CBPF-NF-030/96 CohesiveMechanism and Structure of Cluster-Assembled Solid Al C 12 X.G. Gong Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150-Urca RJ, Brazil Institute of Solid State Physics, Academia Sinica, 230031-Hefei, China Abstract Wehave prop osed a p ossible crystal structure for the cluster-assembled solid Al C, 12 and its electronic structures and stabilityhave b een studied in the framework of the density functional theory and ab-initio molecular-dynamics. We nd that Al C clusters are con- 12 densed byvan der Waals force, with a very small cohesive energy of 1.1 eV. A signi cant energy gap exists in solid, which suggests that it can b e a novel semiconductor. The com- bined steep est descent calculations show that up on the formation of solid, the relaxation of atomic distances of the Al C cluster is very small. The stability of the Al C solid is 12 12 also con rmed by a dynamical simulation at low temp erature. Key-words: Cluster-assembled Al C. 12 PACS. No. 36.40; 61.50Lt; 71.15Mb+Pd -2 - CBPF-NF-030/96 In the past decades, a great deal of e orts have b een devoted to the synthesizing and the fundamental understanding of new materials in atomic dimension[1]. With the discovery of C molecule and its solid phase[2], an enormous interest in the study of cluster 60 and cluster-assembled materials has b een aroused. Since the prop erties of clusters are quite di erent from that of atoms, it is reasonable to exp ect that the cluster-assembled materials haveunusual prop erties, whichwould b e quite di erent from that in atomic solid phase, like what observed in solid C [3]. To obtain the cluster-assembled materials, a high stability 60 of the clusters is usually essential, otherwise the clusters would coalesce when bringing them together, and the merits for synthesizing the cluster-assembled materials would b e lost, it is also necessary to have smaller interaction b etween clusters as compared to the interaction in the cluster itself. Recently, from the total energy and electronic structure calculations[4], it had b een found that the stabilityofAl cluster can b e signi cantly enhanced by doping with a 13 tetravalent carb on atom. Since there exists ab out 2 eV gap b etween the highest o ccupied molecular orbitals(HOMO) and the lowest uno ccupied molecular orbitals(LUMO), the in- teraction b etween Al C cluster can b e exp ected to b e small. Therefor the Al C cluster 12 12 is suggested to b e a go o d candidate to form a cluster-assembled solid. In fact, the high stabilityofAl C cluster was con rmed by a few recent studies[5,6]. Seitsonen et al.[6] 12 studied the dynamical stabilityofAl C cluster by Car-Parrinello metho d, and they found 12 that, even ab ove 900 K, the structure of Al C cluster remains icosahedral-like, which 12 indicates that the Al C cluster is indeed stable. Moreover, Kawai et al.[5] have studied 12 the interaction b etween twoAl C clusters byCar-Parrinello metho d, they found that 12 the structure of Al C clusters remains unchanged. However no successful studies for the 12 cluster-assembled Al C solid have b een made. Seitsonen et al.[6] studied the prop erties 12 of Al C solid with fcc-like structure, but they found that the total energies increased 12 monotonically with the decreasing of the lattice constant, and there is no lo cal minimum which is necessary for the formation of a meta-stable phase. In this letter, based on the recentsimulation on the cluster dimer and cluster- as- sembled solid[7], we prop ose a crystal structure for the Al C solid. In the total energy 12 calculations, wehave obtained a minimum at lattice constant of 30.8 a.u., and wedo nd that the interaction b etween the clusters in Al C solid is very weak, and the cohesive en- 12 ergy is very small. By p erforming the combined steep est descent on the ions and electrons, and dynamical simulation at low temp erature, weshow that Al C solid is a stable van 12 -3 - CBPF-NF-030/96 der Waals solid. As discussed by Khannan and Jena, the geometric e ects are imp ortant in the cluster- assembled materials[8]. In the icosahedral Al C cluster, although 12 aluminum atoms are 12 homogeneously distributed on a spherical surface, it can not b e rotational invariantlike a rare-gas atom. It is well known that, even in the icosahedral fullerene of C , which 60 has a smo other surface since it contains 60 carb on atoms on the surface, various phases with di erent rotational order have b een observed at low temp erature[9]. Obviously, the relative orientation of clusters mayplay an imp ortant role in the formation of a solid from the icosahedral Al C clusters. 12 The recent simulations on the cluster dimer (two icosahedral 13-atom clusters) and cluster-assembled solid with the Leonard-Jones p otential show that[7], the relative cluster orientation is very imp ortant for the stability of the cluster dimer. If we put 12 surface atoms of a b o dy-center icosahedron on the six faces of a cubic b ox, the most stable struc- ture for a cluster dimer is with two cubic b oxes in alternated orientation of 90 degrees, as shown in Fig. 1. In fact, only in this con guration, the mass centers of two icosahedron can approach more closely than any other isomers whichhave higher energies, as con rmed by the charge densityshown b elow. This suggests that, when the clusters are brought together, they should b e prop erly arranged according to their geometric shap e. In fact, the intuitive fcc-like structure, whichisthelowest energy structure for the atomic van der Waals solid, was proved to b e unstable for cluster-assembled Al C solid. So, wehave 12 tried to design a structure for Al C solid, in whicheachAl C cluster is alternated 90 12 12 degrees with all its nearest neighb ours. This turns out to b e a cubic-like structure, each unit cell contains eightAl C clusters. Actually, similar structure has b een observed in 12 AB system[10], where B has icosahedral structure, the large atom A is b elieved to b e 13 13 an electron donor to close the electronic shell of B whichmakes B stable[11]. To show 13 13 whether this structure is stable for Al C solid, wehave p erformed rst principles calcula- 12 tion and ab-initio molecular-dynamics simulation, and its stability is con rmed. With the same crystal structure, wehave studied the prop erties of the cluster-assembled Al Si solid 12 whichwas proved to b e unstable for fcc-like structure[12], and also the cluster-assembled solid Al K, whichwas suggested to have CsCl structure[13] but recent calculation showed 13 that icosahedral Al K cluster would not b e stable in CsCl structure[14]. The results on 13 Al Si and Al K solid will b e published elsewhere[15]. 12 13 All our calculations are based on the density functional theory with the lo cal density -4 - CBPF-NF-030/96 approximation[16] and Car-Parrinello metho d[17]. The electronic density is expressed in terms of Kohn-Sham orbitals[18], which are expanded into plane waves with energy cuto of 35Ry. Only the valence electrons are treated explicitly and their interactions with the ionic cores are describ ed by the Bachelet-Hamann-Schluter typ e pseudop otentials[19] with sp non-lo cality for Al and also for C. The minimization of the energy functional is p erformed with conjugate gradient for the xed atomic distances, also with combined the steep est descent for electrons and ions in Al C solid at a lattice constant of 30.8 a.u. 12 Wehave used time step of 4.0 a.u. and ctitious mass of 300 a.u for electrons in all the calculations. At rst, wehave studied the isolated icosahedral Al C cluster. Due to the plane wave 12 expansion, one is forced to use p erio dical b oundary condition. We use only the p ointof Brilliouin zone in the k-summation. To erase the interaction b etween the cluster and its images, it is necessary to haveavery large cell. As it was observed by Seitsonen et al.[6], wehave found that a fcc-cell with the lattice constantupto30a.u.isenoughtomake the interaction b etween the cluster and its images negligible. This can also b e con rmed by the total charge densityofAl C cluster, as shown in Fig. 2. By calculating the total 12 energies at di erent Al-C distances, wehave got the equilibrium Al-C distance of 4.69 a.u. which is equal to what was obtained in Ref.[6]. The obtained binding energy value of 45.9 eV is also comparable to 45.3 eV obtained by Seitsonen et al., and the small di erence may come from di erent psudop otentials used for carb on. These results are also in agreement with the results of other previous ab-initio metho ds[20]. To calculate the cohesive energy of Al Csolid,wehave used a primitive cell with two 12 Al C clusters. By changing the lattice constant with rigid cluster, the di erentcohesive 12 energies can b e obtained, and its values, relative to the isolated clusters, are shown in Fig.