Neutron diffraction study of the isotope effect in the crystal structure of the solid solution TiN0,26H0,075D0,075

This paper presents a neutron diffraction study of the isotopic effect and structure formation mechanisms in the TiN_0,26H_0,075D_0,075 solid solution. The goal of this study is to experimentally determine the crystal structure and order­ing s^,eque^, nce i^,n the combined isotopic composition, compare it with similar compositions containing only hydrogen or only deuterium, and investigate the contribution of deformation interactions and zero-point vibrations of atoms to the formation of ordered phases. The experimental program included the synthesis of samples by the Sieverts method, homogenizing annealing at 1475 K followed by quenching, X-ray verification of single-phase and detailed registration of neutron diffraction patterns on the DN 500 instrument at a wavelength Z = 1,085 A. Profile Rietveld analysis was performed in the FullProf program in order to refine the lattice parameters, atomic coordinates, interstitial occupancies and thermal factors. The results show that the TiN_0,26H_0,075D_0,075 sample exhibits an ordered layered structure described by the P3m1 space group when quenched from 1375 K, with an optimal order-disorder temperature of ~ 1375 K for this composition. Comparison with previously studied compositions TiN0 26H0₁₅(Tc ~ 1135 K) and TiN0 26H015 (Tc ~ 1275 K) demonstrates a steady trend of increasing the ordering temperature^, whe^, n H is replaced by D an^,d w^,hen a combined H/D composition is formed: In the series H0 15 ^ ^D0,15 ^ H0 075D0 075, there is a consistent increase in Tc (~ 1135 K ^ ~ 1275 K ^ ~ 1375 K). The lattice paramete rs also increase i n the same series: a and c demonstrate a small but statisti­cally significant expansion as the deuterium fraction increases and as the combined isotopic composition is introduced, indicating changes in the local deformations of the crystal lattice with different masses and amplitudes of thermal vi­brations of light elements. A full profile analysis shows that when describing the ordered phase of TiN₀₂₆H₀₀₇₅D₀₀₇₅, the optimal model assumes complete ordering of nitrogen atoms in octahedral positions 1a and the distribut^,ion o^, f hyd^, rogen and deuterium atoms predominantly between two types of tetrahedral positions 2d with different z coordinates, with a small fraction of deuterium (~ 0,061) localized in octahedral positions 1b that are not occupied by nitrogen. For H and D, the refined coordinates and occupancies were obtained: H predominantly occupies 2d with z ~ 0,732, D occupies 2d with z ~ 0,605 and partially 1b, which provides the best agreement between the experimental and calculated intensities. Attempts to assign an alternative distribution of isotopes lead to a significant increase in the incompatibility factor of the fit. This highlights the sensitivity of the neutron method to the difference in coherent cross-sections of H and D and the high reliability of the chosen structural model. The interpretation of the observations relies on two key factors. First, the predominance of the deformation interaction over the electronic interaction explains the directional change in Tc and lattice parameters when H is replaced by D and when isotopes are combined: isotopes with equal charges load the sublattices of non-metals differently due to differences in mass and zero-point oscillation amplitude, which enhances local deformations and increases the stability of the ordered phase. Secondly, the difference in zero-point fluctuations and root-mean-square displacements explains the selectivity of interstitial occupancy: heavier deuterium has a smaller amplitude of zero-point fluctuations, which makes it energetically favorable to occupy slightly different potential wells and, consequently, different positions in the structure compared to hydrogen. These two factors together contribute to the observed isotopic ordering and the increase in the order-disorder temperature. The work provides detailed values of lattice parameters, atomic coordinates, occupancies, thermal factors, and fit quality statistics (Rp, Rwp, Rexp, RBragg, %²), making the results reproducible with the original neutron diffraction patterns and fit parameters. Possible limitations of the study are discussed: the need to assess the contribution of microstructural stresses and crystallite sizes to the width of peaks, the influence of microheterogeneity of composition and the kinetics of ordering under fixed annealing temperature regimes. It is recommended for subsequent works to carry out temperature series in situ, an assessment of size/strain components of profiles and modern calculations of potential wells for H and D (for example, by DFT) to quantify the contributions of deformational and electronic interactions. In summary, the study demonstrates a new experimental example of isotopic ordering in the Ti-N-H/D system, refines the distribution of H and D in the ordered phase of TiN₀₂₆H₀₀₇₅D₀₀₇₅, and provides a well-founded link between the increase in ordering temperature and deforma­tion effects an^,d th^,e diff^, erences in zero-point vibrations of the isotopes. These results are significant for understanding the mechanisms of ordering in insertion alloys and for designing materials with controlled properties through isotopic and chemical regulation.

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