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For the first time, this book unites the theory, experimental techniques and computational tools used to describe the diffusion of atoms, molecules and nanoparticles across metal surfaces. Starting with an outline of the formalism that describes diffusion on surfaces, the authors guide the reader through the principles of atomic movement, before moving on to diffusion under special circumstances, such as the presence of defects or foreign species. With an initial focus on the behaviour of single entities on a surface, later chapters address the movement of clusters of atoms and the interactions between adatoms. While there is a special emphasis on experimental work, attention is paid to the increasingly valuable contributions theoretical work has made in this field. This book has wide interdisciplinary appeal and is ideal for researchers in solid state physics, chemistry as well as materials science, and engineering.