DILUTE ATOMIC H IMPURITIES IN SOLID H2

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DILUTE ATOMIC H IMPURITIES IN SOLID H2

R. Etters, R. Danilowicz

To cite this version:

R. Etters, R. Danilowicz. DILUTE ATOMIC H IMPURITIES IN SOLID H2. Journal de Physique

Colloques, 1978, 39 (C6), pp.C6-99-C6-100. �10.1051/jphyscol:1978645�. �jpa-00217928�

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JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 8, Tome 39, aoiit 1978, page C6-99

DILUTE ATOMIC

H

IMPURITIES

IN

SOLID

H2

r

R.D. Etters and R. Danilowiczt

Physics Department, Colorado State Univ., F t . Collins, CO 80523 t Utica college, Utica, New York 23502

R6sum6.- Nous avons modifid l'approximation du champ dynamique local pour traiter le cas des impu- retLs diluses d'hydrogsne atomique dans H2 solide. Les propristss calcul~es des impuretds atomiques sont leurs fluctuations autour des positions d'dquilibre, l'dnergie liante, la fonction de distribution de la particule seule, et la distortion du cristal.

Abstract.- The dynamic local field approximation has been modified to accomodate dilute atomic H impurities in solid H2

.

Calculated properties of the atomic impurities are their r.m.s. fluctuations about the equilibrium positions, the binding energy, the single particle distribution function, and the lattice distortion.

One interesting property of atomic hydrogen impurities in solid H2 can be demonstrated by com- paring it to 3 ~ e impurities in 4 ~ e . The law of corresponding states shows that H in solid Hz should have about the same zero-point energy as 3 ~ e in solid 4 ~ e . On this basis one would expect the H atom probability density to be broad, with a substantial overlap on neighboring lattice sites. For the 3 ~ e - 4 ~ e system, this large overlap has complicated the analysis of its magnetic properties

111.

The Hei- senberg pair-exchange model is inadequate, and multi-exchange processes have been incorporated in an attempt to improve matters. The H in Hg impurity system should exhibit similar magnetic behaviour, but with an enhanced coupling constant, because the H atom magnetic moment is much larger than it is for 3 ~ e .

The stability of this system for various concentrations of H in Hz is complicated by the strongly attractive H-H singlet interaction which induces recombination into H2, with an energy re- lease of about 5x10~ K per molecule. The ability of the H-solid Hz system to store energy as an in- sulator-hydride depends crucially on the overlap of the H atom probability density on neighboring H atom sites.

In this work we consider a system of N-1 Hp molecules in an fcc arrangement and a single H atom at a substitutional site. The ground state wavefunction can be represented by the form

"work supported by NASA Grant No. NGR 06-002-159

+ +

where $i(ri-Ri) localize the particles about their equilibrium lattice sites

{Zi3 ,

^{and the f}^{(r) ac-}

count for the important short ranged pair correlations. The index 1 always refers tp the H atom.

For f and $ we choose the commonly used paramete- rized forms /2,3/

P i ( ' )

= (f3i/~)3/4exP[$3iri2]

,

fi(r) =

expk

^T(~i/r)1 ^{5 ]}

^,

^where^Biand ri are variational parameters to be determined by minimi- zing the energy.

The expectation value of the Hamiltonian can be written exactly as

where m2 is the Hp mass. All B1, if1 are assumed to be the same, and similarily for K..

U and U are the H-Hz and H2-H2 pair potentials,

I 2

respectively. Within the local field approximation /2,3/

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978645

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The effect of all N-2 particles on a pair (i,j) is -+ -+

embodied in the local molecular field, G(ri,r.), J which is directly proportional to the pair distribution function. Equation (3) differs from the exact expression in that it contains only pair correlations which directly link the N-2 molecular field particles to (i,j). This essential decoupling scheme neglects correlations between different molecular field particles. The products in eq. (3) need include correlations. from only the first two nearest neighbor shells around (i, j) 1 2 1 .

The variational parameters are B1,

B2,

"1, ~ 2 , and the H-H2 and Hz-H2 bond lengths in the vicini- ty of the impurity induced lattice distortion. To make the problem tractable we adopt the following approximations : (a) B2 and ~2 are assumed to be the same as for the pure Hz crystal, (b) only the 1st and 4th nearest neighbor separations from the H atom are varied, (c) all H2 molecules beyond the

4th nearest neighbors to H are assumed to have the same binding energy as in the pure Hz crystal and, (d) the H atom is assumed to be in a substitutional site, as indicated by the ESR work of Adrian 141.

Estimates indicate that these approximations are satisfactory.

Results show that the H-Hz nearest neighbor length is 6 % greater than the corresponding length in a pure Hz solid. Figure I shows the single particle distribution function R(r), versus separation r (in units of = 2.958

i).

The solid line with squares the dashed line with circles represent R(r) for the H atom impurity and for pure fcc Hz, respectively.

Fig. 1 .

The relatively small difference between these two curves is, at first sight, surprising since one

would expect the much larger zero-point energy of H to considerably broaden its probability distribution compared with Hz. However, a comparison on figure 2 of the H-Hz potential 151 (dashed line), and the Hz-H2 potential /3/ (solid line), shows why this is not the case.

Fig. 2. r ( 0.111

The relatively narrow H-Hz potential well acts to localize the H atom impurity, thus counteracting an opposite tendency induced by the large zero-point energy. Figure 2 also shows why the H-Hz bond length is relatively large. The H-Hz repulsive core is at an interparticle separation nearly 6 % greater than the H2-H2 core.

The calculated binding energy of the H atom at normal vapor pressure is E =

-

22 K, and the

H

rms fluctuation of the H impurity about its equilibrium lattice site, at normal vapor pressure, is about 5 % greater than the corresponding value for H2

The results for R(r) and EH show that dilute (,?j 6 %) H atom impurities in solid Hz should be quite localized and stable against recombination, provided the temperature T satisfies kT<<E

H' References

/I/ Mc Mahan,A.,J. Low Temp. Phys.

8

(1972) 115 /2/ Etters,R.D. and Danilowicz,R.L., Phys. Rev. A?

(1974) 1698

131 Etters,R.D., Danilowicz,R. and England,W., Phys.

Rev. A11 (1975) 2199

/4/ Adrian,F., J. Chem. Phys.

2

(1960) 972

/5/ Gengenbach,R., Hahn,C. and Toennies,J., J. Chem.

Phys.

2

(1975) 3620