Influence of Similar Atom Substitution on Glass Formation in (La-Ce)-
Al-Co Bulk Metallic Glasses
Ran Li, Shujie Pang, Chaoli Ma, Tao Zhang *
Department of Materials Science and Engineering, Beijing University of Aeronautics and
Astronautics, Beijing 100083, China
The glass-formation range of bulk metallic glasses (BMGs) based on lanthanum and
cerium was pinpointed in La-Al-Co, Ce-Al-Co and pseudo-ternary (La-Ce)-Al-Co system
respectively by copper mold casting. Through the stepwise substitution of La for solvent
Ce in (LaxCe1-x)65Al10Co25 alloys (0<x<1), the fully glassy rods of the
(La0.7Ce0.3)65Al10Co25 alloy can be successfully produced up to 25 mm in diameter by tilt-
pour casting. Comparing with the glass-forming ability (GFA) of single-lanthanide based
alloys, La65Al10Co25 and Ce65Al10Co25, the coexistence of La and Ce with similar atomic
size and various valence electronic structure can obviously improve the GFA of (LaxCe1-
x)65Al10Co25 BMGs, which can’t be explained by the former GFA criteria for BMGs, e.g.
atomic size mismatch and negative heats of mixing. A thermodynamic model was
proposed to evaluate this substitution effect, which gives a reasonable explanation for the
obvious improvement of GFA induced by the coexistence of similar atoms.
Keywords: Rapid solidification; Rare earth; Bulk amorphous materials; Metallic glasses;
* Corresponding author: Tao Zhang
* Text only
Since a ternary La-Al-Ni bulk metallic glass (BMG) of 2.5 mm in diameter was
successfully produced through adding Ni to a known binary La-Al amorphous alloy by
copper mold casting in 1989 , many new ternary alloys with high glass-forming ability
(GFA), such as Ln-Al-TM (Ln = lanthanide metal; TM = Co, Ni, Cu), Zr-Al-TM, Pd-Ni-
P, Pt-Ni-P, and Mg-Cu-Y etc. [2-6], represented in the component formula as A-B-C,
were discovered through the elemental addition in former binary glassy alloys in
following years. Further investigations indicated that A, B and C can be classified into
large, middle and small atoms according to their significantly different atomic radii . It
could improve the atomic packing efficiency in supercooled liquid and increase the
difficulty of crystallization, which results in a higher GFA comparing with the former
binary amorphous alloys [7-10]. Besides the improvement of rapid solidification
technique, component diversification by multi-element substitution in a known binary or
ternary alloy system to obtain multicomponent alloy systems, well known as “confusion
principle” , is recognized as one of the most effective ways to improve the GFA of
metallic glasses. However, the search of BMGs with high GFA in multicomponent alloy
systems is very tedious and time consuming, and how to choose substituting elements to
improve the GFA of the resulting alloy is still a confused problem.
Some empirical rules were proposed to achieve BMGs with high GFA in
multicomponent systems as follows [7,12,13]: (1) the multicomponent system should
consist of more than three element, and the main constituent elements should be satisfied
with significant difference in atomic sizes above 12 % and negative heats of mixing with
other constituent elements; (2) considering of the reduced glass-transition temperature,
Trg, a deep eutectic composition caused by frustrating crystallization should be chosen in
the multicomponent system with chemical and topological differences of constituent
elements. These criteria suggest that choosing the dissimilar atoms with obvious different
atomic size with other constituent elements as substituting elements could be an effective
way to improve the GFA of multicomponent alloys.
In recent years, many BMGs with super high GFA, e.g. Mg-, Ca-, Ti-, Zr-, Fe-, Co-,
Cu-, Y-, Pd-, Pt-, Ln- (Ln=lanthanide metals) based BMGs [14-25], were successfully
produced through multi-component substitution. (In this paper, we only consider the
partial substitution with atomic content above 5 %, and the role of minor alloying
additions will not be discussed .) We can class the substitution method as follows.
The general substitution method is based on the above empirical criterion of atomic size
mismatch. It can be named as “column substitution”, because elements in the same group
with A, B or C in the Periodic Table of the Elements (PTE) are chosen as substituting
elements, which usually have distinct atomic sizes but similar valence electronic structure
to the substituted one. Many multicomponent BMGs with higher GFA were reported
through the partial column substitution, e.g. partially substituting Ag for solute and
solvent Cu in Mg-(Cu-Ag)-Y and (Cu-Ag)-(Zr-Ti) respectively[14,20], Mg for solvent
Ca in (Ca-Mg)-Ni , Sc for solvent Y in (Y-Sc)-Al-Co  and Ti for solute Zr in Cu-
(Zr-Ti) . Another method of element substitution, which is much less mentioned, can
be named as “row substitution”. By using the neighboring elements in the same period
with A, B or C in PTE as the substituting components, which have similar atomic sizes
but various valence electronic structures to the substituted one, the GFA can also be
improved effectively. The representative samples are the partial substitution of Cu for
solute Ni in Zr-Al-(Ni-Cu), Pt-(Ni-Cu)-P, Pd-(Ni-Cu)-P and La-Al-(Ni-Cu) [17,22,23,28],
Co for solvent Fe in (Fe-Co)-(Si-B)-Nb , Fe for solvent Ni in (Ni-Fe)-(Si-B)-Nb 
and Pt for solvent Pd in (Pd-Pt)-Cu-P , in which GFA can be increased remarkably by
the row substitution. Recently, we reported that the GFA can be evidently improved by
substituting multi-lanthanide atoms for the single-lanthanide solvent atom in (Ce-La-Pr-
Nd)-Al-Co system , which is another example of row substitution. Up to now, little
experimental and theoretical analysis has been performed on this substituting method,
because the neighboring element in the same period has similar atomic radius to the
substituted one, causing almost no change in the magnitude of atomic size mismatch in
the alloy systems.
In this work, we developed a pseudo-ternary alloy, (La-Ce)-Al-Co, with superior GFA
by the row substitution. Through the partial substitution of La for Ce in (LaxCe1-
x)65Al10Co25 alloy system, the fully glassy rod of 25 mm in diameter was produced by tilt-
pour casting. The influences of this row substitution on the glass-forming ability,
crystallization process and behaviors of melting and solidification were evaluated in
detail. A thermodynamic model was proposed to give a possible explanation to
understand this effect of the row substitution with similar atoms on the glass formation.
2. Experimental Procedure
All ingots of (La-Ce)-Al-Co, La-Al-Co and Ce-Al-Co alloys with nominal composition
were prepared by arc melting a mixture of pure Co (99.9 mass%), Al (99.99 mass%), La
and Ce (above 99.5 mass%) in a highly pure argon atmosphere. For the smaller rod-
shaped sample (≤ 12 mm in diameter), the ingot was remelted in a quartz tube using an
induction heating coil in a highly pure argon atmosphere, and then injected into a copper
mold through a nozzle using a highly pure argon atmosphere at 0.2 atm. pressure to
produce glassy rods. For the larger rod-shaped sample (≥ 15 mm in diameter), the ingot
was remelted in a quartz cup using a tilting induction furnace and then the molten alloy
was poured into a copper mold in a highly pure argon atmosphere. Cross sections of as-
cast rods were examined by X-ray diffraction (XRD) using a Bruker AXS D8 X-ray
diffractometry with Cu-Kα radiation at a scanning rate of 1 degree/minute to ensure the
phase structure. The thermal stability of the glassy samples was evaluated by a
NETZSCH DSC 404 C Differential Scanning Calorimeter (DSC) at a heating rate of 0.33
K/s in a flowing purified argon atmosphere. Melting and solidification behaviors of these
alloys were also characterized by DSC at a heating and cooling rate of 0.33 K/s. For
density measurement, the bulk glassy rods with the same diameter of 2 mm were
measured by the liquid displacement method using a density determination kit (YDK01-
0D, Sartorius AG) in 1,1,2,2-tetrabromoethane with an accuracy within 0.5 %.
3. Results and Discussion
3.1 Glass Formation of (La-Ce)-Al-Co system
In order to study the effect of row substitution with similar atoms and pinpoint the
BMGs with superior GFA in the pseudo-ternary (La-Ce)-Al-Co system, a good glassy
former must be found out so that the further substitution can be processed. We adopted
the equiatomic ratio between La and Ce to search the composition map of (La0.5Ce0.5)-Al-
Co system based on the latest research .
Figure 1 shows the composition range for glass formation of (La0.5Ce0.5)-Al-Co BMGs.
It indicates that the BMGs with the glassy critical diameter (dc, dc means the maximal
diameter in which the fully glassy rod can be produced successfully) not less than 2 mm
can be produced in a large composition range (the blue marks), and the fully glassy
samples of at least 12 mm in diameter can also be produced in a local range (the red
marks), confirmed by the smooth XRD patterns in Fig. 2. We evaluated the melting
characteristics of the alloys in the composition map by the DSC analysis, and the 3D
contour map of liquidus surface was plotted, as shown in Fig. 3. Thermal parameters of
(La0.5Ce0.5)-Al-Co BMGs, e.g. the glass transition temperature (Tg), the onset temperature
of crystallization (Tx), the melting temperature (Tm), liquidus temperature during heating
process (Tl), the supercooled liquid region (∆Tx = Tx – Tg), Trg (Trg = Tg / Tl) and γ (γ = Tx
/ (Tg + Tl)) , are shown in Table I. We noticed that the alloys with dc above 12 mm lie
on relative lower liquidus surface, nevertheless deviate from the eutectic composition.
Although the alloy composition with the largest Trg is (La0.5Ce0.5)70Al10Co20, the alloys
having the highest GFA are (La0.5Ce0.5)70Al15Co15, (La0.5Ce0.5)65Al10Co25 and
(La0.5Ce0.5)65Al15Co20 according to their values of dc. The relationship between the GFA
and the ∆Tx or γ is also incoherent. The possible explanations have been mentioned in
some literatures [24,34]. The BMGs with obvious supercooled liquid region ∆Tx over 65
K (the maximum reaches 86 K) can be found in a large composition range of (La0.5Ce0.5)-
Al-Co system, which is hopeful to be a further superplastic application as mentioned in
Considering the melting behavior and GFA, we chose the (La-Ce)65Al10Co25 alloy as an
appropriate glassy former to further study the influence of partial row substitution on the
GFA of (LaxCe1-x)65Al10Co25.
3.2 Substitution Effect on Glass Formation of (LaxCe1-x)65Al10Co25
In order to study the substitution effect of similar atoms of La and Ce on the GFA of
resulting alloys, firstly, we produced the glassy rods of (LaxCe1-x)65Al10Co25 alloys (0 < x
< 1) of 2 mm in diameter through the row substitution of La for solvent Ce. The glass
transition, crystallization and melting behaviors of these alloys were studied by the DSC
at a heating and cooling rate of 0.33 K/s, and the thermal parameters, e.g. Tg, Tx, Tm, Tl,
Tl’ (the liquidus temperature during cooling process), ∆Tx, ∆Tl (∆Tl = Tl – Tl’, ∆Tl is the
nominal supercooled degree at a certain same heating and cooling rate), Tg/Tm, Tg/Tl,
Tg/Tl’ and γ, as well as the density of glassy samples, were listed in Table II. Some other
La- and Ce-based BMGs were also included for comparison [24,25]. Figure 4 (a) shows
the DSC curves of the BMGs of (LaxCe1-x)65Al10Co25 alloys in the heating process. With
the increase of the substituting content of La, the BMGs exhibit higher Tg and Tx. The
substitution of La for solvent Ce in the (LaxCe1-x)65Al10Co25 alloys causes the change of
the number of the main characteristic exothermic peaks for the crystallization process.
When the x ranges from 0.5 to 0.8, the number of main crystalline peaks (n) reaches to
the maximum, four peaks. While more solvent Ce atom was substituted by La (x = 0.9),
the n decreases to 3. Moreover, it has been mentioned that the n of La65Al10Co25 and
Ce65Al10Co25 is only 2 . It indicates that the coexistence of La and Ce in the (LaxCe1-
x)65Al10Co25 BMGs with an appropriate ratio may increase the complexity of
crystallization for the transformation from the metastable undercooled liquid state to the
complete crystalline compound during the heating process. For the melting behavior,
with the increase of the substituting content of La, the change of Tm of the resulting alloys
is indistinctive. So does the change of Tl when the substituting content x is below 0.5.
When x is above 0.5, the Tl increases obviously from 776 K for x = 0.5 to 937 K for x =
0.9. Figure 4 (b) shows the DSC cooling curves of (LaxCe1-x)65Al10Co25 alloys (0 < x < 1).
The change of Tl’ is similar with that of Tl.
Furthermore, we tried to find out the dc for the (LaxCe1-x)65Al10Co25 BMGs in order to
evaluate the influence on the GFA by the substitution with similar atoms. Figure 5 shows
the XRD patterns for the (LaxCe1-x)65Al10Co25 glassy rods with the maximal size in
diameter, which confirms the fully amorphous structure for the samples. Through the row
substitution with similar atoms, we obtained the BMGs with superior GFA in the alloy
composition of (La0.7Ce0.3)65Al10Co25, which can successfully forms a fully glassy rod of
25mm in diameter. The outer shape and surface appearance of the as-cast
(La0.7Ce0.3)65Co25Al10 and (La0.6Ce0.4)65Co25Al10 rods of 25 mm and 20 mm in diameter,
respectively, are shown in Fig. 6.
Figure 7 shows the effect of the substituting content x of La on the dc, and the thermal
parameters of Tg/Tl, γ, ∆Tl and ∆Tx for the (LaxCe1-x)65Al10Co25 alloys. With the increase
of substituting content of La, the change of dc, characteristic of the GFA of alloys, shows
an asymmetrically pyramidic curve. When the x reaches to 0.7, the maximal dc for the
GFA of (La0.7Ce0.3)65Al10Co25 alloy is 25 mm. The coexistence of La and Ce in the alloys
also induces a larger nominal supercooled degree, ∆Tl, above 40 K with the substituting
content x from 0.3 to 0.8, consistent with the composition range with high GFA identified
by dc. The change of ∆Tx is similar with that of dc except for the excursion of their
maximal values. The Tg/Tl, Tg/Tl’ (not shown in Fig. 7) and γ show maximal values at the
substituting La content of 0.5.
In a wide range of substitution composition (0.4 ≤ x ≤ 0.8), the glassy samples with a
diameter above 10 mm can be fabricated, while the value of dc for the corresponding
single lanthanide based alloys, La65Al10Co25 and Ce65Al10Co25, is only 2 mm. In order to
further confirm that the coexistence of similar atoms of La and Ce plays a key role to
improve the GFA in (La-Ce)-Al-Co system, the GFA of La-Al-Co and Ce-Al-Co systems
were also evaluated in the corresponding composition maps, shown in Fig. 8. Although
the compositions with the best GFA for La-Al-Co (Fig. 8 (a)) and Ce-Al-Co (Fig. 8 (b))
are excursive from the optimized one for (La-Ce)-Al-Co, the maximal dc in La-Al-Co and
Ce-Al-Co systems is not more than 6 mm, far smaller than 25 mm of
(La0.7Ce0.3)65Al10Co25. It strongly supports that the similar atom coexistence of La and Ce
can significantly improve the GFA of (La-Ce)-Al-Co BMGs.
Because La (atomic number: 57) and Ce (atomic number: 58) lie in the neighboring
positions in the PTE and both belong to the lanthanide elements, the difference of atomic
size of La (187 pm) and Ce (182 pm) is small (only 2.7 %) , and the chemical
properties of La and Ce are similar, characteristic of the heat of mixing of La-Ce pair is 0
kJ/mol . So the mismatch of atomic sizes and the negative heats of mixing,
mentioned above, can’t give a reasonable explanation for the improvement of GFA by the
substitution of La for Ce in the (La-Ce)-Al-Co system. In the following section, we will
perform a further particular thermodynamic discussion and give a possible explanation
for the effect of the row substitution with similar atoms on GFA.
3.3 Thermodynamic Analysis
Above experiments have demonstrated that the partial substitution of La for solvent Ce
can significantly improve the GFA of (LaxCe1-x)65Al10Co25 alloys. When the similar
atoms, La and Ce, coexist in an appropriate composition ratio, the optimal composition
with the best GFA can be obtained. To explain the remarkable improvement of GFA
induced by the coexistence of similar atoms, we evaluated the mixing Gibbs free energy
(∆G) in our alloy systems.
From the viewpoint of thermodynamics, the GFA of BMGs, to a certain extent, has a
connection with the difference in energy between the solid glass and its liquid state,
Gs−Gl, which reflects the stability of glassy state. It has been assumed that Gs−Gl is
proportional to the free energy of mixing ∆G of the liquid phase , so it is reasonable
to understand the substitution effect on GFA by comparing the mixing Gibbs free energy
of ante- and post-substitution (∆Ga and ∆Gp). ∆G of multicomponent system is defined as
follows for standard states:
where ∆H is the increment of mixing enthalpy, ∆S is the increment of mixing entropy and
T is the temperature.
Because the accurate evaluation of thermodynamic parameters for glassy system is
very difficult, some assumptions must be proposed. Considering the similarity between
La and Ce as solvent atoms in the row substitution, according to Miracle’s structural
model for metallic glasses [37,40], we consider that this partial substitution would not
cause a significant change of glassy structure. It means that the substituting atoms La will
lie on the positions which are previously occupied by the substituted atoms Ce in the
glassy structure, like the atomic replacement in an ideal substitutional solid solution, so
the coordination number and the kinds of coordinated elements are not significantly
changed. In our study, the glassy structure is approximatively regarded as a structure of
ideal multicomponent solid solution without long range periodicity. ∆S is calculated as
the sum of the configurational entropy (∆Sconf) and the mismatch entropy (∆Smis) which is
a function of the mismatch of component atomic size and caused by the structure
modification from the periodic ideal solid solution to nonperiodic glassy structure, that is:
For the ideal multicomponent solid solution consisting of N elements, the ∆Sconf can be
expressed as equation (3):
where R is the gas constant, ci is the mole concentration for i element. ∆H can be
calculated as equation (4):
where Ωij is the interaction parameter of ideal solution between i and j element, related
with the coordination numbers.
For simplicity, we adopted the analysis method by Takeuchi et al.  to deduce the
thermal parameters, ∆H and ∆Smis (∆Smis was approximately replaced by the excess
entropy of an ideal gas at the same pressure according to Takeuchi’s deduction). Based
on the above assumption for atomic substitution, we can calculate the ∆G of pseudo-
ternary metallic glass at liquid state for a certain composition, and further compare the
change of ∆G for ante- and post-substituted alloys. Ωij can be approximately substituted
with the relation equation:
is the enthalpy of mixing which is calculated in a binary i-j system at the
equiatomic composition . ∆Smis can be treated as the discussions in references .
Figure 9 shows the effect of substitution content x of La on ∆G for the (LaxCe1-
x)65Al10Co25 BMGs. The temperature of system was chosen at 1050 K above the liquid
temperature of all alloys. The critical diameter of (LaxCe1-x)65Al10Co25 BMGs,
characteristic of the GFA, is also given in Fig. 9 for comparison. We noticed that because
the enthalpy of mixing (∆Hmix) between La and Ce is 0 kJ/mol, and there is no
considerable difference in ∆Hmix between the atomic pairs of La-Co (-17 kJ/mol) and Ce-
Co (-18 kJ/mol) as well as between those of La-Al (-38 kJ/mol) and Ce-Al (-38 kJ/mol)
, the change of ∆H among the different substituted alloys is indistinctive.
Furthermore, because of the similar atomic size between La and Ce, the change of the
mismatch entropy, resulting from atomic size mismatch, will also be little. So the main
difference in ∆G among the substituted alloys is mainly attributed to the change of ∆Sconf.
The ∆G reduces steeply with the partial substitution of La for Ce (or of Ce for La) in Ce-
Al-Co (or La-Al-Co) alloy, which implies that the coexistence of La and Ce can make the
system more stable and obviously improve the GFA of the resulting alloy comparing with
the single lanthanide based alloys. The minimal value of ∆G, corresponding to the most
stable composition for the glassy alloys by thermodynamic analysis, appears at the
equiatomic ratio for La and Ce. The experimental results of the dc are fundamentally
consistent with the calculation of ∆G except the deviation of the best composition
between the experiments ((La0.7Ce0.3)65Al10Co25) and the thermodynamic analysis
((La0.5Ce0.5)65Al10Co25). The reason for this deviation maybe that the dynamic process for
a competition process of every resulting alloy after the row substitution between
supercooled liquid and crystalline phases was not considered in this model. Nevertheless,
this thermodynamic analysis can give a reasonable explanation for the obvious
improvement of GFA caused by the row substitution, while the conventional criteria,
such as atomic size mismatch and negative heats of mixing, are incompetence.
In this paper, the glass-formation range of BMGs based on lanthanum and cerium was
pinpointed in pseudo-ternary (La-Ce)-Al-Co composition map by copper mold casting.
The influence of the substitution of La for solvent Ce in (LaxCe1-x)65Al10Co25 system on
the GFA was evaluated in detail. The (La0.7Ce0.3)65Al10Co25 alloy with superior GFA,
identified by forming the fully glassy rod of 25 mm in diameter by tilt-pour casting, was
found out through this row substitution. Because this substitution with the similar atoms
of La and Ce can’t be explained by former criteria of GFA, e.g. atomic size mismatch and
negative heats of mixing, a thermodynamic model was proposed to evaluate the effect of
the coexistence of La and Ce in (La-Ce)-Al-Co system. The decrease of ∆G caused by the
configurational entropy can give a reasonable explanation for the obvious improvement
of GFA by this substitution.
This work was financially supported by National Nature Science Foundation of China
(No. 50225103 and No. 50471001).
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Fig. 1 The composition map for the glass-forming range in the (La0.5Ce0.5)-Al-Co system.
The symbols represent: ▲ BMG;
Fig. 2 XRD patterns of the as-cast rods of 12 mm in diameter for (La0.5Ce0.5)65Al10Co25,
(La0.5Ce0.5)65Al15Co20 and (La0.5Ce0.5)70Al15Co15 BMGs.
Fig. 3 The 3D contour map of liquidus surface for (La0.5Ce0.5)-Al-Co alloys. The eutectic
composition and the composition range for 12 mm BMGs are marked.
Fig. 4 DSC curves of the 2 mm glassy rods of (LaxCe1-x)65Al10Co25 alloys (0 < x < 1) at
the rate of 0.33 K/s for: (a) heating procedure; (b) cooling procedure.
Fig. 5 XRD patterns for the (LaxCe1-x)65Al10Co25 glassy rods (0 < x < 1) with the maximal
size in diameter.
Fig. 6 The outer shape and surface appearance of the as-cast (La0.7Ce0.3)65Al10Co25 and
(La0.6Ce0.4)65Al10Co25 rods of 25 mm and 20 mm in diameter, respectively.
Fig. 7 The effect of the substituting content x of La on dc, Tg/Tl, γ, ∆Tl and ∆Tx for the
Fig. 8 The composition map for the glass-forming range in the La-Al-Co and Ce-Al-Co
systems. The symbols represent: ▲ BMGs with dc of 2 mm; ● BMGs with dc of 4 mm;
■ BMGs with dc of 6 mm; crystalline.
Fig. 9 The effect of substitution content x of La on the mixing Gibbs free energy, ∆G, for
the (LaxCe1-x)65Al10Co25 BMGs.
Figure 1 Glass Forming Range of (La-Ce)-Al-Co
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