B4/32Ga28/32Sb10/32As22/32 superlattice is the semiconductor three-dimensional soft X-ray diffraction grating with period 23/2aGaAs = 1.598 nm in the <001> directions, period 22aGaAs = 2.260 nm in the <011> directions and period 31/223/2aGaAs = 2.768 nm in the <111> directions, where aGaAs is the lattice parameter of GaAs. The superlattice is almost lattice matched to GaAs and, therefore, may be grown on the GaAs substrates. However, the stability against disordering should be studied to establish possibility of the practical applications. To describe the disordering processes, the Ga (As) and boron (Sb) lattice sites are considered. The Ga (As) and boron (Sb) sites are the lattice sites on which are Ga (As) and boron (Sb) atoms, respectively, in the superlattice. The transitions of boron and Ga atoms from the boron and Ga sites to the Ga and boron sites are the cationic disordering processes. The other disordering processes are the transitions of Sb and As atoms from the Sb and As sites to the As and Sb sites (anionic processes). Such cationic and anionic processes increase the bond energy since they decrease the quantities of B-Sb and Ga-As bonds and, accordingly, increase the quantities of B-As and Ga-Sb bonds. However, these processes increase the entropy.
The cationic disordering processes are considered as follows. The exchanges of boron and Ga atoms between the nearest sites in the cationic sublattice are taking into account. There is one type of the boron sites since each boron atom in the superstructure is surrounded by only Sb atoms. The Ga sites participating in the processes are also the same from the bond energy standpoint as each Ga atom forms one Ga-Sb bond. After the exchange of the lattice sites boron atom should be on one of the 9 nearest Ga sites. The atomic unit has 24 nearest Ga sites for boron atoms (Fig. 1). The total number of Ga atoms in one unit is 28. The transformation of bonds as a result of the disordering process is 3 B-Sb + 3 Ga-As → 3 B-As + 3 Ga-Sb. The increase of the bond energy after this bond transformation is 2.314×10-19 J. There are two types of the Sb sites in completely ordered B4/32Ga28/32Sb10/32As22/32 superlattice. There are 6 Sb sites with two B-Sb bonds and 4 Sb sites with one B-Sb bond in the unit (Fig. 1). All As sites are the same since they surrounded by only the Ga sites. Therefore, two different anionic disordering processes should be considered. The first anionic process is the exchange such that the transformation of bonds is 2 B-Sb + 2 Ga-As → 2 B-As + 2 Ga-Sb. In this process may participate 60% Sb atoms. Each of 60 % Sb atoms may be allocated on 10 As sites. The increase of the bond energy after this bond transformation is 1.542×10-19 J. The second variant of the anionic processes is accompanied by bond transformation B-Sb + Ga-As → B-As + Ga-Sb increasing the bond energy by 7.713×10-20 J. Moreover, all disordering processes increase the internal strain energy.
Any disordering processes increase the entropy and, therefore, these increases of the entropy term should be taken into account to estimate the variation of the free energy. There are one disordering process for cations and two processes for anions, in accordance with the transformations of the chemical bonds. They are the exchange of the lattice sites between the nearest cations and between the nearest anions. There are 4 boron atoms in the unit. Each boron atom has 9 nearest Ga atoms and 3 nearest boron atoms in the cationic sublattice. Thus, each boron atom may be on one of 9 Ga sites after the exchange of the lattice sites. As a result, the entropy term increases by and is 2.154×10-19 Jmol-1 at RT. There are two types of the Sb sites corresponding to the reactions transforming chemical bonds:
1. 2 B-Sb + 2 Ga-As → 2 B-As + 2 Ga-Sb and 2. B-Sb + Ga-As → B-As + Ga-Sb. Accordingly, two additional changes of the entropy terms should be estimated. In the case of the reaction between pairs of bonds there are 6 Sb atoms with reaction 1 (6 nearest As sites for 1 Sb atom) and 4 Sb atoms with reaction 1 (9 nearest As sites for 1 Sb atom) in the unit. The increase of the entropy term is and is 2.154×10-19 Jmol-1 at RT. There are 4 Sb atoms for bond reaction 2: B-Sb + Ga-As → B-As + Ga-Sb. The increase of the entropy term is and the increase is also equal to 2.154×10-19 Jmol-1 at RT. The amounts of B4/32Ga28/32Sb10/32As22/32 films grown on the GaAs lattice matched substrates, normally, should be significantly smaller than one mole. Therefore, the B4/32Ga28/32Sb10/32As22/32 completely ordered superlattice has to be stable against the disordering processes.