The mechanism of chemical colouring of stainless steels—I. Calculation of the colouring initiation time

Corrosion Science, Vol. 33, No. 6, pp. 873-878, 1992 Printed in Great Britain.

0010-938X/92 $5.00 + 0.00 © 1992 Pergamon Press pie

THE M E C H A N I S M OF C H E M I C A L C O L O U R I N G OF STAINLESS S T E E L S - - I . C A L C U L A T I O N OF THE C O L O U R I N G INITIATION TIME TAN MINGWEI Shanghai University of Science and Technology, Shanghai, P.R.C.

Abstract--The mechanism by which a coloured film forms on stainless steel in a hot solution of chromic and sulphuric acids has been studied by analysing the variation of ion concentration in the colouring solution as a function of time. The coloured film on stainless steel results from chemical reactions at the boundary layer between the specimen and the colouring solution, where ferric hydroxide and probably chromic sulphate (Cr2($04) 3. 18H20 ) are precipitated. The colouring initiation time t0, when colour begins to appear on the specimen, has been calculated approximately. INTRODUCTION

STUDIES on the colouring techniques of stainless steels have been carried out extensively. Owing to the complexity of the process there is not much known about the mechanism by which stainless steel is coloured during immersion in hot solutions containing both chromic and sulphuric acids. The nature of the films formed was examined by Evans et al. ,t who qualitatively described the changing specimen surface and the migration of ions in solution during colouring. Film growth was thought to be a result of hydrolysis of the metal ions formed in both the anodic dissolution in fixed positions at the metal/solution interface and cathodic reduction on the outer film surface. They believed that virtually no film thickening takes place in the first stage of the process, during which no colour appears on the surface of the specimen. X-Ray photo-electron spectroscopy (XPS) studies 2 show no peaks of elements other than those of the substrate metal and its passive film in the first stage. This paper is Part I of an investigation, which deals with the first stage and is intended primarily: (a) to establish the mathematical models of diffusion of ions in colouring solution in the first stage; (b) to reveal the mechanism for the formation of coloured film; (c) to obtain the method with which the important parameter for colouring technique, colouring initiation time to can be predicted. EXPERIMENTAL

METHOD

The stainless steel used in the investigation was type 304 containing 18.5% Cr, 8.8% Ni and 1.7% Mn, whilst the balance was mainly Fe. Specimens were electropolished in a solution containing sulphuric and phosphoric acids before being coloured by immersion in a solution containing 2.5 M chromium trioxide and 5.0 M sulphuric acid at 80°C. The potential of the steel was monitored throughout the process with respect to a saturated calomel electrode. In order not to interrupt the continuous diffusion of ions in solution, the other five specimens Manuscript received 13 May 1991. 873

874

TAN MINGWEI 1065 - -

I

G o c/) >

1055 - -

E

iooo

0

L I

I

120

360 Time

FIG. 1.

l °l

600

(s)

Potential vs time curve during the first stage.

were used in weight loss measurements. They all were weighed before immersion and after different times of immersion, and their mean weight losses were taken as the results. EXPERIMENTAL RESULTS

The experimental results of potential measurement and weight loss are shown in Figs 1 and 2 respectively, where only a part of curves (0 < t < to) has been shown, the others appear in Part 113 of the investigation. Figure 1 shows that in stage one, the potential rises quickly to a peak value, and then descends slightly to a minimum Vo at time to, at which point colour begins to form on the specimen. Figure 2 indicates that the specimen loses weight approximately at a linear rate with time in the first stage. THE M E C H A N I S M

As shown in Fig. 2 the weight loss AW (in dimension of mol cm -2) may be represented approximately as

AW=kzt

(0
(1)

w h e r e t is t i m e o f i m m e r s i o n , k 1 is c o n s t a n t . A s s u m i n g that the a n o d i c d i s s o l u t i o n o f only the t h r e e m a j o r m e t a l l i c c o m p o n e n t s of the s p e c i m e n , F e , Ni a n d C r occurs, the c o r r o s i o n r e a c t i o n can b e e x p r e s s e d b y the following e q u a t i o n : m l F e + m2Ni +

m3Cr----~m l F e 3+ + m2Ni 2+ + m3Cr 3+ + (3mr + 2rn2 + 3m3) e - .

(2) A

x

6O

60 4o

.9 ° E: ~

20

I 0

2OO

4OO Time

600

[s)

FIG. 2. Dependence of weight loss on time in the first stage.

Chemical colouring of stainless steels--I

875

The flux of these ions at the interface of steel/solution is given in dimension of mol cm -2 s - 1 as

_

Ji

.[Oc(x, t)]

D' L Ox L,=o

= mikl

(3)

where subscript i is 1, 2 or 3, standing for Fe 3+, Ni 2÷ or Cr 3+ respectively, D is the diffusion coefficient. Before these ions separate out from solution there are no homogeneous chemical reactions in solution. Their diffusion equations can therefore be presented by Fick's second law

Oc(x, t) _ D 02c(x" t) Ot Ox 2

(4)

The initial and boundary conditions are

c(x, 0) = 0

(5)

lim c(x, t) -- 0.

(6)

X~

zc

The surface concentration c(0, t) of ions, as derived by Laplace transformation, is C1(0 , t) - 2 m l k l t 1/2

C2(0 ,

t) --

C3(0 , t) -

2m2kl

tl/2

2m3k1 t 1/2.

(7) (8) (9)

The initial boundary conditions for H + ion are CH+(X, 0) = CH~

lira cH+(x, t) = c w

(10) (11)

X----~ ~c

where CH+ is initial concentration o f H + ion in the bulk of solution, measured by a pH meter as 2.5 × 10 -3 mol cm -2. It is not possible that the metal hydroxide would precipitate in such a strongly acidic solution to form a coloured film on the specimen. Thus the cathodic reaction in the process definitely involves the consumption of H + ions, most likely as Cr2072- + 14H + + 6e- ~ 2Cr 3 ~ + 7H20.

(12)

From equation (7) and the solubility product of Fe(OH)3, which is easier to precipitate than Cr(OH)3 or Ni(OH)2, the surface concentration of H + ion at to, CH~(0, t) is estimated at about 0.5 M. It is within such a short period of time that the surface concentration of H + ion, c H ~(0, t) changes so sharply that one can reasonably suppose that c~r (0, t) declines exponentially, namely CH*(0, t) = CH+ exp ( - b t ) where b is a positive constant.

(13)

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TAN MINGWEI

Neglecting the ionization of weak acids in solution, the diffusion equation of H + ions can be represented by equation (4). The Laplace transformation and inversion of equations (4), (10), (11) and (13) produce the surface flux of H + ions

r~ +[OcH+(x, JH+= -~'H [ Ox t)]

- / ~ X exp (-bt) I v~ exp (s 2) ds. : 2ell+~ x= 0

(14)

30

From equation (12) it can be seen that, for 7 mol o f H + ion that undergo cathodic reaction at the specimen surface, 1 mol of Cr 3+ ion must be produced. Hence the surface flux of Cr 3+ ion created by cathodic reduction is given by

J~ -

2Cr~+~ Z

exp (-bt) I v~

7

exp

(S2) ds.

(15)

~0

By the application of the conditions (5), (6) and (7), the solution of equation (4) can give the concentration of Cr 3+ ions at the cathodic surface of the electrode according to

c~(O, t) = ell+ /DH+ [1 - exp (-bt)]. T

-bT L

(16)

From equations (9) and (16) one can thus find that surface concentration of Cr 3+ ions is c3(0, t) - 2m3ka

t 1/2 + cH___Z/DH+[1 - exp (-bt)].

(17)

7 "~D 3 According to the values of the solubility products of Fe(OH)3, Cr(OH)3, Ni(OH)2 and the value of surface concentration of Fe 3÷ ions when t = to, which is estimated to an order of magnitude of ca 10 -5 mol cm-3 through equation (7), the surface concentration of Cr 3+ and Ni 2+ ions must reach the orders of magnitude of 10z and 104 mol cm -3 respectively, if Cr 3+ and Ni 2+ ions precipitate on specimens in the form of their hydroxides at time to. Since this is impossible, the precipitation of Cr 3+ and Ni 2+ ions must not be in the form of hydroxides but in the form of their salts. There is a very low content of Ni in coloured films. Evans et al. a found only 2 wt% of Ni by atomic absorption analysis of the stripped film, and X-ray photoelectron spectroscopy studies 2 failed to detect Ni in the coloured film on stainless steel. It is possible that "accompanying precipitation" has happened to Ni 2+ ion, and Cr 3+ deposits on specimens most probably in the form of Cr2(SO4) 3 • 18H20. According to Ansell, 2 who has confirmed the existence of sulphur in the colourecl film by XPS studies, the species present in the coloured film are invariant with thickness. Using transmission electron microscopy of ultramicrotomed sections of stainless steel specimens coloured in a chromic/sulphoric acid solution, Furneaux et al. 4 found that the sections of the film have relatively uniform thickness and texture. From these facts it can be concluded that Fe 3+ and Cr 3+ are precipitated simultaneously when the following chemical reaction equilibria have just been reached at to: Fe 3+ + 3OH-~-Fe(OH)3

(18)

2Cr 3+ + 3SO4 + 18H20 ~ C r 2 ( 5 0 4 ) 3 • 18H20.

(19)

Chemical colouring of stainless steels--I

877

Thus at time to m l k l A t/ 02 X 102] × (

) 3 =Ksp K,~, CH+ exp ( - b t o ) x 103

--to2m3kl ,1/2 x 1 0 3 + CH~*7x 103X/Dw/D3 [1 - exp ( - b t ) ]

(20)

x C3o~ = Ksp s. = 108S; 5

(21) where Kw is the ionic product of water, Ksp and K~p~,are the solubility products of Fe(OH)3 and C r 2 ( 8 0 4 ) 3 • 18H20 respectively, S is the solubility of Cr2(SO4)3 • 18H20, Cso~ is the initial concentration of SO42 ion in bulk solution. In principle one can now calculate the value of to by combining equations (20) and (21), but difficulties arise from the fact that accurate values of the constants in the two equations are lacking at present, especially at higher temperatures• Therefore one can only estimate very approximately the value of to with reference to data now available. As the solubility products change slowly with temperature, the Ks~ and S at 80°C • • are supposed to be equal to their corresponding values at 25 o C, 3.8 × J ' 10 - - 3 8- for K~p'~ and 1.2 M for S. 6 The ionic product of water depends strongly on the temperature. At 80°C the value of Kw is about 3.4 × 10 13. Only very little reliable data on diffusion coefficients of ions at high temperature have been published. Even at ambient temperatures these values are incomplete. These values can be obtained from the following relationship: Di = (RT/ziF) × U~i~

(22)

where Uti~is the ionic mobility. The mobility of Fe 3÷, Cr 3+ , H + ions are 1.55 x 10-3, 1.18 x 10 -3 and 24.2 x 10 -3 cm -2 s 1 V - l , respectively at 18°C, from which the diffusion coefficients of these ions calculated by equation (22) are 0.54 x 10 -5, 0.39 x 10 -5 and 8.0 x 10 -5 cm 2 s -1, respectively. The specimen is in such an acidic and corrosive solution that its dissolution may be considered to be the results of corrosion of underlying steel, namely the dissolution ratio of F e : N i : C r : m l : m 2, m 3 can be given by ml :m2:m3 = (71.0/56):(18.5/52):(8.8/58) -- 0.71:0.20:0.09.

(23)

In addition, the value of kl obtained from Fig. 2 is 2.2 x 1 0 - 9 m o l c m 2s-1, when the average molecular weight of the dissolved species is calculated from rn 1, m2 and m3 to be 55.4. By substituting for all constants in equations (20) and (21) in terms of their respective values assumed above, one obtains the values of to and b, 450 s and 5.0 × 10 -3 s 1 respectively. The value of t0calculated from equations (20) and (21) is fairly consistent with that measured, as shown in Figs 1 and 2,540 s. The values of to measured by the author, Evans et al. 1 and Furneaux et al. 4 were different from each other. Furneaux et al. ascribed the discrepancies in the time scales to the subtle differences in material, or experimental procedure. Now from the above mathematical derivation and calculation it is clear that the time scales in the case of chemical colouring on stainless steels depend strongly on the initial concentration of H ÷ and SO ] - ions in bulk solution and the temperature of the solution by which the values of the constants in equations (20) and (21) are determined.

878

TAN MINGWEI

CONCLUSIONS The various colours c o m e into being on stainless steel i m m e r s e d in a hot solution containing chromic and sulphuric acids when ferric hydroxide (Fe203 • 3 H 2 0 ) and chromic sulphate (Cr2(504) • 1 8 H 2 0 ) are precipitated on its surface. With the given simplification and conjecture, the variation of the surface concentrations of ions that are responsible for the formation of a coloured film can be analysed quantitatively. The coiouring beginning time (t0), that d e p e n d s m a r k e d l y on the initial concentration of H ÷ and SO42- ions and the t e m p e r a t u r e of solution, can also be estimated.

1. 2. 3. 4. 5. 6.

REFERENCES T. E. EVANS,A. C. HARTand A. N. SLEDGELL,Trans. Inst. Metal Finishing 51,108 (1973). R. O. ANSELL,T. DICrlNSONand A. F. POVEY,Corros. Sci. 18,245 (1978). M. TAN, Corros. Sci. 33, 879 (1992). R. C. FURNEAUX,G. E. THOMPSONand G. C. WOOD,Corros. Sci. 21, 23 (1981). Y. Zrtv, Handbook of Electrochemical Data, Press on Science and Technology, Hunan, China (1985). Y. YtNG, Handbook of Chemistry for Students, Press on Science and Technology, Shandong, China (1985).