INTERSTITIAL VOIDS IN TETRAHEDRALLY AND IN THREE-FOLD BONDED ATOMIC NETWORKS

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1 Journl of Non-Oxide Glsses Vol. 5, No 2, 2013, p INTERSTITIAL VOIDS IN TETRAHEDRALLY AND IN THREE-FOLD BONDED ATOMIC NETWORKS F. SAVA, M. POPESCU *, I.D. SIMANDAN, A. LŐRINCZI, A. VELEA Ntionl Institute of Mterils Physics, Atomistilor 105is, RO , P.O. Box MG.7, Mgurele-Ilfov, Romni The im of this letter is to investigte the interstitil voids distriution in simulted networks of disordered silicon nd grphitic mterils. We hve chrcterised these disordered structures nd evidenced the importnce of the SW nd WWW defects on the structure in the newly otined netwoks. The voids distriutions re relted to the posiility to get new mterils y filling the voids with different kind of toms. The chnge of the prmeters of the first diffrction pek (FDP) in morphous silicon nd grphite s consequence of filling the lttice voids hs een determined. (Received Mrch 18, 2013; Accepted April 1, 2013) Keywords: Silicon; Grphene; Topologicl defect; Structure fctor 1. Introduction In this pper we report the results otined y computer simultion of modifictions induced in rther perfect silicon lttice y creting Wooten-Winer-Weire (WWW) defect sttes without introduction of dngling onds or other type of defects. Elliott [1-5] hs demonstrted tht the ordering of the interstil voids round the chlcogen toms in chlcogenide glsses is essentil for the formtion of the first shrp diffrction pek (FSDP) in these mterils. On the other hnd, we simulted similr defects [6] in idel grphene lyers nd we nlyzed the generl effect of the defects on the structure of grphene pcking, especilly on the prticulr first shrp diffrction pek (FSDP) in the clculted X-ry ptterns. The Stone-Wlls defects were previously studied in [7,8]. Kpko et l. [9] firstly clculted the electronic structure of the morphous grphene. Pentgonl puckering in sheet of morphous grphene ws recently demonstrted y Li et l. [10]. The reliztion of the Zchrisen glss in morphous grphene ws remrked y Kumr et l. [11]. The presence nd distriution of voids in these mterils is importnt for the formtion of interclted compounds of the type grphite lkli comintions. Lstly new mterils sed on defected grphene lyers nd disordered lkline insertions could e predicted. 2. Simultion of the defect sttes in silicon nd grphene lttices. We used one silicon lttice with 455 toms nd 5 grphene lttices ech of them with 150 toms. In these networks (which re initil perfectly ordered) we hve introduced numer of topologicl defects to otin disordered networks. Then, these clusters hve een energeticlly relxed using the Monte-Crlo method in the frme of vlence field theory. We consider tht these clusters re t temperture of 0 K. The totl energy of every silicon tom (which is mesure of * Corresponding uthor: mpopescu@infim.ro

2 22 the devition of Si-Si ond lengths nd of ond ngles from the specific vlues of the crystl) ws clculted with the formul of Keting [12] using the force constnts given y Mrtin [12]. To clculte the totl energy of every cron tom, energy which ccounts for the ending nd stretching of the cron onds, we used the formul nd the force constnts given y Jishi [12]. The Wooten-Winer-Weire (WWW) defect is topologicl defect of tetrhedrl lttice formed y interchnge of two neighors of two onded silicon toms without destroying continuity of the lttice [6]. Figure 1 shows the initil stte () nd WWW defect stte () of silicon lttice. The onds etween silicon toms, s function of the distnce from the defect s centre, re more or less deformed. The lttice domin ffected y deformtion extends up to distnce of 0.66 nm from the centre of defect. Fig. 1. Silicon lttices with minimum of the energy eing in ) crystlline stte, ) WWW defect stte (four 5-fold rings nd sixteen 7-fold rings of toms) To otin n morphous silicon lttice we introduced 56 WWW defects in crystlline lttice of silicon (Fig. 2) nd thus deformtion spheres re prtil superposed. Fig. 2. Model of silicon lttice (455 toms) with minimum of the energy in: ) crystlline stte, ) morphous stte with 56 WWW defects. The Stone Wles (SW) defect is topologicl defect of grphene lttice like WWW defect [10]. This similrity etween two types of defects mde Popescu to unify them in single concept nmed deformon. Thrower [13] ws first who studied this type of defect in grphite. Figure 3 shows the grphene lttice (150 toms) (Fig. 3) nd SW defect stte of grphene lttice (Fig. 3). In the cse of grphene with one defect, the defect rdius is 0.31 nm, nd the decrese of the energy is much more rpid thn in the cse of silicon with one defect

3 23 Fig. 3. Top view of grphene lttice with 150 toms with minimum of the energy in: ) crystlline stte, ) the Stone Wles defect stte (two 5 fold rings nd two 7 fold rings of toms. To otin morphous cron monolyers we introduced 9 or 10 Stone Wles defects in the two-dimensionl lttice of five grphene lyers (150 toms) (Fig. 4). These five morphous cron monolyers there pcked in n morphous cron structure (-C) (Fig. 5) nd in Fig 5 is presented grphite lttice. c d e Fig. 4. Disordered lyers of grphene used in simulted stcking of morphous cron - c) 10 Stone-Wles defects, d-e) 9 Stone-Wles defects [7]. Fig. 5. The lttice model of 750 cron toms in ) crystlline stte (grphite), ) morphous stte (-C) (48 SW defects. 3. Voids in silicon nd grphene simulted morphous lttices. The normlized interstitil voids rdius (r v ) distriutions in crystlline nd morphous silicon (455 toms), respectively in five grphene nd in five morphous cron lyers (5 150 toms) re shown in Fig. 6,. While in morphous silicon the interstitil voids re ll sphericl, in morphous cron lyers some re sphericl nd some re of discoidl shpe. In grphene ll the interstitil voids re discoidl in shpe.

4 24 No. of voids r v / r 0 c-si -Si Grphite -C Fig. 6. The normlized voids rdius (r v /r 0 ) distriution in crystlline nd morphous silicon (), in grphene nd in morphous cron lyers of -C with 48 defects () (r 0 is the covlent rdius of silicon nd cron: r 0 (Si) = nm nd r 0 (C) = nm). The interstitil voids in these two types of lttices re importnt for understnding the origin of first diffrction pek in the structure fctor of morphous silicon (Fig. 7) nd second diffrction pek of structure fctor of -C (Fig. 8). Fig. 7 shows the structure fctor of the morphous silicon model fter relxtion. Elliott [3] hs demonstrted in rther seminl pper tht the so-clled FSDP in glsses depends on the distriution, size nd ordering of voids. Popescu nd Sv suggested tht the voids distriution into n morphous mteril is essentil in the mplifiction or vnishing of the first diffrction pek (FDP). We hve simulted the filling of the interstitil voids in morphous silicon, y introduction in the center of the voids of ions with tomic numer identicl to tht of silicon, without covlent onds etween silicon nd ions. The diffrction pttern of the model shows the decrese of the first diffrction pek (FDP) s mesure of filling the voids (Fig. 7). I(Q) (111) -Si (220) (311) c-si -Si + voids (r v >0.120 nm) -Si + voids (r v >0.113 nm) -Si + voids (r v >0.106 nm) -Si + voids (r v >0.089 nm) Q (nm -1 ) Fig. 7. ) The structure fctor of the crystlline silicon model. ) Diffrction pttern of the morphous silicon model with grdully occupied voids with toms non-onded in the lttice. The rrows denote the crystlline peks.

5 Further we hve simulted, s in the cse of silicon, the grdul filling of the interstitil voids in ech morphous lyer from -C with ions hving the tomic numer pproching tht of cron. In this cse the second diffrction pek (SDP) of structure fctor of -C diminishes its height nd grdully vnishes (Fig. 8) I(Q) (002) (100) (101) (110) (112) -C + voids (r v > nm) -C + voids (r v > nm) -C + voids (r v > nm) -C + voids (r v > nm) Grphene Grphite C -C + voids Q (nm -1 ) Fig 8. The structure fctor of grphene lyer nd grphite () compred to the structure fctor of -C with 48 defects when n incresing numer of interstitil voids of morphous lyers re filled (). The rrows denote the crystlline peks. The first diffrction pek (FDP) (situted t Q ~ 20 nm -1 ) is shrp pek nd is followed y smller pek (situted t Q ~ 32 nm -1 ) which is very sensile to the filling of voids of the disordered grphene lyer. In the sme time the FDP increses with the degree of filling the structurl voids. 4. Discussion of the results We hve simulted severl networks of tetrhedrlly onded networks of silicon nd three-fold onded grphite lyers with structurl defects. The interstitil voids hve een clculted. In silicon simulted networks the distriution of voids re determined y the level of disordering. For smll numer of defects the deformtion of the network of toms is strictly loclized. The pcking of defected grphenes, followed y filling-up the voids within the grphene lyer with toms hving the rdius ner tht of cron (e.g. lithium or nitrogen) hs s min consequence the lowering of the second pek in the diffrction pttern down to its disppernce. 5. Conclusions The disppernce of the first diffrction pek (FDP) situted t Q = is explined y the filling of the structurl voids. The second diffrction pek situted t Q = when morphous lyer is integrted in -C grdully vnishes (s in the cse of FDP of silicon) when the interstitil voids re filled y ions with the dimeter pproching tht of cron (e.g. nitrogen ions or lithium ions). The motivtion of this study is to show tht the grdul fill of the interstitil voids with virtul toms hve n importnt effect on some mxim in the structure fctor (FDP in the cse of -Si nd second mximum in the cse of -G). Our min gol ws to show the existence of direct reltionship

6 26 etween the mxim in the structure fctor of the morphous mterils nd the toms tht define the distriution of the interstitil voids. Acknowledgements The uthors kindly cknowledge for the finncil support of the Ministry of the Eductio, Reserch, Youth nd Sports (Romni) in the frme of the Contrct 45N / ; Act d. 2 / 2011, Project: PN References [1] S. R. Elliott, Physics of Amorphous Mterils (Longmn, London, 1990), 2nd ed. [2] S. R. Elliott, Nture 354, (1991). [3] S. R. Elliott, Phys. Rev. Lett. 67(6), (1991). [4] S. R. Elliott, J. Phys.: Condens. Mtter 4, (1992). [5] S. R. Elliott, J. Non-Cryst. Solids 150, , (1992). [6] M. Popescu, Rev. Roum. Phys. 36(10), 907 (1991). [7] A. J. Stone, D. J. Wles, Chem. Phys. Lett. 128(5-6), (1986). [8] F. Wooten, K. Winer, D. Weire, Phys. Rev. Lett. 54, (1985). [9] V. Kpko, D. A. Drold, M. F. Thorpe, Phys. Sttus Solidi B 247(5), (2010). [10] Y. Li, F. Inm. A. Kumr, M. F. Thorpe, D. A Drold, Phys. Sttus Solidi B 248(9), (2011). [11] A. Kumr, M. Wilson, M. F. Thorpe, J. Phys.: Condens. Mtter 24(48), (2012). [12] F. Sv, Ph. D. Thesis, Buchrest, [13] P. A. Thrower, Chemistry nd Physics of Cron 5, (1969).