Rede ining Plas ici y in a Cubic In e me allic: Disloca ion Dynamics in he CaAl2La es
Phase
Ma ina F eunda,∗, Joshua Spilleb, Pei-Ling Suna, Ma a Lipi´
nska-Chwałekc, Joachim Maye b,c, Zhuocheng Xiea,∗, Sand a
Ko e-Ke zela,∗
aIns i u ¨u Me allkunde und Ma e ialphysik, RWTH Aachen Uni e si y, 52056 Aachen, Ge many
bCen al Facili y o Elec on Mic oscopy, RWTH Aachen Uni e si y, 52074 Aachen, Ge many
cE ns Ruska-Cen e o Mic oscopy and Spec oscopy wi h Elec ons, Fo schungszen um J¨ulich GmbH, 52428 J¨ulich, Ge many
Abs ac
In he ealm o ma e ials design, unde s anding and manipula ing he beha iou o disloca ions — key d i e s o plas ic de o ma ion
— is a co ne s one. Howe e , while disloca ions a e well-explo ed in simple c ys alline ma e ials, hei s uc u e and mechanisms
o mo ion emain la gely enigma ic o complex c ys als, such as opologically closed-packed phases. This as class o ma e ials
con ains many in e me allics anging om high- empe a u e s uc u al ma e ials o unc ional c ys als ha can ac as supe con-
duc o s, magne s, magne o-calo ic o hyd ogen s o age ma e ials. In all o hese applica ions, s uc u al in eg i y and he e o e
con olled plas ici y is essen ial. This s udy b idges ou cu en knowledge gap in plas ici y o complex c ys als by del ing in o he
mos p e alen among hem, he La es phase. U ilizing ansmission elec on mic oscopy, we un eil p e iously un epo ed de ec
s uc u es in he cubic CaAl2La es phase. Complemen ing hese obse a ions, a omis ic simula ions elucida e he unde pinning
mechanisms, e ealing no el de o ma ion beha iou s. We spo ligh he ole o ull disloca ions a e sing mul iple {11n}slip
planes, a depa u e om he con en ional con inemen o {111}planes. This mul i-plane disloca ion ac i i y, including equen
c oss-slipping, eme ges as a pi o al ac o in accommoda ing plas ic de o ma ion. Ou indings no only challenge an exis ing
pa adigm in in e me allic plas ici y bu also p opose a angible pa hway o unde s and he duc ili y o b i le complex alloys as a
s ide o wa d in phase selec ion and ma e ials enginee ing.
Keywo ds: Topologically close-packed phase, disloca ions, c oss-slip, ansmission elec on mic oscopy, a omis ic simula ion
1. In oduc ion
Unde s anding he undamen al p inciples o plas ic de o -
ma ion o c ys als has been and is ins umen al in enabling and
d i ing alloy design, as showcased in he explosion o me allic
enginee ing alloys since he i s decades o he las cen u y [1].
Cu en high-pe o mance alloys o s uc u al applica ions a e
ca e ully ailo ed a mul iple leng h scales om he alloying el-
emen s ha may dis o he me al’s la ice a he a omic scale
o e he local s uc u e a la ice de ec s impa ing s eng h o
de o mabili y, o he in e play o di e en g ains and phases
anging om he nanoscale o he size o me allic shee s. In
all bu a ew excep ions, a single me allic elemen si s a he
hea o a gi en alloy, e.g. i on in s eel, nickel in supe alloys
o aluminium, i anium o magnesium in he ligh weigh alloys.
In con as o hese alloys cen ed a ound he simple cubic and
hexagonal uni cells o he pa en me al, alloying o compa able
amoun s o di e en me allic elemen s esul s in he o ma ion
o mo e complex c ys alline packings in all bu he a e cases
whe e he elemen s a e ully miscible. A as class o c ys als
∗Co esponding au ho
Email add esses: [email p o ec ed] (Ma ina F eund),
[email p o ec ed] (Zhuocheng Xie),
[email p o ec ed] (Sand a Ko e-Ke zel)
eme ges — in e me allics — con aining 40,000 [2] epo ed
c ys als o da e and coun ing [3]. E en whe e hei o ma ion
can be ini ially supp essed, such as in bulk me allic glasses o
high en opy alloys, hese phases emain as he he modynami-
cally s able cons i uen s o mos highly alloyed ma e ials. Why
hen, a e hey mos o en conside ed as phases o be a oided
o phases o be cons ained o small p ecipi a e sizes in s uc-
u al alloys? The eason is ha mos o hese c ys als a e, as a
esul o hei c ys al packing, e y b i le. Howe e , he e a e
ema kable excep ions wi h c ys als exhibi ing plas ic de o ma-
ion a oom empe a u e su icien o machining o sus aining
mechanical impac [4,5]. Gi en hei shee numbe and a i-
abili y, he e a e bound o be mo e and exci ing in e me allic
ma e ials o be ound, e.g. o high- empe a u e s uc u al ma-
e ials o o enable unc ions such as supe conduc i i y, mag-
ne ism o hyd ogen s o age in combina ion wi h s uc u al in-
eg i y and o mabili y. To go in sea ch o hese new ma e ials
wi hin ou exis ing and expanding ma e ial da abases o o pu -
pose ully enginee he p ope ies o o he s, we equi e he same
basic ools as o hei simple me allic cousins: a de ailed un-
de s anding o how and when disloca ions, he key enable s o
plas ic de o ma ion, mo e.
In e me allics ha e been ecognized as an impo an and a -
ac i e class o c ys als o a long ime and hei s uc u es a e
well desc ibed [6]. Topologically close-packed (TCP) s uc-
P ep in submi ed o Else ie Oc obe 10, 2025
u es end o o m when me al a oms o di e en sizes combine
and hei o de ed and dense a omic packing yields unique p op-
e ies, such as high mel ing poin s, high ha dness, ele a ed co -
osion esis ance and in many cases also a ac i e unc ional
p ope ies. Howe e , he high ha dness mos o en comes a he
p ize o b i leness below he b i le o duc ile ansi ion em-
pe a u e (BDTT), which o hese o en high-mel ing c ys als
is o en se e al hund ed Kel in abo e ambien condi ions. Fo
his eason, p e ious scien i ic s udies ha e mos ly ocused on
high- empe a u e de o ma ion [7,8,9,10,11,12,13], o we e
con ined o g own-in and no necessa ily mobile de ec s [14].
Consequen ly, he disloca ion mechanisms a e only e y poo ly
unde s ood, pa icula ly in he iew o he complex mecha-
nisms o mo ion encoun e ed in hese phases compa ed wi h
me als. Zonal glide ac oss wo pa allel planes has been e-
po ed in di e en complex c ys als [15,16,17], while he e m
‘me adisloca ions’ has been coined o he la ge co es ound in
quasi-c ys als and hei app oximan s [18,19,20]. A p omi-
nen example o a mechanism unique o complex c ys als is
synch oshea , a synch onized mo emen o pa ial disloca ions
mo ing in di e en pa allel planes c ea ing a change in s ack-
ing [15]. O iginally sugges ed o sapphi e [15], his mecha-
nism was also pos ula ed o he cha ac e is ic iple laye o
he TCP La es phases [21,22] and he i s high- esolu ion
mic og aphs o disloca ion co es consis en wi h his mecha-
nism in a hexagonal La es phase published in 2005 [14], al-
bei using c ys als ha we e no subjec ed o plas ic de o ma-
ion. Since hen, e idence o synch oshea has been ound in
o he TCP c ys als, such as he o he La es phases poly ypes,
µ-phases o he CaCu5s uc u e ype and compu a ional s ud-
ies complemen he g owing body o expe imen al e idence
[23,24,25,26,27,28]. Howe e , his complex, non-plana
mechanism equi es he mal ac i a ion o ake place [29,26]
and na u ally compe es wi h o he mechanisms. I also de ies
he common expec a ion o slip aking place on he mos close-
packed as well as widely spaced se o planes in a c ys al [30].
Indeed, i has been shown ha he ac i e mechanism o mo-
ion in a complex c ys al, e.g. c ys allog aphic ull o pa ial
disloca ion slip o mo ion o synch o-pa ials, may be di ec ly
manipula ed based on small changes in he composi ion o he
alloy, pa icula ly whe e he c ys alline sub-la ice o de is a -
ec ed. This was accompanied by a massi e change in yield
s ess, enabling signi ican plas ic de o ma ion in hose laye s
wi h La es phase packing in la ge bu closely ela ed µ-phase
s uc u e [4,5]. In hexagonal La es and he simila ly s uc-
u ed µ-phases, disloca ions ha e also been ound o mo e on
non-basal planes [31,32,33,34,35,36], ha is ou side o he
iple laye . Con e sely, o he cubic La es phases, plas ic-
i y had been epo ed o ake place exclusi ely on he {111}
planes, which con ain he cha ac e is ic iple laye equi alen
o he basal plane in he hexagonal poly ypes. I is only e y
ecen ly ha he i s expe imen al e idence sugges ed ha de-
o ma ion may ake place ou side o he {111}plane in cubic
La es phases, in con as o wha is obse ed in he much sim-
ple ace-cen ed cubic me als [37].
To un a el he ac i e mechanisms o mo ion in his la ge
and echnologically impo an class o TCP La es phases and
hei c ys allog aphic ela i es, we add ess he e a undamen al
ques ion: which disloca ion mechanisms a e ac i e in he cubic
La es phases and how can hey be unde s ood and ela ed o
p e ious insigh s es ic ed o high- empe a u e beha iou ?
2. Me hods
2.1. Sample p epa a ion
Bina y CaAl2La es phases, which belong o he space g oup
227 ([Fd¯
3m] and Pea son Symbol cF24), we e p epa ed like de-
sc ibed in [38]. Fu he e na y C15 Ca(Al,Mg)2La es phases
we e embedded in a coppe pas e o e eal a s able sample su -
ace. La es phase samples we e p epa ed me allog aphically,
by using ou g inding s eps using SiC pape wi h a g i si e
o 1200 o 4000, whe eas o he e na y addi ional g inding
s eps using diamond g inding pla es (POLARIS M) wi h g ain
sizes o 6 µm and 3 µm, ollowed by mechanical polishing wi h
diamond pas e s a ing wi h 6 µm and ending wi h 0.25 µm us-
ing o all s eps isop opanol wi h 5 % polye hylene glycol 400
(PEG) as lub ican . Final polishing and washing s eps we e ol-
lowed wi h a g ain size o 0.04 µm (using STRUERS OPA) and
cleaning wi h dish washing liquid. Bo h samples we e analyzed
using scanning elec on mic oscopy (SEM) (CLARA, Tescan,
B no, Czech Republic), ene gy dispe si e X- ay spec oscopy
(EDX) (Helios Nanolab 600i, FEI, Eindho en, NL) and addi-
ional elec on backsca e di ac ion (EBSD) (Helios Nanolab
600i, FEI, Eindho en, NL) o analyse he esul ing mic os uc-
u e and he esul ing plas ic zone, he local chemical composi-
ion and he g ain o ien a ions.
2.2. Nanoinden a ion expe imen s
To in es iga e he mechanical p ope ies and esul ing plas-
ici y, nanomechanical es s we e pe o med using an iNano
nanoinden e (Nanomechanics Inc., TN, USA) wi h a diamond
Be ko ich ip (supplied by Syn on-MDP AG, Swi ze land).
The Oli e and Pha me hod was used o calib a e he se up
on a used silica sample by de e mining he diamond a ea unc-
ion (DAF) and ame s i ness o he inden e ip [39,40]
The inden s we e pe o med wi h he same pa ame e s, using
a cons an s ain a e o 0.2 s-1 un il a dep h o 500 nm was
eached. The analysis included he e alua ion o he inden a-
ion modulus, ha dness, and ac i a ed slip sys ems by aligning
su ace aces om he SE images wi h g ain o ien a ion om
he EBSD analysis, as desc ibed in he e iew by Gibson e al.
[41].
2.3. TEM cha ac e iza ion
Indi idual slip bands benea h he su ace we e analysed in a
Jeol JEM F200 TEM a 200 kV. This mic oscope is equipped
wi h a double- il holde , in which x- il ing o ±36° and y-
il ing o ±31° a e allowed. Scanning ansmission elec on
mic oscopy (STEM) was also pe o med wi h he same appli-
ca ion. Addi ionally, highe esolu ion STEM analysis o he
bina y and e na y CaAl2La es phases was pe o med on an
abe a ion co ec ed FEI Tian 60-200 ChemiSTEM a 200 kV
accele a ion ol age. Si e speci ic TEM lamella we e aken ou
2
Figu e 1: (a) Schema ic illus a ion o he simula ion se up o disloca ion mo ion. Climbing image NEB calcula ions we e pe o med on he ini ial (RC:0) and inal
(RC:1) con igu a ions o ind MEPs o disloca ion mo ion. PBCs we e applied in he x ([¯
110]-o ien ed) and y di ec ions. A oms in he ou e mos laye s (ma ked in
g ey) wi h a hickness o 15 Å (2 imes he po en ial cu -o ) we e ixed in he z-di ec ion. The dimensions o he se up in he y and z di ec ions a e 200 Å, and in
he x di ec ion, i is 11.3 Å. The disloca ion line and Bu ge s ec o o sc ew a
2[¯
110] disloca ions a e along he x-di ec ion, and he glide dis ance is one uni leng h
along he y-di ec ion. (b) Co e s uc u e and ene gy o he sc ew a
2[¯
110] disloca ion in he simula ed CaAl2La es phase. Only a oms belonging o he disloca ion
co e, as iden i ied by LaCA, a e highligh ed (Ca and Al a oms a e colou ed in yellow and blue, espec i ely) he e. (c) Nye- enso and di e en ial displacemen maps
o he sc ew a
2[¯
110] disloca ion in he Ca subla ice.
by ion milling in FIB. The lamellae we e il ed o di e en zone
axes and se e al wo-beam condi ions in o de o iden i y edge-
on o ien a ion o he possible slip planes and con i m he co -
esponding habi planes o he disloca ion slip [42]. DPs o he
zone axes and wo-beam condi ion (b igh /da k- ield) images o
he in es iga ed de ec s we e acqui ed.
2.4. A omis ic simula ions
A omis ic simula ions we e pe o med using he open-sou ce
molecula dynamics code LAMMPS [43]. The in e a omic in-
e ac ions we e modelled employing he machine-lea ning mo-
men enso po en ial (MTP) by Poul e al. [44,37] o he Al-
Ca sys em. The machine-lea ning MTP po en ial p o ides be -
e p edic ions in la ice pa ame e , elas ic cons an s and {1 11}
s acking aul ene gy compa ed o he semi-empi ical modi ied
embedded a om me hod (MEAM) po en ial [45] when com-
pa ed wi h ab-ini io and expe imen al esul s [37].
The C15 CaAl2c ys al s uc u es we e cons uc ed using
A omsk [46]. A sc ew ull disloca ion wi h a Bu ge s ec o o
a
2[110] was in oduced on di e en glide planes ollowing he
me hod de ailed in [25]. Pe iodic bounda y condi ions (PBCs)
we e applied in he di ec ions along he glide plane, while semi-
ixed bounda y condi ions we e applied in he no mal di ec ion
o he glide plane. The simula ion se ups a e illus a ed in Fig-
u e 1(a). The a omis ic con igu a ions we e elaxed ug he con-
juga ed g adien algo i hm wi h box elaxa ion and he FIRE
algo i hm [47,48], wi h a o ce h eshold o 10−8eV/Å. The
disloca ion co e ene gy was calcula ed by measu ing he o al
disloca ion ene gy as a unc ion o adius Rand hen ex ap-
ola ing he a - ield elas ic ene gy back o he chosen cu -o
adius b, as shown in Figu e 1(b).
Climbing image nudged elas ic band (NEB) calcula ions
[49,50] we e pe o med on he ini ial (be o e disloca ion glide)
and inal (a e disloca ion glide) con igu a ions o de e mine
he minimum ene gy pa hs (MEPs) o hese disloca ion mo ion
e en s (see Figu e 1(a)). The sp ing cons an s o pa allel and
pe pendicula nudging o ces a e bo h 1.0 eV/Å2. The QUICK-
MIN algo i hm [51] was applied as he damped dynamics min-
imize o ene gy minimiza ion wi h a o ce h eshold o 10−2
eV/Å. The numbe o in e media e eplicas anged om 96 o
312, depending on he glide dis ance and co esponding disso-
cia ion e en s. La es phase c ys al analysis (LaCA) [52] was
used o iden i y disloca ion co es in C15 La es phases and dis-
loca ion analysis (DXA) [53] implemen ed in OVITO [54] was
used o ex ac disloca ion lines.
3. Resul s
3.1. Slip beyond {111}planes
Nanoinden a ion was used o in oduce plas ic de o ma ion
in di e en o ien a ions o a poly-c ys alline CaAl2C15 La es
phase, gi ing ise o signi ican de o ma ion on di e en c ys-
allog aphic planes as seen on he su ace a ound an inden a ion
imp ession o CaAl2(Figu e 2(a)) and CaAl2+Mg (Figu e
3(a)). Se e al ac i e slip planes we e ound. The s aigh ones
can di ec ly be assigned o speci ic planes, like shown o he
CaAl2in (Figu e 2(a)), while some o hem a e wa y and can-
no be di ec ly assigned o a speci ic slip plane (Figu e 2(a)).
Addi ionally, h ee c acks o med along he h ee co ne s o he
inden o he s oichiome ic sample (Figu e 2(a)). T ansmis-
sion elec on mic oscopy (TEM) on elec on anspa en lamel-
lae li ed ou o he ma e ial as a c oss-sec ion o such inden a-
ions allowed us o u he in es iga e he na u e o he unde -
lying c ys allog aphic planes accommoda ing plas ici y. A he
sub-mic on scale o a di ac ion-guided analysis using con en-
ional TEM o he CaAl2+Mg sample (Figu e 3(b)-(d)), we
e eal clea changes in o ien a ion in he slip planes a eling
in o he ma e ial. Addi ionally, (Figu e 3(b)-(d)) shows ha ,
compa ed o he planes obse ed below, he ansi ion be ween
planes can occu in small, al e na ing segmen s embedded be-
ween he la ge s aigh segmen s. Examples o slip aking
place on {111},{1 1 2}and {1 1 5}planes a e shown he e, wi h
3
Figu e 2: De o ma ion s uc u e a ound an inden imaged by elec on mic oscopy. a) Seconda y elec on mic og aph o slip aces on he sample su ace and
b) HRTEM image eco ded in he [110] zone axis o he bina y C15 CaAl2La es phase. c) Con en ional and d) STEM da k ield images o he e na y C15
Ca(Al,Mg)2La es phase a he [110] zone axis. The a ea imaged in (d) is indica ed by a whi e ec angle in (c).
{113},{1 1 4},{1 1 6}and {1 1 11}planes also ound elsewhe e
[37]. Simila ly, some o he c acks eme ging om o o ming
along hese slip planes also p og ess in a zigzag pa e n, con-
sis en wi h hei p e e en ial o ma ion along slip planes ha
ha e accumula ed a high densi y o de ec s [31]. Disloca ion
analyses using di e en wo-beam condi ions show ha in all
cases disloca ions mo ing on hese planes sha e he same Bu g-
e s ec o , which is o ⟨110⟩ ype. HR-TEM imaging, gi en in
(Figu e 2(b)) o he CaAl2sample, a he a omic scale using
an abe a ion-co ec ed scanning ansmission elec on mic o-
scope, e eals ha e en a he smalles scales, simila changes
in slip planes a e obse ed. These a e consis en wi h c oss-
slip aking place ia ⟨110⟩sc ew disloca ions whose Bu g-
e s ec o is con ained in all o he expe imen ally encoun e ed
{11n}planes. As such, he c ys al appea s o de o m on many
mo e planes han p e iously epo ed o an icipa ed. Fu he -
mo e, (Figu e 2(c)) shows a con en ional TEM image o he
C15 e na y sample, which illus a es he p og ession o he slip
planes along a zigzag pa h. This is also shown in mo e de ail
in Figu e 3((b)-(d)) including an indexa ion o he indi idual
plane segmen s imaged on edge. The a ea ma ked wi h a whi e
ec angle in (Figu e 2(c)) is he a ea eco ded in (Figu e 2(d))
using STEM in da k ield mode. In he STEM image, he lowe
ea u e in pa icula is con ained in an ini ial plane, ollowed by
a c oss-slip o he nex plane. This p ocess hen epea s ( om
le o igh in he image, co esponding o inc easing dis ance
o he cen e o he plas ic zone) ia a plane ha is pa allel o he
ini ial one and con inues pa allel o he ini ial c oss-slip plane.
Whe he c ack o ma ion occu s be o e, du ing o a e his p o-
cess has comple ed canno be de i ed om hese pos -mo em
images.
3.2. A omis ic simula ions o disloca ion mo ion
To un a el he unde lying mechanisms o slip, pa icula ly
he new obse a ion o equen c oss-slip in he C15 CaAl2
La es phase a ibu ed o sc ew disloca ion mo ion, we used
a omis ic simula ions. To his end, we pe o med NEB cal-
cula ions using a newly de eloped machine-lea ning MTP o
de e mine he MEPs o sc ew disloca ion mo ion on he di e -
en {11n}planes as well as he low-index {100}and {110}
4
Figu e 3: (a) A SE image showing he slip ace mo phology a e nanoinden a ion o he C15 Ca(Al,Mg)2La es phase. (b) TEM b igh ield image aken unde
g=0¯
2¯
2 in a
g=1¯
11 zone axis ep esen s he unde lying disloca ion s uc u e o he in (a) shown inden . The (2 1 1) plane aces a e shown wi h he o ange line and
he (111) wi h he blue one. TEM b igh ield images aken unde (c) he same condi ions used in (b) and (d)
g=0¯
2¯
2 wo-beam condi ions a , highligh ing he zigzag
s uc u e om (c) in (d) shown wi h he g een dashed ec angle. The (21 1) and (1 1 1) plane aces a e shown nex o he c ack. The c ack is obse ed o ha e a
zigzag ea u e. Di e en colou lines ma k he o ien a ions o he slip planes. The g een ec angle shows a segmen whe e he c ack is qui e wa y.
planes. Fo bo h, he known and new slip planes, we iden i-
ied an iden ical co e o he sc ew a
2[110] disloca ion (Figu e
1(b-c)). As shown in Figu e 1(c), he Nye eno dis ibu ion e-
eals a small bu non-negligible edge componen a he sc ew
disloca ion co e egion, which is a ibu ed o co e sp eading
along he (001) plane, as con i med by he co esponding di -
e en ial displacemen map. While he co e s uc u e emains
unchanged, no able di e ences eme ge du ing he mo ion o
hese disloca ions. The ansi ion p ocesses and associa ed en-
e gy ba ie s o all indi idual ac i a ion e en s o disloca ion
mo emen s in his s udy a e summa ized in Table 1. Fo dislo-
ca ions gliding on (11 0), (1 1 1), and (1 13) planes wi h glide
dis ances smalle han 10 Å, no in e media e s a es ea u ing e-
s o ed disloca ion co es and ze o ela i e ene gy (∆E=0 eV)
5
(a) (b)
y-[001]
z-[110]
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0.4 0.6 0.8 1
∆E (eV/Å)
Reac ion coo dina e
(110)[1
−10]
RC:0 RC:1
y-[112]
z-[111]
RC:0 RC:1
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0.4 0.6 0.8 1
∆E (eV/Å)
Reac ion coo dina e
(111
−)[1
−10], iple
RC:0 RC:1
y-[112]
z-[111]
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0.4 0.6 0.8 1
∆E (eV/Å)
Reac ion coo dina e
(111
−)[1
−10]
(c) RC:0 RC:1
y-[332]
z-[113]
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0.4 0.6 0.8 1
∆E (eV/Å)
Reac ion coo dina e
(113
−)[1
−10]
(d)
Figu e 4: A omis ic con igu a ions and ene gy p o iles along MEPs o he mo ion o he sc ew a
2[110] disloca ion on (a) (110), (b) (1 1 1) iple laye , (c) (1 1 1)
iple-kagome laye , and (d) (1 1 3) planes in he C15 CaAl2La es phase we e calcula ed using he NEB me hod. Only a oms belonging o he disloca ion co e
a e shown he e. The o ange and magen a symbols indica e he posi ion o he disloca ion line in he ini ial ( eac ion coo dina e RC:0) and inal (RC:1) a omis ic
con igu a ions, while he cyan symbols ep esen he posi ion o he disloca ion line a he in e media e minima. Dashed lines indica e he glide planes be ween each
local minimum.
we e ound along he MEPs (see Figu e 4). Al hough a omic
mo emen du ing glide includes ou -o -plane componen s, as
illus a ed in Supplemen a y Mo ies S1–S4, he o e all dislo-
ca ion mo ion emains con ined o he ho izon al glide plane
and is hus conside ed in-plane. Fo he sc ew (001)[110] dis-
loca ion, an in e media e con igu a ion wi h a disloca ion co e
equi alen o he ini ial s a e (a RC=0) and ene gy ∆E=0 eV
was iden i ied a he RC o 0.5 (see Figu e 5(a) and Mo ie S5).
Howe e , his in e media e co e emains con ined o he same
(001) glide plane. Among hese in-plane slip p ocesses, he
sc ew disloca ion on he (11 1) iple-kagome plane exhibi s
he sho es glide dis ance o 4.91 Å and he lowes ene gy ba -
ie o 0.107 eV/Å, which is signi ican ly lowe han ha o
he compe ing (111) iple plane, whe e he mechanism o mo-
ion is domina ed by synch o-Shockley pa ial disloca ions, as
demons a ed in ou p e ious s udies [24,25]. The (1 13)[11 0]
6
disloca ion exhibi s bo h he longes glide dis ance o 9.39 Å
and he highes ene gy ba ie o 0.266 eV/Å among he in-
plane slip p ocesses.
In con as , o disloca ions gliding on (1 1 2), (1 14), (1 1 5)
and (116) planes wi h glide dis ances la ge han 10 Å, he mo-
ion b eaks up in o mo emen be ween di e en glide planes,
accompanied by c oss-slip p ocesses along he ansi ion pa hs
(see Figu e 5(b-e) and Mo ies S6-S9). Fo ins ance, he sc ew
disloca ion gliding on he (112) plane unde goes decomposi-
ion in o wo sub-e en s: one co esponds o he disloca ion
gliding on he (113) plane, and ano he one in ol es he dis-
loca ion gliding on he (111) plane. These e en s a e sepa-
a ed by an ene gy minimum (∆E=0), co esponding o he
disloca ion s a e equi alen o he ini ial con igu a ion (RC =
0), and accompanied by a c oss-slip p ocess. Simila ly, he
mo ion o he sc ew (1 1 5)[1 1 0] disloca ion decomposes in o
gliding along (001) and (2 2 7) planes wi h c oss-slip occu -
ing be ween hem. The (227)[1 1 0] slip exhibi s a simila
ene gy p o ile o he (1 1 3)[1 10] slip bu wi h a highe en-
e gy ba ie . Fu he mo e, he (2 2 7) plane is geome ically
close o he (113) plane, sugges ing ha he (2 2 7) slip can
be conside ed a a ia ion o he (11 3) slip, in ol ing a s uc-
u al ansi ion a he disloca ion co e. Fo disloca ion mo e-
men on he (114) plane, in addi ion o he ansi ions be ween
(001) and (2 2 7) planes as seen in he (1 1 5)[1 1 0] disloca-
ion mo ion, an addi ional in e media e local minimum and a
c oss-slip p ocess om (11 3) o (0 0 1) planes a e iden i ied.
Slip p ocesses on he (114) and (1 1 5) planes exhibi compa a-
ble ene gy ba ie s (0.314 and 0.315 eV/Å, espec i ely), as he
(227) slip ep esen s he a e-limi ing s ep in bo h cases. The
sc ew (11 6)[1 1 0] disloca ion exhibi s he longes glide dis-
ance (34.90 Å) among all simula ed disloca ions. I s mo ion
consis s o mul iple in e media e minima and c oss-slip e en s,
as well as ex ension and cons ic ion o he disloca ion co e (
Figu e 5(e)). Ac oss all simula ed sc ew disloca ions, no dis-
socia ion in o pa ials bounded by s acking aul s was obse ed
along he MEPs.
4. Discussion
Plas ici y in La es phases is clea ly much mo e complex han
indica ed in p e ious in es iga ions. Recen ad ances in expe -
imen al and compu a ional me hods ha e allowed us o d aw
a mo e comple e pic u e o how plas ici y akes place in hese
mos common in e me allic phases [6] and build he ounda ion
ha no only connec s he di e en La es phase poly ypes bu
also enables us o in e and p edic de o ma ion mechanisms
and mechanical p ope ies o o he in e me allic phases ha
con ain he La es phase as an impo an building block [5,6].
4.1. A omis ic mechanisms o c oss-slip in La es phases
One o he cen al indings o his s udy is he equen oc-
cu ence o c oss-slip be ween mul iple {11 n}planes. This
beha io challenges he con en ional iew ha plas ici y in
La es phases is con ined o a na ow se o c ys allog aphic
planes, pa icula ly {1 1 1}. Ins ead, ou esul s show ha pe -
ec sc ew disloca ions can glide and c oss-slip be ween a a-
ie y o planes, enabled by hei undissocia ed co e s uc u es.
A omis ic simula ions con i m ha he sc ew disloca ion co es
emain compac ac oss all s udied slip sys ems, and no dissoci-
a ion in o pa ials o o ma ion o s able s acking aul s occu s
along any o he calcula ed MEPs. These esul s a e consis-
en wi h p io wo k showing an absence o me as able s acking
aul s along hese slip pa hs in C15 CaAl2[37].
Al hough expe imen al obse a ions e ealed disloca ion
mo ion along a ious {1 1 n}planes o e dis ances anging om
ens o hund eds o nanome e s (see Figu es 2and 3), he a om-
is ic simula ions sugges ha hese mac oscopically obse ed
slip aces a e go e ned by a smalle se o undamen al slip
e en s. Speci ically, disloca ion glide occu s h ough elemen-
a y mo ion on he {111},{1 1 3},{0 0 1}, and {227}planes.
These ounda ional slip p ocesses exhibi ene gy ba ie s com-
pa able o hose o indi idual slip e en s o as in e media e
sub-e en s wi hin c oss-slip ansi ions (see Table 1). The cal-
cula ed ene gy ba ie s associa ed wi h hese ansi ions ange
om 0.1 o 0.4 eV/Å, in ag eemen wi h alues epo ed o
o he s uc u ally complex c ys als. Fo ins ance, ou -o -plane
glide- o-climb ansi ions in pe o ski e S TiO3exhibi ba ie s
be ween 0.08 and 0.6 eV/Å, depending on he cha ge s a e o
he disloca ion co e [55]. I is wo h no ing ha he disloca-
ions modeled in his s udy a e s aigh , which esul s om he
limi ed simula ion cell leng h along he disloca ion line di ec-
ion. This cons ain is due o he high compu a ional cos o
he momen enso in e a omic po en ial, which is h ee o de s
o magni ude mo e expensi e han classical semi-empi ical po-
en ials, like embedded a om me hod po en ials. As a esul , he
simula ions do no cap u e local disloca ion line cu a u e, such
as bowing-ou o kink-pai nuclea ion, which can lowe he en-
e gy ba ie o a e-limi ing s eps. The epo ed alues he e may
he e o e ep esen uppe bounds o he ue ac i a ion ba ie s
o hese slip e en s.
Fu he mo e, he sc ew disloca ion in C15 CaAl2shows a
endency o sp ead along he (001) plane, sugges ing ha ou -
o -plane a omic displacemen s play a signi ican ole in dislo-
ca ion mo ion, see Mo ies S1-9 in he Supplemen a y In o ma-
ion. Such ou -o -plane e ec s a e o en associa ed wi h non-
Schmid beha io and ha e p e iously been epo ed in synch o-
Shockley disloca ion mo ion in La es phases ia a omis ic sim-
ula ions [26]. Simila phenomena ha e also been obse ed
expe imen ally in laye ed c ys alline ma e ials such as MAX
phases [56,57]. Ne e heless, o ully unde s and he ole
o no mal s ess componen s in c oss-slip beha io in La es
phases, u he expe imen al alida ion, such as h ough mi-
c opilla comp ession es ing, and mo e ex ensi e a omis ic
modeling will be essen ial.
4.2. Tempe a u e-dependen plas ici y in La es phases
Nanomechanical es ing allowed us o induce plas ici y a
low empe a u es a below he BDTT. In combina ion wi h
imaging and analysis o nume ous inden a ion imp in s a he
mic on scale and dedica ed de ec analysis by TEM, we could
e eal ha slip planes beyond hose p e iously epo ed in he
7
Table 1: Summa y o glide dis ance, ansi ion p ocess, and associa ed ene gy ba ie s o he sc ew a
2[¯
110] disloca ion mo ion on di e en glide planes.
Glide plane Glide dis ance (Å) T ansi ion p ocess Ene gy ba ie (eV/Å)
(110) 8.01 (110) 0.116
(11¯
1) iple-kagome 4.91 (11¯
1) 0.107
(11¯
1) iple 4.91 (11¯
1) 0.160
(11¯
2) 13.87 (11¯
3) +(11¯
1) 0.284, 0.075
(11¯
3) 9.39 (11¯
3) 0.266
(11¯
4) 24.02 (11¯
3) +(001) +(22¯
7) 0.267, 0.115, 0.314
(11¯
5) 14.71 (001) +(22¯
7) 0.115, 0.315
(11¯
6) 34.90 (001) +co e ex ension +co e cons ic ion 0.114, 0.144, 0.144,
+(22¯
7) +(001) +(11¯
6) 0.367, 0.115, 0.159
(001) 5.66 (001) +(001) 0.076, 0.115
li e a u e [13] a e ac i e and, in ac , accommoda e he majo i y
o plas ic de o ma ion. Un a elling ha and how disloca ions
c oss-slip be ween a subse o he mac oscopically obse ed
planes by high- esolu ion mic oscopy and a omis ic modelling
gi es us he basis o in e p e plas ic de o ma ion o he La es
phase mo e gene ally. Fo example, he obse ed c oss-slip
o [110] disloca ions on {1 1 n}planes gi es ise o he o ien-
a ion dependence o de o ma ion e idenced by he changing
su ace ea u es in inden a ion [29]. Simila ly, unco e ing he
mechanisms go e ning disloca ion mo ion is essen ial o con-
nec obse a ions o mechanical p ope ies and ac i e mecha-
nisms ac oss a ange o empe a u es and s ain a es.
P e ious wo k e ealed he he mally ac i a ed na u e o he
synch oshea mechanism [25,26,15,14] and p o ided a basis
on which o unde s and he occu ence o con en ional disloca-
ion mo ion in pa allel {111}in e laye s o he C15 La es phase
o (000 1) in e laye s in he hexagonal poly ypes. I is now ap-
pa en ha he slip o ⟨11 0⟩disloca ions is wha acili a es he
mani old o slip planes by allowing c oss-slip on o he many
a ailable {11n}planes ia a combina ion o undamen al slip
e en s on {111},{113},{001}, and {22 7}planes. This unde -
s anding p o ides a clea pa h o connec de o ma ion a di e -
en empe a u es: a low empe a u es, glide occu s on planes
o e ing leas esis ance and he compac disloca ion co es o
⟨110⟩disloca ions acili a e c oss-slip and he eby disloca ion
mo ion unde maximum esol ed shea s ess ac oss a iable
s ess ields (as induced in inden a ion in his wo k). P e ious
obse a ions a ele a ed empe a u e [13] on he o he hand, a e
consis en wi h he mal ac i a ion a ou ing slip by synch os-
hea , con ining de o ma ion o only {1 11}planes. As synch os-
hea ope a es by he o ma ion and mo ion o pa ials on {111}
planes, his dominance o {111}slip a ele a ed empe a u es
may be ela ed o he mally ac i a ed disloca ion dissocia ion
blocking u he c oss-slip [58], he e on o he {1 1 n}planes on
which only he pa ials canno glide o c oss-slip, he eby de-
p i ing he {1 1 n}planes o mobile disloca ions.
Nanoinden a ion a di e en empe a u es has e ealed a
nea -cons an ha dness below he b i le o duc ile ansi ion
[59], bu ecen wo k expanding in o he egime o d opping
c i ical s esses [60] indica ed possible ha dening wi h empe -
a u e be o e he ha dness d op associa ed wi h he b i le o duc-
ile ansi ion. Whe he his is a ep oducible and mo e gen-
e al ea u e o de o ma ion o La es phases owing o he he -
mally ac i a ed dissocia ion and c oss-slip p ocesses, emains
o be explo ed. T ansmission elec on mic oscopy in es iga-
ions o an inden a ion p in de o med a ele a ed empe a u es
[60,29,59] enable o con i m his hypo hesis o shed ligh
on addi ional ansien mechanisms con olling low in La es
phases, by inding beside pe ec disloca ions, which we e p e-
iously obse ed a ambien empe a u e, addi ionally pa ial
disloca ions o high empe a u e (450°C). Simila ly, expe i-
men s and modelling will build on he newly iden i ied unda-
men al mechanisms o disloca ion mo ion o s udy he e ec
o composi ion on disloca ion mo ion, whe e he in e play o
ha dening and so ening mechanisms in oduced by an excess
o ei he small o la ge a oms and he esul ing o ma ion o
an i-si e de ec s and/o acancies, emains poo ly unde s ood.
4.3. Insigh s in o in e me allic design
The abili y o unde s and, p edic and ailo plas ici y in
La es phases and hose c ys als wi h la ge uni cells whe e
plas ici y akes place p edominan ly in La es phase building
blocks, will enable ma e ials and p ocess design o a ange
o applica ions. Fo example, he equen La es phase p ecip-
i a es in s eels, supe alloys o high en opy alloys may be ha -
nessed in en ionally in he design p ocess. Con olling La es
poly ype o ela ed phases con aining La es phase as a build-
ing block in p ecipi a es may enable shi s in mechanical con-
as o he ma ix phase [5] and mechanisms o ha dening o
damage o ma ion by blocking o enabling co-de o ma ion ia
slip sys em and cohe en in e ace selec ion [61,62]. In use
as unc ional ma e ials, in pa icula o hyd ogen s o age, un-
de s anding and pu pose ul manipula ion can be employed a
se e al s ages o he p ocessing and use o La es phase based
ma e ials. Fo example, p onounced b i leness eases powde
p oduc ion, con e sely, he in oduc ion o c ys al de ec s and
pe haps also selec ion o he mos p e alen de ec ype, can im-
p o e (de)hyd ogena ion kine ics [63,64]. Fo bo h, he abili y
o manipula e which disloca ions o m and unde which s esses
hey mo e is essen ial and may be achie ed by means o al e -
8
y-[110]
z-[001]
RC:0 RC:1RC:0.50
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0.4 0.6 0.8 1
∆E (eV/Å)
Reac ion coo dina e
(001)[1
−10]
(a) RC:0 RC:0.66 RC:1
(113)
y-[111]
z-[112]
(111)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0.4 0.6 0.8 1
∆E (eV/Å)
Reac ion coo dina e
(112
−)[1
−10]
(b)
RC:0 RC:0.49 RC:1
y-[221]
z-[114]
(113)
(227)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0.4 0.6 0.8 1
∆E (eV/Å)
Reac ion coo dina e
(114
−)[1
−10]
(001)
RC:0.30 RC:0 RC:0.40 RC:1
y-[552]
z-[115]
(001)
(227)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0.4 0.6 0.8 1
∆E (eV/Å)
Reac ion coo dina e
(115
−)[1
−10]
(c) (d)
(e) RC:0.50 RC:1
y-[331]
z-[116]
(116)
RC:0 RC:0.12
(001)
(001)
Cons ic ed
Ex ended
RC:0.38RC:0.22
(227)
RC:0.25
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
∆E (eV/Å)
Reac ion coo dina e
(116
−)[1
−10]
Figu e 5: A omis ic con igu a ions and ene gy p o iles along MEPs o he mo ion o he sc ew a
2[110] disloca ion on (a) (001), (b) (1 1 2), (c) (1 1 4), (d) (1 1 5),
and (e) (116) planes in he C15 CaAl2La es phase we e calcula ed using he NEB me hod. Only a oms belonging o he disloca ion co e a e shown he e. The
o ange and magen a symbols indica e he posi ion o he disloca ion line in he ini ial ( eac ion coo dina e RC:0) and inal (RC:1) a omis ic con igu a ions, while
he cyan symbols ep esen he posi ion o he disloca ion line a he in e media e minima. Dashed lines indica e he glide planes be ween each local minimum.
9
