# Comparison of the Solid Solution Properties of Mg-RE  (Gd, Dy, Y) Alloys with Atomistic Simulation

Authors: Yurong Wu; Wangyu Hu
Journal: Research Letters in Physics
 (2008)

---

## Abstract

Molecular dynamic simulations have been performed to study the solid solution mechanism of Mg100-xREx (RE=Gd,Dy,Y, x=0.5,1,2,3,4at.%). The obtained results reveal that the additions of Gd, Dy and Y increase the lattice constants of Mg-RE alloys. Also the axis ratio c/a remains unchanged with increase in temperature, restraining the occurrence of nonbasal slip and twinning. Furthermore, it is confirmed that bulk modulus of Mg alloys can be increased remarkably by adding the Gd, Dy, Y, especially Gd, because the solid solubility of Gd in Mg decrease sharply with temperature in comparison with Dy and Y. Consequently, the addition of the RE can enhance the strength of Mg-based alloys, which is in agreement with the experimental results.


---

## Body

## 1. Introduction

Magnesium alloys are becoming
increasingly important due to potential weight saving in comparison with
aluminum-based alloys. However, the mechanical properties
of magnesium alloys in some respects are inferior to those of aluminum alloys
which are also light-weight materials. Recently,
it was reported that the addition of rare earth elements (REs), such as Gd, Dy,
Y [1–6],
especially Gd [7], can remarkably improve the mechanical properties of
magnesium at room and high temperatures [1–4, 8]. The effects of RE have been explained by two
mechanisms. One is solution-hardening and the other is precipitation-hardening.Experimentally,
the equilibrium solid solubility of Dy, Y, and Gd in magnesium is relatively
high. Their values are 3.5, 3.75, and 4.53 at.%, respectively. The solid
solubility decreases sharply with temperature, especially Gd. For example, the
maximum solid solubility of Gd in Mg is relatively high (4.53 at.% at 821 K) and decreases exponentially with temperature (to 0.61 at.% at 573 K). It has
been reported that the addition of Gd, Dy, and Y is effective for improving
strength and creep resistance of magnesium alloys at elevated temperature [1–3, 9]. So the aim of this
work is to investigate the solid solution properties of the Mg-RE alloy by the
addition of different atomic fraction of Gd, Dy, and Y at room temperature and
elevated temperature (500 K) using
the modified analytical-embedded atom method (EAM) [10], which has been successfully applied in the calculations
of some Mg-rare earth alloys [11–13].


## 2. Simulation Procedure

The interactions between Mg, Gd, Dy, Y
atoms are described by an analytical-embedded atom method (EAM) potential [11–13].In
the simulation runs, simulations were performed for 10944 atoms based on HCP
unit cell, which comprise pure Mg, andMg100-x-Gdx,
Mg100-x-Dyx, and Mg100-x-Yx (x=0.5,1,2,3,4at.%) alloys. The periodic boundary conditions were applied
on the fundamental directions of molecular dynamic (MD) cell. Molecular
dynamics calculations are carried out in two successive ensembles. The lattice
constants for simulation systems are determined from the constant
temperature-constant pressure (NPT) ensemble simulations. And then the constant
volume-constant temperature (NVT) ensemble is used to compute the elastic
constants of the systems. In integration of the classic equations of motion, we
used a fourth-order gear predictor-corrector algorithm with a time step of 3 femtoseconds
[14]. The simulation systems are relaxed by 50 000 time steps at room and elevated temperature, and all of the statistical data are
collected from further 50 000 MD time steps.


## 3. Results and Discussion

### 3.1. Effect of Gd, Dy, and Y on Lattice Parameters in Mg

Magnesium with hexagonal close-packed crystal structure has
three slip systems: a basal slip system of(0001)〈112¯0〉, a prismatic slip system, such as {101¯0}〈112¯0〉, and the
pyramidal slip system, such as {101¯1¯}〈112¯0〉 and {112¯2}〈112¯3〉. The latter two slip systems act together in many cases and
are called the nonbasal slip system versus the basal slip system. Magnesium is
plastic-deformed by the basal slip and twinning mainly at relatively low temperature.
The critical resolved shear stress for the basal slip in pure magnesium is very
low, approximately 0.60–.7 MPa, at room
temperature. It is also independent of temperature. In contrast, the critical
shear stress for the nonbasal slip is over 40 MPa at low temperature, which is
two orders of magnitude higher than that for the basal slip, and drastically
decreases to 2-3 MPa with
increasing temperature [16].The variation of lattice parameters with
temperature in pure Mg,Mg100-x-Gdx, and Mg100-x-Dyx (x=0.5,1,2,3,4 at.%) alloys is shown in Figure 1, along with the experimental
data [17]. The temperature dependence of the lattice parameters for Mg100-x-Yx alloys is similar to those of Mg100-x-Gdx and Mg100-x-Dyx alloys. By adding the Gd and Dy, the lattice parameters a and the axis ratio (c/a) become
larger. The lattice parameters in the
pure Mg, Mg100-x-Gdx and Mg100-x-Dyx alloys increase linearly with temperature increasing. We can also see that the
values from EAM calculations are larger than experimental values. As an example
of Mg-0.5Gd, as shown in Figure 1(c), the c/a in Mg-0.5Gd alloy almost keeps a
constant with increasing temperature, whereas pure metal Mg does not exhibit
this behavior. Thus, the RE metals (Gd, Dy, and Y) give rise to the variation
of lattice parameters, whereas the c/a remains unchanged with increasing
temperature, which indicates that the temperature-independent c/a restrains the
occurrence of nonbasal slip and twinning. Because the slip and twining in HCP
metals may be related to the axis ratio, c/a. Nonbasal slip hardly occurs when
the c/a is large, whereas at high temperature, where the c/a becomes lower, the
nonbasal slip can occur [18, 19]. This phenomenon has been reported in Mg-Y
alloys [19].The lattice parameter as a function of the temperature for Mg-RE alloys by the use of Gd and Dy additions.
(a)(b)(c)


### 3.2. Comparison of the Solid Strength of Mg-RE Alloys

As discussed above, the addition of
RE metals can vary the lattice parameter for Mg-Gd, Mg-Dy, and Mg-Y alloys. The
larger the rare earth metal content, the larger the lattice parameters for
Mg-RE alloys. At the same time, the addition of rare earth metals also varies
the solid strength for Mg-rare earth alloys. As
an example of Mg-Gd alloys, the bulk modulus of pure Mg andMg100-x-Gdx alloys at room and high temperature are presented in Figure 2, along with the
experimental data [15]. It can be noted that the addition of Gd gives rise to
the sudden increase of bulk modulus of Mg at room and high temperature. The
Mg-Dy and Mg-Y alloys exhibit a similar solid strength behavior. This behavior
indicates that the addition of Gd, Dy, and Y can enhance strength of Mg, which
is in agreement with experiments [1–3, 20, 21]. Furthermore, the bulk
modulus of Mg increases with increasing the content of Gd, Dy, and Y.Bulk modulus of Mg as function of Gd content at room and high temperature, as well as the experimental data [15].
(a)(b)The comparison of the bulk modulus for
Mg-RE alloys with various rare earth metal compositions at room temperature is
shown in Figure3. The magnitude of the bulk modulus of Mg-Gd is the largest
one among the three Mg-RE alloys, which demonstrate that the addition of Gd can
further improve the strength of Mg-RE alloys [8]. This behavior may be explained
in terms of the equilibrium solid solubility of Gd in Mg decreasing sharply with
temperature in comparison with Dy and Y. For example, the maximum
solid solubility of Gd in Mg is 4.53 at.% at 821 K and decreases exponentially
with temperature, to 0.61 at.% at 573 K.Figure 3
Comparison of the bulk modulus for Mg-RE alloys with different rare earth content at room temperature.


## 3.1. Effect of Gd, Dy, and Y on Lattice Parameters in Mg

Magnesium with hexagonal close-packed crystal structure has
three slip systems: a basal slip system of(0001)〈112¯0〉, a prismatic slip system, such as {101¯0}〈112¯0〉, and the
pyramidal slip system, such as {101¯1¯}〈112¯0〉 and {112¯2}〈112¯3〉. The latter two slip systems act together in many cases and
are called the nonbasal slip system versus the basal slip system. Magnesium is
plastic-deformed by the basal slip and twinning mainly at relatively low temperature.
The critical resolved shear stress for the basal slip in pure magnesium is very
low, approximately 0.60–.7 MPa, at room
temperature. It is also independent of temperature. In contrast, the critical
shear stress for the nonbasal slip is over 40 MPa at low temperature, which is
two orders of magnitude higher than that for the basal slip, and drastically
decreases to 2-3 MPa with
increasing temperature [16].The variation of lattice parameters with
temperature in pure Mg,Mg100-x-Gdx, and Mg100-x-Dyx (x=0.5,1,2,3,4 at.%) alloys is shown in Figure 1, along with the experimental
data [17]. The temperature dependence of the lattice parameters for Mg100-x-Yx alloys is similar to those of Mg100-x-Gdx and Mg100-x-Dyx alloys. By adding the Gd and Dy, the lattice parameters a and the axis ratio (c/a) become
larger. The lattice parameters in the
pure Mg, Mg100-x-Gdx and Mg100-x-Dyx alloys increase linearly with temperature increasing. We can also see that the
values from EAM calculations are larger than experimental values. As an example
of Mg-0.5Gd, as shown in Figure 1(c), the c/a in Mg-0.5Gd alloy almost keeps a
constant with increasing temperature, whereas pure metal Mg does not exhibit
this behavior. Thus, the RE metals (Gd, Dy, and Y) give rise to the variation
of lattice parameters, whereas the c/a remains unchanged with increasing
temperature, which indicates that the temperature-independent c/a restrains the
occurrence of nonbasal slip and twinning. Because the slip and twining in HCP
metals may be related to the axis ratio, c/a. Nonbasal slip hardly occurs when
the c/a is large, whereas at high temperature, where the c/a becomes lower, the
nonbasal slip can occur [18, 19]. This phenomenon has been reported in Mg-Y
alloys [19].The lattice parameter as a function of the temperature for Mg-RE alloys by the use of Gd and Dy additions.
(a)(b)(c)


## 3.2. Comparison of the Solid Strength of Mg-RE Alloys

As discussed above, the addition of
RE metals can vary the lattice parameter for Mg-Gd, Mg-Dy, and Mg-Y alloys. The
larger the rare earth metal content, the larger the lattice parameters for
Mg-RE alloys. At the same time, the addition of rare earth metals also varies
the solid strength for Mg-rare earth alloys. As
an example of Mg-Gd alloys, the bulk modulus of pure Mg andMg100-x-Gdx alloys at room and high temperature are presented in Figure 2, along with the
experimental data [15]. It can be noted that the addition of Gd gives rise to
the sudden increase of bulk modulus of Mg at room and high temperature. The
Mg-Dy and Mg-Y alloys exhibit a similar solid strength behavior. This behavior
indicates that the addition of Gd, Dy, and Y can enhance strength of Mg, which
is in agreement with experiments [1–3, 20, 21]. Furthermore, the bulk
modulus of Mg increases with increasing the content of Gd, Dy, and Y.Bulk modulus of Mg as function of Gd content at room and high temperature, as well as the experimental data [15].
(a)(b)The comparison of the bulk modulus for
Mg-RE alloys with various rare earth metal compositions at room temperature is
shown in Figure3. The magnitude of the bulk modulus of Mg-Gd is the largest
one among the three Mg-RE alloys, which demonstrate that the addition of Gd can
further improve the strength of Mg-RE alloys [8]. This behavior may be explained
in terms of the equilibrium solid solubility of Gd in Mg decreasing sharply with
temperature in comparison with Dy and Y. For example, the maximum
solid solubility of Gd in Mg is 4.53 at.% at 821 K and decreases exponentially
with temperature, to 0.61 at.% at 573 K.Figure 3
Comparison of the bulk modulus for Mg-RE alloys with different rare earth content at room temperature.


## 4. Conclusions

In this paper, the solid solution properties of Mg-RE (RE=Gd,Dy,Y) alloys with different RE contents have been investigated in terms of molecular dynamic simulation using an analytical-embedded atom method. It has been found that the lattice parameters of magnesium alloys containing Gd, Dy, and Y increase. However, the axis ratio c/a almost keeps a constant with increasing temperature, which restrains the occurrence of nonbasal slip and twinning. Furthermore, the addition of the RE also gives rise to the variation of bulk modulus, which indicates that the strength
of Mg alloys can be improved by Gd, Dy, and Y, especially Gd. This behavior may be interpreted by the idea that the equilibrium solid solubility of Gd in Mg decreasing more sharply with temperature in comparison with Dy and Y.



---

*Source: 476812-2008-11-16.xml*