Theoretical and experimental investigation of the thermochemistry of CrO2(OH)2(g)

Article abstract of DOI:10.1021/jp0647380

In this paper, we report the results of equilibrium pressure measurements designed to identify the volatile species in the Cr-O-H system and to resolve some of the discrepancies in existing experimental data. In addition, ab initio calculations were performed to lend confidence to a theoretical approach for predicting the thermochemistry of chromium-containing compounds. Equilibrium pressure data for CrO₂(OH)₂ were measured by the transpiration technique for the reaction 0.5Cr₂O₃(s) + 0.75O₂(g) + H₂O(g) = CrO₂(OH)₂(g) over a temperature range of 573 to 1173 K at 1 bar total pressure. Inductively coupled plasma atomic emission spectroscopy (ICP-AES) was used to analyze the condensate in order to quantify the concentration of Cr-containing volatile species. The resulting experimentally measured thermodynamic functions are compared to those computed using B3LYP density functional theory and the coupled-cluster singles and doubles method with a perturbative correction for connected triple substitutions [CCSD(T)].

Full text of DOI:10.1021/jp0647380

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J. Phys. Chem. A 2007, 111, 1971-1980
1971
Theoretical and Experimental Investigation of the Thermochemistry of CrO2(OH)2(g)
Elizabeth J. Opila,* Dwight L. Myers,† Nathan S. Jacobson, Ida M. B. Nielsen,‡
Dereck F. Johnson, Jami K. Olminsky,§ and Mark D. Allendorf‡
NASA Glenn Research Center, CleVeland, Ohio 44135-3191, East Central UniVersity,
Ada, Oklahoma 74820-0689, Sandia National Laboratories, LiVermore, California 94551-0969, and
QSS Group, Inc., NASA Glenn Research Center, CleVeland, Ohio 44135-3191
ReceiVed: July 25, 2006; In Final Form: December 22, 2006
In this paper, we report the results of equilibrium pressure measurements designed to identify the volatile
species in the Cr-O-H system and to resolve some of the discrepancies in existing experimental data. In
addition, ab initio calculations were performed to lend confidence to a theoretical approach for predicting the
thermochemistry of chromium-containing compounds. Equilibrium pressure data for CrO2(OH)2 were measured
by the transpiration technique for the reaction 0.5Cr2O3(s) + 0.75O2(g) + H2O(g) ) CrO2(OH)2(g) over a
temperature range of 573 to 1173 K at 1 bar total pressure. Inductively coupled plasma atomic emission
spectroscopy (ICP-AES) was used to analyze the condensate in order to quantify the concentration of Cr-
containing volatile species. The resulting experimentally measured thermodynamic functions are compared
to those computed using B3LYP density functional theory and the coupled-cluster singles and doubles method
with a perturbative correction for connected triple substitutions [CCSD(T)].
Introduction
energies (using the coupled cluster CCSD(T) method with the
PCI-X extrapolation scheme and G2 calculations), from which
The corrosion of chromium-containing materials in oxidizing
environments via the formation of volatile species is a problem
with both broad technological and environmental implications.
Chromium in the +6 valence state is considered to be a
carcinogenic hazard of special concern in waste incineration
processes.1 In addition, loss of chromium in the presence of air
and water vapor is a major technological roadblock in the
development of solid oxide fuel cells, which use chromia-
forming alloys or conductive chromia-containing ceramics as
interconnects.2,3 Deposition of chromium oxides on catalysts
used in steam-methane reformers leads to substantial reductions
in catalyst lifetimes.4 Furthermore, lifetimes of Cr-rich structural
steels used in oxygen- and steam-containing environments are
reduced due to chromia volatility.5,6 Finally, volatile chromium-
containing species formed in atmospheric pressure chemical
vapor deposition reactors used in the semiconductor industry
can contaminate processed wafers, causing increased defect
rates.7
A large number of gas-phase Cr-O-H species could
potentially be involved in these degradation processes, for which
little experimentally measured thermodynamic data are available.
Several systematic theoretical examinations of the Cr-O-H
system have been conducted. In an important study, Ebbinghaus
derived thermodynamic data for a large number of gas-phase
chromium oxides and oxyhydroxides using a combination of
the limited available experimental data and the molecular
constant method.1 Empirical relationships were employed, where
needed, to estimate unknown molecular properties, resulting in
large uncertainties in some cases. Later, Espelid et al.8 used
high-level ab initio calculations to predict equilibrium geometries
and vibrational frequencies (using B3LYP) and electronic
they derived heats of formation for a number of gas-phase
chromium oxides and oxyhydroxides. In several cases, the
predicted values differ from those of Ebbinghaus by more than
30 kJ mol-1. There is thus a critical need for new experimental
data to resolve inconsistencies between theory and published
data, as well as to validate computational methods that are the
only practical means of generating thermodynamic properties
across the large range of molecules that are possible in this
system.
The volatile species CrO3,9-12 CrO2(OH)2,13 and CrO2(OH)12
have all been experimentally identified as contributing to Cr2O3
degradation. The reactions to form these volatile Cr-O-H
species from Cr2O3, H2O, and O2 are as follows:
1/2Cr2O3(s) + 3/4O2(g) ) CrO3(g)
(1)
1/2Cr2O3(s) + H2O(g) + 3/4O2(g) ) CrO2(OH)2(g) (2)
1/2Cr2O3(s) + 1/2H2O(g) + 1/2O2(g) ) CrO2(OH)(g) (3)
Ebbinghaus concluded from equilibrium calculations using his
estimated data that CrO2(OH)2(g) is the dominant vapor species
above chromium-containing materials exposed to oxygen and
water vapor across a wide range of temperatures, as shown in
Figure 1. However, the identity of the volatile species formed
in water vapor-oxygen mixtures at temperatures between 573
and 1173 K has not been definitively established with experi-
ments. Both CrO2(OH)2 and CrO2(OH)+ ions were observed
+
in earlier mass spectrometry experiments conducted at 1373
K.13,14 It is uncertain whether both gas species were formed by
reaction of water vapor and oxygen with Cr2O3(s) or whether
CrO2(OH)+ was formed as a fragment during the ionization of
CrO2(OH)2. In addition, Kim and Belton12 studied the volatiliza-
tion of Cr2O3(s) in oxygen and water vapor in the temperature
* Corresponding author. E-mail: opila@nasa.gov.
† East Central University.
‡ Sandia National Laboratories.
§ QSS Group, Inc..
10.1021/jp0647380 CCC: $37.00 © 2007 American Chemical Society
Published on Web 02/20/2007

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1972 J. Phys. Chem. A, Vol. 111, No. 10, 2007
Opila et al.
TABLE 2: Thermochemical Data (kJ mol-1) from the
Literature Employed in the Computation of the Heat of
Formation for CrO2(OH)2
∆H°
∆H°
f,298.15
f,0
H2O(g)
CrO3(g)
-238.921 ( 0.042a
-241.826 ( 0.042a
-319.5 ( 4.2b
-323.5 ( 4.2c
a Reference 21. b Computed from the reaction Cr(s) + 1.5O2(g) f
CrO3(g) using the ∆H°
[CrO3] value and the enthalpy differences
H°298.15 - H° for Cr(s),fO,2928(.1g5), and CrO3(g) given in ref 1. c From ref 1.
0
situation because their heats of formation predicted by the G2
and PCI(X) methods differ by 50 kJ mol-1. Thus, for both
scientific and practical reasons, there is strong justification for
performing a concentrated investigation of the thermochemistry
of CrO2(OH)2.
The objectives of this work are to experimentally verify that
CrO2(OH)2(g) is the dominant volatile Cr-O-H species for
Cr2O3 exposed in H2O and O2 at temperatures between 573 and
1173 K, to obtain reliable thermodynamic data for CrO2-
(OH)2(g) using both the transpiration technique and ab initio
calculations, to compare experimental data to calculated data,
and to clarify the importance of other volatile species in the
Cr-O-H system.
Figure 1. Equilibrium partial pressures of volatile Cr-O-H species
calculated at P(H2O) ) 0.5 bar and P(O2) ) 0.5 bar based on the data
of Ebbinghaus.1
TABLE 1: Literature Values for the Standard Heat of
Formation, ∆H° , Cr(s) + 2O2(g) + H2(g) ) CrO2(OH)2(g)
f,298
∆H°
f,298
study
method
(kJ mol-1
)
Theoretical Calculations
IVTANTHERMO16
estimation based on like molecules -736 ( 40
Farber & Srivastava14 mass spectrometry measurements -738 ( 29
The heat of formation for CrO2(OH)2 was computed from
the isogyric reaction
Ebbinghaus1
Espelid8
estimation based on ref 15
average, ab initio calculation
G2(MP2/CC)
-748 ( 4.3
-787 ( 36
-812
CrO2(OH)2(g) f CrO3(g) + H2O(g)
(5)
PCI-X
-762
The reaction energy was first computed at 0 K and then
converted to a reaction energy at 298.15 K by application of
temperature corrections
range of 1572 to 1798 K and found pressure-dependent results
consistent with CrO2(OH)(g) formation. Glemser and Mu¨ller15
obtained equilibrium pressure results for CrO2(OH)2(g) from a
different reaction
∆Hr°,298.15 ) ∆H° + H°Thermal(CrO3) + H°Thermal(H2O) -
r,0
HT°hermal(CrO2(OH)2) (6)
CrO3(s) + H2O(g) ) CrO2(OH)2(g)
(4)
where HT°hermal ) H2°98.15 - H°. The heat of formation was then
0
obtained from the expression
at much lower temperatures, between 408 and 458 K. Clearly,
the unambiguous identification of the dominant Cr-O-H(g)
species formed in environments and at temperatures of tech-
nological interest is still needed.
∆H° (CrO2(OH)2) ) ∆H° (CrO3) + ∆H° (H2O) -
f,T
f,T
f,T
∆H° (7)
r,T
Although it is generally assumed that CrO2(OH)2(g) is the
species formed under conditions of practical interest, the
available standard heats of formation for this species vary widely
and have high degrees of uncertainty, as summarized in Table
1. The data in the IVTANTHERMO database16 were estimated
in 1985 and are based on estimated molecular parameters
(geometry and vibrational frequencies) and enthalpies of forma-
tion derived by comparison of CrOx(OH)y with corresponding
CrOxFy species.17 At the time of Ebbinghaus’ assessment of the
Cr-O-H system, the only experimental data available for
analysis were those of Farber and Srivastava14 and Glemser and
Mu¨ller.15 Ebbinghaus rejected the Farber and Srivastava data,
which were derived from mass spectrometric measurements, due
to possible interference from chromium oxychloride species.
The data of Glemser and Mu¨ller15 led Ebbinghaus to estimate
the uncertainty in his reported heat of formation to be only (4.3
kJ mol-1. Experimental equilibrium pressure data for CrO2-
(OH)2(g) are now available from several sources,18-20 and these
newer data do not agree with the equilibrium predictions of
Ebbinghaus.1 Unfortunately, standard heats of formation are not
reported in these studies for comparison with the earlier data.
The recent theoretical results of Espelid8 do not clarify the
for T ) 0 K and T ) 298.15 K, using the literature values for
the heats of formation of CrO3(g) and H2O(g) listed in Table 2.
Although conflicting data for the heat of formation of CrO3(g)
are found in the literature,1,12,16,21 the value provided by
Ebbinghaus has the highest degree of accuracy for any Cr-O
vapor-phase species. This point is addressed further in a
discussion of CrO3(g) stability in a later section of this paper.
Geometries and harmonic vibrational frequencies for the
participating species were computed using the B3LYP density
functional method with the 6-311++G(d,p) basis set,22-25 which
is of triple-ú quality and includes diffuse and polarization
functions on all atoms. Using the B3LYP/6-311++G(d,p)
geometries, the reaction energy was computed with the coupled-
cluster singles and doubles method with a perturbative correction
for connected triple substitutions [CCSD(T)] employing the
frozen-core approximation (freezing 1s on O and 1s2s2p3s3p
on Cr). For the coupled-cluster computations, the Bauschlicher
ANO basis set26,27 was used on Cr, and for H and O the cc-
pVTZ basis28 was employed.
The effect of inclusion of the chromium 3s and 3p core
orbitals in the correlation procedure was computed using second-

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Thermochemistry of CrO2(OH)2(g)
J. Phys. Chem. A, Vol. 111, No. 10, 2007 1973
schematic drawing of the transpiration setup used in these
experiments. The reactive gases, oxygen and water vapor, as
well as a nonreactive carrier gas, argon, flowed over the Cr2O3
pellets that were contained in a Pt-20Rh reaction cell. Flow rates
were chosen to eliminate any diffusion effects or kinetic
limitations so that the equilibrium pressure of volatile Cr-O-H
species was established in the reaction chamber. Volatile species
flowed into the cooler fused quartz tubes and condensed along
with the water vapor. The deposits as well as the water were
collected and quantitatively analyzed for Cr. Knowing the moles
of oxygen and water vapor input as well as the moles of Cr
collected, the equilibrium constant for the volatility reaction was
determined.
The following precautions were taken to ensure accurate data
determination. The gas inlet was constricted by the thermocouple
tube while the outlet was constricted by a small-diameter hole
in the upper Pt-20Rh plug to maintain equilibrium in the cell.
The inner diameter of the bottom of the vertical fused quartz
condensation tube was beveled by grinding with diamond tools.
This bevel was pressure fit to the Pt-20Rh outlet of the
transpiration cell. The horizontal fused quartz condensation tubes
were connected to the vertical tube with polyfluoroethylene
fittings to avoid the introduction of chromium into the system
through stainless-steel fittings. Following tube assembly and
prior to each experiment, the tube end at the water collection
burette was briefly sealed while inlet gases flowed into the cell
until pressures of at least 1.33 bar (1000 Torr) were measured
with the capacitance manometer. This test was used to verify
that the tubing assembly did not leak. The pressure was then
released, and the inlet water flow was initiated. The experimental
time was measured from the start of the inlet water flow to the
time when the water flow was terminated. Water that flowed
through the transpiration system was collected and measured
in a burette. The amount of water collected was within 5% of
the calculated total throughput corrected for the amount of water
expected to be lost to vaporization at room temperature. The
assembly was again tested for leak-tightness after each experi-
ment before disassembling the collection tubes. The condensate
in all collection tubes, as well as the collected water, was
analyzed for Cr content as described below. It was critical to
collect and analyze the deposit from the entire gas train. Prior
to and after each experiment, the liquid water flow for the inlet
was calibrated by flowing into a burette or graduated cylinder.
Water flow rates obtained before and after an experiment were,
on average, constant within 0.06 mL/hr. During each experiment,
the portion of the vertical collection tube outside of the furnace
and the initial portion of the horizontal collection tube were
wrapped with heating tape to ensure that water did not condense
and flow back into the vertical tube. The transpiration cell and
gas train were enclosed in a furnace tube that contained a blanket
of flowing argon. The argon limited the formation of PtO2(g)
from the transpiration cell. In addition, the blanket argon was
analyzed for oxygen and water vapor using a residual gas
analyzer (Dycor/Ametek, Pittsburgh, PA) to detect any leaks
from the transpiration gas train system.
Figure 2. Schematic drawing of the transpiration equipment.
order Møller-Plesset perturbation (MP2) theory in conjunction
with the cc-pVTZ basis for H and O and a modified Bauschli-
cher ANO set for Cr. The Bauschlicher ANO basis set was
modified by decontracting the outermost six s, seven p, and
seven d functions. A correction for basis-set incompleteness was
estimated by computation of large-basis-set MP2 energies using
a completely decontracted Bauschlicher ANO basis set on Cr
and the aug-cc-pVQZ set28,29 on H and O. Scalar relativistic
effects were accounted for at the MP2 level using the Douglas-
Kroll-Hess second-order relativistic correction.30-33 For Cr, the
Bauschlicher ANO set, modified by decontracting the entire s
and p spaces, was employed, and the cc-pVTZ_DK set27,34 was
used for H and O. Temperature corrections H°
- H° were
298.15
0
computed using the B3LYP/6-311++G(d,p) harmonic vibra-
tional frequencies, employing standard formulas from statistical
mechanics35 and including a hindered rotor treatment36 of the
vibrational modes corresponding to internal rotation of the
hydroxide groups.
The relativistic corrections were computed with NWChem,37
the large basis set MP2 computations were carried out with
MPQC,38 and other computations were performed with the
Gaussian03 program.39
Experimental Materials and Methods
Material. The Cr2O3 used for experiments was -20 mesh
powder with a reported purity of 99.997% (Cerac, Milwaukee,
WI). The impurity content was measured by DC arc emission
spectroscopy and found to be 0.011% Bi, 0.001% Ca, 0.0006%
Si, and 0.008% Ti. The powder was cold pressed at 14 MPa
with a 0.64-cm-diameter die using water as a binder. The pellets
were partially sintered for 4 h in air at 1633 K, resulting in a
density of approximately 60% of the theoretical value.
Transpiration Technique. The transpiration technique is a
well-established and versatile technique for studying gas-solid
equilibria and measuring equilibrium pressures in the presence
of large concentrations of other gases.40 Figure 2 shows a
Experimental Conditions. Chromia volatility was measured
over a temperature range of 573 to 1173 K. Temperature
measurements were made with a Type-R thermocouple im-
mersed in the chromia pellets as shown in the detail of Figure
2. The thermocouple was periodically calibrated with a NIST
traceable thermocouple and found to be within 5 K of the
standard. The experiments were conducted at ambient pressure.
The transpiration cell pressure was monitored with a capacitance
monitor and varied between 0.93 and 1.02 bar (695 to 762 Torr)

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1974 J. Phys. Chem. A, Vol. 111, No. 10, 2007
Opila et al.
TABLE 3: B3LYP/6-311++G(d,p) Frequencies (cm-1) for
during the course of these experiments. The pressure measured
with the capacitance monitor was found to vary with ambient
conditions and was within 0.3% of a nearby barometric
standard.41 The temperature- and pressure-dependent experi-
ments were conducted with the total cell flow rates (argon,
oxygen, water vapor, volatile chromium species) between 7.55
and 17.04 mL/s at the experimental temperature. Inlet liquid
water flow rates were controlled with a peristaltic pump (Rainin,
Instrument Co., Woburn, MA) and varied between 0.33 and
6.80 mL/h. Water vapor contents in the cell varied between 4%
and 48% of the total flow. Inlet oxygen flow rates varied
between 50 and 471 sccm. Oxygen contents in the cell varied
between 13% and 100% of the total flow. Inlet argon flow rates
varied between 0 and 268 sccm. Gas flow rates were controlled
with calibrated mass flow controllers (Tylan General, Rancho
Dominguez, CA). Experiment times varied between 15 and 95
h.
Cr Analysis. Care was taken to analyze Cr from all of the
vapor products formed in the reaction cell. This involved careful
collection and analysis of the deposits in the condensation tubes
and the water in the collection burette shown in Figure 2. Several
types of deposits were found in the collection tubes: liquid
brown deposits and solid green deposits. The identification of
these deposits will be discussed in the results section. To collect
the deposited Cr for analysis, the fused quartz condensation
tubes were injected in succession with deionized water, con-
centrated HCl, and concentrated HF. Each solvent was left in
the tube for about 30 min before flushing with the next solvent.
After a final deionized water flush, all solvents were collected
in the same beaker, heated, and diluted to a known volume.
The brown and green deposits adhering to the inner walls of
the tubes were dislodged by attack of the HF on the fused quartz.
Heating the collected solvents dissolved the brown deposit but
not the green deposit. The green deposit was filtered off, and
the filter paper was transferred to a platinum crucible. The
residue was ignited in a muffle furnace at 923 K for 1 h, and
then fused in a mixture of 0.9 g anhydrous sodium carbonate
and 0.1 g sodium tetraborate at around 1073 K for 10-15 min.
When the melt was clear, the crucible was removed from heating
and the solidified melt dissolved in deionized water. The solution
was then acidified with concentrated HCl and diluted to a known
volume. The product of the fusion process was added to the
other washings.
a
CrO2(OH)2
O-Cr-O, OdCr-O,
OdCrdO bend
Cr-O
stretch
Cr-O-H
bend
CrdO
stretch
O-H
stretch
225(A), 269(A), 294(B), 734(A),
323(B), 406(A) 734(B)
763(A),
785(B)
1083(A),
1107(B)
3810(B),
3815(A)
a The symmetry of each mode is given in parentheses. In addition
to the modes included in the table, there were two modes, at 346(A)
and 367(B) cm-1, which were assigned as O-H internal rotations.
TABLE 4: Computation of ∆H° and ∆H°
for
f,0
f,298.15
CrO2(OH)2 from Reaction 5a
∆Ee[HF]
∂[MP2]
241.98
-2.87
-13.13
+0.83
+1.11
-8.45
+11.97
-9.61
∂[CCSD]
∂[CCSD(T)]
∂[core]
∂[basis]
∂[rel]
∂[ZPVE]
∆H°
221.83
-780.3
-791.8
r,0
∆Hf°,0 [CrO2(OH)2]
∆H°f,298.15 [CrO2(OH)2]
a All entries in kJ mol-1. ∆Ee[HF] is the reaction energy computed
at the Hartree-Fock level with the Bauschlicher ANO basis set on Cr
and the cc-pVTZ set on H and O. δ[MP2], δ[CCSD], and δ[CCSD(T)]
designate the changes in the reaction energy relative to the preceding
level of theory. δ[core], δ[basis], δ[rel], and δ[ZPVE] represent the
corrections to the reaction energy from core-correlation, basis set
improvement, scalar relativistic effects, and zero-point vibrational
energy. ∆H° [CrO2(OH)2] and ∆H°
[CrO2(OH)2] are computed
f,0
from ∆H°r,0 as described in the text. f,298.15
sides of the O-Cr-O plane with O-Cr-O-H dihedral angles
of -92.4°. The computed harmonic vibrational frequencies and
their assignments are given in Table 3. The B3LYP/6-311++G-
(d,p) structure and frequencies for CrO2(OH)2 are similar to
previously computed B3LYP values8 obtained with a triple-ú
basis set including diffuse functions and a single set of
polarization functions on H and O, although our Cr-O and Crd
O bond distances are 0.005-0.006 Å shorter, probably due
mainly to inclusion of polarization functions on Cr.
The computation of the heat of formation for CrO2(OH)2 from
reaction 5 is detailed in Table 4. The HF f MP2, MP2 f
CCSD, and CCSD f CCSD(T) increments in the reaction
energy are labeled δ[MP2], δ[CCSD], and δ[CCSD(T)],
respectively. The small size of these increments, and in particular
the δ[CCSD(T)] value of only 0.8 kJ mol-1, indicates rapid
convergence of the computed reaction energy with respect to
improving the treatment of electron correlation. These results
lend confidence in the adequacy of the CCSD(T) method, the
highest level of electron correlation employed, for computing
the reaction energy for reaction 5. The various corrections
applied to the computed CCSD(T) reaction energy, δ[core],
δ[basis], and δ[rel], assume values of 1.1, -8.5, and 12.0 kJ
mol-1. Our final ab initio values for the heat of formation for
The solutions described above, as well as the collected water,
were analyzed separately for total Cr by inductively coupled
plasma-atomic emission spectrometry (ICP-AES) (Varian Vista
Pro Axial View Spectrometer, Varian, Inc.). The collected water
from each experiment was also analyzed for hexavalent Cr by
a spectrophotometric technique (Shimadzu Model UV-160
Ultraviolet-visible Spectrophotometer, Shimadzu Corp) using
1,5 diphenylcarbohydrazide. The 1,5 diphenylcarbohydrazide
reacts with Cr(VI) to develop a vivid pink-purple color that
allows the concentration to be determined by measuring the
absorbance at 540 nm. This technique verified that the Cr was
present in the hexavalent state and, in addition, provided
independent confirmation of ICP-AES accuracy.
CrO2(OH)2 are ∆H° (CrO2(OH)2) ) -780 ( 20 kJ mol-1 and
f,0
∆Hf°,298.15(CrO2(OH)2) ) -792 ( 20 kJ mol-1. The uncer-
tainty of (20 kJ mol-1 takes into account the reported
uncertainties in the employed experimental data and the
estimated residual errors in the computation of the reaction
energy for reaction 5. Our ∆H°f,298.15 value agrees well with the
value of -787 ( 36 kJ mol-1 computed previously by Espelid
et al.8 This may be somewhat fortuitous, however, because their
value was obtained by averaging two widely differing numbers
(-762 and -812 kJ mol-1) computed using variants of the G2
Theoretical Results and Discussion
The optimum B3LYP/6-311++G(d,p) geometry for CrO2-
(OH)2 has C2 symmetry. The bond distances are r(CrdO) )
1.560 Å, r(Cr-O) ) 1.759 Å, and r(O-H) ) 0.967 Å. The
chromium-oxygen bond angles are OdCrdO ) 111.4°, O-
Cr-O ) 109.9°, and O-CrdO ) 110.0°, 107.8°. The Cr-
O-H angle is 116.4°, and the two O-H bonds lie on opposite