The High Temperature Thermodynamic

Properties of Ni-Ti Alloys

R. M. GERMAN and G. R. St. PIERRE

The t h e r m o d y n a m i c p r o p e r t i e s of liquid N i - T i a l l o y s have b e e n d e t e r m i n e d between 1475 ~ and

1725~ by a K n u d s e n c e l l - m a s s s p e c t r o m e t r i c t e c h n i q u e . The liquid N i - T i s y s t e m exhibits s t r o n g
n e g a t i v e d e v i a t i o n s f r o m i d e a l i t y , i n d i c a t i n g a p r e f e r e n c e for unlike a t o m bonding. P r o n o u n c e d
m a x i m a in the e x c e s s s t a b i l i t y function occur n e a r the Ni3Ti and NiTi c o m p o s i t i o n s at 1500 ~ C.

INr e c e n t y e a r s , i n t e r e s t in the N i - T i b i n a r y s y s t e m 99.99 pct p u r i t y w e r e used a s charge m a t e r i a l s , and

has b e e n g e n e r a t e d by a n u m b e r of f a c t o r s . E x t e n s i v e the total alloy charge weights w e r e a p p r o x i m a t e l y one
work h a s b e e n r e p o r t e d on the m e m o r y effects and c o r - g r a m . The t i t a n i u m m a s s peak at 48 a . m . u , and the
r o s i o n r e s i s t a n c e of the e q u i a t o m i c c o m p o s i t i o n . I n - n i c k e l m a s s peak at 58 a . m . u , w e r e used for all i n t e n -
t e r e s t in N i - T i a l l o y s at high t e m p e r a t u r e s r e s u l t s sity m e a s u r e m e n t s . R e s o l u t i o n of t h e s e two peaks was
f r o m the expanding u s e of n i c k e l - b a s e d s u p e r a l l o y s . b e s t when an i o n i z a t i o n potential of 15 V and a t r a p
P r e v i o u s t h e r m o d y n a m i c data for the N i - T i s y s t e m is c u r r e n t of 0.50 /~amp w e r e used. I n t e n s i t y m e a s u r e -
l i m i t e d . K u b a s c h e w s k i I d e t e r m i n e d the heat of f o r m a - m e n t s w e r e made in a n u p - a n d - d o w n m a n n e r between
tion for v a r i o u s N i - T i a l l o y s at 298 K by a c a l o r i m e t - 1475 ~ and 1725~ following a slow h e a t i n g to 1600~
r i c t e c h n i q u e . C h e r k a s o v , A v e r i n , and S a m a r i n z were The p r e s e n t a u t h o r s b e l i e v e that t h e r m a l cycling a s
able to obtain a value of ~ i in N i - T i f r o m e q u i l i b - opposed to d e c r e a s i n g t e m p e r a t u r e m e a s u r e m e n t s r e -
r i u m oxygen c o n c e n t r a t i o n s in v a r i o u s N i - T i - C r m e l t s . sult in l e s s b i a s e d i n t e n s i t y data.
T h e i r r e s u l t s i n d i c a t e a l a r g e n e g a t i v e deviation in Empty cell b a k e - o u t s w e r e p e r f o r m e d b e f o r e e v e r y
t i t a n i u m a c t i v i t y at 1600 ~ C. t h i r d r u n and c h e m i c a l c l e a n i n g of the cell and f u r n a c e
The N i - T i phase d i a g r a m by H a n s e n and Anderko, 3 a s s e m b l y was p e r f o r m e d b e f o r e e v e r y e x p e r i m e n t .
E l l i o t t , 4 and Shunk 5 i s shown in Fig. 1, f r o m which it The cell a s s e m b l y was r e p e a t e d l y m i s a l i g n e d d u r i n g
can be s e e n that the i n t e r m e t a l l i c compounds NiTi and an e x p e r i m e n t to d e t e r m i n e b a c k g r o u n d i n t e n s i t i e s .
NisTi m e l t c o n g r u e n t l y , w h e r e a s NiTi2 d e c o m p o s e s by C o m p a r i s o n of this v a l u e with the s h u t t e r e d i n t e n s i t y
a p e r i t e c t i c r e a c t i o n . The r e l a t i v e s t a b i l i t i e s of the r e v e a l e d no change in e i t h e r b a c k g r o u n d i n t e n s i t y
compounds a r e i n d i c a t e d by t h e i r high m e l t i n g p o i n t s . d u r i n g a n e x p e r i m e n t , i n d i c a t i n g no s u b s t a n t i a l r e v a -
The p r o p e r t i e s of the liquid phase u s u a l l y c o r r e l a t e porization build-up.
with such stable i n t e r m e t a l l i c compounds.
1800 I I I I

EXPERIMENTAL
A Bendix Model 3012 t i m e - o f - f l i g h t m a s s s p e c t r o m -
e t e r equipped with a Model 1031 K n u d s e n cell inlet 1600
s y s t e m 6-8 was u s e d in this i n v e s t i g a t i o n . I n i t i a l l y ,
t h o r i a c r u c i b l e s w e r e used to hold the a l l o y s ; however,
the c r u c i b l e s c r a c k e d f r e q u e n t l y d u r i n g heating. Hence,
it w a s n e c e s s a r y to u s e y t t r i a - s t a b i l i z e d - z i r c o n i a 14o0
c r u c i b l e s and l i d s for m o s t of the m e a s u r e m e n t s .
Sample e x a m i n a t i o n after each r u n r e v e a l e d no e v i - o~
dence of c r u c i b l e d e g r a d a t i o n . An o u t e r t a n t a l u m cell ~ ~20o
was used as a s u s c e p t o r . T e m p e r a t u r e m e a s u r e m e n t s 2
w e r e made with a L e e d s and N o r t h r u p Model 8634 ~<
P r e c i s i o n Optical P y r o m e t e r , a m i c r o f o c u s i n g , d i s a p - ~-
p e a r i n g f i l a m e n t type. P y r o m e t e r s i g h t i n g s w e r e made ~ 10oo
on the K n u d s e n cell o r i f i c e through a p r i s m and v i e w -
ing port. The p y r o m e t e r was c a l i b r a t e d at the m e l t i n g
points of gold, i r o n and nickel as well a s the 7 ~ 6
t r a n s f o r m a t i o n point for i r o n . T e m p e r a t u r e d e t e r m i n a - 8oo
t i o n s w e r e within a r a n g e of +3 ~ C of the set point.
The K n u d s e n cell o r i f i c e had a d i a m e t e r of 0.117 cm.
Sponge t i t a n i u m of 99.98 pct p u r i t y and r o d nickel of
6O0
R. N. GERMAN is with MetallurgyDivisionII, Sandia Laboratories,
Livermore, Calif. 94550. G. R. ST. PIERRE is Professor of Metallurgi-
cal Engineering,The Ohio State University, Columbus, Ohio. This
paper is based upon a thesis by R. M. GERMANis partial fulfillment Ni 20 40 60 80 TI
of the requirements of the degree of Master of Science at The Ohio
State University. ATOM IC ~/o Ti
Manuscript submitted December 8, 1971. Fig. 1--The Ni-Ti binary phase diagram.

METALLURGICALTRANSACTIONS VOLUME 3, NOVEMBER 1972-2819

 RESULTS ~.MPERATURE, ~
1700 1600 1500
The ion intensities for both the Ni-58 and Ti-48 I I I
I l I l l I I 1
atoms have been measured within the temperature
range of 1475 to 1725~ for alloys with 10 to 80 at.pct. TITANIUM COMPOSITIONS
Ti. Fig. 2 shows the ion intensity ratio as a function of
1/T for the liquid alloys studied. A computer l e a s t - ~ e | e
2
squares fit of the data in Fig. 2 provided the tabulation
for Table I at 1600~ Repeated attempts were made I
to observe any possible compound vapor species 0---.-C,%c~ O'C, u C,- 70%
(NiTi § Ni3Ti § and NiTi2) with none detected. Because
no compound peak was observed and the ionization
voltage was relatively low, dissociative ionization of -I
o
~ 55%
60%

gaseous intermetaUic compounds has been discarded

as a major source of e r r o r . However, the possibility .n
+_z
-2 2.5%
of preferential diffusion through the crucible was not
investigated. Based on Speiser and Spretnak, 9 alloy de- 40%--~ ^ .A 0 50%
+,_.= -3
pletion calculations were performed using the activity e-
42.5% ~
data generated in this investigation. As a result of the -4
calculations, an e r r o r of 4-1 pct in the composition is -'; :&,:~:~'~---.. 35%
included in Fig. 3 to account for depletion~ Uncertain- -5 - - 30%
O
ties in the alloys of low titanium content arise p r i - mOO 9 9 9 25%
-6 00 O O u 9
marily from the low Ti-48 intensity generated. Uncer-
tainties at titanium contents above 40 pct may arise
-7
from extraneous vapor contributions as well as the
usual temperature and instrument fluctuations.
-8 -

CALCULATION OF THERMODYNAMIC PROPERTIES -9

Eqs. [1] and [2], derived by Belton and Fruehan, 6 -10 I I I I I I I I

4.8 5.0 5.2 5.4 5.6 5.8
provide the bridge between the ion intensity ratio and
the thermodynamics. 10, [~
7-
Fig. 2--The experimental intensity ratios for liquid Ni-Ti al-
/ny, = _,X2 d In ~X2 [1] loys.

, Fig. 3 shows the activity coefficient integration func-

HM= - R Xz d o ln ( i ; / i : ) tion, In (ITi XN'u/INi XTi), a c r o s s the binary system at
:z a (I/T) [2]
1500 ~ 1600 ~ and 1700~ The phase boundaries are
where Yi is the activity coefficient of species i, X is taken from Fig. 1. E r r o r b a r s indicate 4-1a deviations
the atom fraction, 1 § is the measured ion intensity, T from the l e a s t - s q u a r e s data fit of Fig. 2, plus the 1 pct
is the absolute temperature, R is the gas constant, alloy depletion e r r o r s . In the terminal regions, a
and H/M is the partial molar enthalpy of species i. straight line fit to the data is utilized. Because no
Hence, the activity coefficient for a binary mixture data were obtained in the solid regions, extrapolations
at a given temperature can be determined through an were made of the linear behavior in the terminal r e -
integration involving the measured intensity ratio. gions of the liquid state, based on an undercooled liq-
uid. With increasing temperature, the integration func-
tion becomes linear a c r o s s the binary system.
Table I. Experimental Values for the Intensity Ratio, Free Energy Integration
Integration of the curves shown in Fig. 3 leads to
Function, and Temperature Coefficient for the Ni-Ti System at 1600~ the activity curves shown in Fig. 4. Satisfaction of the
Gibbs-Duhem equation is inherent, by nature of the in-
At. Pct Ti lnl~/~a ln(I~XNi/I;aXTi OIn [(l~/I;a)/O(1/T)] tegration technique. The activity coefficient results
10 -8.708 -6.511 -48200
are tabulated in Table II. Negative deviations from
20 -7.933 -6.546 -22800 ideality occur throughout the system.
25 -5.901 -4.803 200 The activities change rapidly with composition at
30 -5.207 -4.358 ~5900 1500~ near the NiTi and Ni3Ti compositions. This
35 -4.505 -3.885 -1200 behavior indicates an ordering in the melt at lower
40 -2.974 -2.569 -15300
42.5 -3.326 -3.022 -5800
temperatures at both 50 and 25 pct Ti.
45 -3.318 -3.118 -16100 Fig. 5 shows the variation of the temperature coeffi-
50 -2.777 -2.776 -12700 cient, a (/n ITi/I~i )//a (l/T), with composition. The
52.5 -2.113 -2.213 1100 line drawn through these data is estimated. Application
55 -0.333 -0.554 -100 of Eq. [2] to Fig. 5 results in the n~ckel and titanium
60 0.634 -1.039 500
70 0.451 -0.397 1300
partial enthalpies. The integral molar enthalpy is
80 1.735 0.349 -10800 given by Eq. [3].
*Zlrconia crucibles.
x iH i [3]
2820-VOLUME 3, N O V E M B E R 1 9 7 2 METALLURGICAL TRANSACTIONS
The partial Gibbs energy is related to the activity by
SM = XNi SNMi + XTi STMi [101
Eq. [41.
S E= XNiSENi + XTiSETi [11]
G ~ = R T In a i [4]
Fig. 6 presents the integral thermodynamic quanti-
where a i is the activity and R is the gas constant.
ties for the Ni-Ti s y s t e m at 1600~ The negative be-
Eq. [5] gives the integral molar Gibbs energy from
havior of the e x c e s s quantities indicates ordering in
the partial Gibbs energies.
the liquid state. The negative enthalpy is further evi-
~ = x~i ~ i + X T i ~ Ti [q dence for the unlike atom a s s o c i a t i o n s in the liquid.
Similarly for the e x c e s s Gibbs energies,
c~ = ~ r tn ~ [el Tablell. A~ivityCoefficientsforthe Ni-TiSystemat1500~176 1700~

and 1500~ 1600~ I700~

At. Pct Ti Ni Ti Ni Ti Ni Ti
~ = x~i c~i + XTi GT~i [71
100 0.061 1.000 0.042 1.000 0.021 1.000
The partial entropy is given by Eq. [8] and the e x c e s s 90 0.025 1.058 0.022 1.034 0.023 0.964
partial entropy is given by Eq. [9]. 80 0.038 0.977 0.042 0.922 0.052 0.836
70 0.057 0.854 0.072 0.770 0.104 0.663
s M = HM - C~ [8] 60 0.081 0.706 0.117 0.591 0.189 0.481
T 50 0.249 0.260 0.280 0.294 0.313 0.318
40 0.345 0.178 0.394 0.195 0A74 0.192
s~ -- ~ - ~
T
[~] 30 0.421 0.122 0.533 0.I 10 0.659 0.104
20 0.852 0.013 0.758 0.038 0.834 0.051
10 0.916 0.007 0.937 0.011 0.956 0.023
Finally, the integral molar and e x c e s s molar entropies 0 1.000 0.003 1.000 0.003 1.000 0.010
are given by Eqs. [10] and [11].

3 , f i S~)UD
I I . . . . It
I .r
I
_~/'1
' ' 't
I

o
I I

-I
LIQUID I I

-2 SOLID - ~ -2

-3

?
-5 -5

-7

-a

-9
-7

-e 7' T= I ~ ' c
I I t I
T= I~"C 20 4o 6o ~ lq o 2o 40 6o eo too

-10 i i i L ATOMIC '/, ]l ATOMIC 'I, i"i

~o ~o 6o 8o ioo
ATOMIC ~, Iq
(a) (b)
§ +
(C)
Fig. 3 - - T h e variation of the activity coefficient integration function, In ITiXNi/INiXTi, with composition in the N i - T i
s y s t e m . (a} 1 5 0 0 ~ (b) 1 6 0 0 ~ (c) 1700~

, ~ i 1 i
1.0 ' ' T = 1700e C ' ' /

,\ 17!i' '-
O8
\xN LIQUID /4
"N
LQoo //
/ / I I
o8 \ L,oo,o / "7
\ ,, ..... / / : \', // i,, 9 , ~'% // ,

i-
O6 06

\ % ' ../.
J 1 t-

h.,\ /" ~
, sou0--T7
I I

0.2 /
,'\
\
I
I \
i'
= m_
o.l /x/ "\,
/
2O 4O 6O 80 I00
l/I/ 20 4O 6O ~0 I00

AI"O/dlC '/, Tm A~IC % Ti ATOMIC % Tm

6) (b) (c)
Fig. 4--Calculated activities of the Ni-Ti system. (a) 1500% (b) 1600~ (c) 1700~

METALLURGICAL TRANSACTIONS VOLUME 3, NOVEMBER 1972-2821

The s k e w e d shape for the enthalpy i n d i c a t e s that a r e g - b e h a v i o r in the t e r m i n a l r e g i o n s . F u r t h e r m o r e , the
u l a r solution m o d e l i s inadequate for t h i s s y s t e m . a c t i v i t y coefficient d a t a at 1700~ i n d i c a t e a r e g u l a r
H o w e v e r , a c t i v i t y coefficient data d e m o n s t r a t e l i n e a r solution m o d e l m a y be a d e q u a t e for the N i - T i s y s t e m
at t h e s e h i g h e r t e m p e r a t u r e s . The e n t h a l p y of f o r m a -
2.0
} I 1 | tion d a t a by K u b a s c h e w s k i z for v a r i o u s N i - T i a l l o y s
at 298 K shows the s a m e g e n e r a l s k e w e d s h a p e and
m a g n i t u d e o b s e r v e d in t h i s i n v e s t i g a t i o n . The
log~0 Y~i r e s u l t at 1600~ for t h i s i n v e s t i g a t i o n i s
1.0
- 2 . 5 , in r e a s o n a b l e a g r e e m e n t with the e x t r a p o l a t e d
v a l u e of - 3 . 3 r e p o r t e d by C h e r k a s o v , A v e r i n , a n d
Samarin.2
o

DISCUSSION O F R E S U L T S
D a r k e n 1~ d e f i n e s the e x c e s s s t a b i l i t y a s the s e c o n d
-I .0
p a r t i a l d e r i v a t i v e of the e x c e s s Gibbs e n e r g y with r e -
o s p e c t to the c o m p o s i t i o n . M a t h e m a t i c a l l y , the e x c e s s
A X s t a b i l i t y can be r e d u c e d to a f i r s t d e r i v a t i v e of In Yt,
t h e r e b y m a k i n g it a m o r e m e a n i n g f u l quantity with r e -
s p e c t to the p r e s e n t e x p e r i m e n t a l d a t a . The r e l a t i o n -
+~-~
ship is shown by Eq. [12].
d(ln Yi)
-3.0 excess stability = -RT d[(1 - Xi) 2] [12]

F o r m o s t s o l u t i o n s the e x c e s s s t a b i l i t y i s l i n e a r in
the t e r m i n a l c o m p o s i t i o n r e g i o n s . The o c c u r r e n c e of
-4.0
p e a k s in the e x c e s s s t a b i l i t y function for l i q u i d p h a s e
m e a s u r e m e n t s u s u a l l y c o r r e s p o n d s to the c o m p o s i -
t i o n s of s t a b l e s o l i d p h a s e c o m p o u n d s . F i g . 7 shows
-5.0 the e x c e s s s t a b i l i t y a s a function of c o m p o s i t i o n for
the liquid p h a s e m e a s u r e m e n t s a t 1500 ~ 1600 ~ and
l I l I 1700 ~ C. The t e r m i n a l r e g i o n s exhibit the e x p e c t e d
20 40 60 80 100 l i n e a r b e h a v i o r . At the l o w e r t e m p e r a t u r e , p e a k s o c -
ATOM IC ~ TJ
c u r at c o m p o s i t i o n s c o r r e s p o n d i n g to the Ni3Ti and
Fig. 5--The variation of the temperature coefficient integra- N i T i i n t e r m e t a l l i c c o m p o u n d s in the s o l i d p h a s e . No
tion function a In ( I ~ i / I ~ i )/~ (l/T), with composition. i n d i c a t i o n s of an e x c e s s s t a b i l i t y p e a k c o r r e s p o n d i n g
to NiTi2 w e r e found. The o c c u r r e n c e of an e x c e s s s t a -
b i l i t y c o r r e s p o n d i n g to the NiTi2 c o m p o s i t i o n w a s not
I i i i
e x p e c t e d at t h e s e t e m p e r a t u r e s . The compound i s r e l -
T = 1600~
a t i v e l y u n s t a b l e , a s e v i d e n c e d by the p h a s e d i a g r a m ,
hence p o s s i b l e liquid p h a s e a s s o c i a t i o n s would be d e -
20 I I I I

-2

E
o

-4
r
-6
I~JI

-8 4
. . . . . '~. . . . . 17oo.
\ ---1;ooi:---
c--

Z I I I
-10
0 20 40 60 BO 100 0 20 40 60 80 1O0

ATOMI C % Ti ATOMIC I~ Ti
Fig. 6--The integral thermodynamic quantities of the liquid Fig. 7--Excess stabilities of liquid Ni-Ti alloys from 1500 ~
Ni-Ti system at 1600~ to 1700~

2822-VOLUME 3, NOVEMBER 1972 METALLURGICAL TRANSACTIONS

stroyed at 1500~ The negative excess entropy observed is attributable
G e i d e r i k h a n d G e r a s i m o v 11 e x p e r i m e n t a l l y s h o w t h a t t o a l o s s of v i b r a t i o n a l e n t r o p y d u e t o u n l i k e a t o m
t h e s t r e n g t h of b o n d i n g b e t w e e n t r a n s i t i o n m e t a l s c o m - bonding and electronic state changes. The experimen-
bined with the Fe-Co-Ni sequence increases systemati- t a l o b s e r v a t i o n s of t h i s i n v e s t i g a t i o n i n d i c a t e t h a t u n -
cally. The increasing electron affinity in this sequence like atom bonding is the preferred state and dominates
as the d electron subshell becomes filled is responsi- t h e t h e r m o d y n a m i c s of t h e s y s t e m .
b l e f o r t h e i n c r e a s i n g b o n d s t r e n g t h . B e c a u s e of t h e
r e l a t i v e c o m p l e t e n e s s of t h e n i c k e l d s u b s h e l l , i t h a s
ACKNCWLEDGMENTS
the greatest driving force for intermetallic compound
formation. The affinity for titanium by nickel because T h e a u t h o r s w o u l d l i k e t o a c k n o w l e d g e t h e h e l p of
of t h e u n f i l l e d d e l e c t r o n s u b s h e l l m a y a c c o u n t f o r t h e D r . C. W. W e i d n e r i n t h e s o l u t i o n of s e v e r a l e x p e r i -
low t e m p e r a t u r e o r d e r i n g i n t h e l i q u i d N i - T i s y s t e m mental problems. Support for this investigation was
observed in this investigation. provided by the American Iron and Steel Institute and
the Sandia Corporation.

REFERENCES
CONCLUSIONS
1. O. Kubaschewska:Trans. Faraday Soc.. 1958, vol. 54, pp. 814-20
The thermodynamic properties of the Ni-Ti system 2. P. A. Cherkasov, V. V. Avenn, and A. M. Samarm: Russ. J. Phys. Chem., 1968,
exhibit strong negative deviations from ideality. The vol 42, pp. 401-04.
3. M. Hansen and K Anderko: Constitution of Binary Alloys, 2nd ed., p. 1049,
activity data demonstrate large negative deviations McGraw-Hill Book Co., New York, 1958.
from Raoult's Law. Similarly, the enthalpy and excess 4. R. P. Elhott: Constitution of Binary Alloys, First Suppl., p. 559, McGraw-Hill,
entropy exhibit negative characteristics. Indications Book Co., New York, 1965.
are that unlike atom bonding is preferred in the liquid 5 F A. Shunk: Constitution of Binnary Alloys, Second Suppl., p. 676, McGraw-
solution. Activity data indicate strong ordering tenden- Hill Book Co., New York, I969.
6. G. R. Belton and R. J. Fruehan: J. Phys Chem., 1967, vol. 71, pp. 1403-09.
cies in the low temperature liquid at both 25 and 50 pct 7. R B. Reese, R. A. Rapp, and G. R. St. herre Trans. TMS-AIME, 1968, vol
Ti. The increased atomic mobility at higher tempera- 242, pp. 1719-26.
tures destroys this tendency. Accordingly, the role of 8. S. W. Gilby and G. R. St. Pmrre: Trans. TMS-AIME, 1969, vol. 245, pp. 1749-
temperature in affecting tlle ordering tendencies is 58.
easily seen in the excess stability function. The excess 9. R. Speiserand J. W. Spretnak Vacuum Metallurgy, J. M. Blocher,ed., p. 155,
The ElectrochemicalSoc, Boston, 1955.
stability function has pronounced peaks at compositions 10. L S Darken: Trans. TMS-AIME, 1967,vol. 239, pp. 80-89.
c o r r e s p o n d i n g t o N i z T i a n d N i T i a t 1500 ~ C. H o w e v e r , 11. V. A. Geiderildland Y. 1. Gerasimov:Russ. Z Chem., 1963, vol. 37, pp. 1274-
the peaks are destroyed with increasing temperature. 76.

METALLURGICAL TRANSACTIONS VOLUME 3, NOVEMBER 1972-2823