CHARACTERISTICS OF FLUORITE AND FLUORITE-RELATED STRUCTURES

Fluorite-Type and Related Structure Systems

4.3. CHARACTERISTICS OF FLUORITE AND FLUORITE-RELATED STRUCTURES

162

CHAPTER 4

. available sites of the oxygen close-packing layers for rutile and perovskite structures. The cations in rutile and perovskite structures always have the ability to move from one suitable site to another, causing the octahedra to vary the connection from corner sharing to edge sharing or face sharing. In the fluorite structure, however, the cations and the anions both form close-packing layers, but only two oxygen sublattice can create equal numbers of vacancies which make oxygen migration easy without tailoring the cation sublattice. In the C-type rare earth sesquioxide structure the cation frame remains the same as in fluorite, but only two oxygen sublattices have been tailored to form vacancies.

This feature is a key point for understanding the structural characteristics of fluorite- related compounds.

4.3.

CHARACTERISTICS OF FLUORITE AND

where Ilo is the chemical potential of oxygen at the pressure and temperature of concern, Ilo is the standard chemical potential of oxygen, R is the gas constant, T is the absolute temperature, p is the equilibrium and pO is the standard pressure of one atmosphere. We may say that the chemical potential of the rare earth higher oxides is approximately proportional to In P O_{2 '} Thus, the oxygen partial pressure directly determines the oxygen composition in the rare earth higher oxides R02_x' If x is not too high an empirical equation is established:

lnP02 = ajT

+

b - s lnx (4.2)

where a, b are constants, T is temperature (K), x is the deviation value from 2, and s has an empirical value around 5. Some modeling and calculations (Lindemer, 1986; Hillert and Jansson, 1986) have been made for Ceo.s0\.2. Their approach is to create oxidation reaction and then to use thermodynamic method to derive the formula. For example,

1200

a

~1000 () 2.-

e! BOO

:::l

l'!

Q) ⁶⁰⁰ 0.. E

Q) 400

I- 200

5Ceo.s0l.2

+

^O2 = 4Ce02 4Ce01.5

+

O2

=

^4Ce02

\ \

\ I ^\

I

^{a I \}

8+a a

I I \ I I

II

---~

I ap ¹ 1;£0

r II ^o+a

I I II

I II

1.6 1.7 1.B 1.9 2.0

(Lindemer, 1986)

(Hillert and Jansson, 1986)

b

1000

~BOO

_I ^{I a}

e! I

.a

^~ _Q) 600

I

I

0.. E 400 <1>.---, I

Q) a

I- ( II

200 1\

\ \ I; £ ~ 1.5 1.6 1.7 1.B 1.9 Composition x in CeOx Composition x in PrOx

C ^{I I}

(a) /.-J-,~

0 ¹⁰⁰⁰ /,"''' I~ "\ (a)

2.- ( / 'I \

Q) <I> I \

.z

⁸⁰⁰ I \

~ I \

Q)

0.. I \ /"

E 600

Q)

-~L

I- 0' I

400

J

_{I? I}

^~

1.5 1.6 1.7 1.B 1.9 2.0

Composition x in TbOx

2.0

Figure 4.9. Phase diagrams of CeO_{x ,} PrOx , and TbOx in composition range X= 1.5 to 2.0. (Reprinted with permission from Elsevier).

163

FLUORITE-TYPE AND RELATED STRUCTURE SYSTEMS

164

CHAPTER 4

The coefficient of the first compound (5 or 4) determines the s value to be 5 or 4. That can give the oxygen partial pressure related to different R02_x phases, especially Ce02_x as p O₂ ~ x-5 or x-4. We believe that further development is needed for using oxygen- deficient modules in constructing these structures.

Experimentally the phase diagram of CeOx was constructed from the measurements of p, T, and x made from buffered oxygen down to a fugacity of - 30 atm (Bevan and Kordis, 1964). The phase diagrams ofthe praseodymium and terbium oxides were carried out between a few Torr and 1 atm oxygen pressure (Ferguson et al., 1954; Hyde et al., 1966; Jenkins et al., 1970; Hyde and Eyring, 1965). The phase diagrams of CeO_{x ,} PrO_{x ,}

700 a

600

E

⁵⁰⁰

E c :.:=-

0 C\I

-

_~ ^{0 400}

:::J

C/) C/) Q)

.... _c.

ct! 300

t ct!

a..

200

100

1.60 1.65 1.70 1.75 1.80 ^1.85

Composition x in PrOx

Figure 4.10. Isothermal experimental data of Pr0x-02 system at different oxygen partial pressures. The unit of temperature is degrees Celsius. (b) Isobars data of the Prx-02 system at different temperatures. The pressure is measured in Torr. (Reprinted with permission from Elsevier).

and TbOx in composition range x

=

1.5 to 2.0 are given in Fig. 4.9. It can be clearly seen that there are five single-phase regions whose compositions accord with a generic formula, Rn02n-2m, where n

=

7, 9, 40, 11, and 24, and m

=

1, 1, 4, 1, and 2, respectively. The basis of these numbers will be discussed later. In addition, there are two nonstoichiometric phases with wide composition range at higher temper(!tures (the \1.-

phase at higher compositions into which the single phases decompose peritectoidally, and the a-phase in the lower composition range). In the mediate temperatures the five single phases have narrow composition variation or nonstoichiometry, which are called linear phases with narrow nonstoichiometry. These phases are very important for functional materials. If we observe the isothermal experimental data (Fig. 4.lOa) we find that the steepness of the isotherms curves at different temperatures indicates stable single phases of small composition variation, but the flatness of the curves imply easily oxidized compositions usually in two-phase regions. Intermediate slopes of these curves are characteristic of nonstoichiometric phases. From an oxygen partial pressure point of view the oxygen content of Pr0x (others are similar) is sensitive to the oxygen partial pressure, especially at low oxygen partial pressure. At the region of two phases the oxygen contents have large variation if the external oxygen partial pressure reaches the phase transition point at constant temperature. In other words, the large amount of oxygen atoms can be absorbed into or released from the compound if this transition occurs, and this is called

Q....

6'

!£ ::J

~ Q) Cl. E

I-Q)

1100 1000

1100 1000

1000

800

600

400

1'50

b

~~---~---.

1'55 1'60

I I

10 -

1'800 1'833

1·714 1·778 "818

I I I I

1065 1·70 1'80 1·85

Composition x in PrOx

Figure 4.10. (continued)

1000

800

600

400 500 400 500 400 500 400 00

165

FLUORITE-TYPE AND RELATED STRUCTURE SYSTEMS

166

CHAPTER 4

the oxygen storage capacity (OSC) or oxygen pumping. The rare earth higher oxides,

Rn02n-2m (R = Ce, Pr, Tb), are a unique system having OSC without modifying the cation sublattice. This is a very useful character of these compounds.

The relationship between composition and temperature at constant pressure is shown in Fig. 4. lOb. The number on each curve indicates the oxygen partial pressure around the sample. These curves demonstrate following features: (a) stable regions of a homologous series of intermediate phases with narrow compositional variation; (b) two wide ranges of non stoichiometric phases, i.e., oxygen content linearly varying with temperature; (c) a pseudophase formation in some of the two-phase regions; and (d) hysteresis in all the two-phase regions (Hyde et al., 1966). From these data we would like to emphasize that (a) as the temperature is going up and down to make a cycle the oxygen content of the compound can also be decreased and increased following the same cycle, and (b) as oxygen partial pressure increases the oxygen content varying with temperature is close to a monovalue. Based on these two features the oxygen contents of these compounds are almost reversible with temperature and oxygen partial pressure. This is a unique characteristic of rare earth higher oxides, which can have important practical applications.

Equilibrium isobars are meticulously scanned in the nonstoichiometric alpha region with surprising results (Fig. 4.11a) (Jenkins et al., 1970). Rather than showing smooth curves there are small discontinuities at almost constant oxygen activity, clearly outside the limits of experimental error of the measurements. This may be a sign of structural variation, for example, some modulation or other premonitory behavior at temperatures that approach the phase transitions. Similar phenomena have been observed in the terbium oxide system (Hyde and Eyring, 1965). The terbium oxide-oxygen system is considerably simpler than that of praseodymium, having only four phases which have compositions matching a generic formula, RnOZn-2m, for m = 1, n = 7 or 11; m = 2, n = 24; m = 4, n = 48; and m

=

^6, n

=

62. The intermediate phases are nearly stoichiometric, but still have narrow composition variation as temperature increases. It is almost certain that the nonstoichiometry will appear at higher pressures and temperatures.

By varying the cycling of temperature (up and down) and/or the oxygen partial pressure (high and low), the oxygen content of the rare earth high oxide can be reversible.

However, from the viewpoint of oxidation and reduction reaction in any solid state, oxidation-reduction reaction hysteresis (the failure to traverse the same sequence of states in the forward and reverse reaction) must occur and must depend to some extent on the rate over which the cyclic path is traversed. Hysteretic behavior is both marked and complex in the iota-delta region of TbOx (Fig. 4.11b) (Lowe and Eyring, 1975). The complexity is enhanced because an intermediate 8' -phase which occurs in oxidation but not in reduction. The scanning loops in this region depend on the path traversed and whether the oxidation has gone forward all the way to the 8' -phase as it has in this instance. Several theoretical models for hysteresis are tested (Knittel et al., 1977), and the general features can be matched to some degrees only. Of course, the particle size is also a factor affecting the existence and shape of the hysteresis loop. Curiously, the loops are narrower when single-crystal particles of appreciable sizes are reacted (Lowe et al., 1975). Complete understanding the hysteresis behavior must rely on structural information.

The thermodynamic data collected on rare earth oxides establish the extremely rapid rate of the diffusion of oxygen into the solid oxides at temperatures as low as 300°C. The diffusion constants of oxygen in oxides in this region are of the order of 10-⁹ cm2 / s

(Weber and Eyring, 1971; Lau et al., 1976). The rate of oxygen uptake decreases from Ce to Th. These data can be understood from the character of fluorite structure as discussed in Section 4.2.1. A decrease in the order of oxygen migration rate may be understood by the [electron screening effects. The oxygen diffusion rate in these systems can be sorted out as (a) common sense of diffusion and (b) the oxygen migration rate during the phase transition from one homologous phase into others. The oxygen migration rate during the phase transition is higher than the oxygen diffusion rate in the common sense (Inaba et al., 1981; Sugihara et al., 1981a).

4.3.2. SURFACE CHARACTER OF RARE EARTH OXIDES

Fast communication of the oxygen anions with gas oxygen must be related to the surface characteristics of the rare earth oxides. Figure 4.12 shows an atomic resolution TEM image of a surface of a TbOx (x R:i 1.83) particle. The surface is a stepped surface with {Ill} fluorite facets. The oxygen deficiency exhibits on the image as modulation contrast. The dark or white dots, depending on the specimen thickness and defocus (Section 6.3.4), indicate the cation columns projected along the beam direction. Although

a ... --- '"""---.

1 .83

U _____

~-- ~

--...

': 700 ^f-

~.::::::

=---.1.82

~ ~ ~

---.::::::---.: 1 81

~ 600 -

----s::::: ____ ^{:_=:::: .}

~ ---.::::: _ _ _ :---...: 1.80 ---..: '::---:1.79

500 - __

700

~ 600

Ql 2 '§ 500

Ql 0.

~ E 400 300

---178

---

^.

-5.0 -4.0 -3.0 -2.0 -1.0 0.0

b ^t

I

I I

LlG (0₂₎ kcal/mole O₂

- - - - . (8 -t) Hysteresis loop ----(8' -t) Scanning loop

6-=--- =~- ^-;

⁽

_~l

\1

1

<5

1.70 1.82

Composition x in TbOx

Figure 4.11. (a) Isobaric measurements that traverse a region of the ex-phase with different compositions, x. (b) Isobaric hysteresis of TbOx-02 system as a function of composition x. The 8' phase can be seen at the trial of the oxidation from 1 to 8. (Reprinted with permission from Elsevier).

167

FLUORITE-TYPE AND RELATED STRUCTURE SYSTEMS

168

CHAPTER 4

the oxygen atoms cannot be directly seen, a distortion in the cations and anions lattices caused by oxygen vacancies results in a modulation wave in the image, as indicated by arrowheads. Figure 4.13 shows a high-resolution profile image of Tb24044 • The superperiodicity on the surface corresponds to the periodicity of the modulation wave in the interior, indicating communication between the interior phase and the environment gas phase. An increase in surface area via either increasing the grain boundaries or reducing the grain size may promote the oxygen migration rate.

The surfaces of CeOx , PrOx , and TbOx particles usually are composed of {Ill}

facets (Fig. 4.12). These {1ll} facets can be a close-packing layer of oxygen anions or metal cations. Figure 4.14a shows a possible model for the one-atom-high surface step.

This type of step is a part of the unit cell and has very weak positive charges. If the facet of the step is larger than one atom high, the terminating atoms of the facet may be oxygen anions or oxygen vacancies (Fig. 4.14b). The oxygen vacancies can exist underneath the facet as well. These different structures make the surfaces of rare earth high oxides highly active chemically and physically. The surface oxygen anions have lower binding energy due to the unsymmetric interaction with the cations, so, they are easily released from the oxide. The measurements of temperature program reduction indicate an oxygen desorption peak at about 400DC, the intensity of which increases as the particle size decreases or the surface area increases (Trovarelli, 1996). The terminal oxygen anions

Figure 4.12. High-resolution TEM image of TbO_x (x R:J 1.83). The surface profile can .be clearly seen at atomic scale, the modulation structure inside the crystal can also be seen. A dislocation (D) is indicated.

also form the strongest negative charge center on the facet of the surface. It may dissociate the polar molecules and has electron transfer via redox reaction. An oxygen vacancy underneath causes the strongest positive charge center on the facet of the surface. This center can attract negative charge carriers, for example a water molecule which has strong dipole with negative oxygen terminated. This may be the reason that Ce02 can dissociate water to produce hydrogen. The theoretical calculation of the surface energy of Ce02 showed that the (111) surfaces have the lowest energy [Es(111)

=

1.707 (before relaxation), 1.195 J m-2 (after relaxation)] (Stayle et ai., 1992), and it was predicted that CO can be oxidized into CO2 at the oxygen site for COads

+

0 2- +* CO2

+

V2~, where V2- stands for oxygen vacancy. If the temperature and the partial oxygen pressure promote the formation of reduced intermediate phase the oxygen vacancy can be replaced by an oxygen anion due to chemical-potential-driven oxygen migration. The reaction will continue until the eqUilibrium reduced phase is established (Padeste et ai., 1993; Bozon-Verduraz and Bensalem, 1994; Laachir et ai., 1994). Methane can undergo partial oxidation (Otsuka et ai., 1993) or completely dissociated into H20 and carbon spheres, tubes, or amorphous film (Kang and Wang 1996; Wang and Kang 1996). This catalysis character is related to the structural feature of fluorite.

In fluorite-related rare earth higher oxides the lowest energy surfaces are {Ill}.

When the oxygen partial pressure varies the driving force of chemical potential difference between the reducing (or oxidation) phase and the present one can very quickly communicate with the surface oxygens or oxygen vacancies. Then the surface modification can easily occur as a result of atom migration stimulated either by heating or electron beam bombardment in TEM. A Pr02 particle appears immediately under the electron beam in TEM (with vacuum 10-⁶ Torr and beam energy 400 keY) and shows no modulation or superstructure, as shown in Fig. 4.15a, indicating that it is dioxide with fluorite structure oriented in [110]. After lO-min beam illumination, however, the surface morphology had dramatically changed, exhibiting a flat {Ill} surface with some steps (Fig. 4.15b). Some modulation and superstructure pattern also can be seen in the

Figure 4.13. HRTEM surface profile image of Pr24044 showing the relationship between the surface structure and the interior modulation structure.

169

FLUORITE-TYPE AND RELATED STRUCTURE SYSTEMS

170

CHAPTER 4

micrograph, indicating that it has been reduced to PrOx with x ~ 1.83. There are two driving forces for the migration: one is the concentration gradient and the other is the chemical potential difference between the reducing (or oxidizing) phase with the present one. The migration rate is fast in fluorite structure; for example, D(1000 K)

=

8.1 ^X 10-⁸ cm2/s for Ca-stabilized Zr02 and D(1000 K)

=

3.58 x 1O-⁹cm2/s for Pr7012, owing to the oxygen concentration gradient (Haire and Eyring, 1994). But the migration due to reduction or oxidation is faster than the diffusion-caused concentration gradient (Sugihara et al., 1981b).

Direct observation of the modulation movement (Fig. 4.16) proves the structure evolution from a fluorite structure (Fig. 4.16(1» into structures accompanying with the modulation wave sweeping (Fig. 4.16(2-4», while the composition changes from Pr02 to

(b)

The weake t po itive charge center

The sLronge t po itive charge center

v~

...

_

^...

A movable

Figure 4.14. Schematics of surface steps of fluorite-related rare earth high oxides for steps with (a) one cation height and (b) two cations height, where the outer oxygen anions and the underneath oxygen vacancies are shown.

Pr0l.83' That implies that exchanging the oxygen atoms between the solid and gas is directly related to the oxygen vacancies at the surface and in the solid. It is important to note that during that process the cation sublattice may have a minor distortion but never be destroyed. Of course, the cations at or near the surface may be swept away, but inside the crystal the cations are not heavily disturbed. Figure 4.17 gives a typical example. In this high-resolution electron micrograph a small twin (about 50 atom columns) sat on a larger surface step and the atoms in the twin region were hopping and when they absorb enough energy the entire aggregate rearranges to form an epitaxy layer on the substrate

a

Figure 4.15. HRTEM surface profile images of Pr02 showing atom migration on the surface during the reduction process. (a) The starting waving surface of Pr0₂ with one-atom high steps, (b) after a few minutes electron beam irradiation in a 10-⁷ Torr vacuum, where the surface transforms into a flat (111) facet with the formation of modulation structure of Pr₂₄0_{44 .}

Figure 4.16. In situ time-resolved HRTEM observations of the decom- position process from Pr02 to Pr01.g, showing the sweeping of the mod- ulation wave across the specimen when its composition is changed.

(Reprinted with permission from Elsevier).

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FLUORITE-TYPE AND RELATED STRUCTURE SYSTEMS

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CHAPTER 4

crystal. During this process some atoms of this twin were lost. These observations clearly demonstrate the following results: (a) the atoms of Ce, Pr, and Tb oxides on surfaces can easily hop at mediate temperatures and low gas pressures (such as 10-⁵ Torr); (b) sweeping of the modulation, which is due to wave distortion produced by the movement of oxygen vacancies on the cation and the anion lattice, reflects the movement of oxygen atoms and vacancies in the solid and at the surface; and (c) the cation sublattice is never heavily disturbed by this movement of oxygen vacancies. In other words, oxygen diffusion still preserves the cation sublattice.

In contrast, the transition metal oxides are different. Figures 4.18 and 4.19 show atom migration on the surfaces of terbium oxide and lead oxide (PbOz), respectively. In Fig. 4.18 the terbium atoms are hopping on the surface individually, but in Fig. 4.19 the lead atoms of lead dioxide, which has rutile-related structure, are migrating as groups of Pb-O octahedra. This data clearly indicate the basic difference between the ionic bonding in rare earth oxides and the ligand field effect of the d electron orbitals in transition metal oxides. This difference significantly affects the oxygen diffusion process in these materials.

4.3.3. DISPROPORTIONATION OF RARE EARTH HIGH OXIDES

In the lanthanide series only five elements have two valence states: Eu and Yb with 2+ and 3+; Ce, Pr, and Tb with 3+ and 4+. Ce, Pr, and Tb form mixed valent oxides that can be represented by a homologous series RnOZn-Zm' In these oxides the cations have 3+ and 4+ valence states. Their distribution in the lattice could be solved indirectly by structure analysis. As we discussed in Chapter 3 about perovskite structure, the disproportionation of a cation means that a single-valance cation decomposes into two valence states; M n+ decomposes, for example, into M(n-l)+ and M(n+l)+ or M n+ and MCn-l)+ (or MCn+l)+).

It is well known that trivalent terbium can be solved in dilute nitric acid, but tetravalent terbium does not. Diluted nitric acid is used to leach the trivalent terbium and

Figure 4.17. Atom hopping and structure transformation of a tiny twin in ThO_x (x~ 1.83) oxide. (a, b) The hopping took a longer time, while (c, d) the accretion occurred very quickly.

then examine the structure change of Tbll 020 and Pr7012 . The starting material is a solid whose HRTEM image was given in Figure 4.12, but after the leaching process the solid particle exhibits porosity with a form of "Swedish" cheese. X-ray diffraction indicates that the solid is a dioxide. High-resolution electron micrograph (Fig. 4.20a) reveals that this dioxide material has some modulation particularly around the hole region. The surface of the hole is still {Ill} facets, and the modulation surrounds the hole and extends to the surface. This observation implies that Tb³+ and Tb⁴+ have electron exchanging with each other to form local regions with either Tb3+ or Tb⁴+ compound.

The region dominated by Tb3+ cations is de solved into the diluted nitric acid solution, while the region with Tb4+ cations remains unetched. The Tb3+ cations discharged from the solid may accumulate in the regions containing dislocations, as shown in Fig. 4.12 (Kang and Eyring, 1988a and b). From the structure point of view, the trivalent cations should have more oxygen vacancies than their neighbors. The region with accumulation of trivalence cations may be accompanied with segregated oxygen vacancies and electron migration, which means that electron exchange and oxygen diffusion do not lead to reorganization of Tb⁴+ cation sublattices. These processes only tailor some local regions and keep the rest of them unchanged. The pore size is about several tens of nanometers.

The cation sub lattice is a superstable frame, a character of the fluorite structure. Electron hopping may be promoted by the oxygen anion migration during the leaching process. As

Figure 4.18. A sequence of HRTEM images showing individual atom hop- ping on the surface of terbium dioxide.

(Reprinted with permission from Else- vier).

173

FLUORITE-TYPE AND RELATED STRUCTURE SYSTEMS