Parallel molecular dynamics simulations of pressure-induced structural transformations in cadmium selenide nanocrystals

Transcription

1 Lousana Sae Unvesy LSU Dgal Commons LSU Docoal Dsseaons Gaduae School 005 Paallel molecula dynamcs smulaons of pessue-nduced sucual ansfomaons n cadmum selende nanocysals Ncholas Jaba Ouma Lee Lousana Sae Unvesy and Agculual and Mechancal College, nlee3@usc.edu Follow hs and addonal woks a: hps://dgalcommons.lsu.edu/gadschool_dsseaons Pa of he Physcal Scences and Mahemacs Commons Recommended Caon Lee, Ncholas Jaba Ouma, "Paallel molecula dynamcs smulaons of pessue-nduced sucual ansfomaons n cadmum selende nanocysals" 005. LSU Docoal Dsseaons hps://dgalcommons.lsu.edu/gadschool_dsseaons/593 Ths Dsseaon s bough o you fo fee and open access by he Gaduae School a LSU Dgal Commons. I has been acceped fo ncluson n LSU Docoal Dsseaons by an auhozed gaduae school edo of LSU Dgal Commons. Fo moe nfomaon, please conacgaded@lsu.edu.

2 PARALLEL MOLECULAR DYNAMICS SIMULATIONS OF PRESSURE- INDUCED STRUCTURAL TRANSFORMATIONS IN CADMIUM SELENIDE NANOCRYSTALS A Dsseaon Submed o he Gaduae Faculy of he Lousana Sae Unvesy and Agculual and Mechancal College n paal fulfllmen of he equemens fo he degee of Doco of Phlosophy n The Depamen of Physcs and Asonomy by Ncholas Jaba Ouma Lee B.S., Jackson Sae Unvesy, 996 M.S., Lousana Sae Unvesy, 000 Decembe, 005

3 Copygh 005 Ncholas Jaba Ouma Lee All ghs eseved

4 ACKNOWLEDGEMENTS Ths has been a emendous expeence. I am whelmed wh pleasue o ecoun all he people who have affeced my lfe leadng up o hs accomplshmen. I would lke o hank Ds. Pya Vashsha, Rajv Kala, and Acho Nakano, fo he oppouny o pacpae as a gaduae suden n hs excng aea of eseach. I am gaeful fo he encouagemen, geneous suppo and candd advce hey have povded me along hs couse. I appecae he me hey nvesed no my eseach and hess wng, along wh he paence and consdeaon. I consde hs a valuable expeence, whch I wll connue gan fom houghou my caee. I would lke o snceely hank D. Roge McNel, D. James Mahews, D. Eno Sajo and D. Randall Hall fo sevng on my hess commee. A specal hanks goes o Anne Vashsha, Y Chun Chen, Bjaya Kak and Rchad Clak fo he help n pepang hs documen and my dsseaon pesenaon Ths wok a CCLMS and CACS has been suppoed by he Naonal Scence Foundaon and by DURINT Defense Unvesy Reseach Inave on Nanoechnology. I am gaeful fo he me and effo Sanjay Kodyalam so gacously offeed dung my gaduae sudes, goup-elaed pojecs and he ealy sages of my eseach. I consde hm a gea elable esouce- eady wh a quck w and helpful saghfowad pespecves. Sayavan Vempaala and Paulo Banco ae fends wh whom I have shaed many laughs and convesaons ha made my me hee enjoyable. Thank you Ds. Acho Nakano, Hdeak Kkuch, Ashsh Shama as well as Ken-ch Nomua, Sje Zhang fo assemblng and mananng vaous n-house hadwae and sofwae facles

5 ha have been esponsble fo so many CCLMS and CACS poducons. I would lke o hank sysem admnsaos Monka Lee and Hoensa Valdes fo admnseng o ou vaous needs. I have had he pleasue of meeng and neacng wh a wh so many ohe membes and assocaes of he goup ove he yeas ncludng: Mana Bachlechne, Bupesh Bansal, Elzabeh Bouchad, Lauen van Buzel, Tmohy Campbell, Alok Chaejee, Ingva Ebbsojo, James Geguch, Gonzalo Gueez, Elefeos Ldoks, Xnlan Lu, Zhen Lu, Maxm Makeev, Ben Neal, Andey Omelchenko, Takeho Oyakawa, Hsu Pn, Jose Rno, Cndy Rounee, Rchad Seymou, Ashsh Shama, Xaoao Su, Izabela Szlufaska, Kenj Tsuua, Naoo Umezawa, Phlp Walsh, Weqang Wang, Toy Wllams, Zhongbng Yao, Cheng Zhang. I dedcae hs hess o my elaves n he Alfod and Lee famles. I am vey gaeful fo he love, suppo and encouagemen. To my fahe, Nahanel Lee, I have many mes had o ely on you wsdom. Thank you fo beng hee. I love you. To my lle sse, Maya Lee, of whom I am so poud. Thank you fo helpng me o smle. I would no have made o hs pon whou my mohe Vena Lee. He love, undesandng, fah and nfluence have helped me hough all he challenges I have faced. She s a sold ock and nspes me by example. To D. Kunal Ghosh and hs wfe Sushma, I dedcae hs o you as well. As an undegaduae I hough of you as a gea meno fo encouagng and enablng me and many ohe sudens oo pusue eseach oppounes n scence. In he yeas snce JSU, I have only ganed a geae appecaon fo you effos and pespecves on lfe and caee. v

6 I am honoed o have me a numbe of exceponal people n scence ncludng Sylvese Gaes, Wale Massey, Robe Bagg, Sumne Davs, Wale Kohn, Lennad Seabog, Sephen Chu and he lae Waen Heny. I would also lke o dedcae hs hess o he memoy D. Hay Moson, pofesso emeus of he physcs depamen a Bekeley, who mmedaely ook me unde hs wng dung my me hee. Thank you all fo beng so pesonable, suppove and nspng. Seceaes I would lke o hank he seceaes and coodnaos who have helped me n so many dffeen ways ove he yeas: Anell Dangefeld, Bevely Rodguez, Jule Douce, Jade Ehedge, Lnda San, Kaen Rchad, Cahy Mxon, and Cono Champon a Lousana Sae Unvesy; Donna Sakma and Anne Takazawa Unvesy Calfona Bekeley; and Sabna Feely and Paca Wong a he Unvesy of Souhen Calfona. Thanks o D. Ha-Shou Yang, who always commended me as a seous suden and encouaged me o become an engnee; Ds. Zelma Roze, Ds. Booke Spulock, D. Chales Spann, M. Dan Couse and D. Babaa M. Lucke fo helpng handle vaous ssues dung my me a Jackson Sae Unvesy; D. Collee Pa and D. Sumne Davs fo beng gea counselos o me a U. C. Bekeley; Ds. Paul Kk, Robe O Conell n he LSU physcs depamen and D. Keh Sandfod n he LSU englsh depamen fo always havng wods of encouagemen. I would lke o acknowledge he followng people fo ganng me wok expeences n college ha have helped me fame my gaduae school objecves: Pee Levenbeg, Ds. Anne Bouchad and Mashall Lubaen fo my fs nenshp a Ames v

7 Naonal Laboaoy n Iowa; Ds. Bob and Wale Mae a he Amy Hgh Pefomance Reseach Cene and he Unvesy of Mnnesoa; Ds. Keh Jackson, Chales Fadley, Renhad Denecke, Jonde Moas, a he Advanced Lgh Souce a Bekeley; Ds. Lay Mye, Geme Yang a Laweence Bekeley Lab- Eah Scences Dvson; D. Smon Deeluw, and fends Ovdo, Robe, Manx, Dhaj, Laa a Delf Unvesy of Technology n Delf Holland. Seveal goups I would lke o acknowledge fo he connued offengs of suppo hough my undegaduae yeas up o now: Dolly Sacks and Annedoe Kushne of he Davd and Luclle Packad Fellowshp Foundaon; Angnes Coleman, Benne L. Page, Mcheal Bshop, Gloa B. Johnson of he Amecan Assocaon of Blacks n Enegy; M. Leason of EnCon engneeng conacos; Jesse Jones and Shley Bone a I.B.M, CSWUG commee membes- Ds. Wllam & She Wschusen, D. Haold Slveman, D. Valee Benne of Moehouse College, D. John Vllaeal Texas Pan Amecan and D.Augusne O. Esogbue Geoga Tech, and Ds. Doyle Temple and Khn Maung Maung of Hampon Unvesy. To Wlbu, Kevn, Usula and Doug fom he physcs dep a JSU as well as Reg, Ma, Dave, Dan, Chuck, Chale Mack and all he guys ha have kep n ouch fom Dxon Hall hanks you fo he suppo and even he jeeng fo me o gaduae. I wan dedcae hs o my hgh school fend Leon Andeson who los hs lfe as a second yea pe-med majo a Moehouse College, and o hs mohe Ms. Andeson who has always eaed me as he son. Chees o Keh and Dellah Foenbey. Thanks fo keepng n ouch and beng undesandng. To Calvn Bown J., wfe Wleha, and he Bown famly, hanks fo pckng me up and helpng aound ou hee n Los Angeles. v

8 You have always been hee wachng ou fo me snce we wee n nd gade! I have always fel suppo fom my GSAD fends fom Bekeley ove he dsance: Ray Glsap, Ande Lundkvs, Tajh Taylo, Bad Cammon, Duane Glyo, Eka Whney, Mashelle Jones, Doeen Bowens, Jav Dake and John Hakless. To Anon, wfe May, he Books and Jones and Smmons famles, hanks fo keepng me n you houghs and offeng me a place o eea occasonally. To Demeus Mosley, hanks fo walkng wh me hough he enches and fo beng someone who eally lsens and undesands. v

9 TABLE OF CONTENTS ACKNOWLEDGEMENTS.. LIST OF TABLES. LIST OF FIGURES... ABSTRACT... x x xv CHAPTER INTRODUCTION..... MOLECULAR DYNAMICS METHODOLOGY.. 4. Backgound Ineaomc Poenals Foce Calculaon Inegaon Algohms Sascal Ensembles NVT Ensemble NPT Ensemble Compuaon of Physcal Popees Themodynamc Quanes Sucual Coelaons Elasc Modul and Sesses Dynamc Coelaons PARALLEL MOLECULAR DYNAMICS Backgound Flynn s Taxonomy Beowulf Cluses Paallel Compue Memoy Achecues Paallel Pogammng Models Wokload Dsbung Saeges n Paallel Compung Aom Decomposon Foce Decomposon Spaal Decomposon Implemenaon of Paallel Molecula Dynamcs Pocesso ID Neghbo Pocesso ID Aom Cachng and Mgaon Lnk-Ls Cell Mehod on Paallel Cluses Cells Scalably Analyss of Paallel Molecula Dynamcs Algohm Paallel Effcency Consan Poblem-Sze Scalng... 5 v

10 3.3.. Isoganula Scalng Analyss of Paallel Molecula Dynamcs Algohm Consan Poblem-Sze Scalng Isoganula Speedup WURTZITE-TO-ROCKSALT STRUCTURAL TRANSFORMATIONS IN CADMIUM SELENIDE NANO-RODS Expemenal Reseach on CdSe Nano-Rod Ab-Ino Smulaons of Sucual Phase Tansfomaon n Bulk CdSe Molecula Dynamcs Smulaons of Sucual Phase Tansfomaon n GaAs Nanopacles Pessue Medum n MD Smulaon of Sucual Tansfomaons n CdSe Nanoods REVERSE STRUCTURAL TRANSFORMATIONS IN CADMIUM SELENIDE NANORODS Backgound Facue Mechancs Expemen on Facung of CdSe Nanoods dung Compesson MD Smulaons of Revese Sucual Tansfomaon CONCLUSIONS Fowad Tansfomaon Nucleaon and Sngle Doman Fomaon Tansfomaon Pessue vs. Rod Sze Fowad Tansfomaon Mechansm Revese Tansfomaon Fuue Wok... REFERENCES... 3 VITA... 8 x

11 LIST OF TABLES Table.: Paamees fo Cd-Se Ineacon Table 3.: An example of sequenal-veco pocesso ID mappng Table 3.: Example of sequenal-veco neghbo ID mappng Table 4.: Paamees of he LJ lqud used as he pessue medum... 6 Table 4.: Specfcaons fo he fou CdSe nanood sysems.. 66 Table 5.: Inal confguaon paamees fo upsoke smulaons x

12 LIST OF FIGURES Fgue. Tansmsson elecon mcogaph of epesenave CdSe nanoods n he 4-coodnae phase befoe A and afe one B pessue cycle. 4 Fgue. Lengh dsbuon of he pacles befoe blue and afe ed pessue cyclng.. 5 Fgue.3 Smulaed sysem szes n he famewok of densy funconal heoy DFT and molecula dynamcs MD have kep pace wh Mooe s Law due o advances n algohms and hadwae Fgue.4 Inal smulaon seup fo a GaAs sphecal nanopacle suounded by a dsbuon of aoms neacng va Lennad-Jones poenal.. 0 Fgue.5 Molecula dynamcs confguaons of GaAs nanopacles a pessues of A 7.5 GPa and C.5 GPa. Coespondng sphecal shellesolved bond angle dsbuons ae shown n fgues B and D, especvely Fgue. A wo-dmensonal llusaon of peodc bounday condons. An MD cell conanng aoms s shown n blue. Replcas conanng aom mages ae n whe. Ineacons beween aoms and mage aoms ae ndcaed by he black lnes connecng hem. When an aom moves acoss a bounday on one sde of he box, s mage enes hough he oppose sde... 5 Fgue.: An llusaon of a sngly conneced lnk ls. The sold ccle a he end epesens he null elemen, whch conans no daa and smply emnaes he ls... 6 Fgue.3: Illusaon of lnk-cell neghbo ls scheme: The cene cell n dak blue epesens any sub-cell of he subdvded MD sysem. In hs nsance, neacons beween all aoms n he dak blue cell ae compued along wh neacons wh aoms n neghbong cells ndcaed n lgh blue whn he cu-off ange c. Ineacons wh non-neghbong cells no shaded ae no ncluded n he foce sum fo aoms n he dak blue cell. Ths gealy nceases he effcency of MD compuaons Fgue 3.: D llusaon of sysem augmenaon. Aoms n subsysems on pocessos p lyng whn he cu off ange, n lgh pnk, ae cached and ansfeed o subsysem p n dak pnk fo foce calculaons Fgue 3.: Aom mgaon. Fo aoms o move seamlessly beween subsysems on dffeen pocessos p and p dung a smulaon, paallel pogams ncopoae funcons o delee and nsanae aom daa beween p and p, consevng he numbe of aoms x

13 Fgue 3.3: D depcon of lnked-ls cell decomposon. 48 Fgue 3.4: D lnked-cell ls pocessng schemac Fgue 3.5: Toal execuon ccles and communcaon squaes mes pe MD me sep as a funcon of he numbe of pocessos fo he paallel MD algohm wh scaled wokloads,09,000 P aom slca sysems on P pocessos P,...,,90 of Columba 54 Fgue 4.: Enegy-volume elaon fo cysallne CdSe calculaed by DFT. The sold ccles coespond o he wuze sucue, and he open ccles coespond o he ocksal sucue. Fom hese cuves, he anson pessue s esmaed o be abou.5 GPa, whch s n ageemen wh expemens [50] 58 Fgue 4.: MD smulaon of ansfomaon fom he wuze o he ocksal sucues n CdSe. Each fgue shows aomc confguaon n he ohohombc un cell of CdSe. The magena and blue sphees show he posons of Cd and Se aoms, especvely Fgue 4.3: Mulple ocksal domans fom when a GaAs sphecal nanopacle s subjeced o nceasng pessue Fgue 4.4: Schemac of bondng mechansm fo znc-blende o ocksal ansfomaon. Dung fowad sucual ansfomaon he cenal aom foms wo addonal bonds wh any pa of neghbong aoms enccled by he same colo... 6 Fgue 4.5: CdSe nanood embedded n a Lennad Jones flud, whch seves as a hydosac pessue medum. Each nanood has a hexagonal coss-secon, wh a damee of 44Å as shown above Fgue 4.6: Isomec dsplays of CdSe nanoods ae shown above. All nanoods have 44Å damees wh vayng lenghs a 44Å, b 88Å, c 76Å, and d 58Å. The end faces of each nanood ae nomal o he [000] decon n a WZ cysal lace Fgue 4.7: Fowad ansfomaon schedule. The Lennad-Jones lqud s meled and allowed o each hemodynamc equlbum a 300K dung he nal NVE un. CdSe aoms ae fxed n space o avod defec fomaon on he nanood. The sysem hen undegoes a sequence of compesson and elaxaon uns n andem unl eaches a fnal pessue of 4.0GPa Fgue 4.8: Cylndcal shell-slce analyss. A CdSe nanood s spaally esolved by concenc cylndcal shell-slces. Shells ae numbeed n nceasng ode fom nsde o ousde. Slces ae numbeed n nceasng x

14 ode along he z-axs of he nanood. A shell-slce s an nesecon beween a shell and a slce. Sucual quanes ae calculaed fo aoms n each shellslce sepaaely, allowng sucual dffeences beween dffeen egons whn he nanood o be monoed and compaed dung he phase ansfomaon Fgue 4.9: Spaally esolved sucual analyss of psne wuze sysem a T~0K, P~0GPa NVE. a Cd-Cd pa dsbuon funcon. b Se-Se pa dsbuon funcon. c Cd-Se pa dsbuon funcon. d bond-angle dsbuon. e coodnaon hsogam. The cuves n each plo ae coloed ed, blue, geen, coespondng o he s nne-mos, nd mddle and 3 d ouemos shells, especvely Fgue 4.0: Inal wuze sucue a T300K and P80MPa. Peaks ae boadened by hemal flucuaons alhough.he S : nanood emans n he wuze sucue Fgue 4.: Inemedae 5-coodnaed sae a T300 and P.5-.5GPa. The nanood begns sucual ansfomaon above P.0 GPa. Fve-coodnaed phase, as seen n DFT-MD calculaons Shmojo e al. s also found hee as ndcaed by he peak a 0º n he bond angle dsbuon and by fve-fold aomc coodnaon Fgue 4.: Fnal ock-sal confguaon of S : CdSe nanood a T300K and P4.0GPa Fgue 4.3 Enhalpy as a funcon of aomc confguaon η. The wuze WZ and ocksal RS sucues coespond o η 0 and, especvely. The yellow-open and ed-sold symbols show he enhalpy changes calculaed along he ansfomaon pahs fom WZ o RS-I and fom WZ o RS-II, especvely. The ccles coespond o he pahs lnealy nepolang he aomc coodnaes n he WZ and RS sucues. Fo he lnes shown by angles, he enhalpy of he honeycomb-sacked HS sucue s shown by η Fgue 4.4: Snapshos of he ansfomaon sequence fo he 44Å 44Å CdSe nanood fom MD smulaon. Column a shows he wuze-o-ocksal ansfomaon along [000] and column b he coespondng vew pependcula o he z-decon. Rows -5 show he nanood a dffeen pessues Fgue 4.5: Snapshos of he ansfomaon sequence fo he 44Å 88Å CdSe nanood. The wuze-o-ocksal ansfomaon s shown along he [000] decon Fgue 4.6: Snapshos of he ansfomaon sequence pependcula o he z- x

15 decon fo he 44Å 88Å CdSe nanood. Sde vews of he nanood a dffeen pessues fom 0 GPa o 3.0 GPa ae shown hee Fgue 4.7: Snapshos of he ansfomaon sequence along [000] fo he S :4 nanood... 8 Fgue 4.8: Snapshos of he S :4 nanood show he ansfomaon sequence pependcula o he z-decon a dffeen pessues fom 0GPa o 3.5 GPa Fgue 4.9: Snapshos of he ansfomaon sequence fo he 44Å 58Å CdSe nanood. Fgues a-e show he wuze-o-ocksal ansfomaon along he [000] decon of he nanood as he pessue nceases o.5 GPa Fgue 4.0: Snapshos of he ansfomaon sequence fom he 44Å 58Å CdSe nanood smulaon. These snapshos show he wuze-o-ocksal ansfomaon pependcula o he axs of he nanood as pessue nceases o.5 GPa.. 84 Fgue 4.: Snapshos of he nanood afe sucual ansfomaon n smulaon S :. In a, he op vew of he egula shape of he coss-secon afe ansfomaons compaed wh s ognal hexagonal coss-secon oulned n geen. A sde vew of he nanood, shown n b, llusaes he exen o whch he nanood conacs along he z-axs Fgue 4.: Top and sde vews of he nanood fom smulaon S : ae shown above. The nanood coss-secon becomes egula and s lengh along he z- axs conacs dung sucual ansfomaon. The aoms n he nanoods ae aanged n peodc aays as can be seen fom boh vews, demonsang ha he nanood s a sngle ocksal doman Fgue 4.3: Snapshos fom smulaon S :4. A sngle cysal ocksal doman foms n he mddle of he nanood. The doman exends ou o ~7 aomc layes fom he end sufaces whee dsode begns due o hgh-enegy sufaces Fgue 4.4: Snapshos of he S :4, nanood show ha has become a sngle ock-sal doman afe sucual ansfomaon. a The nanood has one shape along s shaf fom end o end. The end faces eman fla as shown n b Fgue 4.5: Snapshos of he wuze-o-ocksal ansfomaon mechansm. S :, nanood befoe and afe ansfomaon. a Psne WZ nanood a T ~ 0K, P ~ 0GPa b Tansfomed nanood n he RS phase a T 300K and P 4GPa. The elave oenaon beween he nal WZ and fnal RS laces ndcaes WZ o RS-II mechansm xv

16 Fgue 5.: Ble maeal subjeced o a sess σ. b The sess causes cacks n he sample o gow o popagae. The sample suffes cleavage dung cack popagaon as planes of aoms ae peeled apa by cack. c Ble facue esuls sufaces Fgue 5.: A sample of ducle maeal unde a ensle sess σ, b exhbs neckng dung whch he coss-secon naows n one secon of he nanood. c Neckng connues unde he nfluence of he appled sess unl he nanood facues coss-secon of he sample naows as long as he sess s appled unl dsconnecs no moe han one pece Fgue 5.3: Snapshos of CdSe nanood coss-secons fom smulaons a S :, b S :, c S :4, d S : afe sucual ansfomaon o a ocksal phase. The coss-secons of he nanoods change fom hexagonal o egula shapes, whle he end faces eman aomcally fla n he peodc wuze sucue Fgue 5.4: Smulaon schedule fo he evese ansfomaon Fgue 5.5: Fnal esul of 44Å 44Å evese ansfomaon, S U-:a. a Snapsho of he nanood a 80MPa and ~40,000 afe fowad ansfomaon. b bond-angle dsbuon, and c hsogam of aomc coodnaons Fgue 5.6: Fnal esul of he 44Å 44Å evese ansfomaon, S U-:b. The empeaue was scaled o say below 900K. The hexagonal coss-secon of he nanood becomes ecangula. The nanood s nealy cubc. a Snapsho of he nanood a 80 MPa and 500,000 afe fowad ansfomaon, b bondangle dsbuon and c hsogam of aomc coodnaon Fgue 5.7: Fnal esuls of he 44Å 88Å evese ansfomaon. a Snapsho of he nanood a 80MPa aken 500,000 afe fowad ansfomaon. b Bond-angle dsbuon and c dsbuon of aomc coodnaons Fgue 5.8: Fnal esuls fo he evese ansfomaon n he 44Å 76Å nanood. a Snapsho of he nanood aken 500,000 afe fowad ansfomaon a 80MPa. b Bond-angle dsbuon and c hsogam of aomc coodnaons Fgue 5.9: Thee oucomes of he upsoke smulaon fo he S U:, 44Å 58Å nanood. The up-soke smulaon begns wh he fnal RS cysal confguaons fom he pecedng down-soke smulaon. Expemens wh dffeen empeaue-pessue schedules esuled n cysallogaphc ansfomaon of he nanood as well as mophologcal ansfomaons ncludng knkng and facung xv

17 Fgue 5.0: The sequence of mages show neckng a seveal places along he shaf of he 44Å 58Å nanood unl dsconnecs no wo peces. a Shows he confguaon a he end of he fowad ansfomaon a 4GPa and 300K. b Shows he nanood lae afe some amoun of decompesson a a empeaue of ~ 600K and a pessue of MPa. c The nanood begns o show noceable neckng along he shaf. The neckng becomes moe ponounced d unl complee sepaaon akes place e... 0 Fgue 5.: A pouson pependcula o he axs of he nanood esuls dung he upsoke afe he nanood empeaue nceases and s hen cooled down. 0 Fgue 5.: The nanood knks a neckng pons afe coolng dung evese ansfomaon Fgue 5.3: Fnal esul fo he evese ansfomaon n S U-: 44Å 58Å nanood.. a Bond-angle dsbuon shows mulple peaks aound 90, 09 and 80. The nanood conans boh ocksal and wuze cysal phases. b The hsogam of aomc coodnaon shows amajoy of 4-coodnaed aoms, whch s an ndcaon of he compleeness of he evese ansfomaon Fgue 5.4: Fnal esuls fo he evese ansfomaon n he 44Å 58Å nanood. a Shell-esolved bond dsbuons show dffeen cysal phases n dffeen shells. The nne-mos shell, n ed, ndcaes mxed phases. The blue cuve peaks a 09, whch s chaacesc of wuze and znc-blende cysal sucues. The oue shell epesened n geen shows a domnan peak a 90, ndcang mosly he ocksal phase mxed wh he wuze phase. b Shows shows 4-coodnaed aoms pedomnang n he aomc coodnaon hsogam Fgue 5.5: Peaks a 90 and 80 dsappea fom all he cuves when he aoms a he ends of he nanood ae excluded fom shell-esolved bond-angle calculaons. Peak a 09.4 n all shells ndcaes complee evese ansfomaon o wuze begns n he mddle of he nanood and speads owads he ends Fgue 5.6: Snapshos of evese ansfomaon of 44Å 58Å CdSe nanood slced a dffeen coss-secons fom end o end afe 5,80. 4, 5, 6- coodnaed aoms ae coloed ed, blue and geen, especvely. 0-3 coodnaed aoms ae n gay. The coss-secon s vually all ed along he ene coe of he nanood xv

18 ABSTRACT Paallel molecula dynamcs MD smulaons ae pefomed o nvesgae pessue-nduced sold-o-sold sucual phase ansfomaons n cadmum selende CdSe nanoods. The effecs of he sze and shape of nanoods on dffeen aspecs of sucual phase ansfomaons ae suded. Smulaons ae based on neaomc poenals valdaed exensvely by expemens. Smulaons ange fom 0 5 o 0 6 aoms. These smulaons ae enabled by hghly scalable algohms execued on massvely paallel Beowulf compung achecues. Pessue-nduced sucual ansfomaons ae suded usng a hydosac pessue medum smulaed by aoms neacng va Lennad-Jones poenal. Fou sngle-cysal CdSe nanoods, each 44Å n damee bu vayng n lengh, n he ange beween 44Å and 600 Å, ae suded ndependenly n wo ses of smulaons. The fs smulaon s he downsoke smulaon, whee each od s embedded n he pessue medum and subjeced o nceasng pessue dung whch undegoes a fowad ansfomaon fom a 4-fold coodnaed wuze WZ cysal sucue o a 6-fold coodnaed ocksal RS cysal sucue. In he second so-called upsoke smulaon, he pessue on he ods s deceased and a evese ansfomaon fom 6-fold RS o a 4- fold coodnaed phase s obseved. The ansfomaon pessue n he fowad ansfomaon depends on he nanood sze, wh longe ods ansfomng a lowe pessues close o he bulk ansfomaon pessue. Spaally-esolved sucual analyses, ncludng padsbuons, aomc-coodnaons and bond-angle dsbuons, ndcae nucleaon begns a he suface of nanoods and speads nwad. The ansfomaon esuls n a xv

19 sngle RS doman, n ageemen wh expemens. The mcoscopc mechansm fo ansfomaon s obseved o be he same as fo bulk CdSe. A nanood sze dependency s also found n evese sucual ansfomaons, wh longe nanoods ansfomng moe eadly han smalle ones. Nucleaon naes a he cene of he od and gows ouwad. xv

20 CHAPTER INTRODUCTION Inoganc semconducos ae he foundaon of moden eleconcs. Snce he md-950 s, semconducos have been esponsble fo a gea numbe of advances n vaous echnologes ncludng communcaons, compue hadwae and he medcal devce ndusy. They ae used n a wde vaey of applcaons among hem wase eamen, a pufcaon, an-mcobal sufaces, chemcal and bologcal deconamnaon and sola enegy conveson. Conducve popees of semconducos make hem useful fo a wde vaey of echnologcal applcaons. Semconducos have specal eleccal conducvy popees due o he enegy band gap wdh, whch s ypcally less han 3.5 ev. Compaed o nsulaos, wh enegy band gaps geneally geae han 5 ev, semconduco enegy band gaps ae small enough fo elecons o be exced no he conducon band by hemal, phoonc o ohe excaons. Inoducng dopans o mpues can also ale he enegy band gap of semconducos and affec he conducvy by odes of magnude. Due o hs ably o manpulae he conducvy of semconducos, hey ae well sued fo he conol of key funcons of many eleconc componens ncludng anssos, dodes, pezoelecc cysal devces and negaed ccus. Semconducos ae sold sae maeals found n goups II hough VII of he peodc able. Semconducos composed of elemens fom he same goups end o have smla chemcal, eleccal and sucual popees; whch ae ofen suded n elaed expemens and employed n smla applcaons. Fo example, S and Ge, goup IV sngle elemen semconducos, ae he mos commonly used maeals n dodes and

21 negaed ccus. Ths makes hem cucal o he eleconcs ndusy. Goup III-V semconducos, lke GaN, have lage and dec enegy-band gaps, whch make hem suable fo blue lases. They ae also sable a hgh empeaues and have good hemal conducves, whch make hem useful n hgh powe anssos. Goup II-VI semconducos ae found n znc-blende o hexagonal wuze cysal sucues a 300 K and have band gaps angng fom.4ev o 3.9eV. As hese eneges coespond o wavelenghs whn he vsble lgh ange of he elecomagnec specum, hey have applcaons n bologcal labelng, opoeleconc sensos and phoovolac devces lke sola cells. Some examples of II-VI semconducos commonly suded nclude ZnO, ZnS, ZnSe, ZnTe, CdS, CdSe, CdTe, HgS, HgSe, and HgTe. Ths nvesgaon concens sucual and mechancal popees of CdSe. I has been shown by ha he eleccal and opcal popees of semconducos depend on he sucual popees as well as sysem sze. Alvsaos e al. have pefomed exensve sudes on he synhess of semconducng nanocysals [], he opcal and eleccal popees [], how hese popees change wh pessue-nduced sucual ansons [3] and he sucual sably [4]. The wok ncludes quanumdo assembles gown on subsaes. They have gown nanocysals of vaous shapes n collodal lqud soluons. Recenly, hey have conduced expemens on pessue nduced sucual ansfomaons and facue. Small sphecal CdSe nanopacles, 45Å n damee, wee obseved o undego evesble, fs-ode phase ansfomaon, beween 4-coodnaed and 6-coodnaed saes unde pessue. The daa ndcaes he ansfomaon naes fom a sngle nucleaon even and esuls n a sngle doman. Lage nanocysals ae expeced o exhb dssmla chaacescs appoachng hose

22 of exended solds evesble sucual change, mulple nucleaon ses and domans, and bulk facue behavo. In he pas decade, quanum do assembles have been suded expemenally by a gowng numbe of nvesgaos. Typcal quanum do assembles ae -dmensonal aays of nano-szed slands of semconducng maeals gown on a subsae. The specal cae confnemen popees enable unable phoo-emsson and hey em lgh a fequences ha can be conolled by adjusng do sze. Ths has poenal applcaons n boacve fluoescen pobes n sensng, magng, mmunoassay, and ohe dagnoscs applcaons. Bawend and co-wokes have epoed a numbe of hese sudes nvolvng CdSe and ZnS [5, 6]. Collodal chemsy synhess s one mehod by whch CdSe nanoods can be poduced whou beng embedded n subsaes and hus has expanded he ange of applcaons. In hs mehod pecusos ae dssolved n ho sufacans whee hey coalesce o fom cysals. Lgand molecules ae used o conol gowh aes of cysals and he fnal sze of he cysal. Aspec ao s conolled by sufacan ao. Rapd coolng of he sufacan emnaes he cysal gowh pocess. The cysals eman suspended n he mxue. Alvsaos and co-wokes have suded dsbuons of hgh-aspec ao nanoods o examne mulple doman chaacescs and evesble sucual ansfomaon. X- ay dffacon paen analyss eveals ha mul-doman behavo nceases wh he aspec ao lengh-o-wdh of nanoods. They sough a ccal lengh scale govenng facue behavo and poposed a mechansm by whch facue mgh occu n CdSe nanood ensembles. Obsevaons of changes n dffacon lne wdhs dung pessue 3

23 cyclng appea o suppo he poposed mechansms of ansfomaon. Dffacon peak wdhs ae nvesely popoonal o cysalle sze. Lne wdhs fo small nanocysals eman he same hough an ndefne numbe of cycles. Lne wdhs of nanocysals wh hghe aspec aos boaden as expeced afe he fs pessue cycle and hen eman consan fo subsequen cycles, ndcang ha longe nanoods no smalle ones. CdSe nanoods have been shown o undego mulple facues dung phase ansfomaon unde compesson. Evdence of longe nanoods facung no shoe ones unde compesson can be seen n he ansmsson elecon mcoscopy mages shown n Fgue.. Fgue. shows ha he aveage lengh of he nanocysals afe compesson s less han half he nal lengh, ndcang ha he nanoods end o facue no moe han wo peces. A B Fgue. Tansmsson elecon mcogaph of epesenave CdSe nanoods n he 4- coodnae phase befoe A and afe one B pessue cycle. A mescale fo phase ansfomaons s esmaed fom knecs of ansfomaons unde abup pessue changes. Ensembles of CdSe nanoods wee demonsaed o ansfom on he ode of seconds o hous n Alvsaos expemen. 4

24 Howeve, s hough ha he me equed fo an ndvdual nanocysal whn an ensemble o sucually ansfom could ypcally be on he ode of pcoseconds. Fgue. Lengh dsbuon of he pacles befoe blue and afe ed pessue cyclng. The mechansm of ansfomaon s beleved o be an even whee he planes slde sequenally n a decon pependcula o he shaf of he od. I s hough ha hs pogesses unfomly houghou he nanocysal fom he slaned shapes of he ods ha esul afe sldng of planes. The CdSe ods suded n hese expemens have zncblende o fauled wuze cysal sucues. I would be neesng o see f hs mechansm also occus n mono-cysallne wuze CdSe ods. Tunng o compue smulaon, advances ove he yeas n algohms and compung hadwae have led o he developmen of a poweful ool. Smulaon s now a well-esablshed mode of eseach; an nemedae beween heoy and expemen ha povdes pespecves naccessble o boh. Smulaon can be appled owads a wde ange of sysems: mechancal devces, ecologcal poblems, meeoologcal sudes, economcs, conol and opeaon eseach 5

25 pocesses, flud flow, and obocs. Specal algohms have allowed smulaons o keep pace wh acceleang advances n hadwae as envsoned by Godon Mooe, havng a synegsc effec on he developmen of hgh-pefomance compung. Sysem szes of aomsc smulaons have also gown a an mpessve ae. By 00, s expeced ha lage-scale compues wll pefom smulaons whn he peaflop egme, nvolvng moe han 0 bllon aoms, and allowng aomsc analyss of physcal sysem whch exceedng cubc mcon n sze. Godon Mooe obseved n 965 ha he numbe of anssos pe squae aea on negaed ccus had doubled evey yea snce he negaed ccu was nvened. Mooe pedced ha negaed ccu complexy would connue o ncease a hs ae ove he yeas leadng no he s cenuy. Snce hen, compue memoy and mcopocesso echnology have geneally followed hs pojecon as daa densy and pocesso speeds have doubled appoxmaely evey 8 monhs. Ths end, now commonly known as Mooe s law, s expeced by mos expes o hold fo a leas anohe wo decades. Fgue.3 chas how aanable sysem szes fo smulaons have gown wh he ongong developmens n algohm and hadwae desgn snce he me of Mooe s pedcon. A numbe of he goups n he compuaonal scence ae followng hs compung evoluon fom eaflops 0 flops o peaflops 0 5 flops. Usng hs unpecedened compung powe, hese goups wll be able o cay ou ealsc smulaons of complex sysems and pocesses n he aeas of maeals, nanoechnology, and boengneeed sysems. Coupled wh mmesve and neacve vsualzaon, hs 6

26 wll offe unpecedened oppounes fo eseach as well as mpovng gaduae and undegaduae educaon n scence and engneeng dscplnes. Fgue.3 Smulaed sysem szes n he famewok of densy funconal heoy DFT and molecula dynamcs MD have kep pace wh Mooe s Law due o advances n algohms and hadwae. Recen compue smulaon sudes have conbued sgnfcanly o ou undesandng of nanosysems n he case of semconducng nanopacles. Numecal expemens have paalleled expemenal wok n he exploaon of CdSe semconducng nanopacles. Molecula Dynamcs MD and Densy Funconal Theoy DFT calculaons have been pefomed o nvesgae sucual phase ansfomaon unde pessue. Calculaons based on DFT by Shmojo and ohes [7], eveal ha seveal possble ansfomaon pahs beween CdSe s chaacesc wuze phase and hgh-pessue ocksal phase. Howeve, DFT sysem szes ae ypcally lmed o only a few hunded aoms. Fne-sze effecs may esul n dffeen mechancal behavo n bulk han n such small sysems. MD smulaons of sucual ansfomaons n CdSe nanofoms, such as he ods we pesen n hs wok may ncease undesandng of physcal popees of CdSe fo lage sysem szes. 7

27 MD smulaons make possble o sudy nanocysals unde deal condons and o compae hem wh expemenal sysems, whch may have defecs. Ths can help n solang compeng facos conbung o a cean phenomenon. Fo example, mcodefecs affec facue n nanomaeals, and hese can be pecsely specfed and esed by MD smulaons. Ths level of conol ove mco-defecs does no exs n expemen. Convenonal MD smulaons ae pefomed n he mcocanoncal ensemble whee he numbe of aoms he oal volume and enegy of he sysem ae held consan. Howeve, many acual expemens nvolve he sudy of physcal sysems unde consan pessue and/o empeaue, whee ehe volume o oal nenal enegy flucuaes. These ensembles eque exenson of convenonal MD mehod o he canoncal NVT o sobac-sohemal ensemble NPT. A numbe of mehods fo NVT MD have been poposed hough he yeas begnnng n he ealy 980 s when Andesen poposed a sochasc pocedue o sample andom veloces fom a Maxwell-Bolzmann dsbuon and assgnng hem o pacles based on a specfed pacle collson ae [8]. Howeve, lmaons n hs mehod wee found when Tanaka e al. appled Andeson s mehod o wae and Lennad- Jones sysems [9]. An undesable couplng beween he sysem s empeaue and s dffuson coeffcen was found o exs above a cean sochasc collson pobably heshold. Hoove noduced a mehod consanng a sysem s knec enegy hough a velocy dependen em n he poenal [0]. Alhough he mehod geneaes a canoncal ensemble, mposes an unphyscal suppesson of knec enegy flucuaons. In 983, Nosé who unfounaely passed away ecenly a age 54 poposed a molecula dynamcs mehod fo smulaons n he canoncal ensemble []. I manans 8

28 consan empeaue n he sysem by noducng an addonal vaable, s, gvng an N- aom sysem 3N+ degees of feedom. The vaable s couples o he knec enegy of he sysem and hus lnks he physcal sysem o a hea bah, wh whch enegy can be exchanged o egulae empeaue. Nosé s mehod does no suffe fom he lmaons of he NVT mehods pevously descbed. Hs mehod s puely dynamcal, nvolvng deemnsc, evesble equaons of moon as opposed o sochasc mehods and geneaes aveaged physcal quanes belongng o he canoncal ensemble. In he lae 970 s, Andeson pesened a consan enhalpy and consan pessue NPH MD echnque []. Hs mehod nvolves an MD cell havng vaable volume deemned by a balance beween he nenal pessue of he sysem and he exenal pessue. The mehod conseves enhalpy and manans consan pessue. Panello and Rahman lae exended hs mehod o ncopoae a paallelepped MD cell, capable of changng shape and volume n me [3]. Ths mehod manans consan sess σ. Thee me-dependen vecos a,b, and c defne he edges of he MD cell and he numbe of degees of feedom of an N-aom sysem ncease fom 3N o 3N + 9. Panello-Rahman fomulaon leads o a modfed Lagangan whee he aomc veloces n he knec enegy ae ansfomed n elaon o he vayng MD cell dmensons. Two addonal ems also appea n he Lagangan; one s a knec-enegy-lke em whch aken no accoun he knec enegy of he MD cell, and he ohe s, assocaed wh he elasc enegy of he MD cell due o he exenal sess on he sysem. Ths exended MD mehod allows he sudy of sold-o-sold sucual ansfomaons and ohe consan pessue calculaons. 9

29 Nosé s mehod fo NVT smulaon can be combned wh he HPN smulaon o geneae NPT ensembles. The NVT and NPT MD smulaons fo hs hess ae mplemenaons of he mehods poposed by Nosé and Panello-Rahman. These mehods wll be fuhe descbed n Chape. MD expemens have been used o smulae pessue-nduced sucual ansfomaons n GaAs semconduco nanocysals o chaaceze defomaon and gan fomaons [4]. These sudes wee movaed and guded by eale ab no smulaons n bulk SC and GaAs whee new sucual ansfomaon mechansms wee denfed [5][6]. The nal confguaon of he smulaon, shown n Fgue.4, conssed of a 30 Å-adus sngle cysal nanopacle of ~5000 GaAs aoms, posoned a he cene of a 3 Å cubc MD cell suounded by a dsbuon of ~500,000 aoms epesenng a flud medum. The flud medum was smulaed by a dsbuon of aoms neacng va Lennad-Jones poenal, and povded a means o apply hydosac pessue o he nanopacle. The aoms of he GaAs nanopacle neaced hough a poenal developed by Vashsha e al. Fgue.4 Inal smulaon seup fo a GaAs sphecal nanopacle suounded by a dsbuon of aoms neacng va Lennad-Jones poenal. 0

30 Inally, he sysem was allowed o each hemal equlbum a.5 GPa. Pessue n he sysem was hen nceased n ncemens of 0.5 GPa pe 0000 me-seps unl he sysem pessue eached.5 GPa. The onse of sucual ansfomaon of he nanopacle fom 4-coodnaed, znc-blende, o 6-coodnaed, ocksal, was obseved a pessues appoachng 6. GPa. The oal ansfomaon occued a a pessue of.5 GPa. A shell-esolved analyss of he nanopacle dung sucual ansfomaon showed nucleaon a he suface of he nanopacle speads nwad o he cene of he nanopacle. Fgues.5 A and C show confguaons of he GaAs nanopacle a 7.5 GPa and.5 GPa, jus befoe ansfomaon. All shells ae concenc abou he geomec cene of he nanopacle and numbeed fom nnemos o ouemos as ndcaed by he yellow ccles. Plos of coespondng bond-angle dsbuons fo each shell ae dsplayed n Fgues.5 B and D. In Fgue.5 B, cuve, he ed peak ceneed abou 09.4º ndcaes ha he coe of he nanopacle emans n he chaacesc znc-blende cysal fom a 7.5 GPa whle he suoundng shells bond angle dsbuon, ndcaed n geen, shows a shf owads 90º. The ouemos shell conans 6-coodnaed aoms n he ocksal sucue, as ndcaed by he blue cuve wh peaks a 90º and 80º. Fgue.5 D shows ponounced peaks a 90º and 80º n all hee cuves, ndcang a complee sucual ansfomaon fom 4-coodnaed znc-blende o 6-coodnaed ocksal sucue. The fnal confguaon of he GaAs nanopacle eflecs he ocksal phase wh mulple domans havng dffeen oenaons. Ths s an ndcaon of mulple nucleaons. Howeve, expemens show ha mulple nucleaon

31 evens ae ae n small nanopacles because hey ae mosly found as sngle cysals. Ths aspec of sucual ansfomaon wll be dscussed fuhe n Chape 4. Eleconc sucue calculaons based on DFT wee pefomed on bulk CdSe sysems by Shmojo e al. Isohemal-sobac MD calculaons wee caed ou on bulk CdSe o denfy ansfomaon pahs. In he nal seup, he empeaue of he sysem was 300 K and he pessue 0.5 GPa. The pessue of he sysem was hen nceased n ncemens of GPa pe 000 me seps me sep fs. Nex, he sysem was allowed o elax fo 5000 me seps. Ths sequence of pessue ampng and elaxaon was epeaed unl he pessue on he sysem eached 6 GPa. Enegy vs. volume elaons fo he bulk CdSe n wuze and ocksal phases wee obaned fom he DFT calculaons. The anson was obseved a.5 GPa. DFT calculaons showed wo Fm3m cysallogaphc, ocksal sucues as beng enegecally favoable a.5 GPa. The wo ocksal sucues RS-I and RS-II, ae eached fom dffeen and have dffeen cysal oenaons. A measable fve coodnaed sae, P6 3 /mmc cysallogaphc sucue, was also obseved beween he 4-fold and 6-fold coodnaed saes. These esuls and sucual ansfomaons n CdSe sphees and od-shaped nanopacles wll be dscussed n deph n Chape 4 and compaed wh ab-no calculaons. The oulne of he emanng poon of hs dsseaon s as follows. Chape conans fuhe descpons of exended molecula dynamcs mehods and mplemenaons of molecula dynamcs on paallel compung sysems ae pesened n Chape 3. Resuls of smulaons and compasons wh expemens on pessuenduced sucual ansfomaons n CdSe nanopacles wll be dscussed n Chape 4.

32 Chape 5 wll focus on hgh-aspec-ao CdSe nanoods and nclude addonal descpons of muldoman fomaon and facue. Conclusons ae pesened n Chape 6. A B C D Fgue.5 Molecula dynamcs confguaons of GaAs nanopacles a pessues of A 7.5 GPa and C.5 GPa. Coespondng sphecal shell-esolved bond angle dsbuons ae shown n fgues B and D, especvely. 3

33 CHAPTER MOLECULAR DYNAMICS METHODOLOGIES In hs chape we dscuss molecula dynamcs MD mehodology n vaous ensembles and numecal calculaons of sucual, hemomechancal and dynamcal quanes.. Backgound Molecula dynamcs MD nvolves numecal soluon of Newon s equaon fo a sysem of aoms neacng va a specfc neaomc poenal. whee V s he neaomc poenal, m & F V. s he poson of aom, and F s he foce exeed on aom by ohe aoms, and & d. d The sysem of 3N second-ode odnay dffeenal equaons can be solved numecally usng fne-dffeence mehods. Gven an nal se of posons and momena { 0, p 0} fo all he pacles, he equaons of moon ae dscezed usng a small me sep,, and popagaed fowad n me {, p } { +, p + }. Ths wll be dscussed n moe deal n secon..3. The aveage DeBogle wavelengh, λ, fo a sysem n equlbum a a empeaue T s gven as. Le a be he aveage dsance beween wo aoms n a sysem. The λ h / mk T B classcal appoxmaon holds wheneve a>>λ. Thus wheneve he aveage spacng beween aoms s geae han he DeBogle wavelengh, quanum mechancal effecs, alhough eve pesen n he sysem, ae nsgnfcan and can be gnoed. A 300K, λ 0.5Å. A he hghes numbe densy eached n ou smulaons s 0.6 /Å 3 a whch a 3 Å. 4

34 In addon o nal condons, s also necessay o specfy appopae bounday condons PBC. Fo example, fo bulk sysems peodc boundaes ae appled by eplcang he MD cell wh all s aoms n all decons. The posons and veloces of he aoms n he eplcaed sysems ae dencal o hose n he ognal MD cell. An aom neacs wh ohe aoms nsde he MD cell and wh he mages of aoms n he eplcaed sysems whn he cu-off ange of he poenal. Ths s known as he mnmum mage convenon. If an aom leaves he MD cell, s mage enes he cell fom he oppose face. Fgue. s an llusaon of peodc bounday condons appled o a wo-dmensonal sysem. PBC mnmzes suface effecs n a well-defned manne. Howeve, hee ae caveas n usng PBC. Popees ha depend on long-wavelengh conbuons, e.g. he sac sucue faco fo small wave vecos, ae lmed by he sze of he MD cell and affec compason wh expemens. Fgue. A wo-dmensonal llusaon of peodc bounday condons. An MD cell conanng aoms s shown n blue. Replcas conanng aom mages ae n whe. Ineacons beween aoms and mage aoms ae ndcaed by he black lnes connecng hem. When an aom moves acoss a bounday on one sde of he box, s mage enes hough he oppose sde. Inal condons ae assgned o posons, and momena, p, of pacles. Inal aomc posons depend on he ype of sysem, s cuen sae and he objecve of 5

35 he smulaon o un. Usually, fo cysallne sysems, he aoms ae placed a he equlbum lace posons and assgned andom veloces chosen fom a Gaussan dsbuon. The numbe of aoms and he sze of he MD cell ae chosen o have he coec densy. An amophous sysem s pepaed by melng a cysallne sysem and quenchng he molen sae. Aomc foces and poenal enegy can be calculaed effcenly usng he lnkedls mehod. A lnked ls s a daa sucue made up of an unboken chan of elemens, whee each elemen consss of wo pas one pa conanng daa and he ohe a efeence, o lnk, o anohe elemen n he sucue as shown below. Fgue.: An llusaon of a sngly conneced lnk ls. The sold ccle a he end epesens he null elemen, whch conans no daa and smply emnaes he ls. The lnked-ls explos he dea ha foces beween aoms beyond a cean cuoff adus, c, ae neglgble. In calculang he foce on a pacula aom, excludng aoms beyond a cean cu-off adus, c, sgnfcanly educes he amoun of compung me whle mananng a easonable appoxmaon fo he oal foce. In he mplemenaon of he lnked-cell ls scheme, all aoms n he MD cell ae spaally sub-dvded no smalle cells. A lnked-cell ls s oganzed fo each cell o conan all daa peanng o each aom whn ha cell. Foce calculaons ae pefomed fo each aom,, wh all s neghbong aoms, j, n he same lnked-cell ls. Foce calculaons ae also pefomed beween aoms acoss adjacen and dagonal cells whn he cu-off ange c. Snce aoms may move beween cells, lnked-cell-neghbo lss mus be econsuced each me aomc coodnaes ae updaed. 6

36 c Fgue.3: Illusaon of lnk-cell neghbo ls scheme: The cene cell n dak blue epesens any sub-cell of he subdvded MD sysem. In hs nsance, neacons beween all aoms n he dak blue cell ae compued along wh neacons wh aoms n neghbong cells ndcaed n lgh blue whn he cu-off ange c. Ineacons wh non-neghbong cells no shaded ae no ncluded n he foce sum fo aoms n he dak blue cell. Ths gealy nceases he effcency of MD compuaons. A bue-foce algohm, one ha would compue he sum of foces on all possble pa combnaons of aoms n he MD cell, would have a compuaonal complexy of ON, whee N s he numbe of pacles. Lnked-cell-neghbo lss educes hs complexy o ON. The advanage of lnked-cell ls ove bue foce compung nceases wh he sze of he sysem... Ineaomc Poenals The neaomc poenal funcon s he mos essenal npu o any MD smulaon, snce deemnes he ealsm of a smulaon. Ove he yeas, a numbe of poenals have been developed fo vaous maeals ncludng he embedded aom 7

37 poenal [7], he shell model [8], bond-ode poenals, ec. [9]. The neaomc poenal s usually aken o be a sum of one-body, wo-body, hee-body conbuons. V,..., 3 N V + V, j + V, j, k < j j< k The fs em epesens neacons of pacles wh an exenal feld. The second em s a -body poenal, whch ncopoaes he neacon beween aomc pas. Typcal -body poenals ae he Lennad-Jones LJ neacon fo sysems of ne gas aoms o he Coulomb poenal fo sysems conanng chaged pacles. The LJ neacon was used n ou smulaons o epesen a lqud hydosac pessue medum. The funconal fom of he LJ poenal s, 6 σ σ V j 4ε j j Hee, ε, s he poenal well deph and σ s he lengh paamee of he poenal. Thee-body ems ae mpoan fo semconducos. The Sllnge-Webe poenal s an example of a 3-body poenal and has he geneal fom: V jk cosθ cosθ 3 j, k,cosθ jk B jk fj j fk k jk jk.3.4 whee f s a decayng funcon wh a cuoff beween he fs- and he second-neghbo shells andθ jk s he angle beween he j and k bonds, j k cos θ jk.5 jk The basc dea of Sllnge-Webe poenal s ha mposes a penaly funcon so ha he angles ae close o he pescbed value θ jk whch eflecs he sucue of he sysem. Fo example, n a eahedally coodnaed sysem, he angle θ jk whn each 8

38 eahendon s 09.4º. Devaons fom hs angle ase he enegy of he sysem. B jk s he sengh of he neacon. 4-body ems have been used n smulaons of polyme chans n SAMs [0] and some meallc sysems [see he wok by Moay a Lvemoe]. Mul-pacle poenals hghe han fou bodes ae no common. Thee ae also neaomc poenals n whch cean paamees vay dependng on he local envonmen of an aom. An example of hese poenals s he so-called bond-ode poenals. The Tesoff poenal s one such poenal, geneally expessed as: V [ VR j bjva j ], j V s an aacve em asng fom he bondng of valance elecons and A j.6 V R j s a epulsve em ha akes no accoun sec effecs. One feaue found n meals and sem-conducos s ha cohesve enegy deceases wh coodnaon. The paamee b j capues hs feaue, as deceases wh nceasng aomc coodnaon. Bond-ode poenals wok well fo a vaey of maeals. Howeve, he dawbacks ae ha such poenals ae sho anged and do no ncopoae chage ansfe whch escs he ange of applcaon o maeals wh covalen bondng. Recenly, Goddad and co-wokes have ncopoaed chage-ansfe effecs n bond-ode poenals. The poenal used n ou MD smulaons of CdSe was developed by Vashsha e al. I consss of wo-body and hee-body neacons and has he followng funconal fom: whee 3 V,..., V,, + V,,.7 N < j j j< k j k 9

39 and V V j η j j / j 4 j / j s j 4 s j 3 jk H B jk e + Z 0 Z j γ γ + j H j k j 0 e + D cosθ jk + Ccosθ e cosθ jk W + jk cosθ Dj α Z j + α j Z Two-body ems epesen sec epulson, sceened Coulomb, chage-dpole, and j 6 j jk.8.9 ηj A σ + σ.0 j j van de Waals neacons. The hee-body ems epesen bond bendng and sechng. The paamees n hs poenal wee fed o epoduce expemenal values fo CdSe, ncludng lace consan, cohesve enegy, and elasc consans fo he cysallne phase. The poenal gves a good descpon of melng empeaue, facue enegy, and phonon densy of saes. The poenal also gves good ageemen wh expemenal X-ay sac sucue faco of amophous CsSe. Addonally, a hgh-pessue phase anson fom wuze 4-fold coodnaon o ocksal 6-fold coodnaon s also coecly descbed. The values fo he poenal paamees used ae gven n Table.. Table.. Paamees fo Cd-Se Ineacon Paamee Value A Cd-Cd A Se-Se A Cd-Se σ Cd σ Se J J J. Å.54 Å η Cd-Cd 7 η Se-Se 7 η Cd-Se 9 Z Cd.0438 e able connued 0

40 Z Se e α Cd 0.0 Å 3 α Se 5.0 Å 3 W Cd-Cd 0.0 J Å 6 W Se-Se 0.0 J Å 6 W Cd-Se J Å Å 4.5 Å B jk J γ.0 Å Å θ jk.. Foce Calculaons The mos compue-nensve pa of a molecula dynamcs smulaon s he calculaon of aomc foces, poenal enegy, aomc-level sesses, ec. Bue foce calculaon of pawse neacons beween N nvolves ON opeaons. Ths compuaonal complexy can be educed o ON fo sho anged foces usng lnkedcell ls echnques whch wll be dscussed lae n Chape 3. Fo long-anged foces he fas mulpole mehod by Geengad and Rokhln [] can educe he complexy o ON...3 Inegaon Algohms The Gea pedco-coeco algohm s one of he ealy fne dffeence mehods used o fnd soluons o odnay dffeenal equaons. Ths mehod was and sll s commonly used o solve he equaons of moon n MD. The basc dea can be descbed n 3 seps.. Pedco-sep: Taylo expansons of posons and he me devaves up o a desed ode ae calculaed o oban appoxmae values fo poson, velocy and acceleaon, ec.

41 /... 6 / / 3 q p q p q p q p O b b O b a a O b a v v O b a v Foce evaluaon- Aomc foces and acceleaons ae calculaed fom he gadens of he poenal enegy. Snce he acual acceleaon s dffeen fom pedced values n sep, he eo mus be coeced. Ths s done n he coec-sep. a a a p c Coeco-sep- Pedcaed values of acceleaons ae calculaed as follows: 3 0 a c b b a c a a a c v v a c p c p c p c p c The values of coeffcens c 0, c, c, and c 3 depend on he ode of he dffeenal equaon beng solved. These coeffcens have been abulaed by Gea fo vaous dffeenal equaons [,3]. The Gea pedco-coeco algohm can be un mulple mes o acheve bee accuacy. Howeve, one should be mndful ha he coeco sep eques foce calculaons, whch ae compuaonally expensve. So one should gauge how much eaon s necessay a each me sep. The mos commonly used negaon algohm n MD s he Vele algohm, whch s expessed as: 4 O a I s obaned by addng.

42 6 / / 6 / / O b a v O b a v The Vele fomulaon s sable and elavely easy o mplemen. As can be seen, he uncaon eo s 4 h ode. Veloces can be calculaed fom he posons, v +..6 One of he mos sable algohms s a vaan of he Vele algohm and s called he velocy-vele algohm. Hee, 3 O a v Fom he posons a me, he foces and acceleaons ae compued a. Subsequenly, he velocy a me s calculaed fom, a v v V m a The velocy-vele algohm s used n all he smulaons epoed hee. The algohm conseves he oal enegy vey well n he mcocanoncal algohm. A me negaon algohm should conseve he phase-space volume. Velocy- Vele algohm peseves phase space and s me-evesble [4]. Tuckeman e al. have demonsaed me evesbly and phase-space volume consevaon fom he Louvlle fomulaon of classcal mechancs. The Louvlle opeao s defned as: + p f q v L.9 3

43 whee f s he foce acng on he h pacle. Le Γ q, p } epesen he nsananeous { L sae of he sysem n he phase space. The classcal popagao s hen U e. Then he sae of he sysem, Γ, can be popagaed as follows: L Γ e Γ0 U Γ0.0 [Noe: U s a unay opeao,.e. me evesble: U U ]. The Louvlle opeao can be spl no wo pas. whee L L + L. L q L f& &,. q p U e L e L L L e e + O We can oban he sae of he sysem, Γ, a a me by applyng he U as 3.3 v q f p v p U U U U e e e.4 The sysem s popagaed o a sae Γ n by successvely applyng he opeao U n mes. Opeang wh hs facozaon on Γ q 0, p 0} and usng he deny, { e x f x f x +, fo he posons and veloces a me ae obaned as.5 q q 0 + p 0 + p & 0.6 m m [ p & 0 + p & ] p p whch ae dencal o he equaons of he velocy-vele algohm. 4

44 . Sascal Ensembles Sascal mechancs s he bass of MD mehodology. In sascal mechancs, macoscopc o hemodynamc quanes ae calculaed fom ensemble aveages ove all possble hemodynamcally dencal saes of he sysem. Coespondngly, n MD, macoscopc quanes ae compued fom me aveages of mcoscopc saes, Γ, p, expessed n ems of aomc posons, and momena, p, whee,,n, fo a sysem of N aoms. Each mcoscopc sae, Γ, can be consdeed a pon n a muldmensonal D N space whee D s he numbe of spaal dmensons. An ensemble n MD s a collecon of mcoscopcally dsnc saes n he 6N-dmensonal phase space, Γ j. Hee, we wll dscuss he mcocanoncal, canoncal, and sobacsohemal ensembles. Mcocanoncal ensemble descbes sysems n hemodynamc saes expessed by consan vaables N, V, E whch denoe fxed numbe of pacles, volume, and enegy especvely. In he NVE ensemble, he Hamlonan and equaons of moon ae N p H m H &, p & p + V { } H NVT Ensemble Exended MD mehods ae used fo ohe ensembles. In he canoncal ensemble, empeaue s fxed and enegy s allowed o flucuae. Ths eques addng a em ha acs lke a hea bah o exchange enegy wh he sysem. NVT-MD, fs poposed by 5

45 Nosé, pescbes a Hamlonan, whch ncludes a hemosa vaable s o egulae consan empeaue. The hemosa has an assocaed mass, Q, and momena p s. The Hamlonan fo NVT MD s, N p p s H ex + φ { } + + f + k BTeq ln s m s Q.30 f whee s he numbe of degees of feedom, k s Bolzmann s consan, and T s he empeaue o be mananed n he sysem by he hea bah. The equaons of moon ae, q & f / ms sq && / s.3 B Qs && mq s f + k BT eq / s The logahmc dependence of he vaable, s, n he Hamlonan, s essenal n poducng he canoncal ensemble [5]. The equaons of moon fo hs Hamlonan ae wen n vual vaables q, p, whch ae elaed o he eal vaables q, p, as, q q,.3 p p / s,.33 d,.34 s and he eal velocy s expessed n scaled fom as, dq d dq s d.35 Nosé-Hoove chans addess he poblem of non-egodcy by lnkng addonal hemosas s o he sysem. All hemosas, s, ae coupled. Tha s, enegy 6

46 can be exchanged beween any hemosa, s and any ohe hemosa, s j. Couplng beween hemosa vaables dves flucuaons n p s, effecvely fllng he phase space. The mehod peseves he advanages and smplcy of he ognal appoach. The Hamlonan fo an MD sysem wh Nosé-Hoove chans s, H N M M p ξ + φ { } + + N f k BTeqξ + k BTeq m Q p.36 ξ whee he addonal degee of feedom s s elaed o he vaable log s N f ξ.37 log s ξ.38 Themosa masses, Q p, ae deemned fom, Q p Q N f kbteq / ω.39 p p k T.40 B eq / ω p whee ω p s he naual fequency of he hea bah. Mayna e al. have mplemened explc evese negaos fo he Louvlle opeao usng he Toe fomula [6]. The Louvlle opeao fo he Nosé-Hoove chan of M hemosas coupled o an N pacle sysem s expessed as, L N N N M M F v + v v v G G ν ξ + ν ξ + ν ξ ν ξ M m ξ ν ξ ν ξ M whee G' s ae gven by, N G mv N Q G Q v kbt Q f k B T eq ξ eq,, > The Toe fomula can be genealzed o expess he evoluon opeao as,

47 3 O e e e e e e L L L L L L NHC NHC +.44 whee and ae defned as L L NHC L N v N v L m F L.45 and M M M M v N NHC G G v L ξ ξ ξ ξ ξ ξ ν ν ν ν ξ ν ν Subsung and no he genealzed Toe fomula fo he me-evoluon opeao yelds he full-me evoluon. The Nosé-Hoove chan pa of he evoluon opeao, L L NHC L L NHC e, s expessed as: c c NHC NHC n n L L e e.47 whee a mulple me sep appoach has been used. The opeao >, c n L NHC e s fs appled o updae he { } v v,, ξ ξ vaables. Nex he updaed veloces ae used as npu o he velocy-vele sep, L L L e e e, and fnally he las L NHC e s appled o he oupu of he velocy-vele sep. Ths pocedue s summazed as follows: 0, ; v V ν.48, ; v v v v NHC ξ.49,, ; v v NHC ξ ξ ξ ξ.50, ; v v v v NHC ξ ξ ξ.5 whee 8

48 v v ; v0, v ξ 0.5 NHC v v ; 0, v.53 ν V ξ ξ ; ξ 0, v0, vξ 0.54 NHC vξ vξ ; v0, vξ 0.55 NHC vv, v vv epesen he oupu of a sngle velocy-vele sep. and { }.. NPT Ensemble The sobac-sohemal ensemble, also known as he NPT ensemble, s a descpon fo sysems havng consan numbe of pacles N, consan pessue, P, and consan empeaue, T. Andeson developed he fs NPT-MD [7], whch was fuhe developed by Panello and Rahman o allow fo a vaable shape MD cell [8]. NPT sysems have hea bahs and baosas. Ths s mpoan fo smulaons of cysal sucue ansfomaons whee he shape of he MD cell may change. The Hamlonan fo an NPT smulaon s, H N p m + M p η + T [ p g p g ] + V { }, h Q W g M N f + d kt η + kt η + PEXT de[ h ] The Hamlonan fo NPT-MD conans he NVT Hamlonan plus addonal ems ha accoun fo he eneges assocaed wh a vaable MD cell. T p g p ] s he [ g sum of he squaes of all he elemens of he cell vaable p g. I s he knec enegy of he MD cell. W s s called he mass of he baosa. I can be used o adjus he elaxaon me fo he MD cell. The poenal V s also a funcon of he sze and shape of he MD cell. P EXT s he exenal pessue appled o he MD cell. The h-max, o cell max, s gven as, 9

49 z z z y y y x x x h h h h h h h h h h whee ae a se of column vecos spannng a paallelepped epesenng he MD cell. The volume of he MD cell s 3 h, h, h 3 h h h ] de[ h. The pacle posons n he MD cell ae scaled by he h-max as follows: s h h s h s h s ,, N K.58 The equaons of moon n he NPT ensemble ae,, ] [,,,, ] [, n kt d N p p T W m p p Q p p Q p I m p N IP P V p W h p h p Q p p W p T N p W p F p W p m p f g g g N g N f EXT g g g g g f g g g g & & & & & & ξ ξ ξ ξ ξ.59 whee I s he deny max, ] [ g p g p T s he sum of he dagonal elemens of g p [9]. αβ αβ αβ β α β α αβ φ φ φ h h h F m p p V P N +, n.60 30

50 If he pessue enso s asymmec, ha s f P P, a ne oque acs on he box and wll cause oae. Ths s avoded by usng symmezed enso P P + P / αβ βα αβ. n he equaons of moon and seng he nal oal angula momenum of he cell o zeo. The dffeence beween he exenal pessue, P, and he nenal pessue P, govens he dynamcs of he box. The box mass s aken o be, ex αβ βα n W N f + d k BTeq / ω b whee ω b s he fequency a whch he box vaable flucuaes. The Louvlle opeao fo.6 he equaon of moon can be wen as whee L L + + αβ αβ NHC [ v ] [ Gg vg v ] αβ αβ ξ v v h g αβ N v h g αβ T + N + v N N F [ ] v + vg + f g g v αβ m v.6 N N N + G m v v m v P V δ + F φ h g αβ.63 α β ex αβ α β αβ Wg Wg N f N G mv + WgT[ v vg ] N f + d kbt.64 g eq Q The me evoluon opeao s wen as whee L L L L L NHCP L NHCP 3 e e e e e e + O.65 3

51 [ ] [ ] v N g g g v N v N f g g g g g P P NHC NHCP v v h h v L m F L v N v T v v v G L L L L ] [ αβ αβ αβ αβ αβ ξ αβ αβ ν.66 The full me-evoluon opeao s appled as n he NVT case and he followng equaons ae obaned fo he pacle and box vaables. [ ] [ ] F F m v v F m v v h c I c h v c I c I c g e g g s g e g whee αβ α α α αβ α δ λ λ λ αβ δ λ αβ snh s e e I e I.68 Hee λ α ae he egenvalues of / v and 0 c s he assocaed max of egenvecos λ g g c v c g..3 Compuaon of Physcal Popees Afe nalzaon, he MD smulaon mus be un o acheve equlbaon. Ths smulaon should un long enough so ha he memoy of he nal confguaon s los. One way o es fo equlbaon n a sysem s o plo vaous hemodynamc quanes such as enegy, empeaue, and pessue wh me. The sysem s equlbaed when 3

52 hese vaables flucuae abou he aveage values. Anohe way s o sa he sysem wh slghly dffeen posons and veloces. Convegence o smla aveages fom dffeen nal values s an ndcao ha he sysem has eached equlbum. Themodynamc, sucual, elasc, and dynamc popees of a sysem can be compued by aveagng ove he phase-space ajecoes..3. Themodynamc Quanes A numbe of hemodynamc quanes can be calculaed as ensemble aveages. The knec, poenal and oal eneges may be calculaed fom, whee he knec enegy, K, s calculaed as fo α x y z E < H >< K > + < V >.69 K N α p α m α.70. The poenal enegy V nvolves a summaon ove all pas, ples ec. of pacles, dependng on he complexy of he poenal funcon. Tempeaue s calculaed fom, K T 3Nk B Pessue s expessed n ems of he val:.7 whee f PV Nk B T + 3 N v.7 j fj j s he foce on pacle. Some quanes ae defned n ems of flucuaons of ohe quanes. Fo example, he specfc head a consan volume n he mcocanoncal ensemble s wen n ems of he flucuaons n he knec enegy as, 33

53 δk.3. Sucual Coelaons K 3k T C B kb ν.73 The sucue can be chaacezed by he pa-dsbuon funcon, g αβ V.74 δ j N N α β { α} j { β } j whee α, β ae aomc speces and K mples an ensemble aveage. Ths funcon gves he pobably of fndng a pa of aoms a dsance apa, elave o he pobably fo a compleely andom dsbuon a he same densy In pacce, he dela funcon s eplaced by a funcon whch s non-zeo n a small ange of sepaaons and a hsogam s compled fo all pa sepaaons fallng whn a gven ange. The Foue ansfom of he pa-dsbuon funcon s he sucue faco, S q αβ, N S q c c / q 3 αβ δ αβ + α β g e d V.75 αβ whee c s he concenaon of speces α c N / N. The sac sucue faco α α α S N q whee measued by neuon scaeng may be obaned fom b α c c / S q δ + c c S q αβ : [ ] / bα bβ α β αβ αβ α β.76 α, β S N q bα cα α s he coheen neuon-scaeng lengh of speces α. The las expesson allows sucual esuls fom neuon scaeng o be compaed decly wh MD esuls. The bond-angle dsbuon chaacezes hee-pacle coelaons n he sysem. A cuoff dsance s used, so ha pacles and j ae consdeed o fom a bond f j < b b. A hsogam of he bond angles s consuced by gong ove all he appopae 34

54 ples of pacles. NMR expemens measue bond-angle dsbuons and povde daa fo compason wh MD esuls..3.3 Elasc Modul and Sesses The nenal sess enso fo a sysem of N aoms may be wen as β V N α β α [ m v v + f ] σ.77 αβ whee α, β denoe he Caesan coodnaes. The elasc consans fom Hooke s Law, C αβγδ, ae calculaed σ αβ C αβγδ u whee he sess σ αβ s defned by equaon.77. In he calculaon of elasc consans γδ.78 C αβγδ a san s appled along one of he sx componens of he san enso u xx, u yy, u zz, u xy, u yz, u zx. A conjugae-gaden appoach s used o elax he sysem and he esulng sess componens ae measued usng equaon.77. Ths san and he esulng sess ae used n equaon.78 o oban specfc elasc consans..3.4 Dynamc Coelaons The me coelaon C AB beween wo dffeen quanes A and B s defned as: C AB A B 0 whee an ensemble aveage s aken. One way o calculae he phonon densy of saes n he hamonc appoxmaon s o calculae he Foue ansfom of he velocy-velocy auocoelaon funcon Z α, whch s defned as,.79 whee α Z v v 0 α α.80 v 0 K denoes an aveage aken ove all aoms of ype α. α 35

55 The dffuson coeffcen s compued fom he mean-squaed dsplacemen as: [ 0] α Dα lm 6 Ths s he Ensen elaon whch s vald a long mes..8 36

56 CHAPTER 3 PARALLEL MOLECULAR DYNAMICS Paallel compung s he pacce of usng mulple compung esouces o complee a shaed ask. In adonal seal compung, poblems ae solved by algohms execued sequenally by one CPU. The pncple n paallel compung s o dvde and dsbue a ask and hen compue smulaneously acoss moe han one pocesso. A paallel compung esouce may conss of a sngle compue wh mulple pocessos, a numbe of pocessng uns o nodes conneced by a newok o a combnaon of boh. The echnque s useful fo solvng poblems wh equemens ha exceed he compung capaces of sngle-pocesso machnes. The mehod bascally saves me and enables soluons of lage scale. 3. Backgound 3.. Flynn s Taxonomy Paallel compung sysems ae classfed n seveal ways. Flynn s axonomy has been wdely used snce he 960 s. I caegozes paallel compung sysems based on how nsucons ae execued and how daa ae pocessed. Paallel compuaon can be pefomed n fou ways. A se of pocessos can each pefom a sngle opeaon on a sngle daum, a sngle opeaon on mulple daa, mulple opeaons on a sngle daum, o mulple opeaons on mulple daa. 3.. Beowulf Cluses Beowulf s a desgn fo hgh-pefomance paallel compung cluses on nexpensve pesonal compue hadwae. In Flynn s axanomy, a Beowulf cluse s a compue ha pefoms mulple opeaons on mulple daa. Ognally developed by 37

57 Donald Becke a NASA, Beowulf sysems ae now deployed woldwde, chefly n suppo of scenfc compung. A Beowulf cluse s a goup of usually dencal PC compues unnng an open souce Unx-lke opeang sysem, such as Lnux o BSD. They ae newoked no a small TCP/IP LAN, and have lbaes and pogams whch allow pocessng o be shaed among hem Paallel Compue Memoy Achecues Thee ae seveal appoaches o desgnng memoy sysems fo paallel cluses. The dffeen knds of memoy achecues ae shaed memoy, dsbued memoy, and hybd dsbued-shaed memoy. In he shaed memoy model, memoy s globally accessble o all pocessos. Each pocesso can opeae ndependenly, bu all pocessos modfy and acque nfomaon fom one memoy esouce. Ths memoy achecue s use-fendly fom he pogamme s pespecve. Snce he memoy can be decly accessed by all CPUs, daa ansfe s fas and unfom. Howeve, a majo dawback of hs mehod s lack of scalably beween memoy and CPUs. In a dsbued memoy model, each CPU has a local memoy neconneced va a newok. Each pocesso compues ndependenly jus as n he shaed memoy model. Howeve, CPUs can only modfy local memoy and f necessay, mus acque nfomaon fo he memoes on ohe pocessos hough he newok. The advanage of dsbued memoy s memoy-cpu scalably. The dsadvanage s ha he pogamme has o manage daa communcaon beween CPUs. Hybd dsbued-shaed memoy achecue s a combnaon of boh dsbued and shaed-memoy achecues. In hs achecue, shaed-memoy 38

58 componen s ypcally a cache coheen symmec mul-pocessng SMP machne and dsbued-memoy componen s he newokng of mulple SMPs. Moden hgh pefomance compung akes advanage of he hybd memoy achecue. The smulaons n hs dsseaon eseach wee pefomed on a 56-pocesso Inel Xeon cluse and 8-pocesso IBM Opeon cluses a he Unvesy of Souhen Calfona. Each node of he Xeon & Opeon cluses has GB of memoy. The pocessos ae neconneced va a hgh-speed Myne LAN newok Paallel Pogammng Models Paallel pogammng models exs as an absacon above hadwae and memoy achecues. Thee ae seveal paallel pogammng models n common use: shaed memoy model, heads model, message passng model, and daa paallel model. Pogammng models ae no specfc o a pacula ype of machne o memoy achecue and can heoecally be mplemened on any undelyng hadwae. The choce of a model s dcaed by wha s avalable. Thee s no "bes" model, alhough hee ceanly ae bee mplemenaons of some models ove ohes. MPI Message Passng Ineface was used fo nepocesso communcaon. MPI s now he "de faco" ndusy sandad fo message passng, eplacng vually all ohe message passng mplemenaons used fo poducon wok. Mos, f no all of he popula paallel compung plafoms offe a leas one mplemenaon of MPI. Vey few have a full mplemenaon of MPI Wokload Dsbung Saeges n Paallel Compung A boad ange of complex sysems have necessaed and connue o movae advances n paallel compung echnology ncludng: meeoologcal foecasng, 39

59 chemcal eacons, econc plae shfs, eleconc and mechancal devce funconng, web seach engne opeaon, compue-aded dagnoss n medcne, he managemen of naonal and mul-naonal copoaons, and advanced gaphcs and vual ealy, used paculaly n he eneanmen ndusy. Cuenly, he sysems n MD smulaons ae ypcally sub-mcon sze; neveheless he amoun of compung powe equed o ealscally sudy dynamcs of hese sysems can be enomous, dependng on he numbe of aoms n he sysem, he numbe of neacons nvolved and how he neacons ae compued. Vaous algohms have been developed fo decomposng asks n paallel compung sysems o acheve geae effcences. Hee we dscuss hee such appoaches: Aom decomposon, foce decomposon, and spaal decomposon Aom Decomposon Paallel compung nvolvng aom decomposon s based on daa eplcaon. Each pocesso s assgned an dencal confguaon. A subgoup of aoms s hen pemanenly assgned o each pocesso fo he duaon of he smulaon. The aom decomposon mehod s bes sued fo 3-body and 4-body neacons ofen used n smulaons of bologcal sysems. The mehod woks bes fo smulaons of small sysems pefomed on paallel compung cluses havng < 64 pocessos, whee he ganulay s fne, ha s, he amoun of compuaon beween communcaons s small. Kollman e al. [30,3]have used he aom-decomposon appoach o pefom he longes smulaon µs o dae of a small poen n soluon. A numbe of commecal smulaon packages CHARMM [3], AMBER [33], and GROMOS [34] use hs mehod. 40

60 3..5. Foce Decomposon Foce decomposon mehods fall no wo caegoes, hose whch make use of sysolc loops as pesened by Rane [35] and hose whch compue foce maces as noduced by Plmpon [36]. Foce decomposon mehods bascally nvolve daa "packes" elang o a subse of aoms e.g. aomc coodnaes, veloces and foce accumulaos beng cculaed beween pocessos. All foce decomposon algohms ae fully dsbued. The memoy demands ae less han ha of he eplcaed daa aom decomposon saegy because each pocesso only woks wh subse of he oal sysem. Foce decomposon algohms ae mos effcen fo fne ganulay paallel compung. Tha s, smulaons whee he amoun of compuaon beween communcaons s elavely small. In he case of MD, ha means he numbe of pacles has o be much smalle han o he numbe of pocessos Spaal Decomposon Spaal decomposon mehods ae used que commonly fo lage MD smulaons [37]. In hs mehod, he MD cell s paoned no P P P P equal x y z sub-volumes, whee P, P, P x y z ae he numbe of subdvsons along x, y and z axes especvely. The wokload s dsbued ove a P -node paallel machne whee each node pefoms calculaons fo he aoms locaed n s pe-assgned sub-volume. Spaal decomposon woks mos effcenly fo smulaons havng lage ganulay whee he amoun of compuaon beween communcaons s elavely lage, whch s he case n MD when he numbe of aoms compaed o he numbe of pocessos s lage. In hs hess, he numbe of aoms, N, s on he ode of a mllon, and 4

61 he numbe of pocessos, P ~ 00, and hus he ganulay, N/P >>. Theefoe, spaal decomposon was he mehod chosen o pefom ou paallel MD smulaons. 3. Implemenaon of Paallel Molecula Dynamcs Ths secon descbes how ou MD smulaon algohm has been mplemened on paallel compues. 3.. Pocesso ID Each pocesso n an aay of P pocessos s assgned a unque sequenal ID p, n he ange [0, p-] as well as a veco ID p p, p, p. The followng elaons x y z expess he mappng beween he sequenal and veco IDs see an example n Table 3.. p p p x y z p / P P y p / P mod P z z p mod P z y o p p P P + p P + x y z y z p z We use he sngle pogam mulple daa SPMD pogammng syle,.e., a sngle pogam wh common vaable names conols mulple pocesses wh dsnc vaable conens. In an SPMD pogam usng message passng neface MPI, each pocess obans s ID fom he ank value euned by he MPI_Comm_ank funcon call hough some use defned vaable. 4

62 Table 3.: An example of sequenal-veco pocesso ID mappng Sequenal pocesso ID, p Veco ID, p p x p y p z Fom a pogammng aspec, sysem-wde asks o be pefomed by all pocessos can be wen saghfowadly as a sngle loop addessng pocessos by he sequenal IDs. Howeve, deemnng opologcal adjacences usng sequenal IDs s awkwad. Alenavely, addessng pocessos usng veco IDs allows nodes o be denfed n a opologcal fashon coespondng o he way he MD cell has been spaally subdvded. Ths smplfes he sep of addessng neghbong nodes ha exchange nfomaon beween hem. 3.. Neghbo Pocesso ID The same basc saegy s used o denfy neghbos of a pocesso o s subsysem. Each pocesso p has a neghbo posoned n one of sx decons adjacen o. We efe o a neghbo as beng noh, souh, eas, wes, up o down fom ou pocesso p and ehe addess hem sequenally by an ndex κ 0,..., 5 o opologcally by a elave shf-lengh veco x, y, z whch denoes neghbong subsysem 43

63 elave o he subsysem on pocesso p. Table 3. lss he sx neghbos fo a subsysem, whee an nege veco δ δ x, δ y, δ z specfes he elave locaon of each neghbo. Table 3.: Example of sequenal-veco neghbo ID mappng Neghbo ID, κ 0 eas wes noh 3 souh 4 up 5 down δ δ x, δ y, δ z -, 0, 0, 0, 0 0, -, 0 0,, 0 0, 0, - 0, 0, x, y, z -L x, 0, 0 L x, 0, 0 0, -L y, 0 0, L y, 0 0, 0, -L z 0, 0, L z The mappngs n Table 3. come fom he followng elaons and p κ [ p + δ κ + P ] mod P α α α p κ p κ P P + p κ P + p κ x y z α y z α z whee α x, y, z Pocesso and neghbo IDs manage foce calculaons beween aoms on neghbong pocessos as well as aom mgaon as hey move fom one subspace o anohe dung a smulaon Aom Cachng and Mgaon Aoms close o he boundaes beween wo subsysems, mus neac seamlessly as f hey ae all on one pocesso. Ths s accomplshed by augmenng he sysem o subsysem. Concepually, a subsysem s augmened by exendng s volume o nclude he aoms fom s neghbong subsysems locaed nea he adjacen faces and cones. Ths s accomplshed n he acual mplemenaon by aom cachng. When aom cachng 44

64 s pefomed fo a subsysem on a pocesso, aom daa ae ansfeed fom s neghbong subsysems on pocessos p p + δ p + δ, p + δ x x,, o p, whee δ δ δ 0 and δ δ + δ 0. An aom s only ansfeed f s dsance o x y z x + y z an neface s shoe han he poenal cu-off dsance c. Foces ae calculaed only afe aom cachng s complee. Ths cache coheence manans pope dynamcs. A D llusaon of sysem augmenaon and aom cachng s shown n Fg. 3.. Hee each pocesso p p, p x + δ p + δ x y y x p y y, wll have 3-8 neghbong subsysems p, and aom cachng s equed fo 8 ses of daa. Fo a 3D sysem, hs numbe s y z z c Fgue 3.: D llusaon of sysem augmenaon. Aoms n subsysems on pocessos p lyng whn he cu off ange, n lgh pnk, ae cached and ansfeed o subsysem p n dak pnk fo foce calculaons. 45

65 Dung a paallel smulaon, pacles mus be allowed o mgae seamlessly acoss boundaes beween subsysems. When an aom eaches a bounday of s subsysem, a ansacon mus be pefomed beween he wo pocessos deleng he aom fom he pevous pocesso p o nsanae on he nex pocesso machne p. Howeve, hese ansacons egadng poson, velocy and foce updaes mus be execued n pope sequence whn paallel MD algohm. Below s he basc sucue fo a paallel algohm.. Pefom half-sep of velocy-vele as descbed n Chape. Updae aomc coodnaes 3. Aom mgaon 4. Aom cachng 5. Calculae foces ncludng cached aoms 6. Pefom second half-sep of velocy-vele Fgue 3.: Aom mgaon. Fo aoms o move seamlessly beween subsysems on dffeen pocessos p and p dung a smulaon, paallel pogams ncopoae funcons o delee and nsanae aom daa beween p and p, consevng he numbe of aoms. 46

66 3..4 Lnk-Ls Cell Mehod on Paallel Cluses The lnked-ls cell mehod was descbed n Chape. I s an effcen algohm fo calculaons of foces and poenal enegy on a sngle pocesso. The echnque can also be mplemened fo paallel sysems. Howeve, some specfc ssues ase fo hs case paculaly fo foce calculaons. When calculang -body and 3-body neacons on a paallel machne, he aoms nvolved n he neacon may no always be on he same node. Theefoe, a poocol mus be followed dung foce calculaons so ha foces on each aom ae calculaed popely. We wll eun o hs lae n he secon afe descbng how lnked-ls cell mehod s mplemened on paallel machnes Cells We fs dvde he sysem conssng of he esden and cached aoms no small cells of equal sze. The edge lenghs of each cell, cx, cy, cz, mus be a leas c ; we use cα L α /L cα, whee L cα L α / c. An aom n a cell neacs wh ohe aoms n he same cell and s 6 neghbo cells. Includng he cached aoms, he ange of aomc coodnaes s [- c, L α + c ] α x, y, z. The numbe of cells o accommodae all hese aoms s L cx + L cy + L cz +. We denfy a cell wh a veco cell ndex, c c x, c y, c z 0 c x L cx +; 0 c y L cy +; 0 c z L cz +, and a sequenal cell ndex, o An aom wh coodnae c c L + L + + c L + + c c c c x y z x c / cy cz [ L + L + ] cy [ c / Lcz + ] mod Lcy + c mod L + cy cz y belongs o a cell wh he veco cell ndex, cz z 47

67 c α [ + / ] x, y, z α α c α ca 0 L cx L cx + L cx + L cy cy cx 0 Fgue 3.3: D depcon of lnked-ls cell decomposon. Fgue 3.3 s a D llusaon of lnked-ls mehod mplemened on a paallel compue cluse wh 9 subsysems. The pocesso fo each subsysem s oulned n sold black lnes and lnk-ls cells on each pocesso ae oulned n doed black lnes. Foce compuaons on a pocesso p, hghlghed n geen, s pefomed on aoms n each lnked-ls cell. Ineacons fo an aom ae only compued beween aoms n he same cell and neghbong cells. Fo example, n Fg. 3.3, foce calculaons fo aoms n he ed lnked-cell s pefomed fo all aoms nsde he blue squae. 48

68 Fgue 3.4: Schemac of D lnked-ls cell pocessng. Fgue 3.4 shows an example of how lnked-lss ae pocessed fo one eaon dung a smulaon. An enlaged vew of a secon of he lnked-ls cells fom Fgue 3.3 s dsplayed n he op gh cone. Nne lnked-ls cells ae labeled 0-8. Lnked-ls cells 4, 5, 7 and 8 ae on pocesso p, n geen. Lnked-cell lss and ae on pocesso ; cells 3 and 6 on p p x, p ; and cell 0 s on p x, p p p x, p y y y p. In hs example, foces ae compued fo aoms 0 and 7 n he ed lnked-cell. The head ls n Fgue 3.4 conans aom IDs fo he fs aom n he lnk-ls fo each cell ndexed 0-8. The lss may vay n lengh. They may also be empy, denfed by E. The 49

69 lnked-ls n Fgue 3.4 conans he ode of aoms n each lnked-ls cell. The ndexed 0- coesponds o he aom IDs. The ls s used o queue up aoms fo foce calculaons as follows:. Head ls ndcaes Cell 0 conans aom 9. Foces on aoms n Cell 4 fom aom 9 ae compued 3. Lnked ls ndcaes aom 9 s conneced o E 9 s he las aom n cell 0 4. Head ls ndcaes Cell conans aom 6 5. Foces on aoms n Cell 4 fom aom 6 ae compued 6. Lnked ls ndcaes aom 6 s conneced o E 6 s he las aom n cell 7. Head ls ndcaes Cell conans aoms 8, and 8. Foces on aoms n Cell 4 fom aom 8 ae compued 9. Lnked ls ndcaes aom 9 s conneced o 0. Foces on aoms n Cell 4 fom aom ae compued. Lnked ls ndcaes aom s conneced o. Foces on aoms n Cell 4 fom aom ae compued 3. Lnked ls ndcaes aom s conneced o E s he las aom n cell Ths pocedue s epeaed fo cells 3-8 unl all foce calculaons fo cell 4 ae complee. Ths s done fo evey lnked cell n Fgue 3.3 hghlghed geen magne he ceneed ed and blue ecangles anslang o each of he 4x46 cells one-by-one n a ase paen. One eaon s complee when evey pocesso n he cluse pefoms hs oveall opeaon fo all aoms n s lnked-ls cells. As menoned a he begnnng of hs secon, somemes neacng aoms may no esde on he same pocesso dung a foce calculaon. On any pocesso, hee wll be esden aoms and aoms cached fo neghbong pocessos. If wo aoms, fo example, and j ae esden on he same pocesso p hen he poenal enegy can be calculaed fo boh. Bu f j has been cached fom a neghbong pocesso he amoun of poenal enegy u, j would be doubled when he global poenal enegy s calculaed by addng poenal enegy conbuons fom all CPUs. Theefoe, fo wo-body poenals, poenal enegy s summed fo each aom and j as u, j u, j fo 50

70 and j esden on he same pocesso p, and hen u, j u, j fo and j on dffeen pocessos p and p. 3.3 Scalably Analyss of Paallel Molecula Dynamcs Algohm In ode o make an effcen use of paallel compung esouces, s essenal o undesand he noon of paallel effcency. Ths secon fs povdes geneal defnons of speedup and effcency of a paallel applcaon. We hen analyze he paallel effcency of he paallel MD algohm Paallel Effcency We defne he effcency of a paallel pogam unnng on P pocessos o solve a poblem of sze W. Le TW, P be he execuon me of hs paallel pogam. Speed of he pogam s hen SW, P W/TW, P. Speedup, S P, on P pocessos s he speed of P pocessos dvded by ha of pocesso,.e., S P SW P, P/SW,. To unambguously defne he speedup, we need o specfy how he poblem sze, W P, scales as a funcon of he numbe of pocessos, P whch wll be dscussed n he nex few paagaphs. The deal speedup on P pocessos s expeced o be P, and heefoe we defne he paallel effcency, E P S P /P Consan Poblem-Sze Scalng In he consan poblem-sze scalng, he poblem sze W P W s fxed. Theefoe, he consan poblem-sze speedup s S P SW,P SW, W /TW,P W /TW, TW, TW,P, and he paallel effcency s 5

71 E P S P P TW, P TW,P Isoganula Scalng In he soganula speedup, he poblem sze W P scales lnealy wh he numbe of pocessos: W P P w, whee he ganulay o he wok pe pocesso, w, s consan. Theefoe, he soganula speedup s S P SP w,p Sw, P w /TP w,p w /Tw, P Tw, TP w,p, and he coespondng soganula paallel effcency s E P S P P Tw, TP w,p Analyss of Paallel Molecula Dynamcs Algohm Usng spaal decomposon and he ON lnked-ls cell mehod, he paallel MD smulaon of N aoms execues ndependenly on P pocessos, and he compuaon me T comp N, P an/p, whee a s a consan. Hee, we have assumed ha aoms ae on aveage dsbued unfomly, so ha he aveage numbe of aoms pe pocesso s N/P. The domnan ovehead of he paallel MD s aom cachng, n whch aoms nea he subsysem bounday whn a cuoff dsance, c, ae coped fom he neaes neghbo pocessos and ae pocessed. Snce hs neaes-neghbo communcaon scales as he suface aea of each spaal subsysem, s me s T comm N, P bn/p /3, whee b s a consan. Anohe majo communcaon cos ases fom global summaons, MPI_Alleduce, whch ncus T global P c logp, whee c s anohe consan. The oal execuon me of he paallel MD pogam can hus be modeled as 5

72 TN,P T comp N,P + T comm N,P + T global P. an /P + bn /P /3 + c log P Consan Poblem-Sze Scalng Fo consan poblem-sze speedup of paallel MD algohm, he global numbe of aoms, N, s fxed, and he speedup s gven by S P TN, TN,P + b P a N an an /P + bn /P /3 + c log P P /3 + c a P logp N, and he paallel effcency s E P S P P + b P /3 + c a N a P logp N. Fom hs model, we can see ha he effcency s a deceasng funcon of P hough P /3 and PlogP dependences Isoganula Speedup Fo soganula speedup, he numbe of aoms pe pocesso, N/P n, s consan, and he soganula paallel effcency s E P Tn, TnP,P an an + bn /3 + c logp + b a n /3 + c. an logp 53

73 Fo a gven numbe of pocessos, he effcency E P s lage fo lage ganulay n. Fo a gven ganulay, E P s a weakly deceasng funcon of P, due o only he logp dependence. Fgue 3.5: Toal execuon ccles and communcaon squaes mes pe MD me sep as a funcon of he numbe of pocessos fo he paallel MD algohm wh scaled wokloads,09,000 P aom slca sysems on P pocessos P,...,,90 of Columba. We have pefomed scalably ess of ou paallel MD algohm on he 0,40 Inel Ianum pocesso Columba supecompue a he NASA Ames Reseach Cene. Fgue 3.5 shows he execuon me of he MD algohm fo slca as a funcon of he numbe of pocessos, P. We scale he sysem sze lnealy wh he numbe of pocessos, so ha he numbe of aoms, N,09,000P P,...,,90. In he MD algohm, he neaomc poenal enegy s spl no long-ange and sho-ange conbuons, whee he long-ange conbuon s compued evey 0 MD me seps. The execuon me nceases only slghly as a funcon of P, and hs sgnfes an excellen paallel effcency. On,90 pocessos, he soganula paallel effcency of 54

74 he MD algohm s Also he algohm nvolves vey small communcaon me, see Fgue

75 CHAPTER 4 WURTZITE-TO-ROCKSALT STRUCTURAL TRANSFORMATIONS IN CADMIUM SELENIDE NANO-RODS Pessue-nduced sucual phase ansons n semconducos have been an excng aea of eseach snce he ealy 980 s [38]. Undesandng he mechansms govenng sucual ansfomaons a he nano-scale can help o develop novel nanomaeals and devces [39,40]. Recen effos n expemenal eseach have focused on pessue-dven phase ansons fom 4-fold o 6-fold coodnaed sucues n semconducng maeals. The mechansms fo phase ansfomaons fom znc-blende o ocksal n GaAs and ohe semconducos, have been suded exensvely. Eleconc sucue calculaons based on densy-funconal heoy and molecula dynamcs smulaons have been used o confm pahways and baes beween pessue-nduced znc-blende o ocksal ansfomaons [4,4]. Tansfomaon mechansms fom fou-fold o sx-fold coodnaed sucues, such as wuze o ocksal n CdSe ae also of consdeable nees. Despe a gea deal of nees and acvy n hs aea, he ansfomaon mechansm fom wuze o ocksal n CdSe s no well undesood [43,44,45,46,47,48]. 4. Expemenal Reseach on CdSe Nanoods Alvsaos goup a Bekeley has expemenally nvesgaed cysal fomaon, gowh, and pessue-nduced sucual ansfomaons n nanoods and vaous ohe shapes of CdSe nanocysals. CdSe nanofoms ae poduced usng collodal chemcal synhess. Sock soluons of Cd and Se pecusos ae dssolved n -n-buylphosphne TBP a vaous aos and soed a 0 C. The goup pefomed seveal expemens ha nvolved njecng hese sock soluons no 360 C bnay sufacan mxues of 56

76 TOPO and HPA. They found ha dffeen aos and dffeen njecon volume aes conolled dffeen nanofoms and he shapes. CdSe nanocysals wee cyclcally pessuzed n damond anvl cells and suded by synchoon X-ay dffacon expemens o nvesgae how nanocysals ansfom evesbly beween 4-fold and 6-fold coodnaed saes. They asse ha mechansms fo sucual ansfomaons can be deduced fom he nanocysal shape afe ansfomaon and popose a mcoscopc mechansm ha nvolves sldng planes. 4. Ab-Ino Smulaons of Sucual Phase Tansfomaon n Bulk CdSe Smulaons have played an mpoan ole n nvesgang phase ansons n nanocysals. Shmojo and co-wokes have pefomed DFT smulaons o chaaceze mechansms of sucual ansfomaons beween 4-coodnaed wuze WZ and 6- cooodnaed ocksal RS cysal sucues n bulk CdSe [49]. Thee possble ansfomaon mechansms beween wuze and ocksal cysal foms wee ealzed and he coespondng enegy baes wee deemned. Resuls of he DFT calculaon fo he vaaon of enegy wh he volume of bulk CdSe s shown n fgue 4.. The cuves show he nenal eneges of ocksal and wuze cysal sucues acoss a ange of denses n bulk CdSe. The pessue of ansfomaon s he common angen passng hough boh ocksal and wuze cuves. Fgue 4. llusaes ansfomaon pahs fo wuze o ocksal as obseved n DFT calculaons. Cd and Se aoms ae epesened n magena and blue, especvely. Fames a hough depc he spaal aangemen of aoms whn an ohohombc un cell as hey pogess hough ansfomaon pahs. Wuze was obseved o ansfom no wo ypes of ocksal sucues, denoed by RS-I and RS-II. A 5-coodnaed 57

77 honeycomb-sacked HS measable sae was also found. Fgue 4.: Enegy-volume elaon fo cysallne CdSe calculaed by DFT. The sold ccles coespond o he wuze sucue and he open ccles coespond o he ocksal sucue. Fom hese cuves, he anson pessue s esmaed o be abou.5 GPa, whch s n ageemen wh expemens [50]. Fgue 4.: MD smulaon of ansfomaon fom he wuze o he ocksal sucues n CdSe. Each fgue shows aomc confguaon n he ohohombc un cell of CdSe. The magena and blue sphees show he posons of Cd and Se aoms, especvely. 58

78 4.3 Molecula Dynamcs Smulaons of Sucual Phase Tansfomaon n GaAs Nanopacles Kodyalam e al. have pefomed MD smulaons o sudy sucual ansfomaons of sphecal and faceed GaAs nanocyals fom he 4-coodnaed zncblende o he 6-coodnaed ocksal cysallne phase [5,5,53]. They have nvesgaed nucleaon pahs and chaacezed gan bounday fomaon n nanopacles of vaous szes. The esuls povde explanaons fo synchoon X-ay expemens on ansfomed GaAs nanocysals. Kodyalam e al. have shown how a GaAs nanopacle ansfoms fom zncblende o polycysallne ocksal sucue. In Fgue 4.3, Ga and As aoms n each egon ae especvely coloed as ed/cyan egon, blue/magena egon, o geen/yellow egon 3. Regons of Ga and As aoms n he znc-blende cysal phase ae pnk and lavende. The lgh geen coloed aoms ndcae small o ndsnc egons. Fgue 4.3 a shows ha he znc-blende phase domnaes he suface of he nanopacle alhough a small facon of ocksal s also pesen a 6 GPa. A 9.4 GPA, he zncblende egon shnks as egons and begn o gow. The ansfomaon complees a.5 GPa. The pesence of mulple domans n he fnal confguaon of he nanopacle ndcaes a leas hee sepaae nucleaons dung hs sucual ansfomaon. One explanaon fo mulple domans and mulple nucleaons s ha cysal defecs ae noduced by aspees lef behnd when a cuved suface s cu ou fom an hcp, zncblende, o any ohe egula lace. These cysal defecs may ac as nucleaon cenes fo phase ansfomaon n he nanopacle. Ths mples ha foms commensuae wh 59

79 he cysal lace sucue, such as hexagonal ods n he case of hcp o znc-blende laces, may have fewe o even sngle pons of nucleaon esulng n a sngle ocksal cysal doman afe ansfomaon. Suffcenly small <5000 aoms pacles ae commonly known o fom sngle cysals whle lage sysems ae expeced o have mulple domans [54,55]. I has also been poposed ha mul-doman fomaon n he elavely small nanopacle suded hee, ~30 Å n adus, may depend on he ae of pessue ncease. Fgue 4.3: Mulple ocksal domans fom when a GaAs sphecal nanopacle s subjeced o nceasng pessue. Thee ae 6 equvalen ansfomaon pahs fom znc-blende o ocksal, each esulng n he fomaon of wo bonds and no bonds ae boken. Each ansfomaon s assocaed wh a unque san n he znc-blende cysal. Ths one-o-one mappng beween he coodnaon change and defomaon of he nal confguaon allows he domans o be dsngushed n he fnal confguaon by nspecng he fomaon of new bonds. I also allows he denfcaon of acual ansfomaon mechansm. 60

80 The sx possble ansfomaon pahs fom znc-blende o ocksal ae epesened by sx dffeen colos n Fgue 4.4. Aoms paed by same-coloed ccles can bond wh he cene aom, whch s nally 4-coodnaed bu changes o 6-fold coodnaon. Fgue 4.4: Schemac of bondng mechansm fo znc-blende o ocksal ansfomaon. Dung fowad sucual ansfomaon he cenal aom foms wo addonal bonds wh any pa of neghbong aoms enccled by he same colo. The ansfomaon mechansms fom fou-fold o sx-fold coodnaed sucues, such as znc-blende o ocksal n GaAs and ohe semconduco compounds, have been suded exensvely and ae well-undesood. Eleconc sucue calculaons based on densy-funconal heoy and molecula dynamcs smulaons have been used o confm pahways and baes beween pessue-nduced znc-blende o ocksal ansfomaons [56,57]. Tansfomaon mechansms fom fou-fold o sx-fold coodnaed sucues, such as wuze o ocksal n CdSe ae also of consdeable nees. Despe a gea deal of nees and acvy n hs aea, he ansfomaon mechansm fom wuze o ocksal n CdSe s no well undesood [58,59,60,6,6,63]. Snce he phase dagam fo he Lennad-Jones has gas, lqud and sold phases, 6

81 one mpoan aspec n usng hs pocedue s he paameezaon of he Lennad-Jones flud [64]. 4.4 Pessue Medum n MD Smulaon of Sucual Tansfomaons n CdSe Nanoods Ths wok adops he smulaon pocedue used by Kodyalam e al [65]. A unfom hydosac pessue s appled hough a lqud medum conssng of aoms neacng va Lennad-Jones LJ poenal. The phase dagam fo he LJ sysem has been well suded and used n sudes of he behavo of fluds confned whn small poes [66]. The paamees fo he pessue medum ae lsed n Table 4. below. Table 4.: Paamees of he LJ lqud used as he pessue medum Paamee Descpon Smulaon Value ε LJ poenal well J σ LJ poenal damee.30å Paamees, σ and ε, fo he Lennad-Jones LJ poenal wee seleced so ha he LJ pessue medum emaned n flud phase ove he ene pessue ange 0-4.0GPa a oom empeaue. The dmensons of he MD cell, and hus he lqud volume, ae dynamc dung NPT smulaon. A maxmum pessue, he volume suoundng he nanood s sgnfcanly educed and so he amoun of lqud suoundng he nanood has o be lage enough o peven neacons beween aoms on oppose sdes of he MD cell. 6

82 Inal Confguaon Nanoods ae cu fom a wuze cysal. The cung planes fo nanoods expose 000 WZ sufaces and he emanng 6 sde faces ae fom he{ 0} WZ famly. The damee, o wdh, of each nanood s ~44Å, whch s vey close o he expemenal damee of he nanoods 40Å. Each nanood s suounded by Lennad-Jones aoms, whch ae nally aanged on a face ceneed cubc fcc lace. The Lennad Jones poenal s paameezed, accodng o s phase dagam as pesened by Johnson, Zollweg and Gubbns [67], so ha he LJ aoms ae n flud phase a a empeaue of T300K T *.0 acoss a pessue ange fom P0 up o P4.0GPa P *.6 a whch he densy of he LJ flud eaches ρ~0.66 ρ*~ A hexagonal-od-shaped hole s cu no he Lennad-Jones medum o embed a nanood. The sze of he hole s lage enough so ha a dsance of 4.0Å exss beween he sufaces of he nanood and fcc lace. 44Å 65Å Fgue 4.5: CdSe nanood embedded n a Lennad Jones flud, whch seves as a hydosac pessue medum. Each nanood has a hexagonal coss-secon, wh a damee of 44Å as shown above. 63

83 Sucual phase ansfomaons unde pessue wee suded n fou ses of ndependen smulaons. Each se of smulaon s pefomed fo a sngle nanood havng a dffeen wdh-o-lengh aspec ao, :, :, :4, :, whch ae denoed by S :, S :, S :4, S :, especvely. The nanoods ae shown n Fgue 4.5. The sysem fo smulaon S : conssed of,77 Cd aoms,,77 Se aoms and 79,994 LJ aoms. The nal MD cell was cubc, spannng 63Å on each sde. The sysem dmensons fo he S : smulaon wee 65Å 65Å 57Å and he nanood dmensons wee 44Å 93Å. Ths sysem conaned 3,795 Cd, 3,795 Se, and 78,064 LJ aoms. Smulaon S :4 conssed of an MD cell ha was also 65Å 65Å n he x-y plane and 57Å along s z-axs. The lages nanood smulaed was 58Å n lengh, wh an MD cell of abou wce s lengh. The S : sysem conaned,64,,64, and,,5,304, Cd, Se and LJ aoms, especvely. Sze paamees fo each smulaon ae gven n able 4.. a b c d Fgue 4.6: Isomec dsplays of CdSe nanoods ae shown above. All nanoods have 44Å damees wh vayng lenghs a 44Å, b 88Å, c 76Å, and d 58Å. The end faces of each nanood ae nomal o he [000] decon n a WZ cysal lace. 64

84 Descpons of Paallel Smulaons Smulaons wee pefomed on a paallel compue usng spaal doman decomposon as dscussed n Chape 3. Spaal decomposon fo each smulaon nvolved an aay of ecangula cubes. In he S : smulaon he sysem was subdvded acoss 6 pocessos wh,, 4 subdvsons n he x,y,z decons, especvely. Fo he S : smulaon, he sysem was subdvded acoss 3 pocessos wh,, 8 subdvsons n he x,y,z decons, especvely. The S :4 sysem was sub-dvded acoss,,, 6 pocessos n he x,y,z decons, especvely. Sysem S :, was subdvded no,, 3 pocessos n he x,y,z decons, especvely. The smulaons epoed n hs and he nex chape wee pefomed on he CACS Xeon and Opeon cluses a he Unvesy of Souhen Calfona. Consan pessue smulaons wee pefomed usng he Panello-Rahman mehod. Foces wee calculaed fom empcal poenals desgned by Vashshsa and cowokes, as descbed n Chape. Peodc bounday condons wee mposed and he mnmum-mage convenon was used o calculae foces and poenal enegy. Equaons of moon wee negaed usng velocy-vele algohm wh a me-sep of fs, whch conseves enegy o pa n 0 7. Smulaon Schedule Smulaons ae dvded no hee phases. The fs phase s pefomed n he mcocanoncal ensemble NVE. The nal empeaue of he sysem s 5K and he sysem s un fo 5000 me seps. Dung hs phase, he CdSe aoms ae held saonay, so ha he lqud mpngng on he nanood suface does no noduce cysal defecs, 65

85 whch may possbly ac as nucleaon ses dung subsequen sages of he smulaon and ale he sucual ansfomaon. Ove he nex 0,000 me seps, he pessue medum mels and edsbues aound he CdSe nanood, elmnang he peexsng vacuum beween hem and esablshng suface conac. Afe he lqud mels, aomc veloces ae scaled o ncease he oveall empeaue of he sysem o 300K ove 0,000 me seps. Nex, he Cd and Se aoms ae allowed o move and he ene sysem of he CdSe nanood and he lqud s hemalzed a 300K fo ~30,000 me seps. The fnal pessue of he sysem s 80 MPa. Table 4.: Specfcaons fo he fou CdSe nanood sysems. SIMULATION S : S : S :4 S : Rod aspec ao : : :4 : MD cell dm.å, Å, Å 63,63,63 63,63,57 63,63,44 63,63,7 # of Cd aoms # of Se aoms # of LJ aoms LJ flud denses Å Rod damee Å ~44 Å ~44 Å ~44 Å ~44 Å Rod lengh Å ~44 Å ~93 Å ~06 Å ~64 Å #Poc. along x #Poc. along y #Poc. along z

86 The second phase of he smulaon s caed ou n he sobac-sohemal NPT ensemble. Hee he MD cell volume adjuss o manan a specfed consan pessue. The sysem s held a oom empeaue and a a pessue of 80 MPa fo 0,000 me seps. The pessue of he sysem s nceased by 0.5GPa ove 0,000 mes seps and hen he sysem s hemalzed fo 50,000 me seps. Ths pocedue s epeaed unl he sysem pessue eaches 4.0 GPa; see Fgue 4.7. In he fnal phase, he oveall pessue s deceased whle he empeaue s kep a 300K. The pessue s deceased by 0.5 GPa ove 5000 me seps and hen he sysem s elaxed fo 0,000 me seps. Ths s done epeaedly unl he pessue eaches 80 MPa. Ths s dscussed fuhe n chape 5. Sucual popees such as bond angle dsbuons, aomc coodnaons, and pa-coelaon funcons ae calculaed dung each smulaon. Poenal enegy and knec enegy pe pacle, aomc sesses, paal pessue and empeaue pe spece ae also compued. Sucual quanes ae calculaed n spaally esolved shells and slces shown n Fgue 4.8. Shell & "slce" esolved calculaons of he bond angle dsbuon, coodnaons cn and pa coelaon funcons g ae pesened n Fgues A shell efes o an annula cylnde a hollow ube wh a hckness -, whee and ae he nne and oue ad of he annula cylnde, especvely. Fo hs analyss n+ n + c, whee c s Max /sh, Max 8Å and sh 3. Each shell, sh, s dvded no a numbe of slces o ccula dscs, efeed o as sl. Sh,, N sh, sl,, N sl. An N sh, N sl shell-slce esolved nanood has been spaally esolved no N sh concenc annula shells, whee each shell s dvded evenly no N sl slces. The calculaons of ba, g, cn ae confned o aoms whn each shell sh, of each slce sl. 67

87 Smulaon Schedule Fgue 4.7: Fowad ansfomaon schedule. The Lennad-Jones lqud s meled and allowed o each hemodynamc equlbum a 300K dung he nal NVE un. CdSe aoms ae fxed n space o avod defec fomaon on he nanood. The sysem hen undegoes a sequence of compesson and elaxaon uns n andem unl eaches a fnal pessue of 4.0GPa. 68

88 A 3,3 shell-slce esolved analyss nvolves hee concenc annula ubes, dvded no 3 slces. An llusaon of a 3,3 shell-slce esolved nanood s shown n Fgue 4.8. A,0 shell-slce esolved analyss nvolves shell dvded no 0 slces, a 0, shell-slce esolved analyss nvolves 0 concenc annula ubes, ec. Fgue 4.9 shows spaally esolved sucual quanes fo he 44Å 44Å nanood befoe hemalzaon. The plos ndcae ha he nanood s n psne wuze cysal fom. Wuze sucue s composed of eaheda sacked n a layeed sucue wh evey ohe laye exacly he same n an ABABAB hexagonal sequence. The eaheda n wuze all ae oened n one decon and poduce a hexagonal sx fold oaonal symmey. Calculaed spaally-esolved sucual quanes n Fgue 4.9 show he nal psne wuze cysal sucue of S : 44Å 44Å CdSe nanood. The cuves n plos a- d ae coloed ed, blue, geen, coespondng o he s nne-mos, nd mddle and 3 d ouemos shells, especvely. Calculaons show a s-4h neaes-neghbo peaks n Cd-Se pa-dsbuon funcon, g, a.63å, 5.046Å, 6.67Å, 9.97Å, especvely and b s-4h neaesneghbo peaks n Cd-Cd/Se-Se pa-coelaon funcons a 4.30Å, 7.45Å, 8.604Å, and.38 Å especvely. These peak posons ae conssen wh he wuze lace sucue. Plos of aomc coodnaon show 4-coodnaed aoms nsde he nanood and 3 and 4-coodnaed aoms a he nanood suface. Fgue 4.0 shows he sucual quanes calculaed fo he 44Å 44Å nanood afe hemalzaon a 300K. The hydosac pessue on he nanood s 80MPa. Peaks n he bond angle and pa-dsbuon funcons have boadened due o hemal effecs, 69

89 compae wh Fgues 4.0 a-d. In Fgue 4.a, he neaes neghbo peaks n Cd-Se pa dsbuon funcon ae sll ceneed abou.63å, 5.046Å, 6.67Å, and 9.97Å. Se-Se, and Cd-Cd pa dsbuon funcons also exhb s -4 h neaes neghbo peaks abou 4.30Å, 7.45Å, 8.604Å, and.38å. The bond-angle dsbuon n Fgue 4.0d dsplays peaks abou 09.4º. Coodnaon plos show ha aoms nsde he nanood sll have 4-coodnaon and he aoms a he suface have 3 and 4- coodnaons. Thus, he S : nanood s sll cysallne afe he fs phase of he smulaon. Shell-Resolved Sucual Analyss Fgue 4.8: Cylndcal shell-slce analyss. A CdSe nanood s spaally esolved by concenc cylndcal shell-slces. Shells ae numbeed n nceasng ode fom nsde o ousde. Slces ae numbeed n nceasng ode along he z-axs of he nanood. A shellslce s an nesecon beween a shell and a slce. Sucual quanes ae calculaed fo aoms n each shell-slce sepaaely, allowng sucual dffeences beween dffeen egons n he nanood o be monoed and compaed dung he phase ansfomaon. WZ cysal sucue s chaacezed by a bond-angle peak a 09.4º, as shown n Fgue 4.9 d and by he Cd and Se coodnaons of 4 as shown n Fgue 4.9 e. 70

90 Sucual Analyss of S :, Psne 44Å 44Å Nanood Sysem a b c d Fgue 4.9: Spaally esolved sucual analyss of psne wuze sysem a T~0K, P~0GPa NVE. a Cd-Cd pa dsbuon funcon. b Se-Se pa dsbuon funcon. c Cd-Se pa dsbuon funcon. d bond-angle dsbuon. e coodnaon hsogam. The cuves n each plo ae coloed ed, blue, geen, coespondng o he s nne-mos, nd mddle and 3 d ouemos shells, especvely. e 7

91 Sucual Analyss of Themalzed 44Å 44Å Nanood Sysem a b c d e Fgue 4.0: Inal wuze sucue a T300K and P80MPa. Peaks ae boadened by hemal flucuaons alhough.he S : nanood emans n he wuze sucue. 7

92 Sucual Analyss of S :, 44Å 44Å Nanood Sysem n HS Phase a.5 GPa a b c d Fgue 4.: Inemedae 5-coodnaed sae a T300 and P.5-.5GPa. The nanood begns sucual ansfomaon above P.0 GPa. Fve-coodnaed phase, as seen n DFT-MD calculaons Shmojo e al. s also found hee as ndcaed by he peak a 0º n he bond angle dsbuon and by fve-fold aomc coodnaon. e 73

93 Sucual Analyss of S :, 44Å 44Å Nanood n Rocksal Phase a 4.0 GPa a b c d e Fgue 4.: Fnal ock-sal confguaon of S : CdSe nanood a T300K and P4.0GPa. 74

94 In smulaons by Shmojo e al. an nemedae fve-fold coodnaed sucue was obseved dung he ansfomaon fom he wuze o he ocksal sucue n bulk CdSe as shown n Fgue 4. d. The sucue foms fom hexagonal basal planes of Cd and Se aoms n he WZ sucue shfng alenavely along he c axs o fom a fla plane. The esulng sucue s a sacked fla honey-comb lace nomal o he z-axs. Fom he calculaons, Shmojo e al., found seveal pahs beween wuze and wo ypes of ocksal phases, RS-I and RS-II. The calculaed enhalpy cuves ndcaed he HS phase as a measable sae lyng beween wuze and ocksal phases. They found ha among he seveal possble pahs fom wuze o ocksal, he mnmal enhalpy pah s o he RS-II phase passng hough he HS phase; see Fgue 4.. Enhalpy cuves fo ansons fom wuze o RS-I phase ae n yellow. The ed cuves show he enegy baes fom wuze o RS-II. The angle and ccle makes epesen he sysem passng hough and no passng hough he HS phase, especvely. We fnd ha ou nanood sysems also pass hough he HS phase dung ansfomaon. As shown n Fgue 4., hee s a peak n he bond angle dsbuon aound 0º and he sysem s populaed pedomnaely by 5-fold coodnaed aoms, boh chaacescs of he HS sucue. Fgue 4. shows esuls fo he S : sysem a 4.0 GPa. The cysal sucue of he nanood has compleely ansfomed fom wuze o ocksal phase. Calculaons fo Cd-Se pa dsbuon funcon, g, show s -4 h neaes-neghbo peaks a.7å, 4.8 Å, 6.Å, and 8.3 Å, especvely. In Cd-Cd/Se-Se pa-dsbuon funcons, he fou neaes-neghbo peaks ae a 3.9Å, 5.6Å, 6.6Å, and 7.8Å, especvely.. These esuls ae conssen wh he ocksal lace sucue. Plos of aomc coodnaon show 6-75

95 coodnaed aoms nsde he nanood and 4-fold and 5-fold coodnaed aoms a he suface. Fgue 4.3 Enhalpy as a funcon of aomc confguaon η. The wuze WZ and ocksal RS sucues coespond o η 0 and, especvely. The yellow-open and edsold symbols show he enhalpy changes calculaed along he ansfomaon pahs fom WZ o RS-I and fom WZ o RS-II, especvely. The ccles coespond o he pahs lnealy nepolang he aomc coodnaes n he WZ and RS sucues. Fo he lnes shown by angles, he enhalpy of he honeycomb-sacked HS sucue s shown by η 0.5. The peaks n bond angle dsbuons a 90 and 80 fo all hee shells also ndcae he ocksal cysal phase. Fgue 4.4 shows snapshos of he 44Å 44Å nanood a dffeen pessues dung he ansfomaon. Columns a and b show op along nanood s z-axs and sde pependcula o he nanood s z-axs vews of he nanood. Numbes -5 along he sde denoe vaous sages of pogess dung he smulaon. Fame shows he nanood befoe hemalzaon n psne wuze sucue. Fame shows he nanood afe hemalzaon a T300K and P80MPa. In fame 3, he nanood s a oom empeaue and unde a pessue of.0gpa. The HS measable sae of he nanood s 76

96 shown n he fouh pa of he fgue. Fame b shows how he nanood fs conacs along he z-axs. Hee, bonds ae fomed paallel o he z-axs as he wuze b-layes nomal o he z-axs flaen no one plane. Fame 5 shows he nanood a 4.0GPa, afe bonds n he x-y plane of he nanood have fomed o ceae he fnal ocksal cysal sucue. Fgues 4.5 and 4.6 show he ansfomaon sequence fo he 44Å 88Å CdSe nanood, jus as was done fo he pevous S : smulaon. In hese pcues, he numbe ndcaes ncease of pessue and a and b show he op and sde vews of he nanoods, especvely. Fgue 4.5 a and Fgue 4.6b show he nanood befoe hemalzaon n he psne cysallne fom. Fgue 4.6 a and Fgue 4.6b show he nanood afe hemalzaon a 300K and 80MPa. Fgue 4.6 3a and Fgue 4.6 3b show he conacon of he nanood along he z-axs and fomaon of he HS nemedae sae. Fgue 4.5 4a and Fgue 4.6 4b show he nanood a 3.0 GPa afe s cysal sucue has compleely ansfomed o he ocksal phase. a b 0 GPa 0 GPa a b 80 MPa 80 MPa fgue connued 77

97 a3 b3.0 GPa.0 GPa a4 b4.0 GPa.0 GPa a5 b5 4.0 GPa 4.0 GPa Fgue 4.4: Snapshos of he ansfomaon sequence fo he 44Å 44Å CdSe nanood fom MD smulaon. Column a shows he wuze-o-ocksal ansfomaon along [000] and column b he coespondng vew pependcula o he z-decon. Rows -5 show he nanood a dffeen pessues. a a 0.0 GPa 0 80 MPa 80 fgue connued 78

98 3a 4a.5 GPa 3.0 GPa Fgue 4.5: Snapshos of he ansfomaon sequence fo he 44Å 88Å CdSe nanood. The wuze-o-ocksal ansfomaon s shown along he [000] decon. b b 0.0 MPa 0 3b 80 MPa 80 fgue connued 79

99 3b.5 GPa 4b 3.0 GPa Fgue 4.6: Snapshos of he ansfomaon sequence pependcula o he z-decon fo he 44Å 88Å CdSe nanood. Sde vews of he nanood a dffeen pessues fom 0 GPa o 3.0 GPa ae shown hee. 0 GPa 0.8 GPa fgue connued 80

100 GPa 3.5 GPa Fgue 4.7: Snapshos of he ansfomaon sequence along [000] fo he S :4 nanood. 0 GPa 0.8 GPa fgue connued 8

101 3 3.0 GPa GPa Fgue 4.8: Snapshos of he S :4 nanood show he ansfomaon sequence pependcula o he z-decon a dffeen pessues fom 0GPa o 3.5 GPa. The ansfomaon sequence fo he 44Å 76Å S :4 CdSe nanood fom op and sde vews s shown n Fgue 4.7 and Fgue 4.8 especvely. Pas hough 4 n each fgue show he nanood a nceasng pessues dung he smulaon. The nal seup fo he nanood s shown n pa. Pa shows a snapsho of he nanood afe has been hemalzed a 300K and 80MPa. In pa 3 he nanood s shown a an nemedae sage and pa 4 shows he nanood afe sucual ansfomaon a 3.5GPa. The pcues n Fgue 4.9 show op vews of he ansfomaon sequence fo he S : nanood. Pa of he fgue s an mage of he nanood n pue cysallne fom befoe he smulaon begns. Pa of he fgue shows a vew of nanood fom he op afe has been hemalzed a 80 MPa. In pa 3, a.0gpa, he sucual 8

102 ansfomaon n he nanood has begun. The pcue n Fgue 4.9 pa 4 shows he nanood jus befoe complees ansfomaon. 0 MPa 80 MPa 3 4.0GPa.0GPa 5.5GPa Fgue 4.9: Snapshos of he ansfomaon sequence fo he 44Å 58Å CdSe nanood. Fgues -5 show he wuze-o-ocksal ansfomaon along he [000] decon of he nanood as he pessue nceases o.5 GPa. 83

103 Fgue ae sde vew snapshos of he S : nanood dung smulaon. In he nanood s shown befoe he smulaon sas. Fgue 4.0 shows he nanood afe hemalzaon; 3 shows sgnfcan conacon n he nanood along he z- axs; 4 shows he nanood along he z-axs jus befoe he ansfomaon s compleed; and 5 shows he nanood afe complee sucual ansfomaon a.5gpa. 0 GPa 80 MPa 3.0 GPa GPa.5 GPa Fgue 4.0: Snapshos of he ansfomaon sequence fom he 44Å 58Å CdSe nanood smulaon. These snapshos show he wuze-o-ocksal ansfomaon pependcula o he axs of he nanood as pessue nceases o.5 GPa. 84

104 Sngle Doman Sucual Phase Tansfomaon Sucual phase ansfomaons n all smulaons esuled n sngle cysal ocksal sucues wh columns of aoms aanged n peodc aays fom end o end n each nanood as a sngle cysal un. Fgue 4. shows sde and op vew mages of he nanood n smulaons S :. In a, he coss-secon of he nanood has changed shape fom s ognal hexagonal shape, oulned n geen, o an egula shape. The nanood also conacs along he z-axs o ~75% of s ognal lengh, see b. The ansfomaon esuls n he fomaon of a sngle doman as boh vews show ocksal phase peodcy fom end o end. Fgues 4. hough 4.4 show ha S :, S :4, S : nanoods ansfomed smlaly o S : hey change coss-seconal shape, conac ~5% along he z-axs, and fom sngle-doman ocksal cysals. a b Fgue 4.: Snapshos of he nanood afe sucual ansfomaon n smulaon S :. In a, he op vew of he egula shape of he coss-secon afe ansfomaons compaed wh s ognal hexagonal coss-secon oulned n geen. A sde vew of he nanood, shown n b, llusaes he exen o whch he nanood conacs along he z- axs. Fgue 4.5 a shows he S : nanood n he wuze cysal fom befoe he onse of he smulaon. Fgue 4.5 b shows he ansfomed nanood afe he smulaon has ended. The sucual ansfomaon pah can be denfed by compang he bondng geomees beween he wo confguaons. 85

105 a b Fgue 4.: Top and sde vews of he nanood fom smulaon S : ae shown above. The nanood coss-secon becomes egula and s lengh along he z-axs conacs dung sucual ansfomaon. The aoms n he nanoods ae aanged n peodc aays as can be seen fom boh vews, demonsang ha he nanood s a sngle ocksal doman. a b Fgue 4.3: Snapshos fom smulaon S :4. A sngle cysal ocksal doman foms n he mddle of he nanood. The doman exends ou o ~7 aomc layes fom he end sufaces whee dsode begns due o hgh-enegy sufaces. Hee, he nanood undegoes ansfomaon fom he WZ o RS-II phase as obseved by Shmojo e al. fo bulk CdSe. We fnd he same WZ o RS-II mechansm n S : and S : nanoods. The mechansm fo ansfomaon n S :4 could no be deemned because he hgh enegy sufaces a end faces become dsodeed dung ansfomaon. 86

106 a b Fgue 4.4: Snapshos of he S :4, nanood show ha has become a sngle ock-sal doman afe sucual ansfomaon. a The nanood has one shape along s shaf fom end o end. The end faces eman fla as shown n b. a b Fgue 4.5: Snapshos of he wuze-o-ocksal ansfomaon mechansm. S :, nanood befoe and afe ansfomaon. a Psne WZ nanood a T ~ 0K, P ~ 0GPa b Tansfomed nanood n he RS phase a T 300K and P 4GPa. The elave oenaon beween he nal WZ and fnal RS laces ndcaes WZ o RS-II mechansm. 87

107 CHAPTER 5 REVERSE STRUCTURAL TRANSFORMATIONS IN CADMIUM SELENIDE NANO-RODS 5. Backgound Ths chape enals he esuls of evese phase ansfomaon n CdSe nanoods. Sold-sold phase ansons ae an mpoan aea of eseach n moden eleconcs echnology. Revesble phase-change echnologes have enabled e-weable magneoopcal ecodng meda and sensos. The capably o manage damac changes n he behavo o fom of nanosucued sysems wh one conol vaable holds pomse fo novel echnologcal applcaons. Fo example, sma maeals ha eac o exenal vaables such as empeaue, elecc o magnec feld, lgh o sess, could be used n nano-szed sensos and acuaos o enable hem o espond o dynamc envonmenal condons. Such devces could seve as dug-delveng mechansms equpped wh specal elease sysems wh age delvey o gealy educe o elmnae dug sde effecs. Ohe applcaons nclude emplaes fo he gowh of naual ssues and sucual maeals ha senghen dung sevce when subjeced o sess [68]. 5. Facue Mechancs Facue mechancs s a sub-feld of maeal physcs ha ncopoaes pncples of sess, san, elascy, plascy and cysal defecs o pedc sucual falue n maeals. Facue s geneally defned as he sepaaon of a sold maeal no sepaae peces due o sess. Facue can occu n a numbe of dffeen ways dependng on he ype of maeal, he condons on he maeal and ohe envonmenal facos. All foms of facues ae classfed as ehe ducle o ble. 88

108 Ble facue occus n maeals subjeced o ensle sess dung whch hee s no plasc defomaon of he maeal. In ble facue, cacks popagae by cleavage wheen cack sufaces ae fomed by sepaang planes of aoms. Meals, ceamcs and semconducos ae all maeals ha may suffe ble facue a suffcenly low empeaues. a b c Fgue 5.: Ble maeal subjeced o a sess σ. b The sess causes cacks n he sample o gow o popagae. The sample suffes cleavage dung cack popagaon as planes of aoms ae peeled apa by cack. c Ble facue sufaces. In 9, Gffh noduced he fs quanave elaon descbng facue. He deved a ceon fo cack popagaon fom he assumpon ha he enegy dsspaed by cack s equal o he suface enegy of he wo newly fomed cack sufaces. He showed ha a ccal sess, σ c, s equed fo a cack o popagae hough a ble maeal: σ c Eγ s πa 5. 89

109 Ths expesson s known as he Gffh s ceon, whch depends on Young s modulus of elascy E, he cack lengh a and he suface enegy γ s. Gffh s expesson fo ccal sess woks easonably well fo ble maeals, bu mus be exended o descbe ducle facue n maeals. Snce mos maeals, even hose maeals classfed as ble, expeence some plasc defomaon dung facue, Gffh s ceon s only an appoxmae descpon fo facue, and mus be exended o descbe ducle facue. a b c Fgue 5.: A sample of ducle maeal unde a ensle sess σ, b exhbs neckng dung whch he coss-secon naows n one secon of he nanood. c Neckng connues unde he nfluence of he appled sess unl he nanood facues. Cosssecon of he sample naows as long as he sess s appled unl dsconnecs no moe han one pece. Ducle facue, nvolves plasc defomaon and s chaacezed by neckng as shown n Fgue 5.. Neckng s localzed flow ha akes place n one secon of a sample dung whch he coss-secon of he sample naows as long as he sess s appled unl facues. 90

110 Ducle facue, nvolves beakng aomc bonds as well as defomaon of he maeal. Gffh s ceon does no wok because only akes no consdeaon he enegy equed fo beakng aomc bonds beween planes of aoms. In he 950 s Iwn added a em γ p o he Gffh s ceon o accoun fo he enegy ha goes no defomng he maeal. The ccal sess fo cack popagaon hen becomes, γ + γ E s p σ c 5. πa whee γ p epesens he plasc defomaon enegy. 5.3 Expemen on Facung of CdSe Nanoods dung Compesson Alvsaos e al. have pefomed expemens ha exhb facue of CdSe nanoods [69]. Nanocysals below 50Å n damee subjeced o cyclc pessue have been shown o undego evesble sngle doman sucual phase ansfomaons n expemens, whle exended solds exhb evesble mul-doman ansfomaons. They have suded 40Å damee nanoods wh wdh-o-lengh aos angng fom : o :0 and epoed a ccal sngle-o-mul doman heshold beween nanoods wh dmensons 44Å 00Å and 44Å 60Å aos ~: and :3. They use TEM o examne he nanoods afe one cycle downsoke and upsoke and obseve he long nanoods <400Å suffe ble facue. The amoun of boadenng n he TEM dffacon paens afe he upsoke ndcaes ha he aveage nanood lengh s less han one-half of he aveage nanood lengh befoe he fs cycle. Ths ndcaes ha some nanoods beak a moe han one place along he shaf. 9

111 5.4 MD Smulaons of Revese Sucual Tansfomaon Smulaon Seup Inal confguaons fo he upsoke smulaons ae he fnal confguaons fom he down-soke smulaons fo S :, S :, S :4, and S :, n whch he 4 nanoods have undegone sucual ansfomaon fom wuze o ock-sal phase. Hee we denoe he upsoke smulaons as S U-:, S U-:, S U-:4, and S U-:, coespondng o he fowad smulaons S :, S :, S :4, and S :, especvely. Each nanood s n sngle cysal ock-sal fom as descbed n Chape 4. A he begnnng of he upsoke ansfomaon, he lenghs of he nanoods ae ~75% of he lenghs po o he fowad sucual ansfomaon. The end face of he nanood fom smulaon S :4 sepaaes b-laye n he 000 planes of wuze cysal. Thus, as a hgh enegy suface, changes sucue dung he fowad ansfomaon n conas o he end faces of he nanoods fom smulaons S :, S :, S :, whch eman aomcally fla as cu fom he wuze cysal. Nanood coss-secons ae no longe hexagonal bu egula n shape, havng damees of oughly 44Å, as depced n Fgue 5.3. A compessed LJ flud suounds he nanoods. The esmaed densy of he LJ flud s ρ~0.8å -3 ρ * ~0.60 and T300K T *.0. MD cell coss-secons n he x-y decons ae ~6% of he nal 65Å 65Å aea. The MD cells conac along he z-axs by facos beween 0.5 and As dscussed n Chape 4, he amoun of he LJ flud was chosen so as o peven he nanoods fom neacng wh he mo mages va peodc bounday condons. 9

112 a b S : S : c d S :4 S : Fgue 5.3: Snapshos of CdSe nanood coss-secons fom smulaons a S :, b S :, c S :4, and d S : afe sucual ansfomaon o ocksal phase. The coss-secons of he nanoods change fom hexagonal o egula shapes, whle he end faces eman aomcally fla n he peodc wuze sucue. Each smulaed sysem s n hemodynamc equlbum a 300K. The nal hydosac pessue fo each smulaon sas above he especve ansfomaon pessue n he pevous fowad ansfomaon smulaons. Deals on he nal confguaon fo each smulaon ae gven n Table

113 Table 5.: Inal confguaon paamees fo upsoke smulaons. Smulaon S U-: S U-: S U-:4 S U-: Rod damee Å Rod lengh Å ~35 ~79 ~64 ~484 MD cell dm. Å, Å, Å 94, 9, 84 84, 94, 34 79, 8, 94 84, 75, 85 Hydosac Pessue GPa LJ flud denses Å # of Cd aoms # of Se aoms # of LJ aoms Toal # me seps Toal CPU mehous ~67 ~800 ~88 ~389 Smulaon Pocedue Each upsoke smulaon, S U-:, S U-:, S U-:4, and S U-:, begns wh he sysem a hemodynamc equlbum, T300K, P>P fowad ansfomaon pessue. All MD smulaons epoed n hs chape ae pefomed n he NPT ensemble. The upsoke smulaon poceeds by a smla scheme as he down-soke smulaon. The basc schedule nvolves decompesson and elaxaon uns execued n andem and epeaed unl complee evese ansfomaon o he fnal pessue of 0.5 MPa s eached as llusaed n he flow cha below. 94

114 6-coodnaed sysem a maxmum pessue Decease pessue a 0.5 GPa / 5,000 NPT Decompessed sysem Hold pessue consan pessue fo 0,000 NPT Relaxed confguaon a new pessue Repea unl "zeo" pessue Hold sysem a "zeo"pessue fo 00,000 NPT Sysem a "zeo" Pessue Repea unl 4-coodnaed aoms domnae sysem 4-coodnaed sysem Fgue 5.4: Smulaon schedule fo he evese ansfomaon Decompesson uns educe he sysem pessue a a ae of GPa/ ove 0,000 fs. Relaxaon uns wee caed ou ove 000. As he densy of he LJ aoms deceased wh loweng pessue, he ae of change of he MD cell volume nceased. Ths equed slowng down he schedule o avod unealsc affecs on he nanood. Ths wll be explaned lae. 95

115 Smulaon Resuls fo S U-: Two S U-: smulaons, S U-:a and S U-:b, wee pefomed as banches of S U-:. Mophologcal changes as well as cysallogaphc changes wee obseved n boh S U-: smulaons. Pa a of Fgue 5.5 shows he esul fo he S U-:a smulaon, whee he coss secon of he nanood appeas sphecal n shape. The bond-angle dsbuon fo he nanood a he end of S U-:a s boad angng fom 75 o 80 whch ndcaes a mxue of dsoed cysallne phases. The hsogam of coodnaons n Fgue 5.5 c shows ha mos of he aoms n he cluse ae 4-coodnaed and ha he numbe of 5- coodnaed aoms s an ode of magnude smalle han he numbe of 4-coodnaed aoms. a b c Fgue 5.5: Fnal esul of 44Å 44Å evese ansfomaon, S U-:a. a Snapsho of he nanood a 80MPa and ~40,000 afe fowad ansfomaon. b bond-angle dsbuon, and c hsogam of aomc coodnaons. 96

116 A second smulaon, S U-:b, was pefomed whee he empeaue was kep below 800K o peven he nanood fom melng/defomng. Resuls ae shown n Fgue 5.6. The hsogam of aomc coodnaon n Fgue 5.6c shows he nanood s pedomnaely 4-coodnaed, bu wh moe 5-coodnaed aoms han n he fs smulaon, S U-:a. The bond-angle dsbuon shows he nanood eans ocksal RS sucue. The egula coss-secon of he nanood changes o squae as he nanood becomes cubc. The change n he nanoods coss-secon o squae only occued n he nanood wh aspec ao of :. a b c Fgue 5.6: Fnal esul of he 44Å 44Å evese ansfomaon, S U-:b. The empeaue was scaled o say below 900K. The hexagonal coss-secon of he nanood becomes ecangula. The nanood s nealy cubc. a Snapsho of he nanood a 80 MPa and 500,000 afe fowad ansfomaon, b bond-angle dsbuon, and c hsogam of aomc coodnaon. 97

117 Resuls fo Smulaon S U-: Smulaon S U-: exhbs esuls smla o hose fo S U-:. In Fgue 5.7 b, he bond-angle dsbuon ndcaes ha he nanood s pmaly n he ocksal phase, alhough Fgue 5.7 c shows ha mos of he aoms n he nanood have become 4-fold coodnaed. The evese ansfomaon has saed, bu as wh he x nanood, he me scale fo evese ansfomaons appeas o be much longe han ha fo he fowad ansfomaon. Ths esul comes 3,65,540 mes seps afe he fowad ansfomaon, whch s oughly 75 days of CPU me! a b c Fgue 5.7: Fnal esul of he 44Å 88Å evese ansfomaon. a Snapsho of he nanood a 80MPa aken 500,000 afe fowad ansfomaon. b Bond-angle dsbuon and c dsbuon of aomc coodnaons. 98

118 Smulaon Resuls fo S U-:4 Smulaon S U-:4, was un fo 880,870. The esuls ae smla o hose of smulaons S U-: and S U-:. Fgue 5.8 c shows ha he numbe of 4-coodnaed aoms exceeds he numbe of 5- and 6-coodnaed aoms. The dffeence beween he numbe of 4- and 5-coodnaed aoms s geae han hose n he fnal uns fo S U-:4, S U-: and S U-:. Ths also suggess ha he evese ansfomaon wll connue o pogess f he smulaon s un longe. a b c Fgue 5.8: Fnal esuls fo he evese ansfomaon n he 44Å 76Å nanood. a Snapsho of he nanood aken 500,000 afe fowad ansfomaon a 80MPa. b Bond-angle dsbuon and c hsogam of aomc coodnaons. 99

119 Smulaon Resuls fo S U-: The nanood complees evese ansfomaon n smulaon S U-:. Thee ae howeve seveal alenave oucomes fom paallel expemens wheen he x nanood exhbs bendng, facung, and banch gowh. Fgue 5.9 dsplays flowcha of hese smulaons. Fgue 5.9: Thee oucomes of he upsoke smulaon fo he S U:, 44Å 58Å nanood. The upsoke smulaon begns wh he fnal RS cysal confguaons fom he pecedng down-soke smulaon. Expemens wh dffeen empeaue-pessue schedules esuled n cysallogaphc ansfomaon of he nanood as well as mophologcal ansfomaons ncludng knkng and facung. We wll dscuss S U-: as hee dffeen sub-smulaons expemens S U-:a, S U- :b, and S U-:c whee he nanood beaks, knks, and complees evese ansfomaon, especvely. The facung sequence of he nanood n smulaon S U-:a s shown n Fgue 5.0. The nanood exhbs neckng befoe facue, ndcang ducle facue. Fgue 5. shows a snapsho of he S U-:b nanood afe coolng fom a pecedng un whee he nanood had exceeded 800K and had begun o neck. Dung coolng he nanood began o heal whee he neckng had occued. Aoms n he necked egon aggegae o fom an am exendng pependculaly fom he z-axs of he nanood. 00

120 a Elapsed 0 T Cd,Se,Sys 3K, 309K, 300K P 4.0 GPa b Elapsed 09,500 T Cd,Se,Sys 644K, 65K, 87K P.3 MPa c Elapsed 3,500 T Cd,Se,Sys 770.K, 77K, 83K P.98 MPa d Elapsed 9,500 T Cd,Se,Sys 897K, 833K, 69K P MPa e Elapsed 7,500 T Cd,Se,Sys 80K, 739K, 8K P MPa Fgue 5.0: The sequence of mages show neckng a seveal places along he shaf of he 44Å 58Å nanood unl dsconnecs no wo peces. a Shows he confguaon a he end of he fowad ansfomaon a 4GPa and 300K. b Shows he nanood lae afe some amoun of decompesson a a empeaue of ~ 600K and a pessue of MPa. c The nanood begns o show noceable neckng along he shaf. The neckng becomes moe ponounced d unl complee sepaaon akes place e. 0

121 Fgue 5.: A pouson pependcula o he axs of he nanood esuls dung he upsoke afe he nanood empeaue nceases and s hen cooled down. The ably o sysemacally manpulae shapes of noganc nanocysals s an mpoan goal of moden chemsy and maeal scence. The shape and sze of noganc nanocysals conol he wdely vayng eleccal and opcal popees [70,7,7]. Reseaches have suded shape conol n he synhess of soluble and pocessable CdSe nanocysals of vaous shapes ncludng eadops, aows and eapods n whch ao of sufacans, njecon volume and me-dependen monome concenaon ae he conollng facos. I would be neesng o see f apd heang and coolng can also be used as shape-conollng faco n acual expemens and how smulaon could ad hose expemens. Fgue 5. shows anohe case of he nanood healng afe neckng. One pa of he nanood knks a a neckng pon o fom a gh angle, whle he es of he od bends no a cuve a he ohe end. The neckng and facung of he nanoods n smulaons S U-:a and S U-:b ae afacs of he mehod used o smulae NPT dynamcs n he upsoke sequence. In smulaon S U-:c, he nanood eves almos compleely o a 4-coodnaed cysal sucue. Fgue 5.3 shows a he bond-angle dsbuon and b hsogam of 0

122 aomc coodnaons fo he nanood n he fnal un of smulaon S U-:. Peaks n bondangle dsbuon ae ceneed a 90º, 09.4º, and 80º. Fgue 5.: The nanood knks a neckng pons afe coolng dung evese ansfomaon. The bond-angle dsbuon and aomc coodnaon plo n Fgue 5.3 ndcae ha moe han one cysal phase s pesen n he nanood. Shell-esolved calculaons fo bond-angles and aomc coodnaon n Fgue 5.4 show dffeen cysal phases pesen n each shell. In Fgue 5.4a, he ed cuve epesenng he bond-angle dsbuon n he nne mos shell eveals double peaks. The mddle shell suoundng he nnemos shell epesened by he cuve n blue dsplays a ponounced peak a 09.4º. The cuve n 03

123 geen shows a ange of angles wh peaks aound 90º and 80º ndcang ha mos of he aoms n he oue shell close o ocksal phase han wuze. a b Fgue 5.3: Fnal esul fo he evese ansfomaon n S U-: 44Å 58Å nanood. a Bond-angle dsbuon shows peaks aound 90, 09 and 80. The nanood conans boh ocksal and wuze cysal phases. b The hsogam of aomc coodnaon shows a majoy of 4-coodnaed aoms. Fgue 5.5 shows he bond-angle dsbuon fo he : nanood excludng 44Å of he nanood fom each end. Peaks n each shell ae now a 09.4º, whch ndcaes ha he evese ansfomaon has advanced o he mddle and coe of he nanood bu no o he ends ye. 04

124 a b Fgue 5.4: Fnal esuls fo he evese ansfomaon n he 44Å 58Å nanood. a Shell-esolved bond dsbuons show dffeen cysal phases n dffeen shells. The nne-mos shell, n ed, ndcaes mxed phases. The blue cuve peaks a 09, whch s chaacesc of wuze and znc-blende cysal sucues. The oue shell epesened n geen shows a domnan peak a 90, ndcang mosly he ocksal phase mxed wh he wuze phase. b Shows modfy 4-coodnaed aoms n he aomc coodnaon hsogam 05

125 Fgue 5.5: Peaks a 90 and 80 dsappea all he cuves when he aoms a he ends of he nanood ae excluded fom shell-esolved bond-angle calculaons. Peak a 09.4 n all shells ndcaes complee evese ansfomaon o wuze begns n he mddle of he nanood and speads owads he ends. Snapshos of he : nanood povde fuhe ndcaon of how he nucleaon has occued. In Fgue 5.6 coss-secons of he nanood cu a dffeen segmens along he shaf ae shown. Aoms wh 4, 5 and 6-coodnaons ae epesened n ed, geen, and blue, especvely. Aoms wh coodnaons less han 3 ae ndcaed n gay. Some 5-coodnaed aoms appea nea he end sufaces. Howeve, he 4-coodnaed aoms ed domnae he shaf of he nanood fom end o end, ndcang he compleeness of evese ansfomaon. fgue connued 06