Effect of alloying elements on the formation of boride layer on steel

Scripta METALLURGICA

Vol. 9, pp. 1153-1156, 1975 Printed in the United States

Pergamon Press, Inc

EFFECT OF ALLOYING ELEMENTS ON THE FORMATION OF BORIDE LAYER ON STEEL M. Bla~on, B. Stanojevi~ Faculty of Mining Engineering and Metallurgy Department of Metallurgy, Bor, Yugoslavia V. VeljkoviE Boris Kidri~ Institute, Department for Theoretical Physics Beograd, Yugoslavia (Received June 24, 1975) (Revised September 22, 1975) Scientific opinions are divided as to the question of the ratio of stability of the borides Fe2B and FeB, which are formed in the prooess of boridization of steel, and as to the effect of alloying elements on the structure and behavior of this layer. In this paper we analyse the above problem starting from the configuration component of ion-ion interaction in metal, believing that this theoretical aspect, with existing experimental results, will give a clearer picture about this process. In order to arrive at the quantitative measure of the stability of borides~ we will start from the configuration component of ion-ion interaction in the metal. This is in fact the potential of the rearrangement of atoms in the fixed total volume. Defined in this way, this quantity is naturally connected with stability of the crystal system/l,2/, As a quantitative measure of the stability of the system, with some approximation, we will take the value of the component ~(R) at the point corresponding to the characteristic minimum, which is in the range R = a (a is the distance between the nearest neighbours), In order to simplify the calculation, we will use the asymptotical form of the configuration component of the ion-ion interaction /3/ (in our case it satisfies the required accuracy):

~(~) = 9~Z~/V(2Kf)/2

cos(2Kfa~

where Kf is Fermi momentum, Ef - Fermi energy of the system, valence of the given system and V(2Kf)

ZX - chemical

formfactor of the pseudopotential

for

electron-ion interaction, taken at the point q = 2K~. Starting from the pseudopotential /4-6/, the values V(2Kf) and Kf are obtained in the following form: ~(2Kf) = C~I._ (Z-Z°)

2

sXn/2-~2(Z-Zo)/exp(-O(3~

Kf = / l , 5 ~ l ~ 2 ( Z - Z o ) 2 / i / 2

(2) (3)

where Z is the atomic number of a given metal, Z is the inert element atomic number that begins the period which includes the°given Z, and the coefficients ~ i , ~ 2 and ~ 3 are C~

- 0.2500 Ry = -

0.0625 Ry

~t ~=

0.520 0.0@8 1153

for short and the first half of long periods for the second half of long periods

1154

THE FORMATION OF BORIDES

9, No,

0.3

for the first and the second groups of the periodic system

0.4

for all other groups

= 3

Vol.

ii

In calculations concerning the borides of iron the pseudoatomic a p p r o x i m a tion /7/ is u s e d The corresponding values for Fe2B and FeB are given in Table I. The results, which were obtained according to relations (1-3) for two systems which are discussed, are present in Fig. 1 and Fig. 2, and Table II. As can be seen, the value of ¢(R) is one order of magnitude higher for Fe~B than for FeB. Since we take this value as a criterion of the stability, itZis clear that Fe2B is the more stable phase, which has the priority during the formation. This conclusion is in a good agreement with experimental results /8/. We will now analyse the effect of alloying elements in steel on the formation of the boride layer, from the aspect of the potentia] for ion-ion interaction. First, we will analyse the effect of carbon, as one of the primary alloying elements. Its effect on Z x and Ef, Eq. (I) is negligible since its place is next to the place of boron in the periodic system of elements. Its effect can be seen through the sinusoidal part of V(2Kf) in Eq. (2). When carbon is present, in the sample, the argument of the sine function is moved to the v a l u e ~ for the case of FeB, and t o ~ / 2 for the case of Fe2B. However, since the value of the sinusoidal part for the system of FeB is nearly zero, contrary to Fe2B, the stability of this phase is much more sensitive to the presence of carbon. This means that the stability of FeB is decreased, and of Fe2B increased, when the concentration of carbon is increased. Experimental results show that the increase of carbon occurs with decrease of the boride layer (because the FeB phase is diminishing, so that in steel with 1,2 1,25%C it is completely absent /9/). At the same time it has been experimentally confirmed /i0/ that the hardness of the boride layer decreases as a consequence of an increase of the Fe2B phase in the layer. The structure of the boride layer will depend very much on the form of carbon in the steel. The form of carbon precipitation will define the local concentration of carbon in the area close to the centers of boride crystallization. For example, in the hypothetical case w h e m carbon exists in steel in the form of a homogeneous solid solution only its effect will be negligible. The influence of silicon, phosphorus, nitrogen, titanium, vanadium, niobium and tantalum is similar, since all these elements because of their places in the periodic system of elements /4/, are very similar in their characteristics from the aspect of potential for ion-electron interaction. This agrees with the experimental results /11,12/. In the case of chromium, molybdenum, tungsten, manganese and nickel, the argument of the sine in the relation (2) is changed to the value O-T/2~ for the case of FeB as well as for Fe2 B. This change, at the usual concentration of the elements is rather small, because of their homogeneous distribution. Therefore, their effects on the structure of the boride layer are negligible, which is in agreement with the experimental results /13/. Finally, we will try to give an explanation of some contradictory experimental findin~ that in the same domain of the concentration of carbon, stagnation of the thickness of the FeB layer appears, and that with further increase of carbon concentration the FeB layer increases. This is possible when carbon is present in the form that gives a large local concentration in the surface layer, and especially in case when chromium, manganese or some other elements from this group are present. In this case the resulting effect appears in the form of increasing of the sinusoidal component. This is possible even at high concentration of carbon in the surface layer. We believe that it would be interesting to investigate experimentally the effect of the displaced carbon form in the steel on the structure of the boride layer. In previous studies, this aspect of the problem has not been considered.

Vol.

9, No.

II

THE

FORMATION

OF BORIDES

1155

REFERENCES i. 2. 3. 4. 5. 6. 7. 8. 9. i0. ll. 12. 13.

C.W. Krause, Acta Met., 22, 767 (1974). V. Veljkovig, D. I. Lalovi~, to be published. W.A. Harrison, Pseudopotentials in the Theory of Metals, W. A. Benjamin (1966). V. Veljkovig, I. Slavig, Phys. Rev. Lett., 29, 105 (1972). V. Veljkovig, Phys. Lett., 45A, 41 (1973). -V. Veljkovid, D. I. Lalovig,~ys. Lett., 45A, 59 (1973). V. Heine, D. Weaire, Pseudopotential Theory of Cohesion and Structure, in "Solid State Physics", V. 24, p. 247, Academic (1970). A.N. Mlnkevxc, L. N. Rastorguev, L. I. Jusfina, Metallovedenie i termxceskaja obrabotka metallov, 3, 36 (]967). M.A. Pcel~ina, J. M. Lahtm. Metallovedenle i termlceskaja obrabotka metallov, 7, 40 (1960) M. A. Balter, I. S. Dukarevic, L. G. Goldstein, Metallovedenle • termxceskaja obrabotka metallov, 12, 52 (1964). M. Deger, M~Riehle, W. Schatt, Neue H~te, 8, 463 (1972). V. G. Permjakov et al., Vlijanie kremnia na formirovanie borirovanyh sloev, MTOM, V.3 (1973). L. G. Voroshnin, L. S. Ljahovi~, Teplofizika v litejnom proizvodstve, Nauka i tehnika, Minsk (1967).

TABLE 1

TABLE ii

The values of parameters for FeB and Fe2B Phase

Z*

1

2

FeB

5.50

0.617

0.975

Fe2B

6.33

0.780

0.573

3

The values of ~(R) for FeB and Fe2B Phase

FeB

Fe2B

0.350

R

~ (R)

~ (R)

0.370

/a.u./

/Ry/

/Ry/

1.00 1.40 1.80 2.20 2,60 3,00 3.40 3.80 4.20 4.60 5.00 5.40 5,80 6.20 6,60 7.00 7.40 7,80 8.20 8.60 9.00

-0.010561 -0.010536 -0.005374 -0,001551 -0.000422 0,001009 0.000816 0.000315 -0.000056 -0,000260 -0.000262 -0,000138 -0.000001 0,000097 0.000113 0.000070 0.000006 -0.000044 -0,000059 -0.000041 -0.000008

-0,078564 -0,281902 -0.196871 -0,098353 -0.029168 -0.000357 0.022496 0,021284 0.013065 0.003772 -0.003086 -0.006216 -0,005979 -0.003655 -0,000748 0.001546 0.002606 0.002411 0.001376 0.000093 -0.000098

1156

THE FORMATION OF BORIDES

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9, No. ii

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