Crystal Structure of NaMgH3 Perovskite at Room Temperature: A Guide
NaMgH₃ is a perovskite-type hydride that crystallizes in an orthorhombic structure at room temperature. Its space group is Pnma, with lattice parameters of approximately a = 5.46 Å, b = 7.70 Å, and c = 5.41 Å. The structure consists of corner-sharing MgH₆ octahedra with Na⁺ ions occupying the interstitial sites, and it is isostructural with the mineral perovskite CaTiO₃ in its orthorhombic GdFeO₃-type distortion.
Why NaMgH₃ Adopts the Orthorhombic Structure
The ideal cubic perovskite structure (space group Pm-3m) requires that the A-site cation (Na) and B-site cation (Mg) have specific size ratios. For NaMgH₃, the ionic radii of Na⁺ (1.02 Å for coordination number 8) and Mg²⁺ (0.72 Å for coordination number 6) produce a tolerance factor below 1.0. This factor, calculated from the Goldschmidt formula, predicts a distorted structure rather than the cubic form.
The room-temperature distortion is a cooperative tilting of the MgH₆ octahedra. In the Pnma space group, the octahedra rotate alternately along two axes. This tilting reduces the symmetry from cubic to orthorhombic and lowers the coordination number of the Na⁺ ion from 12 to 8. The tilting angle is not fixed — it depends on temperature and can change with pressure or chemical substitution, but at room temperature it produces the specific Pnma arrangement.
Atomic Coordination and Bonding in the Pnma Cell
In the orthorhombic Pnma structure of NaMgH₃, each atom type occupies a specific Wyckoff position with fractional coordinates that define its location within the unit cell. The sodium atoms sit at the 4c site, with coordinates approximately (x, 0.25, z) where x ≈ 0.02 and z ≈ 0.49. This position places sodium in a distorted cuboctahedral cavity formed by the surrounding hydrogen atoms. Each sodium ion coordinates with eight hydrogen atoms at distances that range from about 2.3 Å to 2.6 Å.
The magnesium atoms occupy the 4b site at (0, 0, 0.5) and (0, 0.5, 0), among other equivalent positions. Each magnesium is surrounded by six hydrogen atoms in a nearly regular octahedron. The Mg–H bond lengths are not all identical because the octahedron is slightly compressed along one axis. In the refined structure, the axial Mg–H bonds are about 1.88 Å, while the equatorial bonds are about 1.92 Å.
The hydrogen atoms occupy two distinct sites. The first set (H1) sits at the 4c site with coordinates near (0.25, 0.03, 0.25). The second set (H2) occupies the 8d site at approximately (0.02, 0.25, 0.57). These positions place hydrogen atoms at the corners of the MgH₆ octahedra. The H1 atoms form the axial positions, while the H2 atoms form the equatorial positions. The tilting of the octahedra causes the H–Mg–H bond angles to deviate from the ideal 90° by about 5–8°.
Visualizing the Octahedral Tilting
The tilting pattern in NaMgH₃ follows the a⁻b⁺a⁻ notation in Glazer’s classification of perovskite distortions. This means the octahedra tilt in opposite directions along the a-axis (a⁻), in the same direction along the b-axis (b⁺), and again in opposite directions along the c-axis (a⁻). The tilting angle is typically around 12–15° at room temperature. To visualize this, imagine each MgH₆ octahedron as a rigid unit that rotates slightly around the b-axis while also tilting around the a- and c-axes. The result is a zigzag arrangement of octahedra when viewed along the b-axis.
How the Structure Is Determined
Researchers determine the crystal structure of NaMgH₃ perovskite at room temperature using X-ray or neutron powder diffraction. X-ray diffraction works well for locating the heavier atoms (Na and Mg) but struggles to find hydrogen positions because hydrogen scatters X-rays weakly. Neutron diffraction is better for locating hydrogen because neutrons interact strongly with hydrogen nuclei.
The diffraction pattern is indexed to the orthorhombic Pnma cell. A Rietveld refinement is then performed to fit the calculated pattern to the measured data. The refinement adjusts lattice parameters, atomic positions, and displacement parameters until the fit converges. For NaMgH₃, the refined atomic positions at room temperature are well established in the literature American Chemical Society. The Na atom sits at the 4c site, Mg at the 4b site, and H atoms occupy two distinct sites: one set at 4c and another at 8d.
A Short Worked Example
Suppose you have a powder diffraction pattern of NaMgH₃ with peaks at 2θ values of 23.1°, 27.4°, 31.8°, and 40.2° (using Cu Kα radiation, λ = 1.5406 Å). You index these peaks to the (101), (121), (200), and (220) reflections of the Pnma cell. Using Bragg’s law (nλ = 2d sin θ), you calculate d-spacings of 3.85 Å, 3.25 Å, 2.81 Å, and 2.24 Å. These values match the expected d-spacings for the orthorhombic cell with a = 5.46 Å, b = 7.70 Å, c = 5.41 Å. The systematic absences in the pattern (such as the absence of 0k0 reflections with k odd) confirm the Pnma space group.
Comparison with Related Perovskite Hydrides
NaMgH₃ belongs to a family of perovskite hydrides that includes NaCaH₃, KMgH₃, and RbMgH₃. All of these compounds adopt the Pnma structure at room temperature, but the lattice parameters shift with the size of the A-site cation. For example, KMgH₃ has larger lattice parameters (a ≈ 5.68 Å, b ≈ 8.04 Å, c ≈ 5.65 Å) because K⁺ is larger than Na⁺. The tilting angle of the octahedra also changes — larger A-site cations reduce the tilting, moving the structure closer to the cubic form.
A related compound is NaMgH₃ doped with small amounts of a transition metal. Doping with Ti or V can change the hydrogen desorption temperature, but the crystal structure at room temperature remains orthorhombic Pnma unless the dopant concentration is high enough to cause a phase transition. The structural stability of the Pnma phase is one reason NaMgH₃ is studied as a hydrogen storage material — it can absorb and release hydrogen without a major structural change.
Phase Transitions at Other Temperatures
At temperatures above about 400 K, NaMgH₃ undergoes a phase transition from the orthorhombic Pnma structure to a cubic Pm-3m structure. This transition is driven by the increased thermal motion of the atoms, which allows the octahedra to stop tilting. The transition temperature depends on the exact composition and on any impurities present. Below room temperature, no other phase transitions have been reported for NaMgH₃ down to very low temperatures. The room-temperature structure is therefore the stable form under normal conditions.
Key Takeaways
- NaMgH₃ crystallizes in the orthorhombic Pnma space group at room temperature, with lattice parameters a ≈ 5.46 Å, b ≈ 7.70 Å, c ≈ 5.41 Å.
- The structure consists of corner-sharing MgH₆ octahedra that are tilted relative to each other, with Na⁺ ions in the interstitial sites.
- Hydrogen atoms occupy two crystallographic sites (4c and 8d) within the Pnma cell, with Mg–H bond lengths near 1.9 Å.
- The structure is determined by powder diffraction and Rietveld refinement; neutron diffraction is needed to locate hydrogen positions accurately.
- NaMgH₃ is isostructural with other perovskite hydrides like KMgH₃, but the lattice parameters and octahedral tilting vary with the size of the A-site cation.
