Vibrational Contributions to the Excess Entropy
in Ultra-fragile Metallic Glasses
Supplementary Information
Hillary L. Smith,
1
Claire N. Saunders,
2
Camille Bernal-Choban,
2
Stefan H.
Lohaus,
2
Colby Stoddard,
1
Lucy K. Decker,
3
J.Y.Y. Lin,
4
Jennifer L. Niedziela,
5
D.L. Abernathy,
6
Jong-Hyun Na,
7
Marios D. Demetriou,
2, 7
and B. Fultz
2
1
Swarthmore College, Department of Physics and Astronomy, Swarthmore, PA 19081, USA
∗
2
California Institute of Technology,
Department of Applied Physics and Materials Science, Pasadena, CA 91125, USA
3
University of Pennsylvania, Department of Materials
Science and Engineering, Philadelphia, PA 19104, USA
4
Second Target Station Project, Oak Ridge National Laboratory,
Oak Ridge, Tennessee 37831, USA
5
Materials Science and Technology Division,
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
6
Quantum Condensed Matter Division,
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
7
Glassimetal Technology Inc, Pasadena, CA 91107, USA
(Dated: August 13, 2022)
1
-1.5
-1.0
-0.5
0.0
0.5
Heat Flow [W g
-1
] Endo
→
600
580
560
540
520
500
480
460
Temperature [K]
0.04
0.03
0.02
0.01
0.00
-0.01
560
520
480
T
g
T
x
T
x
T
g
FIG. 1.
Differential scanning calorimetry of amorphous Pt
60
Cu
20
P
20
. Differential scanning
calorimetry of amorphous Pt
60
Cu
20
P
20
performed at a heating rate of 2 K min
−
1
reveals the glass
transition, characterized by an endothermic rise in heat capacity, followed by the crystallization
transition, indicated by a sharp exothermic peak. The onsets of
T
g
and
T
x
are indicated by arrows.
I. CALORIMETRY
Differential scanning calorimetry (DSC) measurements with continuous heating were per-
formed at the same 2 K per minute rate of heating as in the neutron scattering experiment.
The DSC curve of amorphous Pt
60
Cu
20
P
20
in Fig. 1 is marked with arrows to indicate the
onsets of the glass transition and subsequent crystallization transition. The large exothermic
heat release on crystallization makes the rise in heat capacity at
T
g
difficult to see, but it is
visible on the narrower scale used in the inset. The crystallization temperature determined
from DSC was used in combination with the in situ diffraction patterns as in Fig. 2 to
determine the absolute sample temperature during the neutron measurements.
II. ELASTIC SCATTERING
Elastic Bragg scattering of neutrons during the inelastic neutron scattering measurements
gives high quality diffraction patterns that can be used to determine the phase of the material
during in-situ experiments. Diffraction patterns were obtained by integrating the intensity
around the elastic peak. Figures 2 and 3 show this elastic intensity as a function of
Q
, with
additional scans offset to show changes in the diffraction as a function of temperature for
Pt
57
Cu
23
P
20
and Pt
60
Cu
20
P
20
.
2
530
535
539
543
547
551
555
559
10
8
6
4
2
Q [
Å
-1
]
520
540
560
580
Temperature [K]
2
4
6
8
10
Q [
Å
-1
]
Intensity [a.u.]
Pt
60
Cu
20
P
20
Glass
FIG. 2.
In-situ Neutron Diffraction of Pt
60
Cu
20
P
20
. Elastic scattering as a function of
momentum transfer
Q
. The sample is amorphous at the lowest temperatures (blue) where Bragg
peaks result from the aluminum sample holder and sample environment. No changes are visible
during heating through the glass transition until the onset of crystallization results in the sudden
formation of new Bragg peaks.
In Fig. 2(left panel) the sample was initially a glass at the lowest temperatures in dark
blue. Diffraction peaks at this temperature are from the aluminum sample holder and sam-
ple environment. The sample was heated continuously through the glass transition and
through crystallization. The diffraction pattern evolves as a function of temperature with
little change until the onset of crystallization when many new Bragg peaks appear. Figure 3
shows the second heating measurement of both samples when they are fully crystalline.
Bragg peaks are present from the sample, aluminum sample holder, and sample environ-
ment. The temperature of the onset of crystallization measured with DSC was compared to
the temperature of emergence of Bragg peaks in the neutron scattering experiment during
heating, and neutron data were offset to match the temperature in the neutron experiment
to the temperature measured with DSC.
Figure 4 compares the diffraction patterns from the first heating of the glass through
T
g
and
T
x
and the second heating of the fully crystalline sample at high temperature above
T
x
. In Pt
57
Cu
23
P
20
(Fig. 4(a)) no differences are observed between the first and second
heating. In Pt
60
Cu
20
P
20
(Fig. 4(b)) small differences around 2.2 and 7
̊
A
−
1
in
Q
suggest
3
that the crystalline phase formed immediately above
T
x
is not identical to the crystalline
phase formed after annealing at high temperature, cooling to room temperature, and re-
heating to the same temperature.
III. INELASTIC SCATTERING
A. Statistical analysis of density of states
Figure 5 shows phonon DOS curves of Pt
57
Cu
23
P
20
at 485 K with varying statistics. We
compared 12 DOS curves with proton charge on target between 0.2 and 1.04 C and size
of energy bin (
E
-bin) between 0.7% and 4.3% of the incident energy. For each curve, we
calculated the number of counts per
E
-bin, taking into account the estimated neutron flux
for a given incident energy, beam power, sample area, sample scattering, detector solid angle
coverage, and fraction of inelastically scattered neutrons
1,2
.
The number of counts per
E
-bin are calculated by first determining the neutrons per
second on the sample, accounting for the estimated flux for the given
E
i
, the sample area, and
the beam power. Estimated flux as a function of
E
i
and the particular chopper settings for
this
E
i
are available online for the four direct geometry chopper spectrometers at the SNS
3
.
The counts per second to produce the DOS is then corrected for sample scattering fraction,
detector solid angle coverage, and the fraction of neutrons that are scattered inelastically.
Based on the number of counts per second producing the DOS, this is then divided by the
number of
E
-bins and multiplied by the counting time to give the number of counts per
E
-bin to produce the DOS. This calculation assumes that corrections have been applied to
remove scattering from the empty can and to produce a single phonon DOS. The sample
geometry or statistical quality of the background data is not accounted for.
Our analysis concludes that for resolution of features at the level of the instrument res-
olution (
∼
2 meV near the center of DOS) a DOS curve requires 20,000 counts per
E
-bin,
where the width of the
E
-bin is between 1 and 3% of the incident energy. This calculation
allows consideration of how quickly a particular sample will generate a DOS of reasonable
statistical quality and provides an important benchmark for experiment planning.
4
520
540
560
580
T
emperature [K]
2
4
6
8
10
Q [Å
-1
]
531
533
535
537
539
541
543
545
547
549
551
553
555
557
559
561
Intensity [a.u.]
10
8
6
4
2
Q [Å
-1
]
P
t
60
Cu
20
P
20
Crystal
520
540
560
580
T
emperature [K]
2
4
6
8
10
Q [Å
-1
]
531
533
535
537
539
541
543
545
547
549
551
553
555
557
559
561
Intensity [a.u.]
10
8
6
4
2
Q [Å
-1
]
P
t
57
Cu
23
P
20
Crystal
10
a.
b.
c.
d.
FIG. 3.
In-situ Neutron Diffraction of Crystalline Pt
57
Cu
23
P
20
(a-b) and Pt
60
Cu
20
P
20
(c-d)
. Elastic scattering as a function of momentum transfer
Q
. The samples are crystalline
throughout the whole temperature range. Bragg peaks are present from the sample, aluminum
sample holder, and sample environment.
5
553
555
557
559
561
8
7
6
5
4
3
2
Pt
60
Cu
20
P
20
First Heating
Second Heating
Aluminum (300K)
553
555
557
559
561
8
7
6
5
4
3
2
Pt
57
Cu
23
P
20
First heating
Second heating
Aluminum (300K)
a.
b.
FIG. 4.
In-situ Neutron Diffraction of Crystalline Materials at High Temperature
Elastic scattering as a function of momentum transfer
Q
for (a) Pt
57
Cu
23
P
20
and (b) Pt
60
Cu
20
P
20
.
The diffraction pattern obtained from the first heating of the glass through
T
g
and
T
x
and second
heating of the fully crystalline samples are compared at high temperature above
T
x
. Dashed grey
lines indicate the position of diffraction peaks from aluminum at 300K.
B. Phonon density of states
Phonon DOS curves of Pt
57
Cu
23
P
20
are shown in Figures 6. The material is originally
amorphous at low temperature, then becomes a undercooled liquid at the glass transition,
indicated by an arrow at
T
g
, followed by crystallization, indicated by an arrow at
T
g
. Data
are binned in 10 K intervals, producing each spectrum in 3-5 minutes. The 455 K DOS of the
amorphous phase (dark blue) is shown also at high temperature, overlaid with the DOS of
the crystalline phase at 585 K. The DOS curves show little change with temperature during
heating through the undercooled liquid. After crystallization above
T
x
, features of the DOS
sharpen slightly, consistent with the changes visible in Figure 2d in the manuscript.
6
50
40
30
20
10
0
5,200
50
40
30
20
10
0
10,300
50
40
30
20
10
0
20,600
50
40
30
20
10
0
31,000
50
40
30
20
10
0
10,100
50
40
30
20
10
0
20,100
50
40
30
20
10
0
40,000
50
40
30
20
10
0
60,000
50
40
30
20
10
0
25,500
50
40
30
20
10
0
51,000
50
40
30
20
10
0
102,000
50
40
30
20
10
0
153,000
0.5 meV
E
bin
0.7%
E
i
1 meV
E
bin
1.4%
E
i
2 meV
E
bin
2.9%
E
i
3 meV
E
bin
4.3%
E
i
0.21 C
~2.5 min
0.41 C
~5 min
1.04 C
~12.5 min
FIG. 5.
Phonon DOS curves of Pt
57
Cu
23
P
20
with varying statistics
. DOS curves were
obtained from the crystalline material at 485 K. Each column represents a different energy binning
of the data from 0.5-3 meV, representing 0.7-4.3% of the incident energy of 70 meV. Each row
represents a different accumulated proton charge from 0.21-1.04 C, corresponding to 2.5-12.5 min
of data collection time at 1.4 MW. The number of counts per
E
-bin are given on top of each plot.
∗
hsmith@swarthmore.edu
1
Islam, F.
et al.
Super-resolution energy spectra from neutron direct-geometry spectrometers.
Review of Scientific Instruments
90
, 105109 (2019). 1906.09482.
2
Abernathy, D. L.
et al.
Design and operation of the wide angular-range chopper spectrometer
ARCS at the Spallation Neutron Source.
Review of Scientific Instruments
83
, 015114 (2012).
3
ORNL. ARCS resolution. URL
https://rez.mcvine.ornl.gov/
.
7
465
475
485
495
505
515
525
535
545
555
565
575
585
Phonon DOS [meV
-1
]
50
40
30
20
10
0
Energy [meV]
Pt
57
Cu
23
P
20
465K
T
g
T
x
FIG. 6.
Phonon DOS curves of Pt
57
Cu
23
P
20
as a function of temperature
. DOS curves
were obtained during the heating from the amorphous state, through the glass transition, and
above crystallization. The DOS curves between the glass transition, indicated by an arrow with
T
g
, and crystallization, marked
T
x
, were obtained where the material is in the undercooled liquid.
The 465 K DOS of the amorphous phase (dark blue) is shown also at high temperature, overlaid
with the DOS of the crystalline phase at 585 K.
8