Study of the composition dependence of the ionic conductivity of LiH x D 1-x alloys

Transcription

1 Stuy of the composition epenence of the ionic conuctivity of LiH x D 1-x alloys Vassiliki Katsika-Tsigourakou Section of Soli State Physics, Department of Physics, National an Kapoistrian University of Athens, Panepistimiopolis, Zografos, Greece Abstract Recent observations have shown that at a certain composition of soli solutions AgCl x r 1-x, AgCl-CCl, Agr-Cr, of ionic crystals, the electrical conuctivity exhibits a value appreciably larger than that of the en constituents. Here, we investigate the electrical conuctivity of LiH x D 1-x soli solutions which are of prominent importance in fuel hyrogen storage applications- an fin that in the whole composition range no maximum is likely to occur in the versus x epenence. PACS: 61.7.b; 61.7.Ji; Fv; 77.- Keywors: ulk moulus; Electrical conuctivity; Soli solutions; Defects vkatsik@phys.uoa.gr 1

2 1. ntrouction n general, the stuy of the hyries LiD an LiH has attracte a strong interest in view of their tentative important technological applications such as in fuel hyrogen storage. Much work has been mae on the high pressure properties of the LiH isotopes, for two reasons: First, the comparison between theory an experiment in this case constitutes an important test of the techniques employe in the electronic structure calculations [1]. Secon, the ata of these isotopes are of chief importance in nuclear fusion research. Synchrotron X-ray iffraction measurements have been mae [] on soli 7 LiH up to 36 GPa an soli 7 LiD up to 94 GPa by using helium as a hyrostatic meium an reporte that the rock-salt structure is stable up to the maximum pressure an that at ambient conitions the isothermal bulk moulus is =3. GPa an its pressure erivative /P=3.53. These measurements also foun an isotopic shift on the equation of state the magnitue of which falls in between various approximations of the contribution of the zero-point lattice vibrations. Note also that, in the conuctivity (σ) measurements [3] in 7 LiH an 8 LiD an isotopic shift has been also observe. Recent conuctivity measurements [4] as a function of temperature an composition have been reporte on soliifie mixtures [5-7] of AgCl-CCl an Agr- Cr. These soli solutions exhibite an important increase in conuctivity with the concentration of C +, until aroun 0 mol% CX (X=Cl, r). At the maximum, the value of electrical conuctivity in the AgCl+ CCl soli solution is about 40 times higher than in pure AgCl an the value of electrical conuctivity in Agr+Cr soli solution is about 3 times higher than in pure Agr. A quantitative explanation of this phenomenon, i.e., the appearance of the maximum conuctivity of the soli solution at a certain concentration of C +, has been recently treate by Skoras [8] by employing an

3 establishe thermoynamical moel terme cω moel [9-11] (see below). Note that the same moel has been employe [1] for the explanation of the emission of electric signals before fracture at ionic solis upon graually increasing stress- which provies the basis for the observation of precursory signals before earthquakes [13-16]. t is the scope of this paper to use this thermoynamical moel to investigate the electrical conuctivity of LiH x D 1-x versus x. Hence, it is our aim to ientify whether the aforementione phenomenon (i.e., a maximum conuctivity of a certain value of x) may appear in the system LiH x D 1-x.. Estimation of the composition of the maximum conuctivity. Following Skoras [8] an consiering aspects on efects [17,18], if V an V enote the molar volumes of the two pure constituents () an (), the molar volume V of the soli solution can be written as [16]: V V (1 x) V x (1) where x stans for the molar concentration of the crystal in the mixe system. Differentiating Eq.(1) with respect to pressure, we fin [16]: Nv 1 x V Nv 1 x V () where an are the bulk moulus of the soli solution an the pure crystal, respectively, an 1 where is the compressibility of the pure crystal. The quantity v stans for a efect volume which may be ientifie as follows: t represents 3

4 the ifference of the volume of a crystal of N molecules of type an the same crystal in which one of its molecules has been exchange by a molecule of type. Assuming that V V we get [16]: Nv V V (3) As for, the quantity in Eq.(), it represents the compressibility of the efect volume v : 1 v v P (4) T This iffers in general from the compressibility of the component, i.e., 1 (5) A combination Eqs.(), (3) an (5) leas to 1 x (6) 1 x where the symbol stans for: V 1 0 (7) V Combining Eqs.(1) an (6) we fin: V (1 x ) V 1 x or 4

5 (1 x) 1x (8) where the symbols an an the pure crystal, respectively. enote the mean volume per atom of the mixe system [9-11]: Accoring to the cω moel the efect Gibbs activation energy act g is given by act act g c (9) where act c is inepenent of temperature an pressure. Thus, we can write: act, x act, x g c act, act, g c (10) where act, x g an the pure crystal (), respectively. act, g stan for the activation Gibbs energies for the mixe crystal an Assuming that act, x c varies only slightly versus the composition, Eq.(10) leas to g g act, x act, (1 x) (11) 1 x We now consier that the conuctivity, for a single conuction process, is given [16] by: act g exp kt (1) Assuming that the preexponential factor in Eq.(1) oes not change markely with composition, we observe that the variation of the conuctivity with the composition is 5

6 governe by the function (1 x) (1 x) appearing in Eq.(11). This function reaches a minimum value when the molar concentration x of the constituent takes the value x m (13) The quantity is obtaine from Eq.(7) because the molar volumes of the en members are always known. As for the quantity it can be estimate by the aforementione thermoynamical moel by the following proceure: Substituting Eq.(9) into the well known [16] relation into Eq.(4), gives: v act g act, we fin v c 1, which when inserte P P T T 1 P T P T 1 (14) The quantities P an P, when they are not experimentally accessible, can be estimate from the moifie orn moel accoring to [16]: P ( n 7) 3 (15) an P n (16) ( ) (4 9)( 3) where n is the well known [16] orn exponent. 6

7 3. Application of the aforementione methoology to LiH x D 1-x. Using the lattice parameters Å for LiH an for LiD (see Ref. 3 an references therein), Eq.(7) leas to (17) y applying Eq.(15) an using the aforementione value P =3.53 we fin n =3.6. This orn exponent, when inserte into Eq.(16) upon using also the value =3. GPa- results in ( ) T 0.09 P GPa -1. y substituting this value into Eq.(14) we get.17 (18) We now turn to Eq.(13) which reveals that, since 0 1, the observation of a maximum value in the curve versus x emans: x m 0 1 (19) An inspection of the inequality (19) in view of the, values etermine above in the relations (17) an (18)- leas to the conclusion that this inequality is violate. 4. Conclusion Here, we investigating whether the electrical conuctivity of the soli solutions LiH x D 1-x exhibits a maximum value at a certain composition, which has been experimentally observe in some other ionic mixe systems. We conclue that this is not the case for LiH x D 1-x, which may be of high importance for future fuel hyrogen storage research. 7

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