* Corresponding author. Tel.: #48-81-5381504; fax: #48- 81-5259385. E-mail address: sangwal@antenor.pol.lublin.pl (K. Sangwal) Journal of Crystal Growth 203 (1999) 434}442 Study of the geometry of KCl clusters nucleating from vapour and in aqueous solutions W. Polak, K. Sangwal* Institute of Physics, Technical University of Lublin, ul. Nadbystrzycka 38, 20-618 Lublin, Poland Received 25 May 1998; accepted 9 February 1999 Communicated by G.B. Stringfellow Abstract The molecular interaction model of cluster formation was used to compute the formation energy of KCl clusters having ions from 4 to ca 10000, taking into consideration repulsion forces between ions. Four types of cluster geometries were analysed: spherical, cube-shaped (perfect cubes or cuboids with steps on one of their 100 faces) and octahedral with 111 and 111  faces. It was found that cube-shaped clusters forming from the vapour phase are always preferential (more abundant) due to Coulomb interactions. In aqueous solutions, the subcritical clusters, both spherical and cube-shaped, can be preferential. Larger KCl clusters should have the cubic geometry due to the small values of the average adsorption energy of water molecules on their surface. Spherical and octahedral 111  clusters adsorb water molecules more strongly, which leads to their signi"cantly lower growth.  1999 Elsevier Science B.V. All rights reserved. PACS: 64.60.Qb; 61.46.#w; 82.30.Nr; 68.35.Bs Keywords: Nucleation; KCl clusters; Cluster geometry; Formation energy; Adsorption 1. Introduction During the last 15 years clusters have been inten- sively studied [1}4]. Typically, clusters are created in the vapour condensation process and investi- gated in experiments with cluster beams in vacuum. Experimental studies of cluster abundance reveal that su$ciently large clusters assume various geo- metrical forms: cube-shaped (cubic and cuboid with "lled rows) for clusters of ionic salts [5,6], icosahed- ral for nickel clusters [7], and icosahedral or cubo- octahedral for large sodium clusters [8]. Detection of clusters present in dense liquid me- dia like solutions is a di$cult task. Experimental studies on clusters in solutions usually provide in- formation about the average cluster size [9}13]. Theoretical calculations also do not give precise information about the cluster geometry because the arrangement of molecules in clusters is predicted on the assumption of negligible interactions with sur- roundings as in the vapour, e.g. for clusters of alkali halides [14], metals [15] and II}VI compounds [16]. Consequently, the geometrical factors of 0022-0248/99/$ - see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 9 ) 0 0 1 1 3 - X