The phenomenon of evaporative segregation in binary alloys has been investigated through a study of some experimental evaporation data relating to the Ni-Cr and Ni-Fr systems. In normal evaporation it is assumed that (1) the evaporating alloy is always homogeneous, (2) the vapor is instantly removed, and (3) the alloy follows Raoult's law. The solutions of the evaporation equations for the two most important cases are presented and experimental data are analyzed with these equations. The difference between observed and calculated values of evaporation constants lies within one order of magnitude. This is surprising because of the major assumptions stated above. Experimental results have shown that the evaporation time and final solute concentration are logarithmically related, further supporting our evaporation equations. It is further shown that neglecting the nonlogarithmic term in these evaporation equations may introduce considerable errors in the analysis

Gupta, K. P.

Li, C. H.

Mukherjee, J. L.

English

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https://ntrs.nasa.gov/search.jsp?R=19730005835 2020-03-23T05:33:46+00:00Z
Grumman Research Department Memorandum RM- 552 
EVAPORATIVE SEGREGATION I N  80% Ni-20% C r  
AND 60% Fe-40% N i  ALLOYS 
t J .  L. Mukherjee 
K. P .  Gupta t 
and 
C .  H. L i  
Materials and St ruc tura l  Mechanics 
October 1972 
'Department of Materia1 Science, State University of 
New York a t  Stony Brook 
Approved by: 
Charles E. Mack, Jr. 
Director of Research 
ACKNOWLEDGMENT 
This work w a s  c a r r i ed  out  a t  Grumman Aerospace Corporation, 
Bethpage, New York, 117.14, under p a r t i a l  support of NASA Contract 
NO. NAS 8-27891.  
ii 
ABSTRACT 
The phenomenon of evaporative segregation i n  binary a l l o y s  has 
been invest igated through a study of some experimental evaporation 
data r e l a t i n g  t o  the N i - C r  and Ni-Fe systems. In normal evap- 
ora t ion  it  i s  assumed t h a t  
homogeneous, b) the vapor i s  in s t an t ly  removed, and c) the a l l o y  
follows Raoultts  l a w .  The solut ions of the evaporation equations 
fo r  the two most important cases are presented and experimental 
data  are analyzed with these equations.  
served and calculated values of evaporation constants lies within 
one order of magnitude. This i s  surpr is ing because of the major 
assumptions s t a t e d  above. Experimental r e s u l t s  have shown t h a t  
the evaporation t i m e  t and f i n a l  so lu te  concentration m are 
logarithmically r e l a t ed ,  fur ther  supporting our evaporation equa- 
t ions .  It  i s  fu r the r  shown t h a t  neglecting the nonlogarithmic 
t e r m  i n  these evaporation equations may introduce considerable 
e r r o r s  i n  the ana lys i s .  
a) the evaporating a l l o y  i s  always 
The difference between ob- 
iii 
TABLE OF CONTENTS 
Page I tern 
Discussion 1 
References ............................................... 10 
............................................... 
iv 
DISCUSSION 
The phenomnon of evaporative segregation i n  binary a l l o y s  has 
been quant i ta t ive ly  t rea ted  by L i  (Refs. 1,2). By evaporative 
segregation, we  mean so lu te  enrichment o r  depletion i n  the evapo- 
r a t ing  a l l o y  as a r e s u l t  of surface evaporation. 
The formalism of evaporative segregation i n  a l loys  works 
surpr i s ing ly  well  f o r  the several  systems so  f a r  studied, 
notwithstanding the several  major assumptions involved. In the 
present memorandum, we  s h a l l  study only some experimental evapora- 
t i on  data r e l a t i n g  t o  the N i - C r  and Ni-Fe systems, as reported 
by N. D.  Obradovic e t  al. (Ref. 3 ) .  Specif ical ly ,  w e  s h a l l  compute 
the degree and rate of so lu te  enrichment o r  depletion i n  the evapo- 
r a t i n g  source a t  d i f f e ren t  temperatures and evaporation times. 
In the treatment of the s i m p l e  "normal" evaporation, i t  i s  
assumed t h a t  a) the evaporating a l l o y  i s  always homogeneous, 
b) the vapor i s  in s t an t ly  removed, and c) the a l l o y  follows Raoult 's  
l a w .  
m e l t  i n  vacuum o r  l i qu id  in  space. The solut ions of the re levant  
d i f f e r e n t i a l  equation f o r  the following two important cases are 
(Ref. 2) :  
Such conditions e x i s t  o r  are near ly  approached i n  an induction 
Case I: The so lu te  i s  much more evaporative than solvent, 
i . e . ,  U >> V. Then the t i m e  to  reach a f i n a l  concentration m 
i s  
m - m  (1 - m o b  + 0 
mo(l - m) (1 - m,)(l - m) 
1 
where 
GI = 
u =  
v =  
m =  
m =  
0 
N =  
0 
A =  
- No(l - m,)/AU (sec )  
evaporation rate of the so lu te  i n  
evaporation rate of the solvent i n  
2 
m o l l c m  /sec 
mol/cm /sec 
2 
i n i t i a l  molar f r ac t ion  of so lu te  
f i n a l  molar f rac t ion  of so lu te  a f t e r  time 
( i n  sec) 
t o t a l  i n i t i a l  number of moles of both solvent 
and so lu te  
evaporating area i n  cm 2 
For nearly equal m and m ( i . e . ,  m 2 m ), or for small 
m and mo ( i . e . ,  m 2 m ov 0 ) ,  Eq. (1) reduces to  the following 
logarithmic expression: 
0 0 
0 -  
Case 11: The solvent i s  much more evaporative than solute ,  
i . e . ,  V >> U, then, 
where G2 = m N /AV. Again, f o r  nearly equal m and m ( i . e . ,  
m 2 m ), Eq. (2) reduces t o  a logarithmic expression very s i m i l a r  
t o  (la) : 
0 0  0 
0 
2 
G l s  are the t i m e  constants of evaporation. For the case 
when U >> V, so lu te  depletion takes place, i .e. ,  m < mo and, 
therefore,  the logarithmic t e r m  i n  the parentheses i s  negative 
( the second t e r m  i n  the parentheses i s  of ten negl igible  by compari- 
son with the logarithmic term). Since the evaporation t i m e ,  t, 
must be posi t ive,  G1 i s  negative, G2 i s  always pos i t ive .  
2 The evaporation rate i n  mol/cm /sec for  solute  and solvent 
i s  given by (Ref. 4)  
where 
K = 5.833 x a constant fo r  metals 
= molecular weights of solute  and solvent,  
r e  spec t ive ly MuyMv 
T = evaporating temperature i n  OK 
AU,BU = evaporating constants f o r  the solute  
= evaporating constants fo r  the solvent .  A v 4  
Obradovic e t  a l .  (Ref. 3) give the f i n a l  solute  concentrations 
for  Ni-Fe and N i - C r  a l loys  a f t e r  various evaporating times a t  
1600°C under various ambient pressures, a s  shown i n  Tables 1 and 2 .  
These data have been analyzed by means of E q s .  (1) and (Z), above. 
The solute  and solvent evaporating constants,  AU, BU, A V’ and Bv, 
are obtained from Ref. 4 .  
3 
rl 
a, 
rl 
P 
(d E-r 
0 z 
m o o  
W d 4 -  
rl 
. . .  
r l m o  
m 
r l w m  
0 0 0 0  m o o 0  
r l m m  
4 
n 
m 
a, 
U 
E 
B 
W 
OF 
n 
m 
E 
k 
a, u 
c) 
H 
h 
$4 u m 
X 
W 
0 
2 
0 0 0 0 0  
m ~ o o o  r l m m  
5 
Relevant data f o r  computation of the G1s are given below: 
a) 60% Fe-40% N i  a l loy :  
= 6.386 x mol/cm 2 /sec;  No = 0.7478 mol; T = 1600°C; *Ni 
'Fe 
= 1,081 x log5 mol/cm 2 /sec;  A = 10.0 em2; Case 11: U << V. 
b) 80% Ni-20% Cr a l loy :  
2 
= 3.479 x l o m 5  mol/cm /sec;  No = 0.7582 mol; T = 1600°C; 
= 6.386 x 10 mol/cm /sec;  A = 10.0 em ; Case I: U >> V. 
'Cr 
'Ni 
-6 2 2 
It can be seen from Table 1 t h a t  f o r  the Fe-Ni a l loy ,  the values 
of G21s a r e  constant within one order of magnitude. The difference 
i s  also within one between observed and calculated values of 
order of magnitude. This i s  very surpr is ing considering the f a c t  
G2 
t h a t  elemental evaporation rates generally d i f f e r  by many orders of 
magnitude. Also, the above analysis  i s  based on the assumptions of 
a )  the evaporating a l l o y  i s  always homogeneous; b) idea l  solut ion 
behavior (and the solut ions here are highly concentrated! ) ; c) the 
vapor is  in s t an t ly  removed. The experimental data of Obradovic e t  a l .  
(Ref. 3) on the Fe-Ni system shows no systematic dependence of 
evaporation k ine t ics  on pressure as  one would expect, and suggests 
large experimental e r ro r s ,  e r r o r s  i n  measurements, o r  both. 
Table 2 a lso shows the calculated and observed values of G 1s 1 
for the N i - C r  a l l oy .  Here, a l so ,  the values of G1's are almost 
constant,  and the differences between the observed and calculated 
values of Glls are small. The data on the N i - C r  system show 
some posi t ive cor re la t ion  between ambient pressure and the weight 
percent of chromium i n  the m e l t  a f t e r  30 minutes. 
6 
The values of computed G ' s  
magnitude. In  par t icu lar ,  f o r  the Fe-Ni system, a t  ambient pres- 
3 sures of 1, 30, 50, 200 (x 10 ) t o r r ,  these same values are ac- 
curate  t o  within 25 percent. Therefore, i n  some cases i t  is  de- 
s i r ab le  to  know these values t o  wi th in  20 percent of t h e i r  real 
values . 
are constant within one order of 
In Tables 1 and 2 the t i m e  constants G I s  have been calculated 
i n  two ways. F i r s t ,  G ' s  were calculated by using only the loga- 
r i thmic t e r m .  Next, the complete equation (1) o r  (2) involving 
both the logarithmic and nonlogarithmic t e r m s  w a s  used. 
te res t ing  to  note tha t  the r a t i o  of G ' s  
i s  constant and has an average value of 1 .67  t- 0.01 for  Fe-Ni 
a l l o y  and 1.26 It 0.005 for  the N i - C r  a l loy .  Mathematically, 
t h i s  means tha t  f o r  the case U >> V ( in  N i - C r  a l loy)  
.It i s  in-  
calculated i n  two c h e s  
In 
_I 
or 
=e 1.26 , (5) 
= 0.26 
7 
and f o r  the case V >> U, i . e . ,  i n  Fe-Ni a l l o y  
m - m  
m m  
0 = 0.67 . 
Experimental r e s u l t s  have shown t h a t  the evaporation t i m e  t 
and the f i n a l  so lu te  concentration m are logarithmically r e l a t e d  
(Refs. 3,5), supporting our Eqs. (1) and ( 2 ) .  However, these same 
equations indicate  tha t  such'relations are t rue only for. v a s t l y  
d i f f e r e n t  solvent and so lu te  evaporating rates, and, i n  addi t ion,  
f o r  small i n i t i a l  and f i n a l  concentrations, m and m. These 
same equations a l s o  allow one to  compute, e . g . ,  the e f f ec t ive  evap- 
ora t ing  area, A ,  the so lu te  o r  solvent evaporating rates U o r  
V, or  the evaporating temperature T. Further, neglecting the 
nonlogarithmic second t e r m s  i n  Eqs. (1) and (2) may introduce 
e r r o r s  i n  T, A, U, o r  V by 26 percent i n  the 80% Ni-20% C r  
case and 6 7  percent i n  the 60% Fe-40% N i  case. 
0 
The equations of normal evaporation can be made more r e a l i s t i c  
by introducing the concept of solvent-solute in te rac t ion .  I f  one 
considers only f i r s t -o rde r  correction, then it can be shown t h a t  
the idea l  evaporation rates of so lu tes  and solvents w i l l  be changed 
by a new fac to r  r e l a t e d  t o  the a c t i v i t y  coe f f i c i en t  of the element 
i n  question. In other  words, 
u' = yuu 
v' = yvv , 
8 
where yuy Y, are a c t i v i t y  coef f ic ien ts  of so lu te  and solvent,  
respect ively,  assumed constant i n  the v i c i n i t y  of m and U' ,  V' 
are e f f ec t ive  evaporating rates of so lu tes  and solvents.  Using 
the a c t i v i t y  data of Fe-Ni alloy (Ref. 6) a t  1600°C, we  have 
reca lcu la ted  the values of G2. Now 
0' 
m n  
0 0  G; = 
where 
v '  = yvv 
- = 0.977 fo r  60 m o l  % Fe a l loy .  'v - 'Fe 
G; (cal)  = 0.4471 x 10 4-4 sec. 
(9) 
On applying s i m i l a r  f i r s t -o rde r  correct ion f o r  N i - C r  system 
(Ref. 7 ) ,  the revised value of Gl becomes, 
4-4 G; (cal)  = 0.2138 x 10 sec.  
These correct ions,  while not very large,  do make a l i t t l e  b e t t e r  
agreement between calculated and experimentally observed G values. 
In conclusion, the s imple  normal evaporation approach seems 
t o  give f a i r l y  accurate and useful  predict ions,  even f o r  the highly 
concentrated N i - C r  and Fe-Ni a l loys .  
9 
REFERENCES ___- 
1. L i ,  C.  H . ,  Phys. S t a t .  S o l . ,  Vol. 15, pp. 3 and 419, 1966. 
2 .  L i ,  C .  H . ,  "Normal Evaporation of Binary Alloys," to  be 
published. 
3. Obradovic, N .  D .  and Bennett, G. H. J . ,  J. Inst .  of Metals, 
Vol. 97, p .  186, 1969. 
4 .  Dushman, S . ,  S c i e n t i f i c  Foundations of Vacuum Techniques, 
Wiley, New York, pp. 68 and 691, 1962. 
5. Chang, Y .  A .  and M i l l e r ,  R . ,  "The Effec t  of Ag on the Ac- 
t i v i t y  Coeff ic ient  of Zn i n  Dilute  Liquid Sn Alloys by 
Torsion Effusion Method," 1972 AIME Annual Meeting, San Fran- 
c i sco .  
6 .  Hultgren, C. e t  a l . ,  Selected Values of Thennodynamic Proper- 
- ties of Metals and Alloys, Wiley, New York, p .  732, 1963. 
7 .  Fruhan, R. J. ,  "The Act ivi ty  of C r  i n  Liquid N i - C r  Alloys," 
Trans. Met. SOC. AIME, 1968, V o l .  242, p. 1769. 
10 


Evaporative segregation in 80 percent Ni-20 percent Cr and 60 percent Fe-40 percent Ni alloys

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