**10. The electronic structure of SbSI cluster at the phase transition region**

### **10.1. Introduction**

In PEP (or in the antiferroelectric phase, according to Ref. [14]), the anomalies of *E*T0 and *V* correlate in the temperature range of 295–400 K. It means that *E*T0 decreases due to the growth of *V*0, and vice versa. **Figures 12** and **13** show that the temperature dependence of *E*T0 is mainly

**Figure 13.** Temperature dependences of the total potential energy *E*TP0 components *E*ee0, *E*ne0, and *E*nn0 in the phase tran‐

In the FEP in the temperature range 280–295 K, a sharp increase of the unit cell volume *V*<sup>0</sup> leads to a decrease of *E*T0, curves 1 and 2 in **Figure 11**. However, in FEP at the temperatures of 220– 280 K, *E*T0 grows if the temperature is decreased, while the unit cell volume *V*0 changes only slightly. Curve 3 in **Figure 11** shows the calculated temperature dependence of *E*T0 provided that *V*0 = constant. In this temperature range, when *V*0 = constant, the growth of *E*T0 is caused by the variable shift of the equilibrium positions of Sb and S atoms. Thus, curve 2 in **Fig‐ ure 11** demonstrating the growth of *E*T0 can also be considered as caused solely by the variation

for the normal mode in the phase transition region. Dashed lines show the temperature dependences of *K* and *c*

\* ) Å and of the anharmonicity factor *c* (B)

determined by the components *E*TP0 = *E*ee0 + *E*ne0 + *E*nn0.

sition region.

104 Piezoelectric Materials

of Sb and S equilibrium positions.

assuming that *V*0 = 354.25 Å<sup>3</sup>

**Figure 14.** Temperature dependences of the harmonic constant *K* = (*K*0 – *KV*

.

As it is known [25, 34, 35], a ferroelectric phase transition of the first kind occurs in SbSI, though it is close to the phase transition of the second kind. What is more, it has been theoretically proved in Ref. [36] that the phase transition in SbSI takes an intermediate position between order-disorder and displacement types. In general, it is known that ferroelectric phase is at *T* < *TC* = 295 K, antiferroelectric phase exists at *TC* < *T* < 410 K, and paraelectric phase at *T* > 410 K.

Lukaszewicz et al. [17] determined the crystal structure of SbSI in the temperature region at 170–465 K. They found that there are three phases in the phase diagram of SbSI: ferroelectric phase (FEP) III (space group Pna21) below *T*C1 = 295 K, antiferroelectric phase (AFEP) II (P 212121) in the temperature region (*TC2* = 295–410 K), and high temperature paraelectric phase (PEP) I above 410 K. AFEP is characterized by the double polar chains [(SbSI)1]2, which are ordered antiferroelectrically: these cause a disorder in the crystal lattice. Experimental investigation of X-ray absorption, fluorescence, and electron emission [37, 38] adjusts the energy band structure of SbSxSe1−xI (*x* = 0.25; 0.5; 1), SbSBr. Its explanation necessitates for a more precise calculation of the contribution of separate atoms to the total density of states. The authors [39] had measured X-ray photoelectron emission spectra (XPS) of the SbSI crystals of valence bands (VB) and core levels (CL). XPS results showed the splitting of the CL. However, they have not explained theoretically the XPS spectra of the VB.
