Atomic structure of glassy Mg<sub>60</sub>Cu<sub>30</sub>Y<sub>10</sub> investigated with EXAFS, x-ray and neutron diffraction, and reverse Monte Carlo simulations
ABSTRACT Journal article
Atomic structure of glassy Mg60Cu30Y10investigated with EXAFS, x-ray and neutron diffraction,
and reverse Monte Carlo simulations
Pál Jóvári,1Karel Saksl,2,3Nini Pryds,4Bente Lebech,5,6Nicholas P. Bailey,7Anders Mellergård,8,* Robert G. Delaplane,8,†
and Hermann Franz2
1Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, P.O. Box 49, Budapest H-1525, Hungary
2HASYLAB am Deutschen Elektronen Synchrotron (DESY), Notkestrasse 85, D-22603 Hamburg, Germany
3Institute of Materials Research, Slovak Academy of Sciences, Watsonova 47, 043 53 Kosice, Slovak Republic
4Fuel Cells and Solid State Chemistry Department, Risø National Laboratory, DTU, DK-4000 Roskilde, Denmark
5Materials Research Department, Risø National Laboratory, DTU, DK-4000 Roskilde, Denmark
6Niels Bohr Institute, University of Copenhagen, DK-2100, Copenhagen, Denmark
7DNRF Center “Glass and Time,” IMFUFA, The Department of Science, Systems and Models, Roskilde University, Universitetsvej 1,
DK-4000 Roskilde, Denmark
8Studsvik Neutron Research Laboratory, Uppsala University, SE-611 82 Nyköping, Sweden
?Received 23 April 2007; revised manuscript received 12 July 2007; published 22 August 2007?
Short range order of amorphous Mg60Cu30Y10was investigated by x-ray and neutron diffraction, Cu and Y
K-edge x-ray absorption fine structure measurements, and the reverse Monte Carlo simulation technique. We
found that Mg-Mg and Mg-Cu nearest neighbor distances are very similar to values found in crystalline
Mg2Cu. The Cu-Y coordination number is 1.1±0.2, and the Cu-Y distance is ?4% shorter than the sum of
atomic radii, suggesting that attraction between Cu and Y plays an important role in stabilizing the glassy state.
Thermal stability and structure evolution upon annealing were also studied by differential scanning calorimetry
and in situ x-ray powder diffraction. The alloy shows a glass transition and three crystallization events, the first
and dominant one at 456 K corresponding to eutectic crystallization of at least three phases: Mg2Cu and most
likely cubic MgY and CuMgY.
DOI: 10.1103/PhysRevB.76.054208PACS number?s?: 61.43.Dq, 61.12.Ld, 61.10.Ht
Metallic glasses are disordered materials lacking the long
range periodicity of crystals, which often results in unique
physical and mechanical properties such as high strength and
hardness, excellent corrosion resistance, low magnetic en-
ergy loss, and easy shaping and forming ability at elevated
temperatures.1–3Generally, to maintain the amorphous struc-
ture of the molten alloy and avoid crystallization during
cooling from the melt to the solid phase, high cooling rates
?105–106K/s? are required. Therefore, only rather thin
?typically 10–50 ?m? amorphous layers can be obtained.
However, in recent years, new multicomponent systems re-
quiring only modest cooling rates ???100 K/s? to become
amorphous have been found. Such materials are referred to
as “bulk metallic glasses.”
Mg-based bulk metallic glasses have attracted attention
due to their high strength to weight ratio and low glass tran-
sition temperature.4The thermal and mechanical properties
of amorphous and partly crystalline Mg60Cu30Y10have been
presented recently.5–7A particularly interesting property of
Mg-based bulk metallic glasses is their excellent microform-
ing ability.8In spite of their potential practical interest, little
is known about the microscopic structure of Mg-based amor-
phous alloys. Detailed knowledge about the structure of bulk
metallic glasses is not only of pure scientific interest but, if
achieved, would open possibilities to better control the prop-
erties of these materials.
The development of experimental and computational
techniques in the past decade significantly improved our
knowledge on the formation and physical properties of me-
tallic glasses. Investigations by high energy x-ray diffraction
and x-ray absorption techniques revealed the existence of
icosahedral local order in liquid metallic alloys.9,10The in-
fluence of atomic radii of the components on packing, short
and medium range order has also been intensely studied.11
Models based on the efficient packing of atoms and atomic
clusters proved to be successful in the prediction of compo-
sitions with high glass forming ability.12,13
The aim of this paper is to explore the structure of glassy
Mg60Cu30Y10. In order to get a reliable structural model, we
combined x-ray diffraction ?XRD? and neutron diffraction
?ND? results with Cu K-edge and Y K-edge extended x-ray
absorption fine structure ?EXAFS? measurements. The four
experimental data sets were fitted simultaneously in the
technique.14,15The resulting atomic configuration was ana-
lyzed in detail in terms of pair and higher order correlations.
Thermal stability and structure evolution upon annealing
were also investigated by differential scanning calorimetry
and temperature dependent x-ray diffraction.
Mg60Cu30Y10, were prepared by arc melting mixtures of pure
Mg, Cu, and Y ?99.99 wt. % each? in a purified argon atmo-
sphere. In order to prevent evaporation of Mg, ingots of
Cu75Y25were prepared separately, and an appropriate mix-
ture of Cu75Y25and Mg was then melted several times to
ensure homogeneity. From these master ingots, amorphous
samples were prepared in two forms:
PHYSICAL REVIEW B 76, 054208 ?2007?
©2007 The American Physical Society054208-1
?i? The alloys were remelted at about 735 K, which is just
above their melting point, and then quenched into a cylindri-
cal copper mold under argon atmosphere ?6?21?2 mm3,
used for hard XRD and ND experiments?.
?ii? Amorphous ribbons ??3?0.04 mm2cross section for
XRD and EXAFS? were prepared using a single-roller melt-
spinning apparatus. The amorphous nature of the samples
was confirmed by x-ray and neutron diffraction and by trans-
mission electron microscopy.
It is usually assumed that the density of bulk metallic
glasses is only marginally lower than that of corresponding
crystalline structures. The mass densities of the amorphous
and crystallized phases ?measured by the Archimedian
are 3.541±0.007 g/cm3
3.580±0.007 g/cm3?0.0507 Å−3?, respectively. Combina-
tion of the molar volumes of Mg2Cu and Y ?10.97 cm3?Ref.
and 19.88 cm3, respectively?
?0.0508 Å−3? for the density of Mg60Cu30Y10. The agreement
between this value and the experimentally determined den-
sity is remarkable and lends support to the reliability of the
experimentally determined densities. A considerably lower
value ?3.13 g/cm3? was reported for the amorphous state in
an earlier study17and adopted later by others.12,18In this
study, we use 3.541 g/cm3as the density of the glassy state.
Differential scanning calorimetric ?DSC? measurements
were carried out by employing a high sensitivity differential
scanning calorimeter ?SII-DSC120?. The DSC curve was re-
corded with the specimen held in an inert He atmosphere.
The temperature was scanned from room temperature to
600 K with a heating rate of 2 K/min. It was done in order
to determine the glass transition temperature ?Tg? and the
crystallization temperatures ?TX?.
XRD measurements were carried out using the BW5 ex-
perimental station19at the Hamburg Synchrotron Radiation
Laboratory, Germany. The energy of the incident beam was
100 keV ??=0.124 Å?. Samples were illuminated for 200 s
by a well collimated incident beam of 1?1 mm2cross sec-
tion. The XRD patterns were recorded using a two-
dimensional detector ?MAR345, MarResearch?. The col-
lected spectra were then integrated into 2? space by using the
FIT2D software.20The sample-detector distance, detector or-
thogonality with respect to the incoming radiation, as well as
precise radiation energy was determined by fitting a standard
High temperature XRD measurements were carried out
from 300 to 625 K at 25 K intervals. In this experiment, a
thin walled ?10 ?m? quartz capillary filled with pieces of
ribbon was mounted on a capillary adapter allowing the
sample to be kept in a vacuum better than 10−5mbar. Simul-
taneously, the sample was heated ?20 K/min? by an infrared
heater designed for in situ measurements.22The temperature
was measured by a thermocouple placed inside the capillary.
Neutron diffraction measurements were performed at
room temperature on the SLAD instrument at Studsvik NFL,
Sweden.23Pieces of ingot were contained in a thin walled
vanadium container. The wavelength of the incident radiation
FIG. 1. Experimental ?open circle? and model simulation ?solid line? of the XRD and ND structure factors and the Cu and Y K-edge
EXAFS signals of amorphous Mg60Cu30Y10.
JÓVÁRI et al.
PHYSICAL REVIEW B 76, 054208 ?2007?
was 1.1 Å. Additional measurements were made for back-
ground, empty container and a solid vanadium rod for nor-
malization. Processing of the raw data was carried out by the
CORRECT program package.24
EXAFS measurements of amorphous ribbon were per-
formed at HASYLAB at the beam lines X1 ?Y K edge? and
E4 ?Cu K edge?. Spectra were collected in transmission
mode using fixed exit double-crystal Si?311? and Si ?111?
monochromators for X1 and E4, respectively. The x-ray in-
tensities were monitored using ionization chambers filled
with gases the type and pressure of which were adjusted to
the corresponding energies. The energy calibration for Y and
Cu was monitored using reference materials measured to-
gether with the samples. Experimentally measured x-ray ab-
sorption cross sections ??E? were analyzed by standard pro-
cedures of data reduction using the program VIPER.25First,
the EXAFS signal ??k? was extracted and weighted by k2.
Next, the region where the amplitude of the nonweighted
??k? is still significant was Fourier transformed ?for details,
see Ref. 26?. Then the main peak contribution to ??k?, i.e.,
the signal from closest atomic neighbors to absorbing atoms,
was obtained by filtering and back transforming over an
r-space ranges 1.71–3.24 and 1.9–3.66 Å for the Y and Cu
K edges, respectively. For the filtering, a Hanning window
function with the coefficient A=0.01 was used. The signals
served later as input for the reverse Monte Carlo ?RMC?
III. REVERSE MONTE CARLO SIMULATION
The reverse Monte Carlo simulation technique offers a
framework to generate large three-dimensional models com-
patible with available structural information. It is used al-
most exclusively to model diffraction and EXAFS results,
but, in principle, any experimental technique can be simu-
lated if the measured signal can be expressed as a function of
atomic coordinates. Atomic structures of disordered systems
are usually described by partial pair correlation functions
?PPCF’s? and bond angle distributions ?BAD’s?. In ternary
alloys, the structural analysis is complicated by the fact that
the number of PPCF’s is 6 ?in our case, Mg-Mg, Mg-Cu,
Mg-Y, Cu-Cu, Cu-Y, and Y-Y?, and thus, a detailed structural
study requires the combination of experimental information
obtained by different techniques ?usually diffraction and
EXAFS? with prior knowledge ?e.g., density and minimum
interatomic distances?. The RMC simulation technique pro-
vides a suitable framework for this task. In this study, we
model simultaneously the four measurements: XRD and ND
structure factors and the two EXAFS data sets. For details of
the simulation, we refer to a recent publication.27EXAFS
backscattering factors needed to calculate the model EXAFS
curves were obtained by the FEFF8.4 program.28The simula-
tion boxes contained 20 250 atoms. The following minimum
interatomic distances were applied throughout the simulation
runs: Mg-Mg, 2.7 Å; Mg-Cu, 2.25 Å; Mg-Y, 3.0 Å; Cu-Cu,
2.25 Å; Cu-Y, 2.55 Å; and Y-Y, 3.3 Å. The initial configura-
FIG. 2. The partial pair correlation functions gxy?r? obtained from RMC simulation ?solid line? and hard sphere model without fitting any
experimental data ?dashed line?.
ATOMIC STRUCTURE OF GLASSY Mg60Cu30Y10…
PHYSICAL REVIEW B 76, 054208 ?2007?
tion was obtained by a hard sphere simulation satisfying the
IV. STRUCTURE OF GLASSY Mg60Cu30Y10
A. Pair correlations
Figure 1 shows the comparison of experimental data sets
with model curves. The agreement between the experimental
and simulated curves is very good for all measurements. The
resulting PPCF’s can be seen in Fig. 2, where we also show
the PPCF’s calculated from the initial hard sphere configu-
ration taken as a reference system. The comparison of the
two sets of g?r?’s may illustrate how the structure of a real
metallic glass deviates from a hard sphere system: The first
peak positions are shifted to higher r values in comparison
with the hard sphere results. The PPCF peak positions and
the corresponding coordination numbers are summarized in
A characteristic feature of the structure of metallic glasses
is the shoulder or splitting of the second peak of metal-
metal-type PPCF’s. In case of Mg60Cu30Y10, the shoulder
and/or splitting can be found on the Mg-Mg, Mg-Cu, Mg-Y,
Cu-Cu, and Y-Y PPCF’s. The Mg-Mg peak is at about
2.93 Å, and the corresponding coordination number calcu-
lated up to 3.9 Å is 7.5. This value is close to the Mg-Mg
distances found in crystalline Mg2Cu ?Table II?. The Mg-Cu
peak is at 2.72 Å. Integration up to 3.75 Å, the minimum
position, gives 3.5 for the Mg-Cu coordination number. This
peak is strongly asymmetric and can be decomposed into a
Gaussian centered at 2.72 Å and a broader peak at
3.03±0.05 Å. The agreement between the first value and the
shortest Mg-Cu distance ?2.74 Å? in orthorhombic crystal-
line Mg2Cu is remarkable. The Mg-Y peak is at 3.35 Å, and
the coordination number is 1.4. The obtained interatomic dis-
tance is close to the sum of their nominal atomic radii
?3.39 Å?. Mg atoms have, on the average, altogether 12.7
neighbors. The Cu-Cu peak position is 2.55±0.03 Å. The
corresponding coordination number calculated up to 3.45 Å
is 2.0. The Cu-Y peak is at 2.94 Å, and the coordination
number is 1.1. This distance is significantly ??5%? shorter
than the sum of corresponding atomic radii ?3.07 Å? and
close to 2.97 Å, the value obtained from orthorhombic
YCu2. These observations suggest a pronounced attraction
between Cu and Y in amorphous Mg60Cu30Y10. The Cu-X
?X=Mg, Cu, or Y? coordination number is 10.5. The Y-Y
distance is 3.69 Å, and the coordination number is 1.6. The
total number of neighbors around Y is 13.3.
The efficient cluster packing ?ECP? model of metallic
glasses12,13is based on the dense packing of solute centered
atomic clusters. The atoms within such clusters should also
be densely packed, which occurs only at specific solute-to-
solvent radius ratios. Another important feature of this model
is that the central solute atoms are surrounded by solvent
atoms only. ECP proved to be especially accurate in the pre-
diction of compositions with good glass forming ability. Co-
ordination numbers around the central solute atoms can also
be estimated by the criterion of efficient packing. For the
Mg-RE-?Cu, Ni? ?RE stands for rare earth? system, the maxi-
mum of glass forming ability is about 25 at. % Cu,29while
ECP gives the highest stability for 24.3 at. % Cu content.12
According to ECP, the number of Mg atoms around Cu is 10,
while Y is surrounded by 15 solvent atoms. These values are
in a reasonable agreement with the total number of neighbors
TABLE III. Percentage of the three icosahedral-like local atomic arrangements in the first peaks of partial
pair correlation functions obtained from CNA.
MgMgMgCuMgY CuCuCuY YY
TABLE I. Mean interatomic distances ?R? and coordination
numbers ?N? in amorphous Mg60Cu30Y10obtained by RMC simul-
taneously modeling of the XRD, ND structure factors, and the Cu
K-edge and Y K-edge EXAFS data sets.
TABLE II. Interatomic distances ?rwa? and coordination num-
bers N in orthorhombic Mg2Cu. Mg atoms occupy the two non-
equivalent 32h Wyckoff sites Mg?1? and Mg?2?.
JÓVÁRI et al.
PHYSICAL REVIEW B 76, 054208 ?2007?
of Cu and Y obtained by RMC ?10.5 and 13.3, respectively?.
However, it should be mentioned that according to the RMC
simulation results, the number of solute-solute pairs ?Cu-Cu,
Cu-Y, and Y-Y? is rather high ?Table I?, which is not empha-
sized by ECP. The existence of such pairs follows directly
from the experimental data. As an illustration, we show the
best fit of Y K-edge EXAFS measurement that could be
achieved by eliminating Cu-Y pairs from the RMC configu-
ration ?Fig. 3, upper panel?. Another remark is that ECP sig-
nificantly underestimates the density of Mg60Cu30Y10 ?
2.71 g/cm3instead of 3.541 g/cm3?, which strongly sug-
gests that the basic assumptions of ECP may not be valid in
case of the Mg-Y-Cu system.
B. Bond angle distributions
Mg-X-Mg ?X=Mg,Cu,Y? BAD’s have also been calcu-
lated and compared with those obtained from the reference
configuration ?Fig. 4?. The upper limit of the “bond” has
been set to the minimum of the corresponding PPCF’s. A
pronounced feature in each case is the peak close to 60° that
corresponds to the close packing of three equal hard spheres.
Besides, the Mg-Mg-Mg BAD shows a broad peak at about
110°. The latter is very close to the second peak of the Mg-
Mg-Mg bond angle distribution in crystalline Mg2Cu
??106°?. No such coincidence can be observed in case of
the Mg-Cu-Mg and Mg-Y-Mg BAD’s, the peaks of which
are at ?120° and at 100° and 150°. The differences between
peak positions of the Mg-X-Mg BAD’s can be qualitatively
explained by taking into account the ratio of atomic radii. Cu
is the smallest one among the three atomic species. There-
fore, the bond angles centered on Cu should shift to higher
values in comparison with the Mg-Mg-Mg distribution, as
the Cu atom can move closer to the line joining Mg atoms.
For the same reason, Mg-Y-Mg bond angles are usually
smaller than Mg-Mg-Mg ones.
C. Common neighbor analysis
Common neighbor analysis30,31?CNA? is an efficient way
of characterizing higher order correlations in disordered sys-
tems. In CNA, each pair of atoms is described by three in-
dices: the first gives the number of common neighbors, the
second is the number of bonds among common neighbors,
while the third index gives the number of bonds in the largest
bonded cluster built up of common neighbors. Two atoms are
considered as neighbors ?or “bonded”? if their distance is
smaller than the minimum of the corresponding PPCF’s. As a
consequence, the first index is always zero if the distance of
atoms is larger than the sum of the two largest cutoffs. An
advantage of this approach is that PPCF’s can be decom-
posed into contributions of pairs with different CNA indices.
This way, it can be possible to distinguish between local
motifs that cannot be resolved by PPCF’s or BAD’s.
Simulation studies on liquid and glassy Mg-Cu alloys re-
vealed that the first peak of metal-metal PPCF’s are built up
mainly from 555-, 544-, and 433-type pairs.30In a perfect
icosahedron, the central atom forms 555 pairs with all of its
12 neighbors. In this sense, a high number of 555 pairs is a
fingerprint of icosahedral local order. 544 and 433 pairs can
be obtained by removing a bond or an atom from a 555
FIG. 4. Selected bond angle distributions calculated from the
RMC model ?solid lines? and from the reference hard sphere con-
figuration ?dashed lines?.
FIG. 5. ?Color online? A 555 pair of two Mg atoms ?Mg, green;
Cu, blue; Y, gray?.
FIG. 3. Fits of Y K-edge EXAFS spectrum with and without
Y-Cu pairs in the RMC configuration.
ATOMIC STRUCTURE OF GLASSY Mg60Cu30Y10…
PHYSICAL REVIEW B 76, 054208 ?2007?