Calorimetric study of the desorption of the interstitial hydrogen atoms in ferromagnetic ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}{\mathrm{BH}}_x$ $(x<~5)$ microcrystals

When heating over 300–800 K in a calorimeter, ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}{\mathrm{BH}}_x,$ $x<~5,$ microcrystals desorb the H atoms in six irreversible endothermic signals. They appear at temperatures $T_p\sim 340,$ 439 (doubly degenerate), 567, 605, and 653 K at the heating rate $\beta =15\mathrm{}\mathrm{K}/\mathrm{m}\mathrm{i}\mathrm{n},$ following the modified Kissinger relation $\ln {(T}_p/\beta {)=(E}_a{/R)T}_p^{-1}+\mathrm{const},$ with $R$ the gas constant. The 340 signal has an extremely weak intensity at a slow heating, $\beta <~40\mathrm{K}/\mathrm{m}\mathrm{i}\mathrm{n},$ because the H atoms in the involved interstitial site in the sample slowly tunnel to neighboring higher-transition-energy sites. The thermogram at 439 K is the most prominent. It contains two signals which could be resolved by selective isothermal desorptions. These six different identified thermal signals are assigned to the desorptions of the H atoms from six specific $4c,$ $16k2,$ $16k1,$ $4e,$ $8j2,$ and $8j1$ crystallographic interstitial sites (between the Fe atoms) in the sample, characterized by six different activation energies $E_a$ between 48 and 123 kJ/mol, taking into account their H occupancies $n_i\left(\mathrm{H}\right).\mathrm{}$ The distribution of partial enthalpies in the thermal signals (at $\beta =15\mathrm{}\mathrm{K}/\mathrm{m}\mathrm{i}\mathrm{n}$) determines $n_i\left(\mathrm{H}\right)\cong 0,$ 6, 5, 2, 5, and 2 H atoms in the respective sites per ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}{\mathrm{BH}}_x,$ $x\sim 5,$ crystal unit cell with a total of $4x=20\mathrm{H}$ atoms. It is found that a significant portion of the thermally excited H atoms in these sites, in the process to the desorption, redistributes over neighboring sites of modified energies to keep the H atoms at high temperatures. The redistribution reaction is exothermic. It has been observed separately in $8j2$ and $8j1$ sites at 616 and 684 K (at $\beta =50\mathrm{}\mathrm{K}/\mathrm{m}\mathrm{i}\mathrm{n}$) in a partially H-desorbed sample in the lower-transition-energy sites by heating it at 583 K. A local redistribution of the interatomic distances and/or the electronic charges occurs within the lattice following the thermal desorption of the H atoms. It results in a monotonically decreasing exothermic (structural relaxation) signal of the rate of the change of the enthalpy, $(\partial H/\partial {t)}_T,$ with time $t,$ after the desorption at $t=0,$ following the primary endothermic desorption signal. The results are discussed with simulations of related processes.