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Peak-finding procedures and the geometric phase method of quantitative high resolution electron microscopy (qHRTEM) were applied to determine the local strain and the chemical composition of nanostructured semiconductor materials. The growth of the structures investigated was induced by minimization of strain energy. The analysis of strain distribution is necessary for the understanding of the self-organized formation of nanostructures. The possibilities and limitations of the methods are discussed in detail by analysing HRTEM images of (Si,Ge) islands and of a double layer of stacked quantum dots of (In,Ga)As and Ga(Sb,As). [ABSTRACT FROM AUTHOR]