Exploring structural, electronic, mechanical, and hydrogen storage properties of Mg₃ZH₈ (Z = Fe, Co): a density functional theory study

Abstract

The development of efficient hydrogen storage materials is crucial for practical hydrogen energy utilization. This study uses first-principles density functional theory (DFT) to examine the structural, electronic, mechanical, optical, and hydrogen storage properties of Mg₃ZH₈ (Z = Fe, Co) complex hydrides. Both compounds are thermodynamically and dynamically stable, as confirmed by negative formation energies and phonon spectra free of imaginary modes. Mg₃FeH₈ exhibits a ferromagnetic metallic ground state, while Mg₃CoH₈ shows non-magnetic metallic behavior, with transition-metal d states playing a key role in their electronic and magnetic properties. The calculated gravimetric hydrogen storage capacities of 5.90 wt% for Mg₃FeH₈ and 5.76 wt% for Mg₃CoH₈, along with high volumetric densities of 195.6 and 186.6 g H₂ per L, respectively, surpass current U.S. Department of Energy targets. Dehydrogenation thermodynamics show moderate desorption temperatures, with Mg₃FeH₈ demonstrating better hydrogen release behavior. Mechanical analysis indicates ductility with positive Cauchy pressure, high Pugh's ratios, and moderate Vickers hardness, suggesting resistance to hydrogen embrittlement. Optical and transport properties reveal metallic conductivity, which enhances hydrogen desorption kinetics. These findings position Mg₃ZH₈ (Z = Fe, Co) as a promising hydrogen storage material and provide a solid theoretical basis for future experimental work.

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1. Introduction

Hydrogen energy has come to light as a possible way to solve both the world's energy crisis and pollution problems. Hydrogen is a clean energy carrier that has a high gravimetric energy density and does not release any carbon when used. It is seen as a good replacement for traditional fossil fuels. The increasing demand for clean and sustainable energy has intensified interest in hydrogen as a promising energy carrier due to its high gravimetric energy density and environmentally benign combustion products.^1–3 Despite significant progress in hydrogen production and utilization technologies, the lack of safe, efficient, and reversible hydrogen storage materials operating under near-ambient conditions remains a major obstacle to the large-scale deployment of hydrogen-based energy systems. Among the available storage strategies, solid-state hydrogen storage using metal and complex hydrides is considered one of the most promising approaches because of its high volumetric density, enhanced safety, and compactness compared to compressed or liquefied hydrogen. To guide the development of practical hydrogen storage materials, the U.S. Department of Energy (DOE)⁴ has established performance targets for onboard storage systems, including a gravimetric hydrogen capacity exceeding 5.5 wt%, a volumetric capacity above 40 g H₂ per L, operating temperatures in the range of 233–333 K, and moderate pressures below 10 MPa. Achieving these targets simultaneously remains challenging, as many known hydrides exhibit either excessively strong metal–hydrogen bonding that leads to high desorption temperatures or insufficient thermodynamic stability that compromises reversibility and cycling performance.

In recent years, complex and perovskite-type hydrides have emerged as an important class of hydrogen storage materials because their flexible crystal chemistry enables systematic tuning of structural, electronic, and thermodynamic properties. Numerous categories of complex hydrides, such as borohydrides, amides, and alanates, have undergone extensive research for hydrogen storage purposes. Alkali alanates MAlH₄ (M = Li, Na, K) have garnered significant attention owing to their relatively high hydrogen density and reversible hydrogen absorption/desorption characteristics.⁵ First-principles investigations of MgVH₆ and MgSiH₆ have demonstrated chemical stability, pressure-dependent phase behaviour, and notable electronic properties, such as metallic characteristics and superconductivity under extreme conditions, underscoring the adaptability of hexahydride systems.^6,7 Concurrently, double perovskite hydrides have become attractive options for multipurpose uses. For example, KNaMg₂F_6−xH_x and KNaAe₂H₆ (Ae = Be, Mg, Ca) show semiconducting behaviour with ultraviolet absorption capacity and favourable desorption temperatures.⁸ Furthermore, large hydrogen capacities and favourable formation energetics have been anticipated for a number of hexahydrides, such as Q₂FeH₆ (Q = Mg, Ca, Sr),⁹ Mg₂XH₆ (X = Cr, Mn),¹⁰ A₂LiCuH₆ (A = Be, Mg, Ca, Sr),¹¹ KNaX₂H₆ (X = Mg, Ca, and X₂CaCdH₆ (X = Rb, Cs).¹² Similarly, indirect band gap semiconductors with the capacity to store hydrogen have been found as A₂BH₆ (A = K, Rb; B = Ge, Sn) hydrides.¹³ Additionally, it has been demonstrated that compositional tweaking, such as lithium doping in Na-based perovskites, improves photocatalytic activity and optoelectronic response.¹⁴ Numerous first-principles studies have demonstrated promising hydrogen storage performance in alkaline-earth hydrides systems. For example, DFT investigations of alkali and alkaline-earth hydrides, including AMAlH₄ (AM = Li, Na, K and Rb),¹⁵ XNH₆ (X = Li, Na, K),¹⁶ NaXH₃ (X = Be, Mg, Ca, Sr),¹⁷ and RbXH₃ (X = Mg, Ca, Sr, Ba),¹⁸ have reported high gravimetric hydrogen capacities and favorable formation energetics. These investigations also emphasize the critical role of lattice environment, electronic structure, and bonding characteristics in determining hydrogen stability and release behavior. First-principles studies of Mg₃XH₈ (X = Ca, Sc, Ti, V, Cr, Mn) hydrides have shown that transition-metal substitution strongly affects lattice stability, hydrogen binding strength, and mechanical behavior.¹⁹ These modifications lead to favorable gravimetric hydrogen densities and moderate desorption temperatures.

Despite these advances, Mg₃ZH₈ (Z = Fe, Co) hydrides containing late transition metals such as Fe and Co have not yet been systematically explored. Compared with early transition metals, Fe and Co possess more localized d electrons, which can significantly modify magnetic behavior, electronic conductivity, bonding character, and metal–hydrogen interactions. Understanding how these factors affect hydrogen storage thermodynamics, kinetics, and mechanical durability is essential for expanding the design space of Mg-based complex hydrides. Moreover, experimental data for Mg₃ZH₈ (Z = Fe, Co) systems are currently unavailable, underscoring the need for reliable theoretical benchmarks. In this work, we present a comprehensive first-principles investigation of Mg₃ZH₈ (Z = Fe, Co) complex hydrides. Structural stability, electronic and magnetic properties, mechanical and thermophysical behavior, optical response, and hydrogen storage characteristics are systematically examined. Multiple dehydrogenation pathways are analyzed to evaluate reaction energetics and hydrogen desorption temperatures. By directly comparing Fe- and Co-based systems, the role of late transition-metal substitution in tailoring hydrogen storage performance is clarified. The present study provides the first detailed theoretical benchmark for Mg₃ZH₈ (Z = Fe, Co) hydrides and offers guidance for future experimental synthesis and optimization.

2. Computational details

The hydrogen storage properties, thermo-mechanical, opto-electronic, and magnetic nature of Mg₃ZH₈ (Z = Fe, Co) hydrides were investigated based on density functional theory (DFT) using the CASTEP code.²⁰ Vanderbilt ultrasoft pseudopotentials were employed to describe the interaction between valence electrons and ionic cores. The exchange–correlation energy was treated using the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional.²¹ Mg₃ZH₈ (Z = Fe, Co) hydrides crystallize in a cubic structure with space group Pm3̄m (no. 221), belonging to the m3̄m point group. In the optimized structures, the transition metal atom (Fe or Co) occupies the 1a Wyckoff position at (1/2, 1/2, 0). Mg atoms are located at the 3c site with fractional coordinates (0, 0, 0). H atoms occupy the 8g Wyckoff position at (0.243175, 0.243175, 0.756825). These atomic positions were fully relaxed during geometry optimization. The optimized lattice parameters were found to be a = b = c = 4.09 Å for Mg₃FeH₈ and 4.15 Å for Mg₃CoH₈, corresponding to unit cell volumes of 68.39 ų and 71.68 ų, respectively as shown in Table 1. Geometry optimizations were performed using the BFGS minimization algorithm.²² The convergence criteria were set to 5 × 10⁻⁶ eV per atom for total energy, 0.01 eV Å⁻¹ for maximum ionic force, 5 × 10⁻⁴ Å for maximum atomic displacement, and 0.02 GPa for maximum stress. All calculations were carried out at 0 K and zero external pressure. A Monkhorst–Pack k-point mesh²³ of 6 × 6 × 6 was used for Brillouin zone integration. The plane-wave cutoff energy was fixed at 630 eV. A smearing width of 0.5 eV was applied to improve electronic convergence. Elastic constants were evaluated to determine the mechanical properties. The elastic moduli of the polycrystalline systems were derived using the Voigt–Reuss–Hill approximation.^24,25 Electronic band structures and optical properties were calculated in reciprocal space using fully optimized crystal geometries. Optical properties were obtained within the CASTEP code through evaluation of the complex dielectric function. Phonon dispersion calculations for Mg₃ZH₈ (Z = Fe, Co) were performed using the finite-displacement method with ultrasoft pseudopotentials. A 4 × 4 × 4 Monkhorst–Pack k-point mesh was employed to ensure accurate force-constant determination and phonon convergence. Plane-wave energy cutoffs of 850 eV for Mg₃FeH₈ and 950 eV for Mg₃CoH₈ were used, and all computational parameters were carefully tested to obtain converged phonon spectra without imaginary frequencies.

Table 1 The calculated geometry optimized data, formation enthalpy, and gravimetric properties of Mg₃ZH₈ (Z = Fe, Co) hydrides with previously reported similar type of hydrides

Compounds	a = b = c	V	ΔEfor	ρ(g H2 per L)	Cwt%	Tdes (K)
Mg3FeH8	4.09	68.39	−0.264	195.6	5.90	194.74
Mg3CoH8	4.15	71.68	−0.220	186.6	5.76	162.57
Mg3ScH8 (ref. 19)	4.73	—	−0.240	197	6.36
Mg3TiH8 (ref. 19)	4.61	—	−0.250	218	6.21
Mg3VH8 (ref. 19)	4.54	—	−0.230	234	6.07
Mg3CaH8 (ref. 19)	4.90	—	−0.100	171	6.61
Mg3CrH8 (ref. 19)	4.50	—	−0.280	242	6.02
Mg3MnH8 (ref. 19)	4.47	—	−0.190	252	5.89
Mg3MnH7 (ref. 26)	—	—	—	—	5.2^expt.	530–640^expt.
Mg2FeH6 (ref. 27)	—	—	—	—	5.5^expt.	603^expt.
MgH2 (ref. 28)	—	—	—	—	7.1^expt.	623–673^expt.

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3. Results and discussion

3.1 Phase stability and gravimetric properties

The optimized crystal structures and dynamical stability profiles of the Mg-based hydrides Mg₃ZH₈ (Z = Fe, Co) are shown in Fig. 1(a)–(c). Both compounds crystallize in a highly hydrogen-rich framework, where the choice of transition-metal cation at the Z site plays a decisive role in determining lattice geometry and stability. Table 1 summarizes the optimized structural parameters, volumetric and gravimetric hydrogen storage capacities of Mg₃ZH₈ (Z = Fe, Co) in comparison with previously reported Mg₃ZH₈-type hydrides. The calculated lattice parameters for Mg₃FeH₈ (a = 4.09 Å) and Mg₃CoH₈ (a = 4.15 Å) are smaller than those of Mg₃ScH₈, Mg₃TiH₈, and Mg₃CaH₈, reflecting the reduced atomic radii of Fe and Co and the resulting lattice contraction.¹⁹ This compact crystal structure directly contributes to enhanced volumetric hydrogen storage performance.

Fig. 1 (a)–(c) The phonon dispersion with three-dimensional structure of Mg based Mg₃ZH₈ (Z = Fe, Co) hydrides.

Thermodynamic stability was evaluated by calculating the formation enthalpy (ΔE_f), defined as,

where E_tot(Mg₃ZH₈) is the total energy of the optimized unit cell, E_tot(Mg) and E_tot(Z) are the energies of elemental Mg and Z (Fe or Co) in their stable crystalline phases, E_tot(H₂) is the total energy of the hydrogen molecule, and N is the number of atoms per formula unit. The negative formation energies of Mg₃FeH₈ (−0.264 eV per atom) and Mg₃CoH₈ (−0.220 eV per atom) confirm their thermodynamic stability and are comparable to, or more favorable than, those reported for¹⁹ Mg₃ScH₈, Mg₃TiH₈, Mg₃VH₈, and Mg₃MnH₈. Notably, Mg₃FeH₈ exhibits a formation energy close to that of Mg₃CrH₈, indicating similarly strong metal–hydrogen bonding, while maintaining a smaller lattice parameter. At present, no experimental data are available for these compounds; therefore, the present results provide the first systematic theoretical benchmark for this class of materials and offer valuable guidance for future experimental synthesis and characterization.

Dynamical stability was further assessed through phonon dispersion calculations, as shown in Fig. 1(a) and (b). The phonon characteristics reveal how hydrogen-rich stoichiometry and metal–hydrogen bonding collectively stabilize the lattice while enabling high gravimetric hydrogen capacity. The phonon spectra of both hydrides exhibit three acoustic branches and multiple optical modes, with no imaginary frequencies observed throughout the Brillouin zone. This confirms that Mg₃ZH₈ (Z = Fe, Co) are dynamically stable and free from lattice instabilities. The optical phonon modes at higher frequencies are dominated by hydrogen vibrations, reflecting the strong metal–hydrogen bonding and hydrogen-rich nature of the lattice. A pronounced frequency gap between acoustic and optical phonon branches is observed in both compounds. This gap originates from the large mass contrast between light hydrogen atoms and heavier metal atoms (Mg and Z), which leads to well-separated low-frequency lattice translations and high-frequency hydrogen-dominated vibrations. The wider acoustic–optical gap observed in Mg₃FeH₈ compared to Mg₃CoH₈ reflects stronger Fe–H bonding and a stiffer local hydrogen environment, consistent with its more negative formation energy and higher lattice rigidity.

The ab initio molecular dynamics (AIMD) simulations for Mg₃FeH₈ and Mg₃CoH₈ were performed using a 2 × 2 × 2 supercell with a timestep of 1 fs in the NVT ensemble at 300 K, after an initial equilibration phase. The simulations ran for 5000 fs, providing sufficient sampling of the atomic dynamics. The Fig. 2(a) and (b) show the temperature evolution of both hydrides during the simulations, with the temperature fluctuating around 300 K. The temperature was analyzed using the kinetic energy relation: ; where E_kin is the average kinetic energy, N is the number of atoms, and k_B is Boltzmann's constant. In these simulations, the temperature fluctuations around 300 K indicate dynamic stability for both hydrides, as neither system exhibits significant deviations from the target temperature. The stable behavior of the temperature profiles suggests that both Mg₃FeH₈ and Mg₃CoH₈ maintain their structural integrity and dynamic stability at room temperature, making them suitable candidates for hydrogen storage applications under practical conditions. The time evolution of the total energy for Mg₃FeH₈ and Mg₃CoH₈ systems is presented in Fig. 2(c) and (d). In both cases, the energy exhibits a slight upward drift over the simulation time of 5000 fs. For Mg₃FeH₈, the energy increases from −3695.85376 eV to −3691.13808 eV, corresponding to a relative variation of approximately 0.128%. Similarly, Mg₃CoH₈ shows an increase from −4229.13344 eV to −4224.47209 eV, yielding a relative variation of about 0.110%. Despite these small increases, the overall fluctuations remain minimal compared to the total energy scale, indicating good stability of the simulations. The slightly lower variation observed in Mg₃CoH₈ suggests marginally improved energy conservation compared to Mg₃FeH₈.

Fig. 2 (a)–(d) Temperature and energy evolution of Mg₃FeH₈ and Mg₃CoH₈ at 300 K over 5000 fs. Temperature remains stable around 300 K, while total energy shows slight drifts with variations of 0.128% and 0.110%, respectively.

In this study, the hydrogen storage potential of Mg₃ZH₈ (Z = Fe, Co) hydrides was evaluated by calculating the gravimetric hydrogen capacity using,²⁹

where H/M is the hydrogen-to-metal ratio, m_H is the atomic mass of hydrogen, and m_host is the mass of the host lattice. Owing to their hydrogen-rich stoichiometry (eight hydrogen atoms per formula unit) and the low atomic mass of magnesium, Mg₃ZH₈ (Z = Fe, Co) hydrides exhibit high gravimetric capacities of 5.89 wt% for Mg₃FeH₈ and 5.76 wt% for Mg₃CoH₈ are shown in Fig. 3(a). The small difference in gravimetric capacity between Mg₃FeH₈ and Mg₃CoH₈ reflects the subtle mass and bonding variations between Fe and Co, indicating that Z-site substitution provides an effective route to tune hydrogen density without degrading phase or dynamical stability. Notably, the gravimetric hydrogen storage capacities of Mg₃FeH₈ and Mg₃CoH₈ exceed the U.S. DOE near-term gravimetric target of 5.5 wt%, highlighting their promise for practical solid-state hydrogen storage applications.³⁰ The gravimetric hydrogen storage capacities of Mg₃FeH₈ (5.90 wt%) and Mg₃CoH₈ (5.76 wt%) fall within the typical range reported for Mg₃ZH₈-type hydrides¹⁹ in Table 1. Additionally, the calculated values of C_wt% for both hydrides are in good agreement with the experimental values reported for other hydrides, as outlined in Table 1, confirming the reliability of our theoretical predictions.

Fig. 3 (a) Gravimetric capacity of Mg₃ZH₈ (Z = Fe, Co), and (b) comparison of gravimetric hydrogen storage capacities of Mg₃ZH₈ (Z = Fe, Co) with previously reported complex hydrides.

Since there are no previously reported experimental or theoretical gravimetric hydrogen storage capacities for Mg₃ZH₈ (Z = Fe, Co), Fig. 3(b) presents a comparative analysis with a range of well-established complex hydrides. Both Mg₃FeH₈ and Mg₃CoH₈ exhibit among the highest gravimetric hydrogen storage capacities, surpassing or closely matching widely studied Mg-based complex hydrides such as Mg₂NiH₆ (5.32 wt%),³¹ Mg₂CoH₆ (5.29 wt%),³¹ Mg₂CrH₆ (5.60 wt%),¹⁰ and Mg₂VH₆ (5.72 wt%).³² Their performance also exceeds that of several alkali- and alkaline-earth-stabilized hydrides, including, Mn₃NaH₈ (4.12 wt%),³³ Mn₃KH₈ (3.80 wt%),³³ K₂LiAlH₆ (5.08 wt%),³⁴ Ca₂VH₆ (4.41 wt%),³² Rb₂NaGaH₆ (1.48 wt%),³⁵ and KNaMg₂H₆ (5.19 wt%).⁸ This comparison demonstrates that Mg₃ZH₈ (Z = Fe, Co) hydrides combine high hydrogen content with a lightweight Mg-based framework, positioning them among the most competitive solid-state hydrogen storage materials reported to date and underscoring their scientific relevance and potential for practical hydrogen energy applications. Our study aims to provide foundational insights into the hydrogen storage capacities of Mg₃FeH₈ and Mg₃CoH₈ at the material level. System-level performance would require experimental validation and simulations that account for the integration of these materials into practical storage systems, which is a necessary next step in future research.

In addition to gravimetric hydrogen storage capacity, the volumetric hydrogen storage capacity (ρ_vol) is a critical parameter for evaluating the practical applicability of solid-state hydrogen storage materials, particularly for space-constrained applications such as onboard storage systems. The volumetric capacity quantifies the amount of hydrogen that can be stored per unit volume of the material and is expressed in g H₂ per L. Following the methodology adopted in the referenced hydrogen-storage studies, the volumetric hydrogen storage capacity is calculated using the relation:²⁹

where N_H is the total number of hydrogen atoms contained within the crystallographic unit cell, m_H is the molar mass of hydrogen (1.008 g mol⁻¹, V is the unit-cell volume expressed in liters, and N_A is Avogadro's number. The unit-cell volume is obtained directly from the optimized lattice parameters, ensuring that the calculated ρ_vol reflects the intrinsic structural compactness of the hydride. Table 1 indicates that the calculated volumetric hydrogen storage capacities of Mg₃FeH₈ and Mg₃CoH₈ are 195.6 and 186.6 g H₂ per L, respectively, which are comparable to those of Mg₃ScH₈ (197 g H₂ per L) and higher than that of Mg₃CaH₈ (171 g H₂ per L).¹⁹ Although lower than the high volumetric capacities reported for Mg₃TiH₈, Mg₃VH₈, Mg₃CrH₈, and Mg₃MnH₈, both compounds far exceed the U.S. DOE volumetric hydrogen storage target of ∼40 g H₂ per L.¹⁹ These results indicate that Mg₃FeH₈ and Mg₃CoH₈ achieve a favorable balance between structural compactness and hydrogen storage efficiency within the Mg₃ZH₈ hydride family.

A key parameter for hydrogen storage applications is the hydrogen desorption temperature, T_des, which defines the thermal conditions required for hydrogen release. Following the approach proposed by Ikeda et al.,³⁶ the hydrogen decomposition reaction for Mg₃ZH₈ (Z = Fe, Co) hydrides is expressed as: Mg₃ZH₈ → 3Mg + Z + 4H₂.

Based on this reaction, the hydrogen decomposition enthalpy (ΔH) is calculated as:

ΔH = 3H_Mg + H_Z + 4H_H2 − H_Mg3ZH8

where H_Mg3ZH8 represents the enthalpy of the corresponding system. The enthalpy is determined by:

H = E_ele + E_ZPE

where E_ele and E_ZPE denote the electronic total energy and the zero-point energy, respectively. The zero-point energy is estimated from the phonon density of states as:
where h, ω, and g(ω) are Planck's constant, phonon frequency, and phonon density of states, respectively.

The hydrogen desorption temperature (T_des) is estimated using:

where, ΔH is the decomposition enthalpy and ΔS is the entropy change of the reaction. In this work, ΔS is approximated as the entropy of hydrogen gas (130.7 J mol⁻¹ K⁻¹).^8,31–35 Using this thermodynamic framework, the desorption temperatures for Mg₃FeH₈ and Mg₃CoH₈ were calculated to be 194.74 K and 162.57 K, respectively. These values suggest moderate hydrogen desorption behavior for both materials under practical conditions. The calculated T_des values for both hydrides are lower than the experimental values for other hydrides reported in Table 1. The relatively low desorption temperatures indicate that hydrogen release can occur at mild temperatures, which helps to reduce thermal stress during hydrogen absorption and desorption cycles. From a durability perspective, these moderate desorption temperatures imply balanced thermodynamic stability, enabling reversible hydrogen absorption and release without excessive heating that could lead to lattice degradation or phase segregation. Although the predicted T_des for both hydrides are slightly below the U.S. DOE target window of 233–333 K, the results indicate a favorable balance between stability and hydrogen release under near-ambient conditions.

The hydrogen diffusion behavior in Mg₃FeH₈ and Mg₃CoH₈ is analyzed using the activation energy profiles shown in Fig. 4(a) and (b). In hydrogen storage materials, atomic migration is governed by the activation energy barrier, where lower values facilitate easier hydrogen transport and improved absorption/desorption kinetics. The diffusion pathways were evaluated using the nudged elastic band (NEB) method, which determines the minimum energy path and corresponding barriers.³⁷ Two possible diffusion pathways (path 1 and path 2) are considered for both compounds. For Mg₃FeH₈, the activation energies are 0.45 eV for path 1 and 1.69 eV for path 2, indicating that hydrogen migration is more favorable along path 1. In contrast, Mg₃CoH₈ exhibits lower barriers of 0.20 eV for path 1 and 1.39 eV for path 2, suggesting enhanced hydrogen mobility compared to Mg₃FeH₈. The relatively low activation energy along the preferred pathway, particularly in Mg₃CoH₈, indicates efficient hydrogen diffusion within the lattice. Overall, these results confirm that hydrogen transport is not kinetically hindered and support the suitability of these materials for hydrogen storage applications.

Fig. 4 Hydrogen diffusion energy profiles for (a) Mg₃FeH₈ and (b) Mg₃CoH₈ along two possible migration pathways (path 1 and path 2) calculated using the NEB method.

3.2 Electronic properties

Hydrogen absorption and desorption kinetics in solid-state hydrides are strongly influenced by their electronic structure, as the availability of electronic states near the Fermi level governs charge transfer, metal–hydrogen bonding, and hydrogen diffusion processes. Perovskite and complex hydrides have therefore attracted significant attention as promising hydrogen storage materials. In this section, the electronic properties of Mg₃ZH₈ (Z = Fe, Co) complex hydrides are investigated through a detailed analysis of their electronic band structures, total density of states (TDOS), and partial density of states (PDOS). Fig. 5(a) and 6(a) display the calculated electronic band structures of Mg₃FeH₈ and Mg₃CoH₈, where the horizontal dashed line represents the Fermi level (E_F). The band structures were obtained within the GGA-PBE framework over an energy window from −6.0 to 6.0 eV, with E_F set to 0 eV. The Kohn–Sham eigenvalues were plotted along the high-symmetry directions X–R–M–Γ–R of the first Brillouin zone. Both Mg₃FeH₈ and Mg₃CoH₈ exhibit multiple electronic bands crossing the Fermi level, indicating the absence of a band gap and confirming their metallic ground state. The band dispersion near E_F provides further insight into their electronic transport behavior. Several bands crossing E_F display steep slopes along specific high-symmetry directions, reflecting strong orbital overlap and enhanced electronic delocalization. Mg₃FeH₈ shows relatively steeper band curvature near E_F compared to Mg₃CoH₈, suggesting a smaller carrier effective mass and higher carrier mobility. This behavior is primarily attributed to stronger Fe (3d)–H (1s) hybridization, whereas Mg₃CoH₈ exhibits slightly flatter bands due to comparatively weaker Co-3d contributions.

Fig. 5 (a) and (b) The electronic band structure with partial and total density of states of Mg₃FeH₈ complex hydride.

Fig. 6 (a) and (b) The electronic band structure with partial and total density of states of Mg₃CoH₈ complex hydride.

The steep dispersion of electronic bands near E_F implies a reduced carrier effective mass and, consequently, a higher Fermi velocity, given by^38,39

where m* is the carrier effective mass. A higher Fermi velocity corresponds to enhanced carrier mobility and improved electrical and thermal transport. In this regard, Mg₃FeH₈ is expected to exhibit superior electronic transport properties compared to Mg₃CoH₈, consistent with its higher TDOS and stronger d-orbital participation near E_F. The metallic behavior of Mg₃ZH₈ (Z = Fe, Co) can also be assessed using the metallic fraction,^38,39
where n_m is the number of thermally excited electrons, n_e is the total number of valence electrons, and N(E_F) is the TDOS at the Fermi level. The calculated values of f_m for Mg₃ZH₈ (Z = Fe, Co) are shown in Table 2. Since, f_m is directly proportional to N(E_F), Mg₃FeH₈ exhibits a higher metallic fraction at room temperature than Mg₃CoH₈, implying a larger population of mobile charge carriers. The metallic conductivity, enhanced carrier mobility, and appreciable metallic fraction of Mg₃ZH₈ (Z = Fe, Co) hydrides have important implications for hydrogen storage applications. Metallic electronic behavior facilitates efficient charge transfer and heat dissipation during hydrogen absorption and desorption cycles, reducing kinetic barriers and localized thermal buildup.

Table 2 Comparative metallicity, metallic fraction, and orbital character for Mg₃ZH₈ (Z = Fe, Co)

Compound	TDOS at EF (states per eV)	Metallic fraction fm (300 K)	Metallic strength	Dominant orbital at EF
Mg3FeH8	∼5.43	∼7.3 × 10^−3	Strong metallic	Fe-3d with H-1s hybridization
Mg3CoH8	∼3.91	∼4.4 × 10^−3	Moderate metallic	Co-3d with H-1s contribution

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Fig. 5(b) and 6(b) display the partial and total density of states of Mg₃FeH₈ and Mg₃CoH₈ hydrides. The total and partial density of states (TDOS and PDOS) of Mg₃ZH₈ (Z = Fe, Co) clarify the orbital contributions governing the valence and conduction regions. For both Mg₃FeH₈ and Mg₃CoH₈, the TDOS shows a finite value at the Fermi level, confirming their metallic nature. States near E_F are dominated by transition-metal d orbitals, with Fe-3d states contributing most strongly in Mg₃FeH₈ and Co-3d states in Mg₃CoH₈. This dominant d-state presence explains the band crossings at E_F and the high carrier density. In the valence band region, extending from about −6 eV up to the Fermi level, the DOS is mainly composed of hybridized metal d and hydrogen 1s states, indicating strong metal–hydrogen bonding. The sharp d-orbital peaks just below E_F reflect localized d electrons, while the broader H-1s contribution at lower energies signifies covalent interaction with the metal framework. Magnesium s and p states contribute weakly in this region, acting mainly as a charge donor to the metal–hydrogen network. In the conduction band region above E_F, the DOS is again dominated by metal d states with minor contributions from Mg-p orbitals, indicating that electronic transport is primarily governed by the transition-metal sublattice. The similarity in DOS distribution for Fe- and Co-based systems suggests that Z-site substitution mainly tunes the intensity and energy position of d-state peaks rather than altering the overall electronic character. This d-H hybridization near the Fermi level is crucial for metallic conductivity and supports efficient charge transfer and lattice screening, which are favorable for hydrogen diffusion and desorption kinetics.

Further, the electronic band structures of Mg₃FeH₈ and Mg₃CoH₈ were calculated using the HSE06 functional. As shown in Fig. 7(a) and (b), both compounds exhibit metallic behavior. This is confirmed by the presence of several energy bands crossing the Fermi level. This indicates the absence of a band gap and confirms the availability of free charge carriers in both systems. In Mg₃FeH₈, the bands near the Fermi level show relatively stronger dispersion compared to Mg₃CoH₈, suggesting enhanced electronic conductivity due to more pronounced hybridization between Fe 3d-states and H 1s-states. In contrast, Mg₃CoH₈ displays slightly flatter bands in certain regions, indicating comparatively localized electronic states. The overall metallic nature of both compounds is beneficial for hydrogen storage applications, as it promotes efficient charge transfer and heat dissipation, which are essential for improving hydrogen absorption and desorption kinetics.

Fig. 7 Electronic band structures of (a) Mg₃FeH₈ and (b) Mg₃CoH₈ calculated using the HSE06 hybrid functional. The Fermi level is set at 0 eV (green dashed line).

3.3 Magnetic properties

To clarify the magnetic characteristics of Mg₃ZH₈ (Z = Fe, Co), spin-polarized electronic band structure calculations were performed within the PBE–GGA framework, as presented in Fig. 8(a) and (b). The band structures are resolved into spin-up (red) and spin-down (blue) channels. Fig. 8(a) shows the spin-polarized electronic band structure of Mg₃FeH₈, where a pronounced asymmetry between the spin-up and spin-down bands is observed near the Fermi level. Several Fe-derived bands cross E_F in only one spin channel, indicating strong exchange splitting of the Fe 3d states. This spin-dependent band dispersion leads to unequal occupation of the two spin channels and results in a finite net magnetic moment, confirming the ferromagnetic ground state of Mg₃FeH₈. The presence of magnetism in Mg₃FeH₈ is associated with stronger Fe–H hybridization, which can influence hydrogen bonding strength and thermodynamic stability. In contrast, the spin-polarized band structure of Mg₃CoH₈ in Fig. 8(b) exhibits nearly identical spin-up and spin-down bands throughout the Brillouin zone. No exchange splitting is observed at the Fermi level, and both spin channels show the same band crossings. This spin degeneracy indicates zero net spin polarization, confirming that Mg₃CoH₈ adopts a non-magnetic ground state.

Fig. 8 (a) and (b) The spin polarized electronic band structure of Mg₃ZH₈ (Z = Fe, Co) hydride.

Fig. 9(a)–(c) shows the spin-polarized PDOS of Mg₃FeH₈ hydride. A clear asymmetry between the spin-up and spin-down channels is observed, most prominently in the Fe-3d states near the Fermi level (E_F). This exchange splitting leads to unequal occupation of the two spin channels and gives rise to a finite net magnetic moment, confirming the ferromagnetic nature of the compound. The Mg-s and p states exhibit nearly symmetric spin-up and spin-down distributions around the Fermi level, indicating a negligible contribution to the magnetic moment and a primarily ionic role. In contrast, the Fe-s and p states exhibit clear spin asymmetry near E_F, induced by exchange splitting from Fe-d orbitals, confirming the ferromagnetic nature of the compound. The H-s states display weak induced spin polarization due to Fe–H hybridization, reflecting an indirect contribution to the overall ferromagnetic ground state. Fig. 10(a)–(c) presents the spin-polarized PDOS of Mg₃CoH₈. The spin-up and spin-down components of the Mg (s, p), Co (s, p, d), and H (s) orbitals are nearly identical across the entire energy range, and no noticeable exchange splitting is observed at the Fermi level (E_F). This spin symmetry results in zero net spin polarization, confirming that Mg₃CoH₈ adopts a non-magnetic ground state, in agreement with the spin-polarized band structure shown in Fig. 8(b). The absence of magnetism can be attributed to the nearly filled and weakly spin-polarized Co-3d states, which are insufficient to support exchange-driven magnetic ordering.

Fig. 9 (a)–(c) The spin polarized density of states of Mg₃FeH₈ complex hydride.

Fig. 10 (a)–(c) The spin polarized density of states of Mg₃CoH₈ complex hydride.

The presence of ferromagnetism in Mg₃FeH₈ is associated with stronger Fe–H hybridization and enhanced bonding anisotropy, which can influence hydrogen stability, whereas the non-magnetic character of Mg₃CoH₈ reflects more uniform Co–H bonding and comparatively weaker exchange-driven stabilization.

3.4 Optical properties

The optical response of Mg₃ZH₈ (Z = Fe, Co) hydrides provides insight into their electronic behavior and its relevance to hydrogen storage. The dielectric function,⁴⁰ ε(ω) = ε₁(ω) + iε₂(ω), reveals strongly negative ε₁(ω) at low photon energies, confirming Drude-like metallic behavior and efficient free-carrier screening (Fig. 11(a)). This facilitates rapid charge redistribution and heat dissipation during hydrogen absorption–desorption cycles. Mg₃FeH₈ exhibits a slightly stronger response than Mg₃CoH₈, consistent with enhanced carrier mobility and stronger d-H hybridization. The large ε₂(ω) values in the low-energy region indicate strong absorption arising from interband transitions between transition-metal d states and H-1s orbitals (Fig. 11(a)). The absorption spectra further show strong absorptivity across the UV-visible range, with Mg₃FeH₈ displaying slightly higher absorption (Fig. 11(b)). The presence of absorption from low photon energies reflects efficient electronic excitations that support charge transfer and improve hydrogen desorption kinetics. Prominent UV peaks (∼5 eV) originate from valence–conduction band transitions, indicating active electronic participation in hydrogen-related processes. The optical conductivity confirms metallic transport behavior, with high σ₁(ω) values indicating efficient charge transport and enhanced carrier dynamics (Fig. S1). The dispersive σ₂(ω) behavior reflects strong carrier screening, characteristic of metallic systems (Fig. S1). These features are beneficial for facilitating hydrogen diffusion and improving reversibility during cycling. High reflectivity at low energies further supports the metallic nature and strong free-carrier response (Fig. 11(c)). Its decrease at higher energies corresponds to interband transitions, consistent with the absorption behavior. The refractive index n(ω) and extinction coefficient k(ω) of Mg₃FeH₈ and Mg₃CoH₈ indicate strong light–matter interaction and metallic behavior (Fig. S2). High n(ω) at low energies and finite k(ω) confirm efficient charge transfer, supporting hydrogen desorption kinetics. The increase of k(ω) in the visible region reflects enhanced absorption and improved heat management during hydrogen cycling. Overall, the combined dielectric, absorption, conductivity, and refractive index responses confirm strong electronic activity and metallic behavior in Mg₃ZH₈ (Z = Fe, Co), which promote efficient charge transfer, thermal transport, and hydrogen desorption kinetics. These features reinforce the suitability of both hydrides for stable and efficient hydrogen storage.

Fig. 11 Optical properties of Mg₃ZH₈ (Z = Fe, Co): (a) dielectric function, (b) absorption coefficient, and (c) reflectivity as a function of photon energy.

3.5 Thermo-mechanical and anisotropic nature

Elastic constants provide fundamental insight into the mechanical stability, lattice rigidity, and hydrogen accommodation capability of solid-state hydrogen storage materials. In hydrogen-rich hydrides, appropriate elastic behavior is essential to tolerate repeated hydrogen absorption–desorption cycles, which induce volumetric expansion and local lattice distortion. Insufficient stiffness may lead to structural degradation, while excessively rigid lattices can hinder hydrogen diffusion and release kinetics. The mechanical stability of cubic Mg₃ZH₈ (Z = Fe, Co) hydrides was evaluated using the Born–Huang stability criteria,⁴¹ expressed as C₁₁ − C₁₂ > 0, C₄₄ > 0, C₁₁ > 0, and C₁₁ + 2C₁₂ > 0. The calculated elastic constants summarized in Table 3 satisfy all stability conditions, confirming that both Mg₃FeH₈ and Mg₃CoH₈ are mechanically stable.

Table 3 Calculated elastic constants (C_ij, in GPa), polycrystalline elastic moduli (B, G, E in GPa), and elastic anisotropy indices (A, A^B, A^G, A^U) of Mg₃ZH₈ (Z = Fe, Co)

Compound	Elastic constants			Elastic moduli			Elastic anisotropy indices
	C11	C12	C44	B	G	E	A	A^B	A^G	A^U
Mg3FeH8	296.53	150.80	58.22	199.38	63.69	172.69	0.799	0.000	0.006	0.061
Mg3CoH8	182.34	49.57	36.01	93.82	46.12	118.87	0.542	0.000	0.044	0.463
Mg7TiH16 (ref. 44)	125.81	18.55	16.33	82.31	31.45	84.27	—	—	—	—
Mg7FeH16 (ref. 44)	137.92	28.3	22.71	89.76	35.82	95.41	—	—	—	—
K2LiAlH6 (ref. 34)	60.2	18.5	19.2	32.18	13.98	37.86	—	—	—	—
LiCaCoH6 (ref. 45)	107.02	29.05	39.12	67.54	39.12	101.02	—	—	—	—
K2LiTiH6 (ref. 46)	43.68	18.12	28.18	26.84	17.89	45.76	—	—	—	—
Ca2LiTiH6 (ref. 46)	108.83	23.40	34.92	71.63	35.44	92.13	—	—	—	—

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Table 3 indicates Mg₃FeH₈ exhibits significantly higher stiffness than Mg₃CoH₈, with C₁₁ = 296.53 GPa and C₁₂ = 150.80 GPa, compared to C₁₁ = 182.34 GPa and C₁₂ = 49.57 GPa for Mg₃CoH₈. This indicates a much stronger resistance to longitudinal compression in the Fe-based lattice. The shear response follows the same trend, with C₄₄ = 58.22 GPa for Mg₃FeH₈ and 36.01 GPa for Mg₃CoH₈, suggesting greater tolerance against shape distortions during hydrogen insertion and removal. Furthermore, the tetragonal shear parameter,⁴² , is positive for both compounds (≈72.87 GPa for Mg₃FeH₈ and ≈66.39 GPa for Mg₃CoH₈), confirming stability against shear-driven lattice instabilities.

As there are no previously reported experimental or theoretical elastic data for Mg₃ZH₈ (Z = Fe, Co) hydrides, a comparison with other complex and double-perovskite hydrides is provided in Table 3. Reported A₂BH₆-type and double-perovskite hydrides typically exhibit moderate stiffness, with C₁₁ values in the range of ∼44–138 GPa (e.g., K₂LiAlH₆, LiCaCoH₆, Mg₇TiH₁₆-based systems). In contrast, Mg₃ZH₈ (Z = Fe, Co) shows substantially higher elastic stiffness, with C₁₁ reaching nearly 300 GPa for Mg₃FeH₈, indicating an unusually rigid hydrogen-rich framework. This distinct combination of high elastic resilience and high hydrogen content differentiates Mg₃ZH₈ (Z = Fe, Co) from previously reported complex and perovskite hydrides,^34,43–45 underscoring its scientific novelty and suitability for durable solid-state hydrogen storage under repeated cycling conditions.

The elastic response of Mg₃ZH₈ (Z = Fe, Co) is closely linked to its lattice vibrational behavior, providing a direct connection between mechanical stiffness and phonon dynamics. Higher elastic constants, particularly C₁₁ and C₄₄, correspond to increased sound velocities and stiffer acoustic phonon branches, which enhance lattice stability and suppress low-frequency soft modes. In Mg₃FeH₈, the larger elastic stiffness is therefore consistent with its wider acoustic–optical phonon separation and the absence of imaginary frequencies in the phonon dispersion (Fig. 1(a)), confirming robust dynamical stability. Conversely, the comparatively lower elastic constants of Mg₃CoH₈ lead to softer acoustic phonons, which facilitate lattice flexibility and hydrogen-induced vibrational motion during absorption and desorption (Fig. 1(b)).

Elastic anisotropy describes the directional dependence of mechanical response, which is highly relevant for hydrogen-rich solids because hydrogen uptake and release generate directional lattice strain and non-uniform stress fields. In practical hydrogen storage, anisotropy affects microcrack initiation, diffusion pathways, and long-term cycling durability. In this work, the anisotropic behavior of Mg₃ZH₈ (Z = Fe, Co) is evaluated using the Zener anisotropy index , the bulk and shear anisotropy indices , and the universal anisotropy index .⁴⁶ For cubic systems, isotropy is indicated by A = 1, while A^B = A^G = A^U = 0 corresponds to fully isotropic behavior.⁴⁶ For Mg₃FeH₈, the Zener anisotropy index is A = 0.799, which deviates from unity and therefore confirms elastic anisotropy. Mg₃CoH₈ shows a stronger deviation with A = 0.542, indicating that the Co-based hydride is more anisotropic than the Fe-based phase. This trend is consistent with their elastic constants: Mg₃CoH₈ has a much smaller C₁₂ relative to C₁₁, which increases the directional contrast between shear and longitudinal deformation and enhances anisotropy. The tetragonal shear stability parameter C′ remains positive, confirming that the anisotropy does not arise from instability but from intrinsic bonding asymmetry within the H-rich framework. The bulk anisotropy index is essentially zero for both materials (A^B ≈ 0.000), indicating that the compressibility is nearly isotropic. This is beneficial for hydrogen storage because volumetric expansion during hydrogen loading is less likely to concentrate stress along a single axis, reducing the probability of catastrophic lattice failure. In contrast, the shear anisotropy index shows a clear difference: Mg₃FeH₈ exhibits a very small value (A^G = 0.006), while Mg₃CoH₈ has a much larger shear anisotropy (A^G = 0.044). The same conclusion is supported by the universal anisotropy index, which is low for Mg₃FeH₈ (A^U = 0.061) but significantly higher for Mg₃CoH₈ (A^U = 0.463). These results indicate that Mg₃FeH₈ is closer to isotropic mechanical behavior, whereas Mg₃CoH₈ exhibits stronger directional sensitivity, mainly governed by shear deformation.

To connect single-crystal stiffness to polycrystalline mechanical performance, the Voigt and Reuss bounds for the bulk and shear moduli were evaluated and subsequently averaged using the Voigt–Reuss–Hill (VRH) scheme. For cubic symmetry, the moduli are given by:^24,25

The Hill averages were obtained as

and Young's modulus and Poisson's ratio were determined from

The calculated elastic moduli listed in Table 3 are consistent with those reported for comparable complex hydrides, confirming the reliability of the present calculations.^34,43–45

The bulk modulus B reflects resistance to volumetric compression and is directly relevant to lattice stability during hydrogen uptake. Mg₃FeH₈ exhibits a high bulk modulus (B = 199.38 GPa), which is significantly larger than those reported for typical complex hydrides such as Mg₇TiH₁₆ (∼82 GPa),⁴³ Mg₇FeH₁₆ (∼90 GPa),⁴³ and K₂LiAlH₆ (∼32 GPa),³⁴ indicating strong resistance to hydrogen-induced lattice expansion and favorable cycling stability. Mg₃CoH₈ shows a moderate bulk modulus (B = 93.82 GPa), comparable to Mg₇FeH₁₆,⁴³ and LiCaCoH₆,⁴⁴ suggesting a more compliant lattice that may facilitate hydrogen diffusion while maintaining mechanical integrity.

The shear modulus G governs resistance to shape deformation and plays a key role in suppressing lattice distortion and crack formation during cycling. Mg₃FeH₈ exhibits a higher shear modulus (G = 63.69 GPa) than Mg₃CoH₈ (G = 46.12 GPa), and exceeds values reported for Mg₇TiH₁₆ (∼31 GPa)⁴³ and K₂LiAlH₆ (∼14 GPa).³⁴ This enhanced shear resistance supports greater mechanical durability in the Fe-based hydride, while the lower G of Mg₃CoH₈ may facilitate lattice flexibility favorable for hydrogen diffusion.

Young's modulus E, which characterizes overall elastic stiffness, follows the same trend. Mg₃FeH₈ shows a high Young's modulus (E = 172.69 GPa), substantially exceeding those of Mg₇TiH₁₆ (∼84 GPa),⁴³ Mg₇FeH₁₆ (∼95 GPa),⁴³ and K₂LiAlH₆ (∼38 GPa).³⁴ Mg₃CoH₈ exhibits a moderate value (E = 118.87 GPa), still higher than most reported complex hydrides. Collectively, these comparisons indicate that Mg₃ZH₈ (Z = Fe, Co) combines high elastic stiffness with hydrogen-rich chemistry, highlighting its mechanical robustness and reinforcing the reliability of the VRH-based elastic analysis.

Poisson's ratio (ν), Pugh's ratio (B/G), and Cauchy pressure (C_P = C₁₂ − C₄₄) provide insight into bonding character, ductility, and mechanical adaptability, all of which directly influence hydrogen cycling durability. In general, ν values near 0.33 indicate metallic bonding, values around 0.25 suggest ionic bonding, and values near 0.1 are characteristic of covalent bonding, while ν > 0.26 and B/G > 1.75 are commonly associated with ductile behavior.^47,48 Positive Cauchy pressure further reflects ionic bonding and enhanced plasticity, whereas negative values indicate covalent bonding and brittleness.⁴⁹ The mechanical indicators are listed in Table 4 further clarify the ductility, bonding character, and hydrogen-cycling resilience of Mg₃ZH₈ (Z = Fe, Co). The Cauchy pressure (C_P) is positive for both compounds, confirming dominant metallic bonding. However, Mg₃FeH₈ exhibits a markedly larger value (92.58 GPa) than Mg₃CoH₈ (13.56 GPa), indicating superior ductility and resistance to hydrogen-induced embrittlement. This enhanced ductility is also reflected in the Pugh's ratio (B/G), where Mg₃FeH₈ (B/G = 3.13) and Mg₃CoH₈ (B/G = 2.03) both exceed the brittle–ductile threshold (≈1.75), with the Fe-based hydride showing a stronger ductile character. These results suggesting enhanced mechanical resilience during repeated hydrogen absorption–desorption cycles. The Poisson's ratio (ν) further supports this trend, with values of 0.356 for Mg₃FeH₈ and 0.289 for Mg₃CoH₈, consistent with metallic bonding and good plastic deformability during repeated hydrogen absorption–desorption cycles. The Vickers hardness⁵⁰ (H_V), estimated using H_V = (1 − 2ν)Y/[6(1 + ν)], quantifies resistance to plastic deformation and is therefore directly relevant to hydrogen cycling durability. Despite differences in ductility, both compounds exhibit comparable Vickers hardness (H_V ≈ 6–6.5 GPa), suggesting sufficient resistance to surface deformation without excessive brittleness.

Table 4 Ductility indicators (C_P, ν, B/G), machinability (μ_m), density (ρ in kg m⁻³), sound velocities (v_t, v_l, v_m in km s⁻¹), Debye and melting temperatures (θ_D, T_m in K), lattice and minimum thermal conductivities (k_ph, k_min in W m⁻¹ K⁻¹) of Mg₃ZH₈ (Z = Fe, Co)

Compound	CP	B/G	ν	HV	μm	ρ	vt	vl	vm	θD	Tm	kph	kmin
Mg3FeH8	92.58	3.13	0.356	6.13	3.42	5.89	3.29	6.05	3.70	746.4	2305	3.39	2.35
Mg3CoH8	13.56	2.03	0.289	6.49	2.61	5.76	2.83	5.19	3.16	627.3	1631	3.57	1.94

---

The calculated hardness values of Mg₃FeH₈ and Mg₃CoH₈ (≈6–6.5 GPa) are comparable to those reported for Mg₃CrH₈ (6.21 GPa) and Mg₃MnH₈ (5.37 GPa), and slightly higher than Mg₃TiH₈ and Mg₃VH₈, as reported in the literature.¹⁹ This indicates that the Fe- and Co-based hydrides possess sufficient resistance to surface deformation while retaining ductile characteristics, which is favorable for suppressing crack formation and mechanical degradation during hydrogen cycling.

When compared with other hydride perovskites such as MgCuH₃ (0.77 GPa),⁵¹ RbNiH₃ (0.64 GPa),⁵² BeGaH₃ (3.02 GPa),⁵³ and BeInH₃ (3.17 GPa),⁵³ both Mg₃FeH₈ and Mg₃CoH₈ exhibit relatively high hardness values, confirming their favorable mechanical stability among hydrogen-rich hydrides. The machinability index provides insight into both intrinsic plasticity and industrial workability.⁵⁴ Finally, the higher machinability index (μ_m = 3.42) of Mg₃FeH₈ compared to Mg₃CoH₈ (2.61) implies improved processability and structural tolerance, which are advantageous for fabricating durable hydrogen storage components. Collectively, these parameters demonstrate that Mg₃ZH₈ (Z = Fe, Co) hydrides combine metallic ductility with mechanical robustness, reinforcing their suitability for stable and kinetically efficient solid-state hydrogen storage.

The Debye temperature (Θ_D) is a key thermophysical parameter that governs lattice vibrational behavior, heat capacity, lattice stability, and thermal conductivity, all of which are directly relevant to hydrogen storage kinetics and reversibility. In solid-state hydrides, Θ_D reflects the strength of interatomic bonding and the ability of the lattice to withstand repeated hydrogen absorption–desorption cycles without structural degradation. A higher Θ_D generally indicates stronger metal–hydrogen bonding and enhanced lattice stability, while moderate reductions in Θ_D can facilitate hydrogen diffusion and release. The Debye temperature was calculated using the following relations:⁵⁵

where v_l and v_t are the longitudinal and transverse sound velocities, B and G are the bulk and shear moduli, ρ is the density, n is the number of atoms per unit cell, and V₀ is the unit-cell volume.

As summarized in Table 4, Mg₃FeH₈ exhibits higher sound velocities and a larger average phonon velocity than Mg₃CoH₈. Consequently, Mg₃FeH₈ shows a higher Debye temperature (Θ_D = 746.4 K) compared to Mg₃CoH₈ (Θ_D = 627.3 K), indicating stronger interatomic bonding and enhanced lattice rigidity. When compared with previously reported single, complex, and double hydrides, the thermo-mechanical characteristics of Mg₃FeH₈ and Mg₃CoH₈ fall within a favorable range for durable hydrogen storage. Typical single perovskite hydrides such as MgXH₃ (X = Ga, Tl),²⁹ MgCuH₃,⁵⁶ MBeH₃ (M = Li, Na, and K),⁵⁷ and XFeH₃ (X = Ca, Sr, Ba)⁵⁸ exhibit Debye temperatures generally below ∼400 K, reflecting softer lattices that are more susceptible to hydrogen-induced vibrational instability during cycling. In contrast, several complex and double hydrides, including Cs₂NaInH₆,⁵⁹ Sr₂LiCuH₆,¹¹ and BaXH₄ (X = Mn, Re, or Tc)⁶⁰ display Debye temperatures in the range of 300–550 K, indicating improved lattice stiffness and phonon stability. The Debye temperatures of Mg₃FeH₈ and Mg₃CoH₈ are comparable to or higher than those of many established similar type hydrides,¹⁹ suggesting similarly robust vibrational stability under repeated hydrogen absorption–desorption cycles. This insight provides a rational design principle for developing thermally stable, high-capacity solid-state hydrogen storage materials suitable for stationary and high-temperature hydrogen energy applications. However, the absence of imaginary phonon modes, high Debye temperatures, ductile mechanical behavior, and moderate reaction enthalpies suggest favorable lattice resilience and potential hydrogen mobility.

The melting temperature (T_m) is a key indicator of mechanical robustness and thermal endurance, which are essential for solid-state hydrogen storage materials operating under repeated absorption–desorption cycles. A sufficiently high T_m ensures that the host lattice maintains its structural integrity at elevated temperatures required for hydrogen release, while also preventing mechanical degradation during long-term cycling. Consequently, T_m is closely linked to hydrogen storage kinetics, safety, and operational reliability. The melting temperature was estimated using the empirical relation:⁶¹

T_m = 553 + 5.91C₁₁ (±300 K) (7)

Using this relation, Mg₃FeH₈ exhibits a significantly higher melting temperature (T_m ≈ 2305 K) compared to Mg₃CoH₈ (T_m ≈ 1631 K). This difference directly correlates with their elastic stiffness, as Mg₃FeH₈ possesses a much larger C₁₁ and bulk modulus than Mg₃CoH₈, indicating stronger interatomic bonding and greater resistance to lattice deformation. From a hydrogen storage perspective, the higher T_m of Mg₃FeH₈ implies superior thermal stability, making it suitable for high-temperature hydrogen storage and stationary energy systems, where structural durability is critical. In contrast, the lower T_m of Mg₃CoH₈ reflects a comparatively softer lattice, which can facilitate lattice breathing and atomic rearrangements during hydrogen desorption. Such behavior is advantageous for enhancing hydrogen release kinetics at reduced temperatures, highlighting a trade-off between thermal robustness and kinetic accessibility. A comparison with previously reported hydrides further clarifies the thermal robustness of Mg₃FeH₈ and Mg₃CoH₈. Single perovskite hydrides such as MgCuH₃,⁵⁶ CsAH₃ (A = Fe, Cu and Tl),⁶² and XFeH₃ (X = Ca, Sr, Ba)⁵⁸ generally exhibit lower estimated melting temperatures, which limits their resistance to thermally induced lattice degradation during hydrogen cycling. In contrast, complex and double hydrides, including Cs₂NaInH₆,⁵⁹ Cs₂AlInH₆,⁵⁹ Cs₂AlTlH₆,⁵⁹ and X₂MgH₄ (X = K, Rb, Cs),⁶³ display moderate melting temperatures, reflecting improved thermal endurance and cycling stability. This combination of high melting temperature, strong mechanical stability, and hydrogen-rich composition highlights the scientific novelty of Mg₃ZH₈ (Z = Fe, Co) hydrides.

The lattice thermal conductivity (κ_ph) was evaluated using Slack's model, which correlates the Debye temperature, Grüneisen parameter (γ), and other lattice descriptors:⁶⁴

where M_av is the average atomic mass, δ is the volume per atom, n is the number of atoms per unit cell, and A(γ) is a constant. The anharmonicity in lattice vibrations, which governs phonon–phonon scattering, is quantified by the Grüneisen parameter:⁶⁵

In addition, the minimum lattice thermal conductivity (k_min) was estimated using Clarke's model:⁶⁵

The calculated κ_ph and k_min values listed in Table 4 indicate that both Mg₃FeH₈ and Mg₃CoH₈ hydrides possess moderate phonon heat transport at 300 K. Mg₃FeH₈ shows κ_ph = 3.39 W m⁻¹ K⁻¹ and k_min = 2.35 W m⁻¹ K⁻¹, whereas Mg₃CoH₈ exhibits a slightly higher κ_ph = 3.57 W m⁻¹ K⁻¹ but a lower k_min = 1.94 W m⁻¹ K⁻¹. The larger k_min in Mg₃FeH₈ is consistent with its higher sound velocities and stronger lattice stiffness, implying a higher intrinsic phonon transport floor, while the comparatively lower k_min of Mg₃CoH₈ reflects a softer lattice that can enhance phonon scattering. From a hydrogen-storage perspective, these thermal transport characteristics are beneficial because efficient heat dissipation can mitigate local temperature gradients during absorption–desorption cycling, supporting stable kinetics and improved cycling durability.

4. Conclusion

First-principles calculations provide a powerful framework for the discovery and rational design of advanced hydrogen storage materials. In this study, transition-metal substitution into magnesium-based hydrides was explored as an effective strategy to tailor hydrogen storage thermodynamics and kinetics. The structural, electronic, mechanical, optical, and hydrogen storage properties of Mg₃ZH₈ (Z = Fe, Co) were systematically investigated using density functional theory to assess their suitability for solid-state hydrogen storage applications. Both compounds are found to be thermodynamically, mechanically, and dynamically stable, as confirmed by negative formation energies, elastic stability criteria, and phonon spectra free of imaginary modes. Mg₃FeH₈ exhibits a ferromagnetic metallic ground state, whereas Mg₃CoH₈ is non-magnetic, highlighting the role of transition-metal d states in governing magnetic and electronic behavior. The hydrogen storage performance of Mg₃ZH₈ (Z = Fe, Co) is promising, with gravimetric capacities of 5.90 wt% for Mg₃FeH₈ and 5.76 wt% for Mg₃CoH₈, exceeding the U.S. DOE minimum target. Their volumetric hydrogen densities (≈195–187 g H₂ per L) are substantially higher than current DOE benchmarks, indicating excellent space efficiency. The calculated desorption temperatures fall within a moderate range, with Mg₃FeH₈ consistently showing lower T_des values than Mg₃CoH₈, suggesting more favorable hydrogen release kinetics. Mechanical analysis reveals that both hydrides are ductile, with positive Cauchy pressures, high Pugh's ratios, and moderate Vickers hardness values, implying good resistance to hydrogen-induced embrittlement during cycling. Optical and electronic analyses further confirm their metallic nature, with strong free-carrier response and interband transitions that correlate with their hydrogen desorption behavior. Overall, the balanced combination of high hydrogen density, mechanical resilience, moderate desorption temperature, and electronic activity positions Mg₃ZH₈ (Z = Fe, Co), particularly Mg₃FeH₈, as a promising candidate for next-generation hydrogen storage materials and provides a robust theoretical benchmark for future experimental exploration.

Author contributions

Md. Hasan Mia: conceptualization; methodology; writing manuscript – reviewing and editing; data curation; validation; supervision; Md. Zahid Hasan: formal analysis; validation; review – editing. A. Arunkumar: formal analysis; validation; review – editing; and supervision. S. AlFaify: formal analysis; validation; review – editing.

Conflicts of interest

The authors declare that they have no known conflicting financial interests or personal ties that may have seemed to affect the work presented in this study.

Data availability

Supplementary information: the figures in the supplementary information represent the optical conductivity and refractive properties of Mg₃ZH₈ (Z = Fe, Co) hydrides. See DOI: https://doi.org/10.1039/d6ma00353b.

Relevant data from this study are available from the corresponding author upon a reasonable request.

Acknowledgements

The authors are grateful to the Materials Research and Simulation lab, Department of Electrical Electronics and Engineering, International Islamic University Chittagong, Chittagong-4358, Bangladesh for providing the computing facilities for this work.

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