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Grain Boundary Segregation of Rare-Earth Elements
in Magnesium Alloys
JOSEPH D. ROBSON, SARAH J. HAIGH, BRUCE DAVIS, and DAVID GRIFFITHS
Small additions of rare-earth (RE) elements have been shown to have a powerful effect in
modifying the texture of wrought magnesium alloys, giving a highly beneficial effect in
improving their formability. Recent work has shown that segregation of RE atoms to grain
boundaries is important in producing this texture change. In this work, two Mg-RE systems
have been studied Mg-Y and Mg-Nd using high-resolution scanning transmission electron
microscopy that permits both imaging and elemental analysis with a spatial resolution of better
than 0.1 nm. The Mg-Y alloy, where the solubility and level of addition are relatively high,
showed the RE texture change effect. This was accompanied by clustering of Y on the grain
boundaries, consistent with previous studies of the Mg-Gd system. The Mg-Nd alloy, where the
solubility and level of addition are relatively low, showed no texture change and no segregation.
In this case, impurity elements binding the RE into insoluble particles, rendering it ineffective.
The results are analyzed by modifying a previous model for the solute drag effect on boundaries
expected due to the RE additions. This predicts that both Gd and Y will strongly inhibit
boundary motion, with Gd being approximately twice as effective as Y.
DOI: 10.1007/s11661-015-3199-3
ÓThe Author(s) 2015. This article is published with open access at Springerlink.com
I. INTRODUCTION
Akey limitation of current wrought magnesium alloy
sheet is poor cold formability.
[1]
It has been demon-
strated that the strong basal textures that characterize
conventional magnesium alloy sheets is a major con-
tributing factor to this poor formability.
[2,3]
Small
additions of rare-earth (RE) elements have been shown
to modify the texture of magnesium sheet after hot
rolling, producing weaker texture and an increased split
in basal pole orientations. Sheets produced from alloys
with these modified textures show significantly improved
formability compared to conventional magnesium alloy
sheets with a strong basal texture.
[2]
It is now known that the amount of RE needed to
activate texture change can be very small.
[2–5]
For example,
for low-solubility REs such as Ce, only 0.03 at. pct
addition is required to produce a strong texture weakening
effect.
[3]
This observation has led to the suggestion that
segregation is likely to be important in enabling much
higher concentrations to be achieved locally at sites such as
grain boundaries and dislocations.
[6–9]
The critical RE concentration required to change the
texture has been observed to vary directly with the
solubility of the element, i.e., for elements with a higher
solubility, more RE is needed.
[10]
However, it has been
concluded that this transition is not associated with
precipitation, since the critical RE concentration
required to produce the texture weakening effect is
below the solid solubility.
[5,10]
A detailed description of
the RE texture weakening effect and proposed mecha-
nisms are reviewed elsewhere.
[11]
One important factor
that has been widely reported is an effect of RE
additions in suppressing dynamic recrystallization
(DRX). This appears to be critical in enabling a
deformed structure to be obtained containing a wider
spread of orientations, deformation heterogeneities, and
higher stored energy.
[5]
When these structures recrystal-
lize, a weaker texture is obtained. Segregation of RE to
grain boundaries would be expected to provide a strong
drag force suppressing DRX. The predictions of simple
classical models for boundary segregation and solute
drag support this hypothesis.
[12]
There is now direct experimental evidence that RE
elements can segregate strongly to grain boundaries.
These data have been obtained using both atom probe
[6]
and high-resolution transmission electron microscopy
(HRTEM).
[7–9]
A recent investigation
[8]
of two Mg-Gd
alloys using high-angle annular dark-field (HAADF)
scanning transmission electron microscope (STEM)
imaging has revealed that the RE atoms can segregate
into small clusters at grain boundaries. It was demon-
strated that the texture associated with the RE effect in
extruded material was only observed in an alloy that
contained sufficient Gd (0.06 at. pct) to produce clearly
detectable boundary segregation. In an alloy with a very
low level of Gd (0.01 at. pct), no grain boundary
segregation was observed and no RE texture was
produced. Bugnet et al.
[9]
have studied the segregation
of Gd at grain boundaries in Mg in detail. They have
shown that there is a high level of enrichment, with
clusters apparently of a cubic phase of Gd located at the
JOSEPH D. ROBSON, Professor, SARAH J. HAIGH, Reader,
and DAVID GRIFFITHS, Research Student, are with the School of
Materials, University of Manchester, MSS Tower, Manchester M13
9PL, UK. Contact e-mail: joseph.robson@manchester.ac.uk BRUCE
DAVIS, Research Manager, is with Magnesium Elektron North
America, 1001 College St., P.O. Box 258, Madison, IL 62060.
Manuscript submitted April 23, 2015.
Article published online October 19, 2015
522—VOLUME 47A, JANUARY 2016 METALLURGICAL AND MATERIALS TRANSACTIONS A
boundary. Interestingly, they have suggested that the
clusters consist of pure Gd and are not an intermetallic
compound as might be expected from the phase
diagram.
In this study, two other important RE additions are
investigated: Y and Nd. Y is an important element in
current commercial magnesium alloys, such as WE43,
where it is added in relatively high concentrations
mainly to produce creep-resistant age-hardening pre-
cipitates rather than to produce a texture change.
Nevertheless, the RE texture effect in a byproduct of
this addition. Y is a relatively high-solubility RE,
being capable of dissolving in Mg up to 3 at. pct at
673 K (400 °C). It has a similar solubility and pre-
dicted tendency to segregate to Gd, which has been
studied in more detail previously. One aim of this
study was to determine whether the segregation
features observed in Mg-Gd alloys are typical of
those found in other Mg-RE systems with high RE
solubility.
Nd is a low-solubility RE [0.4 at. pct at 673 K
(400 °C)]. It has been shown previously that it can
produce a texture change in Mg even when added at a
level of only 0.04 at. pct.
[10]
There is a great interest in
finding RE additions that can be added in very low
concentrations to produce a texture change since RE
additions are expensive.
Previously, Robson
[12]
has demonstrated that a simple
classical grain boundary segregation and solute drag
model (the Cahn–Lu
¨cke–Stu
¨we model
[13,14]
) can be used
to estimate the tendency for RE elements to segregate to
boundaries and the drag pressure they will produce.
This model is based on the assumption that it is the
misfit between the RE atoms (which are large) relative to
the matrix Mg atoms that provides the driving force for
boundary segregation.
The ability to provide a semi-quantitative measure-
ment of the grain boundary composition using the
TITAN G2 80-200 ChemiSTEM employed in this study
has allowed these predictions to be revisited and revised.
With this information, a more accurate assessment of
the likely drag effect of different RE additions can be
made and thus their effect on phenomena that require
boundary migration including recrystallization and
grain growth.
II. EXPERIMENTAL
The Mg-Y and Mg-Nd alloys were cast by Magne-
sium Elektron into rectangular steel molds, homoge-
nized at 823 K (550 °C), and hot rolled at 673 K
(400 °C) to a reduction of 1.4 (true strain) in seven
equal passes. Annealing was performed following rolling
for 1 hour at 673 K (400 °C) to produce a recrystallized
microstructure.
The alloys were nominally binaries that contained
either 0.15 at. pct Y or 0.024 at. pct Nd (determined by
inductively coupled plasma optical emission spec-
troscopy, ICP-OES). Both of these concentrations are
well below the expected solubility limits at the rolling
and annealing temperatures but are above the critical
concentration expected to activate the RE texture
weakening effect.
[3]
As with most other studies on
Mg-RE alloys, high-purity feedstock was not used, so
small amounts of other elements (mainly Fe) are also
present in the alloys. The iron level is a maximum of
0.004 at. pct. The texture of these alloys was compared
to that of an Mg-0.009 at. pct Y alloy prepared in the
same way and with a similar maximum iron level. The Y
in this alloy is present as an impurity and is well below
the critical threshold required to activate the RE texture
effect.
[3]
The textures of the as-rolled and annealed material
were measured by X-ray diffraction using a Bruker D8
Discover diffractometer. Samples were ground and
polished to remove the deformed surface layer prior to
texture measurement. f10
10g, {0002}, f10
11g;and
f10
12gpole figures were measured. After background
and defocusing corrections were applied, the pole
figures were combined to generate an orientation distri-
bution function (ODF) using the MTEX texture anal-
ysis package, from which the recalculated pole
figures presented here were computed.
Specimens of annealed material were prepared for
transmission electron microscope imaging using stan-
dard metallographic procedures followed by dimple
grinding to 20 lm thickness and precision ion polishing
for approximately 20 hours to produce a hole, using a
6 deg incidence angle and 4 kV Ar ion beams. Bright-
field and HAADF STEM imaging were performed using
the Titan G2 80-200 ChemiSTEM operated with an
accelerating voltage of 200 kV, a probe current of
500 pA, a convergence semi-angle of 21 mradn and an
HAADF inner semi-angle of 54 mrad. The instrument is
equipped with a high-brightness X-FEG electron source
and four silicon drift energy-dispersive X-ray (EDX)
detectors (total EDX collection angle = 0.7 srad)
enabling imaging and elemental analysis to be per-
formed with a spatial resolution of better than 0.1 nm.
EDX spectrum images were acquired using all four
EDX detectors, a pixel dwell time of 30 ls and a total
acquisition time of 2 to 10 minutes. Quantification was
performed using an absorption-corrected Cliff–Lorimer
approach within the Bruker Esprit software assuming a
specimen thickness of 100 to 200 nm. Care was taken to
align the sample so that grain boundaries were parallel
to the incoming electron beam in order to prevent
smearing of the projected compositional profiles, but the
accuracy of this correction was limited to 1 to 2 deg
(giving a broadening of 1 nm for an estimated sample
thickness of 100 nm).
III. MODEL
The Cahn–Lu
¨cke–Stu
¨we (CLS)
[13,14]
model for solute
drag on grain boundaries has been described in detail
elsewhere, and its application to predicting drag for
Mg-RE binaries was detailed in a previous publica-
tion.
[12]
This model assumes that there is a free energy
advantage for solute atoms to lie in the grain boundary
region. An additional pressure is required on the
boundary to overcome this attraction. The drag effect
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 47A, JANUARY 2016—523
depends on the depth of the free energy well associated
with solute located on the grain boundary, the diffusiv-
ity of the solute species, and the boundary velocity. The
CLS model predicts that there are two drag pressure
regimes as a function of boundary velocity; in the
low-velocity regime, drag increases as boundary velocity
increases and in the high-velocity regime drag pressure
decreases with increasing boundary velocity. The max-
imum drag effect occurs at the transition between the
regimes.
The physical interpretation of this transition is the
change from a regime where an enriched solute region
can be dragged along with the boundary (low velocity)
to a regime where the boundary breaks away from the
solute-enriched region. Cahn demonstrated that in the
low-velocity limit, slower diffusing solutes will lead to
greater drag, whereas in the high-velocity limit the
opposite is true.
[13]
It was shown previously that for Y in
Mg, and for boundary velocities typical of those
expected during recrystallization, the drag pressure is
close to its peak value and near the transition from the
high- to low-velocity regimes.
[12]
For other typical
additions to Mg (e.g., Al and Zn), it was also shown
that the predicted drag pressure is several orders of
magnitude smaller and is well within the low-velocity
regime.
In the classical implementation of the CLS model, as
described for Mg-RE alloys in Reference 12,itis
assumed that the free energy advantage associated with
solute locating on the grain boundaries is mainly due to
a relaxation of the elastic misfit strain energy associated
with the solute dissolved in the matrix. However, the
CLS model does not prescribe this as the only effect that
can cause solute drag. Other contributions to the free
energy change at boundaries come from the chemical
effect. In previous application of the CLS model to
solute drag in the Mg-Y system, the classical (elastic
only) assumption was used to calculate the free energy
change associated with solute locating on the grain
boundaries. However, as shown later, the equilibrium
boundary solute content predicted using this assumption
is a significant underestimate of the boundary concen-
tration measured in the present work (.6 times too
small). This suggests that the segregation of RE solute to
the boundaries is not only driven by atom size with the
magnesium matrix, but there is also a significant
chemical component as well as an interaction between
the RE and minor impurities present in the alloy that
also segregate to the boundaries (as demonstrated later).
In the present work, the measured Y content on the
boundary has been used to estimate the true depth of the
free energy well at grain boundaries, DGseg.
[15]
This will
implicitly include interaction and chemical effects that
also contribute to the free energy well, in addition to the
relief of elastic misfit strain.
DGseg ¼kT ln XGB
XM
;½1
where XGB is the (measured) maximum solute concen-
tration on the grain boundary, XMis the average solute
concentration, and kand Thave their usual meanings.
Using the revised value of DGseg calculated from
measurement, the CLS model can be applied to predict
the solute drag associated with Y segregation.
According to the CLS model, the drag pressure due to
solute is given by
[13]
Pd¼avXM
1þb2v2;½2
where vis the boundary velocity and aand bare
parameters that depend on the diffusion and free
energy profiles assumed in the vicinity of the grain
boundary (see Robson
[12]
for details), which are
obtained from
[16]
as
a¼RT
dGseg
log D
DGB
;½3
a¼4R2T2
VmG2
segD
1
a3a;½4
a
b2¼2GsegDGB
Vma1D
DGB
;½5
where Dis the bulk diffusion coefficient of solute,
DGB is the grain boundary diffusion coefficient, and
Vmis the molar volume. For Y and Gd in Mg, D0and
Qfor bulk diffusion were given by Reference 17.The
anisotropy in the diffusion coefficient (which is small
at the temperatures of interest here
[17]
) was ignored.
There are no reported data for the impurity diffusion
coefficient of Ni in Mg, and so this was taken from
the values reported for Ni in Al; the justification for
this is discussed later. Since the appropriate values for
GB diffusion are not known, the commonly used
approximation was made that QGB ’0:5Q.
[18]
These
input parameters to the model are summarized in
Table I
IV. RESULTS AND DISCUSSION
A. Texture Measurements and Microstructure
Figure 1compares the {0001} pole figures of Mg
(with very low Y), Mg-Y, and Mg-Nd alloys after hot
rolling (a–c) and annealing (d–f). The Mg with negligible
RE addition has the expected strong basal texture
(maximum=16 multiples of random density, MRD)
with no significant splitting of the basal poles from the
normal direction. After annealing, a slight split in the
basal poles toward the rolling direction (RD) is
observed, but the texture remains very strong (maxi-
mum = 14 MRD). The Mg-Y alloy shows a weaker
texture (maximum = 7.3 MRD) with a significant split
in the basal poles toward the RD in the as-rolled
condition. On annealing, the texture weakens further
(maximum = 4.5 MRD). The Mg-Nd alloy shows a
similar texture strength in the as-rolled condition
(maximum = 8.4 MRD), but the texture strength in
this case does not weaken significantly during annealing
524—VOLUME 47A, JANUARY 2016 METALLURGICAL AND MATERIALS TRANSACTIONS A
(maximum = 7.1 MRD) and so a strong basal texture is
retained. These observations are consistent with previ-
ous work on binary Mg-RE alloys (e.g., References 2,
10).
Segregation was studied in the annealed condition. In
this condition, all specimens were fully recrystallized
with an approximately equiaxed grain structure. The
mean grain size in the annealed state was approximately
25 lm in the Mg-0.15 at. pct Y alloy, 50 lm in the in
the Mg-0.024 at. pct Nd alloy, and 60 lminthe
Mg-0.009 at. pct Y alloy.
B. High-Resolution Imaging and Composition
Measurement
Figure 2shows HAADF images in which the strong
atomic number dependence of HAADF image contrast
clearly reveals the presence of a high-atomic number
element at the grain boundary. HAADF imaging,
Figure 2, also reveals that segregation is not uniformly
distributed along the boundary, but that the boundary is
decorated by nanometer-sized solute clusters. Interest-
ingly, the high-resolution HAADF image in Figure 2(b)
shows that the clusters have some preferential orienta-
tion relationship with the lattice. These results are very
similar to the Gd segregation observed by Hadorn et al.
in their Mg-0.06 at. pct Gd alloy and Bugnet et al. in
Mg-0.28 at. pct Gd.
[8,9]
This suggests that Y, a high-sol-
ubility RE in the same sub-group as Gd, does indeed
behave very similarly to Gd with regard to segregation.
It should be noted that although the RE is observed to
form clusters along the boundary, these clusters are very
closely spaced and form what at low magnification
appears to be a continuous layer of RE on the
boundary. It is difficult to determine the cluster spacing
since the depth of the clusters through the foil is not
easily determined. However, both the present work and
previous studies
[7–9]
suggest that the clusters are so
closely spaced that they will provide a uniform drag
effect on the boundary, and are only a few atom
diameters in size, so are therefore likely to be unsta-
ble and break up once the boundary moves away. Thus
the drag effect the RE exerts is most appropriately
modeled using a solute drag model (e.g., CLS model),
rather than a particle pinning model (e.g., Zener pinning
model
[15]
), where the assumption is that the particles are
inert and widely spaced (relative to their size), forming a
static dispersion through which the boundary can pass
by bowing between particles.
EDX spectrum imaging of the grain boundary region
confirms, as predicted, that Y is strongly segregated to
the grain boundary and also reveals that impurity Ni
segregated to the boundary (Figure 3). The low levels of
Ni contamination observed are presumably introduced
during the casting process, although the source remains
uncertain. As shown in Figure 3(e), a line scan across
the boundary can be obtained by summing pixel spectra
contained in the spectrum image. This reveals a peak
segregation of 2.4 at. pct Y (16 times the average alloy
concentration) and 1.1 at. pct Ni, with both elemental
peaks having a full width half maximum (FWHM) of
1.4 nm. A number of different grain boundaries were
observed with different misorientations and were found
to have peak Y concentrations of 1.4 to 2.5 at. pct and
widths of 1 to 2 nm. Segregation was observed on all the
boundaries studied although more detailed investigation
is required to determine any relationship between the
level of segregation and grain boundary character. This
semi-quantitative analysis supports previous qualitative
work in revealing that the tendency for segregation to
the grain boundaries is very strong, with at least an
order of magnitude increase in local concentration along
the boundary. The identification of the presence of both
Y and Ni together with semi-quantitative analysis of
grain boundary enrichment would be impossible with-
out the high-brightness probe and high-efficiency EDX
spectrum imaging capabilities available using the Titan.
The present results can be compared with predictions
made previously with the CLS model
[12]
assuming that
segregation is driven by size and elasticity mismatch
alone (the Langmuir MacClean (LM) model
[20]
). When
this model is applied to the Mg-Y alloy assuming all of
the solute is available for segregation, the local grain
boundary (GB) concentration is predicted to be
0.42 at. pct (approximately three times the bulk com-
position). The LM model clearly underestimates the true
amount of segregation observed by a factor of approx-
imately 6. There are two explanations for this discrep-
ancy, and both are likely to play some role. Firstly, the
LM model ignores the chemical contribution to the free
energy reduction on segregation of Y to the grain
boundaries. Secondly, the unexpected observation of
enriched Ni on the grain boundary is likely to lead to a
synergistic effect that influences Y segregation. Where
there is an attractive interaction between two elements,
the tendency to co-segregate will be increased.
[21]
This
attraction can be chemical or due to elastic interactions;
it is noteworthy that while Y in solution in Mg is a large
Table I. Input Parameters for the Calculation of Diffusion Coefficients Used in Model
Symbol Parameter Value Source
D
0
(Y) pre-factor for Y diffusion 3.2 910
8
m
2
s
1
[17]
Q(Y) activation energy for Y diffusion 99.1 kJ mol
1
[17]
D
0
(Gd) pre-factor for Gd diffusion 1.8 910
9
m
2
s
1
[17]
Q(Gd) activation energy for Gd diffusion 81.6 kJ mol
1
[17]
D
0
(Ni) pre-factor for Ni diffusion 4.1 910
4
m
2
s
1
[19]*
Q(Ni) activation energy for Ni diffusion 144.6 kJ mol
1
[19]*
*Data for Ni relate to impurity diffusion coefficient in Al (see text for details).
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 47A, JANUARY 2016—525
atom relative to Mg (Y/Mg size ratio 1.14), Ni is small
(Mg/Ni size ratio 1.28).
[22]
The solubility of Ni is Mg is
almost zero,
[23]
and there is thus a highly unfavorable
enthalpy of mixing between Mg and Ni. This favors
rejection of Ni to the grain boundaries, where it is likely
to have a synergistic effect with Y segregation (based on
a size consideration alone), further enhancing the
segregation of both elements. The level of impurity Ni
in this alloy as measured by ICP-OES was only
0.002 at. pct, and the measured concentration on the
boundary of 1.1 at. pct is 550 times higher, indicating a
very strong energy advantage for segregation of this
element in the presence of Y.
As discussed, a key difference between the Mg-Y
alloy and Mg-Nd alloy is that the Nd-containing alloy
does not show significant texture weakening during
Fig. 1—Basal pole figures for (a) Mg-0.009 at. pct Y, (b) Mg-0.15 at. pct Y, (c) Mg-0.024 at. pct Nd, (all as-rolled), (d) Mg-0.009 at. pct Y, (e)
Mg-0.15 at. pct Y, and (f) Mg-0.024 at. pct Nd [after annealing for 1 h at 673 K (400 °C)].
Fig. 2—HAADF STEM images showing segregation of Y at grain boundaries at (a) low and (b) higher magnification.
526—VOLUME 47A, JANUARY 2016 METALLURGICAL AND MATERIALS TRANSACTIONS A
recrystallization on annealing. A similar approach was
employed to analyze grain boundaries in the Mg-Nd
alloy, but no evidence of Nd segregation was observed.
Figure 4(a) shows an example grain boundary with the
corresponding Nd elemental map showing no evidence
of Nd in the grain boundary. Semi-quantitative line
scans of the alloy material confirmed this observation
with no detectable Nd observed in the summed spectra
obtained from the full elemental map of the GB region.
This result was initially surprising, since according to
the LM model Nd should have an even greater
tendency to segregate than Y. However, extensive
STEM imaging also revealed the presence of unex-
pected second-phase particles within the alloy. Some of
these particles can be seen close to the grain boundary
in Figure 4(a), and EDX spectrum imaging revealed
these to be rich only in oxygen. Clusters of larger
facetted particles with sizes ranging from 20 to
>300 nm were also observed within the grains, and
these were revealed to be primarily composed of Nd,
impurity Fe, or a combination of both elements
(Figures 4(b) through (d)). The presence of these
particles, which contain impurity Fe and Nd, will
reduce the availability of Nd in the matrix.
The solubility of Fe in Mg at the annealing temper-
ature [673 K (400 °C)] is very low (<7910
6
at. pct
[24]
).
Using the measured Nd:Fe ratio (8:1) in the largest
particles (Figure 4(d)) and the solubility of Fe in Mg
stated previously, up to an estimated 0.032 at. pct of Nd
could be removed into these particles (assuming iron is
fully precipitated). This exceeds the level of Nd added to
the alloy. Thus, it is conceivable that almost all of the Nd
is locked up in insoluble particles and is not available in
the matrix to segregate to boundaries.
This is an important observation since it highlights
that the level of impurity elements such as Fe and O will
have an effect on the critical level of Nd addition
required to produce segregation, since there must be
sufficient Nd retained in the matrix once the removal of
some of this element into impurity particles has been
Fig. 3—Energy-dispersive X-ray spectrum imaging of grain boundary segregation. (a) HAADF STEM images showing grain boundary region.
(b,c) Elemental maps for Y and Ni extracted from the EDX spectrum image. (d) EDX spectra summed over the region of grain boundary and
of the matrix illustrated by the red and blue dashed lines in (a). Summed spectra have been normalized to the Mg peak. The presence of Ar and
Cu in both spectra are the result of ion polishing sample preparation and scattering from the TEM sample holder, respectively. (e) Semi-quanti-
tative analysis showing Y and Ni enrichment at the grain boundary for the region shown by the dashed rectangle in (b).
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 47A, JANUARY 2016—527
accounted for. Most of the studies reported in the
literature on Mg-RE alloys have not been conducted
using high-purity feedstock. Therefore, the critical RE
level to produce segregation and thus the RE texture
weakening effect will be dependent on the impurity
content, which is often not reported. It is therefore not
possible to take the critical level from one study and
assume that it will be the same in another Mg-RE alloy
if the impurity content is different. Although proven
here for the Mg-Nd system, this is also highly likely to
be the case for other RE alloys, where low-solubility
compounds of the RE and impurity elements are likely
to form.
Finally, these results add further support to the idea
that segregation of RE to grain boundaries is a
necessary condition to provide the RE texture weaken-
ing effect. In the Mg-Y alloy, where strong segregation
occurred, texture weakening was seen. In the Mg-Nd
alloy where no segregation was measured, there was no
texture weakening.
C. Solute Drag Model
The measured level of segregation on the grain
boundaries can be used to provide a more accurate
prediction of the solute drag effect with the CLS model.
It has been shown that in the Mg-Y alloy, both Y and
unexpectedly Ni segregation are observed on the
boundary.
Figure 5shows the calculated values of the grain
boundary segregation energy (DGseg) for Ni and Y from
the present results as well as for Gd using the relative
compositions reported in the literature for matrix and
grain boundary regions.
[9]
Also shown are the lattice
diffusion coefficients at 673 K (400 °C) calculated in the
case of Gd and Y from the data of Das et al.
[17]
and
Fig. 4—Energy-dispersive X-ray spectrum imaging of Mg-0.024 at. pct Nd alloy. (a–d) HAADF images (right) and accompanying elemental
maps (left) for Mg, Nd, and O or Fe. There is no evidence for Nd segregation on the boundary, but large Nd particles are observed in the sam-
ple.
528—VOLUME 47A, JANUARY 2016 METALLURGICAL AND MATERIALS TRANSACTIONS A
estimated in the case of Ni, where no accurate measure-
ments of diffusion coefficient in Mg are reported. The
diffusion coefficient for Ni in Mg was estimated from the
diffusion coefficient (D) of Ni in Al, for which measure-
ments are available.
[19]
The justification for making this
empirical approximation is that the impurity diffusion
coefficients for other solutes (such as Zn) are found to be
similar in both Mg and Al, and the close coincidence of
the melting point of Mg and Al.
[19,25]
For example, at
673 K (400 °C, the annealing temperature in this
study), DZn is 1.2 910
14
m
2
s
1
in Al and
1.9 910
14
m
2
s
1
in Mg, which is within a factor of
2. Given the approximations necessary in estimating
both DGSeg and D, the quantitative accuracy of the
predictions is likely to be low. However, qualitatively
they are still valuable in allowing the relative effect of
different solutes on the drag effect to be estimated.
The values of DGseg shown in Figure 5can be
compared with those predicted previously using the
classical misfit-based model.
[12]
This shows that the
values of DGseg calculated on the basis of the measured
boundary compositions are approximately 4 times
greater than those calculated on the basis of misfit
alone, i.e., the tendency to segregate is also strongly
driven by other factors, including the synergistic inter-
action of Ni and Y, as discussed. The very high level of
Ni segregation measured produces the high DGseg value
reported in Figure 5. However, Ni is also expected to
have a significantly higher diffusion coefficient in Mg
compared to Y or Gd, and these factors are in
opposition in determining solute drag in the low-bound-
ary velocity regime.
Using these values of DGseg, the CLS model has been
used to predict the variation in drag pressure for the
three solutes at 673 K (400 °C) as a function of
boundary velocity, and this is shown in Figure 6. This
plot shows the transition between the low- and high-
velocity regimes, with the peak drag pressure corre-
sponding to the transition point. As discussed elsewhere,
for recrystallization in Mg, boundary velocities of the
order of 10
2
lms
1
would be expected. Figure 6
shows that this lies in the low-velocity regime, well
below the transition point. For this boundary velocity,
the CLS model predicts that Gd will exert a drag
pressure twice that of Y and 5 times that of Ni.
Figure 7shows the predicted solute drag pressure for
Y as a function of boundary velocity over a range of
temperatures typical of that for the thermomechanical
processing of magnesium alloys. This plot illustrates the
very strong dependence of the solute drag effect on
temperature. Note that the true dependence of solute
drag on temperature is likely to be even greater than
predicted by this model since to perform this calculation
it was assumed that the depth of the free energy well
associated with grain boundaries is constant, whereas in
practice it will decrease at higher temperatures due to
the increased contribution from entropy, which opposes
YGd Ni
0
10
20
30
40
Δ Gseg / kJmol−1
0
1
2
3
4
x 10−15
D / m2s−1
Δ Gseg
D
Fig. 5—Grain boundary segregation free energy change DGseg calcu-
lated from measured grain boundary concentrations and lattice diffu-
sion coefficients for Y, Nd, and Ni.
10
−4 10−2 100102104106
10−6
10−4
10−2
100
102
104
Boundary velocity / μms−1
Drag pressure / MPa
Y
Gd
Ni
Fig. 6—Calculated solute drag pressure as a function of boundary
velocity for Y, Gd, and Ni at 673 K (400 °C).
10−4 10−3 10−2 10−1 100
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Boundary velocity / μms−1
Solute drag pressure / MPa
250oC
300
350
400
450
500
550
Fig. 7—Calculated solute drag pressure as a function of boundary
velocity for Y at temperatures ranging from 523 K to 823 K (250 °C
to 550 °C).
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 47A, JANUARY 2016—529
segregation. For example, for a boundary velocity of
10
2
lms
1
, there is a three-order-of-magnitude differ-
ence between the drag pressures predicted at 523 K and
823 K (250 °C and 550 °C). A drop in solute drag
pressure below a critical value required to suppress
dynamic recrystallization and create an RE texture effect
is a plausible reason why the RE texture is not seen in
Mg-RE alloys when the deformation (e.g., extrusion)
temperature exceeds a critical value.
[6]
V. CONCLUSIONS
This study has confirmed the important role of grain
boundary segregation in producing a texture change
during recrystallization when RE additions are present.
In the Mg-Y alloy, strong segregation to grain bound-
aries was detected and texture strength reduced mark-
edly on recrystallization. In the Mg-Nd alloy, no
segregation, or significant texture weakening effect,
was observed after recrystallization. This is probably
because the Nd is present in insoluble particles, both
alone and with varying contents of O and/or Fe
impurities, even at Nd concentrations previously
thought to be well below the solubility limit of Nd in
magnesium. Also observed, but unexpected, was strong
segregation of impurity Ni to the grain boundaries.
A simple classical model has been applied to predict
the solute drag effect associated with the rare-earth (RE)
segregation to grain boundaries. It is demonstrated that
the driving force for segregation is greater than that
predicted in previous studies based on atomic size misfit
alone. There is likely to be a synergistic interaction
between segregated Y and impurity Ni, both of which
concentrate strongly on the grain boundaries. For
conditions typical of those expected during thermome-
chanical processing of magnesium, it is predicted that
Gd will have a drag effect approximately twice that of Y.
The predicted strong decrease in solute drag pressure
with increasing temperature may explain why RE
textures are not observed in Mg-RE alloys deformed
above a critical temperature.
This study provides further evidence to support the
argument that segregation to grain boundaries plays a
key role in enabling the texture change seen on
recrystallization of dilute Mg-RE alloys.
ACKNOWLEDGMENTS
The authors are grateful to Magnesium Elektron for
provision of materials used in this study. The Engi-
neering and Physical Sciences Research Council
(EPSRC) through the Centre for Doctoral Training in
Advanced Metallic Systems and LATEST2 platform
Grant (EP/H020047/1) are thanked for supporting this
research.
OPEN ACCESS
This article is distributed under the terms of the
Creative Commons Attribution 4.0 International
License (http://creativecommons.org/licenses/by/4.0/),
which permits unrestricted use, distribution, and re-
production in any medium, provided you give appro-
priate credit to the original author(s) and the source,
provide a link to the Creative Commons license, and
indicate if changes were made.
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