Application of X-ray Powder Diffraction to Nano-materials - Determination of the Atomic Structure of Nanocrystals with Relaxed and Strained Surfaces

The applicability of standard methods for the evaluation of powder diffraction data of nano-size crystallites is analyzed. Based on theoretical considerations, it is shown that deviations of the structure of small particles from the Bragg approximation on an infinite crystal lattice leads to significant differences in the diffraction patterns, which may lead to an erroneous interpretation of the experimental results. An alternative evaluation of the diffraction data of nano-particles, based on the so-called "apparent lattice parameter", alp , is proposed. Based on this method, it is shown that real nano-crystals constitute a complex, heterogeneous multi-phase structure.

[1]  J. Gilman,et al.  Direct Measurements of the Surface Energies of Crystals , 1960 .

[2]  S. Tolbert,et al.  Size dependence of the solid-solid phase transition in CdSe nanocrystals , 1993 .

[3]  F. Boswell,et al.  Precise Determination of Lattice Constants by Electron Diffraction and Variations in the Lattice Constants of Very Small Crystallites , 1951 .

[4]  M. Flueli,et al.  Surface stress and size effect on the lattice parameter in small particles of gold and platinum , 1985 .

[5]  Sidney Yip,et al.  Materials interfaces : atomic-level structure and properties , 1992 .

[6]  J. Borel,et al.  Surface stress and surface tension: Equilibrium and pressure in small particles , 1985 .

[7]  S. Gierlotka,et al.  X-Ray Characterization of Nanostructured Materials , 2002 .

[8]  E. Pippel,et al.  Dependence of lattice parameters of small particles on the size of the nuclei , 1981 .

[9]  C. Suryanarayana,et al.  Non-Equilibrium Processing of Materials , 1999 .

[10]  Löffler,et al.  Grain-boundary atomic structure in nanocrystalline palladium from x-ray atomic distribution functions. , 1995, Physical review. B, Condensed matter.

[11]  R. Cammarata.  Thermodynamic model for surface reconstruction based on surface stress effects , 1992 .

[12]  Alp,et al.  Structure of copper microclusters isolated in solid argon. , 1986, Physical Review Letters.

[13]  Robert C. Cammarata,et al.  Surface and interface stress effects on interfacial and nanostructured materials , 1997 .

[14]  S. Qadri,et al.  Pressure Induced Structural Transitions in Nanometer Size Particles of PbS , 1998 .

[15]  S. Tolbert,et al.  The wurtzite to rock salt structural transformation in CdSe nanocrystals under high pressure , 1995 .

[16]  A. Stoneham.  Measurement of surface tension by lattice parameter changes: theory for faceted microcrystals , 1977 .

[17]  R. Averback.  Sintering and deformation of nano-grained materials , 1993 .

[18]  P. Buffat,et al.  Size effect on the melting temperature of gold particles , 1976 .

[19]  F. Fujita,et al.  Physics of New Materials , 1994 .

[20]  J. Cahn,et al.  Mean stresses in microstructures due to interface stresses: A generalization of a capillary equation for solids , 1997 .

[21]  Zhong Lin Wang.  Characterization of Nanophase Materials , 2001 .

[22]  Robert C. Cammarata,et al.  Nanomaterials : synthesis, properties, and applications , 1996 .

[23]  Markus R. Silvestri,et al.  High Pressure Phase Stability of II-VI Semiconductor Nanocrystals , 1995 .

[24]  K. Ohshima,et al.  X-ray diffraction study of fine gold particles prepared by gas evaporation technique , 1981 .

[25]  C. Solliard.  Structure and strain of the crystalline lattice of small gold and platinum particles , 1981 .

[26]  S. Qadri,et al.  Pressure induced structural transitions in nanometer size particles of PbS , 1996 .

[27]  C. W. Mays,et al.  On surface stress and surface tension: II. Determination of the surface stress of gold , 1968 .

[28]  P.‐J. Sell,et al.  The Surface Tension of Solids , 1966 .

[29]  C. W. Mays,et al.  On surface stress and surface tension: I. Theoretical considerations , 1968 .