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Lattice parameters of cubic solid solutions in the systems uR2O3-(1-u)MO2
CERAMURGIA
INTERNATIONAL,
Vol.
4, n. 4. 1978
attic
Phase Sc, Y, sition In the
relations in the systems uf?D~ -- (l-uI~lMO2 (W” = Ln; W+ = Zr, Hf) depend on the molar compoand ionic size of PI”’ and M”. case of smaller ions (9 =Y, Yk), Er, Dy), stable cubic vaca s of the fluorite type, the exist in the concentration range of u from 0.05 to 0.50 F&O,. At lower concentrations the F-phases coexist with Zr0, or tiif02, at high concentrations with solid solutions (MI,),, of the B or !-I type. For larger R ions (H = La, Pr, Nd, Sm), in the concentration range of u from -0.17 to 0.50 R,Oa the predominant a ~yro~~io~e P-type phase of composition ~+x~Llix~2~ The solid solutions of this phase th a cubic vacant phase F, when ~~0.33 or with a cubic vacant phase FI when u>O.33. At lower centrations fuO.50 the FGphase coexists with solid solutions (HD&, of the or X type. At I e, higher concentrations Iu>O. y the solid solutions The formation of vacant solid solutions R,h prevents the ma~ensit~c phase transformat clinic @ tetragonal MO2 due to the change in ~ecb~olo~y for the so-call it is ne
“I11S3’and by elimination of anions ‘“0’ (the cationic sublattice retains the most dense cubic packing of F-type, the coordination ‘“8” remains, the anionic deficiency leads only to dist~r~~o~ of oxygen ~o~yb~~r~ “I. Supposing that there is a direct contact between cations (position 4a:O,O,OI and anions (position 8c: l/4. l/4 l/4) in the Fm3m structure type, one can derive a generai formula which will describe the influence of cationic substitutions and of the presence of anionic vacancies on the parameter a in the fluorite-like vacant phase of the type (V”‘R3+)~(V”‘j\n’+)I~r(‘VO*-)2.1,2UxiZ~where R = Sc, Y, Ln and M = Zr, Hf, Th. The dependence of a on tho composition and ionic radius is ex follows: a = The average
4/ 43
ionic
r[“‘JlS,M”‘)
[r(““%,M”+)
radius -:- xrf”“’
-t- r(I’
in position 3’)
.+
Cl]
(4a) is
~~.“x~~~““I~4+~
:21
The effective anionic radius of cations in position f&I, r(‘“O’-).ri. depends on the number of anionic vacancies per one oxygen atom (l-x/4). The space occupied by en ions is V,H = 413 ~[r[‘“Q’~]]’ (1-x/4). Then 21.B -= r(I”02-) (I- X/4)“k, where k = 3 for non-inteng vacancies and k>3 for the ass~cja~~on of vacancies. To make calculations, the fol~ow~~~ expression was used:
r[I” where r[‘“W)
131 ‘I.38 A” (Ref. 3)
The values of x in Eqs. (2) and (3) are cai the molar composition of the system uR according to the formula: the genetic relation between structural types F, and C. it is known ’ that oxide compounds can be joined into large groups of phases owing to their crystal-chemicaii s~rnilar~t~. These phases differ in composition and stoi-
x =
2u/[l
+u)
[4]
The general applicability of the equations thus derived is illustrated in Figs. 1, 2 and in the Table which gives a comparison between calculated and observed data. In our calculations we used ionic radii obtained by Shannon and Prewitt’ by taking into account the valen. cy, the coordination number and the spin of ions. The lattice parameters were determined experimentally for a whole series of cubic fluorite-like vacant solid solu.. tions. The synthesis of solid solutions was carried out 1500” to 1800°C using crystal phases were i lysis at 20°C using diff 1540, Geigerflex D-2
t
I t
CERAMUHGIA
178 2.
and C&IL-radiation. In addition to Ihe valu’es thus obtained, the figures and the table contain the literabetween a,,1 and aoh. shows ture data, Comparison good agreement between them with an accuracy sufficient for solving a number of industrial prablems: a,,) I aUbSdoes not exceed 3- 0.03 A. The greatest deviations are observed at small and great values of x, in which cases the insufficient accuracy of the determination of ionic radii and parameter K shows up most clearly. Thus, knowing the depe~d~~~e of a,.] on the chess com~oai~~on one can calculate the lattice parameter for the non~st~died cubic phases using single X-ray data the homogeneity bounfor binary regions ot determine
arks
of Phese
SHANNON,
4. W.F.
KtEE,
Page
114
(line (line
Page
113
(l~ine 3 1 from
bottwn)
25 from
11 hm
C.T.
Acta
G. WEITZ.
J. Inorg.
Chem.
Bull.
Franc.
9, A.
ROUANET,
IO. Crystal Ondik,
Rev.
int.
W. BAUKAL, (19SSl 610.
12. M.
PEREZ y JORBA, ROUANET,
Ceramurgia
15. R. CQLLQNGUES, ROUX, Bull. Sot.
E(Ef)
31 (1969) N 102
9971. (1969)
925.
2367.
(19741
I
Temp.
chim..
Ber,
instead
of
of
RBfract.
47.
7
(t98a)
267
(1968)
Intern.
d (1975)
8
o,dE ‘1. < 3 % 3
[ Ef, i.e. E(E) 1
Neuk
R/iat.
Re#s.
($9711
Donnay
Dwch.
rend,
Elirn
instead
et
Ed. J.D.H.
Kerd,lri.
and
$77. H.M.
Ges.
45
479, 13283 IO.
J. LEFEVlRE, M. PEREZ‘ y JORBA, Chim. France N. 1 (19621 149.
of
1
Ann.
Comptes
2E
[
625
R. COLLONGUES.
Tables,
R. SCHEIDE~GGEH,
13. A,
14. P. DURAN.
< 30%
Hautes
Data Determinative V. 2. 1973.
a.de bottom)
Ceram.
8. D. MICHEIL. M. PEREZ y JORBA. Bull. 9 (1974) 1457.
instead
bottom)
Sot.
Paris. Cryst.
4, n. 4;1978
7. V.B. GLUSHKOVA. L.U. SAZONOWA. F. HANIC, lzv. &ad, SSSR, Ser. Neorgan. Materialy $4 (1978) 2096.
i/u. A. PYAIENKO. and their Artificial
2E
non-stoechio#m&rie, PREWITT.
5. P. DURAN,
Il.
Elim
La
GOLLONGUES,
Vol.
6. t-l. LANDOLT-R. B~~HNSTEIN. Numerical Data and Functional Relationships in Science and Technology, New Series, Group III, v. 76, Structure Data of Inorganic Compounds, 1975,
phases.
I. AA. VOtlONKOV, N.G. SHU’MYAISKAYA. Crystal Chemistry of Zirconium Minerals Analogs, ccNauka 1~~1978.
R.
3. R.D.
IN’TERNATIONAL,
F. ~~‘~~-,
INTERNATIONAL,
Vol.
4, n. 4. 1978
attic
Phase Sc, Y, sition In the
relations in the systems uf?D~ -- (l-uI~lMO2 (W” = Ln; W+ = Zr, Hf) depend on the molar compoand ionic size of PI”’ and M”. case of smaller ions (9 =Y, Yk), Er, Dy), stable cubic vaca s of the fluorite type, the exist in the concentration range of u from 0.05 to 0.50 F&O,. At lower concentrations the F-phases coexist with Zr0, or tiif02, at high concentrations with solid solutions (MI,),, of the B or !-I type. For larger R ions (H = La, Pr, Nd, Sm), in the concentration range of u from -0.17 to 0.50 R,Oa the predominant a ~yro~~io~e P-type phase of composition ~+x~Llix~2~ The solid solutions of this phase th a cubic vacant phase F, when ~~0.33 or with a cubic vacant phase FI when u>O.33. At lower centrations fu
“I11S3’and by elimination of anions ‘“0’ (the cationic sublattice retains the most dense cubic packing of F-type, the coordination ‘“8” remains, the anionic deficiency leads only to dist~r~~o~ of oxygen ~o~yb~~r~ “I. Supposing that there is a direct contact between cations (position 4a:O,O,OI and anions (position 8c: l/4. l/4 l/4) in the Fm3m structure type, one can derive a generai formula which will describe the influence of cationic substitutions and of the presence of anionic vacancies on the parameter a in the fluorite-like vacant phase of the type (V”‘R3+)~(V”‘j\n’+)I~r(‘VO*-)2.1,2UxiZ~where R = Sc, Y, Ln and M = Zr, Hf, Th. The dependence of a on tho composition and ionic radius is ex follows: a = The average
4/ 43
ionic
r[“‘JlS,M”‘)
[r(““%,M”+)
radius -:- xrf”“’
-t- r(I’
in position 3’)
.+
Cl]
(4a) is
~~.“x~~~““I~4+~
:21
The effective anionic radius of cations in position f&I, r(‘“O’-).ri. depends on the number of anionic vacancies per one oxygen atom (l-x/4). The space occupied by en ions is V,H = 413 ~[r[‘“Q’~]]’ (1-x/4). Then 21.B -= r(I”02-) (I- X/4)“k, where k = 3 for non-inteng vacancies and k>3 for the ass~cja~~on of vacancies. To make calculations, the fol~ow~~~ expression was used:
r[I” where r[‘“W)
131 ‘I.38 A” (Ref. 3)
The values of x in Eqs. (2) and (3) are cai the molar composition of the system uR according to the formula: the genetic relation between structural types F, and C. it is known ’ that oxide compounds can be joined into large groups of phases owing to their crystal-chemicaii s~rnilar~t~. These phases differ in composition and stoi-
x =
2u/[l
+u)
[4]
The general applicability of the equations thus derived is illustrated in Figs. 1, 2 and in the Table which gives a comparison between calculated and observed data. In our calculations we used ionic radii obtained by Shannon and Prewitt’ by taking into account the valen. cy, the coordination number and the spin of ions. The lattice parameters were determined experimentally for a whole series of cubic fluorite-like vacant solid solu.. tions. The synthesis of solid solutions was carried out 1500” to 1800°C using crystal phases were i lysis at 20°C using diff 1540, Geigerflex D-2
t
I t
CERAMUHGIA
178 2.
and C&IL-radiation. In addition to Ihe valu’es thus obtained, the figures and the table contain the literabetween a,,1 and aoh. shows ture data, Comparison good agreement between them with an accuracy sufficient for solving a number of industrial prablems: a,,) I aUbSdoes not exceed 3- 0.03 A. The greatest deviations are observed at small and great values of x, in which cases the insufficient accuracy of the determination of ionic radii and parameter K shows up most clearly. Thus, knowing the depe~d~~~e of a,.] on the chess com~oai~~on one can calculate the lattice parameter for the non~st~died cubic phases using single X-ray data the homogeneity bounfor binary regions ot determine
arks
of Phese
SHANNON,
4. W.F.
KtEE,
Page
114
(line (line
Page
113
(l~ine 3 1 from
bottwn)
25 from
11 hm
C.T.
Acta
G. WEITZ.
J. Inorg.
Chem.
Bull.
Franc.
9, A.
ROUANET,
IO. Crystal Ondik,
Rev.
int.
W. BAUKAL, (19SSl 610.
12. M.
PEREZ y JORBA, ROUANET,
Ceramurgia
15. R. CQLLQNGUES, ROUX, Bull. Sot.
E(Ef)
31 (1969) N 102
9971. (1969)
925.
2367.
(19741
I
Temp.
chim..
Ber,
instead
of
of
RBfract.
47.
7
(t98a)
267
(1968)
Intern.
d (1975)
8
o,dE ‘1. < 3 % 3
[ Ef, i.e. E(E) 1
Neuk
R/iat.
Re#s.
($9711
Donnay
Dwch.
rend,
Elirn
instead
et
Ed. J.D.H.
Kerd,lri.
and
$77. H.M.
Ges.
45
479, 13283 IO.
J. LEFEVlRE, M. PEREZ‘ y JORBA, Chim. France N. 1 (19621 149.
of
1
Ann.
Comptes
2E
[
625
R. COLLONGUES.
Tables,
R. SCHEIDE~GGEH,
13. A,
14. P. DURAN.
< 30%
Hautes
Data Determinative V. 2. 1973.
a.de bottom)
Ceram.
8. D. MICHEIL. M. PEREZ y JORBA. Bull. 9 (1974) 1457.
instead
bottom)
Sot.
Paris. Cryst.
4, n. 4;1978
7. V.B. GLUSHKOVA. L.U. SAZONOWA. F. HANIC, lzv. &ad, SSSR, Ser. Neorgan. Materialy $4 (1978) 2096.
i/u. A. PYAIENKO. and their Artificial
2E
non-stoechio#m&rie, PREWITT.
5. P. DURAN,
Il.
Elim
La
GOLLONGUES,
Vol.
6. t-l. LANDOLT-R. B~~HNSTEIN. Numerical Data and Functional Relationships in Science and Technology, New Series, Group III, v. 76, Structure Data of Inorganic Compounds, 1975,
phases.
I. AA. VOtlONKOV, N.G. SHU’MYAISKAYA. Crystal Chemistry of Zirconium Minerals Analogs, ccNauka 1~~1978.
R.
3. R.D.
IN’TERNATIONAL,
F. ~~‘~~-,