Understanding Solid-State Phase-Formation Processes by Using the High-Temperature Gas Balance: The Example of Zr2PTe2

Article abstract of DOI:10.1002/ejic.201900281

Inorganic solid-state synthesis with phosphorus and tellurium requires a careful control of the reaction parameters because of the high volatility of the components. This initial disadvantage can be used as a benefit for the investigation of phase-formation mechanisms by analyzing the individual vapor pressure behavior. The high-temperature gas balance is introduced as a device for detection of heterogeneous solid-gas equilibria in closed reaction systems. The experimentally challenging synthesis of the phosphide telluride Zr₂PTe₂ is examined as a model system: optimized synthesis runs at lower temperatures (? = 650 °C) in a faster time, while the quantity as well as the crystalline powder quality is increased. A stepwise solid-solid reaction of zirconium and tellurium according to Ostwald's rule of stages and the shrinking core model is revealed while phosphorus sublimes and subsequently condenses to react to the ternary compound. Additional phenomena such as melting, expansion, and mechanical instabilities can be observed that broaden the possibilities of the gas balance.

Full text of DOI:10.1002/ejic.201900281

A Journal of
Accepted Article
Title: Understanding Solid-State Phase-Formation Processes by Using
the High-Temperature Gas-Balance: The Example of Zr2PTe2
Authors: Tanja Scholz, Michael Schöneich, and Peer Schmidt
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To be cited as: Eur. J. Inorg. Chem. 10.1002/ejic.201900281
Link to VoR: http://dx.doi.org/10.1002/ejic.201900281

10.1002/ejic.201900281
European Journal of Inorganic Chemistry
FULL PAPER
Understanding Solid-State Phase-Formation Processes by Using
the High-Temperature Gas-Balance: The Example of Zr2PTe2
Tanja Scholz[b], Michael Schöneich[b], and Peer Schmidt*[a]
Abstract: Inorganic solid state synthesis with phosphorus and
tellurium require a careful control of the reaction parameters because
of the high volatility of the components. This initial disadvantage can
be used as a benefit for investigation of phase formation mechanism
by analyzing the individual vapor pressure behavior. The high-
temperature gas-balance is introduced as a device for detection of
heterogeneous solid–gas equilibria in closed reaction systems. The
experimentally challenging synthesis of the phosphide telluride
Zr2PTe2 is examined as a model system: optimized synthesis runs at
lower temperatures ( = 650 °C) in a faster time, while the quantity as
well as the crystalline powder quality is increased. A stepwise solid-
solid reaction of zirconium and tellurium according to Ostwald’s rule
of stages and the shrinking core model is revealed while phosphorus
sublimes and subsequently condensates to react to the ternary
compound. Additional phenomena such as melting, expansion, and
mechanical instabilities can be observed that broaden the possibilities
of the gas-balance.
components since these are lost by vaporization in open
environments. To overcome this issue, a different approach is
used by the high-temperature gas-balance (HTGB): The vapor
phase is enclosed in a silica glass ampoule and thus forms an
equilibrium gas phase in permanent contact with the solid phase
(elements, mixtures of reaction educts, desired and intermediate
products). The HTGB is a device to directly measure this gas
phase. In the closed chemical system, mass effects are caused
by a change of the leverage in a horizontal balance setup. In case
of an evaporation, decomposition, or condensation, the shift of the
center of gravity of the solid (placed on one side of the ampoule)
and the vapor (distributed over the total length of the ampoule)
changes the bearing-strength, so that we can measure a signal
(Δm) on the electronic balance. The concept of the HTGB is
introduced in detail in ref. [11-12], and a discussion on the potential
for analyzing phase formations is presented in ref. [12-13]. Thus, the
HTGB proves to be one of most suitable methods to analyze
phase formations with highly volatile components such as P, As,
S, Se, Te, Br, and I without mass loss to the ambient area. Due
to containment all reactants, the HTGB allows to gain an insight
into chemical reaction pathways that include several evaporation
Introduction
and condensation steps. This way, running over
a wide
While many ternary inorganic compounds with combined pnictide
and chalcogenide anions exist,[1-4] only three examples of ternary
phosphide tellurides are known and their direct solid-state
synthesis seems to be extremely challenging. The strict control of
the temperature program and, therefore, of the vapor pressure of
the components was described as a prerequisite for a successful
phase-pure synthesis. Small temperature ranges are mostly used
to achieve the kinetic conditions for the phase formation and to
avoid thermal decomposition of the targeted phase. The only
ternary systems that contain isolated phosphide and telluride
anions are U/P/Te (UPTe),[5] Ti/P/Te (Ti2PTe2),[6-7] and Zr/P/Te
(Zr2PTe2, Zr2+xPTe2, Zr2PTe)[8-10]. With this in mind, their phase
formations should be investigated by analyzing the temperature
as well as the temperature dependent vapor pressure while
synthesis. In this way, a general approach for syntheses of
multinary compounds containing volatile components is aimed.
In thermal analysis, several methods are established to
investigate phase formations, phase transitions, and
decomposition reactions. Unfortunately, conventional techniques
reach their limit when analyzing chemical systems with volatile
temperature range (up to 1100 °C), formation of multiple solid–
gas equilibria with constantly changing compositions of the solid
can be observed. In contrast to common synthesis approaches,
here a straightforward screening of optimal reaction conditions is
enabled.
In this project, we have picked the compound Zr2PTe2 as a
chemical system with multiple volatile compounds.[8, 10] Already
the educts, elemental phosphorus and tellurium, sublime at
temperatures of about 500 °C with p(i) > 10–3 bar. Because of this,
the first published synthesis of Zr2PTe2 is quite challenging: The
compound is synthesized from a mixture of the elements in small
silica glass ampoules at high temperatures of 800 °C. Owing to
slow heating and cooling rates, this reaction takes several
weeks.[8] Hence, the goal is pursued to understand the phase
formation of Zr2PTe2, to precisely derive the reaction conditions,
and to evaluate the HTGB method in this complex system.
Results and Discussion
Investigation of solid–gas equilibria with the HTGB during the
phase formation of Zr2PTe2
[a]
Prof. Dr. Peer Schmidt,
Faculty Environment and Natural Sciences, Chair of Inorganic
Chemistry, Brandenburg University of Technology Cottbus—
Senftenberg,
Universitätsplatz 1, 01968 Senftenberg, Germany
Fax: +49-3573-85-809
Zr2PTe2 was first synthesized from a mixture of the elements.[8]
To investigate the phase formation with the HTGB, we therefore
determined the temperature–vapor pressure curve for this
E-mail: peer.schmidt@b-tu.de
reaction up to
a
temperature of 950 °C. The raw
Homepage: https://www.b-tu.de/en/inorganic-chemistry
Dr. Tanja Scholz, Dr. Michael Schöneich, Department of Inorganic
Chemistry, Dresden University of Technology, 01062 Dresden,
Germany
thermogravimetric signal of the HTGB measurement is a mass
difference Δm, that can be transformed into a vapor pressure with
the ideal gas law when assuming phosphorus as P4(g)
[b]
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10.1002/ejic.201900281
European Journal of Inorganic Chemistry
FULL PAPER
(M = 123.90 g·mol–1) as the major gas species.[11] Figure 1
presents both the temperature–mass and the temperature–
pressure curve for the solid-state synthesis of Zr2PTe2.
minimum at about 500 °C. Within range (III), gaseous phosphorus
condensates into the solid to form a new phase in a monotropic
way. During the condensation, the pressure never reaches the
base line of the measurement again because it overlaps with
another increase in pressure that is visible in range (IV). At first
sight, the increase in pressure from about 500 °C is unexpected
because of its linear progression instead of an exponential curve
of a sublimation process. It can be assigned neither to the
sublimation of tellurium nor to an equilibrium pressures of other
binary compounds in the ternary system. Above 600 °C (range
(V)), the progression of the vapor pressure curve changes again
and is characterized by extreme fluctuations. Those can only be
observed in an experiment where the sample has an undefined
center of gravity in the silica ampoule. After cooling the product to
room temperature, X-ray diffraction confirmed the formation of the
phase Zr2PTe2 with smallest amounts of ZrTe2. Therefore, the
plotted vapor pressure curve shows indeed the phase formation
of Zr2PTe2 from the elements, even though not all the ranges
during the heating process can be understood at first sight. In the
next experiments, the focus was on the sublimation of phosphorus
(range (II)) and the linear pressure curve from 500 °C (range (IV)).
The sublimation and the subsequent condensation of phosphorus
from 350 to 500 °C (range (II) and (III)) dominate the vapor
pressure curve of the phase formation of Zr2PTe2. It can be
assumed that phosphorus reacts exclusively as gaseous species
in a solid–gas reaction. To verify this, we determined the vapor
pressure curve of the same starting composition whereas
phosphorus is physically separated from mixed zirconium and
tellurium that are positioned in an inner silica crucible (Fig. 2,
curve B). The curve matches the curve determined for the non-
separated educts except for a rapid increase at exactly 447 °C. In
further experiments, we found that this increase is related to the
melting of tellurium. The melting point at standard conditions is
450 °C[14] which fits perfectly to our experimental results. The
melting phenomenon leads to a change in the center of gravity in
the inner silica crucible and results in a shifted mass signal (and,
therefore, appears as a pressure increase artefact). Due to the
separation of phosphorus, the adhesion in the mixture of
zirconium and tellurium is not sufficient enough to maintain the
balanced set-up. Despite the visible melting of tellurium, the vapor
pressure curve does not show additional features. The product of
this experiment is again Zr2PTe2 with the smallest amount of
ZrTe2 as identified by X-ray diffraction. Therefore, we conclude
that phosphorus exclusively reacts via the gas phase.
Figure 1. Mass (top) and vapor pressure (bottom) curve of the phase formation
of Zr2PTe2 from a stoichiometric mixture of the elements (black) based on HTGB
measurements in comparison with the theoretical equilibrium pressures of Pred
(red), Pviolet (violet), Pblack (black) and liquid Te (gray).
The uneven curve up to 300 °C is characteristic for
measurements containing phosphorus and can be explained by
the sublimation of the smallest amounts of contaminants (e.g.
some white phosphorus; range (I)). The first increase in pressure
The linear pressure increase in range (IV) disagrees with
exponential curves of evaporation processes. We determined
another vapor pressure curve applying similar conditions up to
500 °C but included a subsequent isothermal treatment (Fig. 2,
curve C). This curve is inevitably identical up to 500 °C compared
to the phase formation of Zr2PTe2 discussed above (see also
Fig. 2, curve A). With the beginning of the tempering, the
condensation of gaseous phosphorus proceeds even further. But
again, the pressure does not reach the base line – the
condensation is soon overlapped by an almost linear pressure
increase. This confirms that the course of the linear increase in
range (IV) is not related to a temperature dependent equilibrium
vapor pressure of any compound.
starts at about 350 °C (range (II)) and fits very well to the
[14]
theoretical vapor pressure curve of amorphous Pred
.
From
425 °C, the experimental pressure deviates from the theoretical
curve. This drift indicates a change in the solid–gas equilibrium
and, therefore, a phase transition in the solid. In this system, only
the phase transition from Pred via semicrystalline phosphorus to
other allotropes, Pviolet and Pblack
, matches the transition
temperature. The literature reports this transition at about 450 °C
[15-16]
where it also occurs in DSC measurements of Pred
.
The
pressure reaches a plateau at 475 °C and decreases until a
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10.1002/ejic.201900281
European Journal of Inorganic Chemistry
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(IV)) as well as the extreme fluctuations above 600 °C (range (V))
are not related to the ternary phase.
As mentioned before, these abnormalities in ranges (IV) and (V)
are not due to events under equilibrium conditions and are,
therefore, of a kinetic origin. To glimpse into the system, we
monitored the reaction in a transparent two zone furnace (Fig. 3).
The same reaction conditions have been used as in the
isothermal HTGB experiment (cf. Fig. 2, curve C). Starting at
380 °C, a color change from metallic-gray to black and a
continuous expansion of the solid (exceeding the original volume
multiple times!) became visible. The color change indicates a
solid–solid reaction that happens even before the condensation
of gaseous phosphorus and the phase formation of Zr2PTe2. The
other phenomenon, the enormous expansion, can be related
directly to the HTGB’s mass pressure curve (and, falsely, to the
vapor pressure). Every expansion, in this case a continuous one,
results in a shift of the center of gravity in the solid. Usually, every
shift of the mass in the ampoule from the origin is then assigned
to a “linear” vapor pressure increase in range (IV) dominating the
phase diagram and overlapping actual solid–gas equilibria. The
expanded solid forms fine crumbs with a loose structure that leads
to extreme fluctuations in the vapor pressure curve due to an
undefined center of gravity in the silica ampoule (range (V)).
At this point, we have a good understanding about the phase
formation of Zr2PTe2. Four vapor pressure curves led us to the
result that
– except for the sublimation and subsequent
condensation of phosphorus – no other solid–gas equilibria play
a role: There are no complications during the phase formation due
to constantly changing compositions of the solid. Furthermore, we
observed a feature of the HTGB device – the shift of the center of
gravity not due to a heterogeneous equilibrium reaction but due
to melting, expansion, and mechanical instabilities of the solid –
that could limit the method if not pay special attention to.
Figure 2. Mass (top) and vapor pressure (bottom) curve of the phase formation
of Zr2PTe2 based on HTGB measurements (A/black) from a stoichiometric
mixture of the elements in comparison with (B/blue) separated educts, namely,
phosphorus separated from a mixture of zirconium and tellurium, and (C/green)
an elemental mixture under isothermal conditions (500 °C). The curve (D/gray)
shows the vapor pressure of the product Zr2PTe2 with no visible equilibrium
pressure up to 950 °C. The theoretical equilibrium pressures of Pred (red), Pviolet
(violet), and Pblack (black) are shown for comparison.
Figure 3. Expansion during the phase formation of Zr2PTe2 from the elements
at the moment of (A) no visible reaction at 250 °C, (B) the first visible expansion
and change in color at 380 °C, (C) at the maximum temperature of 490 °C, and
(D) after 24 hours at 490 °C.
Investigation of solid–solid reactions during the phase formation
of Zr2PTe2
In the isothermal measurement, the linear increase proceeds with
a lower rate indicating a process under kinetic (non-equilibrium)
conditions. X-ray diffraction of the product reveals again Zr2PTe2
with the smallest amount of another zirconium telluride, ZrTe3.
This isothermal measurement proves that the phase formation of
Zr2PTe2 correlates with the condensation of P into the solid from
475 to 500 °C. Hence the high temperatures of about 800 °C that
were used in the original synthesis of the ternary compound are
not necessary.[8] To finalize our investigations with the HTGB, we
determined the vapor pressure of the target phase Zr2PTe2 itself
(Fig. 2, curve D). No equilibrium vapor pressure is observed up to
950 °C. That proves that the pressure increases at 500 °C (range
As shown with the HTGB experiments, solid–gas equilibria are a
factor in the phase formation of Zr2PTe2, but solid–solid reactions
take place before the formation of the ternary compound. To
investigate these intermediate solid–solid reactions, we simulated
the reacting starting from the stoichiometric mixture of the
elements (2 Zr + P + 2 Te) as well as the binary boundary
compositions (2 Zr + 2 Te) and (2 Zr + P) and analyzed the
crystalline reaction intermediates quenched at different
temperatures by XRPD (Tab. 1).
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These peritectic temperatures are above the ones we observed
in our experiment so that the stepwise conversion can only be
interpreted by Ostwald’s rule. Furthermore, the shrinking core
model provides an explanation for the expansion of the solid
during the reaction because porous layers of zirconium tellurides
form in a diffusion process from the outside to the inside of the
original metallic zirconium. In order to substantiate this statement,
the first conversion to ZrTe5 (below 400 °C, cf. Tab. 1) goes hand
in hand with the obvious change in color and the beginning of the
expansion of the solid (380 °C, cf. Fig. 3).
To come back to the phase formation of Zr2PTe2, we now know
that phosphorus condensates at temperatures from 475 to 500 °C
into ZrTe3 as the solid. The peritectic transition from residual
monoclinic ZrTe3 to hexagonal ZrTe2 at about 630 °C introduces
a significant change in structure so that the ternary phase
formation overcomes final kinetic inhibitions and the reaction
results in a product of phase-pure quality.
Table 1. Reaction products analyzed by XRPD resulting from different
mixtures of elements depending on the quenching temperature; (minor
crystalline phases in parenthesis, amorphous constituents not determined).
Temperature
400 °C
Initial mixture:
2 Zr + P + 2 Te
Initial mixture:
2 Zr + 2 Te
Initial mixture:
2 Zr + P
ZrTe5
ZrTe5
(Te)
Zr
(ZrTe3, Zr, P,
(Pwhite)
Pwhite
)
ZrTe3
ZrTe3
Zr
500 °C
600 °C
(ZrTe5, Pwhite
)
(Te)
(Pwhite
)
Zr2PTe2
ZrTe3, ZrTe2
Zr
(ZrTe3)
(ZrP, Pwhite
)
Zr2PTe2
ZrTe2
Zr
(ZrP, ZrP2,
700 °C
Pwhite
)
In case of the ternary mixture, the first solid–solid reaction starts
already at 400 °C with the formation of the binary zirconium
tellurides ZrTe5 and ZrTe3 in consecutive steps. The
condensation of phosphorus leads then to the ternary compound.
In this approach, the reaction is under non-equilibrium conditions,
therefore, the ternary compound was evidenced not until 600 °C
instead of 500 °C deduced from the HTGB experiments.
Investigations regarding the binary boundary composition
(2 Zr + 2 Te) showed the same order of zirconium tellurides with
an additional step to ZrTe2 at 700 °C. In contrast, our experiments
with the binary boundary composition (2 Zr + P) suggest the
formation of zirconium phosphides only at high temperatures
(above 700 °C) so that they are not relevant in the phase
formation reaction of Zr2PTe2. A literature report on ZrP[17]
supports our findings by describing the reaction from the elements
below 650 °C as very slow and identifying 800 °C as an optimal
reaction temperature.
The formation of the zirconium tellurides follows the rule of stages
postulated by Ostwald in 1897.[18] That describes the
crystallization as a reaction of an unstable system not directly to
the lowest free-energy state under the given conditions but rather
along the fastest path of several metastable phases with
decreasing Gibbs free energies and small transition energy
barriers. Since the Gibbs free energy of a state corresponds to
the vapor pressure of a compound, elemental tellurium exhibits
the highest free energy due to the highest sublimation pressure in
the binary system Zr–Te followed by the binary compounds with
increasing Zr/Te ratio. To induce a phase change, a sublimation
pressure of tellurium in the order of 10–5 to 10–4 bar is sufficient to
reach the necessary diffusivity. The solution of tellurium in
elemental zirconium is quite small, and the formation of ZrTe5 on
the zirconium surface is the first step according to Ostwald’s rule
of stages. The following conversions apply also the shrinking core
model. With increasing temperature, ZrTe5 converts to ZrTe3 and
ZrTe2 in a stepwise and inward layered fashion. At this point it
shall be noted that binary zirconium tellurides are also formed in
the same order by peritectic transformations:[19]
Figure 4. With increasing temperature, zirconium and tellurium form ZrTe5 that
converts then to ZrTe3 and further to ZrTe2 following the Oswald’s rule of stages
and the shrinking core model (top to bottom).[20-21] In the presents of phosphorus,
Zr2PTe2 is formed from ZrTe3 (rightwards) at elevated temperature.[8]
Zr + Te →
ZrTe5 →505 °C ZrTe3 →630 °C ZrTe2
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10.1002/ejic.201900281
European Journal of Inorganic Chemistry
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Synthesis optimization of Zr2PTe2
mechanical instabilities. If they are taken into account, when
interpreting a vapor pressure curve, they do not limit the high-
temperature gas-balance method.
With the understanding of the solid–gas and solid–solid reactions,
the synthesis of Zr2PTe2 can now be improved: A stoichiometric
mixture of zirconium, phosphorus, and tellurium can be heated up
quickly to a temperature below the sublimation of P (for example
within 2 hours to 250 °C). Afterwards the sample will be heated
with 10 K·h–1 to 650 °C, a temperature 50 K above the “linear”
vapor pressure curve corresponding to the complete expansion of
the solid. This temperature should be held for 48 hours to
homogenize the porous solid. Then, the reaction can be
quenched due to the marginal equilibrium vapor pressure of
Zr2PTe2 resulting in the target compound in phase-pure quality as
evidenced by XRPD (Fig. 4).
Experimental Section
The measurements on the HTGB were performed using the balance
design described in ref. [11-12]. Handmade silica glass ampoules with a
length of about 11 cm and a volume of 16 mL were filled with 1 g of well-
mixed stoichiometric amounts of the elements or Zr2PTe2, evacuated and
sealed under dynamic vacuum (p ≤ 10–5 bar). The elements used are Zr
powder (freshly filed from a rod, ChemPur, 99.8%), red amorphous P
(Aldrich, 99%, purified according to ref. [22]) and Te (Acros, 99.8%, distilled
and reduced in a H2 gas flow). Since some starting materials and Zr2PTe2
are sensitive to air and humidity, all reagents were handled in an argon-
filled glove box (p(H2O, O2)/p0 < 1 ppm, Fa. M. Braun, LAB 130). Prior to
use, the adherent moisture in silica glass ampoules was removed by
heating under dynamic vacuum. The reaction ampoule was positioned at
the end of a lever of the horizontal balance assembly, which is located
inside a two-zone furnace. The ampoule was heated with 10 K·h–1 to a
temperature of 950 °C. According to the lever rule and applying corrections
concerning thermal expansion and buoyancy, the measured difference in
mass is related to a shift of the mass of the gas phase. With the ideal gas
law and assuming P4(g) (M = 123.90 g·mol–1) as major gas species, the
characteristic temperature–vapor pressure curves resulted.
Powder X-ray diffraction pattern of the solid products were collected with
a PANalytical X’Pert Pro diffractometer using CuK-radiation and a
Ge(220) hybrid monochromator. The samples were enclosed in silica
capillaries with a diameter of 0.3 mm and were measured in transmission
mode with a scan range from 10 to 90° 2 and a step size of 0.05° 2.
Figure 5. X-ray powder pattern (CuK) of Zr2PTe2 synthesized from the
elements compared with the theoretical diffraction pattern.
Acknowledgments
The authors gratefully acknowledge the financial support by the
Priority program (Schwerpunktprogramm) 1415 of the German
research funding organization (Deutsche Forschungs-
gemeinschaft - DFG). The high-temperature materials and
Conclusions
By application of high-temperature gas-balance and supporting
experiments, the detailed description of phase formation of
Zr2PTe2 was successful. Zirconium and tellurium react in a solid–
solid reaction according to Ostwald’s rule of stages and the
shrinking core model while phosphorus sublimes and
subsequently condensates to react to the ternary compound. This
insight enables rational planning and optimization of the synthesis
of Zr2PTe2 in terms of quality, amount, and time. While the first
published synthesis was challenging, assuming a small gas
volume in the silica ampoule to prevent the solid composition from
changes due to solid–gas equilibria, this now seems to deteriorate
the phase purity due to the enormous expansion during the
reaction. Furthermore, high temperatures up to 800 °C are not
necessary and even result in side phases.
furnaces
specialist
HTM
Reetz
(http://www.htm-
reetz.de/en/index.asp) is gratefully acknowledged for the
technical support in construction and optimization of the high-
temperature gas-balance.
Keywords: Phase Transition / Phase Diagram / Thermal
Analysis / Phosphide Tellurides / Ostwald’s Rule of Stages /
Shrinking Core Model
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10.1002/ejic.201900281
European Journal of Inorganic Chemistry
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The high-temperature gas-balance is
a powerful method to gain insight into
solid–gas equilibria during chemical
reactions. We examined individual
steps of the phase formation of
Zr2PTe2 and derived the optimal
reaction conditions. Besides the
sublimation and condensation of
phosphorus, Ostwald’s rule of stages
and the shrinking core model play an
important role in the solid.
Key Topic: Synthesis control
Tanja Scholz, Michael Schöneich, Peer
Schmidt
Page No. – Page No.
Title:
Understanding Solid-State Phase-
Formation Processes by Using the
High-Temperature Gas-Balance: The
Example of Zr2PTe2
This article is protected by copyright. All rights reserved.