Trapping of hydrogen by substitutional and interstitial impurities in α-iron

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TRAPPING OF HYOROGEN BY SUBSTITdTIONAL AND INTERSTITIAL IMPURIT[ER IN (~-IRON A. I. Shirley and C. K. Hall Department of Chemical Engineering Princeton University Princeton, New Jersey 08544 (Received (Revised

A p r i l II, 1983) J u n e ]3, 19831)

INTRODUCTION At sufficiently low temperatures hydrogen in a metal may favor sites near an interstitial or substitutional impurity resulting in a trapping effect that hinders hydrogen movement. This phenomenon has been investigated for traps of both impurity types in a number of metals (I-6). A previous study by the authors indicates t~at this effect is the result of an elastic hydrogenimpurity interaction in interstitial trapping (7), whereas both elastic and electronic hydrogenimpurity interactions are known to contribute to substitutional trapping (6,8). Calculations of the elastic interaction energies between hydrogen and interstitial impurities (7) and between hydrogen and substitutional impurities (8) in niobium, vanadium and tantalum have shown that these energies are attractive when the impurity expands the host lattice. For substitutional trapping, the electronic interaction energy is on the order of 0.1 eV, (a considerable fraction of the binding energy) and is a function of the valence structures of both the host and the impurity and of the charge screening ability of the host. Generally, it is attractive if the impurity has fewer valence electrons than the host and repulsive if it has more valence electrons. In this paper the elastic and electronic interactions of hydrogen with substitutional and interstitial impurities in s-iron are calculated. The study of trapping of hydrogen in iron is of practical interest to the iron and steel industry since trapping can suppress hydrogen embrittlement (9). Iron is especially interesting as a trapping host because it has a small lattice parameter, a, (a = .2867 nm) and thus it expands upon alloying with any other transition metal (10). Since lattice expansion is necessary for elastic trapping, this indicates that the presence of substitutional impurities in iron is quite likely to result in hydrogen trapping. To better understand the relationship between trapping and embrittlement it is helpful to be able to predict which impurities will trap hydrogen and to quantify the magnitude of this interaction. The results of the present calculation on substitutional impurities show that all of the impurities considered here have an elastic interaction with hydrogen in iron which is attractive. The electronic interaction, however, is found to be_ attractive for impurities which lie to the left of iron in the periodic table but is repulsive for impurities lying to the right. Since the electronic interaction energy is as large or larger than the elastic interaction energy, we conclude that only impurities which lie to the left of iron in the periodic table will trap hydrogen. This conclusion is supported by the good agreement obtained between the calculated and experimental values for the signs of the binding energies. These results are similar to the results of previous studies on trapping of hydrogen by substitutional impurities in niobium, vanadium and tantalum (8). The results of the present calculation on interstitial impurities tend to support our earlier conclusion (7) that it is primarily elastic effects which determine whether interstitial impurities will trap hydrogen. It is assumed here that interstitial carbon or nitrogen impurities in iron occupy octahedral sites and can trap hydrogen either at the tetrahedral site (300) or at a ring of tetrahedral sites (212)-(232). See Fig. I. These assumptions are based on the results of previous studies concerning interstitial trapping of hydrogen in b.c.c, metals (7).

1003 0036-9748/83 $3.0(I + .00 Copyright (c) 1 9 8 3 P e r g a m o n Press

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(Io5)0 cx>4)O

0.o4) ~0)

.........

-Fj

....

! "'-. I

F~q---~-~.

O~4z,)

\ I i

in,-, ,

.o)o

: . . . . . . . . .

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Fig. i. The relative location of the impurity atom and the t e t r a h e d r a l sites w h i c h might be a v a i l a b l e for h y d r o g e n occupation. The vector (x,y,z) refers to the v e c t o r distance between the t e t r a h e d r a l site and the impurity atom in units of a/4.

"

. . . . . . . . . . . . .

The a g r e e m e n t b e t w e e n the e x p e r i m e n t a l values of the binding energy and the values calculated on the basis of these a s s u m p t i o n s is good for n i t r o g e n - h y d r o g e n pairs but is poor for carbonh y d r o g e n pairs. One p o s s i b l e source of the poor agreement for c a r b o n - h y d r o g e n pairs is the a s s u m p t i o n that carbon is always p r e s e n t as an interstitial in iron. It is p r o p o s e d instead that dilute amounts of carbon may be a b s o r b e d s u b s t i t u t i o n a l l y in iron. Experimental evidence is cited to support this proposal. C A L C U L A T I O N OF THE H Y D R O G E N - I M P U R I T Y B I N D I N G ENERGY The elastic i n t e r a c t i o n energies Wab b e t w e e n a h y d r o g e n and an interstitial impurity and b e t w e e n a h y d r o g e n and a s u b s t i t u t i o n a l impurity were calculated using the procedures described in Refs. (7) and (8). The subscripts a and b refer to the sites occupied by the h y d r o g e n and the impurity respectively. It was assumed that h y d r o g e n occupies tetrahedral interstitial sites, and that i n t e r s t i t i a l impl]rities occupy octahedral sites. The former assumption is based on the work of P l u s q u e l l e c et al. (11) and Brasnin et al. (12) who found that h y d r o q e n dissolves i n t e r s t i t i a l l y in iron, p r o b a b l y in tetrahedral sites. This a s s u m p t i o n is further supported by the lack of a h y d r o g e n Snoek peak in iron (13) indicating almost no a n i s o t r o p y as is the case for h y d r o g e n in t a n t a l u m (14). The B o r n - y o n K a r m a n force constants of iron used to determine the phonon frequencies were o b t a i n e d from Ref. (15). The values of the force dipole tensor P ~ for both types of impurities in iron were c a l c u l a t e d as in Refs. (7) and (8) using the elastic constants for iron and the e x p e r i m e n t a l l y d e t e r m i n e d values for the lattice expansion, da/dc, where c is the solute concentration. All p e r t i n e n t data on da/dc and the resulting values for P ~ are listed in Table I. The two entries for carbon and n i t r o g e n in Table I refer to the two p r i n c i p l e axes of symmetry a s s o c i a t e d w i t h each defect which because of the tetragonal nature of the distortion field have d i f f e r e n t values of da/dc and Pp~. The tensor P ~ is c a l c u l a t e d as 'tin (7,8) using the following p h y s i c a l p r o p e r t i e s for ~-Fe: c11 = 2.42 x 1011 Pa, c12 = 1.465 x 10' Pa, and B = 1.783 x 1011 Pa (20,21). Values of da/dc for h y d r o g e n in iron were estimated based on the findings of Peisl (24) w h o showed that the change in lattice volume per h y d r o g e n atom is a p p r o x i m a t e l y 2.9 x 10 -3 nm 3, i n d e p e n d e n t of lattice type. Hirth (9) has reviewed measurements of change in lattice volume per h y d r o g e n atom and lists values between 2.6 x 10 -3 n m3/H a t o m and 4.3 x 1 0 - 3 n m 3/H atom. The resulting elastic i n t e r a c t i o n energies are listed in Table II as Wab for interstitial i m p u r i t i e s and W a b / P i m p u r i t y for s u b s t i t u t i o n a l impurities for several h y d r o g e n - i m p u r i t y separations (Qa - Qb) in units of a/4. The vector Qa refers to the location of a point defect at site

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a. Because of the u n c e r t a i n t y in the value of Phydrogen, the total error in the Wab results are e s t i m a t e d to be 25%. It can be seen that the resulting values of Wab are similar to the values o b t a i n e d p r e v i o u s l y for d e f e c t pairs in vanadium, n i o b i u m and tantalum (7,8). TABLE I L a t t i c e Expansion, F0r--ce Dipole Tensor and N e a r e s t N e i g h b o r i n g Wab for Solutes in G-Iron

(Ref.)

Ida/dc (10 -I nm)

2Pimp~Kity ( I0-'~ J)

WI (eV)

(20) (10) (10,19,20) (20) (10,20) (20) (18) (20) (20) (20) (20) (20) (16) (17) (20) (20) (10) (20) (20) (calc.) (22) (23)

0.695 0.207 0.12 0.563 0.381 0.371 0.370 0.092 0.313 1.049 0.092 0.544 0.149 0.009 0.023 0.123 0.048 0.500 0.567 0.289 -.26,2.47 -.20,2.38

15.31 4.56 2.66 12.40 8.39 8.17 8.15 2.02 6.89 23.11 2.02 11.98 3.28 0.19 0.50 2.71 1.05 11.01 12.49 5.17 21.5,10.8 21.3,11.2

.213 .063 .037 .172 .117 .114 .113 .028 .096 .321 .028 .017 .046 .003 .007 .038 .015 .153 .174 .... .... ....

Solute Nb V Ta Mo W Cr Ti Zr Mn Cu A1 Co Ni Pd Pt H C N

TABLE 2 Values of Wab for S u b s t i t u t i o n a l and Interstitial Substitutional (Qa-Qb)4/a Wab/Pimpurityx104 201 203 205 423 421 425

(Qa-Qb) 4/a

-223.0 -107.0 1.6 12.0 -25.6 - 0.32

100 210 300 212 232 203

Impurities

in ~-Iron

Inters titial WC_H, e V WN_H, eV -.8814 -.3751 -.1706 -.1071 -.0385 .0597

-.8868 -.3802 -.1739 -.1102 -.0373 .0564

T R A P P I N G BY S U B S T I T U T I O N A L IMPURITIES The elastic portion of the binding energy b e t w e e n a hydrogen and a s u b s t i t u t i o n a l impurity is taken to be the value of Wab at n e a r e s t - n e i q h b o r i n q h y d r o g e n - i m p u r i t y positions. These values, called W I are listed in the last column of Table I for the fifteen s u b s t i t u t i o n a l solu-

T F o r C and N, the first entry is da/dc along the p e r p e n d i c u l a r axes, a l o n g the p r i n c i p a l axis. 2For C and N, the first entry is P ~ for the principal PD~ for the p e r p e n d i c u l a r lattice directions.

the second entry is da/dc

lattice direction,

the second entry is

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tes c o n s i d e r e d here. Because most impurities expand the iron lattice, the sign of W I is usually negative i n d i c a t i n g an a t t r a c t i v e elastic interaction. The total b i n d i n g energy, B, h o w e v e r , must also include an e l e c t r o n i c

contribution,

U I, giving

B = UI + W I

(I)

T r a p p i n g is expected to occur when the sign of the binding e n e r g y is neqative. The electronic i n t e r a c t i o n may be a p p r o x i m a t e d by ZVhost (8,25) where Z is the d i f f e r e n c e in the number of valence electrons b e t w e e n the impurity and the host and Vhost is a measure of the screening ability of the host. []sing m e a s u r e d values for B and calculated values for W I the authors have p r e v i o u s l y d e t e r m i n e d that for v a n a d i u m and niobium, V h o s t ~ 0.08 eV, (8). Since e x p e r i m e n t a l l y d e t e r m i n e d values of the b i n d i n g e n e r g y of h y d r o q e n - i m p u r i t y pairs in iron are not available, and since b.c.c, iron is similar to v a n a d i u m and niobium, we have a p p r o x i m a t e d V h o s t for iron to be Viron ~ 0.08 eV. Although the magnitude of B is difficult to determine experimentally, its sign may be i n f e r r e d from magnetic r e l a x a t i o n (4,5) and d i f f u s i v i t y measurements (26). Trapping of h y d r o g e n in iron c o n t a i n i n g cobalt, nickel, palladium, titanium and z i r c o n i u m has been studied by K r o n m u l l e r et al. (4) whose results are listed in the first column of Table III. The binding energy TABLE 3 C o m p a r i s o n B e t w e e n E x p e r i m e n t a l and C a l c u l a t e d Values T r a p Pair

Co-H Ni-H Pd-H Ti-H Zr-H Cr-H Mn-H Mo-H V-H C-H N-H

(Ref)

(4) (4) (4) (26) (4) (27) (27) (27) (27) (3) (3)

B,eV

Z

~0 >0 >0 -.27 to -.45 <0 <0 <0 <0 <0 -.034 -.138

+I +2 +2 -4 -4 -2 -I -2 -3 ---

IWI,eV

-.007 -.038 -.153 -.096 -.321 -.113 -.028 -.117 -.037 -.107,-.171 -.110,-.174

for the B i n d i n g Energies UI,eV

+.08 +.16 +.16 -.32 -.32 -.16 -.08 -.16 -.24 ---

IBcalc'eV

+.07 +.12 +.01 -.42 -.64 -.27 -.11 -.28 -.28 -.107,-.171 -.110,-.174

of t i t a n i u m - h y d r o g e n pairs in iron has been estimated from h y d r o q e n p e r m e a t i o n experiments to be b e t w e e n -0.27 e V and -0.45 e V (26). No other data for h y d r o g e n t r a p p i n g in iron could be found in the literature; h o w e v e r results on the trapping of nitrogen by chromium, manganese, molybd e n u m and v a n a d i u m have been r e p o r t e d by D i j k s t r a and Sladek (27). In order to complete Table III we have made the a s s u m p t i o n that binding energy of h y d r o g e n to these impurities in iron is of the same sign as the b i n d i n g energy of nitrogen to these impurities in iron. This is the b a s i s on w h i c h the e x p e r i m e n t a l values for B in Table VI for Cr, Mn, Mo and V are determined. Values of W I, U I (calculated from Z) III. There is good a g r e e m e n t b e t w e e n the m e n t a l l y m e a s u r e d b i n d i n g energy. It can p e r i o d i c table s h o u l d trap h y d r o g e n since

and c a l c u l a t e d values of B are also listed in Table sign of the c a l c u l a t e d b i n d i n g energy and the experibe seen that impurities to the left of iron in the they have an attractive U I as w e l l as an attractive

W I• Impurities c o n t r i b u t i o n of s h o u l d not trap a l s o been f o u n d

to the right of iron in the p e r i o d i c table also have an attractive W I but the the much larger and repulsive U I offsets this, i n d i c a t i n g that these impurities hydrogen. This dominance of the electronic over the elastic interaction has for s u b s t i t u t i o n a l trapping in n i o b i u m and v a n a d i u m (8).

IFor C - H and N - H pairs,

the first entry is Wab for the (212)-(232) p o s i t i o n

second e n t r y is for the

(300) position.

(averaged),

the

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In reference (7), it was p r o p o s e d that i n t e r s t i t i a l oxygen and n i t r o g e n o c c u p y i n g octahedral sites in b.c.c, metals can trap h y d r o g e n either at the t e t r a h e d r a l site (300) or at a ring of t e t r a h e d r a l sites (212)-(232) (see Fiq. I). The binding or t r a p p i n g e n e r g y was taken to be the elastic i n t e r a c t i o n energy at these sites. (Smaller pair separations were a s s u m e d to be p r o h i b i t e d due to a s h o r t - r a n g e e l e c t r o n i c repulsion.) In this paper, these assumptions are p r e s u m e d to be valid for i n t e r s t i t i a l carbon or n i t r o g e n impurities in a-iron. Table II shows the elastic i n t e r a c t i o n energies between h y d r o g e n h e d r a l sites and carbon or n i t r o g e n impurities s i t u a t e d at octahedral

atoms sites

situated at tetraas a function of

(Qa - Qh). Since two defect structures are suggested, two b i n d i n g energies were calculated, one for the (300) site and one for the ring structure, (122)-(322). These are given in Table III a l o n g with the e x p e r i m e n t a l values for the binding energies of Au and B i r n b a u m (3). The calculated b i n d i n g enerqies for n i t r o g e n - h y d r o g e n pairs are in reasonable a g r e e m e n t with the e x p e r i mental values, h o w e v e r poor a g r e e m e n t is found for c a r b o n - h y d r o g e n pairs. Since carbon and n i t r o g e n are a l m o s t the same size one w o u l d have expected them to have h y d r o g e n trapping e n e r g i e s of the same order as is p r e d i c t e d by the calculations. A possible e x p l a n a t i o n for the d i s c r e p a n c y between the c a l c u l a t e d and e x p e r i m e n t a l values for the b i n d i n g energy b e t w e e n carbon impurities and h y d r o g e n is that the carbon in the e x p e r i ments of Au and B i r n b a u m (3) may have been p r e s e n t in the iron samples as s u b s t i t u t i o n a l s rather than as i n t e r s t i t i a l s . Generally, the n o n - m e t a l l i c elements of the second period in the p e r i o d i c table go into transition metals as interstitials. However, if the n o n m e t a l l i c e l e m e n t is large e n o u g h relative to the h o s t atoms, a s u b s t i t u t i o n a l solution may form. For example, boron d i s s o l v e s s u b s t i t u t i o n a l l y in y - i r o n and a - i r o n (28-30). This is due to boron's c o m p a r a t i v e l y large radius, 0.083 nm (31), which allows it to replace iron atoms in the lattice. The atomic radii of carbon and n i t r o g e n are 0.077 nm and 0.0701hm r e s p e c t i v e l y (31), indicating a p o s s i b i lity of s u b s t i t u t i o n a l s o l u t i o n f o r m a t i o n in iron (although at high temperatures these are known to be i n t e r s t i t i a l s in y - F e (10)). When q u e n c h e d to room t e m p e r a t u r e both carbon and n i t r o g e n r e m a i n i n q as i n t e r s t i t i a l s in the resulting m a r t e n s i t e s (22,23,32) but if slowly a n n e a l e d to room t e m p e r a t u r e at dilute concentrations, carbon atoms m i g r a t e to s u b s t i t u t i o n a l sites in e - i r o n (30,32). The s m a l l e r n i t r o g e n atoms however, remain i n t e r s t i t i a l even when a n n e a l e d (32-34). Because the samples used in the magnetic r e l a x a t i o n studies of Au and B i r n b a u m (3) we re dilute and annealed, it may be that some or all of the carbon was s u b s t i t u t i o n a l l y dissolved. Thus the low e x p e r i m e n t a l value for the binding energy may be a result of a limit on the number of carbon atoms w h i c h are capable of forming i n t e r s t i t i a l traps. ACKNOWLEDGEMENT A c k n o w l e d g e m e n t is made for support of this work.

to the N a t i o n a l

Science

Foundation

(Grant N u m b e r

ChE-8109557-A01)

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8