Measurement and evaluation of hydrogen trapping in thoria dispersed nickel
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than was pure nickel. The results suggested that the t h o r i a particles trapped the hydrogen, removing it from the bulk of the nickel and thus reducing the embrittling effect of the hydrogen. The results of the present work confirm that the thoria particles do indeed strongly trap hydrogen, in agreement with the suggestion of Thompson and Wilcox. In the following sections, w e will present f i r s t the theory of McNabb and Foster, 1 with some comment on the more simplified theories of Ellerbrock, Vibrans and Stuwe3 and of Allen-Booth and Hewitt.4 We will present in this f i r s t section some n u m e r i c a l calculations of permeation results b a s e d on these theories. In succeeding sections, we will present the calculations which were used to evaluate the various p a r a m e t e r s ; and finally, present a discussion of the results, relating them t o some models of hydrogen trapping in thoria-dispersed nickel. II. THEORY A. McNabb and F o s t e r Theory We present here the theory of McNabb and Foster, 1 specialized t o the case of hydrogen diffusion through a m e t a l medium of thickness a. F i g u r e 1 shows s c h e matically the situation b e i n g treated. Hydrogen enters at one side, × = a, and e x i t s at the other, × = 0. Following McNabb and Foster, 1 it is assumed that t h e r e are N t r a p s per unit volume in the medium, and of these, a fraction n a r e filled at any t i m e . The hyd r o g e n dissolved in the bulk of the m e t a l has a concentration C. The t r a p s will be described in t h e i r o v e r a l l effect by two parameters, p and k. The para m e t e r p is the rate constant for r e l e a s e of trapped hydrogen from the traps. The rate constant k is the rate at which hydrogen is captured by the traps. S c h e matically, we can represent the interchange of hydrogen atoms between the bulk and the t r a p s by the r e a c t ion: k Hbulk ~Htrap. [1] McNabb and F o s t e r1 wrote a dimensionless form of the diffusion equation, as follows: 0u _ 02u
0w
OT
87"
Ox2
ISSN 0350-2133/79/0411-0489500.75/0 © 1979 AMERICAN SOCIETY FOR METALS AND THE METALLURGICAL SOCIETY OF AIME
[2] VOLUME 10A, APRIL 1979-489
T, t h e n they s h o w e d that a t l o n g t i m e s G(r) ~- A T + B . T h e i n t e r c e p t Ti o f t h i s e x p r e s s i o n o n the r a x i s i s given by:
TRAPS
1 +fR(*') r i = ~ " =-~ A
[5]
where,
'CO
R ( r ) = ~ + r [ 1 - (1 J r ) I n ( 1 + f P2
•
]]
/
f
/
/
[6]
In t h e a b s e n c e of t r a p p i n g , E q . [6] r e d u c e s t o t h e w e l l known result,6
PI
•
)].
Dhi = ~ a2
Co0 q
]=
_1
I I
~"--Metal Specimen
a --x
0 F i g . 1--Schematic description of m e t a l of thickness a containi n g d i s p e r s e d t r a p s . Hydrogen e n t e r s at p r e s s u r e P1 and l e a v e s at p r e s s u r e P 2 . D a s h e d l i n e : hydrogen concentration in m e t a l at s t e a d y state; s o l i d l i n e : hydrogen concentration b e f o r e attainment of s t e a d y s t a t e .
o_~ = v [ . ( f - w ) - rw] 0T
[3]
w h e r e E q . [3] d e s c r
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