Archived Data are from a publication Physical Review B. See manuscript at https://doi.org/10.1103/q75z-gk3l The results are simulations of coherent X-ray reflectivity for a one-dimensional surface (along x) with a assumed topography, h(x), where x is in units of Angstroms and h(x), where h(x) clat is the surface height in angstroms (we use a layer spacing of clat = 3 Angstroms). Simulations assume a beam energy of 10 keV with a Gaussian beam shape having a width of 0.5 micrometers. Simulated scattering intensities are calculated for vertical momentum transfer centered at Q0 = 1.99 Ang^-1 = 0.95 QB, where QB = 2 * pi/clat, is the momentum transfer of the Bragg peak. The complex valued structure factor is calculated as a function of vertical and lateral momentum transfer (Qx, Qz), over a range of momentum transfer with full width of deltaQ = 0.01 QB in both the vertical and lateral directions. The effective density, rho_eff(x,z), is then obtained by inverse fourier transform. Description of Archived data: Topography: this file contains the surface topography that is used in all calculations (shown in Figure 1, 5av, 5bv, 6ai, 6bi). This is in the form: x, h(x) Figure 2a: This includes documents the complex valued intrinsic effective density for an ideally terminated lattice calculated for each layer ,n, as a function of height, z. The figure shows the results for n = 1 to 20, over the range -200 Angstrom < z < 200 Angstrom. This archived data file includes the calculation for n = 1 to 500, and for 4500 Angstrom < z < 4500 Angstrom. This was calculated for the attenuation parameter beta = 0.99. Data is in the form: n, z, abs(rho_eff(n,z)), angle(rho_eff(n,z)) Figure 2bc: This is effectve interfacial density as a function of height, which corresponds to the sum of intrinsic effective densities for all layers. Data is in the form: z, abs(rho_eff(z)), angle(rho_eff(z)). Figure 4abc_i: This documents the effective densities determined from the complex structure factors, a) using the orthogonal ROI, b) the experimental effective densites obtained from data that simulates the effect of the tilt of the Ewald sphere, and c) the density after unskewing experimental densities. Data are in the form: x, z, abs(rho_eff_orth(x,z)), abs(rho_eff_EXP(x,z)), abs(rho_eff_EXP_unskew(x,z)). Figure 4abii: This documents the structure factor magnitudes that contain a) the orthogonal ROI, b) the experimentally observed intensities that included the tilting the Ewald sphere. Data are in the form: qx, qz, I_tot(qx,qz), I_tot_exp(qx,qz). Here, qz is the reduced momentum transfer, qz = Qz - QB, and QB is the momentum transfer of the Bragg peak. Figure 4c_ii: This documents the structure factor magnitudes that contain c) the experimentally observed intensities recovered from the unskewed densities. Data are in the form: qx, qz, I_tot_exp_unskew(qx,qz). Here, qz is the reduced momentum transfer, qz = Qz - QB, and QB is the momentum transfer of the Bragg peak. Figure 5a_i_ii: This documents the unskewed effective densities determined from the complex structure factors, a) the magnitude, and ii) phase of the effective density calculated at Q0 = 0.95 QB and deltaQ = 0.01 QB. Data are in the form: x, z, abs(rho_eff_exp_unskew(x,z)), abs(rho_eff_exp_unskew(x,z)). Figure 5b_i_ii: This documents the unskewed effective densities determined from the complex structure factors, a) the magnitude, and ii) phase of the effective density calculated at Q0 = 0.55 QB and deltaQ = 0.01 QB. Data are in the form: x,z,abs(rho_eff_exp_unskew(x,z)),abs(rho_eff_exp_unskew(x,z)). Figure 6a_ii_iii: This documents the unskewed effective densities determined from the complex structure factors after Fourier interpolation along the surface normal direction, including a) the magnitude, and ii) phase of the effective density calculated at Q0 = 0.95 QB and deltaQ = 0.01 QB. Data are in the form: x, z, abs(rho_eff_exp_unskew_interp(x,z)), abs(rho_eff_exp_unskew_interp(x,z)). Figure 6b_ii_iii: This documents the unskewed effective densities determined from the complex structure factors after Fourier interpolation along the surface normal direction, including a) the magnitude, and ii) phase of the effective density calculated at Q0 = 0.55 QB and deltaQ = 0.01 QB. Data are in the form: x, z, abs(rho_eff_exp_unskew_interp(x,z)), abs(rho_eff_exp_unskew_interp(x,z)).