Stress transmission through three-dimensional granular crystals with\n stacking faults

We explore the effect of stacking fault defects on the transmission of forces\nin three-dimensional face-centered-cubic granular crystals. An external force\nis applied to a small area at the top surface of a crystalline packing of\ngranular beads containing one or two stacking faults at various depths. The\nresponse forces at the bottom surface are measured and found to correspond to\npredictions based on vector force balance within the geometry of the defects.\nWe identify the elementary stacking fault as a boundary between two pure\nface-centered-cubic crystals with different stacking orders. Other stacking\nfaults produce response force patterns that can be viewed as resulting from\nrepetitions of this basic defect. As the number of stacking faults increases,\nthe intensity pattern evolves toward that of an hexagonal-close-packed crystal.\nThis leads to the conclusion that the force pattern of that crystal structure\ncrystal can be viewed as the extreme limit of a face-centered-cubic crystal\nwith a stacking fault at every layer.\n