Kinetic study of neodymium oxide chlorination with gaseous chlorine

Article abstract of DOI:10.1016/j.tca.2012.04.014

The kinetics of the chlorination of neodymium oxide has been investigated by thermogravimetry between 312°C and 475°C, and for partial pressures of chlorine ranging from 10 kPa to 50 kPa. The starting temperature for the reaction of neodymium oxide with chlorine was determined to be about 250°C, leading to neodymium oxychloride as product. The results showed that, for temperatures below 425°C, the system is under chemical control and the formation of the oxychloride progresses through a nucleation and growth mechanism. The influence of chlorine mass transport through the bulk gas phase and through the boundary layer on the overall reaction rate was analyzed. In the absence of these two mass-transfer steps, a reaction order of 0.39 with respect to chlorine partial pressure, and an activation energy of 161 ± 4 kJ mol^-1 were determined. A complete rate equation has been successfully developed.

Full text of DOI:10.1016/j.tca.2012.04.014

Thermochimica Acta 540 (2012) 98–106
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Kinetic study of neodymium oxide chlorination with gaseous chlorine
Marta V. Boscoa,∗, Gastón G. Fougaa,b, Ana E. Bohéa,b,c
a Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina
b Complejo Tecnológico Pilcaniyeu, Comisión Nacional de Energía Atómica, Avenida Bustillo 9500, CP 8400 San Carlos de Bariloche, Argentina
c Centro Regional Universitario Bariloche, Universidad Nacional del Comahue, CP 8400 San Carlos de Bariloche, Argentina
a r t i c l e i n f o
a b s t r a c t
Article history:
The kinetics of the chlorination of neodymium oxide has been investigated by thermogravimetry between
312 ◦C and 475 ◦C, and for partial pressures of chlorine ranging from 10 kPa to 50 kPa. The starting tem-
perature for the reaction of neodymium oxide with chlorine was determined to be about 250 ◦C, leading
to neodymium oxychloride as product. The results showed that, for temperatures below 425 ◦C, the sys-
tem is under chemical control and the formation of the oxychloride progresses through a nucleation and
growth mechanism. The influence of chlorine mass transport through the bulk gas phase and through
the boundary layer on the overall reaction rate was analyzed. In the absence of these two mass-transfer
steps, a reaction order of 0.39 with respect to chlorine partial pressure, and an activation energy of
161 4 kJ mol−1 were determined. A complete rate equation has been successfully developed.
© 2012 Elsevier B.V. All rights reserved.
Received 30 September 2011
Received in revised form 4 April 2012
Accepted 13 April 2012
Available online 21 April 2012
Keywords:
Neodymium oxide
Chlorination
Chlorine
Kinetics
Thermogravimetry
1. Introduction
development of a neodymium–iron–boron (Nd–Fe–B) permanent
magnet, which has the strongest magnet power [4].
In recent years, new materials, such as high performance per-
manent magnets (Sm2C017(s), Nd2Fe14B(s) and Sm2Fe17Nx(s)),
phosphors for lamps or color displays, and hydrogen storage alloys
for anode materials of secondary batteries (LaNi5(s) and related
intermetallic compounds), in all of which rare earth elements
play an important role, have been developed in the correspond-
ing research fields [1]. The group called rare earth elements (REE)
is formed by 17 chemically similar metallic elements that includes
Sc, Y, and lanthanides. The lanthanides are composed by elements
with atomic numbers between 51 and 71, being neodymium (Nd)
one of them with atomic number 60 [2].
Significant quantities of Nd are contained in minerals like mon-
azite [(Ce, La, Pr, Nd, Th, Y)PO4(s)] and bastnäsite [(Ce, La)CO3F(s)].
In nature, it is found as oxide or sulfide, and it is accompanied
by other lanthanides. Neodymium compounds were first commer-
cially used as a glass dye and they are still used as a popular additive
in glass. Its color, due to the Nd(III) ion, is often reddish-purple
but changes with the type of lighting due to fluorescent effects.
Neodymium oxides are also used as a laser material to replace ruby
in order to produce a coherent light, as components of advanced
materials such as high temperature ceramics and superconduc-
tors, and in catalytic systems [3]. In particular, the production
volume of Nd has dramatically increased in 1980 decade since the
Resources of these rare metals are often limited and unevenly
distributed around the world. Hence, their cost and supply depend
strongly on political circumstances, resulting in a repeated short-
age of supply and a sudden rise in cost in recent years [5]. Therefore,
it becomes essential to recover these rare metals from the scrap of
intermetallic materials by profitable methods and to avoid envi-
ronmental damage.
A feasible alternative which allows the selective extraction of
these metals from the respective ores and concentrates, as well as
the refining and recovering of them from slags, is the application
of chlorination and carbochlorination processes. Both processes
are well-known dry methods for producing metal chlorides [6,7].
Although there are many studies concerning the chlorination
of REE, a few investigations have been addressed to the kinet-
ics, mechanisms, and structural changes involved in the direct
chlorination reaction. Gimenes and Oliveira [8] focused their inves-
tigations on the reaction between xenotime (YPO4(s)) (REEPO4) and
chlorine in the presence of carbon over a temperature range from
600 ◦C to 950 ◦C, as well as the microstructural changes occurring
during the reaction. Gaviría and Bohé [9] investigated the direct
chlorination of yttrium oxide in the temperature range between
575 ◦C and 975 ◦C, and they reported the formation of yttrium oxy-
chloride (YOCl(s)) as only reaction product in the initial stage.
The chlorination of neodymium oxide (Nd2O3(s)) has not been
reported in the literature until this moment. Consequently, the
aim of this work is to analyze the kinetics of the Nd2O3(s) chlo-
rination reactions by thermogravimetric (TG) measurements with
∗
Corresponding author. Tel.: +54 2944 445293; fax: +54 2944 445293.
E-mail address: marta.bosco@cab.cnea.gov.ar (M.V. Bosco).
0040-6031/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.tca.2012.04.014

M.V. Bosco et al. / Thermochimica Acta 540 (2012) 98–106
99
the purpose of establishing the rate equation, elucidating the reac-
tion stages, and obtaining kinetics parameters. Furthermore, the
solids were analyzed by X-ray diffraction (XRD), scanning electron
microscopy (SEM), and energy dispersive spectroscopy (EDS).
was used with the experimental setup described above. The mass
changes were monitored and acquired every 3 s, using the data
acquisition system.
In isothermal runs, samples were heated in flowing Ar(g) up to
the working reaction temperature. After the temperature was sta-
bilized (around 1 h), Cl2(g) was injected into the hang-down tube
while mass changes were continuously monitored. The data were
carefully analyzed to determine the time at which the chlorina-
tion reaction began. This procedure was employed to analyze the
influence on the reaction rate of the gaseous flow rate, the initial
mass of the sample, the temperature, and chlorine partial pressure.
Partially chlorinated samples were examined by SEM to observe
morphological changes during the reaction progress.
2. Experimental
2.1. Materials and methods
Gases used were Cl2(g) 99.8 pct purity (Indupa, Bahía Blanca,
Argentina) and Ar(g) 99.99 pct purity (AGA, Buenos Aires,
Argentina). Solid reactant used was Nd2O3(s) powder 99.9 pct
(Sigma–Aldrich Chemical Company Inc., Milwaukee, MI), and
consisting of nonporous crystalline spherical particles of approx-
imately 0.4 ␮m in diameter, which form agglomerates from 5 ␮m
to about 40 ␮m in size, as characterized by SEM (SEM 515, Philips
Electronics Instruments, Netherlands).
The Nd2O3(s) is very unstable at ambient conditions form-
ing neodymium oxide carbonate (Nd2O2CO3(s)) and neodymium
hydroxide (Nd(OH)3(s)). For this reason, previous to the chlorina-
tion, a thermal treatment under Ar(g) atmosphere was performed
to ensure the presence of Nd2O3(s) as single phase. The thermal
treatment or calcination, consisted of a 40 min ramp until 850 ◦C,
followed by a 20 min stabilization at this temperature.
TG measurements, such as isothermal and non-isothermal runs
have been widely used to establish the kinetics of the chem-
ical reactions of many solids. Mass changes occurring during
Nd2O3(s) chlorination reaction were measured using a high reso-
lution thermogravimetric analyser (TGA). This analyser consists of
an electrobalance (Cahn model 2000, Cahn Instruments Inc., Cer-
ritos, CA), appropriate for working with corrosive atmospheres, a
gas line and a data acquisition system. This experimental set-up
has a vertical tube furnace for heating and the electrobalance has a
sensitivity of 0.1 ␮g and mechanical and electrical tares of 1 g and
100 mg, respectively. While operating at 1000 ◦C under a gas flow
rate of 2–8 L/h, measured at normal temperature and pressure, it
has a sensitivity of 5 ␮g.
2.3. Data handling
The reaction rate under several experimental conditions was
evaluated from the temporal evolution of the relative mass changes
of Nd2O3(s). The conversion degree is defined as
mt − mi
˛ =
× f
(1)
mi
where mt and mi refer to the sample mass at a given time and at
the initial time, respectively, and f is a factor relative to a mass
change of main reaction. In this particular case, f is equal to 6.128
and corresponds to the neodymium oxychloride (NdOCl(s)) forma-
tion stoichiometry. This consideration is further analyzed on next
sections. According to Eq. (1), ˛ takes values in the range of 0–1.
In a mathematical form, the reaction rate for a process controlled
by chemical reaction, can be expressed as a function of temperature
(T), chlorine partial pressure (pCl2), and conversion degree (˛) as
follows:
d˛
Rate =
= K(T) × F(pCl2) × G(˛)
(2)
dt
where K(T) refers to an Arrhenius equation, F(pCl2) shows the
dependence of the rate on pCl2, and G(˛) is a function that describes
the geometric evolution of the reacting solid.
Samples of 2.5–40 mg were placed on a flat silica glass cru-
cible forming a loose packed bed. Inside the reactor, an argon flow
of 1.3 L/h was maintained. External mass transfer resistance was
eliminated by reducing the thickness of the sample layer, and it is
further discussed in Section 3.2.2. The cylindrical silica glass cru-
cible (7.2 mm inner diameter, 4.2 mm deep), hangs from one of
the arms of the electrobalance on a silica glass wire. A silica glass
hang down tube carries the gases to the sample. The temperature
of the sample was measured using a Pt–Pt (10% Rh) thermocouple
encapsulated in silica glass, which was placed 2 mm below the cru-
cible. Flows of Ar(g) and Cl2(g) gases were controlled by means of
flow meters, and they were dried by passing through silica gel and
CaCl2(s) beds, respectively.
2.4. Thermodynamical considerations
A preliminary thermodynamic analysis of the potential reac-
tions that could take place in the Nd2O3(s)–Cl2(g) system was made,
in order to determine the feasibility of them. When the chlorinat-
ing agent is Cl2(g), the following reactions are thermodynamically
feasible:
(1/3)Nd2O3(s) + Cl2(g) = (2/3)NdCl3(s, l) + (1/2)O2(g)
Nd2O3(s) + Cl2(g) = 2NdOCl(s) + (1/2)O2(g)
(1/2)Nd2O3(s) + Cl2(g) = NdCl2(s) + (3/4)O2(g)
NdOCl(s) = (1/3)Nd2O3(s) + (1/3)NdCl3(s, l)
NdOCl(s) + Cl2(g) = NdCl3(s, l) + (1/2)O2(g)
(3)
(4)
(5)
(6)
(7)
2.2. Procedure
Isothermal and non-isothermal runs were performed. The sam-
ples were well spread in the crucible forming a thin layer. Before
reaching the selected reaction temperature for each experiment,
the samples were pre-treated. They were heated to 850 ◦C in Ar(g)
flow in order to remove water, hydroxides and carbonates since
Nd2O3(s) is easily hydrolyzed and carbonated when exposed to
air, as mentioned before. After this heat treatment, samples were
cooled again to room temperature in Ar(g) atmosphere, to prevent
decomposition.In non-isothermal runs, the Cl2(g) was introduced
since the beginning of the experiment, and the sample was heated
from room temperature to 950 ◦C in the resulting mixture of
In Fig. 1, the Ellingham diagram for the formation of different
compounds, as a function of temperature, is shown. Inverse of reac-
tion (7) (dash line) was added to the diagram and it will be useful
for further analysis of the results.
From the analysis of this Ellingham diagram, if the reactions
are considered to be independent from each other, NdOCl(s) has
the highest thermodynamic tendency to be produced in all tem-
pera◦ture range studied since reaction (4) has the most negative
ꢀGr value. According to equilibrium considerations, NdOCl(s)
would be the most probable specie to be formed by the reac-
tion of Nd2O3(s) with chlorine. Besides, NdOCl(s) formed could
Ar(g) and Cl2(g) (PCl = 35 kPa). A linear heating rate of 4 ◦C min−1
2

100
M.V. Bosco et al. / Thermochimica Acta 540 (2012) 98–106
Fig. 1. Ellingham diagram for the neodymium oxide chlorination reactions. Dash
line is the inverse of reaction (7).
be chlorinated (according to reaction (7)), or decomposed (accord-
ing to reaction (6)) to give NdCl3(s,l) as final product (because the
Nd2O3(s) produced by decomposition is expected to react with
Cl2(g) to give NdCl3(s,l) as final product as well). As reaction (6)
◦
has a positive ꢀGr value in the range of temperatures considered,
this reaction is thermodynamically not feasible. On the other hand,
◦
reaction (7) has negative value of ꢀGr for temperatures below
430 ◦C while, above this temperature, reverse reaction is expected.
If formation of NdCl3(s,l) occurs through reaction (3) or reaction
(7) this would lead to an increment of the O2(g) partial pressure
enhancing the inverse of reaction (7).
The thermodynamic calculations were performed with the HSC
6.1 software [10], and the reactions were considered per mole of
chlorine. A few thermodynamic and physicochemical data about
NdOCl(s) are available in the literature. It was found in [11] that
NdOCl(s) decomposes at 1500 ◦C with formation of Nd2O3(s) and
NdCl3(s,l) (according to reaction (6)).
Fig. 2 shows the phase stability diagram of Nd–O–Cl system at
350 ◦C (data obtained from [10]). The axes of the diagram are the
partial pressure of O2(g) and Cl2(g), respectively, and the exper-
imental conditions used in our experiments are indicated by (*),
corresponding to a chlorine partial pressure of 0.35 atm and oxygen
partial pressure below 10−4 atm. The oxygen partial pressure is due
to impurities in the carrier argon gas. The possible stable condensed
phases are Nd2O3(s), NdOCl(s) and NdCl3(s,l). This graph shows
that there is not a thermodynamic equilibrium between Nd2O3(s)
Fig. 3. Non-isothermal thermogravimetry for chlorination of Nd2O3(s). Right inset
plot shows the loss mass stage and the effect of the chlorine shutoff.
and NdCl3(s,l). Therefore, NdOCl(s) has to be formed prior to the
formation of NdCl3(s,l) from Nd2O3(s).
Equilibrium constants as a function of temperature are shown
in Table 1. The high values of K observed for reaction (4) confirm
that the formation of NdOCl(s) as chlorination product is thermo-
dynamically more feasible than the formation of NdCl3(s,l) and
NdCl2(s).
3. Results and discussion
3.1. Non-isothermal thermogravimetric measurements
The starting temperature for the chlorination of Nd2O3(s) was
determined by a non-isothermal thermogravimetric measurement.
The chlorination curve is shown in Fig. 3 and it is seen the rela-
tive mass change vs. temperature of the Nd2O3(s) in argon-chlorine
atmosphere from room temperature to 950 ◦C. The conditions of the
experiment were described inside the plot.
Four different regions can be distinguished in the figure. At the
beginning of the reaction, zone (I), a small mass increase is observed
at about 250 ◦C, revealing that the chlorination reaction has started.
The second zone (II) is located between 330 ◦C and 410 ◦C showing
a sharp mass increase; and the third zone (III) occurs where not
significant mass changes are observed between 410 ◦C and 860 ◦C;
and, finally a fourth zone above 860 ◦C shows a small mass loss.
The highest value of relative mass change during all temperature
range was 18% and this value is in agreement with the mass change
involved in reaction (4).
At temperatures above 860 ◦C, the thermogravimetric curve
shows a mass decrease after a mass gain. This behavior can be
explained by two processes: (a) evaporation of NdCl3(s,l) produced
Fig. 2. Phase stability diagram of Nd–O–Cl system at 350 ◦C.

M.V. Bosco et al. / Thermochimica Acta 540 (2012) 98–106
101
Table 1
Equilibrium constants as a function of temperature.
Temperature (◦C)
Equilibrium constants (K)
R(3)
R(4)
R(5)
R(6)
R(7)
0.683
0.535
0.4
0.277
0.164
300
325
350
375
400
425
450
475
600
700
800
900
1000
5.44 × 104
2.49 × 104
1.22 × 104
6. 31 × 103
3.44 × 103
1.96 × 103
1.16 × 103
7.18 × 102
99.07
30.08
13.54
8.707
6.139
6.89 × 1012
1.31 × 1012
2.84 × 1011
6.94 × 1010
1.89 × 1010
5.64 × 1010
1.84 × 109
6.44 × 108
8.55 × 106
6.08 × 105
7.15 × 104
1.22 × 104
2.79 × 103
6.03 × 10−40
1.32 × 10−38
2.20 × 10−37
2.86 × 10−36
2.99 × 10−35
2.58 × 10−34
1.87 × 10−33
1.16 × 10−32
1.72 × 10−29
1.17 × 10−27
3.01 × 10−26
3.78 × 10−25
2.78 × 10−24
7.17 × 10−5
1.12 × 10−4
1.69 × 10−4
2.49 × 10−4
3.54 × 10−4
4.92 × 10−4
6.68 × 10−4
8.89 × 10−4
2.92 × 10−3
6.12 × 10−3
0.01208
0.06
−0.036
−0.124
−0.478
−0.681
−0.737
−0.642
−0.548
0.02361
0.0418
by chlorination of NdOCl(s) through reaction (7), or (b) decom-
position of NdOCl(s) according to reaction (6). NdCl3(s) is a very
hygroscopic light violet solid with a melting temperature of 758 ◦C
and a boiling point of 1600 ◦C [12–14]. Baev and Novikov suggested
in [11] that it sublimates at 1310 ◦C and, consequently, the evapora-
tion of NdCl3(s,l) could also lead to the mass loss in the experiment
observed. Also, the volatilization of NdCl3(s,l), although having a
and there are not significant morphological difference between
residues obtained for ˛ = 0.5 and those obtained for ˛ = 1. On the
other hand, the NdOCl(s) produced at 950 ◦C is not much differ-
ent than the material obtained at 400 ◦C since only changes in
the grain size can be distinguished, being the latter slightly larger.
This performance is in agreement with the behavior expected for a
nucleation and growth reaction mechanism [9].
The EDS measurements on samples given in Fig. 5 showed that,
for the partially reacted samples, the mean molar fractions of Nd
and Cl are 60 wt% and 40 wt%, respectively (Fig. 5(b)). These results
are in a good agreement with those expected for the theoretical
molar fractions of Nd2O3 and NdOCl for this reaction degree (57 wt%
Nd and 43 wt% Cl for ˛ = 0.50). The EDS measurements on sam-
ples completely reacted at 950 ◦C (Fig. 5(d)) are 50.4 wt% Nd and
49.6 wt% Cl. The molar fractions expected for these samples are
50 pct Nd and 50 pct Cl since they are 100 pct NdOCl.
◦
positive value of ꢁGr for temperatures below 758 ◦C, should be
taken into account in a flowing system like the experiment set-
up, due to the Cl2(g)–Ar(g) gas stream that might enhance the
volatilization process.
In order to determine whether Cl2(g) is involved in the mass loss
observed, a reaction was produced at 950 ◦C in which the Cl2(g) flow
was suspended after oxychloride formation. The corresponding TG
curve is shown in the inset plot given in Fig. 3. As can be observed,
the sample did not suffer any mass change under Ar(g) atmosphere
(after Cl2(g) flow shut off), indicating that the mass loss at high
temperature can be explained by the a reaction between NdOCl(s)
and Cl2(g) which generates NdCl3(s,l), according to reaction (7).
This behavior is corroborated in Fig. 3, since the vapour pressure of
NdCl3 reaches a value of 1.1 × 10−4 atm at 900 ◦C [10] which suggest
that the mass change due to the volatilization will be significant
above that temperature.
The solid residue obtained was analyzed by XRD and it resulted
100% of NdOCl(s), since no diffraction peaks other than NdOCl(s)
were observed. Fig. 4 shows the diffractogram for the residue
after non-isothermal run and the NdOCl(s) pattern (ICSD Reference
Code: 85-1198, Crystal system: Tetragonal Space group: P4/nmm,
Space group number: 129) [15]. As can be seen, representative
peaks of unreacted Nd2O3(s) does not appear and this fact also
reveals that the high temperature reaction (7) is occurring. How-
ever, due to the absence of NdCl3(s,l), another possible reaction
pathway could be the reaction (3) followed by inverse of reaction
(7).
In normal conditions of pressure and temperature, exposed to
environmental moisture, the formation of neodymium hydroxy-
chloride, Nd(OH)2Cl(s) has been verify by XRD (ICSD Reference
code: 01-072-1812, Crystal system: Monoclinic Space group:
P21/m, Space group number: 11) [15]. In agreement with the results
obtained by Roy and Kipouros [16] the dehydration of Nd(OH)2Cl(s)
proceeds at high temperatures, decomposing to NdOCl(s).
3.1.1. Morphological analysis
Fig. 5 shows SEM images of: (a) pure analytical Nd2O3(s) after
heat treatment for hydrate removal, (b) NdOCl(s) produced at
400 ◦C at ˛ = 0.5, (c) NdOCl(s) produced at 400 ◦C at ˛ = 1, and (d)
NdOCl(s) produced at 950 ◦C at ˛ = 1. It is observed that the NdOCl(s)
formed at 400 ◦C has a smaller grain size than the initial Nd2O3(s),
Fig. 4. XRD for the residue after the non-isothermal run, and the NdOCl(s) pattern
(ICSD Reference Code: 85-1198).

102
M.V. Bosco et al. / Thermochimica Acta 540 (2012) 98–106
Fig. 5. SEM images of: (a) pure Nd2O3(s) obtained by calcination, (b) NdOCl(s) produced at 400 ◦C at ˛ = 0.5, (c) NdOCl(s) produced at 400 ◦C at ˛ = 1, and (d) NdOCl(s) produced
at 950 ◦C at ˛ = 1.
3.2. Isothermal thermogravimetric measurements
boundary layer was estimated by using the Ranz–Marshall equation
[19–20]:
Taking into account the starting temperature for the chlorina-
tion in the non-isothermal runs and the fact that, at temperatures
above 475 ◦C the reaction rate is controlled by diffusion (as it is
confirmed in Section 3.2.1.), the temperature range selected for
isothermal thermogravimetric measurements ranged from 312 ◦C
to 475 ◦C.
DCl −Ar × (2.0 + 0.6Re1/2Sc1/3) × (PCBl − PCSl ) × A
2
2
2
N =
(9)
R × T × l
where N refers to the molar flow of chlorine; D is the binary dif-
fusion coefficient for Cl2(g)–Ar(g); Re = U × l/v and Sc = v/D are the
Reynolds and Schmidt numbers, respectively (U is the linear fluid
velocity and v is the kinematic viscosity); PCBl and PCSl are the Cl2(g)
3.2.1. Effect of gaseous flow rate
2
2
partial pressure in the gas stream and solid surface, respectively;
A is the sample external surface (crucible area = 0.43 cm2); and l is
the sample characteristic dimension (crucible diameter = 0.74 cm).
Chlorination reactions were performed by increasing the
gaseous flow rate in order to guarantee that the system was not
in gaseous reactant starvation condition. Starvation occurs when
a sufficient portion of the reactant is consumed by the solid so
that the particle is not in contact with a gas of bulk composi-
tion but the local reactant concentration is less than this value
[17,18]. This effect can be estimated by analyzing the influence of
the total flow rate on the reaction rate. Fig. 6 shows the effect of
the gaseous flow rate when it raised from 2 L/h to 8 L/h in the chlo-
rination of 10 mg of Nd2O3(s) at 400 ◦C. The reaction rate depends
on the flow rate for 2 L/h but it can be seen that, for flow rates
from 4 to 8 L/h, the reaction rate are the same (within the experi-
mental scattering). When changes in the flow rate of the reacting
gas do not produce significant changes in the reaction rate, it
may be concluded that the reacting gas starvation phenomena is
absent. From the results presented in Fig. 6, it can be concluded
that Ar(g)–Cl2(g) flow rate above 4 L/h is high enough for avoid-
ing starvation effects in the Nd2O3(s) chlorination at 400 ◦C and
pCl2 = 35 kPa. Therefore, the flow rate employed in further experi-
ments was greater than QCl
= 4 L/h.Another gas phase mass
(g)−Ar(g)
2
transfer process is the convective mass transfer through the bound-
ary layer surrounding the sample. In order to analyze the role of this
convective mass transfer process, the molar flow of Cl2 through the
Fig. 6. Effect of flow rate of Ar(g)–Cl2(g) mixture on the chlorination rate of Nd2O3.
Mass sample and chlorine partial pressure were kept constant in all experiments
(10 mg of Nd2O3(s) and 35 kPa at 400 ◦C).

M.V. Bosco et al. / Thermochimica Acta 540 (2012) 98–106
103
Table 2
Comparison between calculated and theoretical molar flows of chlorine at different temperatures.
Temperature (◦C)
N Theoretical (mol Cl2/s)a
Ne Experimental (mol Cl2/s)b
N/Ne
312
325
337
350
375
400
425
450
475
4.40 × 10−06
4.50 × 10−06
4.50 × 10−06
4.60 × 10−06
4.70 × 10−06
4.80 × 10−06
5.00 × 10−06
5.10 × 10−06
5.20 × 10−06
5.63 × 10−10
1.15 × 10−09
2.20 × 10−09
4.49 × 10−09
1.08 × 10−08
3.81 × 10−08
1.16 × 10−07
4.63 × 10−07
5.62 × 10−07
7815.28
3913.04
2045.45
1024.50
435.19
125.98
43.10
11.02
9.25
Conditions used for the calculus: L = 0.74 cm, A = 0.43 cm2, mass = 20 mg, pCl2 = 35 kPa, and QAr(g)−Cl (g) = 6 L/h.
2
a
Calculated from Eq. (9).
b
Obtained from the lineal range of the thermogravimetric curves (stoichiometry of reaction (4)).
Table 2 shows the values of N for pCl2 = 35 kPa, QCl (g)−Ar(g)
=
evaluate the effect of gas flow rate is valid for masses of 20 mg,
we performed the chlorination assays at different flows rates with
20 mg giving the same results.
6 L/h, and temperatures between 312 ◦C and 475 ◦C, as 2calculated
by Eq. (9). The values of DCl
(binary diffusion coefficient) and
−Ar
2
v (kinematic viscosity) were obtained from the Chapman/Enskog
theory [17,21]. The experimental values (Ne) were calculated from
the slope of the mass changes vs. time curves, corresponding to the
thermogravimetric isothermal measurements of the chlorination
reactions at different temperatures (mass = 20 mg, pCl2 = 35 kPa,
3.3. Kinetic analysis
The intrinsic kinetic parameters of Nd2O3(s) that produces
NdOCl(s) by chlorination with gaseous chlorine are determinate
in this section. The results described in the previous sections show
that, the reaction rate is not affected by mass transfer phenom-
ena like transport in the gas phase and through the sample pores
at temperatures below 425 ◦C. Then, the kinetics of the reaction is
under chemical control and the reaction rate can be expressed as a
function of T, pCl2, and ˛ as it was previously shown by Eq. (2).
and QAr(g)−Cl
= 6 L/h). The slope was calculated by a linear fit-
(g)
ting of these2of the isothermal measures at different temperatures
in the zone that show a sharp mass increase. To convert the values
of the reaction rate, mg/s, to mol Cl2/s, is necessary to establish the
stoichiometry of the reaction (in this case reaction (4)) and deter-
mine which relationship exists between gained mg of the sample
and the moles of Cl2 which reacted for the mass increase. Also it
was assumed that reaction (4) is irreversible: as the equ◦ilibrium
constant for the formation of NdOCl(s) is 1.89 × 1010 at 400 C while
the equilibrium constant of the reverse reaction is 5.29 × 10−11 [10].
Table 2 also shows the values of the reaction rate (in mol Cl2/seg)
and the ratio of the theoretical and experimental chlorine molar
fluxes.
3.3.1. Effect of temperature on the reaction rate
Fig. 8(a) illustrates the effect of temperature on the chlorination
of 20 mg of Nd2O3(s) at pCl2 = 35.5 kPa. As can be seen, the reaction
is faster as the temperature increases.
The combination of Eq. (2) with the Arrhenius law leads to:
As Eq. (9) is strictly valid for a pellet in a freely flowing gas and
not for a sample contained within a crucible, Hills [18] and Hakvoort
[22] concluded that the values given by Eq. (9) are more than one
order of magnitude higher than the actual mass transfer rates for
powders contained within crucibles. It can be seen in Table 2 that,
for temperatures lower than 425 ◦C, the experimental reaction rate
is about two orders of magnitude less than the theoretical rate
which indicates that the convective mass transfer process is not
the rate-controlling step for the chlorination of Nd2O3(s).
d˛
/RT)
a
Rate =
= F(pCl2) × G(˛) × A × e−(E
(10)
dt
where ˛ is the reaction degree defined by Eq. (1) and t is the time.
The activation energy (Ea) can be calculated from Eq. (10) even if
the functions F(pCl2) and G(˛) are unknown, by applying a “model-
free” method [23,24]. Rearranging Eq. (10) and integrating:
ꢀ
ꢀ
˛
t
i
i
d˛
a
=
F(pCl2) × A × e−(E /RT)dt
(11)
G(˛)
0
0
3.2.2. Mass transfer through the sample pores
Mass transfer into the sample pores can influence the overall
reaction rate. By analysis of the effect of reaction bed thickness
on the overall reaction rate the role of mass transfer through the
sample pores was characterized. This analysis was performed by
varying the initial mass of the solid reactant, Nd2O3(s). If the gas
diffusion through the pores plays a significant role in the control of
the reaction rate, it should decrease as the sample mass increases.
Fig. 7 shows the thermogravimetric curves obtained by chlorina-
tion of Nd2O3(s) at 400 ◦C for samples with different initial masses
contained within a cylindrical crucible, while keeping the other
experimental conditions constant. The masses in experiments used
were, 5, 10, and 20 mg. As can be seen, the reaction rate does not
depend on the mass sample at this experimental conditions. There-
fore, it can be concluded that the mass transfer through the sample
pores is not affecting the overall reaction rate. In the further exper-
iments, a mass of 20 mg was used, since the experimental scatter is
smaller and sufficient material remained as solid residue for sub-
sequent analysis. To ensure that the previous study realized to
Fig. 7. Effect of the sample size on reaction rate for chlorination of Nd2O3(s) at
400 ◦C. Flow rate and chlorine partial pressure were kept constant in all experiments
(6 L/h and 35 kPa).

104
M.V. Bosco et al. / Thermochimica Acta 540 (2012) 98–106
Fig. 9. (a) Effect of chlorine partial pressure on chlorination of Nd2O3(s); (b) lineal
fit obtained from Eq. (13). Experimental conditions: temperature = 400 ◦C, QAr−Cl
=
2
6 L/h, and initial mass = 20 mg.
Fig. 8. (a) Effect of reaction temperature on chlorination of Nd2O3(s). Experimental
conditions: pCl2 = 35 kPa, QAr−Cl = 6 L/h, and initial mass = 20 mg. The stoichiometry
2
x
considered corresponds to reaction (4) and (b) plot of ln t(˛) vs. 1/T for the calculation
of activation energy (Ea) by applying a “model-free” method.
is assumed to have a form of B · pCl2 (where B is a constant and
x is the reaction order with respect to pCl2), temperature is main-
tained constant, and natural logarithms are applied. The resulting
expression for these conditions is:
After solving the integral and applying the natural logarithm, we
have:
−ln t(˛) = H(˛) + x ln pCl2
(13)
Ea
R
1
T
ln t(˛) = C(˛) +
×
(12)
where t(˛) is the time at which the reaction reaches a conversion
degree ˛ at temperature T, and H(˛) is a function that depends on ˛
(since T is kept constant). The reaction order for a given conversion
degree is obtained by plotting −ln t(˛) vs. pCl2 (Fig. 9(b)). From the
slope of the straight lines of the −ln t vs. ln pCl2(g) plot for different
conversion degrees, calculated in the 10–30 kPa range, it was found
that the chlorination rate is proportional to a potential function of
the partial pressure of chlorine whose exponent x is around 0.39.
For pressures greater and equal to 30 kPa this exponent is close to
cero.
where t(˛) is the time at which the reaction reaches a conversion
degree ˛ at a temperature T, being R the universal gas constant and
C(˛) a function that depends on ˛ (since pCl2 is kept constant during
experiments).
The Ea for a given conversion degree is obtained by plotting
ln t(˛) vs. 1/T and calculating the slope of the curve. The values
of time needed to calculate ln t were obtained from the curves of
˛ vs. t at different temperatures (Fig. 8(a)). The results are shown
in Fig. 8(b) for ˛: 0.2, 0.4, and 0.8. From the slope of the straight
lines, an activation energy of 169 5 kJ mol−1 was determined. The
constant value of Ea, obtained as a function of the reaction degree
across the temperature range, indicates that the rate-controlling
step does not change during the complete reaction.
3.3.3. Determination of reaction model
As confirmed by several authors, the sigmoidal shape of the ther-
mogravimetric curves is characteristic of a “nucleation and growth
reaction model” [9]. The conversion curves were fitted according
with the Johnson–Mehl–Avrami (JMA) model [25–28], as follows:
3.3.2. Effect of chlorine partial pressure
n
˛ = 1 − e[−K(T)·t]
(14)
The effect of chlorine partial pressure (pCl2) in the range from
10 to 50 kPa was analyzed at 400 ◦C, initial sample mass of 20 mg,
and gas flow rate of 6 L/h, and the results are given in Fig. 9(a). As
can be seen, the chlorination rate shows a slight increase in the
reaction speed when pCl2 goes from 20 to 30 kPa, and for pressures
between 35 and 50 kPa, the values are between the experimental
error. Therefore, we can say that for pressures greater than 30 kPa
the kinetics is not influenced by pCl2.
with n as the JMA exponent constant and K(T) given by:
/RT)
K = K0e−(E
(15)
a
where K0 is the pre-exponential factor and Ea is the effective acti-
vation energy. The JMA kinetic parameters K0, n, and Ea depend on
the nucleation and growth mechanism.
To determine the reaction order with respect to pCl2, the fol-
lowing procedure is applied: Eq. (2) is integrated over time, F(pCl2)
The isothermal ˛–t curves were fitted with Eq. (14) in a non-
linear way and they are shown in Fig. 10, where the scatter

M.V. Bosco et al. / Thermochimica Acta 540 (2012) 98–106
105
Note that the reaction is under chemical control and that
the mechanism by which formed and grows the new phase is
nucleation and growth. The activation energy associated with the
intrinsic rate constant is equal to the sum of the energies of activa-
tion of nucleation and growth processes.
Following, from Eq. (2) and (14):
G(˛) = n · (1 − n) · [−ln(1 − ˛)](n−1)/n
= 1.65 · (1 − ˛) · [−ln(1 − ˛)]0.39
(16)
Finally, from the slope of the curve ln K vs. T−1 shown in Fig. 11,
intrinsic activation energy of 161 4 kJ mol−1 is estimated for the
chlorination reaction of Nd2O3(s). As expected, this value is sim-
ilar to the activation energy calculated in Section 3.3.1 with the
isoconversional method.
Fig. 10. Isothermal ˛–t curves fitted with Eq. (14). Scatter graphs correspond to the
experimental values and line graphs are the fitted curves.
4. Conclusions
Table 3
The chlorination reaction of Nd2O3(s) has been studied in the
range of 312–425 ◦C. It was observed that the chlorination reac-
tion starts at 250 ◦C, leading to the formation of solid neodymium
oxychloride which is further chlorinated to neodymium trichloride
at temperatures above 860 ◦C. This neodymium trichloride evapo-
rates.
By using kinetic analysis, it has been demonstrated that
the chlorination reaction is under chemical control for tem-
peratures below 425 ◦C. The ˛–t curves were analyzed with
the Johnson–Mehl–Avrami description for nucleation and growth
reaction mechanism. The calculated ˛–t curves showed a good
agreement with the experimental data and they provided a good
description of the mechanism by which formed and grows the new
phase with n ≈ 1.65, which corresponds to a mechanism controlled
by diffusion and continuous nucleation.
The isoconversional method showed that the reaction mecha-
nism is the same for during the complete reaction. The activation
energy obtained with the isoconversional method was estimated
to be 169 5 kJ mol−1 which is very close to the value calculated
with the Johnson–Mehl–Avrami model (Ea = 161 4 kJ mol−1).
Finally, the effects of the different parameters studied in this
system could be described by a global reaction rate equation, as
follows:
Values of kinetic parameters K and n, obtained from the fits of conversion curves
with the Johnson–Mehl–Avrami (JMA) model (Eq. (14)).
Temperature (◦C)
˛
n
K (s−1
)
R2
312
325
337
350
375
400
425
0.10–0.95
0.08–0.95
0.09–0.95
0.10–0.95
0.15–0.91
0.09–0.90
0.10–0.90
1.62
1.82
1.94
1.87
1.57
1.54
1.15
0.000047
0.00009
0.00016
0.00033
0.00092
0.00316
0.01049
0.9944
0.9979
0.9984
0.9996
0.9981
0.9994
0.9986
corresponds to the experimental values and the line graphs are the
fitted curves. As can be seen, the JMA model adjusted well in a wide
range of the ˛–t curves. Table 3 shows the values of n, K, R2 obtained
for each temperature in the different ranges of ˛ evaluated.
With exception of experiments performed at 425 ◦C, the cal-
culated values of n ranged between 1.5 and 2 were obtained.
These values can be understood if it is assumed that the chlo-
rination reaction mechanism has a diffusion-controlled growth.
According to studies realized by Kempen and Sommer [29,30] for
diffusion control growth mechanism, the value of n is expected to
vary as follows: (I) between 1/2 (one-dimensional growth) and 3/2
(three-dimensional growth) for site saturation, and (II) between 3/2
(one-dimensional growth) and 5/2 (three-dimensional growth) for
continuous nucleation. Consequently, an average value of n = 1.65
is compatible with growth of the new phase, whose is controlled
by diffusion and continuous nucleation.
−1
d˛
dt
)/RT)
Rate =
= 1.04 × 105(s kPa0.4
)
−1 × e−((161 kJ mol
× pCl02.39 × {1.65 × (1 − ˛) × [−ln(1 − ˛)]}0.39
Acknowledgments
The authors wish to thank to Agencia Nacional de Promoción
Científica y Tecnológica (ANPCyT), Consejo Nacional de Investiga-
ciones Científicas y Técnicas (CONICET), and Universidad Nacional
del Comahue for the financial support of this work.
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