The size dependence of the rms amplitude 〈u2〉1/2 of the atoms in free clusters of krypton is determined for the first time, by an electron diffraction technique. The mean size N̄ of the clusters formed in supersonic jets of krypton varied from 1×103 to 2×104 atoms/cluster. It is found that 〈u2〉1/2 increases with decreasing cluster size. A comparison of the dependence observed in experiment with that calculated with allowance for the fractional contribution of surface atoms shows that for clusters with N̄⩾4×103 atoms/cluster the increase of 〈u2〉1/2 with decreasing N̄ is due solely to the growth of the relative number of surface atoms. The correlation between the calculation and experiment vanishes when N̄⩽4×103 atoms/cluster. In that case the experimental values are considerably higher than the calculated value, a circumstance which indicates that in small aggregations there are other factors besides the surface which contribute to the growth of 〈u2〉1/2.

The dependence of the rms amplitudes of atoms in free clusters of solidified inert gases on the cluster size is investigated theoretically and experimentally. Free clusters are produced by homogeneous nucleation in an adiabatically expanding supersonic stream. Electron diffraction is used to measure the rms amplitudes of the atoms; the Jacobi-matrix method is used for theoretical calculations. A series of distinguishing features of the atomic dynamics of microclusters was found. This was necessary to determine the character of the formation and the stability conditions of the crystal structure. It wass shown that for clusters consisting of less than N∼103 atoms, as the cluster size decreases, the rms amplitudes grow much more rapidly than expected from the increase in the specific contribution of the surface. It is also established that an fcc structure of a free cluster, as a rule, contains twinning defects (nuclei of an hcp phase). One reason for the appearance of such defects is the so-called vertex instability (anomalously large oscillation amplitudes) of the atoms in coordination spheres.

An electron-diffraction study of clusters formed in supersonic jets of carbon dioxide is reported. The mean size of the clusters varies from 4×102 to 2×104 molecules/cluster. From an analysis of the diffraction patterns obtained it is established that clusters of these sizes have the structure of the bulk crystal. Stacking faults are observed for the first time in clusters with an average size of less than 1.7×103 molecules/cluster; the density of these stacking faults increases with decreasing size of the aggregations. It is found that the density of stacking faults in (CO2)N clusters is considerably lower than rare-gas clusters.

The experimental diffraction patterns from Kr cluster beams are compared with the diffraction functions calculated for rare-gas clusters with dimensions of 3×103 and 1×104 atoms/cluster. The experimental results are found to correlate well with the calculation if it is assumed that the clusters have a face-centered cubic structure with a constant number of intersecting stacking faults. Additional confirmation is obtained for the decisive role of the kinetic factor in the formation of the crystalline phase of the clusters. Conjectures are offered concerning the possible reasons why the densitometer traces presented by M-F. de Feraudy, G. Torchet, and B. W. van de Wall at the conference ISSPIC (1998) showed no substantial changes when the cluster size was increased by more than an order of magnitude.

The structure of N2 clusters is studied by the electron diffraction method over a wide range of their mean sizes N̄. It is found that, as the value of N̄ increases, the structure of the clusters is transformed in the sequence quasi-crystal (icosahedron) →α-N2 (cubic) phase with stacking faults →β-N2 (hcp) phase. The formation of the cubic phase from the icosahedral structure follows a mechanism typical of rare gases, while the transition α→β is due to an increase in the cluster temperature with the size.

The structure of Ar-N Kr-N Xe-N and (N-2)(N) clusters are studied by the electron diffraction method in a wide range of mean sizes (N) over bar. It is found that rare-gas clusters of mean sizes (N) over bar greater than or equal to 2000 atoms/cluster have a fee structure with the "deformation"-type stacking faults. It is found that in the case of nitrogen clusters as N increases the cluster structure transforms in the sequence: quasi-crystal (icosahedron) --> alpha (cubic) phase --> beta (hcp) phase. The formation of the cubic phase from the icosahedral structure follows the mechanism typical of rare gases. The transition alpha --> beta is due to the increase of the cluster temperature with size. The results obtained support the theoretical hypothesis on the important role of the kinetic factor in the formation of atomic cluster structures. (C) 1998 Elsevier Science B.V. All rights reserved.

The structure of clusters formed in supersonic jets of heavy rare gases is studied by the methods of electron diffractometry. It is found that a crystalline fcc structure with “deformation-type” stacking faults (SF) is formed in aggregates consisting of N⩾2⋅103 atoms/cluster. The SF density is a linear function of N−1/3. The number of “defective” planes does not depend on the cluster size and is equal to four in all cases. Such a number of intersecting SF leads to the formation of nonvanishing atomic steps ensuring a rapid and subsequently defectless growth of the cluster on all densely packed planes facing the cubooctahedron. The obtained results confirm experimentally the important role of the kinetic factor in the formation of the atomic structure of a cluster.

The theoretical prediction by van de Waal of stacking faults in rare gas clusters has been verified experimentally. It was established that a defect fee structure has been formed in clusters of mean sizes (N) over bar greater than or equal to 1500 atoms/cluster. The stacking fault density is a linear function of (N) over bar(-1/3). The number of 'defect' planes does not depend on the cluster size and is four.

An electron diffraction investigation of the clusters formed in supersonic Ar and N2 jets has been carried out. It is shown that in clusters containing less than 800 particles a dimensional phase transition of the crystalline structure into a quasi-crystalline (icosahedral) one takes place. This transition is observed both in argon and nitrogen clusters, the interaction of particles in the latter being more complicated than in noble gases. The effect of the average Ar cluster size on the root-mean-square atom amplitude [u2]1/2 was investigated. The dependence of [u2]1/2 on the average number of atoms in the cluster was analysed. The diagnostic characteristics of clustered beams of the gases studied were obtained, and fairly good correlation of these to the theory of "corresponding" jets is shown.

Electron diffraction studies have been carried out in clusters formed in supersonic jets of Ar and N2. It is shown that a dimensional phase transition of the crystal structure into a quasicrystalline (icosahedral) structure takes place in clusters containing less than 800 particles. The phase transition takes place in clusters of argon as well as nitrogen in which the interaction between particles is more complex than in inert gases. The effect of the mean size of Ar clusters on the mean-square amplitude ⟨u2⟩1/2 is studied, and the dependence of this quantity on the average number of atoms in a cluster is analyzed. Diagnostic characteristics of clusterized beams of investigated gases are obtained, and a good correlation with the theory of corresponding ” jets is demonstrated.