral function of the I41/acd and Im-3 m structures at 150 GPa.*

**Figure 9.** *The* Tc *of the I41/acd and Im-3 m structures as a function of pressure.*
