Hartman–Perdok analysis of crystal morphology and interface topology of β-LiNaSO 4

Abstract

The trigonal β-LiNaSO 4 low temperature polymorph belongs to the family of double sulphates with general formula LiMSO 4 (M=Na, NH 4, Rb, …), which have very specific electrical properties. In this paper we present the β-LiNaSO 4 theoretical growth morphology based on the Hartman–Perdok theory. Therefore, Periodic Bond Chains (PBCs) have been identified in order to determine the influence of the crystal structure on the crystal morphology. The shortest PBC is parallel to 〈1 0 0〉 and consists of a one-step proto-PBC with sulphate(I)–cation–sulphate(I, 1 0 0) strong bonds. All the other PBCs are built up from strong bonds in two or more consecutive steps, e.g., sulphate (I)–cation–sulphate(II)–cation–sulphate (I, u v w ). The corresponding F forms are in order of decreasing d hkl : {1 0 1 ̄ 0} , {1 0 1 ̄ 1} , {0 0 0 2}, {1 0 1 ̄ 2} , {1 1 2 ̄ 0}={2 1 ̄ 1 ̄ 0} , {1 1 2 ̄ 2}={2 1 ̄ 1 ̄ 2} , … For many F forms several different slice configurations can be defined. Attachment energies have been calculated in electrostatic point charge models with formal charges. In addition, the effect of covalent S–O bonds on the growth forms has been taken into account by decreasing the effective charge on oxygen, q O. The theoretical growth form of β-LiNaSO 4 based on attachment energies calculated in the LiNaS 6+O 4 2− point charge model shows the hexagonal prism {1 0 1 ̄ 0} , the hexagonal pyramid {1 0 1 ̄ 1} and the pedion (0 0 0 1). When the influence of the S–O bond decreases (LiNaS 4+O 4 1.5− model), the habit is slightly less elongated parallel to the c-axis due to the increased relative morphological importance of the pyramid form with respect to the prism. When we assume that the hexagonal prism face grows with halved slices d 20 2 ̄ 0 and thus using the attachment energies of E a 20 2 ̄ 0 instead of those of E a 10 1 ̄ 0 , the growth forms changes drastically by the absence of the hexagonal prism form in both models. In addition, the trigonal prism {1 1 2 ̄ 0} is present as a minor form on this LiNaS 4+O 4 1.5− model with halved d 20 2 ̄ 0 slices. Experimentally grown LiNaSO 4 crystals show habits that deviate from the theoretical growth forms. This must be due to external factors such as supersaturation and interaction of the crystal surface with the aqueous solutions during the growth. Growth experiments confirm that the growth morphology is strongly influenced by the degree of supersaturation.