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
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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
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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
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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
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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. D.L. acknowl-
edges suppo by he Eu opean Regional De elopmen Fund
in he IT4Inno a ions na ional supe compu ing cen e - Pa h
o Exascale p ojec , No. CZ.02.1.01/0.0/0.0/16_013/0001791
wi hin he Ope a ional P og amme Resea ch, De elopmen
and Educa ion and he p ojec e-INFRA CZ (ID:90140) by
he Minis y o Educa ion, You h, and Spo o he Czech
Republic. We would also hank D . S. Zhang o his help ul
discussions.
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