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COMPUTER SIMULATION OF HYDROGENATED
AND DEUTERATED CuTi AMORPHOUS ALLOYS
B. Rodmacq, L. Billard, Ph. Mangin, A. Chamberod
To cite this version:
COMPUTER SIMULATION OF HYDROGENATED AND DEUTERATED C u T i AMORPHOUS ALLOYS
B. Rodmacq, L. B i l l a r d , P h . Mangin and A. Chamberod
DRF-Service de Physique, Métallurgie Physique, CEN-Grenoble, 85 X, 38041 Grenoble Cedex, France
* Institut Laue-Langevin, 156 X, 28042 Grenoble Cedex, Franoe
Résumé. Des expériences de diffraction de neutrons ont été effectuées sur des alliages amorphes CuxTI-|_x avec différentes teneurs en hydrogène ou en
deutérium. t a combinaison de longueurs de diffusion positives (cuivre et deutérium) et négatives (titane et hydrogène) a été utilisée afin d'identifier sans ambiguïté les pics supplémentaires qui apparaissent dans les fonctions de corrélation de paires des alliages CuTiH et CuTiD. Sur la base de ces résultats expérimentaux, un modèle structural a été construit par relaxation d'un ensemble d'atomes de cuivre et de titane dans un potentiel de Johnson modifié. L'hydrogène et le deutérium ont ensuite été Introduit dans le modèle et les fonctions de corrélation de paires totales ainsi obtenues ont été comparées aux fonctions expérimentales correspondantes.
Abstract. Neutron scattering experiments have been performed on amorphous CuxTi-|_x alloys with various amounts of hydrogen and deuterium. The combination
of i) negative and positive scattering lengths of titanium and copper and ii) negative and positive scattering lengths of hydrogen and deuterium has been used to identify unambiguously the supplementary peaks which appear in the pair correlation curves of CuTIH and CuTID alloys. Taking into account these experimental results, a structural model has been built up by relaxing an assembly of Cu and Ti atoms in a modified Johnson potential. Then hydrogen and deuterium atoms have been introduced in this model and the resulting total pair correlation functions have been compared to the experimental ones.
I. INTRODUCTION
Besides the study of mechanical and dynamic properties of amorphous metal-hydrogen systems interest has recently focused on the study of the location of hydrogen atoms in amorphous materials, in this case, hydrogen can be used as a local probe of the structure of the amorphous state. The study of the hydrogenation sites and the comparison with the corresponding crystalline hydrides give Information on the structure and chemical characteristics of the host material.
In this paper we present some of the- results obtained by neutron diffraction on hydrogenated and deuterated CU50TI50 amorphous alloys / I / . The modifications of the interference functions and pair correlation functions with hydrogen or deuterium loading correspond to the appearance of new metal-hydrogen correlations which are discussed with reference to the crystalline hydrides. A structural model is presented for the a s -quenched CuTi alloys. Hydrogen and deuterium atoms are then introduced in this model on the basis of the experimental results and the pair correlation functions obtained from this model are compared to the experimental ones.
II. EXPERIMENTAL RESULTS
Large-angle neutron scattering experiments have been performed at ILL Grenoble on D2
+Permanent address. Laboratolre de Physique du Solide <CNRS. LA. 155), University de
Nancy I. BP 239. 54506 Vandoeuvre. France
C8-416 JOURNAL
DE
PHYSIQUEInstrument. The dlffraction curves were corrected as usual for detector cell efficiency. parasitic background. sample holder and sample transmlsslon. A supplementary correction was introduced to account for the large inelastic effects in the case of hydrogenated and deuterated samples. In this case. the combination of a small mass and a large incoherent scattering cross-section (for hydrogen) leads to a rapld decrease of the diffracted intenslty as a function of scattering angle. Thls makes the correction difficult and leads to some uncertainty on the lntenslty of the flrst peaks of the resulting Interference functions. Nevertheless It Is possible to dlscuss the experimental results by foilowlng the evolution of the interference functions and pair correlation functlons with varlous hydrogen or deuterium contents.
Flg. 1. interference functlons for amorphous
Cue.
50Ti0. 50 (H, D) alloys : (a) ~ ~ ~ 0 . 3 3 (b) XH=O. 15(c) X=O (d)x~=O. 20
Fig. 2. reduced palr correlatlon functlons G(r)=4srpor(g( r) -1) for
Cue.
50TIo. 50 t H, D l x alloys: (a)xt(=O. 33. ( b ) x ~ = O . 15, (c)x=O, ( d l XD= 0.20Fig. 1 presents the interference functions S(q) = / < f a for a Cu50TiSO amorphous ailoy with various hydrogen and deuterium contents. Curve (c) corresponds to the non- hydrogenated ailoy and is very slmllar to the curves obtained by Sakata et al. /2,3/ and Fukunaga et ai. /4/. Thls curve is typical of amorphous alloys with posltive and negative scattering lengths. the usual first intense peak at about 3 being replaced by a deep minimum. The prepeak at about 2
k1
is also apparent and is characteristic of chemical order between Cu and TI atoms wlth a tendency for Cu atoms to be surrounded by Ti atoms. it can also be seen on figure I c that In addition to this prepeak. a shoulder is present at even smaller q-value. This shoulder transforms Into a maximum as hydrogen concentration increases. and on the contrary it completely disappears for deuterated samples (figure I d ) . Such a variation wlth hydrogen or deuterium content means that this small-angle signal arises from titanium-hydrogen (deuterium) rich reglons / 5 / . The corresponding pair correlation functions are presented In flgure 2. It can be seen that the overall shape of these curves is not greatly modified as hydrogen or deuterium Is introduced in the samples. Nevertheless some systematlc varlatlons can be observed as a function of hydrogen or deuterlum loadlng. The same modifications are observed for Cu35T165 and C U ~ ~ T I ~ ~ alloys /I/.Moreover this distance corresponds exactly to the distance from the center to one of the Ti atoms in a Ti4 tetrahedra. with d ~ = 2. ~9
&.
- In the same way. no evidence Is found of ~ ~ CU-H (CU-D) dlstances at about 1. 5A,
despite the larger weight of the CU-H correiatlons as compared to the Ti-H ones.Two other components appear at about 3.2
a
and 3.8a
i n the total pair correlation curves. The first one decreases with hydrogen absorption and increases with deuterium absorption. whereas the second one varies in the opposite way. Thus these two peaks can be attributed to CU-H and Ti-H correlations respectively. The possibility of observing such rather large distances in the total pair correlation functlons shows that these distances are relatively well defined in the amorphous structure. As shown in tableL
metal-metal and metal-hydrogen distances for CuTiH (D) amorphous alloys compare well to those found in crystalline y-CuTiD /6/.Table I . F i r s t neighbour d i s t a n c e s
(8)
i n c r y s t a l l i n e /6/ and am0rphous CuTi a l l o y s CuCu CuTi T i T i TiK TiE CUK H KIll. MODEL CALCULATIONS
The experimental results presented above have been used to built up a computer model of the structure of hydrogenated CuTi amorphous alloys. The flrst step has been to obtain a model able to reproduce reasonnabiy well the structure of the as-quenched materials. Hydrogen and deuterium atoms were then introduced in this model by taking into account the preferred Ti-H (TI-D) interactions.
y-CuTiD 2 . 4 9
$:$I
3:SZ
1 . 9 3 3.60 3 . 1 6 2 . 1 41 ) As-quenched CuTi amorphous alloy am-CuTi (H,D) 2.5 2 . 7 2 . 9 1 . 8 3 . 8 3.2
Two models have been built up to simulate the structure of these as-quenched alloys. In each case. one starts with an Initial monoatomic packing relaxed i n a modified Johnson potentiai /7/. Cu and TI atoms are then chosen at random to give the desired composition CU5~Ti50.
For the first model. this initial alloy Is relaxed in a modified Johnson potential in which the position r and depth e of the minimum of each metal-metal potentiai are given by :
€Cu-Cu = €Ti-Ti = -1
e c u - ~ j = a with a 6
-
1The initial values of the metal-metal dlstances correspond to those determined experimentally
/I/.
In the same way. the CU-TI potential i s chosen deeper than the Cu-Cu and Ti-Ti ones in order to favour heterocoordinatlon. These values of r and a are then adjusted to give the best agreement with both X-ray and neutron interference functlons and patr correlation functions i n tdrms of posltions and intensities of the various peaks. Figure 3a shows the correspond,hg neutron S(q) obtained with a=-4. Curve c is the experimental S(q). One can see that the agreement between these two curves is rather oor. particularly for the positions and Intensities of the peaks in the region from about 3C8-418 JOURNAL
DE
PHYSIQUEFig. 3. Interference functions for amorphous
Cue.
50Ti0. 50 alloy : (a) first model (b) second model (c) experlmental.Flg.4. Slmuiated neutron pair correlation functions G ( r) for
Cue.
50Ti0.50 t H, D), alloys : (a) x ~ = 0 . 12. (b) x=O ( c )XD = 0.12
In the second construction. one starts wlth the same initial alloy as above but now one tries to reproduce the experimental results by a Monte-Carlo procedure. In this case CU-Ti pairs are randomly permuted wlth a given probability If this permutation favours chemlcai order / 9 / . After that the sample Is relaxed In the same Johnson potential as above but wlth
a = -1 ( l e ecu-cu = ~TI-TI = e c U - ~ 1 ) . Flgure 3b shows the resulting neutron Interference function S ( q ) . It can be seen that a better agreement is obtained with thls model. The second peak Is found at the right q-value (although its wldth is larger than the experimental one) and the third peak at q
=
5A-1
is clearly vislble. The intensities are also much closer to those obtained experimentally. Simulated X-ray interference functions and pair correlation functlons are also Improved by this procedure. A good agreement is also obtained for the neutron pair correlation functions. as it can be seen by comparing flgures 2c and 4b.2) Hydrogenated and deuterated alloys
An analysis of the second model has been carried out in terms of VoronoX polyhedra In the same way as for monoatomic models / 7 / . On the basls of the experimental results / I .
lo/.
which show that Ti4 tetrahedra are the preferentlal hydrogenatlon sltes, hydrogen atoms were introduced in the model wlth the following hypotheses :
-
no modlficatlon of the metal-metal distances Is Induced by the lntroductlon of hydrogenor deuterium
- all the tetrahedral sltes defined by four titanlum atoms can be occupied by hydrogen or deuterium
-
among these sltes. only those correspondlng to hydrogen-hydrogen distances larger than 0 . 6A
can be effectively occupied.Figure 4 shows the simulated neutron palr correlation functlons for CuTiHg. 12 (fig. 4a). CuTi (fig. 4b) and CuTiDo. 12 (fig. 4c) samples. By comparison wlth the experimental palr correlation functlons of figures 2a. 2c and 2d. one observes that a rather good agreement is obtained concerning both posltions and lntensitles of the supplementary TI-H (Ti-0) and CU-H (CU-D) correlations.
Thls shows that despite the approxlmations used for the construction. thls model is able to reproduce the general features of CuTl ( H , D) amorphous alloys. As for the experimental
results. one sees that rather large metal-hydrogen distances are well deflned In the model wlthout havlng to introduce any long-range order in the Initial construction. This also Indicates that the method we have used here to simulate the structure of these amorphous CuTl alloys can relatively well reproduce the observed chemical order between Cu and Ti atoms. It has to be recalled that the comparison wlth the neutron interference function and palr correlation function of an alloy with positlve (copper and deuterium) and negative (titanium and hydrogen) scattering lengths Is a rather severe test of the quality of the model.
A more complete study of these computer simulations Is in progress. including various tests on the reproduciblllty of the structure obtained by the Monte-Carlo procedure and on the stability of such a structure durlng a structural relaxation by mechanical deformation / 7 / . It could also be Interesting to improve the "hydrogenation" procedure. by relaxing the host structure or by taking Into account posslble hydrogen-hydrogen Interactions. In thls way it could be posslble to favour the creation of titanium-hydrogen rich reglons. as it Is experimentally observed in these amorphous hydrides /1.5/.
REFERENCES
/ 1 / Rodmacq. €4.. Mangln. Ph.. Chamberod, A , . to be published In J. Phys. F : Met. Phys.
/ 2 / Sakata, M. , Cowlam. N.
.
Davles, H. A. , J. Physique (Paris)41
( 1980) C8-190/ 3 / Sakata, M . . Cowlam, N.. Davies. H . A . . Proc. 4th Int. Conf, on Rapldly Quenched Metals (Sendal. 1981) p 327
/ 4 / Fukunaga. T. , Kai. K . , Naka. M.. Watanabe. N.. Suzukl. K. Proc. 4th Int. Conf. on Rapidly Quenched Metals (Sendal. 1981) p 34
/5/ Goudeau, P.. Naudon. A . . Rodmacq. 8.. Mangin. Ph.. Chamberod. A . . this conference
/ 6 / Santoro. A.
.
Maeland. A..
Rush. J. J..
Acta Cryst. 8 3 4 ( 1978) 3059/ 7 / Langon. F.. Blllard. L.. Chamberod. A.. J. Phys. F : Met. Phys.
14
(1984) 579 / 8 / Boudreaux. D. S..
IEEE Trans. Mag..
MAG-17 ( 1981) 2606/ 9 / Spaepen. F.
.
Cargill Ill. G. S.. Proc. 5th Int. Conf. on Rapldly Quenched Metals( Wurzburg
