Surface pinning and grain boundary formation in magnetic flux-line lattices of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Bi</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow…

Magnetic decoration has been used to investigate the role of surface pinning on the flux-line lattice (FLL) of high-quality ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ single crystals. We find that surface steps pin flux lines at the sample surface, and that strong pinning along large steps creates grain boundaries (GBs) in the FLL. Analysis of the competing energetics of pinning versus GB formation leads to a criteria for the formation of extended GBs, and also indicates that these GBs penetrate through the entire sample. Surface pinning, which should occur in all real samples, will thus significantly affect the bulk FLL structure in these materials.