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Ordering of the two incommensurate charge density waves (CDW), $\mathbf{q_1}$ = (0.0, 0.243, 0.0) and $\mathbf{q_2}$ = (0.5, 0.263,0.5) in the quasi-one-dimensional NbSe$_3$ structure is studied by means of low temperature scanning tunneling microscopy. Larger (100) van der Waals surfaces are analyzed using one-dimensional Fourier transforms along the three types of trigonal prismatic columns, running parallel to the monoclinic $\mathbf{b_0}$ direction. The procedure enables unambiguous differentiation between both CDWs modulating individual columns. In addition, it allows a quantitative comparison of modulation amplitudes along different columns of the same type and, in case of sufficiently large images, also along individual columns. It is confirmed that each CDW modulates both type-III and type-I columns with the narrowest isosceles bases. As a consequence beating is observed between the two slightly different modes. The bridging type-II columns appear not to be modulated. On a large scale the modulation amplitudes along individual columns vary, suggesting formation of CDW nanodomains. The possibility of interchanging both CDWs along columns forming symmetry-related pairs results in a charge difference, which might be the possible origin of CDW sliding.

Titanium borates show promissing hydrogen storage characteristics. Structural relaxation around individual hydrogen atoms and the binding energies are studied by means of the density functional theory methods for a number of hydrogenated TiB2, TiB and Ti2B structures. Starting with the possible symmetric hydrogen sites a random structure searching has been performed, in addition to locate all energetically stable adsorption sites. It is shown that for the three bulk compounds considered, the lowest binding energies are obtained for TiB2 (in the 0.3-1.8 eV range), the largest for Ti2B (in the 3.9-4.7 eV range), while for TiB they are intermediate (in the 2.8-3.5 eV range). Calculations performed on hydrogenated Ti2B result in two energetically stable sites for two different starting environments, suggesting a posible soft mode solution.