Determination of internal residual strain induced by cryogenic thermal cycling in partially-crystalized Fe-based metallic glasses

Article abstract of DOI:10.1016/j.jallcom.2018.12.097

The intrinsic heterogeneities of the metallic glasses can be activated through cryogenic thermal cycling, making irreversible structural changes after the treatment and inducing rejuvenation to the materials. Although the energy rise after cryogenic thermal cycling can be easily determined from calorimetry, the energy change made by the heterogeneities is unknown because of the difficulty in witnessing these heterogeneities. In this paper, we investigated the changes of a typical heterogeneity: the Fe₃Si crystallite, embedded in two partially-crystallized Fe-based metallic glasses, and subsequently deduced its influence on the neighbouring glassy matrix. It was found that even in the initial, partially-crystallized alloys, the Fe₃Si nanocrystals were under residual expansion. Furthermore, both expansion and contraction can be detected after cryogenic thermal cycling depending on the applied number of cycles. The maximum residual volumetric strain preserved after CTC is in the order of 0.1%. Moreover, the stored energy of both crystals and glasses are calculated and the total energy rise is determined at the order of 5–50 mJ/g. The study of partially-crystallized alloys not only provides a useful model of heterogeneous materials but also reflects the structural change of the glassy phases, making this method attractive in understanding the effects of thermo-mechanical processing on heterogeneities.

Full text of DOI:10.1016/j.jallcom.2018.12.097

Journal of Alloys and Compounds 781 (2019) 357e361
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: http://www.elsevier.com/locate/jalcom
Determination of internal residual strain induced by cryogenic
thermal cycling in partially-crystalized Fe-based metallic glasses
,
,
b
,
,
b
,
, b, c, **
M.C. Ri a b, Y.H. Sun a d, Z.Y. Xue c, D.W. Ding a *, W.H. Wang a
a Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, P.O. Box 603, China
b Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China
c Institute for Advanced Materials, North China Electric Power University, Beijing, 102206, China
d Center of Materials Sciences and Opto-Electronic Engineering, University of Chinese Academy of Sciences, Beijing, 100049, China
a r t i c l e i n f o
a b s t r a c t
Article history:
The intrinsic heterogeneities of the metallic glasses can be activated through cryogenic thermal cycling,
making irreversible structural changes after the treatment and inducing rejuvenation to the materials.
Although the energy rise after cryogenic thermal cycling can be easily determined from calorimetry, the
energy change made by the heterogeneities is unknown because of the difficulty in witnessing these
heterogeneities. In this paper, we investigated the changes of a typical heterogeneity: the Fe3Si crys-
tallite, embedded in two partially-crystallized Fe-based metallic glasses, and subsequently deduced its
influence on the neighbouring glassy matrix. It was found that even in the initial, partially-crystallized
alloys, the Fe3Si nanocrystals were under residual expansion. Furthermore, both expansion and
contraction can be detected after cryogenic thermal cycling depending on the applied number of cycles.
The maximum residual volumetric strain preserved after CTC is in the order of 0.1%. Moreover, the stored
energy of both crystals and glasses are calculated and the total energy rise is determined at the order of 5
e50 mJ/g. The study of partially-crystallized alloys not only provides a useful model of heterogeneous
materials but also reflects the structural change of the glassy phases, making this method attractive in
understanding the effects of thermo-mechanical processing on heterogeneities.
Received 15 November 2018
Received in revised form
5 December 2018
Accepted 6 December 2018
Available online 8 December 2018
Keywords:
Metallic glasses
Cryogenic thermal cycling
X-ray crystallography
Nanocrystalline alloy
Rejuvenation
© 2018 Elsevier B.V. All rights reserved.
1. Introduction
Unlike the crystalline metals in which the constituent atoms
reside at the thermodynamic equilibrium, the amorphous metals
The amorphous metals possess unusual structures that can be
rejuvenated through cryogenic thermal cycling (CTC) [1e3]. Reju-
venation of a metallic glass (MG) could greatly affect the structure
and improve the mechanical and other functional performance [4].
One of the major applications of the Fe-based glassy and nano-
crystalline composite is the soft magnets which are widely used
in the field of the electrical and electronic devices [5e8]. However,
the lack of macroscopic ductility of these Fe-based alloys de-
teriorates their performance and hence limits their engineering
applications. It is then interesting to explore the effect of CTC on
these materials.
are metastable materials in far-from-equilibrium states [9]. The far-
from-equilibrium nature can be easily changed by subsequent
thermal treatment or mechanical deformation through ultrasonic
loading [10], laser treatment [11e13], confined deformation [14,15],
ion irradiation [16,17], heavily plastic deformation [18e20], elasto-
static loading [21,22] or re-quenching from the supercooled liquids
[23]. Among all these methods, CTC is especially attractive because
of its non-destructive nature and the uniform deformation applied
on the entire sample, neglecting the shape and size of the materials.
It was presumed that the internal deformation of the heterogene-
ities of the materials are the major input of the stored energy but
the ideas have never been proved experimentally. Therefore, we are
motivated to explore the changes of the microstructures and
attempting to correlate them to the stored energy.
* Corresponding author. Institute of Physics, Chinese Academy of Sciences, Bei-
jing, 100190, P.O. Box 603, China.
** Corresponding author. Institute of Physics, Chinese Academy of Sciences, Bei-
jing, 100190, P.O. Box 603, China.
E-mail addresses: dingdawei@iphy.ac.cn (D.W. Ding), whw@iphy.ac.cn
(W.H. Wang).
Many methods have been widely used to study the micro-
structure of MGs, including Transmission Electron Microscope
(TEM) [18,24], Scanning Electron Microscopy (SEM) [13,24], X-ray
Photon Correlation Spectroscopy (XPCS) [25,26], Dynamic
https://doi.org/10.1016/j.jallcom.2018.12.097
0925-8388/© 2018 Elsevier B.V. All rights reserved.

358
M.C. Ri et al. / Journal of Alloys and Compounds 781 (2019) 357e361
Thermomechanical Analysis (DMA) [27,28], Differential Thermal
Analysis (DTA) [29], Differential Scanning Calorimeter (DSC)
[11,28], and, of course, the X-ray Diffraction (XRD). Although XRD is
commonly used in detecting the crystallinity of an MG alloy, people
seldomly analyze the lattice parameters of these nanocrystals and
use that as a sign of structural change in response to thermo-
mechanical treatments. These partially crystallized MGs are good
candidates for CTC due to their heterogeneous combination of both
amorphous and crystalline phases and hence making XRD a useful
technique to monitor the change of lattice parameters. In fact, Fe-
based, partially crystallized alloys are widely used as soft mag-
nets [6,30] so a knowledge of the structural changes after CTC is
useful. More importantly since the treated specimens are un-
stressed, by monitoring the changes of the crystals we could also
work out the change of their neighbouring glassy matrix that is
uneasy to be resolved directly by any techniques. Therefore, in this
work we applied XRD crystallography to systematically investigate
the effect of CTC on the lattice parameters of Fe-based partially-
crystallized alloys.
0
@
1
n
X
A
Wa
¼
1 ꢁ
WjðCorrÞ ꢀ 100ð%Þ
(3)
morphous
j¼1
WstdðKnownÞ
WstdðKnownÞ
WaðCorrÞ ¼ Wa
(4)
(5)
SaðZMVÞa
Wa
¼
n
P
SkðZMVÞk
kꢁ1
Here WaðCorrÞ stands for the corrected weight fraction of a standard
material, WstdðKnownÞ the weight fraction of the known standard
material, WstdðMeasÞ- the relative fraction of the standard material,
Wa-the weight fraction of phase
is the Rietveld scale factor, Z the number of the unit cell for
chemical formula, M the molecular mass and V the molar volume.
a in an n phase mixture. Besides, S
2. Experimental methods
3. Results
Commercially available, FINEMET-type amorphous ribbons of
Fe73.5Si13.5B9Nb3Cu1 (supplied by Ningbo Zhongke B Plus New Ma-
terials Technology Co. Ltd.) and Fe50Co10Ni15.5Si12B8.5Nb3Cu1 (sup-
plied by An Tai Inc. of China Iron & Steel Group) alloys were selected
as the raw materials. Both ribbons were made via melt-spinning
Annealing induces crystallization in the MG samples. By
increasing the annealing temperature, the glassy samples were
partially crystallized and made heterogeneous as they contained
both glassy and crystalline phases [6,35]. The diffraction peaks
(Fig. 1a &b) of both series of the annealed alloys, heat-treated at
813 K for 1 h, could be indexed as Fe3Si (~98% in vol. %) and Si
(~2 vol %). Since Fe3Si is the major crystalline phase, we only
consider its contribution to the structural change hereafter. In both
alloys, the Fe3Si were face-centered cubic structures and at the Fm-
3m point group. The effects of annealing temperature on the lattice
parameters are presented in Fig. 1c and d. The initial lattice pa-
rameters were taken from the samples annealed at 733 K for 1 h.
With the increase of the annealing temperature, the lattice pa-
rameters were reduced from 5.7169 Å to 5.6735 Å in Fe73.5S-
and acquired a uniform thickness of 25 mm and a width of 25 mm
(the former) or 6 mm (the latter) respectively. Thermal properties
of the two MGs were measured by a DSC (NETZSCH DSC404 F3)
under a flow of purified argon atmosphere at a heating rate of 20 K/
min. To make partially-crystallized alloys, thermal annealing were
performed at a temperature between the primary (Tx1) and the
secondary (Tx2) crystallization temperature [6,30]. For Fe73.5S-
i13.5B9Nb3Cu1, Tx1 and Tx2 are 804 K and 930 K respectively and for
Fe50Co10Ni15.5Si12B8.5Nb3Cu1, Tx1 and Tx2 are 729 K and 844 K
respectively but there is a ternary crystalline peak with the
exothermic peak maximized at 937 K. Therefore, we annealed both
ribbons at 733 K, 753 K, 773 K, 793 K and 813 K for 1 hour before
subjecting them to CTC [3]. The procedure of CTC follows that of
Ketov et al. [1,2] with one cycle immerging the sample into liquid
nitrogen for 1 min and blowing the specimen in air at 320 K for
1 min with a hair dryer. The XRD (Bruker D8 Advance with typical
Cu-Ka radiation) is applied on all samples to check the
crystallinities.
The exact composition, lattice parameters and the volume
fraction of the crystals were analyzed by commercial softwares
“Bruker AXS DIFFRAC.EVA V4.2” and “Bruker AXS DIFFRAC TOPAS
V5.0” respectively. The lattice parameters of the crystals are ob-
tained from the Bragg equation as,
i13.5B9Nb3Cu1
and
from
5.7291 Å
to
5.6904 Å
in
Fe50Co10Ni15.5Si12B8.5Nb3Cu1 alloys. The relative changes in lattice
parameters were ꢁ0.76% and ꢁ0.71%, equivalent to a density
reduction of ꢁ2.3% and ꢁ2.1% respectively. Fig. 1e and f exhibit the
evolution of the weight fractions of the crystalline and glassy
phases. At the highest annealing temperature, e.g. 813 K, the
remaining phases are 65 w.t.% crystals, with a typical size of 18 nm,
and 35 w.t.% glasses in Fe73.5Si13.5B9Nb3Cu1 and 55 w.t.% crystals,
with a typical size of 25 nm, and 45 w.t.% glasses in Fe50Co10
-
Ni15.5Si12B8.5Nb3Cu1. We then took these 813 K, 1 h annealed spec-
imens as Sample A and Sample B and continued to study the effects
of CTC.
Fig. 2 showed that the lattice parameters were altered in the two
samples by CTC but the responses were serrations and the trends
are different in Sample A and Sample B. In comparison with the
initial lattice parameter of Sample A, lattice parameter went up
after 5, 15 and 20 cycles and went down after 10, 25 and 30 cycles.
On the other hand, in Sample B the 5, 10, 15 cycles increased the
lattice parameter whereas 20, 25 and 30 cycles decreased it. The
biggest extents of change were 0.0015 Å (5.6767 Åꢁ5.6752 Å) and
0.004 Å (5.6927 Åꢁ5.6887 Å) respectively, leaving volumetric re-
sidual strains (εv, re.) of 0.08% (3 ꢀ 0.0015 Å/5.6759 Å) and 0.21%
(3 ꢀ 0.004 Å/5.6904 Å).
2d sinQB ¼ n
l
(1)
where d is the atomic spacing, qB the incident angle (Bragg angle),
l
the X-ray wavelength (1.54056 Å). For a cubic structure, the lattice
parameter (a) is,
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a ¼ dhkl
ꢀ
h2 þ k2 þ l2
(2)
where (hkl) are the Miller indexes. To confirm the reproducibility,
all the samples were measured at least three times.
The CTC needs to be performed at low temperature, and it is
important to know how much changes in lattice parameters are
affected by the low temperature itself. Fig. 3a and b shows the
changes of the lattice parameter when the temperature was
increased from 93 K to 298 K. At 93 K, the lattice parameters were
In particular, the volume fraction of crystallization was deter-
mined via the Rietveld refinement method [31]. The weight fraction
of crystallinities and the corresponding weight fraction of the
glasses are calculated as follows [32e34]:

M.C. Ri et al. / Journal of Alloys and Compounds 781 (2019) 357e361
359
Fig. 1. Effects of thermal annealing. The XRD patterns of two Fe-based alloys, Fe73.5Si13.5B9Nb3Cu1 (a) and Fe50Co10Ni15.5Si12B8.5Nb3Cu1 (b), show crystallinities after thermal
annealing. In both samples, the observed diffraction peaks are mainly Fe3Si crystals. Increase of the annealing temperatures leads to decrease of the lattice parameters and the
volume fraction of the amorphous phases and correspondingly increase of the crystalline phases in both Fe73.5Si13.5B9Nb3Cu1 (c, e) and Fe50Co10Ni15.5Si12B8.5Nb3Cu1 (d, f).
5.6630 Å and 5.6779 Å and they were reduced by ꢁ0.22% (5.6630 Å/
5.6758 Åꢁ1) and ꢁ0.22% (5.6779 Å/5.6904 Åꢁ1) from that at 298 K.
Three times these changes result in the volumetric strain (εv)
of ꢁ0.66% in both alloys. Clearly εv were larger than εv, re. and the
ratio of ꢁεv, re./εv were 12% and 32% for Sample A and Sample B
respectively. Besides, the coefficients of linear thermal expansion
(CTEs) were worked out by linearly fitting the lattice parameters
with temperature and taken the slopes as CTEs, which are
10.7 ꢀ 10ꢁ6 Kꢁ1 for both Sample A and Sample B.
and 5.6904 Å for Sample B (Fig. 1c and d). In fact, the reported
lattice-constant of Fe3Si is 5.653 Å, which is 0.4% and 0.67% lower
than the measured values [36], in equivalence to 1.2% or 2.0%
volumetric expansions of the Fe3Si after crystallization. This reflects
the influence of the amorphous phase on the crystalline Fe3Si,
indicating that in the original partially-crystallized alloys, e.g.
Sample A and Sample B, there are residual tensile stresses in
crystals and compressive stresses in glasses. In other words, the
Fe3Si crystals are under expansion while the Fe-based glasses are
under compression.
By decreasing the temperature, the lattice parameter of Fe3Si
crystals are decreased but the crystals are still expanded with less
extent. The reduced lattice parameters, e.g. 5.663 Å and 5.6779 Å,
are still larger than the lattice constant (5.653 Å). The change of εv is
4. Discussion
We first noticed that although Fe3Si appeared in both alloys,
their lattice parameters are not the same, i.e. 5.6758 Å for Sample A

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M.C. Ri et al. / Journal of Alloys and Compounds 781 (2019) 357e361
Fig. 2. Effects of cryogenic thermal cycling (CTC). Serrations of the lattice parameters are observed on Sample A (a) and Sample B (b).
Fig. 3. Effects of low temperature. Thermal contraction is observed at low temperature and when temperature increases, the lattice parameter goes up in Sample A (a) and Sample
B (b). The coefficients of thermal expansion are deduced from the slopes of the fitted straight line.
Fig. 4. Changes of the volumetric-strain (εV) during CTC results in irreversible, residual strains for both samples.
thus very similar to that represented by Fig. 4. If cooling and heating
in CTC were performed slowly, εv will follow A/C and C/A and
hence no εv-T loop would form. However, because the alloys were
cooled and heated rapidly, the CTC then includes four steps: rapid
cooling (A/B), contraction (B/C), rapid heating (C/D) and
homogeneous material where the εv is totally reversible. In the case
of a heterogeneous material like our partially-crystallized alloy,
some irreversibility (A/B/C/D/A0) can be expected due to the
non-equilibrium nature of the MGs and hence εv, re. was preserved.
At least for our Sample A and Sample B, a maximum of 12% or 32% of
expansion (D/A). This represents the ideal case for
a
the total Dεv are preserved in εv, re., manifesting the effectiveness of

M.C. Ri et al. / Journal of Alloys and Compounds 781 (2019) 357e361
361
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sitions of the minimum energy in the sense that they are under
stress, it is expected that εv, re. can either go up or down and thus
one saw serrations in their cycling behaviors.
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It was known that rejuvenation increases the stored energy of
MGs so how would the εv, re. affects the stored energy of the alloys?
Assuming the strains preserved in both Fe3Si crystals and the glassy
matrix are elastic, the stored energy can be estimated from 1 Bεv2;re
2
The bulk modulus (B) of an Fe3Si crystal is 178 GPa [37] and B of the
Fe-based MGs are ~170 GPa [38]. εv, re. are the same for both crystals
and glasses. Therefore, the stored elastic energy of the CTC-ed Fe3Si
crystal and the Fe-based glass are 57 kJ/m3 and 54 kJ/m3 for Sample
A and 392 kJ/m3 and 375 kJ/m3 for Sample B. Because the density of
Fe3Si crystal and Fe-based glasses are 7.22 g/cm3 (deduced from the
lattice parameters and molar mass) and ~7.85 g/cm3 [38] respec-
tively, the total stored energy for Sample A is 7.5 mJ/g (57 kJ/
m3÷7.22 Mg/m3 ꢀ 65% þ 54 kJ/m3÷7.85 Mg/m3 ꢀ 35%) and for
Sample
B
51 mJ/g (392 kJ/m3÷7.22 Mg/m3
ꢀ
55%
þ
375 kJ/
m3÷7.85 Mg/m3 ꢀ 45%). The stored energy after CTC measured in
calorimetry is ~3 J/g [1] and in comparison with this, the contri-
bution of the heterogeneities is about tens or hundreds times
smaller, implying that there must be other resources pumping
energy into the alloy systems.
5. Conclusion
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Acknowledgements
This work was supported by National Key Research and Devel-
opment Plan (Grant No. 2016YFB0300500, 2017YFB0903900), the
Key Research Program of Frontier Sciences, CAS (Grant No. QYZDY-
SSW-JSC017), the financial support of the NSF of China (Grant No.
51571209, 51461165101, and 51601215) and the National 973 proj-
ect (Grant No. 2015CB856800). We thank B. S. Dong and S. X. Zhou
in An Tai Inc. of China Iron & Steel Group, L. S. Huo in Ningbo Zhongke
B Plus New Materials Technology Co. Ltd. for supplying samples and
T. Wang, X. Q. Zhu in the Bruker Co. Ltd., for experimental assistance
and helpful discussion, CAS-TWAS support.
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