Short Notes

phys. stat. sol. (b) 171, K5 (1992)

Subject classification: 63.20; S1.2

K5

Department of Physics, D. A. V . College, Kanpur’ ) (a) and Department of Physics, D . B‘. S . College, Kanpur (b)

A Lattice Dynamical Study of Nickel Based on the M o r s e Potential

BY M.K. MISHRA (a) , P. SRIVASTAVA (b) , and S . K . MISHRA (b)

A new approach to the lattice dynamical study of nickel based on the Morse potential, has been developed. This study finds better agreement between experimental and theoretical results. Again the same findings have been compared with other recent studies.

Recently Prakash and Upadhyaya 11, 21 and Upadhyaya and Prakash I31 investigated the lattice dynamics of some f.c.c. metals using the transition metal model potential (TMMP) incorporating many-body forces. It is to be remembered that the TMMP of Animalu /4/ in local approximation and also the scheme of Eschrig and Wonn 151 use only central pairwise forces in the interaction system. Studies /I to 31 showed that their three-body forces, in conjunction with the TMMP of Animalu 141, give the phonon dispersion curves for several f .c.c. metals using different systems of units for the same three-body parameter. In case of nickel, first they 121 calculated the phonon dispersion curves by using the tabulated model parameters of Animalu with the lattice parameter and ionic mass in the Fermi surface approximation of the TMMP 141. Next they apply the non-local scheme of Eschrig and Wonn, exactly following Kulshrestha and Upadhyaya 161 and computed the dispersion results of nickel. Results obtained by Prakash and Upadhyaya 121 are in less agreement with the experimental findings of Bergeneau et al. IT/.

In the present note we have used the three-body Morse potential on the lines of Mishra 181 in conjuncton with the scheme of Animalu 141. This three-body potential coupling the a t o ~ (1,k) with two common nearest neighbours (1’ , 1; ) and (f , If’ ) may be written as

where A(k) is the three-body parameter,rl and r2 are separations of the atoms ( l ’ , k ) and (1” , d ) from the atom (1, k ) , respectively, and a , B are the usual parameters of the potential. The prime on first summation in (1) means

l’ , k * l”, d ’) MIG-370, Avas-Vikas Colony, Panki Road, Scheme l,Kalyanpur, Kanpur, India.

K6 physica status solidi (b) 171

The three-body potential @ ( 3 ) is first used to build up the dynamical matrix.

The usual procedure leads to the following diagonal and off-diagonal elements of the matrix:

(rl,p2)

Short Notes K7

(2)

.:?if = 4B3[Caf (cg’ + cy, - 21 ,

where 8, is the second derivative of $I ( 3 ) (v1,r2) ’

(a 9,f 1 Caf = cos 7 and CZaf = cos(a qaf ) .

From Fig. 1, we reached the conclusion that combination of the three-body potential developed by Mishra / 8 / with the scheme / 4 / using a central pairwise potential, gives better results. Dispersion curves by Mohammad et al. / 9 / and by Vra t i / l o / are also shown in the figure for comparison. The present investigation provides a good agreement and satisfies the equilibrium condition also. The three- body parameters are

A(k) = - 0 . 4 3 6 ~ 1 0 - ~ ~ J and B3 = 0.414 Nm-’

We conclude that this new approach in f.c.c. nickel has turned out to be fairly encouraging for extending it to calculate other lattice dynamical properties, which work is in progress and will be reported in due course.

The authors are highly obliged to Prof. D r . J. Shankar, Head of the

Department of Physics, Agra University, for helpful discussions on the revised manuscript.

References /I/ D. PRAKASH and J.C. UPADHYAYA,

J. Phys. Chem. Solids 49, 91 (1988).

/ 2 / D. PRAKASH and J.C. UPADHYAYA,

phys. stat. sol. (b) 148, K109 (1988).

131 J. C . UPADHYAYA and D. PRAKASH, Phys. Rev. B 33, 1416 (1986).

/ 4 / A.O.E. ANIMALU, Phys. Rev..B!, 3542, 3555 (1973) . / 5 / H. ESCHRIG and H. WONN, phys. stat. sol. 40, 163 (1970) .

/ 6 / O.P. KULSHRESTHA and J.C. UPADHYAYA, J. Phys. Chem. Solids 38, 213 (1977) .

/7/ R.L. 3ERGENEAU, J . CORDES, G. DOLLING, and A.D.B. WOODS,

/ 8 / M.K. MISHRA, phys. stat. sol. (b) 162, K73 (1990) .

Phys. Rev. 136, 1356 (1965).

K8 physica status solidi (b) 171

/9/ K. MOHAMMAD, M.M. SHUKLA, F. MILSTENI, and J.L. MERZ, Phys. Rev.B 29, 3117 (1984).

/ lo / S.C. VRATI, A.U. Thesis, 1980.

(Received November 25, 1991; in revised form April 7, 1992)