Anomalous bond softening mediated by strain-induced Friedel-like oscillations in a BC2N superlattice

PHYSICAL REVIEW B 106, L060101 (2022) Le e Anomalous bond so ening media ed by s ain-induced F iedel-like oscilla ions in a BC2N supe la ice Teng ei Xu,1,2Zhao ui Liu,1,2Dominik Legu ,3,4and Rui eng Zhang 1,2,* 1School o Ma e ials Science and Enginee ing, Beihang Uni e si y, Beijing 100191, People’s Republic o China 2Cen e o In eg a ed Compu a ional Enginee ing (In e na ional Resea ch Ins i u e o Mul idisciplina y Science) and Key Labo a o y o High-Tempe a u e S uc u al Ma e ials & Coa ings Technology (Minis y o Indus y and In o ma ion Technology), Beihang Uni e si y, Beijing 100191, People’s Republic o China 3IT4Inno a ions, VSB-Technical Uni e si y o Os a a, 17. lis opadu 2172/15, 708 00 Os a a, Czech Republic 4Nano echnology Cen e , CEET, VSB-Technical Uni e si y o Os a a, 17. lis opadu 2172/15, 708 00 Os a a, Czech Republic (Recei ed 19 Ap il 2022; accep ed 26 July 2022; published 15 Augus 2022) The c ys al s uc u e o BC2N and he o igin o i s supe ha dness emain unde cons an deba e, hinde ing i s de elopmen . He ein, by e alua ing he x- ay di ac ion pa e n, he he modynamic s abili y a no mal and high p essu es o a se ies o BC2N candida es, he (111) BC2N2×2supe la ice (labeled R2u−BC2N) is iden i ied as he ealis ic c ys al s uc u e o he expe imen ally syn hesized BC2N. We u he e eal ha he s ain-induced F iedel-like oscilla ions domina es he p e e able slip sys ems o R2u−BC2N by d as ically weakening he he e ogenous bonds ac oss he slip plane and hus leads o i s ul alow disloca ion slip esis ance, which o igi- na es om he me alliza ion igge ed by he educ ion in ene gy sepa a ion be ween bonding and an ibonding in e ac ions o he so ened bonds. Ou esul s ule ou R2u−BC2N as he in insic supe ha d ma e ial su passing c-BN, whe eas he expe imen ally de e mined ex eme ha dness can be a ibu ed o he nanoc ys alline g ains glued by in e acial amo phous ca bon which p o ides a s ong ba ie o plas ic de o ma ion. These indings p o ide a iew o he longs anding issue o he possible s uc u e o expe imen ally obse ed BC2N, and es ablish a mechanism unde lying he s ain-d i en elec onic ins abili y o supe la ice s uc u es, p o iding guidance owa ds a ional design o supe ha d ma e ials. DOI: 10.1103/PhysRe B.106.L060101 Supe ha d B-C-N e na y compounds ha e gained signi - ican in e es because o hei unique he modynamic and mechanical p ope ies as well as nume ous po en ial applica- ions [1–6]. Howe e , un esol ed challenges ega ding hei heo e ical and expe imen al aspec s hinde hei de elop- men . The success ul syn hesis o single BC2N phase a high p essu e [7,8] ini ia ed a longs anding disag eemen ega d- ing i s ac ual c ys al s uc u e, i.e., whe he ca bon can be andomly dis ibu ed in BN la ice o ice e sa because hey a e he modynamically immiscible wi h mino la ice misma ch [9,10]. Al hough expe imen ally syn hesized BC2N was epo ed o possess ex eme ha dness, he o igin o i s su- pe ha dness emains unde deba e [9–13]. This is because he plas ici y migh shi om c ys al’s inside o in e ace when he c ys alline size app oaches he nanome e scale, e en ually inducing he s onges size e ec [6,14,15], ye hese ac s a e gene ally igno ed in p e ious s udies. Gene ally, wo classes o candida e s uc u es ha e been p oposed o i he expe imen ally syn hesized BC2Nby e- p oducing expe imen ally de e mined x- ay di ac ion (XRD) pa e ns and ollowing calcula ed o ma ion en halpy un- de ambien condi ions. The i s class includes subs i u- ional solid solu ions wi h diamondlike pa en la ices, e.g., BC2N−n(n=1–7) [16], -BC2N, z-BC2N, and z*-BC2N *Co esponding au ho : z @buaa.edu.cn [17,18]. Al hough hese s uc u es p o ide somehow con- sis ence o he XRD pa e ns, mino de ia ion s ill exis s, challenging he a ionali y o hese s uc u es, ye his ag ee wi h he high o ma ion en halpy o hese compounds unde ambien condi ions. To accoun o his de iciency, Chen e al. [12], Li e al. [19] and Liu e al. [20] successi ely sugges ed he second-class candida es, i.e., (111) supe la ice s uc u es o med by sequen ially s acking c-BN and diamond laye s, which ha e be e he modynamic s abili y han he solu ion ypes because o he immiscible ea u e be ween c-BN and diamond unde ambien condi ions. Howe e , he o ma ion en halpy unde ambien condi ions does no gua an ee he s abili y a high p essu e (i.e., he eal expe imen al p essu e ∼20 GPa o BC2N) which migh s abilize some no el un- s able/me as able s uc u es ia la ice dis o ion in ol ing he local bond wis ing, o a ing, and e en econs uc ion. Rega ding he o igin o he ex eme ha dness o BC2N, i is belie ed ha he diso de ing o BC2N solid solu ion may induce s eng h enhancemen owing o he andom dis- ibu ion o C-C bonds ha a e s onge han B-N bonds, and consequen ly his was used o explain he in insic su- pe ha dness o BC2N[17,18]. Un o una ely, his explana ion is only plausible i he s uc u e o BC2N is de e mined o be a solid solu ion, whe eas he ac ha he o ma ion en- halpy o BC2N solid solu ion is highe han ha o BC2N supe la ice unde ambien condi ions does no seem o sup- po his ype o s uc u e. In BC2N supe la ice, he pe iodic he e ogenous in e aces o med by he o de ed alignmen o 2469-9950/2022/106(6)/L060101(8) L060101-1 ©2022 Ame ican Physical Socie y XU, LIU, LEGUT, AND ZHANG PHYSICAL REVIEW B 106, L060101 (2022) FIG. 1. (a) Rela i e en halpy s p essu e o BC2N. bc-BC2N is aken as e e ence. (b) Simula ed XRD pa e ns o R2u−BC2Nand expe imen al pa e n ep oduced om Re . [8]. (c) C ys al s uc u e o R2u−BC2N. (d) Enla ged di ac ion peaks o simula ed XRD pa e ns o Rnu−BC2N(n=1–4) and expe imen al pa e n ep oduced om Re . [8]. B-N and C-C bonds may cause peculia elec onic beha io , e.g., cha ge pe u ba ions obse ed in nano winned c-BN [21] and TmN/SiNxnanocomposi e sys ems [22], which would also signi ican ly a ec he mechanical s eng h. Conside ing BC2N supe la ice is he mos ealis ic expe imen ally syn he- sized BC2N, we need o cla i y whe he BC2N is an in insic supe ha d ma e ial exceeding c-BN o no , and he o igin o i s expe imen ally obse ed supe io ha dness. This equi es a mo e ealis ic jus i ica ion based on bo h he in insic plas ic esis ance o cons i u e c ys al and he nano-size e ec s uned by s ongly bonded in e ace, because hese wo aspec s may compe e o se e as he majo plas ic and ac u e mechanisms o he expe imen ally syn hesized nanos uc u ed BC2N. He e we show ha supe la ice s uc u es main ain he op- imal he modynamic s abili y om no mal o high p essu es compa ed o any solid solu ions, and he R2u−BC2Nis u - he e i ied as he syn hesized BC2N phase no only based on i s s abili y, bu also by i s pe ec ly ep oduced XRD pa e n. By compa ing he plas ic desc ip o s, such as ideal s eng h [23,24] and Peie ls s ess [25,26], o R2u−BC2N and c-BN unde a ious de o ma ion condi ions, i is su p isingly ound ha he F iedel-like oscilla ions o alence cha ge densi y ema kably limi he disloca ion slip esis ance o R2u−BC2N by so ening he he e ogenous bonds ac oss he slip plane. Th ough la ge scale a omis ic simula ions, we demons a e u he ha he in e acial amo phous ca bon, a he han he c ys al’s inside, domina es he plas ic low in nanos uc u ed BC2N, p o iding a ealis ic explana ion o he measu ed ex- eme ha dness, albei weak bonding na u e o R2u−BC2N. The modynamic s abili y a no mal p essu e does no gua an ee he s abili y a high p essu e because p essu e will undamen ally change he s abili y sequence o di e - en phases depending on hei o ma ion en halpy. Howe e , since i s disco e y h ough high p essu e expe imen s, he possible s uc u es o BC2N we e p oposed based on he ene - ge ic s abili y unde ambien condi ions, while neglec ing he p essu e con ibu ions. To demons a e he eal candida e o BC2N, we sys ema ically in es iga ed he p essu e-dependen he modynamic s abili ies o wo sho pe iod (111) BC2N supe la ices (i.e., R1u-BC2N and R2u−BC2N), and hose o se e al subs i u ional solu ions p oposed in p e ious s udies [12,16,18,27–29] [Fig. 1(a)]. I is clea ly seen ha wo BC2N supe la ices possess he lowes o ma ion en halpy among all he p oposed candida es unde ze o p essu e, which is consis- en wi h heo e ical calcula ions [12,19,20]. As he p essu e inc eases om 0 o 200 GPa, he supe la ice R2u−BC2N emains he mos ene ge ically s able phase, wi h o ma- ion en halpies much lowe han hose o he solu ions and ∼0.07 eV/a om lowe han ha o R1u-BC2Na anex- pe imen al p essu e o 20 GPa [8]. The XRD pa e n o R2u−BC2N was simula ed wi h x- ay wa eleng h λ= 0.424 Å and g ain size d=5 nm, which a e iden ical o L060101-2 ANOMALOUS BOND SOFTENING MEDIATED BY … PHYSICAL REVIEW B 106, L060101 (2022) FIG. 2. (a) Tensile and shea s ess-s ain cu es o R2u−BC2N, and hose o c-BN along i s weakes ensile di ec ion and shea pa h. Inse s shows he key bond leng hs (ma ked as “L1” o “L4”) a ia ions in R2u−BC2Nandc-BN unde ensile and shea s ains. Snapsho s o de o med s uc u es a equilib ium, peak and ins abili y s ains: (b)–(d) R2u−BC2N and (e)–(g) c-BN unde ensile s ains, (h)–(j) R2u−BC2N and (k)–(m) c-BN unde shea s ains. The s uc u e ans o ma ion o B-N laye s in R2u−BC2N unde shea loading a e highligh ed as pale b own a eas. he expe imen al condi ions [8]. Ob iously, all he simula ed di ac ion peaks o R2u−BC2N show excellen ag eemen wi h he expe imen al ones [Fig. 1(b)] ha can be seen as he s acking o wo laye s o c-BN and wo double laye s o diamond as illus a ed in Fig. 1(c). I is in e es ingly ound u he ha he o al ene gy dec eases as he numbe o s ack- ing laye s (i.e., supe la ice pe iod) inc eases, sugges ing ha he longe pe iod s uc u es a e mo e ene ge ically a o ed han R2u−BC2N[9,12]. Ne e heless, he simula ed XRD pa e ns o he o he supe la ice candida es do no ma ch he expe imen al XRD pa e n, which shows wo signi ican de ia ions be ween 5 ° and 10 ° [Fig. 1(d)], disquali ying hem as BC2N candida es. The la ice s abili y o R2u−BC2Nis u he e alua ed. In Fig. S2, he phonon dispe sions a p es- su es om 0 o 20 GPa a e posi i e o all wa e ec o s in he whole B illouin zone, i.e., no imagina y modes a e p esen , indica ing i s dynamical s abili y a ze o and high p essu es. Addi ionally, he mechanical s abili y o R2u−BC2N is co - obo a ed by calcula ing i s single-c ys al elas ic cons an s a ze o and high p essu es, all o which sa is y he elas ic s abili y c i e ion [30,31] (Table S1 in he Supplemen al Ma e- ial [32], Re s. [14,24,25,31,33–63]). Hence, he supe la ice R2u−BC2N ep esen s he mos ealis ic c ys al s uc u e o he expe imen ally syn hesized BC2N, which suppo s he indings o Li e al. [19] albei he p essu e dependence being neglec ed o he la e . The in insic la ice and ex insic mic oscopic con i- bu ions [14] we e conside ed simul aneously o ob ain a ealis ic quan i ica ion o he mechanis ic o igin o he BC2N supe ha dness. We i s demons a e he o me by compa ing he calcula ed ideal s eng h, ideal clea age/slide s ess, and Peie ls s ess. Figu e 2(a) shows he aniso opic s ess-s ain ela ionships o R2u−BC2N unde a ious a ine ension and shea loadings. The ensile s ess o R2u−BC2N along he [001] di ec ion exhibi s he lowes peak alue (74.8 GPa), which is highe han ha o c-BN (65.4 GPa) along he [111] di ec ion. The bond leng h a ia ions unde he [001] s ain clea ly show ha , while he ou non-equi alen bonds [“L1” o “L4” in Fig. 2(b)] weaken wi h inc easing s ain and b eak a he same s ain o 0.13, “L3” (1.51 Å) and “L4” (1.50 Å) a e much sho e han he B-N bond (1.55 Å) in c-BN [“L1” in Fig. 2(e)] unde equilib ium condi ion. This cha ac e is ic is main ained o a wide s ain ange o 0.00–0.12, indica ing hese wo s onge bonds a e he main load-bea ing uni s e- sis ing he applied s ain, he eby p oducing a la ge ensile s ess han ha o c-BN. A simila s acking sequence be ween (001) o R2u−BC2N and (111) o c-BN allows simila b eak- age modes unde ensile de o ma ion [Figs. 2(d) and 2(g)], i.e., s ain-induced g aphi iza ion [64,65]. In e es ingly, along he weakes (001) [¯ 2¯ 10] shea pa h, he ideal shea s eng h o R2u−BC2N (62.7 GPa) is sligh ly lowe han ha o c-BN (65.3 GPa). This o igina es om he mo e p o ound so ening o B-N bond in i s B-N laye s han B-N bond in c-BN when s ain inc eases, i.e., he bond leng h o “L1” in R2u−BC2N [Fig. 2(h)] inc eased by 0.23 Å when he s ain inc eases om 0.00 o 0.24, whe eas ha o “L2” in c-BN inc eased by 0.10 Å [Fig. 2(k)]. In s a k con as o he la ice ins abil- i y mode o c-BN, “L1” in R2u−BC2N immedia ely b eaks L060101-3 XU, LIU, LEGUT, AND ZHANG PHYSICAL REVIEW B 106, L060101 (2022) FIG. 3. (a) Topological s uc u e o R2u−BC2N wi h he possible weakes clea age/slip planes ma ked as do ed lines. (b) GSFEs o di e en slip planes, (c) de i ed slide s ess o shu le-se planes, and (d) Peie ls s ess o di e en slip planes in R2u−BC2N, oge he wi h hose in c-BN shown o compa ison. R2u−n(n=1–4) in (d) ep esen s he co esponding Peie ls s ess o S/G1-4. when he s ess d ops, and he ini ial la ice con igu a ion is ans o med in o a new one ha exhibi s mi o like symme y wi h he o iginal B-N laye [highligh ed a eas in Figs. 2(i) and 2(j). This unexpec ed in e io shea s eng h ela i e o c-BN cas s a doub on he p e ious conclusion o he in insic supe ha dness o BC2N. The weakes links o he R2u−BC2N c ys al we e de e - mined h ough compa ing aniso opic ideal s eng hs along di e en c ys allog aphic di ec ions o slip sys ems o co - ela e he clea age ac u e o slip disloca ion mobili y, espec i ely [14,42,66]. As shown in Fig. 3(a), he e a e eigh nonequi alen (001) clea age/slip planes including ou shu le-se (“S1” o “S4”) and ou glide-se (“G1” o “G4”) planes. The clea age ene gies o shu le-se planes a e much lowe han ha o he glide-se planes (Fig. S3) because he e ical bonds wi hin he shu le-se plane a e much weake han he connec ed iple-bonds ela ed o he glide-se planes when he alias ensile de o ma ion is applied. The shu le-se planes we e u he examined and a minimum ideal clea age s ess o 96.47 GPa o R2u−BC2N is obse ed along he no - mal di ec ion o “S4”, which is lowe han ha o c-BN (99.2 GPa), sugges ing i s in e io decohesion esis ance o c-BN. The key desc ip o ep esen ing he h eshold s ess ha makes he disloca ion mo e i e e sibly, i.e., Peie ls s ess, which is ul ima ely linked o he ha dness o a eal ma e ial [14], was analyzed ho oughly o de e mine he plas ici y e- sis ance. As seen in Fig. 3(b), he p o iles o he gene alized s acking aul ene gy (GSFE) o R2u−BC2N ag ee wi h hose o c-BN. The e o e, simila o c-BN, he uns able s acking aul ene gies (SFEs) o shu le-se planes along he [¯ 12¯ 10] di ec ion wi h he associa ed Peie ls s ess, and hose o he glide-se ones along he [¯ 1010] di ec ion wi h he associa ed Peie ls s ess o a pa ial disloca ion a e c ucial o com- p ehending he ha dness o R2u−BC2N[40]. As shown in Fig. 3(d), he lowes Peie ls s ess (1.17 GPa) o glide-se plane in R2u−BC2N is obse ed in “G4” and lowe han ha o c-BN (3.28 GPa) because o i s lowe SFE compa ed o c-BN [Fig. 3(b)]. Su p isingly, he lowes Peie ls s ess o shu le-se plane obse ed in “S2” is much lowe han c-BN (10.13 GPa), a 3.87 GPa, which is highly unusual because he R2u−BC2N has much highe SFE and slide s ess in “S2” han c-BN [Figs. 3(b) and 3(c)]. By compa ing he shape o hei GSFE cu es, a “ la peak” can be obse ed o R2u−BC2N [g een a ea in Fig. 3(b)], ha co esponds o a “smoo h u n” in i s slide s ess cu e s a ing om u=0.35 [g een a ows in Fig. 3(c)]. This beha io sugges s he appea ance o bond so ening, which may be esponsible o i s anomalously ul alow Peie ls s ess. To gain in-dep h insigh in o he unp eceden ed bond so - ening in R2u−BC2N, we aced he bond leng h a ia ions o L060101-4 ANOMALOUS BOND SOFTENING MEDIATED BY … PHYSICAL REVIEW B 106, L060101 (2022) FIG. 4. (a) Bond leng h a ia ions in se e al laye s a ound slip plane “S2” as a unc ion o he displacemen u in R2u−BC2N, compa ed wi h hose in c-BN. VCDD o (b)–(d) R2u−BC2N and (e)–(g) c-BN. DOS cu es o (h) R2u−BC2Nand(i)c-BN unde a ious displacemen s u. The same isosu ace le el o ±0.017 elec ons/Boh 3is used. Yellow and blue egions signi y he s a es o cha ge accumula ion (posi ion) and deple ion (nega i e), espec i ely. The Fe mi le el is se o ze o. The elec onic pe u ba ions a e highligh ed as ligh pu ple a eas in VCDDs. se e al laye s a ound he slip plane “S2” wi h he associa ed alence cha ge densi y di e ence (VCDD) e olu ions, and compa ed hese wi h hose o c-BN. As shown in Fig. 4(a), when he s ain inc eases om 0.00 o 0.30, he C1-N1 bond wi hin “S2” in R2u−BC2N emain sho e han he B1-N1 bond in c-BN, indica ing he s onge bonding cha ac e o C1-N1 bond han B1-N1 bond. A e he s ain o 0.30, unex- pec edly, he C1-N1 bond leng h inc eases s eeply o 2.40 Å a he s ain o 0.50, being much longe , i.e., weake han he B1-N1 bond (2.16 Å) in c-BN. This sugges s ha signi ican bond so ening occu ed in C1-N1 bond because o he la ge shea s ain, explaining he appea ance o he “ la peak” in i s L060101-5 XU, LIU, LEGUT, AND ZHANG PHYSICAL REVIEW B 106, L060101 (2022) FIG. 5. COHP cu es o se e al bonds a ound slip plane “S2” in R2u−BC2N unde di e en slip displacemen s u: (a) u=0.00, and (b) u=0.50. The co esponding esul s o (c) c-BN a e shown o compa ison. The Fe mi le el is se o ze o. GSFE cu e. E en mo e s ikingly, simila beha io can also be ound in he i s and second adjacen laye s o “S2”, in which he su ges in he bond leng h a ia ions appea when he s ain su passes 0.30, whe eas hese bond leng h changes a e negligible in c-BN. The no able di e ence in he bond leng h a ia ions be ween R2u−BC2N and c-BN is a ibu ed o hei dis inc localized cha ge ans e p ocess du ing slip- ping whe e a wide elec onic pe u ba ion pe pendicula o he “S2” is obse ed in R2u−BC2N, in ol ing he sequen- ial s eng hening/weakening o he bonds adjacen o C1-N1 bond [ ed and blue a ows in [Figs. 4(b)–4(d)]. These oscil- la ions o bond leng hs and s eng h ep esen he F iedel-like oscilla ions o alence cha ge densi y, shown in Figs. S4(a) and S4(b), analogous o he phenomenon ound adjacen o he su aces and in e aces o elec onically pe u bed solids [22,67]. As a consequence, he bond s eng h o C1-N1 de- c eases d as ically, leading o i s ul alow Peie ls s ess. While in c-BN, he cha ge pe u ba ions occu p edominan ly wi hin he slip plane, and a ely a ec he nea -neighbo ing a oms [Figs. 4(e)–4(g) and Figs. S4(c) and S4(d)]. Densi y o s a e (DOS) analysis e eals ha he s ain-induced F iedel-like oscilla ions accompanied by he me alliza ion o R2u−BC2N, which co esponds o he eme gence o elec onic s a es a he Fe mi le el a e he c i ical shea displacemen [ ed a ows in Fig. 4(h)]. In con as , he band gap o c-BN dec eases wi h inc easing s ain and no me alliza ion is obse ed [Fig. 4(i)]. By u he analyzing he c ys al o bi al Hamil on pop- ula ion (COHP) o he bonds a ound he slip plane in R2u−BC2N, and compa ed wi h ha o c-BN, a deep un- de s anding is ob ained on he a o emen ioned me alliza ion. Unde equilib ium condi ion, he C1-N1 bond o R2u−BC2N displays an an ibonding inge p in below he Fe mi le el [blue a ow in Fig. 5(a)], which may explain i s me as able ea u e wi h espec o diamond and c-BN. A e slipping along “S2”, he ema kably weakened B1-N2 and C2-C3 bonds caused by he F iedel-like oscilla ions, exhibi la ge bonding s a es a ound he Fe mi le el [ ed a ow in Fig. 5(b)]. These ascina ing bonding ea u es indica e ha , as he B1-N2 and C2-C3 bonds weaken, he ene gy o he bonding s a es inc eases and ha o he an ibonding ones dec eases, esul ing in he closu e o he ene gy gap. This d i es he localized bonding elec ons a ound “S2” in o a delocalized an ibonding s a e, he eby elici ing he me alliza ion. In compa ison, no bonding s a es a e ound in c-BN ha c oss he Fe mi le el [Fig. 5(c)]. I is no ed ha hese oscilla ions do no occu when slipping in he weakes glide-se plane “G4” in R2u−BC2N. As shown in Figs. S5(a)–S5(g), he bond leng h a ia ions and cha ge dis ibu ions a ound “G4” in R2u−BC2N a e essen- ially equi alen o hose in c-BN. The e o e, no me alliza ion is ound in ei he R2u−BC2No c-BN [Figs. S5(h) and S5(i)], while a lowe Peie ls s ess han c-BN is mainly a - ibu ed o he lowe in insic bonding s eng h o N1-B1 bond wi hin “G4” han ha o he N1-B1 bond in c-BN, because as he s ain inc eases, he la e becomes mo e sho e and s onge han he o me . Besides, di e en om he F iedel oscilla ions obse ed o occu in Ti-Si-N nanocomposi es sys ems [68,69] a equilib ium and leads o poo s eng h unde uni o m s ain, he me alliza ion in R2u−BC2N does no occu unde hese condi ions (Fig. S6), which explains i s ideal shea s eng h is only sligh ly lowe han ha o c-BN. Based on he a o emen ioned in es iga ions on he in insic mechanical p ope ies o R2u−BC2N, i can be concluded ha R2u−BC2N canno be anked as he in insic supe - ha d ma e ial supe io o c-BN, due o i s lowe ideal shea s eng h, weake in e plana clea age, and disloca ion slip esis ance. This conclusion s ongly challenges he p e i- ous conclusion on he supe ha dness o BC2N based on he in insic mechanical s eng h [11,12,20]. The mic oscopic o igin o nanos uc u ed BC2N ma e ials was u he in es- iga ed using la ge-scale molecula dynamics simula ions. Acco ding o expe imen al in o ma ion, he BC2N ma e ials wi h a nanoc ys alline s uc u e adhe ed oge he by ca bon amo phous in e acial laye (AIL) wi h a ying hicknesses (illus a ed in Fig. S7) we e cons uc ed and hen loaded by uniaxial s ess. Compa ed wi h he BC2N nanos uc u e wi h- ou AIL, he disloca ion nuclea ion and pene a ion a g ain bounda ies educed conside ably in he BC2N nanos uc u e con aining a 1-nm- hick AIL [Figs. S7(b) and S7(c)]. As he hickness o AIL inc eases o 2 nm [Fig. S7(d)], such as ha in he expe imen ally syn hesized sample [8], almos no la ice disloca ions a e obse ed, indica ing ha he de o ma- ion mechanism swi ched om la ice disloca ion o in e ace sliding. This phenomenon is consis en wi h ha obse ed in he nanos uc u ed diamond and me allic ma e ials [15,70,71]. Hence, he amo phous bounda y is e i ied as being p ima ily esponsible o he expe imen ally obse ed ex eme ha dness o BC2N. L060101-6 ANOMALOUS BOND SOFTENING MEDIATED BY … PHYSICAL REVIEW B 106, L060101 (2022) In summa y, h ough e alua ing he XRD pa e ns, and p essu e-dependen he modynamic, mechanical, and phonon s abili ies, we iden i ied he expe imen ally syn hesized BC2N phase as R2u−BC2N. We u he unco e ed a non adi ional bond de o ma ion mechanism media ed by a peculia s ain- d i en elec onic beha io . A e he c i ical shea s ain, owing o he appea ance o me alliza ion, F iedel-like os- cilla ions o alence cha ge densi y in ensely weaken he he e ogenous bonds ac oss he slip plane, hus ema kably limi ing he disloca ion slip esis ance o R2u−BC2N. The in e acial amo phous ca bon, a he han he c ys al’s inside, p edominan ly con ibu es o i s measu ed ex eme ha dness. Ou ongoing wo k sugges ha such oscilla ions a e likely o be a ubiqui ous phenomenon ha occu s also in o he (111) supe la ice bo on ca bon ni ides, e.g., BC4N[72,73] and BC10N[74], which emind us ha a oiding hese os- cilla ions h ough combining nanos uc u e enginee ing and g ain bounda y enginee ing is necessa y o achie e supe io ha dness o B-C-N ma e ials. The au ho s acknowledge he Na ional Na u al Science Founda ion o China (NFSC) wi h No. 51672015, Na ional Key Resea ch and De elopmen P og am o China (G an No. 2017YFB0702100), “111 P ojec ” (No. B17002), Na ional Thousand Young Talen s P og am o China, and Fundamen al Resea ch Funds o he Cen al Uni e si ies. 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