Catalyst for Ammonia Synthesis

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Study of the Iron Catalyst for Ammonia Synthesis by Chemical
Potential Programmed Reaction Method
Bartłomiej Wilk, Rafał Pelka,* and Walerian Arabczyk
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West Pomeranian University of Technology, Szczecin, Institute of Chemical and Environment Engineering, 10 Pułaskiego Str, 70-322
Szczecin, Poland
ABSTRACT: A new method, entitled chemical potential programmed reaction, for determining the physicochemical properties
of iron ammonia synthesis catalyst has been proposed. Two model
reactions were applied: nitriding of the iron catalyst and reduction
of the obtained nitrides. Measurements of the rates of those
reactions were carried out at 350 °C in a differential tubular reactor.
The reactor is equipped with a system that allows us to perform
simultaneous thermogravimetric measurements and a catharometric
system to determine hydrogen concentration in the gas phase. The
reactor was fed with a mixture of ammonia and hydrogen of varying
composition, which was changing in a controlled way. Different
accelerations of the nitriding potential change were applied. During the processes of nitriding of nanocrystalline iron and
reduction of the obtained nanocrystalline iron nitrides rates of these processes were measured. The minimum nitriding potential,
at which the phase transformation of nanocrystallites of a certain size took place, was determined. As a result, the relative
nanocrystallite size distribution related to the active surface of nanocrystallites was calculated. Then, making use of the mean size
of nanocrystallites the absolute size distribution was obtained. Bimodal size distribution of nanocrystallites in test samples was
observed. The dependence of the minimum nitriding potential on the mass of crystallites was determined. During the reduction
of iron nitrides, similarly as in the iron nitriding process, nanocrystallites underwent a phase transition in their entire volume in
the order of the largest to the smallest in size.
■
INTRODUCTION
Iron catalyst for ammonia synthesis was the object of research
performed in order to verify the effectiveness of a new method
for determining the physical and chemical properties of
nanomaterials. The fused iron catalyst for ammonia synthesis
is industrially prepared by melting iron oxides with structural
promoters (Al2O3, CaO) and an activating promoter (K2O). By
reduction with hydrogen of the resultant alloy, an active form of
the catalyst having nanocrystalline structure is obtained.1,2
Metal oxide (mainly Al2O3, CaO) bridges connecting the
individual crystallites of iron form the 3-dimensional (3D)
structures.3 Promoters placed on the surface of the crystallites
form the 2-dimensional (2D) structures.4 In the active iron
catalyst, there is a thermodynamic equilibrium between iron
nanocrystallites and promoters located in the 2D and 3D
structures.4,5 Therefore, the structure of the active iron catalyst,
due to the presence of structural promoters, is stable at high
temperatures. The structure of the catalyst after fixing at a given
temperature did not change at lower temperatures.6
The surface of iron nanocrystallites is wetted by a layer of K
+O, and iron atoms are combined with potassium atoms by
oxygen bridges. The presence of activating promoter (K2O)
after the reduction process increases the number of active sites
on the catalyst surface, which is dependent on the chemical
composition of the surface of the catalysts and temperature.7−9
Oxygen atoms prevent the extraction of potassium from the
surface during the processes.3−12
© 2017 American Chemical Society
A model of interactions between iron nanocrystallites and
promoters and the explanation of the resulting nanometric
structure is presented elsewhere.4,5
By studying the kinetics of the nitriding of nanocrystalline
iron, it was found that the reaction rate was limited by the rate
of dissociative adsorption of ammonia on the surface of iron. A
reaction model of nanocrystalline materials with a gas phase
was elaborated, wherein the chemical process rate is limited by
a surface reaction rate.13 According to this model, in the
nitriding process with ammonia, each nanocrystallite forming a
solid solution of nitrogen in α-iron, α-Fe(N), after reaching the
critical concentration of nitrogen undergoes a phase transition
in its whole volume to a phase γ′-Fe4N. The phase transition of
nanocrystallites occurs in the order from the smallest to the
largest in size.14
Based on studies of nitriding of nanocrystalline iron and
reduction of obtained nanocrystalline nitrides of iron at a
constant temperature and at different nitriding potentials, it was
found15−18 that for each composition of the mixture of
ammonia and hydrogen steady states were fixed. In these
states, the reaction rate in the solid was zero (constant content
of nitrogen in the solid sample), and the rate of catalytic
ammonia decomposition reaction was constant. Additionally, in
Received: September 22, 2016
Revised: April 4, 2017
Published: April 5, 2017
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the single-phase areas chemical equilibrium states occurred
between the ammonia−hydrogen mixture, the catalyst surface,
and the solid-phase volume (chemical potentials of nitrogen
present in the gas phase, on the surface and in the volume of
iron nanocrystallites were equal to each other, μg = μs = μb). In
turn, in the multiphase areas chemical equilibrium states
occurred between the gas phase and catalyst surface, and the
nonequilibrium state held between the gas-phase and solidphase volume. It was also observed that specific nitriding
degrees are a function of the nitriding potential and the
nanocrystallite size distribution.15−18
In the steady-state conditions, hysteresis was observed for a
dependence of the iron nitriding degree on nitriding potential
for processes carried out at temperatures of 300,19 350,16−18
and 400, 450, 500, and 550 °C.15
It has been shown that phase transformations occurring in a
nanocrystalline iron−ammonia−hydrogen system at a given
temperature are observed in a range of potential, and not as in a
coarse-grained system, at the specific value of nitriding
potential.15−22 It has been shown that for the nanocrystalline
iron, apart from the single component areas, there are areas of
the coexistence of two phases, and furthermore, in the
reduction process there is the area of coexistence of the three
solid phases.15−19,23−25 In the nitriding processes of nanocrystalline iron α-Fe(N) to iron nitride γ′-Fe4N which were
conducted in conditions of stationary states, there were
simultaneously nanocrystallites that formed a solid solution of
nitrogen in iron and those, which were converted into iron
nitride phase,17,21,26 according to the extended phase rule of
Gibbs due to the presence of an additional degree of freedom
associated with the size of the nanocrystallites.27
On the basis of X-ray diffraction (XRD) studies, it was
found17,21,26 that the minimum nitriding potential at which the
phase transition of each nanocrystallite of a certain size begins
is a function of the nanocrystallite mass distribution. It was
observed that the smaller the crystallite the greater the value
must be for the gas-phase nitriding potential to begin the phase
transition of the crystallite from α-Fe(N) phase to nitride γ′Fe4N. Theoretical studies proved that the active surface area of
nanocrystallite which undergoes phase transition depends
proportionally (linear dependence) on the nitriding potential
at which the phase transition takes place for both nitriding18
reaction and reduction.27 Consequently, a model of the
transformation of nanocrystallites for the nanocrystalline iron
nitriding and reduction process has been proposed where
nanocrystallites undergo phase transition throughout their
volume in the order from the largest to the smallest.17,27
Therefore, it has been concluded14−22,27−29 that the
phenomena occurring in a nanocrystalline iron−ammonia−
hydrogen system cannot be described on the basis of the wellknown Lehrer’s diagram30−34 for bulk materials.
Because of the long time it might take for some processes to
approach the equilibrium state, conducting measurements in
these conditions might not be experimentally feasible. There
may also arise a question whether the observed states are
actually equilibrium ones or only very close to equilibrium.
Therefore, the chemical potential programmed reaction
(CPPR) method has been elaborated and is presented in this
paper to perform studies on close-to-equilibrium states. As
mentioned above, properties of nanomaterials, with changing
chemical potential of a gas phase, μ, depend both on
nanocrystallite sizes (crystallite size distribution, CSD) and
chemical composition of their surface
d(physicochemical property)
dμ
= physicochemical property (CSD,
∑ θi)
i
where θi is the surface coverage degree of the ith chemical
species.
Commonly used temperature-programmed methods are
based on the dependencies of physical and/or chemical
properties of the test substances on temperature. These
methods, however, work in conditions far from equilibrium.
In analogy, one can use the dependencies of physical and/or
chemical properties of nanomaterials on chemical potential of
the gas phase, with which they react. This is possibly due to the
fact that one of the properties of nanomaterials is that
nanocrystallites of a certain mass undergo a phase transition at
the specific chemical potential of a gas phase.18,27 Additionally,
the new method operates at close-to-equilibrium states which
leads to a significant extension of research opportunities. Thus,
the idea of this method is (analogically to other programmed
techniques) to continuously change the chemical potential of a
gas phase and observe the reaction of the solid sample. Change
in concentration of the gas reactant occurs in such a way that
close-to-equilibrium states can be established. Then, conversion
degree in the solid phase is measured. On the basis of
dependence of the measured values of parameters characteristic
for a given method to measure the conversion degree on
change in the concentration of the gas reactant it is possible to
define physicochemical properties of a nanomaterial. The
conversion degree can be measured, for example, by means of
thermogravimetry, X-ray diffraction (XRD), mass spectrometry,
infrared (FTIR), Raman, Mössbauer spectroscopy, and electron
paramagnetic resonance (EPR). The physicochemical properties to be determined may include: phase composition, average
crystallite size, crystallite size distribution, lattice constants
changes, and so on.
When dealing with nanomaterials, crystallite size distribution
determination has become the fundamental measurement
because their physical (e.g., melting temperature, absorption
of electromagnetic wave, magnetic characteristics) and chemical
(e.g., catalytic activity, selectivity, creation of new materials)
properties depend on the nanoparticle size.35−42 Adsorption
depends on the morphological characteristics of the nanoparticles (their size and shape). On the other hand, chemical
environment (presence of adsorbates) determines the
morphology of nanoparticles.39
As mentioned above, the equilibrium states were considered
in previous studies (with step-wisely changed chemical
potential of a gas mixture); however, continuous change in
chemical potential of a gas phase was not applied yet.
Summing up, not only were the above-mentioned phenomena experimentally observed and reported but also thermodynamic basic principles of them were published. In particular
equilibrium state in nanoscale structures was described in
previous works.5,18 The hysteresis for a dependence of the iron
nitriding degree on nitriding potential was explained in terms of
the energy demand of individual components of the studied
nanoscale system.18,27 These three works are the theoretical
basis of the proposed method.
Using the proposed new method, in this paper, research of
the nanocrystalline iron−ammonia−hydrogen system has been
presented on the basis of measuring the rate of nanocrystalline
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out in hydrogen flow of 9 dm3/h at atmospheric pressure, poly
thermally, increasing the process temperature to 500 °C at 10
°C/min and then the sample was annealed for 0.5 h in order to
stabilize the nanocrystalline structure of the catalyst.
The change in mass of the sample in the thermogravimetric
measurements was expressed by nitriding degree, α, defined as
the mass ratio of nitrogen attached at a given moment of time
during the chemical process with respect to the initial weight of
iron contained in the solid sample (XN/XFe [mol/mol]).
Nitriding process of iron and reduction of the obtained iron
nitrides were carried out at varying nitriding potentials.
Nitriding potential values of the gas mixture at a given moment
of the process were calculated from the equation
pNH
P = 3/23 [Pa−0.5]
pH
(1)
iron nitriding and reduction of the obtained iron nitrides in a
controlled way in states close to chemical equilibrium. During
the studies, the CPPR method was applied using thermogravimetry and XRD.
■
EXPERIMENTAL SECTION
Industrial prereduced triply promoted nanocrystalline iron
catalyst for ammonia synthesis in the form of irregular particles
with a diameter of 1.0−1.2 mm was studied.43 By atomic
emission spectrometry with inductively coupled plasma using
the spectrometer PerkinElmer Optime 5300DV, the chemical
composition of the catalyst was determined. The catalyst in
addition to the metallic iron contained (wt %) 3.3 Al2O3, 2.8
CaO, and 0.65 K2O. By X-ray diffraction using a Philips X-ray
diffractometer X’Pert X-ray with a copper lamp and using the
Rietveld method, the average crystallite size of iron (45 nm)
was determined. Apart from that, using X-ray diffraction,
nanoCSD was determined by means of the method proposed
by Pielaszek.44 Fityk software45 as well as an online calculator
by Pielaszek46 were used to analyze the diffraction patterns.
The surface area of the catalyst determined by the BET method
using a Quadrasorb SI apparatus (Quantachrome Instruments,
Automated Surface Area & Pore Size Analyzer) was 12 m2/g.47
Nanocrystalline iron nitriding process and reduction of the
resulting nanocrystalline nitrides of iron were conducted using
gases supplied by Air Liquide: ammonia having a purity of
99.998% and hydrogen of 99.999%.
Nanocrystalline iron nitriding process and reduction of the
resulting nanocrystalline nitrides of iron were carried out in a
differential tubular reactor35 connected to a system for
regulating gas flows (Figure 1). Processes were carried out at
2
where pNH3 and pH2 represent partial pressures of ammonia and
hydrogen, respectively, in the gas phase.
Chemical processes were performed at a constant ammonia
flow rate, V̇ NH3 = const, and hydrogen flow changing constantly
according to the following expression
⎡ 3⎤
̇ ± β t ⎢ cm ⎥
VḢ 2 = V0H
H2
2
⎣ min ⎦
(2)
where βH2 is the hydrogen flow acceleration and V̇ 0H2 is the
initial hydrogen flow at t = 0.
The change of the nitriding potential of ammonia−hydrogen
mixture during the conducted processes can be expressed as
follows:
P(t ) =
̇ (VNH
̇ + V0H
̇ ± β t )0.5
VNH
H
3
3
2
2
̇ ± β t )1.5
pat0.5 (V0H
H
2
2
[Pa−0.5]
(3)
Hydrogen concentration changes in time in the gas phase can
be described by the following nonlinear equation:
X H 2 (t ) =
̇ +β t
V0H
H
2
2
̇ + V0H
̇ +β t
VNH
H
3
2
2
(4)
The change in hydrogen flow at the inlet to the reactor and the
calculated (eq 4) participation of hydrogen in a nitriding
mixture for one of the processes carried out at a constantly
changing flow rate of hydrogen (βH2 = ± 0.4 cm3/min2) and the
flow of ammonia (V̇ NH3 = 35 cm3/min) are shown in Figure 2.
Nitriding processes of nanocrystalline iron were initiated
from fixing the initial nitriding potential in the system, which
was lower than the minimum nitriding potential necessary for
the development of phase γ′-Fe4N. The minimum nitriding
potential of the gas mixture was determined based on data
obtained for nanocrystalline iron nitriding process performed in
the stationary states at 350 °C, which was described in previous
papers.22,24 A gas mixture of the determined initial nitriding
potential was fed to the reactor to establish the steady state.
After the composition of the reaction mixture was fixed in the
reactor, the flow of hydrogen was reduced constantly in the
nitriding process. The processes of nitriding were carried out
up to the moment when the nitriding potential corresponding
with the obtaining of saturated with nitrogen γ′-Fe4N phase in
the nitriding process conducted in stationary states was
achieved.
Figure 1. Experimental setup used in the CPPR method: 1, sample
holder; 2, single layer of grains; 3, reactor furnace; 4, reactor wall; 5,
thermocouple; 6, electronic flowmeters.
350 °C, which was measured with a thermocouple placed in the
vicinity of the sample. The measurement setup was equipped
with a system to stabilize and control the temperature during
the processes. The reactor was equipped with a magnetic sensor
system to measure sample mass. A sample of the catalyst of
approximately 1 g was placed in a platinum basket in a form of
a single layer of grains. The reactor was fed by the reaction gas
mixture of varying composition. The change in the composition
of the nitriding mixture was carried out by a system of
electronic mass flowmeters (by Brooks) connected to a
computer. The computer was equipped with software that
allows simultaneous control of flows on all flowmeters
according to predefined programs. The hydrogen content in
the outlet gas of the reaction space was determined by means of
katharometric method.
A test sample was preprepared by the reduction of the
passive layer of the catalyst. The reduction process was carried
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In order to better present experimental data, nitriding potential
values were expressed by the natural logarithm of the nitriding
potential.
Figure 2. Dependences of the hydrogen flow and of its content in a
nitriding mixture on time of the nitriding process and reduction of the
obtained nanocrystalline iron nitrides at 350 °C; V̇ NH3 = 35 cm3/min,
βH2 = ± 0.4 cm3/min2.
Figure 4. Dependence of the nitriding degree of sample on the
nitriding potential for nitriding of nanocrystalline iron and reduction
of nanocrystalline iron nitrides conducted at different hydrogen flow
accelerations.
In the process of reducing of obtained nitride, hydrogen flow
was increased constantly up to a final nitriding potential at
which total reduction of the nanocrystalline nitrides to
nanocrystalline iron, α-Fe(H), took place.
■
For the performed cycles of processes with different
hydrogen flow acceleration, as in the case of processes carried
out in stationary conditions, one can observe the phenomenon
of hysteresis for each cycle. Along with an increase in
acceleration βH2, a shift in isotherms for nitriding process to
higher nitriding potentials and a shift in isotherms for reduction
process toward lower nitriding potentials were observed.
Nanocrystalline iron nitriding process and reduction of iron
nitrides can be described by the general equation of chemical
reactions:
nitriding
3
α ‐Fe + NH3 XooooooooY γ ′‐Fe4N1 − x + H 2
reduction
2
Rates of the nitriding process can be described by the following
equation:19
RESULTS AND DISCUSSION
Four cycles of nitriding of nanocrystalline iron to nanocrystalline iron nitride γ′-Fe4N were performed and its reduction for
different hydrogen flow accelerations, βH2, amounting to ±0.1
cm3/min2, ±0.2 cm3/min2, ±0.3 cm3/min2, and ±0.4 cm3/
min2. Nitriding processes were conducted at a constant flow of
ammonia V̇ NH3= 35 cm3/min. Hydrogen flow was changed from
the initial value V̇ 0aH2 = 58 cm3/min (corresponding with the
minimum nitriding potential, P0a = 0.24 × 10−2 Pa−0.5) up to
V̇ H2= 7 cm3/min (corresponding with the maximum nitriding
potential P = 3.85 × 10−2 Pa−0.5). Reduction processes of the
obtained nanocrystalline nitrides of iron were performed
starting from the hydrogen flow, at which their preceding
nanocrystalline iron nitriding processes were completed, i.e.,
from V̇ 0rH2 = 7 cm3/min to a value of V̇ H2 = 136 cm3/min, for
which the nitriding potential was P = 0.06 × 10−2 Pa−0.5. For
these processes, Figure 3 shows the relationship between the
nitriding potential of a gas mixture and the nitriding degree of
sample versus time of the process at different βH2.
For the performed cycles of nitriding processes of nanocrystalline iron and reduction of the obtained nanocrystalline
iron nitrides the dependence of the nitriding degree on the
nitriding potential was developed, which is shown in Figure 4.
ra = kaα(t , CMD)[P(t ) − P0a(α)]
(5)
In an analogous manner, one can describe rates of the
reduction process
rr = k rα(t , CMD)[P(t ) − P0r(α)]
(6)
where a and r refer to the nitriding and reduction process,
respectively; k is the reaction rate constant; P(t) is the nitriding
potential changing according to predefined dependence; P0a
and P0r are the nitriding potential in equilibrium states; and P0
= f(α) where α = f(CSD). For a single crystallite,
Sact, i
mi
= const
and P0 = const where Sact,i is the active surface area of the ith
nanocrystallite and mi is the ith nanocrystallite’s mass.
In previously conducted processes of nanocrystalline iron
nitriding and reduction of nanocrystalline iron nitrides in the
states of equilibrium, in which P(t) = P0(α), the rates of
nitriding of nanocrystalline iron or reduction of the obtained
nanocrystalline iron nitrides were zero.
Based on the dependence of the nitriding degree on the
process time, the rates of reduction and nitriding process were
determined. Nitriding rates are presented as functions of the
nitriding degree in Figure 5a and those of the natural logarithm
of the nitriding potential in Figure 6a. Figures 5b and 6b,
respectively, present dependences of the reduction process
rates on the nitriding degree and on the natural logarithm of
the nitriding potential. By arrows the directions of the processes
were marked.
Figure 3. Dependence of the nitriding potential of gas mixture
(dashed line) and of the nitriding degree of sample (solid line) versus
time for nitriding of nanocrystalline iron and reduction of the obtained
nanocrystalline iron nitrides at 350 °C.
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Figure 5. Dependence of (a) the nitriding process rate and (b) the reduction process rate on the nitriding degree for the processes conducted at
different hydrogen flow accelerations
Figure 6. Dependence of (a) the nitriding process rate and (b) the reduction process rate on the natural logarithm of the nitriding potential for the
processes carried out at different hydrogen flow accelerations.
Figure 7. Dependence of hydrogen flow accelerations, βH2, on the nitriding potential for two maximum values of nitriding degree observed during
(a) nitriding process and (b) reduction process.
higher value, the greater step βH2 is applied, so the chemical
reaction will be faster as well. For the process carried out in
stationary states (βH2 = 0), the rates of nitriding and reduction
are zero because the value of P in eqs 5 and 6 are equal to P0.
Based on the determined dependences of the process rate on
the βH2 parameter value one can evaluate how far the process
conducted with a specific change in nitriding potential differs at
a given moment from the process carried out in stationary
conditions.
For maxima of the dependence of the nitriding and reduction
process rate for processes carried out with different hydrogen
flow acceleration on the nitriding degree the dependence of the
hydrogen flow acceleration on the nitriding potential is shown
in Figure 7. The minimum nitriding potential, required to
complete the conversion of iron nanocrystallites saturated with
For the conducted processes of nitriding of nanocrystalline
iron and reduction of the obtained nitride γ′-Fe4N a similar,
bimodal pattern of changes in the rate of chemical reactions as a
function of the nitriding degree was observed (the same
number of peaks occurring and similar values of the nitriding
degree corresponding to the maximum rate). The observed
maxima of the reaction rate correspond to the phase transition
of a fraction of nanocrystallites most abundant in the sample.
Nitriding and reduction rate depend on βH2 with which the
process was conducted. The higher the βH2 parameter value, the
higher reaction rates corresponding to different nitriding
degrees.
At a constant process temperature (k = const) and at a given
nitriding degree (
Sac, i
mi
= const), the expression (P − P0) has the
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Figure 8. Crystallite mass distribution determined using reaction rate data for (a) nitriding and (b) reduction processes carried out at different
hydrogen flow accelerations
Figure 9. Crystallite size distributions determined using reaction rate data for (a) nitriding and (b) reduction processes carried out at different
hydrogen flow acceleration rates. For comparison, the results obtained using Pielaszek’s method44 were added.
nitrogen, α-Fe(N), having a size corresponding to a specific
nitriding degree (in this case there are crystallites of sizes
prevailing in the test samples) to the phase of iron nitride γ′Fe4N, was extrapolated. The maxima for the dependence of the
nitriding and reduction process rate for processes carried out
with different hydrogen flow acceleration shown in Figure 5 are
present at a specific nitriding degree. A similar dependence as
shown in Figure 7 can be determined for any value of the
nitriding degree.
On the basis of the presented dependences of the rates of
nitriding and reduction processes carried out in conditions
close to the stationary ones, nanocrystallite mass distributions
(CMD) for single-stage phase transition α-Fe(N) → γ′-Fe4N
and γ′-Fe4N → α-Fe(N) were determined using a method
described elsewhere28 (Figure 8). The nitriding degree, XN/XFe
[mol/mol], as the conversion degree, α [mol/mol], of the
phase α-Fe(N) to γ′-Fe4N was presented on the x-axis. The
conversion degree is defined as a ratio of mass of nitrogen in
iron at a given moment of reaction to the nitrogen mass in γ′Fe4N.
The symmetry of the above plots leads to a very interesting
conclusion. During reduction of iron nitrides under conditions
close to equilibrium nanocrystalllites undergo a phase transition
in the order of their size from the biggest to the smallest. The
same order was previously observed during the nitriding
reaction. However, as far as reduction is considered, that was
the first time such a phenomenon was observed.
Using CMD plots for transitions taking place in both
directions the CSD for each of the processes carried out with
different hydrogen flow acceleration was determined. Ratios of
individual fractions were chosen so that the area under the
CMD = f(α) curve was equal to unity. On the basis of previous
studies on nitriding of nanocrystalline iron catalyst by means of
XRD, it was assumed that nanocrystallite size range was 20−
100 nm and a shape factor, Sact,i/(mi ρ−1), as for the sphere.
With the selected range of diameters of crystallites the mean
crystallite size calculated based on the obtained CSD is equal to
the average diameter obtained by XRD. The obtained CSDs are
shown in Figure 9 together with CSDs obtained using
Pielaszek’s method.44
For all the processes carried out with continuously variable
nitriding potential by constant variation of the hydrogen flow
with varying acceleration βH2 bimodal distributions of
crystallites were observed. These distributions were observed
regardless of the phase transformation direction in a region of
α-Fe(N) and γ′-Fe4N. Increasing the hydrogen flow acceleration in the nitriding mixture during the conducted process
resulted in reduced accuracy of the resulting size distribution of
crystallites present in the system. Determination of the
crystallite size distribution with maximum accuracy is possible
in the case of processes performed in the equilibrium states.
Processes carried out at low βH2 values make it possible to
obtain approximate information on the shape of distribution in
a shorter time compared to the processes in stationary states.
As presented in Figure 9, results obtained by XRD Pielaszek’s
method do not show the real structure of the studied iron
catalyst, since the maximum no. 2 is not detected.
Nowadays, a better understanding of the structure and
properties of catalysts containing nanoparticles as active species
is a key factor in many industries. Size distribution of
nanoparticles can be measured by, e.g., electron microscopies
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(SEM, TEM, STM)48 and atomic force microscopy. The
measurement is performed directly by measuring the length of
nanoparticle. It is also possible to determine the shape of the
observed objects. However, these techniques require a lot of
grains to be observed and analyzed due to inhomogeneity of
nanomaterials.17 Apart from that, it can be difficult to
distinguish borders inside the agglomerates of nanoparticles
and, therefore, the analysis by means of microscopies may be
sometimes sort of subjective. Using techniques based on gas
sorption measurements49 we obtain information related to the
surface area of the whole solid sample. However, agglomerates
and single particles are not distinguished which may lead to
incorrect information about the solid structure. Methods based
on X-ray diffraction can be applied to characterize the whole
sample of nanocrystalline substances. Generally, XRD-based
methods are related to the volume of a crystallite. One of these
methods uses the Scherrer’s equation for determining the
average size of nanocrystallites. The Rietveld method,50
originating from Hall method, enables us to determine the
average crystallite size together with lattice strains. To
determine size distributions of nanocrystallites, the whole
diffraction line profile has to be analyzed.44,51−54 As an example,
Pielaszek44 presented a method for determining the nanocrystallite size distribution which is a modification of classical
methods for determining the mean size of crystallites. Other
XRD-based techniques for determination the crystallite size
distribution are the Warren−Averbach method or the method
proposed by Vogel.55
The most important feature of the proposed in this paper
method is that it is a chemical method in which the whole solid
sample can be analyzed. In this method, a response of a
chemical system to changes in chemical potential of a gas phase
is studied. The phenomenon that nanocrystallites of a certain
Sact/V ratio undergo a phase transition at the specific chemical
potential of a gas phase is used, assuming that the chemical
composition of the surface of each nanocrystallite is the same.
This means that the obtained CSD is related to active surface
area. Active surface is a very important parameter when dealing
with processes occurring on the surface of catalytic nanomaterials. However, this method also has some limitations. One of
them is the requirement to operate in the close-to-equilibrium
state. To show how far we can be from equilibrium let us
consider the following examples. In the region of classical
kinetics where P(t) ≫ P0(α), every nanocrystallite may react
and undergo the phase transition. We can, of course, assess the
shape of GSD under kinetics conditions,56 but the obtained
result might not be accurate. On this end, we are maximally far
away from equilibrium. At the opposite end, where P(t) =
P0(α) we deal with real equilibrium. This state, however, can be
difficult to achieve. But the results obtained in equilibrium
states are the most accurate. Therefore, we propose the CPPR
method which operates in an intermediate region, viz. where
P(t) changes in some vicinity of P0(α). The closer the
equilibrium we operate the better. When the distance between
P(t) and P0(α) is increased the accuracy of the method
decreases because we approach the kinetic region (Figure 9).
The second limitation is connected with β parameter. Namely,
the proposed method requires a phase transition to occur. It
means that value of β must change in such a way to allow the
phase transition. If there are several phase transition then mass
increments (reaction rate in the solid phase: Figure 5, the
nitriding reaction rate changes from 0 at the beginning to 0 at
the end of the chemical reaction) should be zero between one
and another crystallographic phase.
Each technique uses different assumptions which results in
differences between e.g. “volumetric” and “surface” methods.
Agglomerates of small crystallites in the “surface” method can
be treated as one large “crystallite”. In turn, XRD-based
methods use a sometimes very complicated mathematical
apparatus and assume a rather unimodal distribution of
particles. This is, however, correct only for some cases, because
many times one deals with substances that are characterized by
bi- or trimodal distributions.17,35,56,57 An example of such a
substance is iron ammonia synthesis catalyst (Figure 9).
Therefore, results obtained by means of different methods
should not be strictly compared with each other, because this
can lead to different conclusions.
■
CONCLUSIONS
By using the CPPR method it was possible to conduct kinetic
studies in states close to chemical equilibrium. Several
accelerations of nitriding potential change have been applied
during investigations of the nitriding process of nanocrystalline
iron α-Fe(N) to iron nitride γ′-Fe4N and reduction of the
obtained iron nitride. Critical nitriding potentials, at which
phase transformations of nanocrystallites of a certain size occur
in the above-mentioned reactions, have been determined.
Furthermore, hysteresis phenomenon for a dependence of the
iron nitriding degree on nitriding potential has been confirmed.
Iron nanocrystallite size distribution in the iron ammonia
synthesis catalyst has been determined and it occurred to be
bimodal. Accuracy of size distribution measurement depended
on nitriding potential change accelerations. In comparison to
other known methods of determining size distributions, the
proposed method is based on the relation of the active surface
to the mass (volume) of a nanocrystallite. It is advantageous
since it enables studying elementary processes due to
connection of measured values with surface phenomena. It
was also discovered that during both the nitriding and
reduction of iron nitrides nanocrystallites underwent phase
transition in their entire volume in the order of their sizes from
the largest to the smallest. All of the results were obtained in a
significantly shorter period of time in comparison to the case
when processes would be carried out under conditions of
equilibrium state.
■
AUTHOR INFORMATION
Corresponding Author
*Tel: +48 91 449 47 30. Fax: +48 91 449 46 86. E-mail:
rpelka@zut.edu.pl.
ORCID
Rafał Pelka: 0000-0002-0896-8839
Author Contributions
The manuscript was written through contributions of all
authors. All authors have given approval to the final version of
the manuscript.
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
The scientific work was financed by The National Centre for
Research and Development, program ‘Lider’, Project No.
LIDER/025/489/L-5/13/NCBR/2014.
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