Supplemental
Information Appendix
Observation of
a
n apparent
first order glass transition in ultra
-
fragile Pt
-
Cu
-
P bulk metallic glasses; Ideal glasses that melt
Jong.H. Na, Sydney L. Corona, Andrew Hoff, and William .L. Johnson
A.
Glass Formation and Physical Properties of Alloys
The ternary Pt
80
-
x
Cu
x
P
20
bulk gla
ss forming alloys used in the present work were
developed as part of a project to create processable Pt
-
based
bulk metallic glasses
free of
Ni. The alloys are described along with related quaternary and quinary alloys containing
small additions of B, Ag, and Au in recently issued U.S. Patent [1]. Amorphous rods were
prepared by melting
the
alloyed components at 900
̊C
or above
in thin
walled quartz tubes
(1 mm wall thickness) and quenching into water at ambient T. Fig. S1 shows DSC scans
carried out with a Netzsch 404 F3 calorimeter
on
as
-
cast rods
. Scans are
from room
temperature
through
alloy melting at
a relatively high
heating rate
of
20 K/m
in
.
As seen in
the figure, the onset glass transition temperature T
g
»
503
-
505
K
is nearly independent of
Cu content. The
glassy samples
exhibit a significant undercooled liquid region, T
x
-
T
g
,
where T
x
is the onset of crystallization. The melting
endotherms are relatively sharp with
solidus
/liquidus
temperatures, T
S
and T
L
,
separated by a
temperature interval that is
minimum
near the composition x=23. The
alloy
glass forming ability, as measured by the
maximum rod diameter that can be cast
in a
f
ully
glassy state
, increases dramatically with
Cu content as shown in Fig.S
2
. When small amounts
(~1 at. %)
of B, Ag, or Au are added,
the glass forming ability at high
er
Cu content
rises sharply
to ~5 cm as
shown
for the case
of B. The reader is referred
to ref. 1
for additional details.
The glassy alloys are rheologically fragile. Viscosity was measured using beam
bending [2] in a Perkin
-
Elmer TMA for the x=23 and x=20 compositions as shown in
Fig.S
3
. For x=20 the Newtonian viscosity was difficult to measure more than ~10 K above
T
g
as non
-
Newtonian shear thinning was observed at the lowest strain rates accessible in
the Perkin
-
Elmer
TM
A instrument
. As such, only data for viscosity above 10
10
Pa
-
s are
shown
for the x=20 case
. Fitting
log(
h
)
vs.
T
g
/T
to a simple exponential
form
and defining
the rheological
T
g
by
h
(
T
g
)
= 10
12
Pa
-
s, one obtains the
fits to the viscosity data
shown in
the figure.
The rheological
T
g
is found to be 500.4 K and 501.7 K resp
ectively for the x
=23 and x=20 glasses.
The
fits were
used to determine the apparent
rheological
Angell
Fragility parameter “m” [3] as
indicated
in the figure.
For x = 23, the viscosity data
w
ere
combined with
an
ultrasonically measured shear modulus
G
for
the x=23
glass
to estimate
the Maxwell configurational relaxation time
s,
t
a
=
h
(
T
)
/
G
,
in the liquid above
T
g
.
The
ultrasonic
pulse echo method
was applied on
3 mm
diameter
glassy
rods at ambient
www.pnas.org/cgi/doi/10.1073/pnas.1916371117
temperature
using
a 25 MHz transducer to
determine
the longitudinal and shear sound
velocities. The
sample mass
density at ambient T was measured using the Archimedes
method
. For x =23,
one obtains
r
=
15.22 g/cc
. This yields a
shear modulus of G = 30.7
GPa
for the cast g
lassy rod
. Following annealing at 230 C for 15 hours
, the ambient T shear
modulus
increase
s
to G = 32.5 GPa due to relaxation of the as
-
cast
glass
during
the
annealing. The latter value was used to
estimate
the Maxwell relaxation times
shown
in
Fig.1c of t
he main text.
Fig.S1
Standard DSC scans
of Pt
80
-
x
Cu
x
P
20
alloys taken at
a commonly used scan rate of
20 K/m
in
.
Vertical lines (left)
indicate the onset of the
calorimetric glass transition,
T
g
,
and (right) the onset of
melting at 543
̊C
(solidus
temperature). Arrows (left
and right) indicate the onset
of crystallization,
T
X
, and the
completion of the melting
tran
sition
(liquidus
temperature) The width of the
melting
transition
is
minimum for the Cu23 alloy.
As such, we designate this as
the eutectic composition. The
onset temperature of the glass
transition increases very
slightly with increasing Cu
content.
Fig.S2.
Glass forming ability versus Cu content for
the
series of Pt
80
-
x
Cu
x
P
20
alloys
studied
in this report
. The glass forming ability is defined by the maximum diameter
, d
C
,
of a fully
glassy rod that can be produced by melting the alloy at ~900
̊C
is a sealed silica tube of
wall thickness 1mm and then quenching into water at room temperature.
The reader is
referred to reference 1 for a detailed summary of the glass forming a
bility of the ternary
alloys along with quaternary alloys formed by adding 1
-
2 at.% of Ag or B to the ternary
alloys. Such additions are observed to increase the glass forming ability to as high as d
C
~
6 cm,
0
5
10
15
20
25
30
10
12
14
16
18
20
22
24
26
28
30
Critical Rod Diameter (mm)
Copper Content (at. %)
Fig.S
3
. Viscosity data obtained fr
om beam bending using a Perkin
-
Elmer TMA for Cu23
(blue) and Cu20 (red) samples. For the Cu20 sample, the viscosity was observed to be non
-
Newtonian at the smallest loading force available in the TMA. Data below 10
10
Pa
-
s could
not be obtained due to appar
ent strain
-
rate induced crystallization. The fragility, m, for the
Cu20 sample should be considered as a lower bound.
5
6
7
8
9
10
11
12
13
14
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
log{Visocosity Pa-s}
Tg/T
Cu-23
Tg = 500.4, m=72.1
Cu-20
Tg = 502.6, m=81.4
B.
Equivalence of eqn.(1) and eqn.(2) of the main text
In the
main
text eq
n.(2)
is derived from
eqn.(
1
)
. Below is an outline of the steps:
Starting with the normalized
equation 1,
ℎ
#
(
%
)
ℎ
#
(
∞
)
=
)
1
−
,
-
.
%
/
0
1
(
1
)
the configurational enthalpy can be rearranged
ℎ
#
(
%
)
=
ℎ
#
(
∞
)
)
1
−
,
-
.
%
/
0
1
Ignoring any pressure dependence of
h
C
(
¥
)
and
q
h
at ambient pressure
(essentially ignoring the Pv
term in the free energy)
,
the
specific
configurational
heat capacity
becomes
2
#
=
34
(
%
)
3%
=
35
(
%
)
3%
=
3
ℎ
#
(
%
)
3%
=
3
3%
6
−
ℎ
#
(
∞
)
-
.
0
%
0
7
=
+
9
ℎ
#
(
∞
)
-
.
0
%
0
:
;
For the entropy,
referenced to the high temperature limit,
<
#
=
−
=
>
2
#
%
?
@
A
B%
=
−
=
6
ℎ
#
(
∞
)
-
.
0
%
0
:
C
7
B%
@
A
<
#
=
<
#
,
@
−
9
ℎ
E
(
∞
)
-
.
0
9
+
1
1
%
0
:
;
From eq
n.(
1
)
in the main text
,
ℎ
#
(
∞
)
−
ℎ
#
(
%
)
ℎ
#
(
∞
)
=
,
-
.
%
/
0
or
6
ℎ
#
(
∞
)
−
ℎ
#
(
%
)
ℎ
#
(
∞
)
7
;
0
=
,
-
.
%
/
So
,
-
.
%
/
0
:
;
=
6
ℎ
#
(
∞
)
−
ℎ
#
(
%
)
ℎ
#
(
∞
)
7
;
0
6
ℎ
#
(
∞
)
−
ℎ
#
(
%
)
ℎ
#
(
∞
)
7
=
6
ℎ
#
(
∞
)
−
ℎ
#
(
%
)
ℎ
#
(
∞
)
7
0
:
;
0
where
<
#
=
<
#
,
@
−
9
ℎ
#
(
∞
)
-
.
(
9
+
1
)
6
ℎ
#
(
∞
)
−
ℎ
#
(
%
)
ℎ
#
(
∞
)
7
0
:
;
0
=
<
#
,
@
−
F
6
ℎ
#
(
∞
)
−
ℎ
#
(
%
)
ℎ
#
(
∞
)
7
0
:
;
0
With eq
n,(2)
in the main text
written in terms of
the configurational potential energies
G
and
G
H
:
these are equivalent to
h
C
(T)
and
h
C
(
¥
)
. It
follows that eq
n.(
1
)
is equivalent to
<
#
(
G
)
∝
<
#
(
G
H
)
−
F
(
G
H
−
G
)
J
K
L
J
(2)
C.
Undercooling DSC
experiments on Cu20 and Cu23 glasses.
Liquid undercooling measurements of the heat of crystallization were performed on
each of the alloy compositions [4]. For both x=20 and x=23, it was possible to achieve deep
undercooling of the liquid below the eutec
tic temperature
T
E
following cyclic overheating
to 900
̊C
and cooling down to 200
̊C
For samples with Cu content x < 20, only shallow
undercooling (< 80 K) were achieved.
The experiments were performed in the same
Netzsch 404c F3 DSC using silica crucibles
.
Fig.S4
Examples of DSC undercooling scans
taken at a cooling/reheating rate of 10
K/min
for Cu20 and Cu23 samples: (
a
-
upper left) raw data for 40 undercooling cycles
of Cu20; (
b
-
upper right) heat of crystallization,
h
LX
(T)
,
normalized to heat of fusion
(69.5 J/g) of Cu20 versus temperature for undercooling measurements showing that
h
LX
(T)
is nearly constant down to an undercooling of ~145 K. Inset shows an expanded
view of the d
ata indicating a change of only ~2% over this range. (
c,
lower)
DSC
cooling scans for 40 undercooling cycles for the eutectic Pt
57
Cu
23
P
20
alloy. Up to
roughly
cycle 15,
only
limited undercooling is achieved
and the
recalescence
exhibits
a small shoulder at
~480
̊C
. Later cycles
display
much deeper undercooling (to ~365
̊C
)
and
a single sharp recalescence event.
Figures were taken from ref.[4].
Samples of size 60
-
80 mg were cyclically heated and cooled at 10 K/m between the upper
temperature (900
̊C
) and lowe
r temperature (200
̊C
). Crystallization is indicated by the
single sharp recalescence event which occurs during all of 40 undercooling/overheating
cyclic scans carried out for each individual sample. With increasing cycle number, the
undercooling achieved
increases progressively as seen in Fig. S4a below for the x=20
sample. The total heat release on crystallization was measured during each cycle. Fig.S4b
shows a plot of this measured heat release as a function of the peak temperature for the
exothermic cry
stallization peak. The inset shows a magnified view of the data. Over the
range of undercooling (from
T
E
= 815 K down to 670 K), the heat of crystallization is nearly
constant decrease
s
from the alloy heat of fusion (69.5 J/g) by only
~
2% at the deepest
un
dercooling. Fig. S4c shows the corresponding undercooling data for an x =23 at. % Cu
sample. The undercooling up to roughly cycle 15 is clustered between 440
̊C
to about 480
̊C
(undercooling of only 60
-
80 K below the eutectic). For x = 23, the undercooling
achieved significantly increases to about 180
̊C
during subsequent cycles. These
undercooling
h
LX
data obtained were included in Fig.2a of the main text.
D.
High resolution SEM
and chemical mapping
High resolution SEM and chemical mapping results were carried out at ETH
-
Zurich
using the LAMP facility by Prof. Joerg Loeffler. The glassy Pt
57
Cu
23
P
20
eutectic alloy is
featureless and chemically uniform down to length
scales of several nm’s as seen in Fig.
S5 below.
Fig.S5
. High resolution SEM chemical mapping using EDS showing featureless
microstructure and uniform distribution of chemical elements (left) in an as
-
cast
Pt
57
Cu
23
P
20
sample down to length scales of ~10 nm
. Color maps on the right show
distribution of the 3 components (Pt
-
red, Cu
-
green, and P
-
blue) and dark field
microstructure image (gray). Figure courtesy of Prof. Jorg Loeffler, ETH Zurich,
Switzerland.
E.
X
-
ray diffraction scans of Cu16 glass versus therm
al history
Fig.S6 shows a sequence of x
-
ray diffraction scans taken during and following pre
-
annealing at 230
̊C
of the Pt
64
Cu
16
P
20
followed by isothermal crystallization at 245
̊C
.
The sample was subsequently heated in steps to 350
̊C
, 390
̊C
, and 480
̊C
and then
cooled following each step to room temperature to obtain the diffraction scans. On heating
to 350
̊C
, the scan indicates that an order
-
disorder transition occurs for the
Pt
-
Cu
-
rich fcc
phase to an
ordered
Pt
7
Cu.
Fig.S6
. Sequence of x
-
ray diffraction curves for Pt
64
Cu
16
P
20
glass in its initial
glassy condition and following crystallization and exothermic heat release during
an isothermal crystallization at 245
̊C
(scans #1
and #2). Upon subsequent heating
to 350
̊C
and 390
̊C
, the intensity of several diffraction peaks changes (e.g. peak
at 2
q
~ 44 deg. disappears)
as observed from scans #2 through scan #3. This is
attributed to chemical order/disorder transition for the Pt
7
Cu
-
phase [5]. From the
data, one also identifies the monoclinic
Pt
5
P
2
-
type phase containing Cu in solution
on the Pt
-
sites. [6].
Heating
to 480
̊C
results in sharpening of diffraction peaks
(scan #5) suggesting that significant grain growth of the cryst
alline phases occurs.