The effect of light impurities on the binding energy of hydrogen in magnesium metal and magnesium hydride

Transcription

1 The effect of light impurities on the binding energy of hydrogen in magnesium metal and magnesium hydride Finnbogi Óskarsson Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavík, Iceland Hannes Jónsson Faculty of Science, University of Iceland, VR-II, IS-107 Reykjavík, Iceland With the goal of finding a way to reduce the temperature at which hydrogen gas gets released upon heating, we have used density functional theory calculations to study how the binding energy and charge distribution of hydrogen atoms in magnesium and magnesium hydride are modified by the addition of impurities of some of the lighter elements, namely aluminium, silicium, sodium, carbon and boron. The binding energy is reduced by the addition of aluminium and silicium, elements that are more electronegative than magnesium, but increased by the addition of sodium, a less electronegative element. The most electronegative additives, carbon and boron, do not remain in substitutional sites in the magnesium lattice but spontaneously move into interstitial sites where they bind hydrogen atoms by strong covalent bonds. The charge of the interstitial hydrogen atoms as judged by the charge density partitioning scheme of Bader is -1.1 to -1.3 e in the magnesium metal, but -0.8 e in the hydride and is not affected strongly by the substitution of magnesium by the other elements. A promising result was obtained by introducing aluminium into the magnesium lattice, as the binding energy of hydrogen in the hydride was found to decrease linearly with the amount of aluminium and reach 0.25 ev on average at about 15% Al. This is the target binding energy for hydrogen atom release at 300 K. The weight percent of hydrogen in such an alloy would still be high, nearly the same as in pure MgH 2. Such a material could possibly be made as an amorphous Mg xal y alloy, stabilised by a small amount of a third component. PACS numbers: I. INTRODUCTION One of the greatest hindrances on the road to a hydrogen economy is the problem of storing and transporting hydrogen in a safe and economical manner. Some of the requirements for a suitable hydrogen storage device are the ability to contain at least 6.5 weight percent hydrogen when full, release hydrogen in the temperature range between 0 C and 100 C, and reversibly absorb/desorb hydrogen fast enough. One of the possibilities under consideration is storage of hydrogen in metal hydrides. Magnesium can absorb hydrogen and form a hydride, Mg + H 2 MgH 2 where the weight percent of hydrogen is 7.6%. However, hydrogen binds too strongly in pure magnesium hydride. It needs to be heated to 300 C to release hydrogen gas at 1 atm 1,2. Also, the diffusion of hydrogen through the hydride is extremely slow and this results in only a thin film of hydride forming at the surface of the crystal 3. We have in a previous article 4 presented results of a theoretical study of hydrogen in magnesium metal and magnesium hydride using density functional theory calculations. The binding energy of hydrogen in magnesium hydride was found to be 0.38 ev/h atom, in close agreement with experimental measurements. This illustrates the ability of such theoretical calculations to predict how the binding energy could be modified by changing the composition of the solid. For the system to reach a hydrogen equilibrium pressure of 1 bar at 300 K, H should amount to ev/h atom 2,5. In order to see how the binding energy of hydrogen in magnesium hydride could be lowered, while not sacrificing the favourable hydrogen to metal weight ratio, we have calculated the effects of the substition of a magnesium atom by some relatively light elements, namely aluminium, boron, carbon, sodium and silicium. II. THEORETICAL METHODS In our calculations, we made use of density functional theory (DFT) 6,7 with the PW91 functional 8 and the VASP code Ultrasoft pseudopotentials 13 were used to represent the core electrons, and only the valence electrons were treated explicitly. A plane wave basis set was used with an energy cutoff of 340 ev. The simulation cells for studies of the magnesium metal were orthogonal (measuring ( Å) and contained 64 Mg atoms in a HCP lattice. The k-point grid used to sample the Brillouin zone was reduced to 4 k-points due to symmetry. In studies of the magnesium hydride, the simulation cells used contained 16 Mg atoms and 32 H atoms in a rutile structure (corresponding to unit cells) and the k-point grid was reduced to 8 k-points due to symmetry. During structural optimisation, all the atoms in the simulation cell were allowed to move but the size of the cell, which had previously been optimised to obtain the lattice constants, was kept fixed. A decomposition of the electron density along minimal

2 2 density dividing surfaces 14 was used to map the electron density of the system to the individual atoms, thus obtaining the charges of the atoms. The size of the grid used was points. A fast and robust algorithm based on finding the steepest ascent path that assigns each grid point to the nearest density maximum was used 15. III. RESULTS AND DISCUSSION A. Impurities in magnesium metal Within the hexagonal close packed magnesium crystal there are two sets of holes which the hydrogen atom can occupy, tetrahedral (T d ) holes where the hydrogen atom is fourfold-coordinated and octahedral (O h ) holes where the hydrogen atom is sixfold-coordinated. Energy minimisation has been conducted in order to determine the optimum geometry for both types 4. The hydrogen prefers to occupy the T d holes with a binding energy of ev (negative binding energy means that the energy of hydrogen in the hole is higher than that of hydrogen in a gas phase molecule). The octahedral holes, O h, are less favorable, giving a binding energy of ev. Aluminium impurity Aluminium is slightly heavier and more electronegative than magnesium. An Al-atom has a smaller atomic radius than magnesium by 0.25 Å. The substitution of a magnesium atom with aluminium (one out of sixty-four) results in a slight contraction (about 0.06 Å) of the magnesium lattice close to the aluminium atom, see table I, and a charge transfer of 0.3 e from the closest magnesium to the aluminium, see table II. When a hydrogen atom is introduced in a hole adjacent to the aluminium atom, a relatively high charge density is located between the hydrogen atom and the aluminium atom, suggesting covalent bonding, as shown in figure 1. When hydrogen is inserted into the lower energy T d hole closest to the substitutional aluminium atom, it moves 0.12 Å closer to the aluminium atom than the magnesium atoms coordinating the hole. The fourfold symmetry of the T d hole is therefore broken. The energy of the hydrogen atom in this hole is 0.13 ev higher than in pure magnesium. The same applies to the O h hole, except that the hydrogen atom moves even further away from the magnesium atoms, having a Al-H bond length of 1.93 Å as opposed to 2.26 Å for Mg-H in an O h hole. The binding of hydrogen in the hole is also decreased as compared with the binding in pure magnesium, but only by 0.06 ev. To summarise, it appears that a low concentration of aluminium decreases the binding of hydrogen by about 0.1 ev without drastically changing the structure. Therefore, it might be a suitable substitutional impurity in magnesium to reduce the binding energy. The effect of aluminium substitution on the hydride is discussed in section III B. Silicium impurity Silicium is even heavier and more electronegative than aluminium and has a smaller atomic radius, 1.10 Å. Therefore, it causes a similar effect as the aluminium, only to a larger extent. The silicium atom contracts the magnesium lattice around it by 0.10 Å and has a negative charge of 2.5 e, see table II. The large contraction of the lattice leads to a decrease in the volume of the T d hole and as a result the hydrogen atom does not fit in there anymore. When a hydrogen atom is introduced in a T d hole adjacent to the silicium atom, it spontaneously moves away from the silicium atom into the next T d hole. The energy of the hydrogen atom in this second-neighbour hole is still less than in a T d hole of the pure magnesium. The elimination of the site in the nearest-neighbour hole makes silicium substitution less interesting in a magnesium based hydrogen storage medium, since the addition of silicium reduces the number of holes available for hydrogen, thus reducing the efficacy of the storage. Although the O h hole is also contracted by the substitution by the silicium atom it can still house a hydrogen atom, and shows the same trend as aluminium, the Si-H bond is even shorter than the Al-H bond, only 1.73 Å, and the insertion of hydrogen is endothermic by 0.39 ev, see table I. Sodium impurity Sodium, being less electronegative than magnesium and having a larger atomic radius (see table I) shows the reverse effect. The lattice around the sodium atom is expanded by 0.03 Å and the energy of an interstitial hydrogen atom is lower than in the case of pure magnesium. The binding energy of hydrogen in the O h hole being ev and ev in the T d hole, which is the first exothermic hydrogen addition seen in these calculations. The Na-H bonds are both approximately 0.15 Å longer than the corresponding Mg-H bonds in pure magnesium crystal. The lower electronegativity of sodium causes it to transfer some of its charge (0.7 e) to the surrounding magnesium atoms, thus negatively charging them, see table II. The stronger binding of the sodium doped magnesium makes it a worse candidate for hydrogen storage than the pure magnesium crystal, since the temperature needed to release the hydrogen would be even higher. Boron impurity When substituting a magnesium atom with a boron atom we found that boron, having an atomic radius of less than 60% of that of magnesium would hop into the nearest octahedral hole and leave a vacancy in the Mg-lattice. As the interaction between magnesium and boron is stronger than the Mg-Mg interaction, a magnesium atom would then hop into the vacancy, leaving another vacancy further away from the boron atom. The binding energy of boron in the O h hole of a perfect magnesium crystal was calculated and found to be 0.65 ev. Positioning the

3 3 boron atom in the O h hole causes the magnesium lattice to expand by 0.05 Å around the interstitial boron atom. A calculation of the energy of hydrogen in the O h hole closest to the one occupied by boron, a B-H distance of 3.05 Å, yielded a binding energy of ev. When the hydrogen was positioned in the T d hole next to the boron and the energy of the system minimised, the hydrogen spontaneously hopped into the same hole as boron was occupying forming a covalent B-H bond with a bond length of 1.26 Å, which is only slightly longer (by 0.03 Å) than the gas phase B-H bond length as measured by spectroscopy 16. The binding energy of hydrogen was found to be 0.11 ev, see table III. When the charge density of the magnesium crystal with boron impurities was analysed, we found that in the final state, where the boron atom is positioned in an O h hole it has a charge of -3.2 e and the surrounding magnesium atoms have a positive charge of +0.6 e. The addition of hydrogen into the nearest O h hole causes the charges of the magnesium atoms in between the two holes to acquire a positive charge of +0.7 e, whereas the ones next to the hydrogen atom have a charge of +0.5 e. The charges on the magnesium atoms next to the boron atom stay the same when the hydrogen atom is introduced to the nearest-neighbour O h hole but when the hydrogen atom is positioned in the nearest-neighbour T d hole, after hopping into the same O h hole as boron, much of the charge density of the boron atom is transferred to the hydrogen atom, leaving boron with a charge of -1.2 e and hydrogen with a charge of -1.8 e, see table IV. It is interesting to see that in the former case, both the hydrogen atom and the boron atom bind strongly to the magnesium lattice, but there seems to be no bonding between the Mg-H and Mg-B clusters, see figure 2. Carbon impurity In much the same way, a substitution of a carbon atom, which has an even smaller atomic radius than boron, ends in a hop of both the carbon atom and the resulting vacancy to form a vacancy in a second-nearest neighbour lattice site to the carbon atom. As in the case of boron, the binding energy of carbon as an interstitial in a perfect magnesium crystal was calculated and found to be 1.41 ev. However, unlike boron, the interstitial carbon causes the magnesium lattice to contract by approximately 0.10 Å. This is probably due to higher electronegativity of carbon and smaller atomic radius. A calculation of the energy of hydrogen in the O h hole closest to the one occupied by carbon yielded a binding energy of ev, which is lower energy than in the case of boron. The C-H distance is 2.95 Å, and as for boron, positioning the hydrogen in a T d hole next to the carbon caused a hop of the hydrogen and a formation of a covalent C-H bond of 1.14 Å, which is close to the gas phase C-H bond length (1.12 Å) as estimated by spectroscopy 16. The calculated binding energy of hydrogen was ev, see table III. Charge density analysis of the magnesium crystal with carbon impurities shows that the interstitial carbon atom has a charge of -3.1 e in the magnesium crystal, causing the nearest magnesium atoms to keep a positive charge of +0.8 e. Addition of hydrogen into an adjacent tetrahedral hole results in a charge of -1.2 e for the hydrogen, -3.0 e for the carbon, +0.8 e for the magnesium atoms in between the hydrogen and the carbon and a charge of +0.4 e for the magnesium atoms next to the hydrogen. Again, the addition of hydrogen has no effect on the second nearest neighbour magnesium atoms (see table IV). In the case where the hydrogen atom hops into the O h hole occupied by carbon, some of its charge is transferred to the carbon atom, leaving carbon with a charge of -2.3 e and hydrogen with a charge of -0.4 e. This is the opposite of what happened in the case of boron and is in accordance with what one would expect from the Pauling electronegativities of the elements; hydrogen, boron and carbon having electronegativities 2.10, 2.04 and 2.55, respectively. B. Impurities in magnesium hydride The more important issue is the effect of impurities on the hydride. It is the energy of H-atoms in the hydride compared with gas phase hydrogen molecules which determines the desorption temperature. Below approximately 2 GPa and 1100 K, magnesium hydride has a rutile structure (α-mgh 2 ), where the hydrogen ions are arranged approximately octahedrally around the magnesium ions, which in turn are arranged trigonally around the hydrogen ions The binding energy of hydrogen in the magnesium hydride has been calculated to be 0.38 ev/atom within the DFT/PW91 approximation as described in a previous article 4. From the preliminary studies in section III A, it is clear that aluminium was the most promising candidate of the elements tried. Therefore, we substituted magnesium atoms from a MgH 2 cell with aluminium and calculated its effects on the average binding energy of hydrogen in the compound (as one cannot decompose the total energy into a sum of atomic contributions, the effect on the average binding energy of the hydrogen atoms in the simulation cell is the only thing that can be calculated rigourously). This was done using a cell which originally contained 16 Mg-atoms and 32 H-atoms. Aluminium impurity When a magnesium atom of the hydride was substituted by an aluminium atom, the lattice contracted around the aluminium atom in much the same way as it did for the substitution in magnesium metal, i.e. the distance between the aluminium atom and the surrounding equitorial hydrogen ions was found to be 1.79 Å instead of 1.95 Å in the pure magnesium hydride and the distance between the aluminium atom and its apical hydrogen ions was reduced from 1.92 Å to 1.82 Å. The average binding

4 4 energy of hydrogen in the hydride was, however, lowered by ev/atom. Substitution of another magnesium by an aluminium atom, corresponding to Al concentration of 12.5%, yielded a similar contraction of the lattice around it, and lowered the average binding energy of hydrogen in the hydride even more, to ev/atom. The substitution of a third magnesium atom by an aluminium atom also lowered the average binding energy of hydrogen, now to ev/atom, see table V. However the substitution of a fourth magnesium atom lead to an instability of the crystal structure. A Bader charge density analysis was performed on both the pure magnesium hydride and the hydride after a substitution of a magnesium atom by an aluminium atom. We found that the substitution has very little effect on the charge distribution of the system, see table VI. The only noticeable difference is a partial electron transfer (0.1 e) from the aluminium atom to the nearest magnesium ions. There is only a very small charge transfer to the hydrogen ions, about 0.02 e for the equitorial hydrogen ions, but less than 0.01 e for the apical ones, see figure 3. This small effect of the substitution is not surprising as MgH 2 is an insulator and its electrons are highly localised. IV. CONCLUSIONS We have found that the effect of impurities on the binding energy of hydrogen in magnesium metal depends on the difference in electronegativity between magnesium and the impurities. Less electronegative impurities lower the charge density around them and thereby attract the hydrogen atoms and bind them more strongly than the rest of the metal. Slightly more electronegative impurities decrease the binding of hydrogen in the metal and may, therefore, be suitable for doping of magnesium in order to improve its hydrogen storage properties. However, if the impurities have a significantly higher electronegativity than magnesium, hydrogen tends to form covalent bonds with the impurity atoms, and thus bind much stronger. Charge density analysis showed that when a magnesium atom is substituted by a more electronegative atom, such as aluminium or silicium, the negative charge of the interstitial hydrogen atom is diminished. In pure magnesium, the charge on an interstitial hydrogen atom is e in the O h hole and -1.1 e in the T d hole 4. These electronegative substitutional atoms also absorb some of the charge on the nearest magnesium atoms, leaving them more ionised than in the pure magnesium crystal. This effect is reversed for sodium, which is less electronegative than magnesium and therefore transfers some of its charge onto the next magnesium atoms. More surprisingly, sodium causes the interstitial hydrogen atoms to lose some of their charge to the magnesium atoms as well. Of the impurities tried, the effect of aluminium was most promising; it raised the energy of an interstitial H- atom in the metal by 0.13 ev in the tetrahedral holes and 0.06 in the octahedral holes, without having much effect on the lattice structure even in concentrations as high as 19%. Furthermore, since aluminium is only slightly heavier than magnesium, the effect on the weight percent of hydrogen is small. When the binding energy of the hydride was calculated, it was found that adding aluminium again reduced the average binding energy of hydrogen in the crystal. In fact, increasing the concentration of aluminium seemed to weaken the binding of hydrogen in the hydride almost linearly, as shown in figure 4. At a concentration of 15%, the binding energy has dropped to 0.25 ev, the value appropriate for thermal release at room temperature 1,2. However, according to the phase diagram 17 for the Al/Mg system, the solubility of aluminium in the magnesium hcp (δ) phase is only 3%. At higher concentrations of aluminium, a different (γ) phase starts forming alongside the hcp phase. At present, we have not studied the latter phase. Another possibility is that an amorphous phase of magnesium, aluminium and a third element, preferably one with a larger atomic radius than magnesium, could be formed and used for hydrogen storage. An amorphous solid made of magnesium and aluminium may offer the flexibility in composition that is needed to be able to tune the hydrogen binding energy. The difference in atomic size of aluminium and magnesium is about 20% based on atomic radii so it should be possible to form an amorphous phase. A third element could be needed to stabilise the amorphous phase, especially as the system needs to be able to go through multiple cycles of hydrogen absorption/desorption. V. ACKNOWLEDGEMENTS We would like to thank William Stier and Sveinn Ólafsson for helpful discussions on modifications of the magnesium-hydrogen system. We would also like to thank Andri Arnaldsson and Graeme Henkelman for helpful discussions, in particular with regard to the charge analysis. This work was supported by the research council of Iceland (RANNIS) and by the U.S. Department of Energy, Division of Materials Research. FÓ was supported in part by the Icelandic Research Fund for Graduate Students 1 L. Schlapbach, in Hydrogen in Intermetallic Compounds I: Electronic, Thermodynamic and Crystallographic Properties, Preparation, Vol. 67 of Topics Appl. Phys., edited by

5 L. Schlapbach (Springer Verlag, Berlin, 1988). 2 L. Schlapbach and A. Züttel, Nature 414, 353 (2001). 3 A. Krozer and B. Kasemo, J. Vac. Sci. Technol. A 5, 1003 (1987). 4 F. Óskarsson, W. Stier, and H. Jónsson, submitted to Phys. Rev. B (2003). 5 K. Buschow, P. Bouten, and A. Miedema, Rep. Prog. Phys. 45, 937 (1982). 6 P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). 7 W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). 8 J. P. Perdew, in Electronic Structure of Solids, edited by P. Ziesche and H. Eschrig (Akademie Verlag, Berlin, 1991). 9 G. Kresse and J. Hafner, Phys. Rev. B 49, (1994). 10 G. Kresse and J. Furthmüller, Comp. Mat. Sci. 6, 15 (1996). 11 G. Kresse and J. Furthmüller, Phys. Rev. B 54, (1996). 12 G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993). 13 D. Vanderbilt, Phys. Rev. B 41, 7892 (1990). 14 R. Bader, Atoms in Molecules: A Quantum Theory (Oxford University Press, New York, 1990). 15 G. Henkelman, A. Arnaldsson, and H. Jónsson, in preparation (2003). 16 K. P. Huber and G. Herzberg, Molecular spectra and molecular structure. IV Constants of diatomic molecules (Van Nostrand Reinhold Company, New York, 1979). 17 L. Taylor, in Metallography, structures, and Phase Diagrams, Vol. 8 of Metals Handbook (American Society for Metals, Metals Park, Ohio, 1973), p J. C. Slater, J. Chem. Phys. 39, 3911 (1964).

6 6 Table I: The effects of substitution of a magnesium atom by aluminium, silicium and sodium on the crystal lattice and the binding energy of hydrogen. Aluminium and silicium cause the crystal lattice to contract around the substitutional atom and thus decrease the binding of the hydrogen in both holes. In the case of silicium, the contraction is so great that the hydrogen atom does not fit into the T d hole anymore and moves into the next T d hole, coordinated by magnesium atoms (the results for hydrogen in the T d hole with silicium are in parentheses). Negative binding energy means higher energy as compared with hydrogen in a H 2 molecule. Property Mg Al Si Na Pauling electronegativity of X Atomic radius of X 18 (Å) Mg-X bond length (Å) H-X bond length in O h hole (Å) H-X bond length in T d hole (Å) (3.42) 2.17 Binding energy of H in O h hole (ev) Binding energy of H in T d hole (ev) (-0.14) Table II: Atomic charge estimates using Bader decomposition of the charge density. When a magnesium atom is substituted by a more electronegative atom, such as aluminium or silicium, the negative charge of the interstitial hydrogen atom is somewhat diminished. The substitutional atoms also attract some of the electrons from the nearest magnesium atoms (see explanation of parentheses in table caption I). A substitutional Na-atom looses some of its electrons to nearby Mgatoms, making them more negative than in the pure metal. Charge (e) Mg Al Si Na X in Mg lattice Mg next to X Mg second to X H in O h hole X next to H in O h Mg next to H in O h H in T d hole (-1.1) -1.0 X next to H in T d (-2.5) +0.7 Mg next to H in T d (+0.6) +0.3 Table III: Properties of B- and C-atoms and their interaction with H-atoms inside the magnesium crystal. The impurity atoms occupy O h interstitial sites. When a hydrogen atom is inserted into a T d hole next to the impurity atoms, it hops into the same O h hole, thus forming a covalent bond. Property B C Pauling electronegativity of X Atomic radius of X 18 (Å) Mg-X bond length (Å) H-X bond length in next O h holes (Å) H-X bond length in same O h hole (Å) Binding energy of H in next O h hole (ev) Binding energy of H in same O h hole (ev)

7 7 Table IV: Atomic charge estimates using Bader decomposition of the charge density. Both B- and C-atoms are quite ionised in the O h holes of the magnesium metal, having charges of -3.2 e and -3.1 e, leaving the nearest magnesium atoms with charges of +0.6 e and +0.8 e, respectively. The hydrogen ions in the adjacent O h holes are a bit more negatively charged than in pure magnesium. When the hydrogen ions are in the same holes as the boron/carbon atom it is interesting that in the case of boron, there is more charge on the hydrogen than the boron atom, but this is reversed for carbon. Charge (e) B C X in O h hole Mg next to X H in next O h hole X in O h hole Mg between H and X Mg next to H Mg next to X H in same O h hole X in O h hole Mg next to H Mg next to X Table V: The effect of Al substitution into MgH 2. As in the case for the metal, aluminium causes a contraction in the lattice and the binding energy of hydrogen decreases. When the concentration of aluminium is increased, the binding energy continues to decrease. An Al concentration of about 15% in the magnesium lattice would decrease the binding enough for hydrogen to be released at 1 atm at a temperature around 100 C. Property Mg Al Atomic radius of X 18 [Å] H(e)-X bond length (Å) H(a)-X bond length (Å) Average binding energy of H in hydride (1:16) (ev) Average binding energy of H in hydride (2:16) (ev) Average binding energy of H in hydride (3:16) (ev) Table VI: Atomic charge estimates using Bader decomposition of the charge density. Substitution of a magnesium atom by an aluminium atom has little effect on the charge distribution of the hydride, it only causes the electron density around the very closest magnesium atoms to increase by 0.1 e. Charge of (e) Mg Al X in hydride Mg next to X in hydride H in hydride H(a) next to X in hydride H(e) next to X in hydride

8 8 (a) (b) Figure 1: (a) Charge density iso-surfaces around the substitutional aluminium atom (in the centre) in a magnesium crystal as reported from the Bader analysis. It can be seen that the charge density of the aluminium atom (-2.5 e) is higher than on the magnesium atoms (+0.3 e). The triangular distortion seen in the charge density of aluminium is because of the magnesium atoms in the next layer of the crystal. (b) The hydrogen atom in a T d hole, along with the three Mg-atoms and the Al-atom that define the hole. Note that the large charge density between hydrogen and aluminium suggests covalent bonding between the two atoms, while no charge density appears between hydrogen and magnesium.

9 9 (a) (b) Figure 2: Charge density iso-surfaces around the boron atom in an O h hole of a magnesium crystal as reported from the Bader analysis (a) before and (b) after the addition of hydrogen in the closest O h hole. Note that the Mg-B and Mg-H clusters seem to be quite isolated from each other.

10 10 Figure 3: Charge density iso-surfaces for the surroundings of an aluminium atom substituted for a magnesium atom in magnesium hydride. As can be seen, there is more charge density between the aluminium ion and the equitorial hydrogen than between the aluminium and the apical hydrogen ions. The charges of the aluminium, equitorial hydrogen and apical hydrogen ions are +2.0 e, -0.8 e and -0.8 e, respectively Average binding energy of hydrogen (ev/atom) Molefraction of Al Figure 4: The calculated average binding energy of hydrogen in magnesium hydride with aluminium impurities as a function of the concentration of aluminium. This relationship is nearly linear. At an aluminium concentration of 15%, the binding energy is as low as 0.25 ev/h-atom, whereas in pure magnesium hydride it is 0.38 ev/h-atom.