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1 Tis is a repository opy of Extent of staking disorder in diamond. Wite Rose Resear Online URL for tis paper: ttp://eprints.witerose.a.uk/93345/ Version: Aepted Version Artile: Salzmann, CG, Murray, BJ and Separd, JJ (2015) Extent of staking disorder in diamond. Diamond and Related Materials, 59. pp ISSN ttps://doi.org/ /j.diamond , Elsevier. Liensed under te Creative Commons Attribution-NonCommerial-NoDerivatives 4.0 International ttp://reativeommons.org/lienses/by-n-nd/4.0/ Reuse Unless indiated oterwise, fulltext items are proteted by opyrigt wit all rigts reserved. Te opyrigt exeption in setion 29 of te Copyrigt, Designs and Patents At 1988 allows te making of a single opy solely for te purpose of non-ommerial resear or private study witin te limits of fair dealing. Te publiser or oter rigts-older may allow furter reprodution and re-use of tis version - refer to te Wite Rose Resear Online reord for tis item. Were reords identify te publiser as te opyrigt older, users an verify any speifi terms of use on te publiser s website. Takedown If you onsider ontent in Wite Rose Resear Online to be in brea of UK law, please notify us by ing inluding te URL of te reord and te reason for te witdrawal request. ttps://eprints.witerose.a.uk/

2 Extent of staking disorder in diamond Cristop G. Salzmann, a, * Benjamin J. Murray, b Jaob J. Separd a a Department of Cemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom b Institute for Climate and Atmosperi Siene, Sool of Eart and Environment, University of Leeds, Leeds LS2 9JT, United Kingdom * Corresponding autor. (Cristop G. Salzmann) Abstrat Hexagonal diamond as been predited omputationally to display extraordinary pysial properties inluding a ardness tat exeeds ubi diamond. However, a reent eletron mirosopy study as sown tat so-alled exagonal diamond samples are in fat not disrete materials but faulted and twinned ubi diamond. We now provide a quantitative analysis of ubi and exagonal staking in diamond samples by analysing X-ray diffration data wit te DIFFaX software pakage. Te igest frations of exagonal staking in materials previously referred to as exagonal diamond are below 60%. Te remainder of te staking sequenes are ubi. We sow tat te ubi and exagonal sequenes are interlaed in a omplex way and tat naturally ourring Lonsdaleite is not a simple pysial mixture of ubi and exagonal diamond. Instead, it is struturally best desribed as staking disordered diamond. Te future experimental allenge will be to prepare diamond samples beyond 60% exagonality and towards te so far elusive perfet exagonal diamond. Keywords: diamond; Lonsdaleite; diffration; staking disorder; memory effets 1

3 1. Introdution Te ommon form of diamond is ubi. Yet, a metastable exagonal polymorp as been identified in fragments of te Canyon Diablo meteorite from te nortern Arizona desert and oter impatites.[1, 2] To onour te aievements of te rystallograper Katleen Lonsdale exagonal diamond as been named Lonsdaleite.[1] Syntetially, exagonal diamond an be prepared, for example, by eating grapite in te GPa range.[3-8] Tere is onsiderable urrent interest in te targeted preparation and pysial properties of exagonal diamond as it as been predited to display superior meanial properties, su as ardness and ompressive strengt, ompared to its ubi ounterpart.[9, 10] Furtermore, ubi and exagonal diamonds are expeted to ave different band gaps and dieletri properties.[11] Cubi and exagonal diamond bot onsist of sp 3 ybridized and terefore tetraedrallybonded arbon atoms. Bot allotropes ontain pukered layers of arbon atoms wit sixmembered rings in te armair onfiguration. Te differene between ubi and exagonal diamond lies in ow tese layers are staked on top of ea oter to build up te treedimensional rystal struture (f. Fig. 1). In ubi diamond, idential layers are staked on top of ea oter wit a sift alf way aross te diagonal of a six-membered ring. In exagonal diamond on te oter and ea layer is te mirror image of te previous layer.[12] Te strutural onsequene of tese different staking reipes is tat te six-membered rings linking te various layers are in te armair onformation in ubi diamond but boat-type in exagonal diamond. Consequently, ubi diamond onsists of only armair rings wereas exagonal diamond is a 50:50 mixture of rings in te armair and boat onformations, respetively. 2

4 (a) (b) ubi diamond exagonal diamond () staking disordered diamond Figure 1. Crystal struture projetions along te exagonal a axis for (a) ubi diamond, (b) exagonal diamond and () staking disordered diamond. Te diamond strutures are isostrutural wit ie if only te oxygen atoms in ie are onsidered. For ie, te exagonal polymorp (ie I) is te most stable at ambient pressure and a metastable ubi form (ie I) as been tougt to exist.[13] Te field as progressed in reent years and it as been sown tat wat was previously onsidered to be ubi ie is in fat staking disordered ie (ie Isd) ontaining variable frations of bot exagonal as well as ubi staking.[14-18] Te perfet ubi ie, ontaining only ubi staking, as so far not been identified. As predited for diamond, te differenes in staking ave pronouned effets on te pysial properties of ie inluding te vapour pressure,[19] rystal sapes,[20] spetrosopi properties[21] and potentially surfae emistry.[22] Originally, it was assumed tat exagonal and ubi diamonds often oexist wi elped understanding te observed X-ray diffration data.[1, 2] Yet, very reently it as been sown 3

5 by using ig-resolution eletron mirosopy tat wat as been originally lassified as exagonal diamond is in fat not a disrete material but faulted and twinned ubi diamond.[8] Following our reent work on ie we sow ere ow staking disorder an be araterised quantitatively in diamond samples on te basis of X-ray diffration data using te DIFFaX software pakage.[23] We tereby take so-alled memory effets, were te staking depends on te previous staking istory, into aount. Te aim is to fully desribe te staking disorder in te various samples of exagonal diamond tat ave been made so far and to sow wi experimental reipes lead to te most exagonal staking in diamond. 2. Metodology Diffration patterns of a ubi diamond sample in a 0.6 mm glass apillary were olleted on a Stoe Stadi-P diffratometer (Cu K, = Å) wit a Myten area detetor. Additional diffration data was taken from refs [6-8]. All diffration patterns were bakground-orreted using sifted Cebysev polynomials. For te alulation of diffration patterns of staking disordered diamond struture we used te DIFFaX software pakage[23] as previously employed for ie samples.[16, 18] To refine te a and lattie onstants, staking probabilities, profile parameters (u, v, w and GL ratio) and zero-sift we used our own MCDIFFaX programme wi embeds DIFFaX in a least-squares environment. 1 A typial refinements started wit te optimisation of te lattie onstants and te peak profile parameters. Tis was followed by refining te various staking probabilities. Typially, several tens of tousands of individual DIFFaX alls were needed before te refinements onverged. To prevent false minima, MCDIFFaX uses a Monte-Carlo-type parameter tat allows a defined fration of unfavourable moves to take plae. 1 Salzmann CG, 4

6 3. Results and Disussion Te arateristis of staking disorder in diamond are onveniently summarised wit a soalled stakogram as sown in Figure 2(a). In su a diagram, 1 st order memory effets are taken into aount; tese are desribed wit two independent staking probabilities. Te probability of ubi staking following a ubi event is given by wereas desribes te probability of a ubi event after exagonal staking. Sine te staking an only be eiter ubi or exagonal it follows tat = 1 and = 1. Te stakogram is a plot of against and te orresponding dependent probabilities, and, ave also been inluded. Te four orners of tis diagram define te end-member states. If and are bot zero te probability for ubi staking is zero and onsequently tis orner represents exagonal diamond. In turn, ubi diamond is defined by and bot equal to one. A pysial mixture of ubi and exagonal diamond implies = 1 and = 0 (i.e. = 1) wereas te stritly alternating ()x polytype is defined by = 0 (i.e. = 1) and = 1. Te latter two ases are extremes of 1 st order memory effets. Eiter one in a ertain staking sequene it as to ontinue indefinitely or it must be stritly alternating. Depending on te exat loation on te stakogram te 1 st order memory effets will be more or less pronouned. In fat, along te diagonal onneting te exagonal diamond orner wit ubi diamond and are equal wi means no memory effets. Te staking is purely random and independent of te previous staking istory. 5

7 (a) pysial mixture 0.1 ubi diamond = random staking = exagonal diamond () x polytype (b) () Figure 2. (a) Stakogram used for te strutural desription of staking disorder in diamond inluding 1 st order memory effets. Te blak solid line indiates strutures wit random staking wereas te dased lines desribe strutures wit a onstant exagonality. (b,) 6

8 Calulated powder diffration patterns (Cu K ) along te random staking as well as te 0.5 exagonality line. A quantity of primary interest to desribe a given staking disordered material is te fration of ubi staking wi is also alled te ubiity.[17] Tis parameter,, an be alulated from te 1 st order staking probabilities aording to. [1] For diamond in partiular, te interest lies more in te fration of exagonal staking and it is terefore sensible to define te exagonality of a sample,, wi is 1. Te stakogram in Figure 2(a) sows lines of onstant exagonality wi originate from te orner desribing te pysial mixture of polymorps. Stritly speaking, te exagonality is not defined in tis orner sine no switing between te two kinds of staking is allowed. In fat, division by zero would take plae in equation 1. Figure 2(b) sows alulated X-ray diffration patterns using DIFFaX along te randomstaking line ( = ) from exagonal to ubi diamond. Hexagonal diamond displays te arateristi trident between 40 and 50 degrees also observed for ie I in a different angle range. Te entral (002) peak persists as te fration of ubi staking inreases. Yet, broad and asymmetri diffration features develop on bot te ig as well as low angle side wi are te allmarks of staking disorder. Moving away from defined spots in reiproal spae for perfetly rystalline materials te staking disorder leads to streaking. Te rystallograpi rule is tat only Bragg peaks (kl) were ( k)/3 is not an integer number are affeted by staking disorder.[24] Generally, Bragg peaks wit greater values of l are more affeted by staking disorder.[25] For te ubi end member, one peak remains in te degrees angle range wi is te (111) refletion of te ubi system. Te effets of 1 st order memory effets are sown in Figure 2() were alulated diffration patterns along te 7

9 0.5 exagonality line are sown. Again, diffuse sattering is only observed for te staking disordered states, i.e. neiter for te pysial mixture nor te stritly alternating ()x polytype. We next analyse various experimental diamond diffration patterns wit MCDIFFaX wit te aim to pinpoint teir respetive positions in te stakogram. For tis, we additionally inlude 2 nd order memory effets wi are desribed by four independent staking probabilities,, and. Te orresponding 1 st order probabilities and onsequently te orresponding exagonality are alulated aording to 1 and [2]. [3] Figure 3(a) sows a diffration pattern of a natural diamond sample wit ~1 µm sized rystallites. Te diffration pattern is fitted very well wit = 1 and no signs of staking disorder ave been deteted. As previously for ie, we suggest tat a diamond sample is onsidered to be staking disordered if it ontains more tan one perent of te minor staking omponent.[16, 18] Below tis limit it is probably more appropriate to speak of staking faults, altoug tis boundary is arbitrary. 8

10 normalised intensity (a) Cu K (1) natural diamond (2) grapite, 1300 C, 15 GPa (ref. 7) (3) grapite, 1200 C, 20 GPa (ref. 6) grapite / degrees (b) Mo K (1) grapite, 2200 C, 19 GPa (ref. 8) normalised intensity (2) grapite, 1800 C, 20 GPa (ref. 6) (3) grapite, 800 C, 20 GPa (ref. 6) (4) Lonsdaleite Canyon Diablo Meteorite (ref. 8) / degrees Figure 3. Experimental powder diffration data of various diamond samples (dased blak lines) fitted wit MCDIFFaX (tik grey lines) and differene urves (tin grey lines). Te X- ray soures are Cu K ( = Å) for (a) and Mo K ( = Å) for (b). Several powder diffration patterns of staking disordered diamond from te literature were analysed next.[6-8] For tis kind of analysis it is essential to ave as mu diffration data above te trident angle range as possible and literature patterns were only tis range was sown were not analysed. Te staking disordered diamond samples were obtained by eating grapite to te pressures and temperatures indiated in Fig. 3.[6-8] Te issue of preferred orientation was addressed in ref. [6] and we were able to fit all teir diffration data. Te data from Fig. 3 in ref. [7] on te oter and was more problemati in tis respet and we ave only been able to fit one of teir diffration patterns. Comparing te diffration data 9

11 from ref. [7] wit te alulated patterns in Fig. 2 learly sows tat preferred orientation effets must ave ad an effet on some of te peak intensities. Tis is in fat not surprising onsidering tat igly-oriented pyrolyti grapite was used as te starting material in ref. [7] wereas in ref. [6], for omparison, fine grapite powders were used. Pattern (4) in Fig. 3(b) is tat of a Lonsdaleite sample reovered from te Canyon Diablo meteorite after dissolving te iron parts in dilute ydrolori aid.[8] Te diffration features of te Lonsdaleite sample are te broadest of all diffration patterns sown in Fig. 3 wi points towards smaller domain sizes. Te 1 st order staking probabilities obtained from fitting te diffration data of te various diamond samples are sown in Fig pys. mixture C 1800 C 2200 C 800 C 1300 C ubi diamond = exagonal diamond () x polytype GPa (ref. 8) GPa (ref. 6) GPa (ref. 7) Lonsdaleite CD meteorite (ref. 8) Figure 4. Stakogram wit te 1 st order memory staking probabilities obtained from MCDIFFaX fits of te diffration data sown in Figure Conlusions Several important points an now be made: (1) No sample displays a exagonality greater tan 0.6. Tis quantitative statement supports te onlusion from ref. [8] tat pure exagonal 10

12 diamond as so far not been prepared. (2) All analysed diamond samples lie above te random staking line in te stakogram. As disussed earlier, tis indiates a propensity in diamond to stay in a given staking sequene rater tan to alternate between exagonal and ubi staking. In tis respet, te situation is similar as previously observed for ie I.[16, 18] (3) All samples are quite far away from te pysial mixture orner wit te natural Lonsdaleite sample being te losest. Tis underpins te fat tat Lonsdaleite sould not be regarded as a mixture of ubi and exagonal diamonds but staking disordered diamond instead. (4) In ref. [8] it was stated tat Lonsdaleite is faulted and twinned ubi diamond. However, as it an be seen in Fig. 4, te Lonsdaleite sample is lose to te 0.5 exagonality line and terefore quite far away from te ubi diamond orner. Tis means tat Lonsdaleite is in our opinion best desribed as staking disordered diamond. (5) It is inaurate to desribe Lonsdaleite as exagonal diamond. In summary, we ave sown tat quantitative information about te staking disorder in diamond samples an be obtained from X-ray diffration patterns. It is interesting to note in tis ontext tat te igest exagonality was obtained for a sample wi was pressureannealed at 1200 C, a temperature between two oter experiments were more ubi samples were obtained.[6] Tis seems to igligt te very omplex kinetis of te formation of diamond from grapite. Te experimental allenge is now to prepare diamond samples well beyond te 0.6 exagonality line and towards te perfet exagonal diamond wi as been predited omputationally to be a igly extraordinary material.[9-11, 26] Aknowledgments We tank te Royal Soiety (CGS, UF100144) te Leverulme Trust (RPG ) and te European Resear Counil (FP7, ICE) for finanial support. Referenes 11

13 [1] Frondel C, Marvin UB. Lonsdaleite, a exagonal polymorp of diamond. Nature. 1967;217: [2] Hanneman RE, Strong HM, Bundy FP. Hexagonal diamonds in meteorites: Impliations. Siene. 1967;155: [3] Bundy FP, Kasper JS. Hexagonal Diamond - A New Form of Carbon. J Cem Pys. 1967;46: [4] Erskine DJ, Nellis WJ. Sok-indued martensiti pase transformation of oriented grapite to diamond. Nature. 1991;349: [5] Bundy FP, Bassett WA, Weaters MS, Hemley RJ, Mao HK, Gonarov AF. Te pressure-temperature pase and transformation diagram for arbon; updated troug Carbon. 1996;34: [6] Yosiasa A, Murai Y, Otaka O, Katsura T. Detailed Strutures of Hexagonal Diamond (Lonsdaleite) and Wurtzite-type BN. Jpn J Appl Pys. 2003;42: [7] Isobe F, Ofuji H, Sumiya H, Irifune T. Nanolayered diamond sintered ompat obtained by diret onversion from igly oriented grapite under ig pressure and ig temperature. J Nanomater. 2013;380136:1-6. [8] Német P, Garvie LAJ, Aoki T, Dubrovinskaia N, Dubrovinsky L, Busek PR. Lonsdaleite is faulted and twinned ubi diamond and does not exist as a disrete material. Nat Comm. 2014;5:5447:doi: /nomms644. [9] Pan Z, Sun H, Zang Y, Cen C. Harder tan diamond: superior indentation strengt of wurtzite BN and lonsdaleite. Pys Rev Lett. 2009;102: [10] Quingkun L, Yi S, Ziyuan L, Yu Z. Lonsdaleite - a material stronger and stiffer tan diamond. Sripta Mater. 2011;65: [11] Gao S-P. Band gaps and dieletri funtions of ubi and exagonal diamond polytypes alulated by many-body perturbation teory. Pys Status Solidi B. 2014;252:

14 [12] Nakamuta Y, To S. Transformation of grapite to lonsdaleite and diamond in te Goalpara ureilite diretly observed by TEM. Amerian Mineralogist. 2013;98: [13] König H. Eine kubise Eismodifikation. Z Kristallogr. 1943;105: [14] Kus WF, Bliss DV, Finney JL. Hig-Resolution Neutron Powder Diffration Study of Ie I. J Pys Colloq, C ;48: [15] Hansen TC, Koza MM, Kus WF. Formation and Annealing of Cubi Ie: I. Modelling of Staking Faults. J Pys: Condens Matter. 2008;20: [16] Malkin TL, Murray BJ, Brukno AV, J. A, Salzmann CG. Struture of Ie Crystallized from Superooled Water. Pro Natl Aad Si USA. 2012;109: [17] Kus WF, Sippel C, Falentya A, Hansen TC. Extent and Relevane of Staking Disorder in "Ie I". Pro Natl Aad Si USA. 2012;109: [18] Malkin TL, Murray BJ, Salzmann CG, Molinero V, Pikering SJ, Wale TF. Staking Disorder in Ie I. Pys Cem Cem Pys. 2015;17: [19] Silling JE, Tolbert MA, Toon OB, Jensen EJ, Murray BJ. Measurements of te Vapor Pressure of Cubi Ie and Teir Impliations for Atmosperi Ie Clouds. Geopys Res Lett. 2006;33:L [20] Murray BJ, Salzmann CG, Heymsfield AJ, Dobbie S, Neely RR, Cox CJ. Trigonal ie rystals in Eart's atmospere. Bull Amer Meteor So. 2015: /BAMS-D [21] Carr THG, Separd JJ, Salzmann CG. Spetrosopi Signature of Staking Disorder in Ie I. J Pys Cem Lett. 2014;5: [22] Ber P, Terziyski A, Zellner R. Aetone Adsorption on Ie Surfaes in te Temperature Range T = K: Evidene for Aging Effets Due to Crystallograpi Canges of te Adsorption Sites. J Pys Cem A. 2006;110:

15 [23] Treay MMJ, Newsam JM, Deem MW. A General Reursion Metod for Calulating Diffrated Intensities From Crystals Containing Planar Faults. Pro Roy So Lond. 1991;A433: [24] Pusey PN, van Megen W, Bartlett P, Akerson BJ, Rarity JG, Underwood SM. Struture of rystals of ard olloidal speres. Pys Rev Lett. 1989;63: [25] Weiss Z, Capkova P. Effet of staking disorder on te profile of te powder diffration line. In: Snyder R, Fiala J, Bunge HJ, eds. Defet and Mirostruture Analysis by Diffration. New York: Oxford University Press 1999, p [26] Kvasnin AG, Sorokin PB. Lonsdaleite Films wit Nanometer Tikness. J Pys Cem Lett. 2014;5: