The ZrB2 volatility diagram

Article abstract of DOI:10.1111/j.1551-2916.2005.00599.x

A volatility diagram was calculated for temperatures of 1000, 1800, and 2500 K to understand the oxidation of ZrB₂. Applying the diagram, it can be seen that exposure of ZrB₂ to air produces ZrO₂ (cr) and B₂O₃ (l) over the temperature range considered. The pressure of the predominant vapor species was predicted to increase from ～10^-6 Pa at 1000 K, to 344 Pa at 1800 K, and to ～10 ⁵ Pa at 2500 K. Predictions were consistent with experimental observations that ZrB₂ exhibits passive oxidation below 1200 K, but undergoes active oxidation at higher temperatures due to B₂O ₃ (l) evaporation.

Full text of DOI:10.1111/j.1551-2916.2005.00599.x

J. Am. Ceram. Soc., 88 [12] 3509–3512 (2005)
DOI: 10.1111/j.1551-2916.2005.00599.x
r 2005 The American Ceramic Society
ournal
J
The ZrB2 Volatility Diagram
William G. Fahrenholtz*,w
Materials Science and Engineering, University of Missouri-Rolla, Rolla, Missouri 65409
A volatility diagram was calculated for temperatures of 1000,
1800, and 2500 K to understand the oxidation of ZrB2. Applying
the diagram, it can be seen that exposure of ZrB2 to air pro-
duces ZrO2 (cr) and B2O3 (l) over the temperature range con-
sidered. The pressure of the pꢀre6dominant vapor species was
predicted to increase from B10 Pa at 1000 K, to 344 Pa at
1800 K, and to B105 Pa at 2500 K. Predictions were consistent
with experimental observations that ZrB2 exhibits passive oxi-
dation below 1200 K, but undergoes active oxidation at higher
temperatures due to B2O3 (l) evaporation.
II. Calculations and Diagram Construction
Several thermodynamic databases were examined to identify
relevant species containing Zr, B, and/or O, but only data from
the NIST-JANAF tables were used to maximize consistency.20
After eliminating ionized species, duplicate data, and condensed
species that were not observed in oxidized specimens, 13 species
of interest were identified (Table I). Based on oxidation studies
reviewed in the introduction, the oxidation of ZrB2 (cr) to ZrO2
(cr) and B2O3 (l) by Eq. (1) was used to determine the equilib-
rium partial pressure of oxygen (pO2) for oxidation of ZrB2.
5
2
ZrB2 ðcrÞ þ O2 ðgÞ ! ZrO2 ðcrÞ þ B2O3 ðlÞ
(1)
I. Introduction
Tabulated data were used to calculate the change in Gibbs’ free
energy (DG0rxn) for Reaction (1) and for reactions that produced
volatile species from ZrB2 (cr) or from ZrO2 (cr) and B2O3 (l).
The DG0rxn values were converted to equilibrium constant (Keq)
values using Eq. (2), and then to equilibrium partial pressures
using expressions for the equilibrium constant for each reaction
such as the one presented as Eq. (3) for Reaction (1). Unit ac-
tivity was assumed for all condensed phases. The results are re-
ported as partial pressures (e.g., no units, assuming an ambient
pressure of 1.013ꢁ 105 Pa or 1 atm). At 1800 K, the pO2 cal-
culated for the co-existence of ZrB2 (cr), ZrO2 (cr), and B2O3 (l)
was 4.2 ꢁ 10ꢀ16 (vertical line in Fig. 1).
HE borides, carbides, and nitrides of the early transition
metals are considered ultra-high temperature ceramics
T
(UHTCs) because of melting temperatures above 3000 K,
high hardness, and resistance to chemical attack.1,2 Among
the UHTCs, zirconium diboride (ZrB2) is a candidate for ther-
mal protection systems and scramjet engine components for
hypersonic flight vehicles as well as high temperature electrodes,
molten metal containment systems, and incinerators.3–6 Heating
ZrB2 in air produces a scale composed of ZrO2 and B2O3.7,8 Be-
low 1200 K, liquid B2O3 forms a continuous layer that wets the
ZrO2 and the underlying ZrB2. The B2O3 (l)z layer acts as
a barrier to oxygen diffusion resulting in passive oxidation of
ZrB2 and parabolic (diffusion-limited or t1/2) oxidation kinet-
ics.9–11 At intermediate temperatures (1200–1700 K), the rates of
formation and volatilization of B2O3 (l) are similar, resulting in
para-linear kinetics because of competition between mass gain
(ZrO2 and B2O3 formation) and mass loss (B2O3 vaporiza-
tion).12,13 Above 1700 K, active oxidation with rapid linear
kinetics has been attributed to loss of B2O3 (l) by evaporation,
which leaves behind a porous, non-protective ZrO2 (cr) layer.7,14
Interactions between gases and condensed phases can be in-
terpreted with volatility diagrams.15 Volatility diagrams plot the
vapor pressure of the predominant gaseous species as a function
of oxygen partial pressure and temperature. Gas–solid interac-
tions have been studied for systems such as Mg–O, Al–O, Si–O,
Si–C–O, Si–N–O, and Mg–O–C using volatility diagrams.16–18
A recent study of UHTCs employed volatility diagrams for
metals (e.g., Zr, Si, B) to evaluate the thermal stability of oxide
scales.19 However, to date, a true volatility diagram for ZrB2 has
not been reported. The diagram is needed to understand the
oxidation of pure ZrB2 as well as the oxidation of ZrB2-based
ceramics containing additives such as SiC, MoSi2, or graphite.
The purpose of this paper is to describe the construction and
interpretation of a volatility diagram for ZrB2.
DG0rxn ¼ ꢀRT ln Keq
(2)
where R is the ideal gas constant and T is the absolute temper-
ature
ðaB O ÞðaZrO
Þ
1
2
3
2
Keq
¼
¼
(3)
5=2
5=2
ðaZrB ÞðaO
Þ
ðpO2Þ
2
2
where a is the activity of the species involved in the reaction
Below the equilibrium pO2 for Eq. (1), the gases are in equi-
librium with ZrB2 (cr). For example, B2O3 (g) can form by
Eq. (4). Other gases that form by reaction of ZrB2 are listed in
Table II.
5
2
ZrB2 ðcrÞ þ O2 ðgÞ ! ZrO2 ðcrÞ þ B2O3 ðgÞ
(4)
As pO2 increases, the amount of B2O3 (g) should increase since
O2 is a reactant. This relationship can be seen in the portion of
Table I. Zr, B, and O Species of Interest for Calculation of the
Volatility Diagram
A. Heuer—contributing editor
Zr species
Zr–O species
Zr–B species
B species
B–O species
Zr (g)
ZrO (g)
ZrO2 (cr)
ZrO2 (g)
ZrB2 (cr)
B (g)
B2 (g)
B2O3 (g)
B2O3 (l)
BO (g)
Manuscript No. 20394. Received April 8, 2005; approved May 15, 2005.
This material is based upon work supported by the National Science Foundation under
Grant DMR 034680.
BO2 (g)
B2O (g)
B2O2 (g)
*Member, American Ceramic Society.
wAuthor to whom correspondence should be addressed. e-mail: billf@umr.edu
zNote: The NIST-JANAF convention is used whereby physical state is indicated in pa-
renthesis with (cr) for crystalline solids, (l) for liquids or amorphous solids, and (g) for gases.
3509

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Communications of the American Ceramic Society
Vol. 88, No. 12
undergoes four major vapor transitions at 1800 K: (1) from B (g)
to BO (g) at a pO2 of B2 ꢁ 10ꢀ27; (2) from BO (g) to B2O2 (g) at
a pO2 of B3 ꢁ 10ꢀ17; (3) from B2O2 (g) to B2O3 (g) at a pO2 of
B3 ꢁ 10ꢀ16; and (4) from B2O3 (g) to BO2 (g) at a pO2 of
B8 ꢁ 101. Vapor pressure calculations were also completed at
1000 and 2500 K to show how the diagram changed with tem-
perature (Fig. 2(b)). Interestingly, the transition from stability of
B2O2 (g) to B2O3 (g) falls near the equilibrium pO2 for Eq. (1)
(B4 ꢁ 10ꢀ16) at 1800 K and also at 2500 K so that the vapor
transition is obscured by the transition in stable condensed
phases.
ZrB (cr)
ZrO (cr)
and
2
2
B O (l)
2
3
BO
2
B O
2
3
BO
B O
2
2
III. Discussion
The volatility diagram was used to interpret experimental ob-
servations of ZrB2 oxidation in air. At 1000 K, the predominant
species above B2O3 (l) and ZrO2 (cr) was BO2 (g) with a partial
pressure of B10ꢀ11 (B10ꢀ6 Pa). The next highest vapor pres-
sure was B10ꢀ12 (B10ꢀ7 Pa) for B2O3 (g). The calculated pres-
sures of the other species were all dramatically lower (Table IV).
The vaporization rate for B2O3 (l) in air is expected to be low at
1000 K based on the partial pressures of the various gases, none
B
B
2
B O
2
Fig. 1. Partial pressure of B species as a function of oxygen partial
pressure at 1800 K.
of which exceeds B10ꢀ11
.
Above B1650 K, rapid, linear (active) oxidation kinetics have
been attributed to a significant increase in the rate of B2O3 (l)
evaporation.7 Examination of ZrB2 oxidized at 1773 K by scan-
ning electron microscopy (Fig. 3) and X-ray diffraction (not
shown) revealed that the oxide layer was made up almost ex-
clusively of porous ZrO2 (cr), which does not provide passive
oxidation protection. From the volatility calculations, the pre-
dominant vapor species at 1800 K in air was B2O3 (g) with a
pressure of B10ꢀ2 (344 Pa). Two other species had vapor pres-
sures predicted to be greater than 10ꢀ10 (B10ꢀ5 Pa) at 1800 K in
air, BO2 (g) at B10ꢀ3 (86 Pa), and BO (g) at B10ꢀ8 (B10ꢀ3 Pa).
Based on the nine order of magnitude increase in the pressure
of the dominant species compared to 1000 K, the rate of B2O3
(l) vaporization would be expected to be significantly higher
at 1800 K, which is consistent with B2O3 evaporation from
the surface of ZrB2 that is oxidized in air at 1650 K or above.
Active oxidation of ZrB2 is also expected at higher temperatures,
unless the ZrO2 scale becomes protective. Oxidation of ZrB2-SiC
above 2000 K in arc jet testing suggests that ZrO2 may become
protective at these temperatures by sintering into a coherent
scale.21
Fig. 1 to the left of the ZrB2/ZrO2–B2O3 line. Above the equi-
librium pO2 for Eq. (1), the gases are in equilibrium with ZrO2
(cr) and B2O3 (l). In this regime, B2O3 (g) forms by direct va-
porization of B2O3 (l) according to Eq. (5).
B2O3 ðlÞ ! B2O3 ðgÞ
(5)
Because oxygen is neither consumed nor produced by Eq. (5),
the partial pressure of B2O3 (g) does not vary with pO2 (Fig. 1)
in this regime. Other gases that form in this regime are listed in
Table III. Pressures for all of the B-containing gases were de-
termined in this manner and plotted in Fig. 1. The pressures of
Zr-containing gases were calculated, but not plotted since they
were much lower than those of B species. At the equilibrium pO2
for Eq. (1), the partial pressure of B2O3 (g) above ZrB2 (cr) must
be the same as it is above ZrO2 (cr)–B2O3 (l) since the gas is in
equilibrium with all of the condensed phases simultaneously.
Pressures for all of the gases met this criterion for consistency,
which can be seen in Fig. 1 for B-containing gases.
The vapor pressures of all of the gases were calculated to
compile a volatility diagram at 1800 K (Fig. 2(a)). The system
Table II. Volatilization Reactions Involving ZrB2 (cr) as the Primary Condensed Phase
Reactions producing volatile B species
Reactions producing volatile Zr species
5
2
ZrB2 (cr)13O2 (g)-ZrO2 (cr)12BO2 (g)
ZrB2 ðcrÞþ O2 ðgÞ ! ZrO2 ðgÞ þ B2O3 ðlÞ
5
ZrB2 ðcrÞþ O2 ðgÞ ! ZrO2 ðcrÞ þ B2O3 ðgÞ
ZrB2 (cr)12O2 (g)-ZrO (g)1B2O3 (l)
2
3
2
ZrB2 (cr)12O2 (g)-ZrO2 (cr)1B2O2 (g)
ZrB2 (cr)12O2 (g)-ZrO2 (cr)12BO (g)
ZrB2ðcrÞ þ O2ðgÞ ! ZrðgÞ þ B2O3ðlÞ
3
2
ZrB2 ðcrÞþ O2 ðgÞ ! ZrO2 ðcrÞ þ B2O ðgÞ
ZrB2 (cr)1O2 (g)-ZrO2 (cr)1B2 (g)
ZrB2 (cr)1O2 (g)-ZrO2 (cr)12B (g)
Table III. Volatilization Reactions Involving ZrO2 (cr) and B2O3 (l) as the Primary Condensed Phases
Reactions producing volatile B species
Reactions producing volatile Zr species
B2O3 (l)-B2O3 (g)
ZrO2 (cr)-ZrO2 (g)
1
1
2
B2O3 ðlÞ þ O2 ðgÞ ! 2BO2ðgÞ
ZrO2 ðcrÞ ! ZrOðgÞ þ O2 ðgÞ
2
1
2
1
B2O3ðlÞ ! B2O2 ðgÞ þ O2 ðgÞ
ZrO2 (cr)-Zr (g)1O2 (g)
B2O3 ðlÞ ! 2BO ðgÞ þ O2 ðgÞ
2
B2O3 (l)-B2O (g)1O2 (g)
3
2
3
2
B2O3 ðlÞ ! B2 ðgÞ þ O2 ðgÞ
B2O3 ðlÞ ! 2B ðgÞ þ O2 ðgÞ

December 2005
Communications of the American Ceramic Society
3511
(a)
ZrO2
ZrB2
ZrB (cr)
ZrO (cr) + B O (l)
2 2 3
2
BO (g)
2
B O (g)
2
3
B O (g)
2
2
BO (g)
B (g)
20 µm
Fig. 3. A zirconium diboride (ZrB2) ceramic oxidized at 1773 K in air
for 30 min showing a surface layer of porous ZrO2.
(b)
ZrO (cr)
of a surface layer of B2O3 (l). The partial pressure of the pre-
dominant species, BO2 (g), was predicted to be 10ꢀ11 (10ꢀ6 Pa)
at 1000 K in air, consistent with the observation of passive ox-
idation. Increasing the temperature to 1800 K in air increased
the partial pressure of the predominant species, B2O3 (g), to
B10ꢀ2 (344 Pa). The substantial increase in vapor pressure was
consistent with the observed transition from passive to active
oxidation kinetics between these temperatures.
2
ZrB2 (cr)
+ B O (l)
2
3
2500 K
1800 K
1000 K
BO (g)
2
B O (g)
2
3
Acknowledgments
B O (g)
2
2
The author thanks Drs. Mark Opeka and Inna Talmy of the Naval Surface
Warfare Center-Carderock Division and Professor Jeff Smith of UMR for many
educational discussions. The SEM image was provided by UMR graduate student
Adam Chamberlain.
BO (g)
B (g)
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8 ꢁ 10ꢀ32
1 ꢁ 10ꢀ47
7 ꢁ 10ꢀ72
6 ꢁ 10ꢀ4
3 ꢁ 10ꢀ3
1 ꢁ 10ꢀ10
4 ꢁ 10ꢀ8
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