thermodynamics of rare-earth sesquioxidesproject.tyndall.ie/realise/workshop/zinkevich.pdf ·...

Thermodynamics of rare-earth sesquioxides

Matvei Zinkevich

Max-Planck Institut für MetallforschungStuttgart, Germany

Now at Heraeus Sensor Technology GmbH, Kleinostheim, Germany

Zinkevich M., Thermodynamics of rare earth sesquioxides, Progress in Materials Science, 52 (4) 597-647 (2007)

Realise Workshop Dresden, September 19, 2008 2

Crystal Structures

A-type, e.g. La2O3 B-type, e.g. Sm2O3 C-type, e.g. Y2O3

High-temperature phases

H-type X-Type


Polymorphism


Objectives

Gibbs energy is a fundamental thermodynamic function, from which many important materials properties can be derived:

Enthalpy, entropy, heat capacity

Isothermal compressibility, thermal expansion

Aim of the work: to revise the Gibbs energy functions of rare-earth sesquioxides as well as to estimate the unknown energetics of phase transformations

0

( , ) ( ) ( , ) ( )P

physm m m m

PG T P G T V T P dP G T° = ° + + ∆∫

( ) ln( ) nm n

nG T a bT cT T d T° = + + +∑

Zinkevich M., Thermodynamics of rare earth sesquioxides, Progress in Materials Science, 52 (4) 597-647 (2007)


The molar volume of solid phases

Filled symbols: measured values

Open symbols: extrapolated values

C

BA

C ⇒ B

B ⇒ A


High-pressure phase transitions

transH SP TV V

∆° ∆°= − +∆ ∆

Enthalpies and entropies of phase transitions were estimated from high-pressure data using thermodynamic relationships

transH VT PS S

∆° ∆= +∆° ∆°

dP SdT V

∆=∆


Enthalpies and entropies

Low-temperature phases

Filled symbols: measured values

Open symbols: derived from high-pressure transition data

Correlated behaviour of the volume change and the entropy change

∆S/∆V = const.


Enthalpies and entropies

High-temperature phases

Calculated under assumption of a constant entropy change for given phase transition


The molar volume of liquid phases


The entropy of fusion

∆Sfus = nRln2 + γGCV(∆V/V)

metals: n = 1oxides: n = 2.5

Entropies of fusion of rare-earth sesquioxides are estimated based on the known values for yttria


The enhalpy of fusion


Heat capacity

Effect of cation size on the lattice heat capacity of R2O3


Heat capacity

Effect of f-electrons on the heat capacity of A-R2O3

La3+ ⇒ 4f 0

Ce3+ ⇒ 4f 1

Pr3+ ⇒ 4f 2

Nd3+ ⇒ 4f 3


Heat capacity

Effect of f-electrons on the heat capacity of B-R2O3

Sm3+ ⇒ 4f 5

Eu3+ ⇒ 4f 6

Gd3+ ⇒ 4f 7


Heat capacity

Effect of f-electrons on the heat capacity of C-R2O3

Tb3+ ⇒ 4f 8

Dy3+ ⇒ 4f 9

Ho3+ ⇒ 4f 10

Er3+ ⇒ 4f 11

Tm3+ ⇒ 4f 12

Yb3+ ⇒ 4f 13

Lu3+ ⇒ 4f 14


Phase diagram calculation

Regular solution model

Minimizing Gm at each temperature ⇒ phase diagram

ln αrefm i i i i ij i j

i i i j iG xG RT x x x x

>° = + +∑ ∑ ∑∑

mechanical mixture of oxides

ideal entropy of mixing

interaction parameter



Similar ionic radii ⇒ ideal mixing behaviourno interactions in solution phases



large differences in the sizes of Sc+3 and Yb+3/Er+3

repulsive interactions in solid solution phases



small differences in ionic radii of Sm+3/Gd3+ and Y+3

weak repulsive interactions in B, H, and X-phasesweak attractive interactions in C and A-phases ⇒ SRO



large differences in ionic radii of Y+3/Yb3+ and Nd+3

strong repulsive interactions in solid solution phasesinterim monoclinic phase (B), entropy-stabilized



XXL differences in ionic radii of Dy+3/Ho3+ and La+3

strong repulsive interactions in solid solution phasesinterim monoclinic phase (B), entropy-stabilized


Conclusions I

Reexamination of all known thermodynamic data for rare earth sesquioxides lead to improved values of the Gibbs energy functions.

Using ionic radius of a trivalent rare earth cation as an universal parameter, it was possible to generate a new knowledge.

In this way, reasonable estimates for the relative stabilities of different structures, including metastable modifications as wellas for the enthalpies and entropies of melting were obtained.

It is hoped that all these data will be useful for many practical applications of rare earth sesquioxides, but also for thermodynamic calculations of phase diagrams.


Thermodynamics of rare-earthoxides - zirconia systems

Wang Ch., Zinkevich M., Aldinger F., Phase diagrams and thermodynamics of rare-earth doped zirconia ceramics, Pure and Applied Chemistry, 79 (10) 1731-1753 (2007)


Research objectives

Chemistry

ZrO2 − YO1.5

ZrO2 − LaO1.5ZrO2 − NdO1.5ZrO2 − SmO1.5ZrO2 − GdO1.5ZrO2 − DyO1.5ZrO2 − YbO1.5

ExperimentalMethods

XRDSEMEDX

EPMAWDXDSCTEMDTA

Modeling and Calculations


Thermodynamic models

Liquid: (Zr+4,RE+3)p(O-2,Va-q)q

Cubic, Tetragonal, Monoclinic:

(Zr+4,RE+3)2(O-2,Va)4

C, B, A, X and H − RE2O3:

(Zr+4,RE+3)2(O-2)3(O-2,Va)1

Pyrochlore:

(RE+3,Zr+4)2(Zr+4,RE+3)2(O-2,Va)6(O-2)1(Va,O-2)1

(RE+3,Zr+4)2(Zr+4,RE+3)2(O-2,Va)8 (for RE=Gd)

RE4Zr3O12 (δ):

(Zr+4)1(RE+3,Zr+4)6(O-2,Va)12(Va,O-2)2


ZrO2 - La2O3/Nd2O3

highly-stable pyrochlore phaselow solubility of Zr in the A-form


ZrO2 - Sm2O3/Gd2O3

pyrochlore phase domain widens and becomes less stableZrO2-Gd2O3: second-order phase transition, the C-phase emerges


ZrO2 - Dy2O3/Yb2O3

pyrochlore phase becomes unstable, δ-phase appearshigh solubility of Zr in the C-phase


Enthalpy of formation


Conclusions II

Phase equilibria in ZrO2-REO1.5 (RE = La, Nd, Sm, Gd, Dy, Yb) systems have been experimentally investigated in the temperature range 1400-1700°C.

Thermodynamic modeling and calculations have been carried out for above systems to obtain self-consistent thermodynamic parameters.

The characteristic evolutions in those ZrO2-REO1.5 systems are established for the first time, including the phase relations, solubility ranges, thermodynamic properties and ordering.

These rules can be generalized for other uninvestigated binary and even multicomponent systems.

thermodynamics of rare-earth sesquioxidesproject.tyndall.ie/realise/workshop/zinkevich.pdf ·...

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