Oxidation of differently prepared Al-Mg alloy powders in oxygen

Article abstract of DOI:10.1016/j.jallcom.2016.05.302

Powders of both commercial atomized spherical Al-Mg alloy and mechanically alloyed Al-Mg were oxidized in oxygen using thermo-gravimetry (TG). For both powders, the Al/Mg mass ratio was equal to 1. Fully and partially reacted powders were recovered and characterized using scanning electron microscopy and x-ray diffraction. Voids grow within oxidized alloy particles for both atomized and mechanically alloyed powders. Results were interpreted accounting for the measured particle size distribution for the spherical powder and distributing the TG-measured weight gain among the individual particle size bins. The reaction interfaces were always located at the internal surface of the oxide shell as determined by matching the oxidation dynamics for particles with the same sizes but belonging to powders with different particle size distributions. Thus, the reaction is always rate limited by inward diffusion of oxygen ions through the growing oxide shell. Two oxidation stages were identified for both materials. Both Al and Mg oxidize during both observed oxidation stages. The second oxidation stage is caused by formation of the spinel phase, most likely occurring at a threshold temperature. In the present measurements, the step in the oxidation rate, or switch between the oxidation stages, occurs when the oxide shell grows above a certain thickness of approximately 1.5 μm. The apparent activation energy during the first oxidation stage energy changes during the first oxidation stage suggesting that more than one reaction occur in parallel, e.g., causing formation of MgO and amorphous alumina. For the second oxidation step, controlled by diffusion of oxygen through spinel layer, the activation energy remains nearly constant around 185 kJ/mol.

Full text of DOI:10.1016/j.jallcom.2016.05.302

Journal of Alloys and Compounds 685 (2016) 402e410
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: http://www.elsevier.com/locate/jalcom
Oxidation of differently prepared Al-Mg alloy powders in oxygen
Hongqi Nie, Mirko Schoenitz, Edward L. Dreizin*
New Jersey Institute of Technology, Newark, NJ 07103, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Powders of both commercial atomized spherical Al-Mg alloy and mechanically alloyed Al-Mg were
oxidized in oxygen using thermo-gravimetry (TG). For both powders, the Al/Mg mass ratio was equal to 1.
Fully and partially reacted powders were recovered and characterized using scanning electron micro-
scopy and x-ray diffraction. Voids grow within oxidized alloy particles for both atomized and mechan-
ically alloyed powders. Results were interpreted accounting for the measured particle size distribution
for the spherical powder and distributing the TG-measured weight gain among the individual particle
size bins. The reaction interfaces were always located at the internal surface of the oxide shell as
determined by matching the oxidation dynamics for particles with the same sizes but belonging to
powders with different particle size distributions. Thus, the reaction is always rate limited by inward
diffusion of oxygen ions through the growing oxide shell. Two oxidation stages were identified for both
materials. Both Al and Mg oxidize during both observed oxidation stages. The second oxidation stage is
caused by formation of the spinel phase, most likely occurring at a threshold temperature. In the present
measurements, the step in the oxidation rate, or switch between the oxidation stages, occurs when the
Received 13 April 2016
Received in revised form
27 May 2016
Accepted 28 May 2016
Available online 30 May 2016
Keywords:
Intermetallic
Oxidation
Kinetics
Thermal analysis
oxide shell grows above a certain thickness of approximately 1.5 mm. The apparent activation energy
during the first oxidation stage energy changes during the first oxidation stage suggesting that more than
one reaction occur in parallel, e.g., causing formation of MgO and amorphous alumina. For the second
oxidation step, controlled by diffusion of oxygen through spinel layer, the activation energy remains
nearly constant around 185 kJ/mol.
© 2016 Elsevier B.V. All rights reserved.
1. Introduction
oxidation stage. A general rule used to estimate the tendency of
metals to continuously oxidize, the Pilling-Bedworth ratio [15] of
Various Al-Mg alloys find multiple applications in structural
materials [1,2], for hydrogen storage [3], and as components of
energetic formulations [4e6]. Most of the published work on
oxidation of such alloys deal with compositions with small con-
centrations of Mg, varied from less than 1e5% [7e9]. For such
materials, it was observed that the oxide includes different layers,
with MgO typically observed on top of MgAl2O4 and/or Al2O3. At the
same time, alloys with much higher concentrations of Mg are of
interest for propellants, explosives, and pyrotechnics [10e13].
Oxidation of such high-Mg content materials is not well under-
stood. In Ref. [14], oxidation of an Al3Mg2 alloy was considered. The
reaction was observed to proceed in three stages with three distinct
rates: an MgO layer was reported to form initially; then MgAl2O4
oxide was produced, which finally cracked, leading to the third
the molar volumes of oxide and metal is close to unity for high-Mg
aluminum alloys, and is therefore not expected to be particularly
predictive for oxidation behavior. Further, kinetic details enabling
the quantitative description of these reactions are not available.
Such descriptions are important for reactive materials for predic-
tion of both aging and ignition behaviors of the relevant compo-
sitions. Recently, thermo-analytical studies were used to clarify
reaction mechanisms and describe them quantitatively for both Al
[16,17] and Mg [18] powders. Here, a similar experimental approach
and data processing techniques are applied to characterize high
temperature oxidation in Al-Mg alloys with equal mass fractions of
aluminum and magnesium. The objectives are to identify the
interface for heterogeneous oxidation reactions and describe re-
action mechanisms and rates quantitatively. The experiments per-
formed with two types of Al-Mg alloys prepared by different
techniques, and thus having distinct initial structures and
morphologies.
* Corresponding author.
E-mail address: dreizin@njit.edu (E.L. Dreizin).
http://dx.doi.org/10.1016/j.jallcom.2016.05.302
0925-8388/© 2016 Elsevier B.V. All rights reserved.

H. Nie et al. / Journal of Alloys and Compounds 685 (2016) 402e410
403
2. Experimental
7
As received
Sieved
2.1. Materials
6
5
4
3
2
1
Two Al-Mg alloy powders with Al/Mg mass ratio of 50:50 were
used in thermo-gravimetric (TG) experiments. An atomized
spherical alloy, ꢀ270 Mesh was provided by Valimet Inc. A me-
chanically alloyed powder was prepared at NJIT as described in
detail elsewhere [19e21]. Briefly: starting materials for the me-
chanically alloyed powder were elemental powders of Al (Atlantic
Equipment Engineers, 99.8% pure, ꢀ325 Mesh) and Mg (Alfa-Aesar,
99.8% pure, ꢀ325 Mesh). Mechanical alloying was performed using
a Retsch PM-400 MA planetary mill operated at 350 rpm. Powder
mass load was 30 g per vial; 9.5 mm-diameter hardened steel balls
served as milling media. The ball to powder mass ratio was 10; the
milling time was 2 h. Each vial was filled with 50 mg of hexane used
as a process control agent.
Scanning electron microscope (SEM) images for both Al-Mg
alloy powders are shown in Fig. 1. The particles have roughly
spherical shapes for atomized Al-Mg alloys. Mechanically alloyed
powder particles have characteristic angular shapes; they also are
noticeably coarser than the atomized powders.
For detailed TG measurements described below, the spherical
atomized alloy powder was split into two fractions with different
but partially overlapping particle size distributions. The powder
0
10-1
100
101
102
Particle size, μm
Fig. 2. Particle size distributions for coarse (as received) and fine (sieved) fractions of
the spherical atomized Al-Mg alloy powder used in experiments.
argon oxidizing mixture; the respective flow rates of argon were 90
and 20 mL/min. The oxygen flow rate was 10 mL/min so that oxygen
comprised 30% of gas supplied to the sample. The powders were
held on a 17-mm diameter flat corundum sample holder and
heated up to 800 ꢁC. Heating rates varied from 2 to 20 ꢁC/min in
different experiments.
Fully and partially oxidized powders were recovered and
examined using a scanning electron microscope (LEO 1530 Field
Emission SEM); their compositions were characterized using x-ray
diffraction (XRD) using a PANalytical Empyrean diffractometer. The
diffractometer was operated at 45 kV and 40 mA using unfiltered
was passed through a 550 Mesh (25 mm opening) sieve. The particle
size distributions for both obtained size fractions were measured
using a Beckman-Coulter LS230 Enhanced Particle Analyzer as
shown in Fig. 2. These measured particle size distributions were
directly used to process the TG measurements for the atomized
alloy powder. The TG measurements for the mechanically alloyed
powder were interpreted qualitatively and did not rely on the
particle size distribution measurements.
Cu K
a
radiation (
l
¼ 1.5438 Å).
2.2. Oxidation experiments
3. Results and discussion
Both Al-Mg powders were oxidized in an oxygen/argon mixture
using a Netzsch STA409PC/PG thermal analyzer with a thermog-
ravimetric sample carrier. The customized furnace used in experi-
ments provided the oxidizer flow from the top of the furnace down
to the sample. This flow pattern helped to oxidize and condense
evaporating magnesium directly in the sample holder. Magnesium
evaporation and deposition of the oxide elsewhere in the furnace
presented a serious experimental problem in preliminary experi-
ments, when a regular furnace was used, in which the oxidizing gas
was rising from the bottom up.
3.1. Phases and morphologies formed upon oxidation
Initial oxidation TG measurements were performed for both
atomized and mechanically alloyed powders at a fixed heating rate
of 5 ꢁC/min. The resulting TG traces are shown in Fig. 3. A charac-
teristic, two-stage oxidation pattern is observed for both materials.
For the atomized powder, an appreciable oxidation begins above
350 ꢁC. For mechanically alloyed powder, the mass increase be-
comes detectable above 400 ꢁC. For both materials, reaction ac-
celerates substantially around 500 ꢁC. The second oxidation stage
begins above ca. 530 ꢁC, when the rate of oxidation becomes slower.
It remains nearly constant for the mechanically alloyed powder at
In these experiments, argon was introduced as both a protective
gas surrounding the thermobalance and as a carrier gas for oxygen/
Fig. 1. Backscattered SEM images for Al-Mg powders: atomized spherical alloy (a) and mechanically alloyed powder (b).

404
H. Nie et al. / Journal of Alloys and Compounds 685 (2016) 402e410
is also observed, qualitatively similar to those seen in Fig. 4 (b) and
(c).
0.8
0.6
0.4
0.2
0.0
Atomized
Mechanically alloyed
Results of the XRD analyses for partially oxidized samples of the
atomized alloy are shown in Fig. 6. At 450 ꢁC, the sample mostly
comprises an Al12Mg17 intermetallic phase. Only small amounts of
MgO are detectable. At 520 ꢁC, strong peaks of both MgO and
elemental Al appear. At 650 ꢁC, peaks of MgO remain nearly un-
changed. Peaks of elemental Al become much weaker and strong
peaks of the spinel group, MgAl2O4 appear.
XRD patterns for partially oxidized samples of the mechanically
alloyed powder are shown in Fig. 7. Note that the as-prepared
material was characterized by XRD earlier [19]. Unlike atomized
powder, comprising the intermetallic Al12Mg17, the pattern for the
mechanically alloyed powder was dominated by the broadened
peaks of elemental Al and Mg, with relatively minor peaks of the
intermetallic. For the sample recovered at 520 ꢁC, peaks of
elemental Al and MgO become strong, similar to that observed in
Fig. 6 for the atomized powder. Also similar to the atomized pow-
der, peaks of spinel, MgAl2O4 become well-visible for the sample
recovered from 800 ꢁC.
XRD results for both powders consistently indicate formation of
MgO during the first stage of oxidation. The second stage is
accompanied by formation of the ternary MgAl2O4 spinel. It is,
therefore, tempting to interpret the present observations as sug-
gesting a selective oxidation of magnesium during the first oxida-
tion stage, and oxidation of both aluminum and magnesium during
the stage two. However, it is also possible that oxidation of
aluminum occurs during stage one as well, producing amorphous
alumina, undetectable by XRD. Both possibilities will be examined
below.
100 200
300
400
500 600
700
800
900
Temperature, °C
Fig. 3. TG traces for the atomized spherical Al-Mg alloys (black) and mechanically
alloyed Al-Mg powder (blue) in oxygen at 5 ꢁC/min. (For interpretation of the refer-
ences to colour in this figure legend, the reader is referred to the web version of this
article.)
higher temperatures. An additional acceleration in the oxidation
rate is observed for the atomized powder at approximately 600 ꢁC.
Open circles in Fig. 3 show the temperatures, from which each
powder was quenched and recovered for SEM and XRD analyses.
These temperatures were 450, 520, and 650 ꢁC for the atomized
powder and 520 and 800 ꢁC for the mechanically alloyed powder;
they were selected to observe possible differences in the oxidation
products formed at different reaction stages.
SEM images of the partially oxidized powders are shown in
Figs. 4 and 5 for atomized and mechanically alloyed powders,
respectively. The atomized powder recovered at 450 ꢁC, retains its
spherical shape; however, the particle surface is not as smooth as
for the original material. Minor surface depressions are noticed,
which may indicate shrinkage of the thermally expanded particles.
For the powder recovered from higher temperatures, as shown in
Fig. 4 (b) and (c), many broken hollow particles are observed. While
breakage of the particles was most likely caused by the handling of
the powder samples transferred to the SEM sample holder, as
shown earlier [17], the hollow shells were clearly formed during
oxidation. No qualitative difference was observed between samples
shown in Fig. 4 (b) and (c).
If a general Al-Mg alloy is expressed as AlaMgb where a þ b ¼ 1,
then the composition of Al-50 wt-% Mg used in this study corre-
sponds to a ¼ 0.47 and b ¼ 0.53. The complete oxidation of this
material yields MgO and MgAl2O4. The global reaction is:
ꢀ
ꢁ
2
xMg ꢀ 3xAl b þ 3xAl
AlaMgb þ
O /
2
4
ꢂ
ꢃ
1 ꢀ b
1 ꢀ b
MgAl2O4
(1)
xMgb ꢀ xAl
þc Al
MgO þ xAl
2
2
Þa=cMg
ð1ꢀxAl
1ꢀxMg
b c
Þ =
ð
where the fractions of oxidized Mg and Al are expressed with the
parameters xMg ¼ ðnMgO þ n
Þ=b and xAl ¼ 2nMgAl O =ð1 ꢀ bÞ
MgAl2O4
4
using the stoichiometric coefficients of the products,2 nMgO and
nMgAl O , and c ¼ 1 ꢀ (1 ꢀ b)xAl ꢀ bxMg. Overall reaction progress as
4
deriv2ed from the TG experiments is defined as the relative mass
For the partially oxidized mechanically alloyed powders, the
changes in the surface morphology upon oxidation were more
noticeable as shown in Fig. 5 (compare to the as prepared powder,
Fig. 1 (b)). In addition to multiple fine crystallites formed on the
surface of particles shown in Fig. 5, formation of hollow structures
change Dm/m0. Considering that formation of amorphous alumina
is possible, it is not known a priori how either oxide fraction varies
with overall reaction progress. It is interesting that the most strictly
segregated case, the complete oxidation of Mg up to xMg ¼ 1 while
Fig. 4. SEM images of partially oxidized atomized powder particles recovered from 450 ꢁC (a), 520 ꢁC (b) and 650 ꢁC (c).

H. Nie et al. / Journal of Alloys and Compounds 685 (2016) 402e410
405
Fig. 5. SEM images of partially oxidized mechanically alloyed powder particles recovered 520 ꢁC (a) and 800 ꢁC (b).
3.2. TG data processing and location of the heterogeneous reaction
interface
When a powder with different particle sizes is oxidized in a TG
experiment, the mass can increase at different rates for particles
with different sizes, particularly when the oxidation reaction oc-
curs at the particle surface. In order to account for this, and to allow
for a more meaningful interpretation of TG measurements, a
methodology was developed in previous research [16e18,22] that
distributes the weight change from the TG measurements among
particles of different sizes using the measured particle size distri-
bution. This methodology was applied to the measurements for the
spherical atomized powder in this study.
The heterogeneous oxidation reaction on the particle surface
implies a particular geometry. Several different scenarios, charac-
terized by the interface where new oxides form, are illustrated in
Fig. 8. All scenarios lead to the formation of a void in the particle
interior, as observed in SEM images of the partially oxidized par-
ticles. In all cases, a metallic core with an interior void is sur-
rounded by an oxide shell, but in each individual case the available
reactive interface varies differently with reaction progress.
Fig. 6. XRD pattern for the reaction products of spherical Al-Mg alloys powder
quenched and recovered at 450 ꢁC, 520 ꢁC and 650 ꢁC.
Following the TG measurements of stepwise oxidation and the
XRD observation of MgO as initially the only detectable product, for
the purpose of splitting the TG measured weight change among
particles of different sizes, it was assumed that the oxidation is
strictly selective: the top panels in Fig. 8 describe oxidation of Mg
only, producing MgO, followed by the oxidation of the Al compo-
nent and reaction with MgO yielding MgAl2O4 in the bottom panels
in Fig. 8. This assumption affected the thickness of the oxide layer
predicted to grow on each particle, because of different densities of
the products formed at different reaction stages. The difference in
densities of MgO (3.58 g/cm3), Al2O3 (3.95 g/cm3), and Al2MgO4 (ca.
3.55 g/cm3 [23]) is relatively minor, having only a weak effect on the
predicted oxide thickness caused by the assumed selective oxida-
tion sequence. In the present calculations, oxide densities were
considered as functions of temperature. For MgO, the density was
calculated following experimental data presented in Ref. [24]. For
Al2O3, date from Ref. [25] were used. For spinel, the calculations
used a weighted average of respective temperature-dependent
alumina and magnesia densities. Different oxidation schemes
such as strict simultaneous oxidation of Al and Mg as well as
different assumptions regarding densities would have given oxide
thicknesses that are up to 1% different from the current values up to
Fig. 7. XRD pattern for the reaction products of mechanically alloyed Al-Mg powder
quenched and recovered at 520 ꢁC and 800 ꢁC.
the Al component remains unoxidized with xAl ¼ 0, corresponds to
the formation of 0.53 mol of MgO, and a mass change of 33.17%.
Cursory examination of the TG measurements shown in Fig. 3
suggests that the first oxidation step near 500 ꢁC can be entirely
and satisfactorily explained by this selective oxidation scheme.
However, in the following analysis tracking oxidation of particles of
different sizes, this explanation will be shown to be incorrect.
an estimated thickness of 0.7 mm, and do not reach 1.5% difference
until full oxidation. More detailed considerations regarding oxide
densities were therefore not pursued for the purpose of distrib-
uting the observed oxide mass over the particle size distribution.
Three possible reaction sequences were considered, referred to
as Cases I, II, and III in Fig. 8. The reaction interface is shown by a

406
H. Nie et al. / Journal of Alloys and Compounds 685 (2016) 402e410
Case I
Case II
Case III
Reaction step
Oxide shell
Metal Core
1: product
MgO
Void
Reaction
interface
Oxide shell
Metal Core
2: product
MgAl2O4
Void
Fig. 8. Schematic diagram illustrating different reaction mechanisms: Case I. Reaction always occurs at the interface between metallic core and oxide shell. Case II. During the first
stage, oxidation occurs at the interface of metallic core and oxide shell. During the second stage, reaction occurs at the outer surface of the oxide shell. Case III. Reaction always
occurs at the outer surface of the oxide shell.
bold dashed line. For Case I, oxidation for both stages one and two
occur at the internal interface between the metallic core and
growing oxide shell. For Case II, oxidation during stage one occurs
at the internal metal-oxide interface, while the remaining oxidation
takes place at the external particle surface. Finally, for Case III, both
stage one and two reactions occur at the outer particle surface. In
other words, for Case I, it is assumed that the oxidation rate always
is limited by the inward diffusion of the oxidizer (oxygen ions). For
Case II, oxidation during the first stage is limited by the inward
diffusion of oxidizer, and during the second stage, it is limited by
outward diffusion of metal ions. Finally, in Case III all reactions are
assumed to be rate limited by outward diffusion of metal ions.
The mass gain measured in a TG experiment as a function of
time or temperature for the powder sample was split among
powder particle size bins:
each size bin while allocating new material at the interface e inner
or outer e indicated for each case in Fig. 8. The respective other,
non-growing radius was allowed to change only to account for
thermal expansion.
TG measurements were performed for two size fractions of the
same powder (cf. Fig. 2). For each reaction mechanism shown in
Fig. 8, the TG data were distributed among all particles as described
above. The fundamental assumption in the processing described
here is that the oxidation of particles of a given size is not affected
by the oxidation of particles with different sizes, i.e. it is not rele-
vant for the oxidation reaction of particles with this size whether
they belong to a powder with a coarse, fine, wide, or narrow size
distribution. To judge which case shown in Fig 8 represents the
experiment most accurately, and therefore which interface location
is consistent with the measurement, the oxide mass of the over-
lapping size bins calculated for one size distribution was compared
to the one calculated for the other distribution.
X
dM
dt
dmn
dt
¼
(2)
The measured TG traces used in this analysis for both coarse (as
received) and fine (sieved) powder size fractions are shown in
Fig. 9. The inset in Fig. 9 expands the temperature range, for which
the most significant differences were observed between mass gains
n
where M is the total powder mass, mn is the mass of particles in an
individual particle size bin, and t is time. Index n numbers particle
size bins. Solving the diffusion equation for a spherical particle with
a growing oxide shell (appropriate for any of the reaction scenarios
shown in Fig. 8), and assuming that the mass fraction of the
diffusing species changes from 1 to 0 across the oxide layer, one
obtains:
1.7
1.6
1.5
1.4
1.3
1.2
1.1
ꢂ
ꢃꢀ1
1
1
r1r2
r2 ꢀ r1
_
m ¼ 4pr
D
ꢀ
¼ 4prD
(3)
r1 r2
where r1 and r2 are inner and outer radii of the growing oxide layer,
_
across which diffusion occurs; m is the mass flow of the diffusing
species; D is the diffusion coefficient (generally defined by Arrhe-
nius kinetics), and
r is the oxide density. Thus, the measured mass
As received
Sieved
ꢂ
ꢃ
uptake for each assumed reaction model was distributed propor-
1.0
0.9
r1r2
tionally to the function Nn$
where Nn is the number frac-
tion of particles in each size rb2ꢀinr1 nnas determined experimentally,
and the radius-dependent factor is equivalent to the surface area at
the geometric mean radius divided by the oxide layer thickness.
The algorithm was applied iteratively, starting with a uniform
initial oxide thickness of 2.5 nm, and integrating the mass change of
0
100
200
300
400
500
600
700
o
Temperature,
C
Fig. 9. TG traces for two size fractions of the atomized spherical Al-Mg alloys powder
oxidizing in oxygen. The heating rate was 5 K/min.

H. Nie et al. / Journal of Alloys and Compounds 685 (2016) 402e410
407
for different powder size fractions.
0.8
Quantitatively, following previous work [16e18], functions of
mass as a function of time for all overlapping particle sizes were
compared to each other using the parameter, Ern, calculated for
each particle size bin, n:
Heating
rate,
K/s
0.6
0.4
0.2
0.0
2
5
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u
10
20
K
ꢄ
ꢅ
uX
2
1
t
Coarse
n;k
Fine
n;k
pffiffiffi
Ern ¼
m
ꢀ m
(4)
mn;0
K
k¼1
where summation is done for all K time steps for the measurements
Coarse
n;k
Fine
n;k
shown in Fig. 9, and m
and m
are the mass changes for
coarse and fine powder fractions respectively, corresponding to the
kth time step. Parameter Ern quantifies discrepancy between
oxidation scenarios for the particles belonging to the same size bin
n, present in both powder samples. This parameter should be
minimized for the reaction model that best describes the actual
oxidation processes. Values of Ern implied by each model are
plotted in Fig.10 for all overlapping particle sizes of the two powder
fractions. The parameter Ern is minimized for Case I, which assumes
that both reaction steps occur at the internal interface between
metallic core and oxide shell. Thus, Case I describes the reaction
best for the Al-Mg alloys and oxidation of both Mg and Al is gov-
erned by the inward diffusion of oxidizer. This is similar to the
oxidation mechanism identified for pure Mg [18], but different from
the oxidation mechanism for pure Al [17]. We can speculate that
diffusion on the oxygen sublattice is easier in the presence of Mg,
perhaps due to point defects. However, it is not clear which diffu-
sion process actually changes substantially e diffusion on the metal
or the oxygen sublattice. Future work aimed to clarify this is war-
ranted, and could provide insights in the kinetic phenomena
described in the later sections of the manuscript.
300
400
500
600
700
800
o
Temperature,
C
Fig. 11. TG traces for atomized spherical alloys powder oxidized at different heating
rates.
For the isoconversion analysis the value of activation energy, Ea
is determined at each given value of the reaction progress,
without specifying f( ) by minimizing the function
a,
a
F:
n
n
X X
J½Ea; TiðtaÞꢂ
Â
Ã
F
ðEaÞ ¼
(6)
i¼1 jsi J Ea; TjðtaÞ
where the subscript
a refers to selected values of the reaction
progress that were observed at time ta and the corresponding
temperature T, and which are associated with the activation energy
Ea. The sums are taken over all included experiments. The functions
J are integrals of the exponent of activation energy over experi-
3.3. Reaction sequence and kinetics
mental temperature over a chosen interval Da
:
ta
TG measurements were repeated at different heating rates for
the spherical atomized alloy powder, as shown in Fig. 11. The traces
shift consistently to higher temperatures at greater heating rates.
These measurements were used to identify the apparent activation
energy of oxidation as a function of the reaction progress [26e28].
A model free isoconversion method [29,30] was employed. In
the general case, the reaction rate is considered a function of a ki-
netic triplet, including activation energy, E, pre-exponent, C, and a
ꢆ
ꢇ
Z
ꢀEa
J½Ea; TiðtaÞꢂ ¼
exp
dt
(7)
RTiðtaÞ
taꢀ
Da
First, the measurements presented in Fig. 11, and representing
oxidation of the entire powder sample were used. The reaction
progress was defined here as the relative mass change of the entire
powder,
a
¼ (m ꢀ m0)/m0. The resulting activation energy is shown
function of reaction progress, f(a):
in Fig. 12. For the first rapid mass increase step, observed in Fig. 11
ꢂ
ꢃ
d
dt
a
E
gasT
¼ C$exp
ꢀ
$f ð
aÞ
(5)
250
200
150
100
50
R
0.20%
0.15%
0.10%
0.05%
0.00%
Case I
Case II
Case III
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1
10
100
whole powder mass change, (m-m )/m
Overlapping particle size bins, μm
0
0
Fig. 10. Cumulative discrepancy measure calculated using Eq. (4) for data on oxidation
of spherical Al-Mg alloys in oxygen.
Fig. 12. Apparent activation energy of oxidation for an Al-Mg alloy powder in oxygen
as a function of reaction progress defined through the sample mass change.

408
H. Nie et al. / Journal of Alloys and Compounds 685 (2016) 402e410
around 470e550 ꢁC for different heating rates, the relative mass
increases by approximately 0.3, and the apparent activation energy
decreases from above 200 to below 50 kJ/mol. As the reaction
proceeds to the next oxidation stage, the activation energy in Fig.12
increases stepwise and remains approximately stable around
190 kJ/mol.
To understand why the apparent activation energy decreases
during the initial reaction stage, consider the effect of different
oxidation rates for particles of different sizes, which is unaccounted
for by analysis of the whole powder.
applied. First, following the approach used to obtain the result
shown in Fig. 12, the sample mass change was treated as reaction
progress indicator. The activation energies obtained for different
particle sizes are shown in Fig. 14. Qualitatively, a stepwise change
in the activation energy is still observed, suggesting a step-wise
change in the oxidation mechanism. The step occurs at different
values of mass change for different particle sizes, suggesting that
mass may not be a useful progress indicator for this reaction, and
that therefore the transition does not occur at a specific degree of
Mg oxidation, despite data from Fig. 3, which appeared consistent
with strict selective Mg oxidation corresponding to a 33.2% mass
change. The activation energy changes much after all Mg has been
oxidized for smaller particles, and before the start of Al oxidation
for larger particles. Calculations show that this situation does not
qualitatively change if selective Mg oxidation is not strict.
The thickness of the grown oxide layer may serve as a more
natural indicator of the reaction progress than the mass change.
The activation energies for several individual particle size bins were
thus obtained as a function of the oxide thickness as shown in
Fig. 15. Interestingly, all apparent activation energy trends merge
together, suggesting a fairly narrow range of oxide thicknesses, for
which the reaction mechanism changes. Specifically, the transition
Under the premise of early selective Mg oxidation, implying
xMg
ꢃ
xAl, finer particles with a relatively large surface area oxidize
Mg more quickly than coarser particles. Generally, different particle
sizes have oxidized different amounts of their Mg content, i.e. have
different values of xMg. With strict segregation as assumed for the
purpose of the TG data processing described in the previous sec-
tion, where xMg reaches 1 before xAl > 0, there is a range of tem-
peratures where Al oxidation in smaller particles occurs
simultaneously with selective oxidation of Mg in larger particles.
Even if the Mg oxidation is not strictly selective, using the whole
powder to characterize reaction progress implies a mix of simul-
taneous reactions on the surface of particles with different relative
degrees of oxidation, and therefore different compositions of the
metal core regardless of geometry, oxide shell thickness, etc., and
cannot give a consistent value for the activation energy.
occurs between 1.24 and 1.56 mm for strictly selective Mg oxidation.
However, since the oxide thickness is a weak function of the details
of selective Mg oxidation as pointed out in section 3.2, the transi-
tion occurs near the same thickness range regardless of how strictly
selective oxidation of Mg occurs. In any case, Fig. 15 suggests rather
clearly that the oxide thickness is indeed a useful indicator of the
reaction progress for oxidation of Al$Mg alloys.
The activation energy still changes substantially during the first
oxidation stage. These changes can no longer be attributed to the
interference effects between different particle sizes, however.
Instead, they may indicate that oxidation proceeds through
different parallel reactions. For example, formation of MgO and
amorphous alumina occurring simultaneously and at different rates
could explain the observed changes in the apparent activation
energy.
This reasoning is illustrated in Fig. 13. The solid curve shows the
relative sample mass (right axis) recorded at 5 K/min. The open
circles indicate the onset of Al oxidation (xAl ¼ 0) and the end of Mg
oxidation (xMg ¼ 1) for each particle size bin (left axis). For the
smallest particles in the size distribution, 1
m
m, all Mg is consumed
close to 470 ꢁC. Thus, aluminum oxidation begins for 1-
mm particles
just above 470 ꢁC. When the first rapid mass gain stage is finished,
just above 500 ꢁC, magnesium is completely oxidized in all particles
smaller than approximately 15 mm. Clearly, the apparent activation
energy obtained for the entire powder shown in Fig. 12 represents
different processes for different particle size bins.
The processing of TG traces described above and involving re-
distribution of the measured mass gain among individual particle
size bins enables one to avoid interference between different
oxidation reactions occurring simultaneously for particles of
different sizes.
TG traces representing the oxidation of individual particle size
bins were thus obtained using the reaction mechanism shown as
case I in Fig. 8. For each size bin, the isoconversion processing was
It remains unclear why the switch between the oxidation stages
occurs at a specific oxide thickness. Relying on the data from XRD
analyses (Fig. 6), the switch between the oxidation stages may be
explained by the formation of the spinel phase, which happened to
occur in the present experiments around 500 ꢁC (Figs. 3, 9 and 11),
or when the oxide thickness was in the range of 1.24 and 1.56
previous work on pure aluminum oxidation [31], a similar stepwise
oxidation process was attributed to the formation of alumina,
mm. In
g
which has a disordered spinel structure. A different oxide structure
100
10
1
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
300
For strict selective oxidation of Mg
5 μm
8 μm
13 μm
40 μm
Mg oxidation
Al oxidation
250
200
150
100
50
TG
ξ
Mg=1, ξAl
=0
All Mg
consumed
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
400
450
500
550
600
650
700
750
800
Reaction progress, (m-m )/m
Temperature, °C
0
0
Fig. 13. Size bins with all Mg selectively oxidized (open circles) vs. respective tem-
perature and the corresponding TG trace for a spherical Al-Mg alloy in oxygen (solid
curve).
Fig. 14. Apparent activation energy of oxidation for individual size bins of an Al-Mg
alloy powder in oxygen as a function of reaction progress defined through the sam-
ple mass change.

H. Nie et al. / Journal of Alloys and Compounds 685 (2016) 402e410
409
Voids are formed in the oxidized particles due to the re-distribution
of material within the metal core. Two oxidation stages were
observed for both powders. Although the total mass change for the
first stage and respective product phase analysis by XRD may be
interpreted as showing selective Mg oxidation, analysis of the TG
measurements using the particle size distribution for the spherical
powder shows conclusively that this is not the case. Both Al and Mg
oxidize during both observed oxidation stages. The second oxida-
tion stage is caused by formation of the spinel phase, most likely
occurring at a threshold temperature.
300
250
200
150
100
50
5 μm
8 μm
13 μm
40 μm
In the present measurements, the step in the oxidation rate, or
switch between the oxidation stages, occurs when the oxide shell
grows above a certain thickness of approximately 1.5 mm. However,
this switch may be expected to occur at a different oxide thickness
for alloys with different particle sizes, different compositions, or at
significantly different heating rates. The apparent activation energy
changes during the first oxidation stage suggesting that more than
one reaction occur in parallel, e.g., causing formation of MgO and
amorphous alumina. For the second oxidation step, the activation
energy remains nearly constant around 185 kJ/mol while the oxide
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Oxide thickness, μm
Fig. 15. Apparent activation energy of oxidation for individual size bins of an Al-Mg
alloy powder in oxygen as
grown oxide thickness.
a function of reaction progress defined through the
causes different diffusivity, and thus provides a reasonable expla-
nation for a changed reaction rate. In the case of Al-Mg alloys, Al-
Mg spinel forms instead of
shell grows up to approximately 3
mm. This activation energy
g alumina. Since there is no unambig-
characterized diffusion of oxygen through a spinel layer. At greater
oxide thicknesses, a slow decrease in the apparent activation en-
ergy is observed, due to changes in morphology of the oxidizing
powder.
uous indication that Al does not participate in the oxidation from
the beginning, amorphous alumina is likely present on the particle
surface. The formation of spinel from MgO and Al2O3 below a
certain temperature is then possibly limited due to kinetic reasons.
Indeed, the formation of Al-Mg spinel from sol-gel precursors has
been observed only above approximately 600 ꢁC [32]. Elsewhere
[33], it was observed that spinel forms after annealing to about
500 ꢁC independent of the synthesis method. Formation of spinel
nearly simultaneously for all powder particles at a threshold tem-
perature may also explain why the activation energy obtained for
the second stage of oxidation is nearly constant, at least while the
Acknowledgement
This work was supported by Defense Threat Reduction Agency
(HDTRA1-11-1-0060).
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