The deposition of thin alternating layers of Cu and Nb on Si(100) substrates has been studied by transmission electron microscopy as a function of layer thickness. For layer thickness above 25 Angstrom, there is a strong texture orientation relationship with the close packed planes of fee Cu parallel to close packed planes of bcc Nb, forming the so-called ''Kurdjumov-Sachs'' orientation relationship. However, at thicknesses of under 12 Angstrom, the Cu is constrained to grow as a slightly distorted bcc structure. It is thought that, when it reaches a critical thickness between 12 and 20 Angstrom, the bcc Cu loses coherency and transforms martensitically to the fee phase, resulting in the observed Kurdjumov-Sachs orientation relationship. Electron energy loss spectroscopy observations indicate a difference of 2 eV in the L-3 edge suggesting that the Fermi energy is lower in the constrained bcc form of Cu than in the equilibrium fee structure. (C) 1997 American Institute of Physics.