PSI - Issue 54

Jelena Zagorac et al. / Procedia Structural Integrity 54 (2024) 453–459 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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supercell and the PCAE methods (Zagorac et al. , 2012, Zagorac, Zagorac, Schon , et al. , 2018, Dovesi et al. , 2018, Zagorac et al. , 2022, Zagorac et al. , 2023). Further information about previous successful combinations of these methods can be found elsewhere (Zagorac et al. , 2022, Škundrić et al. , 2021, Matović et al. , 2023, Zagorac, Zagorac, Djukic , et al. , 2018). Full structural relaxation of the unit cell and atomic positions has been performed without symmetry restrictions with local optimizations employing analytical gradients (Civalleri et al. , 2001, Doll et al. , 2001, Doll et al. , 2004). In each structural optimization, Fock/KS matrix mixing was set in the range between 30 - 80%, and the tolerances for the convergence on energy were set to 10 -7 . Monkhorst-Pack scheme has been used with K-point mesh set to 8 x 8 x 8. All-electron basis sets (AEBS) were used in all ab initio calculations: a [ 3s2p1d ] for boron (Doll et al. , 2008, Doll, 2021), a [ 4s3p1d ] basis set for aluminum, (Zagorac et al. , 2017, Montanari et al. , 2006, Cvijović - Alagić et al. , 2019) and a [ 3s2p1d ] basis set for nitrogen, (Zagorac, Zagorac, Jov anović , et al. , 2018, Zagorac, Zagorac, Djukic , et al. , 2019) respectively. Structure optimization was performed using a hybrid B3LYP (Becke, three-parameter, Lee-Yang Parr) exchange-correlation functional (Becke, 1993, Lee et al. , 1988, Vosko et al. , 1980, Stephens et al. , 1994). The symmetries and the space group of the calculated structures were determined using the algorithms SFND and RGS (Hannemann et al. , 1998), respectively. The results have been analyzed in the KPLOT code (Hundt, 2016) and visualized using the VESTA program (Momma & Izumi, 2008). 3. Results and Discussion In order to study the structural properties of AlN/BN compounds it is important to analyze all possible modifications in the respective chemical composition, where initial structures are h-BN , wurtzite, sphalerite, and rock salt. The resulting summary of all computed AlN/BN compounds and modifications with their respective space groups, unit cell parameters, and volumes of the primitive cell for the initial h-BN structure is shown in Table 1. We note the following: the structure changes from h-BN in pure BN compound, over various distortions to 5-5 structure in pure aluminum nitride, the symmetry is highest in the pristine AlN and BN compounds, while lowest in Al 0.25 B 0.75 N compound, unit cell parameters and volume changes are not following any trend and are fully dependent on structural changes in the respective system (Table 1). Table 1. Summary of all computed AlN/BN compounds and modifications with their respective space groups, unit cell parameters, and volumes of the primitive cell for initial h-BN structure. Compound Initial structure: h-BN Space group (no.) Modification Unit cell (Å) Volume (Å 3 ) BN P 6 3 / mmc (194) h-BN a = 2.51, c = 6.36 V=17.35 Al 0.125 B 0.875 N P 3 m 1 (156) h-BN (s-dis) a = 5.14, c = 6.03 V=17.27 Al 0.25 B 0.75 N Cm (8) post-h-BN-1 V=16.20

a = 8.89, b = 5.14, c = 5.19, β = 91.58 a = 5.80, c = 4.84 a = 6.08, c = 4.41 a = 4.29, b = 3.11, c = 5.42; a = 6.41, c = 4.22 a = 3.29, c = 4.16

Al 0.375 B 0.625 N Al 0.50 B 0.50 N Al 0.625 B 0.375 N Al 0.75 B 0.25 N Al 0.875 B 0.125 N

P -6 m 2 (187) P 3 m 1 (156) P -6 m 2 (187) Pmm 2 (25) P -6 m 2 (187)

h-BN (h-dis) a = 5.33, c = 14.18

V=21.81 V=17.61 V=17.69 V=18.13 V=18.76 V=19.53

post-h-BN-2 5 – 5 (s-dis) 5 – 5 (h-dis) 5 – 5 (s-dis)

AlN

P 6 3 / mmc (194)

5 – 5

A summary of all computed AlN/BN compounds and modifications with their respective space groups, unit cell parameters, and volumes of the primitive cell for initial wurtzite structure is shown in Table 2. We note that the initial structure remains a prototypical type for the whole AlN/BN compositional range, while there are even higher