VERIFICATION OF INTERATOMIC INTERACTION ENERGIES

BY MEIu'JS OF MONTE-CARLO SIMULATION OF SHORT-RANGE

ORDER Iu~ INTERNAL FRICTION SPECTRA

M.S.Blanter

Moscow Instrumentation Institute

Stromynka 20, Moscow 107076, Russia

INTRODUCTION

To calcu:ate "Lfle structure and phase transformations in so] 1d solutions H is nec~essary to J<J10W the energies of solute atoms interaction. In the case cf inter::;t1Clal seJ lei soi.ution the energies of stI'aln-1.nduced (elasT1c; InteracUon in b. c. e. metals were prelim1nar:i.1y ealeula ted 8,(?(;!irdJn,g tc Khachaturyan's tr180ry f 1 ]. However tl18 analysis of il.,Y(ir''y,l(

structure and structure of other .long-range or,1ered. so] L(j solutions showed that in the nearEst eoord1rlatlun slle1hi there are also the repulsive interaclioTI probably d;Jf? [.0

screen Coulomb interaction of eharged :Lm;ersL1·~ial atoms. There 1s a lack of re11able calculations of the re~llslon

in transition metals. This effect was calculated roughly for H·-H interactJ.on in NO [2). Therefore it .1s nee8ssary 1:0 deter

Statics and Dynamics of Allay Phase Transformations, Edited by P.E.A. Turchi and A. Oonis, Plenum Press. New York, 1994 179

mine the radius of repulsive interact1on.In the instance of Nb-H-O alloys the task 1s achived by computer simulation of internal friction spectrum.

THE CALCULATION METHOD

The used energies of pair stra:I.n-induced (elast1c) inter-­action of H--H were calculated up to the 12th. coordination she1l1nRef.[2J and of H-Oup to the Sthshell--1nRef.[3J. The elastic interaction is strongly attract1ve at the nearest d1stances up to the third coordination shell. The add1tional repulsion is taken into account by the compensation of elastic attraction in the nearest shells.

To calculate internal friction we used the method described in [4]. The long-range interaction of interst1tlals causes cIlanges in (1) arrangement of interst1tials (the short-range order ~J2~earanCe);(2)the energy in tetrahedral lnterstlce -by thi~ AE\ L! value. Thus the diffusion barrier Hp of pth inter­st1tial atom 1.8 equal to

( t ) Hp=HD-fi~ (1 )

where HD 1s the aetivation energy of diffusion. The contrlbu­Uon of each pth atom 1s given hy the Debye equation with the aet1vation energy Hp' HD and the pre-exponential coefficient c;f relaxation t1m8 'to weri:3 taken from experimental diffusion data [5J For calculation of the short-range order and fiE a Montf.-Carlo Simulation was carried. out using the Metropo~1S approaCh. Hydrogen concentration was 0.26 at.%,concentration of ftX8\1 oxygen atoms was 1.85 at.%.

RESULTS

In experimental spectrum of Nb~H-O alloys there is one peak due to "diffusion under stress" of hydrogen atoms near fixed oxygen a toms (6,7]. The temperature of maximum is equal to 50K at O.8Hz. The reslll ts of computer simulation of spectra in the range 3D-SDK are displayed for different radii of H-H and H-O repulsive interaction in Table 1 . Only in three cases the cal­Gulated spectrum is in a good agreement with experiment. For

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such agreement it is necessary that the repulsion compensates the H-O elastic attraction up to the third-a shell and H-H elastic attraction no less than in three shells. The analysis 1n broad freguency range Gonfirms this result (Table 2).

The resalts of simulation showed that the method of calculation of internal friction spectra is very fYJ.1tful for verification and improvement of interatomic interaction potentials.The method ean be used for many other lnterstltial and substitutional sol:l .. d sol.utions.

Table 1.Calculated internal friction spectra of Nb-H-O alloys

(30-80K, f=1 Hz).

H-O interaction

Radius of repulsion (811e11 number N) I

0 I ,) 33 I I 3b I

<-

H-H 0 D D I D D D "I I ~ I

1 D D I

D D j D I i n I

i

I

___ .l-

t 2 D D D D D e N r 3 D D B A i D a I I

t-I c 4 D

I D C A i D

t 5 D D C i A T\

I I l! I i

~

Types of internal friction 8pectra:A-one peak at 56K;B-one peak at 76K;C-two or three peaks;D-peaks are absent. The third-a and third-b coordination shells are different by the vector separated. 0 and H atoms:{3/4,O,O}aO and {1/2,1/2,1/4}30 respectively (30 1s a lattice par&l1eter).

CONCLUSIONS

1. Spectra of internal friction due to "diffusion under stress" of interst1tial atoms in b.c.c. metals are very sensitive to interatomic interaction energies.

2. The long-range strain-induced (elastiC) energies of H-H and H-O interaction supplemented by repulsion in the three nearest coordination shells are applicable for description of the Nb-H--O solid solutions.

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Table 2.Temperature Tl and effective activation energy H fi' e .... of hydrogen internal riction maximum in Nb-H-O alloys.

1 r-:: H-G repulsive Tp,K at H eft,eV ! interactlon up to: 1000Hz 10000Hz

I the second shell 104 118 0.19 the thlrd-a shell 74 83 0.145 Experiment [8,9] 79 93 0.135

REFERENCES

1 .A.G.Khachaturyan. "Theory of Structural Transformations in Solids,"WilleY,New York (1983).

2.V.G.Vaks,N.E.Zeln,A.G.Orlov et el.,On the theory of inter­action and phase transformations of hydrogen in tran­Sition metals,mBTw.87:2030 (1984) (In Russian).

3.A.I.ShirleY,C.K.Hall and N.J.Prlnce,Trapplr~ of hydrogen by oxygen and nl trogen impurities in niobium, vanadium and tantalum,Acta Metall.)1:985 (1983).

4.M.S.Blanter and M.Y.Fradkov,Solute interactior. and internal friction in solid solutions,Aota Met. (to be published).

5.M.S.BI8.t">1ter ,Yu. V .Piguzov et e1. "The method of internal friction in metallurgical researcl1" (a reference book), Metallurgia.Moscow (1991 ).(In Russian).

6.J.Volkl and G.Alefeld, Hydrogen diffusion 1n metals, In. "Hydrogen 1n Metals".I,G.Alefeld,ed., Springer-Verlag, New York (1978).

7 • R.Hanada ,M.Shlnohara , Y.Sado et e1. ,An internal friction st11dy of N-·H and O-H pairs in single crystal of niobium at low temperatures,J Phys.(Fr.)42:C5,751 (1981).

8.G.Cannelli and L.Verdinl,Relaxation effect due to diffusion of interstitlal llYdrogen in tantalum and nlobium, Ricerca Sci.3§:98 (1966).

9.P.Schlller and A.Schneiders,On the hydrogen relaxation peak in nlobium,Physica status solidi(a).29:375(1975).

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Keywords:internal friction/interatomic interact1on/hydrogen/ niobium/Snoek relaxation/Monte-Carlo simulation/Coulomb interaction/strain-induced interaction/elastic interaction.

Abstract: Calculation of the internal friction spectrum of Nb-H-O alloys was used for verification of the model of O-H and H--H interaction. The strain--induced long-range interaction energtes supplemente<..'l. by l~oulomb repulsion in the nearest coorctinaHon shells were used. It was shown that the rac.ius of Coulomb repulsive interaction 1s equa: to three coordination shell. The used model of interatomic interaction Is applicable to description O!' interstitial sol1d. solution.

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