Length-scale-dependent deformation mechanism of Cu/X (X=Ru, W) multilayer thin films
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The microstructure and deformation/strengthening behavior of Cu/Ru (face-centered cubic (fcc)/hexagonal close-packed) and Cu/Cr (fcc/body-centered cubic) multilayered films with equal individual layer thickness h ranging from 0.8 to 200 nm were investigated. Based on systematic X-ray diffraction and transmission electron microscopy analyses, as h was varied, interface structure transitions from semi-coherent to fully coherent structures were observed in Cu/Ru rather than Cu/W. These structure transitions were found to play crucial roles in length-scale dependent strengthening mechanisms. Specifically, the multilayer strength derived for relatively large h   (class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0921509316303343&_mathId=si0003.gif&_user=111111111&_pii=S0921509316303343&_rdoc=1&_issn=09215093&md5=792b92ae4f2f0330090ee510a553e394">class="imgLazyJSB inlineImage" height="10" width="34" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0921509316303343-si0003.gif">class="mathContainer hidden">class="mathCode">50nm) followed the classic Hall–Petch relation, while the load-bearing effect was proposed to be the dominant mechanism for relatively small h   (class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0921509316303343&_mathId=si0004.gif&_user=111111111&_pii=S0921509316303343&_rdoc=1&_issn=09215093&md5=e5a83cd5506efb8e6d7cb6c1763ff128">class="imgLazyJSB inlineImage" height="11" width="82" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0921509316303343-si0004.gif">class="mathContainer hidden">class="mathCode">50nmh4nm). More importantly, as h was further reduced to below 4 nm in Cu/Ru, a strengthening mechanism based on dislocation loop crossing several coherent interfaces was proposed and quantitatively evaluated, The number of layers needed to be crossed by the dislocation loop was found to determine the strength.

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