  We used archival very long baseline interferometry (VLBI) data of active
galactic nuclei (AGN) observed from 1.4 GHz to 86 GHz to measure the angular
size of VLBI radio cores in 8959 AGNs. We analysed their sky distributions,
frequency dependencies and created the most densely sampled and complete to
date distribution map of large-scale scattering properties of the interstellar
medium in our Galaxy. Significant angular broadening of the measured AGN core
sizes is detected for the sources seen through the Galactic plane, and this
effect is especially strong at low frequencies (e.g., at 2 GHz). The scattering
screens containing electron density fluctuations of hot plasma are mainly
concentrated in the Galactic plane and manifest clumpy distribution. The region
of the strongest scattering is the Galactic centre, where the Galactic bar and
the compact radio source Sagittarius A* are located. We have also found the
enhancement of scattering strength in regions of the Cygnus constellation,
supernova remnants Taurus A, Vela, W78 and Cassiopeia A, and the Orion Nebula.
Using multi-frequency observational data of AGN core sizes, we separated the
contribution of the intrinsic and scattered sizes to the measured angular
diameter for 1411 sources. For the sources observed through the Galactic plane,
the contribution of the scattered size component is systematically larger than
for those seen outside the Galactic plane. The derived power-law scattering
indices are found to be in good agreement with theoretical predictions for the
diffractive-dominated scattering of radio emission in a hot plasma with
Gaussian distribution of density inhomogeneities.
