- Email: [email protected]
Calculation of quasibinary and quasiternary oxyntiride systems-IV
CALPHAD vo1.5, No.3, Printed in the USA.
pp.163-184,
1981.
0364-5916/81/030163-22$02.00/O (c) 1981 Pergamon Press Ltd.
CALCULATION OF QUASIBINARY AND QUASITERNARY OXYNTIRIDE SYSTEMS-IV* Larry Kaufman, Fred Hayes+ and Dunbar Bimie ManLabs, Inc., 21 Erie Street Cambridge, Massachusetts 02139 USA (This paper was presented at CALPHAD X, Vienna, Austria, July 1981) ABSTRACT. A data base is being developed for calculation of quasi-binary and quasi-ternary phase diagrams of ceramic systems (l-3). Previous segments of this base cover combinations of Cr203, MgO, A1203, Fe203, Fe304, "FeO", SiO2, CaO. SijN4 and AlN. Lattice Stability, Solution and Compound Phase Parameters were derived covering the liquid, spinel,corundum,periclase, crystobalite, tridymite, quartz, hexagonal and beta prime phases which appear in the binary systems composed of pairs of these compounds. Compound phases formed from specific binary combinations of these compounds (i.e. MgO-Cr 0 ) were also characterized. This description is 2I y and phase diagrams for the binary systems of based on observed thermochemxst interest. Selected ternary systems have been computed based on the foregoing data base for comparison with experimental sections in order to illustrate the usefulness of the data base. The present paper extends the data base to cover BeO, Y203 and Ce203 additions. Moreover, ternary sections in the Si02-MgO-Si3N4, Si02-Y203-Si3N4 and Si02-Ce203-Si3N4 were calculated between 1900K and 2100K for comparison with experiment. 1. Introduction The utility of computer based methods for coupling phase diagrams and thermochemical data for metallic systems has been well documented in many papers published in this journal. A considerable effort is being applied toward developing an extensive base for metallic systems. Recently similar efforts have begun in order to provide a similar facility with ceramic systems. The expanded studies of SIALON composites, combining silicon and aluminum nitrides with oxides of silicon, aluminum, magnesium, beryllium, cerium and yttrium and other metals has provided additional motivation for predicting multicomponent phase diagrams of ceramic systems. 2. Description of the Thermochemical System Employed to Characterize Solution and Compound Phases The method utilized for describing solution and compound phases is the same as that employed earlier (l-3) comprising so e symbolic usage which facilitates data handling as indicated below. The free energy, G1 , of a liquid (solution) phase, L. in the binary system Y203-Be0 is given by Equation (1) where T is in Kelvins, R=8.314 J/g. atoK, while x is the atomic fraction of BO(i.e. BO=+BeO)
and(l-x)is the fraction of YO(i.e. 1/5Y203).
The mass basis is thus one mole of atoms (i.e. a gram-atom) * This work has been sponsored by the Air Force Office of Scientific Research, Bolling AFB, Washington, D.C. under Contract F44620-80-C-0020
t
On leave from Department of Metallurgy, University of Manchester-UMIST, Manchester, England.
Received 15 June 1981
163
L. Kaufman, F. Hayes and D. Birnie
164
L L G =(1-x) “GYO+x~~O+RT(x&-~x+(l-x)&(1-x1+x(1-x)
[LYOBO(l-x)+xLBOYO] J/g.at
L and ‘Gko are the free emrgies of are gram atom of pure liquid \Jmre0GYo
YOand BO.
Table 1 defines
the lattice stabilities of the liquid and solid forms of YO. BO and the other components of current interest. These data derived from earlier studies and compilations of thermochemical and phase diagram data, (l-8), when combined with the solution and compound phase parameters shown in Tables 2 and 3 permit calculation of the binary phase diagrams shown in Figures 1-12. The solution parameters LYOBOand LBOYO,which describe the liquid Y203-Be0 solution are listed in Table 2 (LYOBO=LBOYO=-2092 Joules/g.at). Similar parameters for the liquid and solid phases are listed in Table 2. The free energy of the solid phases are described in a manner similar to equation (1). Thus, for example, the free energy of the body centered cubic (Mn203)Y phase in the YO-BO system is given by Y OY G =(1-x) Gyo+xti,+RT(&nx+(l-x)&(1-x))+x(l-x)
[YYOBO(l-x)+xYBOYO] J/g.at.
(2)
The solution parameters for the Y phase (YYOBO=YBOYO=-2092 J/g.at) are listed in Table 2.Thefree energy difference between the L and Y forms of YO and BO, i.e. YOYOLY-‘GL-‘GY YO YO and ‘Gko- ‘Gio= BOBOLYare listed in Table 1. The free energy of a compound phase such as G=(1/7)(Si02’2BeO)=SOD~42gBOD~571 is defined phase,
the compound parameter,
on the basis
C, and the stoichiometry
of Table 3 in terms of the base by equation
(3)
GG=O.429G~o+O.S7lG~o+(O.429)(O.S7l)[O.429LSOBO+O.S7lLBOSO -C] J/g.at. Reference Thus
to Table 2 shows that LSOBO=LBOSO=41840 J/g.at
G N G =0.429GS0+0.571GB0 N -4971+1.8133
(3)
while Table 3 shows that C=62132-7.406T.
J/g.at.
(4)
At 298K reference to Figure 1 shows that the stable form (designated R). Table 1 shows that
form of quartz
GN SO-G~0=SOSOLR-SOS0LN=S042-1.004T J/g.at.
is the beta (S)
Substitution of equation (5) into equation (4) yields an expression for the free energy of formation of (1/7)(Si02’Be0) at 298K from the stable forms of it s compound components as, AGf[298K]=GG-0.429G~o-0.S71G~o=-2808+1.382T
J/g.at.
(6)
Reference to Table 4 shows that this result is in keeping with the experimental(8) thermochemical data on the free energy of formation of2BeO*Si02. Table 4 also displays the calculated free energy of formation for the remaining compounds listed in Table 3 and shown in Figures l-12. It should be noted that this compound parameter for SNo ,SOo 3 currently shown . . as C=62760-1.25ST J/g.at. has been revised from the previously stated value C=llSOdO-25.lOT J/g.at.(S)Fhe current value is based on the assessment of Doerner et al (5) and leads to slight revisions in the previously calculated SN-SO and SO-AO-SN phase diagrams presented earlier (3). The revised versions, which differ slightly from the earlier results are shown in Figures 8 and 13. 3.
Calculation
of Quasi-Ternary
Phase Diagrams
The free energy of ternary solution phases was synthesized from the binary solution phases on the basis of Kohler’s equation as in the previous papers (l-3). On this basis the free energy of the liquid phase in the SO-MO-SNsystem where x is the atom fraction MO, y is the atom fraction SN and l-x-y is the atom fraction SO is given by
165
QUASIBINARY AND QUASITERNARY OXYNTIRIDE SYSTEMS IV
TABLE 1 SUMMARY OF LATTICE STABILITY PARAMETERS (All units in Joules per gram atom (mole of atoms), T in Ke1vin.s) A0 = (WAl203,
SO = (1/3)SiO2, MO = (1/2)MgO, AN = (1/2)AlN, Sty= (1/7)Si3N4
BO = (1/2)BeO, YO = (1/5)Y203, CE = (1/5)Ce203 P = Periclase, C = Corundum, X = Crystobalite, T = Tridymite, H = a quartz R = 6 quartz, B = beta Si3N4, N = hexagonal AlN and BeO, Y = body centered cubic (Mn203)Y203 and Ce203 structure BOBOLN' = (l/Z)BeO(Liquid)-(1/2)BeO(hexagonal) YOYOLY = (l/S)Y,O,(Liquid)-(l/5)Y203(body centered cubic) YOYOLY YOYOLN YOYOLX YOYOLB YOYOLC
= 22694 - 8.3683 = O- 14.1423 = 0 - 2.092T = o- 12.510T = o- 10.209T
CECELY CECELN CECELX CECELB CECELC
= 20334 - 8.368T 0 - 14.142T = = 0 - 2.092T 0 - 12.510T = = 0 - 10.209T
BOBOLN BOBOLX BOBOLC BOBOLB BOBOLY
= 40376 - 14.142T 1.674T = o= o- 10.209T = o- 12.510T = o8.3681
AOAOLY ANANLY SNSNLB SNSNLY SOSOLY SOSOLN SOSOLX SOSOLR
= 0 - 8~3683 0 - 8.368T = = 33949 - 12.510T = 0 - 8.368T 0 - 2.092T = = 0 - 2.092T = 3347 - 1.674T = 5042 - 3.0963
* These differences specify the free energy of one phase (i.e. liquid) minus the free energy of the second phase (i.e. hexagonal) for a given compound. L L L G =(l-x-y)"GSO+~oGMO+yOGSN L +RT[(l-x-y)k(l-x-y)+xkx+ykry] +(l-x-y)x(l-y)-1[(l-x-y)LSOMO+xLMOSO]+xy(x+y)-1[xLMOSN+yLSNMOJ +(1-x-y)y(l-x)-l[(l-x-y)LSOSN+yLSNSO] J/g.at.
(7)
The solution parameters required to specify GL were defined previously (2,3) as and LSOMO=LMOSQ=-106274+42.01Tfor 0.4_rx~&l.O and LSOSN=LSNSO=lMOSN=LSNMO=29288J/g.at. LSOMO=-24267+24.27T;LMOSO=-229283+68.62Tfor 0.0~31&0.40.
These parameters permit explicit
definition of GL in composition ranges where (x/l-x-y) is more than 0.667 and ranges where (x/l-x-y) is less than 0.667. In the latter range the miscibility gap present in the SO-MO binary system propagates into the ternary SO-MO-SN as shown in Figure 14a. Here the ternary miscibility gap shows the tie lines connecting the coexisting liquid compositions Ll and L2. The remaining solution phases in this system, i.e. P, X, B, etc. are defined in similar fashion to Equation 7. The resulting equilibria between the L and P solutions are depicted by the tie lines traversing the two phase L+P field shown in Figure 14(b). The compound phases F,R and BP which appear in the SO-MO, SO-SN and MO-SN binary systems are defined Thus for example along the lines previously established (l-3) and are specified in Table 3. ;ie free energy of the SN0.7S00.3 (R) phase in the SO-MO-SN system is defined by Equation 8
L. Kaufman,F.
166
Ifayes
and
D.
Bisnie
TABLE 2 SUWARY OF SOLUTIONPHASE PARAMETERS (Allunits in Joulesper gram atom (moleof atoms),T in Kelvins) L = Liquid,N = hexagonal,X = Crystobalite, T = Tridymite,Y = body centeredcubic B = beta Si3N4,A0 = (l/S)A1203, SO = (1/3)SiO2,AN = (1/2)AlN, SN = (1/7)Si3N4, BO = (1/2)BeO YO = (1/5)Y203,CE = (l/S)Ce203 LSOBO = LBOSO = 41840 NSOBO = NBOSO = 83680 XSOBO = XBOSO = 83680 TSOBO = TBOSO = 83680
LBOSN = LSNBO = 20920 BBOSN = BSNBO = 83680 NBOSN = NSNBO = 83680'.
LYOBO = LBOYO = -2092 YYOBO = YBOYO = -2092 NY080 = NBOYO = 83680
LYOAO = LAOYO = 12552 YYOAO = YAOYO = 83680
LAOBO = LBOAO = 8368 CAOBO = CBOAO = 83680 NAOBO = NBOAO = 83680
LYOAN = LANYO = 20920 WOAN = YANYO = 83680 NYOAN = NANYO = 83680
LBOAN = LANBO= 20920 NBOAN = NANBO = 83680
LSNSO
LCESN = LSNCE = 4180 BCESN = BSNCE = 62760 YCESN = YSNCE = 62760
GR =
bYOA0
= CAOYA = 83680
=
LSOSN = 29288 XSNSO = XSOSN = 125520 TSNSO = TSOSN = 125520 LYOSN = LSNYO = 4180 BYOSN = BSNYO = 83680 YYOSN = YSNYO = 83680
0'xs&0.60* LYOSO = LSOYO = -92048+36.821 0.6zxs&l.0 LYOSO = LSOYO = woso = XYOSO = TYOSO =
-216,000+66.94T -9414+16.74T YSOYO = 83680 XSOYO = 83680 TSOYO = 83680
0&xs&0.60 LCESO = LSOCE = -92048+ 36.82T 0.6
z”GB SN+x”G~o+~o~o+(‘-~~l~‘-x))lbGA+~~/~~-~~~A~B +RT(y&y+z&z-(1-x).fZn(l-x)j+AGE J/g.at.
(8)
where x=xso,y=yMO and z=zSN. Since the compoundphase runs from p=(x,-x:)/(1-x,)=0 and x=x~+yp=x~=O.J, and r=l-xi-y(l+p)= SN0.70S00.30 to M00.70S00.30~ 0.7-y. Since = -7029 + 0.263T J/g.at. AGA = (0.3)(0.7)[0.7LSNSO+O.3LSOSN-C] and AGB = (0.3)(0.7)[0.7lMOS0+0.3LSOM0-C] = -22318t 8.8221 J/g.at.
(9) *
from Tables 3 and S and the previousvalues of LSNSO,LSOSN,lMOS0 and LSOMO (2) given in the above text. The excess free energyof mixing,AGE, for the compoundis given (3) by AGE
= CAByz/(1-x)
However,CAB is taken as zero in all the cases treatedhere thus Equation8 can be written explicitlyas follows: GR = (0.70-y)'G~N+0.3"G~o+y~~o - (I-(y/O.7))(7029-0.263T) -(y/O.7)(22318-8.822T)+RT(y~ny+(O.7-y)~n(0.7-y)-0.7~0.7) (11) where y=yMo. Since the latticestabilitiesof SN, SO and MO (i.e.SNSNLB,SOSOLB and MOMOLB) have alreadybeenspecifiedthe R-L equilibria(Figure14~) can be computed.Figs.(14a)through
QUASIBINARY AND QUASITERNARY OXYNTIRIDE SYSTEMS IV
167
TABLE 3 SUMMARY OF COMPOUND PARAMETERS FOR BINARY SYSTEMS (All units in Joules per gram atom (mole of atoms) T in Kelvins) Compound
Name
Stoichiometry
Stability
Base
Compound Parameter (Joules/g.at.)
(1/7)(Si0;2BeO) L
G
so 0.429B00.571
stable
N
o2132-7.406T
(1/17)(3A1203*Be0)
Q
A0
stable
C
75312
(1/7)(A1203.Be0)
I
stable
C
76567
(l/ll)(A1203*3Be0)
J
stable
N
61923+9.9161
(1/15)(2Y203~A1203)
U
stable
Y
70291
(l/10)(Y2Q3*A1203)
V
stable
C
48534+20.083T
(l/40)(3Y2035A1203)
WA
YO 0.37SA00.625
stable
C
82425
(l/S)(Si2N20)
R
SNO . 7soo. 3
stable
B
62760-1.255T
(l/12)(Y203*Si3N4)
S
stable
B
44769+14.6443
(1/8)(Y203*Si02)
M
stable
Y
-15900+29.288T
(1/19)(2Y203*3Si02)
K
stable
Y
-30334+36.819T
(l/ll)(Y203*2Si02)
0
stable
Y
-2218+23.849T
(l/12)(Ce203*Si3N4)
S
stable
B
44769+14.644T
(1/8)(Ce,O;SiO,)
M
stable
Y
418+24.058T
stable
Y
6276+24.434T
stable
Y
7531+25.230T
stable
B
83680+4.184T
stable
B
71128+4.184T
stable
B
83680+4.1841‘
stable
B
83680+4.180T
(1/62)(7Ce203.9Si02) 2 (l/ll)(Ce203.2Si02)
0
0.01(14Si3N4.Be0)
.BP
(1/150)(21Si,N;Si02) BP 0.0040(35Si3N4~Y203)
BP
0.0040(35Si3N4*Ce203) BP
o.882BQo.118
A"0.714Bo0.286 AQ0.455B00.545 y"@.667Ao0.333 YQ0.500AQ0.500
Y00.417SN0.583 y"0.62Sso0.375 y"0.527so0.473 YO o.455S00.545 CE0.417SN0.583 [email protected] CE0.565So0.435 CE o.455s00.545 SN0.98B00.02 SN0.98S00.02 SN 0.98yo0.02 SN0.98CE0.02
14(d) illustrate the steps which are taken in sythesizing the ternary system SO-MO-SN, (i.e. 1/3SiO -1/2MgO-1/7Si N ) from the component binary systems. Initially each of the equilibria b&ween pairs OS 2olution and or compound phases are calculated individually. In the present case these pairs consist first of the liquid miscibility gap (L -L in 14a) followed by L-Periclase in Figure 14b. Next the L-F and L-R equilibria whi. &h are shown in Figures 14a and 14c are calculated. Overlaying the Ll-L2, L-F,L-P,and L;R equilibria shows that there are no interactions between any of the phase pairs except in the case of the L-R/LlL2 interaction. The latter, which is shown in Figure 14~ results in a three phase field between R, Ll and L2.
The boundaries
of this
three phase field
Ll+L2 miscibility gap illustrated in Figure 14a and the tie equilibria shown in Figure 14~.
are the lines
ines which define
traversing the R-L
the
L.
168
Kaufmsn,
F. Hayes
and D. Birnie
Be0 -
W/O
48
59
71
Be0
85
2800.
L+N
2000
1800 1770 G+T 1080 G+aQuart z (H) 850
4oc -
C+N
G+BQuartz(R)
(l/7)
( 1/3)Si02 Figure
1.
1
I
I
1
I
*
) Be0
(Si02-2BeO)=C=S
Calculated
Phase Diagram.
(1/3)Si02-(1/2)BeO
w/o BeO-+ y2 O3 L T’K 2800 ,
3
7
11
I
1
‘
16
22
29
1
I
I
39
53
71
I
I
I
Be0 .
4
_ P
I_ Y+N
I_
tm B0=(1/2)8eO
(1/5)Y20,=Y0 Figure
2.
Calculated
(1/5)Y203-(1/2)BeO
Phase
Diagram.
169
QUASIBZNARYAND QUASITERNARY OXYNTIRIDESYSTEMSIV
1
I
A0 0 714B00 mJrl * ' (l/S ]A12O;=AO
I
1
J=~-i_(A120~~3BcO) I
~J=A00.455B00.545
Figure 3. Calculated(l/S)Al20~-(l/~)BcO Phase
w/o Be0
I
I
AIN
I
BO=(l/Z)BeO
Diagram.
_c
AIN
15
29
41
52
62
71
79
86
94
T”K
Metastable! -ALN decomposes above 28SO'K into Alland N2
28OC
N1 +N2
2000
(Miscibility Gap)
l2OC
4oc
t-
,
,
4
t
I
1
*
I
(l/Z)BeO=BO Figure 4. Calculated(l/Z)BeO-(lf2)AlN Phase Diagram.
I
I
AX=(If2 )AlN
170
L. Kaufman, F. Hayes and D. Birnie
w/o. Be0
S’
15
29
41
52
62
1
I
I
*
I
%N4 71
79
I
I
a7
94
SiiN4
I
L(Liquid)
Metastablc!
’ Si3N4 decomposes at one atmosphcr above 2129'K into Si and N 2
N+BP
(1/7)Si3N4=SN
(l/Z)BeO=BO Figure 5.
Calculated l/ZBeO - 117 Sf3N4 Phase Diagram
w/o At2 Y203
5
10
16
23
31
03-
40
51
T°K V=YO, .AO, ~=(l/lO)(Y,O;AL,O,)
____
WA+C
U+WA
1 (1/5)Y203=Y0 Figure 6.
U=Yo0.667A00.333
1
1
1
I
WA=Yo0.375A00.625 (1/5)Ak203=AC
Calculated 1/5Y203 - 1/5A%203 Phase Diagram
QUASIBINAXY AND QUASITERNARY OXYNTIRIDE SYSTEMS IV
10
16
- 23
31
41
51
65
SO
171
ALN
Metastable! +-A&N decomposes above 285O'h: into AL and K2 at one atmosphere
L (Liquid)
2215 2000 -
Y+N
1200 -
YO=
(1/2)AH=AN
(1/5)Y*03
Figure 7.
Calculated 1/5Y203 - 1/2A9.N Phase Diagram
w/o SiO2-c 30
40
50
60
70
80
90
Net
SN=(1/7)Si3N4 Figure 8.
R=SNo~7SOo~j=l/5(Si2N20)
(l/3)Si02=S0
Calculated l/7Si3N4 - 1/3SiO2 Phase Diagram
L. Kaufman, F. Hayea and D. Birnie
172
w/o Si34 N T°KY203
10
5
16
23
40 . 51
31
64
80
Si3N4
L (liquid)
2800
Mctastable A_
- ;$&
;;;;:;ose*
into Si and N2 at one atmosphere Y+S
S=1/12(Y203.Si3N4)
(1/7)Si3N4=SN
(I/5~,O,=YO
Figure 9.
Y00.417SN0.583=S Calculated 1/5Y203 - 1/7Si3N4 Phase Diagram
Si3N4
w/o SiO2-c Y203
5
10
16
23
31
40
51
64
80
Si02
T'K 2800
(1/3)SiO,=SO YOw5)Y203
Y00.625S00.3755M
Figure 10.
0=YDo.455soo.545
Calculated 1/5Y203 - l/3Si02 Phase Diagram
173
QUASIBINARY AND QUASITERNARY OXYNTIRIDE SYSTEMS IV
w/o Si N --C 34
Ce203 4
8
14
19
27
35
59
46
Si3N4
77
T°K 2800 Metastable - Si3N4 2000
decomposes above 2129'K into Si and N2 at one atmosphere
Y+S
1200
S=l/12(Ce203.Si3N4) 400
I
I
I
(1/5)Ce203=Ce
*
2800
I
I
I
(l/7)Si3N4=SN
Calculated l/5 Ce203 - 1/7Si3N4 Phase Diagram
w/o
T°K
I
CE0.417SN0.583=S
Figure 11.
Ce20s
1
4
8
14
I
,
I
Si02-
19
27
35
46
1
I
I
I
59
77
I
0
s 02 .
L (liquid)
1/62(7Cr203+ 9Si02)=
2000
1200
0+8 Quartz (R) 400 -
l/B(Ce,O;SiO,)=ki I -.z 1 L , 1 I (l/S)Ce203=CE CE0.625S00.37S=u Figure 12.
I
O=l/ll(Ce203.2Si02) 1 I 1 I
O=CE o.455soo.545
(1/3)siO2=SO
Calculated l/SCe,O, - 1/3SiO, Phase Diaeram
174
L. Kaufman, F. Hayes and D. Birnie
TABLE 4 CALCULATEDFREE ENERGYOF FORMATIONOF COMPOUNDPHASES (All Units in Joulesper gram atom (moleof atoms),T in Kelvins) Compound
Name
Stoichiometry
(1/7)(Si02*2BeO)
G
(1/17)(3A1203*BeO)
Q
(1/7)(A1203.Be0)
I
(l/ll)(A1203 -3BeO)
J
(l/15)(2Y203*A12G3)
U
(l/10)(Y2G3~A1203)
V
(1/40)(3Y203.5A1203)
WA
(1/5)(Si2N20)
R
(1/12)(Y203.Si3N4)
S
(l/81(Y203'Si02)
M
(1/19)(2Y203*3Si02)
K
(l/ll)(Y203.2Si02)
0
(1/12)(Ce203*Si3N4)
S
(1/8)(Ce20;Si0,)
M
CE 0.62Sso0.375
-19787+ 2.61ST
(1/62)(7Ce203*9Si02)
2
CE .435 0.56Sso0
-21974+ 2.606T
(1/11)(Ce203.2Si02)
0
0.01(14Si3N4*Be0)
BP
(l/lSO)(21Si3N4~Si02) BP 0.004(35Si3N4.Y203)
BP
0.004(3SSi3N4*Ce203
BP
s"o.429BGo.571 A"o.BB2B00.11B A"0.714B00.2B6 A00.455BD0.545 Y00.667A00.333 y"o.500Aoo.500 y"0.375Ao0.625 SN0.700SG0.300 YO . 0 417SN0.583 y"0.62Sso0.375 y"0.S27so0.473 y"o.455soo.545 CE0.417SN0.5B3
CE0.4ssS00.545 SN0.9B0B00.020 SN0.9B0S00.020 SN0.9B0Y00.020 SN 0.9BOCE0. 020
-2808 + 1.382T/-2809+0.777T(B) -2203 - 0.4641 -2381 - 1.125T -2524 - 1.049T -4950 - 0.615T -2351 . - 4.100T -7866 + 0.690T + 0.40T(S) -5514 - O.O3BT/-5781 -404 - 1.833T -15958+ 1.389T -13000- 0.4751 -19527- 2.669T. -1389 - 1.8281
-21945+ 2.326T -423 - 0.113T -720 - 0.102T -1104 -1158
The calculationof the isothermalsectionat 2100K can be concludedby adding the L-BP equilibria as shown in Figure 14d. In this case, as in the R-L case., there are interactions with phase pairs which have been previouslyconsidered. First there is an interactionbetweenL-BP and the liquidgap, Ll-L2,as illustratedin Figure 14d, then there is a second interaction between the L-BP and L-P pairs. Comparisonof Figures14b and 14~ with 14d shows that while
the L-R/L-BPand the L-BP/L-Pinteractionpairs form stablethree phase fields,the L-BP/ Ll-L2 interaction pair which is shown in Figure 14d is metastable. This can be seen by comparing14c and 14d and notingthat the three phase BP+Ll+L2 field is "covered" by the R+LZ+L2 and R+L fields. Detailed calculation of the L-BP equilibria can be performed by defining the free energy of the BP phase on the bases of Tables l-4.
QUASIBINARYAND QUAsITERNARYOXYNTIRIDESYSTEMSIV
(bf=B/L
(cl=rc/L md N/L SO-fi/56i02J
&SN
m=WSJ
(Al*O,J
SN-(l/7)
WSN,J
1-5
and C/L
stnKture
c=AO stnrcturc
L4iquid M=1(1/21J(JL1203-2Si02J
C-COmsd~ n-(i/SJ(Si~N~OJ Oxy
Silicon
Nitride
x=so0.2$a0.6Sm0.1S e-z:,c.47,700 AGf
ff-
C-J
=-$a60 J&A.
Figure 13 CalcuiatadPainrise (8-c) and Ccqostt? Eqwilibrlu fd) in the (1/3)(Si02~- (I/?)(Si~N~)-fI/5fAl~O~ System at 20001:and one rtwsphere
For the case of the SO-MO-SN(BP) phase, where the compoundruns from SNO 980SOo 020 to SO00&fO . 50 and from SNO 98MO0 2* to MOO 50SO0 so similar proceduresare followed. For the , formercase GBP
B oGSO+y B = zo GSN+x D "~o+~~-fy/(:-x)))~GA+(y/(1-x))3GB+~GE +RT(y.kZny+&nz-(I-x)b(l-x))
(11)
here x,=0.50and x:=0,02so that p=O.96,x=x~+yp=0.02*0.96y=xSo, y=yMo and z=l-x-y=0.98-1.96y= -. Moreover,bGE=O and AGA and AGB can be explicitlydefinedas ?N' AGA AGB
= (0.02)(0.98)(0.98 LSNSO+O.OZLSOSN-c)=-820 -0.082T J/g.at.
(12)
= (0.50)(0.50)(0.50 LSOMO+O.SOWOSO-C)=-26568+10.503TJ/g.at.
(13)
with AGE--O, and y=yMo B B o~~-(l-(y/(i-x))(820+0.082~) GBP = ~0.98-l~96y)"GsN+(0.02+0.96y)*Gso+y -fy/(1-x))(26568-10.503T)+RT(y~ny+(0.98-1.96y)~(0.98-1.96y)-(0.98-0.96y)~n (0.98-0.96y))
(14)
176
L. Kmfman,
F. Aayea aud D.
Birnie
QUASIBINARYAND QUASITERNARY OXYNTIRIDESYSTEMSIV
177
TABLE 5 SUMMARYOF COUNTERPHASESTOICHIOMETRY AND 'ARAMETERS EMPLOYEDIN TERNARYCALCULATIONS System SO-MO-SN
SO-YO-SN
Stable Phase (Name)
Base
Counterphase
Base
Counterphase Parameter
S"o.429MQo.571(F)
0
S"o.300SNo.700(R)
0
SN0.980So0.020(BP)
0
SN0.980Mo0.020(BP)
0
Y"0.625So0.375(M) Y"0.527So0.473(K) y"o.455sQo.545(Q) S"o.300SNo.700(R) SN0.980So0.020(BP) SNo.980YCo.020(BP)
SO-CE-SN
CE0.625So0.375(M)
Y
CE0.565So0.435(Z) CEo.455SQo.545(C) S"o.300SNo.700(R) SN0.980So0.020(BP) SN0.980CE0.020(BP) Thus the equilibriumbetweenthe liquidand BP phase can be computedas in Figure 14(d). Combinationof the pairwiseequilibriumin Figure 14 yields the computedisothermalsection at 2100K shown in Figure 15. Isothermalsectionssimilarlyderivedat 2000K and 1900 are shown in Figure 15 along with an observedsectiondue to Mueller (9) at 1500K. The latteris in keepingwith the calculationsshown at 1900K. (See "Note in Proof") Similarcalculations were performedin the SO-YO-SNand SO-CE-SNsystems. The results,which are complicatedby the existenceof stablequasi-ternary compounds(listedin Table 6) are displayedin Figures16-19. The SO-YO-SNand SO-CE-SNsectionswere computedin a manner similarto the SO-MO-SNcase in that the systemswere first computedas if the ternary phases were absent. Subsequently the ternaryphases,designatedas C,D and E were inserted. In keepingwith previouspractice(l-3)the free energyof the ternaryphases C, D and E were definedby choosinga base phase and then defininga compoundparameterin conformitywith experimentalobservation. In the presentcase the Y structurewas chosenas the base phase since the ternaryphase compositionoccursnear the YO and CE cornersof the SO-YO-SNand SO-CE-YOsystemsas is seen in Figures17 and 18. The free energyof the ternarycompoundD in the SO-YO-SNsystemD=(1/1S)Y4Si20,N2= SOo~100YOo~667SNo~223 is definedas
L. Kaufman, F. Hayes and D. Birnie
178
TABLE6 DESCRIPTION OF QUASI-TERNARY COMPOUNDS IN THE SiO2-Y203-Si3N4 ANDSi02-Ce203-Si3N4 SYSTEMS Compound
Base
Stoichiometry
Compound Parameter (C) (Joules/g.at.)
Free Energy of Formation from Component Compounds (AGf [2Q8K])
Melting Point (OK)
(Joules/g.at.) C= (l/S)YSi02N
Y
D=(1/15)Y4Si207N2
Y
E=(l/Zl)YS(Si04)3N
Y
C=(l/S) CeSiO2N
Y
D=(1/1S)Ce4Si207N2
Y
E=(1/21)Ceg(Si04)3N
Y
*S00.322CE0.S9SSN0.083
SD0.150YD0.500SN0. 350 SG0.100Y00.667SN0.233 S00.322Y00.59SSN0.083 S00.1s0CE0.s00SN0.3s0 S00.100CE0.667SN0 . 233 S00.322CE0.S9SSN0.083 decomposes peritectically
29096+8.3687
1953
-4393-2.410T
13004+16.736T
2110
-678-4.127T
-2155+20.921
1996
-11456-0.8831
31505+8.368T
1914
-5422-2.4101
14769+16.736T
2020
-1259-4.127T
3975+20.92T
2109*
-13585-0.883T
into
2 and Liquid above 2lOOK
D G =0.10aG~0+0.6670G~0+0.2330G~N+(O.10)(0.667)(0.767)-l[0.1LSOY0+0.667LYOSO-C] *(0.l0)(0.233)(0.333)-1[O.l~OSN+0.233LSNSO-C]+(O.667)(O.233)(O.QO)-1[O.667LYOSN+ 0.223LSNYO-C] J/g.at. (15) Since C=13004+16.736T for this
phase
D G =0.10°G~O+0.6670G~o+0.2330G~N-9094-3.062T
J/g.at.
(16)
Thus the free energy of formation of D from the Y form of SO, YO and SN is -9094-3.062T J/g.at.. The free energy of formation of D from the stable forms of SO, YD.and SN (i.e. R, Y and 8 respectively) can be computed by using the lattice stability values given in Table 1. With SOSOYR=S042-1.004T and SNSNYB=33949-4.142T J/g.at. Y D R G .o.10°GS0+0.6670Gy0+0.2330GsNB 678-4.1271
J/g.at.
(17)
or AGf[298K]=-678-4.127T
J/g.at.
(18)
The free energy and free energy of formation of the remaining compounds listed in Gn this basis the isothermal sections and pairTable 6 can be computed in a similar fashion. wise equilibria shown in Figures 16-19 were developed. Figure 16 shows the computed sections at 2100 and 2000K in which phases present in the binary systems and the ternary compound D Figures 16(a) and 16(b) and Figure 17(a) illustrate pairwise interactions at are present. 1900K in SO-YO-SN. These pairwise interactions combine to yield the calculated isothermal section at 1900K which contains two small liquid regions. A computed section at 1823K given This in Figure 17(c) shows how these regions have grown smaller with decreasing temperature. section is in good agreement with the observed section (10) at 1823 shown in Figure 17(d) which illustrates the ternary compounds and the existence of a small liquid field as well. The computation of isothermal sections in SO-CE-SN is displayed in a similar manner isothermal section given in Figure 18 at 2100, 2000 and 19OOK. At 2100K the calculated contains only the phases stable in the edge binary systems. At 2000K the calculated section Pairwise equilibria calculated displays the ternary D (Ce4Si207N2) and E(Ces(Si04)3N) phases.
Figure
BP
15.
Calculated and Observed (See “Note in Proof”)
(9)
Isothermal
Sections
-A
in the
L1
F+P+LZ
System
P=periclase
SiOZ-MgO-Si3N4
(1 /3)Si02=S0
Figure
(1/7)Si3N4=SN 16.
D=(l~15)(Y,Si20,N2)
D=S00.100Y01L667SN0.2
Calcujated I&thermal Sections System Si02- Y203- Si3Nq
and Pairwise
Component Equilibria
(1/12)~Si3N,~Y203)=S=SN0,S~3YOo~417
K=(1/19) (3Si02*2Y203
in the
YO=( I /5) Y203
(a)
SYOO .SSNO. 35
L-C,
L-1)
Figure
17.
(I/7)Si3N4=SN
L-E,
Equilibrium
X-
Y
BP
1900°K
(b) A..
Crystobalite.
Equilibria at 1900°K, Calculated (IO) Si02-Y203Si3Y4Scction at
S=(1/12)(Y203*Si3N4)
Calculated Pairwise 1823OK and Observed
19W.1°K I’airwise
(:=SOO. 1
(l/J)siO_=SO
fl
L
Isothermal 1823’~
L,
(1/3)SiO,=SO
1
L
at
1900°K
L
and
L J
(ZSiO;Y,O,)
_ L_+O+M
O= (l/11)
Sections
i
d
.
R+L.
Figure
18.
calculated Isothermal Sections 1900°K in the Si02-Ce203-Si3N4
SN=(1/7)Si,N,
2100’K
(1/3)SiO,=SO
at 2100° System
and 2000’K
and Pairwise
(1/3)SiO2=SO
Equilibria
at
(l/S)Ce,O,=CE
T(nelt)=2002’K
L-N,
w
L-O,
I
Figure
SN=(l/
19.
calculated
(cl
”
L
”
A
”
”
y
-X=crystohalite
Calculated Pairwise*Equilibria (11) Subsolidus Equilibria
*
L-M
Equilibria
SN=(1/7)Si3N4
Ll-L2,
Pairwise
(l/~)sio_=so
”
at
observed 1923-2023-K S and D were expe ted but not
1
Equilibria
and Isothermal Sections at 16OO’K and Observed 192%.2023°K in the SiO2-Ce203-Si3 N4 System
u
Pairwise
f 1/3lSiO,=SO
184
L. Kaufman, F. Hayes and D. Birnle
at 1900K are shown in Figures 18(a), 18(b), 19(a) and 19(b). The latter combine to yield the calculated isothermal section at 1900K given in Figure 19(c). The latter is in relatively good agreement with the observed subsolidus equilibria (11) determined between 1923 and 2023K. The observed section does not show evidence of the S or D compound phases which was expected but not observed (11). The SO-MO-SN, SO-YO-SN and SO-CE-SN sections calculated above serve to illustrate how the synthesis of multicomponent phase diagrams can be performed in support of experimental studies of practical problems which must often be performed with great difficulty and some measure of uncertainty. References 1.
2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
L. Kaufman and H. Nesor, CALPHAD 2 35 (1978) L. Kaufman, CALPHAD 2 27 (1979) L. Kaufman, CALPHAD J 279 (1979) L.J. Gaukler. H.L. Lukas, E.Th. Henig and G. Petzow, CALPHAD 2 349 (1979). P. Doerner. L.J. Gaukler, H. Krieg. H.L. Lukas, G. Petzow and J. Weiss, CALPHAD J 239 (1979). J. Weiss, H.L. Lukas, J. Lorenz, G. Petzow ans H. Krieg, CALPHAD 2 123 (1981). E.M. Levin, C.R. Robbins and H.F. McMurdie, Phase Diagrams for Ceramists, American Ceramics Society, Columbus, Ohio (1964), First Supplement (Ibid) (1969) Second Supplement, Ibid (1975) 0. Kubaschewski and C.B. Alcock, Metallurgical Thermochemistry Fifth Edition (1979) Pergamon Press, Oxford. R. Mueller, Thesis University of Stuttgart (1981) To be Published in CALPHAD by J. Weiss, R. Mueller, H.L. Lukas, H. Krieg, G. Petzow and T.Y. Tien. L.J. Gaukler, H. Hohnke and T.Y. Tien, J. American Ceramic Society -63 35 (1980) F.F. Lange, Ceramic Bulletin g 239 (1980). Note in Proof
Note in Proof H. L. Lukas has pointed the following solid phases
out that the Gibbs free
energy change for the reaction
between
Si3N4 + 4MgO+ Mg2Si04 + 2Mg SiN2 is equal to 3953 - 8.85T Joules or 264 - 0.59 T Joules/ g. at. On this basis the SN - MDbinary edge is slightly metastable with respect to the formation of F (l/i (Si02 * 2MgO))and l/S (kg Si N2)above 446’K. Thus the sections shown in Figure 15 represent metastable equilibria.
pp.163-184,
1981.
0364-5916/81/030163-22$02.00/O (c) 1981 Pergamon Press Ltd.
CALCULATION OF QUASIBINARY AND QUASITERNARY OXYNTIRIDE SYSTEMS-IV* Larry Kaufman, Fred Hayes+ and Dunbar Bimie ManLabs, Inc., 21 Erie Street Cambridge, Massachusetts 02139 USA (This paper was presented at CALPHAD X, Vienna, Austria, July 1981) ABSTRACT. A data base is being developed for calculation of quasi-binary and quasi-ternary phase diagrams of ceramic systems (l-3). Previous segments of this base cover combinations of Cr203, MgO, A1203, Fe203, Fe304, "FeO", SiO2, CaO. SijN4 and AlN. Lattice Stability, Solution and Compound Phase Parameters were derived covering the liquid, spinel,corundum,periclase, crystobalite, tridymite, quartz, hexagonal and beta prime phases which appear in the binary systems composed of pairs of these compounds. Compound phases formed from specific binary combinations of these compounds (i.e. MgO-Cr 0 ) were also characterized. This description is 2I y and phase diagrams for the binary systems of based on observed thermochemxst interest. Selected ternary systems have been computed based on the foregoing data base for comparison with experimental sections in order to illustrate the usefulness of the data base. The present paper extends the data base to cover BeO, Y203 and Ce203 additions. Moreover, ternary sections in the Si02-MgO-Si3N4, Si02-Y203-Si3N4 and Si02-Ce203-Si3N4 were calculated between 1900K and 2100K for comparison with experiment. 1. Introduction The utility of computer based methods for coupling phase diagrams and thermochemical data for metallic systems has been well documented in many papers published in this journal. A considerable effort is being applied toward developing an extensive base for metallic systems. Recently similar efforts have begun in order to provide a similar facility with ceramic systems. The expanded studies of SIALON composites, combining silicon and aluminum nitrides with oxides of silicon, aluminum, magnesium, beryllium, cerium and yttrium and other metals has provided additional motivation for predicting multicomponent phase diagrams of ceramic systems. 2. Description of the Thermochemical System Employed to Characterize Solution and Compound Phases The method utilized for describing solution and compound phases is the same as that employed earlier (l-3) comprising so e symbolic usage which facilitates data handling as indicated below. The free energy, G1 , of a liquid (solution) phase, L. in the binary system Y203-Be0 is given by Equation (1) where T is in Kelvins, R=8.314 J/g. atoK, while x is the atomic fraction of BO(i.e. BO=+BeO)
and(l-x)is the fraction of YO(i.e. 1/5Y203).
The mass basis is thus one mole of atoms (i.e. a gram-atom) * This work has been sponsored by the Air Force Office of Scientific Research, Bolling AFB, Washington, D.C. under Contract F44620-80-C-0020
t
On leave from Department of Metallurgy, University of Manchester-UMIST, Manchester, England.
Received 15 June 1981
163
L. Kaufman, F. Hayes and D. Birnie
164
L L G =(1-x) “GYO+x~~O+RT(x&-~x+(l-x)&(1-x1+x(1-x)
[LYOBO(l-x)+xLBOYO] J/g.at
L and ‘Gko are the free emrgies of are gram atom of pure liquid \Jmre0GYo
YOand BO.
Table 1 defines
the lattice stabilities of the liquid and solid forms of YO. BO and the other components of current interest. These data derived from earlier studies and compilations of thermochemical and phase diagram data, (l-8), when combined with the solution and compound phase parameters shown in Tables 2 and 3 permit calculation of the binary phase diagrams shown in Figures 1-12. The solution parameters LYOBOand LBOYO,which describe the liquid Y203-Be0 solution are listed in Table 2 (LYOBO=LBOYO=-2092 Joules/g.at). Similar parameters for the liquid and solid phases are listed in Table 2. The free energy of the solid phases are described in a manner similar to equation (1). Thus, for example, the free energy of the body centered cubic (Mn203)Y phase in the YO-BO system is given by Y OY G =(1-x) Gyo+xti,+RT(&nx+(l-x)&(1-x))+x(l-x)
[YYOBO(l-x)+xYBOYO] J/g.at.
(2)
The solution parameters for the Y phase (YYOBO=YBOYO=-2092 J/g.at) are listed in Table 2.Thefree energy difference between the L and Y forms of YO and BO, i.e. YOYOLY-‘GL-‘GY YO YO and ‘Gko- ‘Gio= BOBOLYare listed in Table 1. The free energy of a compound phase such as G=(1/7)(Si02’2BeO)=SOD~42gBOD~571 is defined phase,
the compound parameter,
on the basis
C, and the stoichiometry
of Table 3 in terms of the base by equation
(3)
GG=O.429G~o+O.S7lG~o+(O.429)(O.S7l)[O.429LSOBO+O.S7lLBOSO -C] J/g.at. Reference Thus
to Table 2 shows that LSOBO=LBOSO=41840 J/g.at
G N G =0.429GS0+0.571GB0 N -4971+1.8133
(3)
while Table 3 shows that C=62132-7.406T.
J/g.at.
(4)
At 298K reference to Figure 1 shows that the stable form (designated R). Table 1 shows that
form of quartz
GN SO-G~0=SOSOLR-SOS0LN=S042-1.004T J/g.at.
is the beta (S)
Substitution of equation (5) into equation (4) yields an expression for the free energy of formation of (1/7)(Si02’Be0) at 298K from the stable forms of it s compound components as, AGf[298K]=GG-0.429G~o-0.S71G~o=-2808+1.382T
J/g.at.
(6)
Reference to Table 4 shows that this result is in keeping with the experimental(8) thermochemical data on the free energy of formation of2BeO*Si02. Table 4 also displays the calculated free energy of formation for the remaining compounds listed in Table 3 and shown in Figures l-12. It should be noted that this compound parameter for SNo ,SOo 3 currently shown . . as C=62760-1.25ST J/g.at. has been revised from the previously stated value C=llSOdO-25.lOT J/g.at.(S)Fhe current value is based on the assessment of Doerner et al (5) and leads to slight revisions in the previously calculated SN-SO and SO-AO-SN phase diagrams presented earlier (3). The revised versions, which differ slightly from the earlier results are shown in Figures 8 and 13. 3.
Calculation
of Quasi-Ternary
Phase Diagrams
The free energy of ternary solution phases was synthesized from the binary solution phases on the basis of Kohler’s equation as in the previous papers (l-3). On this basis the free energy of the liquid phase in the SO-MO-SNsystem where x is the atom fraction MO, y is the atom fraction SN and l-x-y is the atom fraction SO is given by
165
QUASIBINARY AND QUASITERNARY OXYNTIRIDE SYSTEMS IV
TABLE 1 SUMMARY OF LATTICE STABILITY PARAMETERS (All units in Joules per gram atom (mole of atoms), T in Ke1vin.s) A0 = (WAl203,
SO = (1/3)SiO2, MO = (1/2)MgO, AN = (1/2)AlN, Sty= (1/7)Si3N4
BO = (1/2)BeO, YO = (1/5)Y203, CE = (1/5)Ce203 P = Periclase, C = Corundum, X = Crystobalite, T = Tridymite, H = a quartz R = 6 quartz, B = beta Si3N4, N = hexagonal AlN and BeO, Y = body centered cubic (Mn203)Y203 and Ce203 structure BOBOLN' = (l/Z)BeO(Liquid)-(1/2)BeO(hexagonal) YOYOLY = (l/S)Y,O,(Liquid)-(l/5)Y203(body centered cubic) YOYOLY YOYOLN YOYOLX YOYOLB YOYOLC
= 22694 - 8.3683 = O- 14.1423 = 0 - 2.092T = o- 12.510T = o- 10.209T
CECELY CECELN CECELX CECELB CECELC
= 20334 - 8.368T 0 - 14.142T = = 0 - 2.092T 0 - 12.510T = = 0 - 10.209T
BOBOLN BOBOLX BOBOLC BOBOLB BOBOLY
= 40376 - 14.142T 1.674T = o= o- 10.209T = o- 12.510T = o8.3681
AOAOLY ANANLY SNSNLB SNSNLY SOSOLY SOSOLN SOSOLX SOSOLR
= 0 - 8~3683 0 - 8.368T = = 33949 - 12.510T = 0 - 8.368T 0 - 2.092T = = 0 - 2.092T = 3347 - 1.674T = 5042 - 3.0963
* These differences specify the free energy of one phase (i.e. liquid) minus the free energy of the second phase (i.e. hexagonal) for a given compound. L L L G =(l-x-y)"GSO+~oGMO+yOGSN L +RT[(l-x-y)k(l-x-y)+xkx+ykry] +(l-x-y)x(l-y)-1[(l-x-y)LSOMO+xLMOSO]+xy(x+y)-1[xLMOSN+yLSNMOJ +(1-x-y)y(l-x)-l[(l-x-y)LSOSN+yLSNSO] J/g.at.
(7)
The solution parameters required to specify GL were defined previously (2,3) as and LSOMO=LMOSQ=-106274+42.01Tfor 0.4_rx~&l.O and LSOSN=LSNSO=lMOSN=LSNMO=29288J/g.at. LSOMO=-24267+24.27T;LMOSO=-229283+68.62Tfor 0.0~31&0.40.
These parameters permit explicit
definition of GL in composition ranges where (x/l-x-y) is more than 0.667 and ranges where (x/l-x-y) is less than 0.667. In the latter range the miscibility gap present in the SO-MO binary system propagates into the ternary SO-MO-SN as shown in Figure 14a. Here the ternary miscibility gap shows the tie lines connecting the coexisting liquid compositions Ll and L2. The remaining solution phases in this system, i.e. P, X, B, etc. are defined in similar fashion to Equation 7. The resulting equilibria between the L and P solutions are depicted by the tie lines traversing the two phase L+P field shown in Figure 14(b). The compound phases F,R and BP which appear in the SO-MO, SO-SN and MO-SN binary systems are defined Thus for example along the lines previously established (l-3) and are specified in Table 3. ;ie free energy of the SN0.7S00.3 (R) phase in the SO-MO-SN system is defined by Equation 8
L. Kaufman,F.
166
Ifayes
and
D.
Bisnie
TABLE 2 SUWARY OF SOLUTIONPHASE PARAMETERS (Allunits in Joulesper gram atom (moleof atoms),T in Kelvins) L = Liquid,N = hexagonal,X = Crystobalite, T = Tridymite,Y = body centeredcubic B = beta Si3N4,A0 = (l/S)A1203, SO = (1/3)SiO2,AN = (1/2)AlN, SN = (1/7)Si3N4, BO = (1/2)BeO YO = (1/5)Y203,CE = (l/S)Ce203 LSOBO = LBOSO = 41840 NSOBO = NBOSO = 83680 XSOBO = XBOSO = 83680 TSOBO = TBOSO = 83680
LBOSN = LSNBO = 20920 BBOSN = BSNBO = 83680 NBOSN = NSNBO = 83680'.
LYOBO = LBOYO = -2092 YYOBO = YBOYO = -2092 NY080 = NBOYO = 83680
LYOAO = LAOYO = 12552 YYOAO = YAOYO = 83680
LAOBO = LBOAO = 8368 CAOBO = CBOAO = 83680 NAOBO = NBOAO = 83680
LYOAN = LANYO = 20920 WOAN = YANYO = 83680 NYOAN = NANYO = 83680
LBOAN = LANBO= 20920 NBOAN = NANBO = 83680
LSNSO
LCESN = LSNCE = 4180 BCESN = BSNCE = 62760 YCESN = YSNCE = 62760
GR =
bYOA0
= CAOYA = 83680
=
LSOSN = 29288 XSNSO = XSOSN = 125520 TSNSO = TSOSN = 125520 LYOSN = LSNYO = 4180 BYOSN = BSNYO = 83680 YYOSN = YSNYO = 83680
0'xs&0.60* LYOSO = LSOYO = -92048+36.821 0.6zxs&l.0 LYOSO = LSOYO = woso = XYOSO = TYOSO =
-216,000+66.94T -9414+16.74T YSOYO = 83680 XSOYO = 83680 TSOYO = 83680
0&xs&0.60 LCESO = LSOCE = -92048+ 36.82T 0.6
z”GB SN+x”G~o+~o~o+(‘-~~l~‘-x))lbGA+~~/~~-~~~A~B +RT(y&y+z&z-(1-x).fZn(l-x)j+AGE J/g.at.
(8)
where x=xso,y=yMO and z=zSN. Since the compoundphase runs from p=(x,-x:)/(1-x,)=0 and x=x~+yp=x~=O.J, and r=l-xi-y(l+p)= SN0.70S00.30 to M00.70S00.30~ 0.7-y. Since = -7029 + 0.263T J/g.at. AGA = (0.3)(0.7)[0.7LSNSO+O.3LSOSN-C] and AGB = (0.3)(0.7)[0.7lMOS0+0.3LSOM0-C] = -22318t 8.8221 J/g.at.
(9) *
from Tables 3 and S and the previousvalues of LSNSO,LSOSN,lMOS0 and LSOMO (2) given in the above text. The excess free energyof mixing,AGE, for the compoundis given (3) by AGE
= CAByz/(1-x)
However,CAB is taken as zero in all the cases treatedhere thus Equation8 can be written explicitlyas follows: GR = (0.70-y)'G~N+0.3"G~o+y~~o - (I-(y/O.7))(7029-0.263T) -(y/O.7)(22318-8.822T)+RT(y~ny+(O.7-y)~n(0.7-y)-0.7~0.7) (11) where y=yMo. Since the latticestabilitiesof SN, SO and MO (i.e.SNSNLB,SOSOLB and MOMOLB) have alreadybeenspecifiedthe R-L equilibria(Figure14~) can be computed.Figs.(14a)through
QUASIBINARY AND QUASITERNARY OXYNTIRIDE SYSTEMS IV
167
TABLE 3 SUMMARY OF COMPOUND PARAMETERS FOR BINARY SYSTEMS (All units in Joules per gram atom (mole of atoms) T in Kelvins) Compound
Name
Stoichiometry
Stability
Base
Compound Parameter (Joules/g.at.)
(1/7)(Si0;2BeO) L
G
so 0.429B00.571
stable
N
o2132-7.406T
(1/17)(3A1203*Be0)
Q
A0
stable
C
75312
(1/7)(A1203.Be0)
I
stable
C
76567
(l/ll)(A1203*3Be0)
J
stable
N
61923+9.9161
(1/15)(2Y203~A1203)
U
stable
Y
70291
(l/10)(Y2Q3*A1203)
V
stable
C
48534+20.083T
(l/40)(3Y2035A1203)
WA
YO 0.37SA00.625
stable
C
82425
(l/S)(Si2N20)
R
SNO . 7soo. 3
stable
B
62760-1.255T
(l/12)(Y203*Si3N4)
S
stable
B
44769+14.6443
(1/8)(Y203*Si02)
M
stable
Y
-15900+29.288T
(1/19)(2Y203*3Si02)
K
stable
Y
-30334+36.819T
(l/ll)(Y203*2Si02)
0
stable
Y
-2218+23.849T
(l/12)(Ce203*Si3N4)
S
stable
B
44769+14.644T
(1/8)(Ce,O;SiO,)
M
stable
Y
418+24.058T
stable
Y
6276+24.434T
stable
Y
7531+25.230T
stable
B
83680+4.184T
stable
B
71128+4.184T
stable
B
83680+4.1841‘
stable
B
83680+4.180T
(1/62)(7Ce203.9Si02) 2 (l/ll)(Ce203.2Si02)
0
0.01(14Si3N4.Be0)
.BP
(1/150)(21Si,N;Si02) BP 0.0040(35Si3N4~Y203)
BP
0.0040(35Si3N4*Ce203) BP
o.882BQo.118
A"0.714Bo0.286 AQ0.455B00.545 y"@.667Ao0.333 YQ0.500AQ0.500
Y00.417SN0.583 y"0.62Sso0.375 y"0.527so0.473 YO o.455S00.545 CE0.417SN0.583 [email protected] CE0.565So0.435 CE o.455s00.545 SN0.98B00.02 SN0.98S00.02 SN 0.98yo0.02 SN0.98CE0.02
14(d) illustrate the steps which are taken in sythesizing the ternary system SO-MO-SN, (i.e. 1/3SiO -1/2MgO-1/7Si N ) from the component binary systems. Initially each of the equilibria b&ween pairs OS 2olution and or compound phases are calculated individually. In the present case these pairs consist first of the liquid miscibility gap (L -L in 14a) followed by L-Periclase in Figure 14b. Next the L-F and L-R equilibria whi. &h are shown in Figures 14a and 14c are calculated. Overlaying the Ll-L2, L-F,L-P,and L;R equilibria shows that there are no interactions between any of the phase pairs except in the case of the L-R/LlL2 interaction. The latter, which is shown in Figure 14~ results in a three phase field between R, Ll and L2.
The boundaries
of this
three phase field
Ll+L2 miscibility gap illustrated in Figure 14a and the tie equilibria shown in Figure 14~.
are the lines
ines which define
traversing the R-L
the
L.
168
Kaufmsn,
F. Hayes
and D. Birnie
Be0 -
W/O
48
59
71
Be0
85
2800.
L+N
2000
1800 1770 G+T 1080 G+aQuart z (H) 850
4oc -
C+N
G+BQuartz(R)
(l/7)
( 1/3)Si02 Figure
1.
1
I
I
1
I
*
) Be0
(Si02-2BeO)=C=S
Calculated
Phase Diagram.
(1/3)Si02-(1/2)BeO
w/o BeO-+ y2 O3 L T’K 2800 ,
3
7
11
I
1
‘
16
22
29
1
I
I
39
53
71
I
I
I
Be0 .
4
_ P
I_ Y+N
I_
tm B0=(1/2)8eO
(1/5)Y20,=Y0 Figure
2.
Calculated
(1/5)Y203-(1/2)BeO
Phase
Diagram.
169
QUASIBZNARYAND QUASITERNARY OXYNTIRIDESYSTEMSIV
1
I
A0 0 714B00 mJrl * ' (l/S ]A12O;=AO
I
1
J=~-i_(A120~~3BcO) I
~J=A00.455B00.545
Figure 3. Calculated(l/S)Al20~-(l/~)BcO Phase
w/o Be0
I
I
AIN
I
BO=(l/Z)BeO
Diagram.
_c
AIN
15
29
41
52
62
71
79
86
94
T”K
Metastable! -ALN decomposes above 28SO'K into Alland N2
28OC
N1 +N2
2000
(Miscibility Gap)
l2OC
4oc
t-
,
,
4
t
I
1
*
I
(l/Z)BeO=BO Figure 4. Calculated(l/Z)BeO-(lf2)AlN Phase Diagram.
I
I
AX=(If2 )AlN
170
L. Kaufman, F. Hayes and D. Birnie
w/o. Be0
S’
15
29
41
52
62
1
I
I
*
I
%N4 71
79
I
I
a7
94
SiiN4
I
L(Liquid)
Metastablc!
’ Si3N4 decomposes at one atmosphcr above 2129'K into Si and N 2
N+BP
(1/7)Si3N4=SN
(l/Z)BeO=BO Figure 5.
Calculated l/ZBeO - 117 Sf3N4 Phase Diagram
w/o At2 Y203
5
10
16
23
31
03-
40
51
T°K V=YO, .AO, ~=(l/lO)(Y,O;AL,O,)
____
WA+C
U+WA
1 (1/5)Y203=Y0 Figure 6.
U=Yo0.667A00.333
1
1
1
I
WA=Yo0.375A00.625 (1/5)Ak203=AC
Calculated 1/5Y203 - 1/5A%203 Phase Diagram
QUASIBINAXY AND QUASITERNARY OXYNTIRIDE SYSTEMS IV
10
16
- 23
31
41
51
65
SO
171
ALN
Metastable! +-A&N decomposes above 285O'h: into AL and K2 at one atmosphere
L (Liquid)
2215 2000 -
Y+N
1200 -
YO=
(1/2)AH=AN
(1/5)Y*03
Figure 7.
Calculated 1/5Y203 - 1/2A9.N Phase Diagram
w/o SiO2-c 30
40
50
60
70
80
90
Net
SN=(1/7)Si3N4 Figure 8.
R=SNo~7SOo~j=l/5(Si2N20)
(l/3)Si02=S0
Calculated l/7Si3N4 - 1/3SiO2 Phase Diagram
L. Kaufman, F. Hayea and D. Birnie
172
w/o Si34 N T°KY203
10
5
16
23
40 . 51
31
64
80
Si3N4
L (liquid)
2800
Mctastable A_
- ;$&
;;;;:;ose*
into Si and N2 at one atmosphere Y+S
S=1/12(Y203.Si3N4)
(1/7)Si3N4=SN
(I/5~,O,=YO
Figure 9.
Y00.417SN0.583=S Calculated 1/5Y203 - 1/7Si3N4 Phase Diagram
Si3N4
w/o SiO2-c Y203
5
10
16
23
31
40
51
64
80
Si02
T'K 2800
(1/3)SiO,=SO YOw5)Y203
Y00.625S00.3755M
Figure 10.
0=YDo.455soo.545
Calculated 1/5Y203 - l/3Si02 Phase Diagram
173
QUASIBINARY AND QUASITERNARY OXYNTIRIDE SYSTEMS IV
w/o Si N --C 34
Ce203 4
8
14
19
27
35
59
46
Si3N4
77
T°K 2800 Metastable - Si3N4 2000
decomposes above 2129'K into Si and N2 at one atmosphere
Y+S
1200
S=l/12(Ce203.Si3N4) 400
I
I
I
(1/5)Ce203=Ce
*
2800
I
I
I
(l/7)Si3N4=SN
Calculated l/5 Ce203 - 1/7Si3N4 Phase Diagram
w/o
T°K
I
CE0.417SN0.583=S
Figure 11.
Ce20s
1
4
8
14
I
,
I
Si02-
19
27
35
46
1
I
I
I
59
77
I
0
s 02 .
L (liquid)
1/62(7Cr203+ 9Si02)=
2000
1200
0+8 Quartz (R) 400 -
l/B(Ce,O;SiO,)=ki I -.z 1 L , 1 I (l/S)Ce203=CE CE0.625S00.37S=u Figure 12.
I
O=l/ll(Ce203.2Si02) 1 I 1 I
O=CE o.455soo.545
(1/3)siO2=SO
Calculated l/SCe,O, - 1/3SiO, Phase Diaeram
174
L. Kaufman, F. Hayes and D. Birnie
TABLE 4 CALCULATEDFREE ENERGYOF FORMATIONOF COMPOUNDPHASES (All Units in Joulesper gram atom (moleof atoms),T in Kelvins) Compound
Name
Stoichiometry
(1/7)(Si02*2BeO)
G
(1/17)(3A1203*BeO)
Q
(1/7)(A1203.Be0)
I
(l/ll)(A1203 -3BeO)
J
(l/15)(2Y203*A12G3)
U
(l/10)(Y2G3~A1203)
V
(1/40)(3Y203.5A1203)
WA
(1/5)(Si2N20)
R
(1/12)(Y203.Si3N4)
S
(l/81(Y203'Si02)
M
(1/19)(2Y203*3Si02)
K
(l/ll)(Y203.2Si02)
0
(1/12)(Ce203*Si3N4)
S
(1/8)(Ce20;Si0,)
M
CE 0.62Sso0.375
-19787+ 2.61ST
(1/62)(7Ce203*9Si02)
2
CE .435 0.56Sso0
-21974+ 2.606T
(1/11)(Ce203.2Si02)
0
0.01(14Si3N4*Be0)
BP
(l/lSO)(21Si3N4~Si02) BP 0.004(35Si3N4.Y203)
BP
0.004(3SSi3N4*Ce203
BP
s"o.429BGo.571 A"o.BB2B00.11B A"0.714B00.2B6 A00.455BD0.545 Y00.667A00.333 y"o.500Aoo.500 y"0.375Ao0.625 SN0.700SG0.300 YO . 0 417SN0.583 y"0.62Sso0.375 y"0.S27so0.473 y"o.455soo.545 CE0.417SN0.5B3
CE0.4ssS00.545 SN0.9B0B00.020 SN0.9B0S00.020 SN0.9B0Y00.020 SN 0.9BOCE0. 020
-2808 + 1.382T/-2809+0.777T(B) -2203 - 0.4641 -2381 - 1.125T -2524 - 1.049T -4950 - 0.615T -2351 . - 4.100T -7866 + 0.690T + 0.40T(S) -5514 - O.O3BT/-5781 -404 - 1.833T -15958+ 1.389T -13000- 0.4751 -19527- 2.669T. -1389 - 1.8281
-21945+ 2.326T -423 - 0.113T -720 - 0.102T -1104 -1158
The calculationof the isothermalsectionat 2100K can be concludedby adding the L-BP equilibria as shown in Figure 14d. In this case, as in the R-L case., there are interactions with phase pairs which have been previouslyconsidered. First there is an interactionbetweenL-BP and the liquidgap, Ll-L2,as illustratedin Figure 14d, then there is a second interaction between the L-BP and L-P pairs. Comparisonof Figures14b and 14~ with 14d shows that while
the L-R/L-BPand the L-BP/L-Pinteractionpairs form stablethree phase fields,the L-BP/ Ll-L2 interaction pair which is shown in Figure 14d is metastable. This can be seen by comparing14c and 14d and notingthat the three phase BP+Ll+L2 field is "covered" by the R+LZ+L2 and R+L fields. Detailed calculation of the L-BP equilibria can be performed by defining the free energy of the BP phase on the bases of Tables l-4.
QUASIBINARYAND QUAsITERNARYOXYNTIRIDESYSTEMSIV
(bf=B/L
(cl=rc/L md N/L SO-fi/56i02J
&SN
m=WSJ
(Al*O,J
SN-(l/7)
WSN,J
1-5
and C/L
stnKture
c=AO stnrcturc
L4iquid M=1(1/21J(JL1203-2Si02J
C-COmsd~ n-(i/SJ(Si~N~OJ Oxy
Silicon
Nitride
x=so0.2$a0.6Sm0.1S e-z:,c.47,700 AGf
ff-
C-J
=-$a60 J&A.
Figure 13 CalcuiatadPainrise (8-c) and Ccqostt? Eqwilibrlu fd) in the (1/3)(Si02~- (I/?)(Si~N~)-fI/5fAl~O~ System at 20001:and one rtwsphere
For the case of the SO-MO-SN(BP) phase, where the compoundruns from SNO 980SOo 020 to SO00&fO . 50 and from SNO 98MO0 2* to MOO 50SO0 so similar proceduresare followed. For the , formercase GBP
B oGSO+y B = zo GSN+x D "~o+~~-fy/(:-x)))~GA+(y/(1-x))3GB+~GE +RT(y.kZny+&nz-(I-x)b(l-x))
(11)
here x,=0.50and x:=0,02so that p=O.96,x=x~+yp=0.02*0.96y=xSo, y=yMo and z=l-x-y=0.98-1.96y= -. Moreover,bGE=O and AGA and AGB can be explicitlydefinedas ?N' AGA AGB
= (0.02)(0.98)(0.98 LSNSO+O.OZLSOSN-c)=-820 -0.082T J/g.at.
(12)
= (0.50)(0.50)(0.50 LSOMO+O.SOWOSO-C)=-26568+10.503TJ/g.at.
(13)
with AGE--O, and y=yMo B B o~~-(l-(y/(i-x))(820+0.082~) GBP = ~0.98-l~96y)"GsN+(0.02+0.96y)*Gso+y -fy/(1-x))(26568-10.503T)+RT(y~ny+(0.98-1.96y)~(0.98-1.96y)-(0.98-0.96y)~n (0.98-0.96y))
(14)
176
L. Kmfman,
F. Aayea aud D.
Birnie
QUASIBINARYAND QUASITERNARY OXYNTIRIDESYSTEMSIV
177
TABLE 5 SUMMARYOF COUNTERPHASESTOICHIOMETRY AND 'ARAMETERS EMPLOYEDIN TERNARYCALCULATIONS System SO-MO-SN
SO-YO-SN
Stable Phase (Name)
Base
Counterphase
Base
Counterphase Parameter
S"o.429MQo.571(F)
0
S"o.300SNo.700(R)
0
SN0.980So0.020(BP)
0
SN0.980Mo0.020(BP)
0
Y"0.625So0.375(M) Y"0.527So0.473(K) y"o.455sQo.545(Q) S"o.300SNo.700(R) SN0.980So0.020(BP) SNo.980YCo.020(BP)
SO-CE-SN
CE0.625So0.375(M)
Y
CE0.565So0.435(Z) CEo.455SQo.545(C) S"o.300SNo.700(R) SN0.980So0.020(BP) SN0.980CE0.020(BP) Thus the equilibriumbetweenthe liquidand BP phase can be computedas in Figure 14(d). Combinationof the pairwiseequilibriumin Figure 14 yields the computedisothermalsection at 2100K shown in Figure 15. Isothermalsectionssimilarlyderivedat 2000K and 1900 are shown in Figure 15 along with an observedsectiondue to Mueller (9) at 1500K. The latteris in keepingwith the calculationsshown at 1900K. (See "Note in Proof") Similarcalculations were performedin the SO-YO-SNand SO-CE-SNsystems. The results,which are complicatedby the existenceof stablequasi-ternary compounds(listedin Table 6) are displayedin Figures16-19. The SO-YO-SNand SO-CE-SNsectionswere computedin a manner similarto the SO-MO-SNcase in that the systemswere first computedas if the ternary phases were absent. Subsequently the ternaryphases,designatedas C,D and E were inserted. In keepingwith previouspractice(l-3)the free energyof the ternaryphases C, D and E were definedby choosinga base phase and then defininga compoundparameterin conformitywith experimentalobservation. In the presentcase the Y structurewas chosenas the base phase since the ternaryphase compositionoccursnear the YO and CE cornersof the SO-YO-SNand SO-CE-YOsystemsas is seen in Figures17 and 18. The free energyof the ternarycompoundD in the SO-YO-SNsystemD=(1/1S)Y4Si20,N2= SOo~100YOo~667SNo~223 is definedas
L. Kaufman, F. Hayes and D. Birnie
178
TABLE6 DESCRIPTION OF QUASI-TERNARY COMPOUNDS IN THE SiO2-Y203-Si3N4 ANDSi02-Ce203-Si3N4 SYSTEMS Compound
Base
Stoichiometry
Compound Parameter (C) (Joules/g.at.)
Free Energy of Formation from Component Compounds (AGf [2Q8K])
Melting Point (OK)
(Joules/g.at.) C= (l/S)YSi02N
Y
D=(1/15)Y4Si207N2
Y
E=(l/Zl)YS(Si04)3N
Y
C=(l/S) CeSiO2N
Y
D=(1/1S)Ce4Si207N2
Y
E=(1/21)Ceg(Si04)3N
Y
*S00.322CE0.S9SSN0.083
SD0.150YD0.500SN0. 350 SG0.100Y00.667SN0.233 S00.322Y00.59SSN0.083 S00.1s0CE0.s00SN0.3s0 S00.100CE0.667SN0 . 233 S00.322CE0.S9SSN0.083 decomposes peritectically
29096+8.3687
1953
-4393-2.410T
13004+16.736T
2110
-678-4.127T
-2155+20.921
1996
-11456-0.8831
31505+8.368T
1914
-5422-2.4101
14769+16.736T
2020
-1259-4.127T
3975+20.92T
2109*
-13585-0.883T
into
2 and Liquid above 2lOOK
D G =0.10aG~0+0.6670G~0+0.2330G~N+(O.10)(0.667)(0.767)-l[0.1LSOY0+0.667LYOSO-C] *(0.l0)(0.233)(0.333)-1[O.l~OSN+0.233LSNSO-C]+(O.667)(O.233)(O.QO)-1[O.667LYOSN+ 0.223LSNYO-C] J/g.at. (15) Since C=13004+16.736T for this
phase
D G =0.10°G~O+0.6670G~o+0.2330G~N-9094-3.062T
J/g.at.
(16)
Thus the free energy of formation of D from the Y form of SO, YO and SN is -9094-3.062T J/g.at.. The free energy of formation of D from the stable forms of SO, YD.and SN (i.e. R, Y and 8 respectively) can be computed by using the lattice stability values given in Table 1. With SOSOYR=S042-1.004T and SNSNYB=33949-4.142T J/g.at. Y D R G .o.10°GS0+0.6670Gy0+0.2330GsNB 678-4.1271
J/g.at.
(17)
or AGf[298K]=-678-4.127T
J/g.at.
(18)
The free energy and free energy of formation of the remaining compounds listed in Gn this basis the isothermal sections and pairTable 6 can be computed in a similar fashion. wise equilibria shown in Figures 16-19 were developed. Figure 16 shows the computed sections at 2100 and 2000K in which phases present in the binary systems and the ternary compound D Figures 16(a) and 16(b) and Figure 17(a) illustrate pairwise interactions at are present. 1900K in SO-YO-SN. These pairwise interactions combine to yield the calculated isothermal section at 1900K which contains two small liquid regions. A computed section at 1823K given This in Figure 17(c) shows how these regions have grown smaller with decreasing temperature. section is in good agreement with the observed section (10) at 1823 shown in Figure 17(d) which illustrates the ternary compounds and the existence of a small liquid field as well. The computation of isothermal sections in SO-CE-SN is displayed in a similar manner isothermal section given in Figure 18 at 2100, 2000 and 19OOK. At 2100K the calculated contains only the phases stable in the edge binary systems. At 2000K the calculated section Pairwise equilibria calculated displays the ternary D (Ce4Si207N2) and E(Ces(Si04)3N) phases.
Figure
BP
15.
Calculated and Observed (See “Note in Proof”)
(9)
Isothermal
Sections
-A
in the
L1
F+P+LZ
System
P=periclase
SiOZ-MgO-Si3N4
(1 /3)Si02=S0
Figure
(1/7)Si3N4=SN 16.
D=(l~15)(Y,Si20,N2)
D=S00.100Y01L667SN0.2
Calcujated I&thermal Sections System Si02- Y203- Si3Nq
and Pairwise
Component Equilibria
(1/12)~Si3N,~Y203)=S=SN0,S~3YOo~417
K=(1/19) (3Si02*2Y203
in the
YO=( I /5) Y203
(a)
SYOO .SSNO. 35
L-C,
L-1)
Figure
17.
(I/7)Si3N4=SN
L-E,
Equilibrium
X-
Y
BP
1900°K
(b) A..
Crystobalite.
Equilibria at 1900°K, Calculated (IO) Si02-Y203Si3Y4Scction at
S=(1/12)(Y203*Si3N4)
Calculated Pairwise 1823OK and Observed
19W.1°K I’airwise
(:=SOO. 1
(l/J)siO_=SO
fl
L
Isothermal 1823’~
L,
(1/3)SiO,=SO
1
L
at
1900°K
L
and
L J
(ZSiO;Y,O,)
_ L_+O+M
O= (l/11)
Sections
i
d
.
R+L.
Figure
18.
calculated Isothermal Sections 1900°K in the Si02-Ce203-Si3N4
SN=(1/7)Si,N,
2100’K
(1/3)SiO,=SO
at 2100° System
and 2000’K
and Pairwise
(1/3)SiO2=SO
Equilibria
at
(l/S)Ce,O,=CE
T(nelt)=2002’K
L-N,
w
L-O,
I
Figure
SN=(l/
19.
calculated
(cl
”
L
”
A
”
”
y
-X=crystohalite
Calculated Pairwise*Equilibria (11) Subsolidus Equilibria
*
L-M
Equilibria
SN=(1/7)Si3N4
Ll-L2,
Pairwise
(l/~)sio_=so
”
at
observed 1923-2023-K S and D were expe ted but not
1
Equilibria
and Isothermal Sections at 16OO’K and Observed 192%.2023°K in the SiO2-Ce203-Si3 N4 System
u
Pairwise
f 1/3lSiO,=SO
184
L. Kaufman, F. Hayes and D. Birnle
at 1900K are shown in Figures 18(a), 18(b), 19(a) and 19(b). The latter combine to yield the calculated isothermal section at 1900K given in Figure 19(c). The latter is in relatively good agreement with the observed subsolidus equilibria (11) determined between 1923 and 2023K. The observed section does not show evidence of the S or D compound phases which was expected but not observed (11). The SO-MO-SN, SO-YO-SN and SO-CE-SN sections calculated above serve to illustrate how the synthesis of multicomponent phase diagrams can be performed in support of experimental studies of practical problems which must often be performed with great difficulty and some measure of uncertainty. References 1.
2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
L. Kaufman and H. Nesor, CALPHAD 2 35 (1978) L. Kaufman, CALPHAD 2 27 (1979) L. Kaufman, CALPHAD J 279 (1979) L.J. Gaukler. H.L. Lukas, E.Th. Henig and G. Petzow, CALPHAD 2 349 (1979). P. Doerner. L.J. Gaukler, H. Krieg. H.L. Lukas, G. Petzow and J. Weiss, CALPHAD J 239 (1979). J. Weiss, H.L. Lukas, J. Lorenz, G. Petzow ans H. Krieg, CALPHAD 2 123 (1981). E.M. Levin, C.R. Robbins and H.F. McMurdie, Phase Diagrams for Ceramists, American Ceramics Society, Columbus, Ohio (1964), First Supplement (Ibid) (1969) Second Supplement, Ibid (1975) 0. Kubaschewski and C.B. Alcock, Metallurgical Thermochemistry Fifth Edition (1979) Pergamon Press, Oxford. R. Mueller, Thesis University of Stuttgart (1981) To be Published in CALPHAD by J. Weiss, R. Mueller, H.L. Lukas, H. Krieg, G. Petzow and T.Y. Tien. L.J. Gaukler, H. Hohnke and T.Y. Tien, J. American Ceramic Society -63 35 (1980) F.F. Lange, Ceramic Bulletin g 239 (1980). Note in Proof
Note in Proof H. L. Lukas has pointed the following solid phases
out that the Gibbs free
energy change for the reaction
between
Si3N4 + 4MgO+ Mg2Si04 + 2Mg SiN2 is equal to 3953 - 8.85T Joules or 264 - 0.59 T Joules/ g. at. On this basis the SN - MDbinary edge is slightly metastable with respect to the formation of F (l/i (Si02 * 2MgO))and l/S (kg Si N2)above 446’K. Thus the sections shown in Figure 15 represent metastable equilibria.