Surface Structure of Stripe ordered 1x2 phase on (Ba, Ca)(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$*

Low energy electron diffraction (LEED) and scanning tunneling microscopy/spectroscopy (STM/S) have been utilized to investigate the geometric structure of the stripe 1$\times $2 surface phase of (Ba, Ca)(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$ iron pnictides. STM images show that the surface consists of competing ordered and disordered regions. The 1$\times $2 phase appears on the surface of all compounds but coexist with ($\surd $2 $\times \surd $2)R45$^{\circ}$ phase on the surface of Ba122. Quantitative structural analysis of LEED-I(V) using the fractional spots of the 1$\times $2 phase on both parent compounds as well as Ca(Fe$_{0.925}$Co$_{0.075})_{2}$As$_{2}$ gives a similar surface structure with a termination layer of 50{\%} Ca/Ba atoms. The surface Ca/Ba layer has a large inward relaxation $\sim $ 0.5 {\AA} and the underneath As-Fe-As layer displays a buckling distortion. The Pendry Rp factor ($\sim $ 0.24) obtained in the structural refinement is excellent for all three systems.