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The morphological evolution of copper nanolines induced by focused ion beam at normal bombardment has been investigated by in situ scanning electron microscopy. A periodic array of particles is observed when the width of lines reaches a certain value. The stability of a nanoline is studied in terms of a model based on Nichols and Mullins [Trans. Metall. Soc. AIME 233, 1840 (1965)] instability and curvature-dependent sputtering yield. A critical line width is found by linear analysis. When the line width is below this value, unstable mode whose wave vector is parallel to the line axis develops and a chain of periodic particles forms. When the width is above this critical value, the sputtering etching only leads to the decrease of width. The flux and temperature dependence of wavelength is measured and explained based on this model. The predictions of the model are in good agreement with the experimental results.