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chemistry
Perspective
https://doi.org/10.1038/s42004-024-01319-8
Quasicrystal synthesis by shock
compression
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Jinping Hu
1
,PaulD.Asimow
1
,ChiMa
1
,PaulJ.Steinhardt
2
&LucaBindi
3
Quasicrystals are of interest because of their unique nonperiodic structures and physical properties.
Motivated by naturally occurring icosahedral AlCuFe- and decagonal AlNiFe-phases hosted in a
shocked meteorite, different laboratories have undertaken a series of shock recovery experiments to
understand their formation mechanism. Shock experiments generate a complex series of processes
andconditions,includinganear-instantaneousexcursiontohighpressureandhightemperature,large
shear stresses, local melting, rapid decompression, fast quenching and post-shock annealing. This
highly dynamic scenario offers a very useful but imperfect tool for exploring the stability of novel alloys,
such as quasicrystals. So far, all the shock-synthesized quasicrystals differ considerably in
composition from any thermodynamically stable or metastable quasicrystals synthesized by
metallurgical techniques at low pressure, leaving plenty of questions to be answered about their
formation conditions and their nucleation and growth mechanisms occurring during shock
experiments. In this Perspective, we summarize the previous studies of shock-synthesized
quasicrystals and discuss the advantages and dif
fi
culties caused by the experimental complexity. We
also propose a few directions for future experiments to better control the shock conditions and
understand the properties of quasicrystals.
Quasicrystals are special types of solid
s that have neither the periodicity of
regular crystals nor the disorder of amorphous materials. Instead, the atomic
arrangement of quasicrystals show
s Bragg peak diffraction and point
symmetries but lacking periodic transl
ational order, which is referred to as
quasiperiodicity
1
. The discovery of quasicrystals
in the laboratory stimulated
intense efforts over decades, dedicated to characterizing this new form of
solid matter
2
. Because most of the observed quasicrystalline phases are
metallic alloys, metallurgy provides t
he primary methods and techniques
applied to synthesize and characterize them. The
fi
rst con
fi
rmed Al-TM
(transition metal) quasicrystal is meta
stable relative to crystalline phases
3
.
Likewise, numerous other metastable
quasicrystals have been discovered
using dynamic techniques including rapid quenching by melt spinning,
vapor deposition and mechanical alloying
2
,
4
. Subsequently, the discovery of
thermodynamically s
table quasicrystals
in, e.g., the Al-Cu-Li
5
and Al-Cu-
Fe
6
systems
greatly improved the size, crystallinity and uniformity of
samples that could be generated and contributed many advances to the basic
understanding of quasicrystalline structures
7
.
Based on the
fi
rst stable quasicrystals, a large number of stable quasi-
crystals were proposed and synthesi
zed using predictive conceptual tools
such as valence electron concentration, ratios of atomic radii, and the
existence of approximants
7
,
8
. In particular, the Al-Cu-Fe quasicrystal is of
great interest because of its low-cost starting materials and the high level of
perfection of its icosahedral structur
e, with unambiguous pentagonal tiling
and long-range order
9
. The icosahedral point symmetry is still the only
experimentally con
fi
rmed structure that is aperiodic in all three dimensions.
By contrast, the octagonal, decagonal,
dodecagonal and theoretical hepta-
gonal symmetries are all two-dimensional aperiodic tilings, built up in the
third dimension with periodic arrays of
stacked layers. Icosahedral quasi-
crystal phases (i-phases) possess
5-, 3- and 2-fold rotation axes with
m-3-5
point group and can be viewed as projections of primitive or face-centered
cubic Bravais lattices in six dimensions
8
. Both electron and X-ray diffraction
are capable of characterizing this 3D con
fi
guration of symmetry axe
6
,
10
,
11
.
More recently, it has also been shown that the 5-fold tiling can be repro-
duced by cyclic twinning of primit
ive prolate golden rhombohedra
12
.
Contrary to previous twinning models, such an elaborately designed crys-
tallographic con
fi
guration eliminates the need for pervasive twinning
boundaries when producing icosahedral
domains. However, it still requires
repeated twin domains of equal size and twinning that is high correlated on
large scales to maintain quasiperiodicity, which is not commonly expected
in natural or experimental conditions
13
.
The synthesis of thermodynamicall
y stable quasicrystals, such as the
Al-Cu-Fe i-phase, can be achieved with conventional casting
7
.Incontrastto
1
Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, USA.
2
Department of Physics, Princeton University, Princeton, USA.
3
Dipartimento di Scienze della Terra, Università degli Studi di Firenze, Firenze, Italy.
e-mail:
jinping@caltech.edu
;
luca.bindi@uni
fi
.it
Communications Chemistry
| (2024) 7:232
1
1234567890():,;
1234567890():,;
systems that produce stable and metas
table quasicrystals of different
compositions
6
, rapid solidi
fi
cation plus solid-state annealing at various
temperatures works consistently in t
he Al-Cu-Fe system, yielding the same
stable phase as the casting procedure
6
,
14
. Despite the varied and complex
intermetallic assemblages and reaction sequences observed at different
cooling rates, i-phases are consi
stently recovered in a narrow
fi
eld around
Al
60-65
Cu
21-26
Fe
11-15
composition
15
,
16
. These highly reproducible results
indicate the robustness and high stability of the Al-Cu-Fe i-phase, consistent
with the observed perfection of its icosahedral structure.
In the last
fi
fteen years, Al-Cu-Fe i-phases became the center of
attention again because of the discovery of naturally occurring quasicrys-
talline phases
17
.The
fi
rst discovered quasicrystal is an Al
63
Cu
24
Fe
13
i-phase,
which was subsequently given the of
fi
cial mineral name icosahedrite
10
.A
second natural quasicrystal with decagonal symmetry, Al
71
Ni
24
Fe
5
,was
of
fi
cially named decagonite. Both wer
e discovered in fragments of the
Khatyrka meteorite
18
. Like icosahedrite, decagonite is also thermo-
dynamically stable over a narrow com
positional range. However, unlike
icosahedrite, whose stability
fi
eld extends from the solidus down to room
temperature
14
, decagonite decomposes to intermetallic crystalline phases at
sub-solidus temperatures
19
. In addition, contrary to the reproducible
synthesis of the well-de
fi
ned stable icosahedrite composition, rapid
quenching in the Al-Ni-Fe system yields a range of metastable decagonal
quasicrystals with 9-21 at% Ni and 9-16 at% Fe, deviating considerably from
the stability
fi
eld
20
. These results show that Al-Ni
-Fequasicrystalsaremore
sensitive to their formation conditio
ns, which raises essential questions
about the formation mechanism of natu
ral quasicrystals, because the geo-
logical processes that affected the Khatyrka meteorite hardly resemble any
standard metallurgical processing technique
21
,
22
.
The story became more interesting with the discovery of the third
natural quasicrystal
23
, another Al-Cu-Fe i-phase with the composition
Al
62
Cu
31
Fe
7
, known as i-phase II. This composition is outside the known
stability
fi
eld of the i-phase in the Al-Cu-Fe system and had not been
produced in any experimental study at that time. As mentioned above, all
kinds of cooling rates and annealing temperatures in metallurgical studies
reproducibly yield the consistent sta
bleAl-Cu-Fei-phasecomposition.
Hence, the natural occurrence of i-p
hase II is a powerful hint that novel
formationmechanismsorconditionsneedtobeevaluatedinorderto
understand the natural quasicrystals
22
. The very recent discovery of the
fourth natural quasicrystal, an Al
52
Cu
31
Fe
10
Si
7
i-phase, in a micrometeorite
has further deepened this puzzle
24
.
The host rock and type locality of icos
ahedrite, decagonite, and i-phase
II is the Khatyrka CV3 chondritic mete
orite. This sample contains abundant
shock-induced high-pressure sili
cate minerals such as ahrensite
[(Fe,Mg)
2
SiO
4
in spinel structure] and stishovite (SiO
2
in rutile structure),
which motivated the idea of a high-velocity impact origin for natural
quasicrystals
25
. As summarized below, this hypothesis received very strong
support from the successful synthesis of Al-Cu-Fe and Al-Ni-Fe quasi-
crystals via impacts involving Al-alloys in the laboratory. These shock
recovery experiments produced a range of new Al-Cu-Fe and Al-Ni-Fe
compositions outside the low-pressure stability
fi
eld of icosahedrite and
decagonite (including compositions very
close to i-phase II). It indicates that
such laboratory shock recovery ex
periments offer a strategy for de
fi
ning the
impact conditions experienced by the h
ost meteorites of the natural qua-
sicrystals and, more generally, for unde
rstanding what distinctive aspects of
dynamic compression lead to the synthesis of quasicrystals different from
those created by conventional metallurgy.
In this Perspective paper, we will s
ummarize the shock compression
studies dedicated to quasicrystal synthesis. We will present the chemistry
and mineralogy of shock-induced quas
icrystal assemblages in comparison
to low-pressure phase equilibria and
discuss the possible effects of high
pressure, high temperature, shear stress, turbulent
fl
ow, short timescales,
and other unique aspects of dynamic compression. Experiments that pro-
duced quasicrystals and those that di
d not will both be discussed, with the
aim of demonstrating both the adva
nces that have been made and the
incompleteness of our understandi
ng of material synthesis in shock
experiments. To overcome the uncerta
inties and complexity associated with
shock synthesis of quasicrystals, several advanced techniques are proposed
for future studies.
Shock-wave recovery of quasicrystal: How to set up
Shock recovery facilities are useful tools for creating and characterizing the
transformations experiencedby material undershock compression. To date,
successful shock-synthesis of quasicrys
tals has been achieved exclusively by
propellant-gun recovery techniques (Table
1
), although other means of
generating experimental shocks exist, with or without a gun
26
,
27
.Inthis
section, we will summarizethe experimental setup for successful synthesis of
quasicrystals by gun-driven plate impact; below we will discuss the potential
use of laser shock in a later section. The gun shock-recovery technique was
fi
rst developed in the late 1950s following earlier explosive experiments
28
,
29
,
and applied to investigate failure and deformation in metals and the effects
Table 1 | Summary of shock recovery experiments target quasicrystal synthesis
Shot No.
Starting material
Capsule
material
Peak
pressure, GPa
Icosahedral quasicrystal
Associated phase Ref
S1230
Olivine, CuAl
5
, Canyon Diablo, bronze
SS304
21
Al
68-73
Cu
10-12
Fe
11-16
Cr
1-4
Ni
1-2
i-phase aggregate
21
S1233
Olivine, CuAl
5
Ta liner
31
x
11
S1234
CuAl
5
SS304
25
Al
70-75
Cu
11-12
Fe
9-13
Cr
2-4
Ni1
i-phase aggregate
11
S1253
Al-Cu-W GDI wedge (Al-rich)
SS304
30
Al
62
Cu
30
Fe
7
Cr
1
/
Al
68
Fe
20
Cr
6
Cu
4
Ni
2
β
+
θ
/
λ
22
,
43
S1255
Al-Cu-W GDI wedge (W-rich)
SS304
35
Al
69
Cu
11
Fe
14
Cr
4
Ni
2
β
+
λ
22
Al
63
Cu
24
Fe
13
pellet of pure metal powders Cu
21
x
40
Laser
shock
Al
63
Cu
24
Fe
13
pellet of pure metal powders PET
+
LiF
10
x
40
Vial-mixed Ti
45
Zr
38
Ni
17
pure metal
powders
Cu
x
39
Mechanically alloyed Ti
45
Zr
38
Ni
17
pure
metal powders
Cu
, composition not reported
39
Decagonal quasicrystal
S1235
Aluminum alloy 2024, permalloy 80
SS304
27
Al
73
Ni
19
Fe
4
Cu
2
Mg
0.6
Mo
0.4
Mn
0.3
β
37
The shot number corresponds to experiments at Caltech Lindhurst laboratory. GDI: graded density impactor; Canyon Diablo: iron meteorite consistin
g of Fe-Ni alloys; SS304: 304 stainless steel. Phase
identi
fi
ers:
β
: Al(Cu,Fe,Ni),
Pm
-3
m
, stolperite;
λ
:Al
13
(Fe,Ni)
4
,
C
2/
m
, hollisterite;
θ
:Al
2
Cu,
I
4/
mcm
, khatyrkite.
https://doi.org/10.1038/s42004-024-01319-8
Perspective
Communications Chemistry
| (2024) 7:232
2
of impact metamorphism in geological materials
30
,
31
. The apparatus consists
of a recovery target assembly, most commonly a capsule made of strong
metal with the sample embedded (Fig.
1
), attached to an explosive pro-
pellantorgasgun.Theimpact-facingfrontsideofthecapsuleactsasthe
driver plate to generate a strong parallel shock wave and the side and back
walls act as momentum traps to reduce the tensile stress, prevent spallation,
and enable coherent sample recovery
31
. Upon hypervelocity impact of the
fl
yer plate on the capsule, a shock wave is generated in both
fl
yerand capsule.
Thepressureiscontrolledbytheimpactvelocityandtheshockequationof
state (or Hugoniot) of each material involved in the collision. The behavior
of the shock wave each time it traverses a material interface is determined
from continuity of particle velocity and normal stress at the interface, a
method known as impedance matching
32
.
To reproduce the shock condition
s inferred from the host rock of
natural quasicrystals
25
,
33
, the peak shock pressures in corresponding
experiments were designed to be around 20
30 GPa (Table
1
). For a starting
sample of Al-Cu-Fe mixtures, the Al-rich phases have lower density and
shock impedance than the Cu-Fe-rich p
hases, resulting in a stage with lower
initial shock pressure before reverberation among materials raises the
pressure to the peak value. The shoc
k pulse duration is dependent on the
thickness of the
fl
yer plate. For a common millimeter-thick
fl
yer, the
duration is on the order of microseconds
22
. In most cases, a coherent disk of
sample or a stack of such disks is placed normal to the impact direction,
yielding some central area that experiences uniaxial
fl
ow.Inthisscenario,
the pressure-time history of the sample can be conveniently calculated using
known or estimated Hugoniot parameters and the impedance match
solution
11
,
21
,
22
. Because the starting materials are mostly pure metals and
common alloys, their Hugoniots can be readily found in, e.g., the LASL
Shock Hugoniot Data handbook
34
and their microscopic mixtures can be
modeled using a simple kinetic energy averaging method
35
.Thepeakshock
temperature can also be estimated f
rom such a solution if the Grüneisen
parameter and heat capacity of the target materials is known or estimated
36
.
However, at the 20
30 GPa shock pressures of interest, the increase in
temperature due to uniaxial shock compression of a coherent disk made of
Al-Cu-Fe-Ni alloys would be below 400 °C
37
. Solid state interface-mediated
reactions do not occur to any observab
le extent under such temperatures
even in hours or days, much less microseconds
14
. Therefore, local
mechanisms to generate hot areas are needed to promote melting and
intermetallic reactions: these include
high-strain shear zones and collapse of
voids or porosity, which can result from (deliberate or accidental) mis
fi
ts
between parts of the sample and capsule. For instance, the machined sample
is naturally smaller than the counter
bore in the capsule, leaving tens of
microns of open space. Collapse of th
e open space under shock compression
is an irreversible process that increas
es the waste heat and therefore local
temperature, in addition to the effects of shear friction on the sample-
capsule interface
11
. These effects in combination can account for local partial
melting and greatly enhance the reactions among alloys, which turns out to
be essential for successful synthesis of quasicrystals (Fig.
1
).
Oblique impact is another techniqu
e to enhance friction, deformation
and local melting. In practice, the most convenient method is to make a
wedged sample with sample-capsule interface at an inclined angle to the
impact direction (Fig.
1
). The oblique impact yields signi
fi
cant shear
fl
ow of
material in both lateral and longitudinal directions
22
. In this case, the shock-
wave propagation is clearly not uniax
ial and the pressure history experi-
enced by different parts of the interface could be dependent on relative
position of the high- and low-impedance
materials. Nevertheless, for sample
and
fl
yer plate of millimeter thickness, th
e peak shock pressure across the
sample can still reach equilibrium within about half a microsecond
22
.
As mentioned, random or designed mis
fi
ts between parts of the sample
or at the sample-capsule interface can be useful for creating concentrated
friction and melting at particular locations in the assembly. However, the
local shear and turbulent
fl
ow also mix the different components in a poorly
controlled way and may or may not create the
correct
melt composition
during a shock experiment. Hence, it is a desirable strategy to build in a
systematic compositional gradient alo
ng the frictional interface, aiming to
ensure that local melting samples a ra
nge of compositions. Hu et al. (2020a)
used a graded density impactor (GDI), originally manufactured as a
fl
yer
plate for quasi-isentropic loading experiments
38
,asthesamplefortwo
experiments. This GDI was manufactur
ed by tape-casting layers of powder
mixtures, starting with Al at the top and proceeding through the full range
Al-Cu mixtures to pure Cu, followed by the full range of Cu-W mixtures to
with pure W at the bottom. This disk was cut at an angle to expose the
compositional gradient along an incl
ined plane that was placed in contact
with 304 stainless steel as an Fe source. Unsurprisingly, in the recovered
Fig. 1 | Schematic cross sections of target assem-
blies for synthesizing quasicrystals by the Caltech
shock-wave lab.
The outlines of the chamber cap-
sules are not to actual scale. Experiments S1230
21
,
S1234
11
, S1253
22
and S1255
22
produced icosahedral
phases and S1235
37
produced decagonal phase. The
locations of intermetallic quasicrystal reactions are
highlighted by the light-yellow boxes. Details of each
starting material is in the main text.
https://doi.org/10.1038/s42004-024-01319-8
Perspective
Communications Chemistry
| (2024) 7:232
3
sample, the Al-Cu-Fe i-phases occurred in areas with starting Al/Cu ratio
close to the product phase, along the inclined surface of the wedge, where the
strongest vertical and lateral shear
fl
ow occurred (Fig.
1
). In contrast,
although a
fi
ne powdery starting material can provide a well-controlled
uniform starting composition, the shea
r friction at grain boundaries in this
case is also uniformly distributed through the sample. The resulting average
shock temperature elevation remains well below the solidus at 20
30 GPa
and is insuf
fi
cient to enable noticeable intermetallic reactions
11
.Indeed,it
appears to be dif
fi
cult to synthesize quasicrystal by shocking metallic
powders, as demonstrated by trials i
n at least two other laboratories
39
,
40
.The
result is somewhat counterintuitive, but it appears empirically true that
concentrated friction and temperature
along an interface is more likely than
powder consolidation to yield a quasicrystalline product.
Shock-synthesized quasicrystals: How to distinguish
Most experiments to date targeting th
e impact conditions of the natural
quasicrystals were performed on a serie
s of Al-Cu-Fe-Ni samples, primarily
in the Caltech shock wave laboratory (Table
1
). Because of the common
usage of stainless-steel 304 (SS304; Fe
71
Cr
18
Ni
8
Mn
2
Si
1
)capsulesinthe
Caltech experiments, there is a source of Cr, and Ni (plus minor Mn and Si)
in the system. This allowed the growth of quasicrystals with compositions
more complicated than the pure terna
ry systems previously explored,
although the synthesized quasicrystals still have two or three predominant
elements.
The
fi
rst successful attempt (S1230; Table
1
) to experimentally
reproduce the formation of icosahedr
ite used a series of materials that
resemble aspects of the mineralogy of the Khatyrka meteorite:
(Mg
0.75
Fe
0.25
)
2
SiO
4
olivine, CuAl
5
alloy (mixture of Al and CuAl
2
domains),
Canyon Diablo iron meteorite (Fe-Ni alloys) and Al
14
Cu
4
Fe
1
Ni
1
bronze
21
(Fig.
1
). To speci
fi
cally test whether the Fe in the quasicrystal was derived by
reduction from olivine or incorporat
ion from the steel chamber, a follow-up
trial used CuAl
5
and olivine wrapped in a Ta liner (S1233). This experiment
did not produce quasicrystals or other Cu-Al-Fe alloys, suggesting that the
potential Al-metal/olivine electron e
xchange reaction cannot produce suf-
fi
cient metallic iron to form intermetallic phases
11
.Ontheotherhand,the
shot of exclusively CuAl
5
in SS304 capsule (S1234), where steel is the only
iron source, closely reproduced the com
position and texture of icosahedrite
seen in S1230. This indicate that non-metallic starting materials are not
essential for synthesizing quasicrystals. If this applies to quasicrystal
synthesis in the Khatyrka meteorite par
ent body during asteroidal impact, it
implies that the proximity of Fe-Ni and Cu-Al metallic alloys is essential
whereas the presence of Fe-bearing silicates and oxides are not necessary.
Guided by that, subsequent shock experiments were focused on metallic
starting materials (Table
1
).
Metallurgical studies have de
fi
ned the phase equilibria and reaction
sequences for quenching of Al-Cu-Fe me
lts at low-pressure. The appearance
of the quasicrystalline icosahedral
phase is highly dependent on the com-
position of the starting melt, the cooling rate and the degree of
undercooling
41
. Since the shock event does not necessarily achieve phase
equilibrium, the observed co-existing intermetallic phases can represent
either liquidus, supra-solidus, or subsolidus conditions, depending on
mixing and cooling processes. The sample recovered and investigated in
regular shock recovery experiments captures only the end-state of the path,
and it is dif
fi
cult to distinguish when during the sequence of complex
pressure-temperature-strain-ti
me conditions a given phase may have
nucleated and grown. The fact that forma
tion of quasicrystal requires local
excursions of shock conditions devi
ating from the bulk Hugoniot have
increased such dif
fi
culty, even though many techniques can be used to
measure the shock equation of state of bulk samples
26
.
Icosahedral quasicrystal phases
IntheAl-Cu-Fesystem,shockingCuAl
5
within a SS304 capsule produced
large domains containing almost ex
clusively aggregates of the i-phase
(Fig.
2
a). Other intermetallic phases surround the i-phase region but are not
intergrown with the i-phase aggregates
11
,
21
. Both scanning and transmission
electron microscopy (SEM & TEM) imag
es show variation in grain size of
i-phase from several
μ
m down to <100 nm (Figs.
2
aand
3
a). The chemical
analyses from TEM energy dispersive spectrometry (EDS) and electron
microprobe wavelength dispersive sp
ectrometry (WDS) agree well on the
Al
70-75
Cu
11-12
Fe
9-13
Cr
2-4
Ni
1
i-phase composition
11
.Thisdeviatessig-
ni
fi
cantly in Al and Cu contents from the narrow thermodynamic stability
fi
eld of ~Al
65
Cu
23
Fe
12
icosahedrite at ambient pressure (Fig.
4
). In previous
metallurgy studies starting with a melt of the ideal Al
65
Cu
20-25
Fe
12-15
composition, Tsai et al. (1987) observed a
single i-phase from quenched melt
at solidus temperature to annealing at 595 °C, whereas Rosas and Perez
(1998) produced the
β
phase [Al(Cu,Fe),
Pm
-3
m
, corresponding to the
mineral stolperite]
fi
rst and then grew i-phase by a peritectic reaction,
during annealing at 950-700 °C. At the solidus the peritectic reaction is
complete, leaving i-phase being the only product. Technically, either sce-
nario would potentially agree with th
e formation of i-phase aggregate in a
shock experiment because the temperature of reaction during shock is not
precisely known, with estimates mostly constrained by the observation of
local melting and alloying.
A separate shot using the Al-Cu-W GDI (S1255; Fig.
1
)produced
i-phase of composition Al
69
Cu
11
Fe
14
Cr
4
Ni
2
, very similar to that grown in
the CuAl
5
experiments (Fig.
4
). The distinctive result from this experiment is
that the i-phase is in direct association with intermetallic phases
λ
(Al
13
Fe
4
;
C
2/
m
; corresponding to the mineral hollisterite) and
β
(Fig.
2
d). This
assemblage agrees better with the natural icosahedrite occurrence
23
,
33
.The
co-existence of i-phase,
λ
and
β
is expected from subsolidus isothermal
sections of the Al-Cu-Fe phase diagram
22
, although the reaction sequence
may also involve other unobserved intermediate phases, such as the
θ
phase
(Al
2
Cu;
I
4/
mcm
; corresponding to the mineral khatyrkite) and the
orthorhombic Al
5
Fe
2
phase
15
.
In the same study
22
, another experiment using a GDI loaded with the
gradient direction reversed (S1253; Fig.
1
) reproduced a near exact match in
structure and composition to a natural i-phase for the
fi
rst time (Fig.
2
c).
The Al
61.5
Cu
30.3
Fe
6.8
Cr
1.4
composition of the i-phase in S1253 closely
resembles the natural Al
61.9
Cu
31.2
Fe
6.8
Cr
0.1
i-phase II in Khatyrka, a com-
position outside the ambient-pressure stability
fi
eld
23
. The directly asso-
ciated phases are
β
and
θ
, whose assemblage and chemistry also match the
natural occurrence. However, in the n
atural occurrence, the i-phase II is
enclosed in
β
, which is the opposite of the texture expected from a peritectic
growth of i-phase from
β
and melt
16
. By contrast, the texture of the
experimental assemblage indeed suggests
β
being consumed in peritectic
reactions and shows i-phase surrounded in turn by
θ
.Thistextureisin
agreement with the reaction sequence expected from metallurgy experi-
ments with melt compositions close to
icosahedrite. In such cases, i-phase
forms after the liquidus phase
β
, persists to the solidus and comes before the
subsolidus
θ
phase
42
.
The GDI experiment yielded another serendipitous outcome, found
in the Al-rich region
43
(Table
1
). Unlike all previous Al-Cu-Fe i-phases,
whose Cu/Fe ratios vary between ~1 and 4, this experiment created an
Al
68
Fe
20
Cr
6
Cu
4
Ni
2
i-phase (Cu/Fe = 0.2), which has not been observed
in metallurgy studies either. This low-Cu i-phase was found in direct
association with an Al
13
(Fe,Ni)
4
λ
phase with nearly identical chemical
composition. Searching ternary systems, it is hard to
fi
nd a close analogy
to this i-phase composition. In the Al-Fe-Cr system, a thermo-
dynamically stable decagonal quasicrystalline phase (d-phase) is known
with the Al
72
Fe
12
Cr
16
composition
44
and an i-phase Al
91
Fe
4
Cr
5
was
formed by laser melting of Al plus Al
65
Cu
20
Fe
10
Cr
5
i-phase
45
.The
application of Hume-Rothery rules for alloy stability based on valence
electron density can be applied to this
fi
ve-component i-phase
11
.The
calculations suggest that high Fe and low Cu would have sharply limited
capacity to contain Cr or Ni. The 20 at% Fe and <4 at% Cu content in this
i-phase place it precisely on the estimated stability boundary with ~5 at%
Cr
+
Ni. The coexistence of this i-phase and
λ
with near-identical com-
position is a new observation. Given that
λ
is a common liquidus phase in
these compositions, it seems likely that there is a pressure-induced phase
transition from
λ
to i-phase upon compression.
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Shock experiments on metallic powders have been attempted in
several laboratories (Table
1
). Takasaki and Matsumoto (2009) shocked
mixtures of pure Ti, Zr and Ni powders with bulk atomic contents of
45%, 38%, and 17%, respectively. Ti
45
Zr
38
Ni
17
is one of the compositions
of the thermodynamically stable i-phase for this system. When starting
with 50-100 μm grain-size powders hand-mixed in a vial, i-phase and
intermetallic phases were absent in all their experiments under a range of
shock conditions. In contrast, a ball-milled
fi
nely-mixed powder starting
material yielded i-phase coexisting with Ti
2
Ni (and hence different in
stoichiometry from the starting material) at moderate pressure. It can be
inferred that,
fi
rst, the mechanically alloyed starting material is advan-
tageous for synthesizing quasicrystals and, second, the shock-induced
quasicrystal does not necessarily follow the low-pressure stable com-
position. In fact, studies on Ti-Zr-Ni and Al-Cu-Fe powders both show
that it is easier to make quasicrystals from mechanically alloyed powders
than from samples prepared by other methods in solid state
46
,
47
.Simi-
larly, Takagi et al. (2018) shocked a pressed pellet of pure Al/Cu/Fe
powder with 63:24:13 atomic contents to 20.5 GPa using a propellant
gun and no reaction of the pure metal domains was observed. They also
performed laser shock on the same type of sample up to 10 GPa and at
least 600 ns, for which in situ X-ray diffraction (XRD) did not show
quasicrystalline signature either. These experiments suggest that suc-
cessful quasicrystal shock-synthesis requires either inhomogeneous
targets that generate concentrated shear friction or mechanical alloying
of the starting powders. Although they have not (yet) produced quasi-
crystals, from homogeneous powdery starting samples, laser shock is a
promising technique with the capability of time-resolved measurements
to better indicate the timing of phase formation, which will be discussed
in the following section.
Decagonal quasicrystal phases
The natural decagonite has a formula of Al
71
Ni
24
Fe
5
, nearly identical to
the thermodynamically stable composition of Al-Ni-Fe d-phase, just as
the natural icosahedrite closely matches the stable i-phase in the Al-Cu-
Fe system
48
. Starting with permalloy (Ni
80
Fe
15
Mo
4.5
Mn
0.5
) and alumi-
num alloy 2024 (Al
94
Cu
4
Mg
1.5
Mn
0.5
) in a SS304 capsule, experiment
S1235 at Caltech resulted in shock-induced d-phase with composition
Al
73.3
Ni
19.3
Fe
4.3
Cu
1.8
Mg
0.6
Mo
0.4
Mn
0.3
, slightly more Al-rich than the
low-pressure stability
fi
eld
37
. In contrast, rapidly quenched d-phases
from metallurgical experiments have a composition range of Al
70-
75
Ni
9-21
Fe
9-16
, different from both natural decagonite and the shock
product, due to their higher Fe contents
19
. The d-phase in recovered
S1235 shows a topotaxial relationship with an Al(Ni,Fe) phase (Figs.
2
b
and
3
b) of space group
Pm
-3
m
[also referred to as
β
but not to be
confused with
β
-Al(Cu,Fe)]. This
β
phase is different from known Al-Ni-
Fe liquidus phases such as Al
13
(Fe,Ni)
4
and Al
3
(Fe,Ni)
2
and is not
observed in phase equilibrium studies even after d-phase decomposition
at <800 °C. The distinct composition and phase-assemblage of the
shock-synthesized d-phase could re
fl
ect the effects of minor Cu and/or
high-pressure conditions
37
.
Shock condition, composition and stability of quasi-
crystals: How to move forward
The distinctiveness of shock-synthesized quasicrystals must result from
some combination of the multi-component starting materials and the
complex sequence of conditions experienced during a shock recovery
experiment. Identifying the key factor
s that lead to novel quasicrystals is
essential for better understanding the properties of quasicrystals as well as
for guiding the design of future experiments.
Fig. 2 | SEM backscattered images of experimental shock-synthesized quasi-
crystals. a
d
correspond to the shot S1234, S1235, S1253 and S1255 respectively.
The insets in a-b are electron-backscatter diffraction patterns showing icosahedral
(i-phase) and decagonal (d-phase) symmetries. In image (
b
),
β
is
Pm
-3
m
Al(Ni,Fe)
phase. In images (
c
) and (
d
),
β
is stolperite,
λ
is hollisterite, and
θ
is khatyrkite.
Adapted and altered from
11
,
22
,
37
.
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5
Pressure, temperature and shear stress in shock recovery
experiments
Strong plastic shock waves in metals and alloys create a quick increase in
pressure, over a time scale of about 1 ns
49
. In the pressure range of 15-30 GPa
that is indicated by the shock state of the Khatyrka meteorite, a dense and
coherent starting material of Al plus
transition metals would be heated to
less than 400 °C and would not experience bulk melting
11
.Moreover,fora
typical shock recovery setup, with ~1 mm thick
fl
yer and sample, the high-
pressure pulse duration is ~ 1
μ
s, which is not long enough for intermetallic
reactions to proceed appreciably at
400 °C. In the Caltech shock recovery
setup, the back wall of the sample capsule is much thicker than the driver
plate, so that the pressure release in the sample occurs when a rarefaction
wave originating at the rear surface of the
fl
yer traverses the sample and
overtakes the shock front. In this scenario, the time scale of the pressure
release is much slower than the pressure rise, commonly taking another
microsecond for complete decompression
22
. The pressure release is semi-
adiabatic, leaving moderately elevate
d post-shock temperature in the sam-
ple. It is also unlikely that there would
be noticeable intermetallic reaction in
this post-shock state
19
. Hence, local variations in pressure-temperature-time
paths are essential to achieve the necessary temperatures to drive high-
pressure reactions among metals. The shock pulse is long enough for
deformation and
fl
ow to accumulate signi
fi
cant strain and cause additional
heating before the onset of pressure release
22
. A hand-mixed powder of
metals may reach higher shock tempera
ture than a dense starting sample,
butstillnotsuf
fi
cient to melt and alloy the bulk sample, likely being the
reason why shocked powder mixes did not produce quasicrystals
39
,
40
.
In addition to the pressure-temperature history of the shocked bulk
sample, incoherent or oblique edges of dense samples (Fig.
1
) cause con-
centrated shear friction and
fl
ow that lead to melting and reaction at the
sample boundaries
11
,
22
.Thisprocessaddsgreatcomplexitytothelocal
temperature history of the sample b
ecause the temperature is no longer
exclusively controlled by the shock-wave propagation in a dense sample.
Instead, frictional melting varies spatially in intensity and may occur at any
stage during shock or release, depending on the intersection between the
release adiabat and the Hugoniot of the sample, the level of potential local
superheating, and the kinetics of melting
50
.
When a shock recovery experiment generates local hotspots within the
chamber, the resulting gradients can either help or hinder recovery of
quasicrystals (and likewise can both help and hinder understanding of the
synthesis mechanism). Conduction dr
iven by extreme local temperature
gradients between hotspots and bul
k sample, superimposed on the tem-
perature drop upon adiabatic release
can achieve rapid local cooling rates
51
on the order of 10
5
-10
8
Ks
1
. While splat-quenching can achieve 10
6
Ks
-1
cooling rate for container-less samples
52
, most other metallurgical rapid-
quench techniques
4
cool at ~10
1
Ks
1
. It means that the shock approach has
a much higher potential to quench metastable phases while maintaining
some coherent relationship between
phases that form in contact using a
container that prevents the sample from experiencing as much strain as in a
splat quench. Nevertheless, the shock and deformation history that forms
and dissipates a hotspot is complex and the product could sample any point
along the pressure path, from rise, to dwell, to release, to post-release. This
leaves us with unanswered questions about the conditions of nucleation and
subsequent growth of the synthetic quasicrystals. In other words, although
shock recovery allows very detailed
aposteriori
microscopic analyses of the
sample, understanding the exact fo
rmation and quench condition of the
quasicrystal requires further techniques for time-resolved measurements
under shock plus sample recovery.
Although the low-pressure
thermodynamic stability
fi
elds of quasi-
crystalline phases in the relevant terna
ry systems are well known, the shock-
synthesized quasicrystals rarely plot in these
fi
elds and we do not know
whether the synthesized compositions are growing under stable or meta-
stable conditions. We do not know the st
ability boundaries in the expanded
compositional systems at given non-a
mbient conditions and, moreover (as
explained above), we do not know the synthesis conditions at a speci
fi
ctime
of shock processes. If the quasicrystals were stable at their synthesis con-
ditions, then some combination of pre
ssure, temperature, shear stress, and
minor components must have played a ro
le in shifting the boundaries of the
Fig. 3 | Bright
fi
eld TEM images of icosahedrite
and decagonite. a
,
b
are shot S1234 and S1235,
respectively. The insets are selected area electron
diffraction patterns of quasicrystals showing 5-/10-
fold symmetries. Adapted and altered from
11
,
37
.
Fig. 4 | Representative compositions of natural and shock-synthetic Al-Cu-Fe
icosahedral phases.
The natural i-phase I has the low-pressure thermodynamically
stable composition and the rest is separated into Al-rich and Cu-rich groups.
Chemical data are from
10
,
11
,
21
,
22
.
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6
stability
fi
eld. If they were metastable, the ultra-fast quenching that occurs in
some parts of a properly-designed sho
ck recovery experiment may explain
why the products do not resemble the phases known from metallurgical
studies. In the Al-Cu-Fe system, for inst
ance, the shock-synthesized i-phase
splits into Al-rich and Cu-rich groups (Fig.
4
). Although the presence of up
to 6 at% Cr
+
Ni may stabilize these novel compositions
11
,therearealsocases
ofAl>70at%andCu>30at%i-phaseswithCr
+
Ni < 2 at%, and both are
signi
fi
cantly different from the narrow ambient-pressure stability
fi
eld
around Al
60-65
Cu
21-26
Fe
11-15
(Fig.
4
). Static high-pressure experiments
demonstrated that the equilibrium
fi
eld of the i-phase may shift towards
high-Al and low-Cu
53
. This evidence, together wi
th the frequent recovery of
Al-rich i-phase in multiple experiments (Table
1
), makes it reasonable to
hypothesize that this material is thermodynamically stable under high-
pressure shock conditions.
Shock recovery with time-resolved in situ measurements
To test the hypothesis of that the stability
fi
eld of Al-Cu-Fe i-phase shifts
towards Al-rich compositions under s
hock, one approach is in situ time-
resolved analysis during the shock and release. Although in situ instru-
mentation and measurement is common for shock experiments, it is still
dif
fi
cult to do so for traditional prop
ellant gun recovery experiments
because the need of a strong bulky chamber that works as a momentum trap
(Fig.
1
). In addition to plate impact recovery now available at three major
synchrotron facilities
26
, laser-driven shocks are also available with in situ
synchrotron X-ray diffraction diagn
ostics, and this could be a very useful
technique to explore the timing and co
nditions of shock-induced quasi-
crystals formation. In this setup, the sample is sandwiched between an
ablator that absorbs the drive laser a
nd an optical window. Laser-driven
shocks can generate tens to hundreds of GPa pressure for tens of nanose-
conds duration, depending on the energy of the laser
54
. The pressure and
velocity history of the sample are determined by rear-surface velocity
interferometry (VISAR). A high-
fl
ux, high-brightness X-ray pulse can be
fi
red at the sample at a given time duri
ng shock. The corresponding X-ray
diffraction (XRD) pattern therefore i
s captured in situ with known timing
relative to the high-pressure pulse. For instance, time-resolved XRD can
potentially indicate quasicrystal nucl
eation and growth under shock, during
high-pressure dwell, post-shock or all o
f these. Forming novel quasicrystals
and growing them large enough to show c
lear diffraction patterns during the
high-pressure pulse would con
fi
rm the importance of a pressure effect. In
contrast, quasicrystal formation an
d growth continuing beyond release of
the high-pressure pulse would point to minor elements or other factors as
the explanation for the compositional shift.
The formation mechanism of Cu-rich i-phase (such as i-Phase II in
Khatyrka or one of the products in shot S1253) appears to be more complex,
judgingbythedif
fi
culty of its serendipitous synthesis
22
.Itispossiblethatthe
high-pressure stability
fi
eld of i-phase is extended towards both Al-rich and
Cu-rich compositions. Alternatively, it may be that the free energy surface of
the i-phase changes
41
relative to other liquidus p
hases under shock, making
it easier to quench Cu-rich metastabl
e compositions. New quench experi-
ments also suggest that very low Fe content in the starting Al-Cu-Fe melt
leads to slightly higher Al and Cu content in the resulting i-phase
55
.In
addition to the in situ time-resolved
X-ray techniques, carefully tuned
starting sample preparations could h
elp explore the extended stability
fi
eld
of the i-phase.
Texture and chemistry of starting sample preparation
As discussed above, hotspots from co
ncentrated shear friction in shock
experiments appear to yield quasicrystal synthesis more reliably than uni-
formly elevated temperatures. Howev
er, the process of friction-induced
melting involves local shear
fl
ow and turbulence so that the concentration of
each component cannot be precisely
controlled upon shock melting (Fig.
1
),
which is a major design limitation for
shock recovery synthesis with pro-
pellant guns. In contrast, mixtures of
fi
ne metallic powders offer well-
de
fi
ned starting compositions and then can precisely match Al-rich or Cu-
rich i-phases (Table
1
), but yield overall temperatures insuf
fi
cient to enable
reaction
40
. To solve this problem, previous studies demonstrated that pro-
cesses such as mechanical alloying with a ball mill
47
and magnetron
sputtering
56
could greatly enhance the formation of quasicrystals. Both
techniques mix pure metallic compone
nts into a metastable high-energy
and/or amorphous state that tends to cry
stallize intermetallic phases readily
upon disturbance by shock-wave compr
ession, and so they work better than
regular hand-mixed powders or compressed pellets
39
.Meanwhile,the
starting composition of shock samples can still be governed by the materials
used for ball-milling or sputtering, making it possible to prepare mixtures
matching the Al
74
Fe
16
Cu
10
and Al
62
Cu
31
Fe
7
i-phase compositions
21
,
22
.If
they are thermodynamically stable under shock as hypothesized, we expect
to obtain single i-phase aggregates from shocking mechanically alloyed
amorphous material with these compositions.
Minorelementsintroducedbytheca
psule in shock recovery experi-
ments, such as Cr and Ni from SS304, add complexity to the compositions of
synthesized quasicrystals. Although no
t all shock-synthetic quasicrystals
have signi
fi
cant amounts of four or
fi
ve elements, it is likely that Cr and Ni
help to stabilize the novel high-Al and low-Cu i-phase, with up to 20 at% of
Cr
+
Ni
11
. Therefore, it would be helpful to use a copper capsule
39
,
40
or Al-Fe
liners of high purity for future experiments as a test of whether pure Al-Cu-
Fe still exhibits a signi
fi
cant compositional shift in i-phase stability upon
shock compression. Laser shock experiments are also an option because the
sample is sandwiched between plastic
ablator and halide optical window,
not in contact with a metallic capsule
. However, pressure release history of
material spalled from a laser-driven
shock and recovered in some way would
be different from that experienced by en
capsulated sample and this raises an
additional layer of uncertainty.
Conclusion and outlook
It has been shown that shock recovery experiments provide an effective
technique for producing novel quasicrystals, some of which match the
rare natural quasicrystals produced by asteroidal impacts. The compo-
sitions, reaction sequences, and phase-assemblages of shock-synthetic
quasicrystals are all different from those of stable or metastable phases
synthesized by metallurgical techniques. The complex pressure-
temperature-shear paths induced by shock loading and release provide
a series of states where intermetallic reaction may occur but also add
complexity and dif
fi
culties in understanding the mechanism of those
reactions. With the possibilities of time-resolved in situ analysis from
advanced laser shock techniques and of customized mechanically alloyed
starting materials, new experiments have the potential to systematically
explore the stability of quasicrystals under shock conditions in the future,
which will help reveal the fundamental mechanism underlying these
transient syntheses, and whether or not they are due to high-pressure
expansion on quasicrystal stability
fi
elds.
Received: 20 April 2024; Accepted: 2 October 2024;
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