Diffusion in the binary systems of molybdenum with nickel,
iron and cobalt
Citation for published version (APA):
Heijwegen, C. P. (1973). Diffusion in the binary systems of molybdenum with nickel, iron and cobalt. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR36206
DOI:
10.6100/IR36206
Document status and date: Published: 01/01/1973
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DIFFUSION IN THE BINARY SYSTEMS
OF MOL YBDENUM WITH
NICKEL, IRON AND CO BALT
DIPFUSION IN THE BINARY SYSTEMS
OF MOL YBDENUM WITH
DIFFUSION IN THE BINARY SYSTEMS
OF MOL YBDENUM WITH
NICKEL, IRON AND COBALT
PROEFSCHRIFT
ter verkrijging van de graad van doctor in de technische wetenschappen aan de Technische Hogeschool Eindhoven,
op gezag van de rector magnificus, prof. dr. ir. G. Vossers,
voor een commissie aangewezen door het college van dekanen in het openbaar te verdedigen
op dinsdag 29 mei 1973 te 16.00 uur.
door
Cornelis Petrus Heijwegen geboren te Helmond
dit proefschrift is goedgekeurd door de promotoren prof dr. G. D. Rieck en
Aan de nagedachtenis van mijn vader Aan mijn moeder
Aan allen die bijgedragen hebben aan het tot stand komen van dit proefschrift mijn dank.
CONTENTS
CHAPTER 1 INTRODUCTION
1.1 Interditfusion in roetal systems 1.2 The object of this thesis
CHAPTER 2 THEORY
2.1 Ditfusion mechanisms 2.2 Ditfusion equations
2.3 Approximating equations to calculate the ditfusion coefficients
2.4 Ditfusion in multiphase binary systems 2.4.1 Determination of the ditfusion
coefficients
2.4.2 Determination of the phase diagram by way of multiphase ditfusion 2.4.3 The kinetics of layer growth 2.5 The temperature dependenee of the
diffu-Page 11 11 13 14 1 6 17 17 1 8 18 1 8 sion process 2.6 Short-circuit ditfusion 19
2.7 The Kirkendall effect and its consequences 19 CHAPTER 3 CALCULATION OF THE INTERDIPFUSION
COEFFICIENTS AND THE RATIO OF THE INTRINSIC DIPFUSION COEFFICIENTS
3.1 A computer program for the calculation of 21 interditfusion coefficients in binary
systems
3.2 The ratio of the intrinsic diffusion coef- 26 ficients
CHAPTER 4 CONSTITUTION OF THE Mo-Ni, Mo-Fe AND Mo-Co SYSTEMS AND PROPERTIES OF THEIR PHASES
4.1 The equilibrium diagram of the Mo-Ni system 28 and the structure of the various phases
4.2 The equilibrium diagram of the Mo-Fe system 29 and the structure of the various phases
4.3 The equilibrium diagram of the Mo-Co system 30 and the structure of the various phases
CHAPTER 5 DIPFUSION IN THE Mo-Ni, Mo-Fe AND Mo-Co SYSTEMS
5.1 Ditfusion in the Mo-Ni systern 5.2 Diffusion in the Mo-Fe system 5.3 Diffusion in the Mo-Co system
32 33 35
CHAPTER 6 EXPERIMENTAL PROCEDURES 6.1 Introduetion
6.2 Preparatien of the ditfusion couples 6.3 Microscopie examinatien
6.4 Mieroprobe analysis 6.5 X-ray diffraction
6.6 Micro-indentation hardness testing CHAPTER 7 DIFFUSION IN THE Mo-Ni SYSTEM
7.1 Experimental results
7.1.1 Layer growth measurements
7.1.2 Mieroprobe measurements 7.1.3 Hardness measurements 7.1.4 X-ray diffraction 7.2 Evaluation of the results
7.2.1 Determination of the phase diagram 7.2.1.1 Introduetion
7.2.1.2 Experimental procedures 7.2.1 .3 Experimental results 7.2.1 .4 Discussion
7.2.2 Calculations of ditfusion data 7.2.3 Kirkendall effect
7.3 Conclusions
CHAPTER 8 DIFFUSION IN THE Mo-Fe SYSTEM 8.1 Experimental results
8.1.1 Layer growth measurements 8.1.2 Mieroprobe measurements 8.1.3 Hardness measurements 8.1.4 X-ray diffraction 8.2 Evaluation of the results
8.2.1 Determination of the phase diagram 8.2.2 Calculations of ditfusion data 8.2.3 Kirkendall effect
8.3 Conclusions
CHAPTER 9 DIFFUSION IN THE Mo-Co SYSTEM
36 36 38 39 42 42 43 43 49 53 54 56 56 56 57 57 60 61 64 67 69 69 72 77 77 78 78 84 88 89 9.1 Experimental results 90
9.1.1 Layer growth measurements 90
9.1.2 Mieroprobe measurements 95
9.1.3 Hardness measurements 98
9.1.4 X-ray diffraction 98
9.1.5 Texture in the layer of the ~- 100 (Co7Mo~) phase formed in Mo-Co
diffuslon couples
9.2 Evaluation of the results 105 9.2.1 Determination of the phase diagram 105 9.2.2 Calculations of ditfusion data 109
9.2.3 Kirkendall effect 113
CHAPTER 10 THE INFLUENCE OF CARBON ON THE INTER-DIPFUSION OF Mo AND Ni
1 0.1 Introduetion
10.2 Experimental procedures 10.3 Experimental results
10.3 .1 Layer growth measurements 10.3.2 X-ray diffraction 10.3.3 Hardness measurements 10.3.4 Mieroprobe measurements 1 0. 4 Discussion 1 0. 5 Conclusions CHAPTER 11 DISCUSSION 115 116 117 117 122 124 125 130 132 SUMMARY 137 REPERENCES 140
C H A P T E R
INTRODUCTION
1.1 Interditfusion in roetal systems
If two metals are in contact with each other at a high temperature, they will interdiffuse, and then farm what is known as a diffusion couple; atoms of the one roetal move into the matrix of the other, and vice versa. During diffusion, the concentratien differences between the starting materials are levelled. A new concentratien distribution will set up. If for a system the inter-ditfusion coefficient is available as a function of concentratien and temperature, this new distribution at a certain time may be predicted.
Knowledge of diffusion data is important in many cases: (a) in metallurgy many processes are controlled by
diffusion, e.g. homogenisation, precipitation, sintering, oxidation, phase-transformations;
(b) in solid-state bonding and finishing techniques the interaction between substrate and coating at
elevated temperatures must be known in cantrolling the joining process so as to ensure the reliability of the joints in service;
(c) in studying e.g. point defects in crystals and thermadynamie activities of the components; (d) another important application of interditfusion
experiments is the examinatien of the phase diagram of a system.
1.2 The object of this thesis
Molybdenum has a wide scope as a structural material for high-temperature applications. A very imposing barrier to its use, however, is its poor oxidation
resistance. The product of the oxidation reaction, which is Mo03 , volatilises above 730°c resulting in a loss
weight. Mo can be protected from oxidation by applying a coating or by alloying withother elements.
Apart from the general reasans mentioned above the study of the interditfusion in the systems Ma-Ni, Mo-Fe, Mo-Co and Mo-Ni-C is carried out for several reasons:
(a) Nickel~ iron-, and cabalt-base heat-resisting
alloys often include Mo. This element is added to
12
salution strengthener, participates in the formation of precipitates (carbides or intermetallic compounds) and even promotes certain phenomena such as order-disorder reactions. Knowledge of its diffusion kinetics in the alloys is useful in that i t allows certain inferences to be made regarding the behaviour, especially at high temperatures, of the complex alloy. (b) Nickel-, iron-, and cabalt-base alloy claddings are
aften applied as coatings. Growth kinetics and mechanical properties of diffusion layers between the various starting materials have to be known. (c) Carbon is almest always present in heat-resisting
alloys and aften in coatings. The influence of carbon on the diffusion behaviour of Mo and Ni is, there-fore, investigated.
(d) The phase diagrams are also very important. The thesis wants to contribute to a better knowledge on this subject.
C H A P T E R 2
THEORY
2.1 Diffusion mechanisrns
The basic assumption·rnade to explain diffusion in any crystal is that each diffusing atorn makes a series of jumps between the various equilibrium lattice sites or interstitial positions. These jumps are in more or less random directions and allow the atoms to migrate through the crystal.
A number of possible mechanisms has been suggested. Manning1 gives an excellent survey. The most important will be discussed briefly.
(a) The simplest mechanism is the direct interchange of two neighbouring atoms. This mechanism is unlike1y in crystals with tightly packed lattices, because of the large lattice distortions occurring with the mechanism. On the other hand the mechanism may be possible in very loosely packed crystals. A variation of the exchange mechanism is the ring type. Here, three or more atoms situated roughly in a ring move tagether so that the whole ring of atoms rotates over one atom distance. The lattice distortions required here are not as great as in a direct exchange
mechanism. It is obvious that in an exchange mecha-nism no new lattice sites are formed, and, therefore, i t is obviously impossible to obtain a nett displace-ment of atoms relative to the crystal lattice.
Furthermore, the activation energy necessary for this mechanisrn is much higher than the observed activation energies (Kirkendall effect, see later). Therefore, the exchange mechanisrn is unlikely in most metal systems.
(b) When there are imperfections in the lattice, other rnechanisms requiring considerably less energy may occur. An example i s the interstitial mechanism. Here, an atom (mostly a small impurity atom) moves through the crystal by jumping from one interstitial site to another. When the interstitial atom is nearly equal in size to the lattice atoms, diffusion is more likely to occur by the interstitialcy mechanism, also called the indirect interstitial mechanism. The
interstitial atom moves into a normal lattice site and the atom which originally occupied the latt ice site is pushed into a neighbouring interstitial site. (c) Any crystal in thermal equilibrium contains a certain
14
provide an easy path for diffusion. Each atom moves through the crystal by making a series of exchanges with the various vacancies which from time to time are in its vicinity. Mechanisms invalving vacancies are the most probable, explaining bath the Kirkendall effect and the observed low activation energies. (d) Dislocation pipe, grain boundary and surface
ditfu-sion mechanisms appear in regions where the regular lattice structure breaks down. Ditfusion should occur more easily in the open regions of the crystal at dislocations, grain boundaries and surfaces. Because of their low activation energies these mechanisms may be dominant at lower temperatures. The first three are all mechanisms which describe volume diffusion i.e. diffusion in the bulk. The mechanisms mentioned at point (d) describe what is known as short-circuit diffusion.
2.2 Diffusion equations
Surveys on the theory of ditfusion are given by
Den Broeder2 , Van Loo3 , and Bastin4 • We will give only the equations used in this thesis and we refer to refs 2, 3, 4 for their derivation.
The following general assumptions will be made:
(a) Ditfusion takes place only in the direction perpen-dicular to the contact interface between the two metals (this will be called the x-direction) .
(b) The diffusion process will nat extend to the end of the ditfusion couple ("infinite diffusion couple"). The concentration at the ends remains constant. (c) The cross-section of the ditfusion couple remains
constant.
(d) No pores are formed.
If the total volume of the ditfusion couple is constant, Fick's first law gives the definition of the interdit-fusion coefficient:
J i
=
Dv(a Ci
;a
x) ( 1 )where Ji
=
flux of atoms in moles/cm2Ci
=
concentration of component i in moles/cm3<lci/élx
=
the concentration gradientExperiments show that Dv is a function of Ci and the temperature. Combination of Fick's first law and the law of conservation of matter leads to Fick's second law:
Eqs. (1) and (2) only apply if the total volume of the diffusion couple remains constant during diffusion. In practice, this is rarely the case. In 1962, Sauer and Freise5 derived an equation which permits of calculating the interditfusion coefficient in the case of volume changes during diffusion. Recently, Wagner6 and Den Broeder2 obtained the same equation in a different way. The equation is derived for a ditfusion couple, con-sisting of two "semi-infinite" rods of alloys with the composition Nb1 and Nb2 • During diffusion, volume changes occur. According to Den Broeder the interdit-fusion coefficient can then be written as:
(3)
in which vm is the molar volume in cm3/mole, as function of Nb; t is the diffusion time in seconds; Nb is the mole fraction of component B in at%;
x
is the coordinatein )Jm;
K
n (1-K ) n
If Va
=
Vb=
vm, then vm is eliminated from eq. (3) and if the pure metals are used as starting materials, eq.(3) is transformed into:
Ref. 3 has derived an equation for the calculation of the intrinsic diffusion coefficients:
(4)
(5)
where xk is the position of the Kirkendall interface and Cb the concentratien of component B in grammoles/cm3
With eq. (5) the marker displacement need not be measured. In this thesis only the ratios of the intrinsic diffusion coefficients have been calculated. For this reason eq.(S) is also written for the component A. Division of these
x 00
Ik
Nb-;:{blJ
N -N Nb2 ( v )dx - N ( b2 b)dx Db vb -oo m bi xk V mn
V xk N -N 00 (6) a aJ
N -N NI (
b bi) dx N ( b2 b)dx a2 v al v -oo m xk min which v~ and vb are the partial molar volumes for the concentrat1on in the Kirkendall interface.
2.3 Approximatinq equations to calculate the diffusion coefficients
If the molar volume is constant a solution of Fick's second law is given by Boltzmann7 and Matano8 ,
with the Matano condition
0
where Nb is the mole fraction of component b.
If D is a constant, and independent of concentration~ Fick's second law can be solved with the result:
eb + ca + eb - c
-=~--=a erf ( x )
2 2
2(Dt)~
The error function erf( ___ x __ ~)is defined by: 2(Dt) erf ( x ) 2(Dt)~ lJ!
~~
J
exp (-n 2 )dn 0 (7) ( 8) ( 9) ( 1 0)where c ~s.t~e concentrati~n in moles/cm3 a~d ca and eb 16 are the 1n1t1al concentrat1ons of the start1ng materials.
The error function is available in tabular ferm. From eq. (10) i t fellows that the penetratien curve is symmetrical with respect to the Matano interface, where the concentratien gradient reaches its maximum.
Eq. (10) can be useful in predicting a penetratien curve in particular diffusion· problems using an average value of D (Lee9 , Van den Broek10 ). Since in many systems the diffusion coefficient is a function of concentration, this seems to be a rather rough approximation.
Grube11 has derived a salution of Fick's secend law with
a constant D. This is: 2 c - cmin
c
max- c .
m~n -erf ( 2(Dt)~ x ) ( 11 )where Cmin is the initial concentratien of the diffusion element in the part of the couple that is poorer in this element. Cmax is the initial concentratien of the dif-fusion element in the part of the couple that is richer in i t . x is the distance between a plane in the coupl~
and Grube's interface. The latter is defined as the plane along which after diffusion the concentratien Cg is such that:
c - c .
g m~ncmax - cmin 0,5 i . e .
c
g( 12)
C is the concentratien at a distance x from Grube's interface after a diffusion of t seconds. The erf is the s~e as in eq.(9). This methad is aften applied to
couples consisting of a pure roetal and a dilute alloy of that metal.
2.4
Diffusion in multipbase binary systems2.4.1
Q~t~E~!~~t!Q~_Qf_tt~_Q!ÉÉ~ê!Q~-~Q~fÉ!~!~~têJost12 has shown that the Boltzmann-Matano analysis applies also to multipbase systems. The only condition is that the penetratien curve can be diff€rentiated and integrated. It is necessary that the diffusion process is the rate determining step.
Approximations for calculating the
Dy
in these systems are given in the literature. Heumann 3 has given anequation that applies to diffusion in an intermetal l ic
phase if the concentrat ien profile in this phase is
linear. The value of that Dy must be regarded as an
average value of the diffus1on coefficients in the phase.
Wagner1~ derived a salution of Fick's secend law fora
2.4.2 Q~~~~~~~É~Q~_Qf_~b~_Qb~§~_Q!~g~~-QY_~~Y-QÉ_~~!É!:
Qb~ê~_Q!!!~ê!Q~_(see also Chapter 7)
Multiphase diffusion is an important tool in investiga-ting phase diagrams. If two metals interdiffuse, a number of stable intermetallic compounds will be formed by
chemica! reaction. The sequence of the layers is deter-mined by the sequence of the single-phase areas in the phase diagram at the diffusion temperature. The concen-tratien values at the· interfaces of the layers follow froro the phase diagram. But only if i t is supposed that the equilibrium state is attained during layer growth. The literature gives a very great number of cases where the boundary concentrations of the layers are in agree-ment with results obtained in another way. The experimen-tal results gained in our laboratory are also very
favourable (Van Loo3 , Bastin4 ). 2.4.3 !b~-~~~~É~~ê-QÉ_!~Y~~-g~Q~Éb
The parameter used in the Boltzmann-Matano analysis x/lt is very important. This parameter is at a particular temperature only a function of concentration. This means that all concentrations, also the phase boundary concen-trations, move parabolically with time. So the width of a particular layer increases ~arabolically with t ime, according to the relations: d
=
kt or d=
kàlt, where d is the layer thickness, t the diffusion time and k and kà are the penetratien constants in cm2/sec and cm/sec~ respectively. In practice, the observation of this law is aften used as a criterion for an undisturbed diffusion process.From equations derived by Kidson15 i t can be shown that k and kà depend on the compositions of the starting
mate-rials and on all the interdiffusion coefficients in the entire diffusion region. k and kY are no material con-stants. However, in many practical problems, the values of k and kà can be of great use.
2.5 The temQerature dependenee of the diffusion process The temperature dependenee of a diffusion coefficient can aften be described by an Arrhenius-type relationship:
D
=
D0 exp (-Q/RT) ( 1 3) where R is the gas constant, T the absolute temperature, D0 is the frequency factor, independent of temperature,and Q the activatien energy. By platting log D versus 1/T, Q and Do can be determined graphically. Dv is a linear function of the intrinsic diffusion coefficients which are each dependent on temperature with an Arrhenius-type relationship. It is, therefore, remarkable that in 18 many experiments the Arrhenius' rule can yet be applied.
It is obvious that the value of Q and Do must be regarded as an empirica! one, which can easily describe the
temperature dependenee of the ditfusion coefficient. The same remarks apply in a still larger measure for the penetratien constant. The latter depends on all the ditfusion coefficients throughout the whole ditfusion couple. Besides, at different temperatures, different equilibrium concentrations at the phase boundaries will arise.
2.6 Short-circuit ditfusion
Since the number of dislocation, grain boundaries and surfaces is more or less independent of temperature, ditfusion by these mechanisms might be expected to have a slighter temperature dependenee than that with
mechanisms invalving point defects (e.g. vacancies), whose concentratien increases with temperature. The relation between the activatien energies is:
Qvolume > 0 grain bounoary > Qsurface·
For the few systems in which these activatien energies are determined i t appears that:
0vol : Qgr.b : Qsur ~ 4 : 2 : 1
At the same time one finds Dovol> Dogr > Dosur·
Transport along grain boundaries and surfaces becomes only important at low temperatures. A plot of log D vs. 1/T showing a bend, is an indication that short-circuit diffusion effects may be present.
In sectien 2.4.3 i t is stated that the layers grow para-bolically with time when there is only volume diffusion. This is always true if only one type of ditfusion
mechanism is present. When two types of ditfusion mecha-nisms operate simultaneously the growth of a layer wil! be roughly proportional to t 1/n, where n has a value
between 2 and 4. The factor n can be calculated from log d vs. log t plots.
2.7 The Kirkendall effect and its consequences
Interditfusion is often accompanied by a nett displace-ment of atoms relative to the crystal lattice. This was first demonstrated by Kirkendall and Smigelskas16 •
They marked the contact interface between the two diffu-sing materials, viz. copper and brass, with molybdenum wires. After a certain ditfusion time this marker inter-face showed a pronounced displacement relative to a point outside the diffusion zone. This phenomenon is called the
20
This shift requires that the flux of zinc atoms that passes the markers in one direction is appreciably
greater than that of capper atoms in the reverse direction. The phenomenon has proved to be quite general. The
vacancy mechanism can explain this effect but i t excludes the possibility of the ring mechanism.
Besides, the formation of pores which is aften observed in the diffusion zone, and the agreement between the theoretically calculated activatien energy (Huntington and Seitz17 ) for the vacancy mechanism with the observed activatien energy, show that this vacancy mechanism is the most probable.
C H A P T E R 3
CALCULATION OF THE INTERDIPFUSION COEFFICIENTS AND THE RATIO OF THE INTRINSIC DIPFUSION COEFFICIENTS
3.1 A computer program for the calculation of inter-ditfusion coefficients in binary systemsR
In almest all papers published up to now, the method used for the calculation of the interditfusion coeffi-cient is the classica! Boltzmann-Matano analysis7 ' 8 , for which a computer program is given by Hartley19 • It is well known, however, that such an analysis can oe applied only to systems with constant partial molar volumes. Van den Broek10 has shown that the calculation of coefficients by this analysis rnay cause considerable errors.
The concentratien dependenee of the partial rnolar volumes have been taken into account in an e~uation derived by Sauer and Freise5 , Ballufi20 , Wagner , and Den Broeder2 • Starting frorn this equation, a program is written in ALGOL 60, calculating the coefficients frorn the concen-tration-penetration curves of ditfusion couples. The forrnula used is given by Den Broeder,
00
I
N -NJ
( b
~
m b) dx ( 1 4)x
vm is the rnolar volurne in cm3/rnole, as a function of Nb;
t is the ditfusion time in seconds; Nb is the rnole fraction of component B in at%; x is the coordinate in
~rn; Nb1 and Nbz are the starting compositions in at% of
the two "serni-infinite" rods which forrn the ditfusion couple;
NbZ-Nb
(1-K )
=
N -N •n b2 bi
The equation permits of the calculation of the chemical interditfusion coefficient Dv without the position of the Matano-interface being known.
published in Scripta Metallurgica (ref.18). This paper is written in co-operation with Dr. G.J. Visser, of the Cornputing Centre of the University of Technology, Eindhoven, for whose help
22
To make i t possible to calculate the ratio of the intrinsic ditfusion coefficients, Da and Db, in the Kirkendall interface, the integrals in the following equation are calculated by the program,
x N -N 00 N -N
lN
fk ( b b>)dx - N fk(b~m
b)dxl Db vb b2 -"' V m bl { 15} Da va N x Jk { N -N b"'
N -N bl}dx - Nf { b2
b}dx a2 v al k vm -oo mVb and va are the partial rnalar volumes belonging to the concentratien at the Kirkendall interface.
'r!2L~!'Qg;:~IE
The program is structured in such a way that i t can handle all possible cases in binary systems. There is no limit to the number of compounds {and therefore to the number of phase boundaries} present in the concentration-penetration curve.
The program consists of the following steps: 1. smoothing of the experimental points; 2. polynomial curve fitting all these points;
3. calculation of the interditfusion coefficients at
concentratien Nb. For each Nb this calculation implies: {a} determination of the coordinate x,
{b} calculation of the integrals of eq.{14}, {c} determination of the gradient dx/dNb, {d} calculation of vm;
4. platting of a picture of the smoothed points and the polynomial through these points {this step is not necessary} .
All these steps will be considered in some detail in the following sections.
§:!:~E-1
In most cases the experimental points do not lie on a smooth curve. When a polynomial is drawn through the points, its degree should be relatively low to obtain a smooth curve. This is necessary to get a gradient which does not go up and down depending on the incidental gradient in a point of the curve. When the degree is too low, however, the curve does not fit the experimental points very well and the deviation from the true curve is very high {Fig.3.1} .The deviation hardly affects the values of the integrals, but for the calculation of the gradient dx/dNb i t is disastrous. Therefore, i t is
necessary that the experimental points should be smoothed. The m experimental points are corrected by the formula:
~
i+3r
-I
x. -xkI
l [
i+3-I
x· -xkI
l
exp (~
0 ) ilNbkI
r
exp (~
0 )k=~-3 k=~-3
( 1 6)
This is a 7-point forrnula, which corrects a point by the three preceding and the three following points. The weight of each point is deterrnined by an exponential function which decreases as the distance to the point which must be corrected increases. The value of the factor 10 in eq.(16) depends on the spacings of the experirnental points and also on the units of the coordi-nates. In our experirnents the factor 10 is excellent for this 7-point approach (Fig.3.2) .In this way the first and the last three points cannot be corrected and rernain unchanged.
Ta get an irnpression of the difference between the un-corrected and corrected points, the root-rnean-square
value is calculated. 5~0 54.5 6 1h dtgttt 54.0 53.5 AI.%Ni 53.0 52.5 52.0 51.5 51.0
/
'
/
"'
49.5 .,. .•!
50.5 50.0 550 54.5 54.0 53.5.
/
.~r
::: 52.0 / 51.5 / 51.0 50.5 50.0 49.5 25 th dtgtee At.%Ni ···~,~.~.~.~..
~~..
~.~..
~.~,.~..
~.~.
.
~.~..
~.~,~.~.~,~,. - ~m 49.ok2~0~4e;;0~6':-0 -'---:f.80~~100::-'-:",7:,0,...,.,,.!-::-0""-:-!,6~0 ~.~ • • ~,~00~22;".-0 -·~Fig. 3.1 The 6th and 25th degree polynomial curve fitting of a measured concentration profi le in the Ti-Ni system~
(crosses represent the experimentaZ points)
55.0 5~0 54.5 54.5 SMOOTHED 54.0 UNSMOOTHED 54.0 At.~ .. Ni 53.5 ~3.5 At.% Ni 53.0 ~~ 53.0 ",. ,./ / 52.5 .~ 4 ' 52.5 / 52.0 / 52.0 51.5
/ /
~1.5 51.0/
'"
51.0 / . / " 50.5 ;-"'- 50.5I
,.. 50.0 50.0.,..
U.5•o.o'-:;2~0 ~.'::-o ~oo;-'-a;!;o;-'-;1,!"00.-'--:"12b0~14;;;-0~1 a"""o ._,,±ao"...._"2boo,..._",2 2!:::-'o 48·0'-2:-'0:~•"="o..."e'=-o --='ao:,-.-,..:1 o-=-o -1,.:.20::--:1-7:4o:-'-:"••O-:o~1 a~o~2~o7o ._,2,:.20=-'
- ~m - ~m
Fig. 3.2 The 77th degPee polynomial cuPVe fitting of
the uncorrected and corrected points of the
same concentration profile as in Fig. 3. 7
(cposses represent the uncorrected and cor-rected experimental points
ê!:~I?-~
To get an impression of the difference between the un-corrected and the un-corrected points a polynomial curve fit is carried out on both series.
The polynomial y=a0+a1x+a2x2+a3x3+ . . . . +anxn is adapted
to the points using the procedure ORTHOPOL, described by Forsythe21 and available in a similar form in nearly
every computing centre. This is a least-squares method using orthogonal polynomials. The degree of the poly-nomial is chosen to be the number of points divided by four. The result is rounded off downwards, but is at least three to obtain a reasonable curve even if only a few points are available. We chose this degree in order that the ratio of the number of points to the number of coefficients in the polynomial should be favourable. Experiments have shown that a higher degree does not yield a better curve. The fitting of the points may be
better, but the curve also exhibits the measuring errors. Therefore the error in the gradient cannot be reduced further.
The standard deviation in the Nb values of the polynomial is given by:
li,[Nbk(measured) - Nbk(calculated) ]'/(m-n-1)]\ 24 n is the degree of the polynomial.
ê!:~E-~
In every measuring point a value of Nb (calculated) is determined by means of the polynomial using the YAPPROX procedure, which procedure calculates the y-value
belonging to a certain x-value and belongs to the ORTHOPOL procedure.
The x is calculated by (reversed) interpolation between the two nearest values of Nb (calculated).
The integrals of eq.(14) are calculated with the rule of Simpson:
xn
XOJ y(x)dx '\.(h/3) ryo+4y +2y +4y + . . . +2y ~ 1 2 3 n-2 +4y n-1 +y n
J
(17) where h is the step size in the x-direction (xi=Xi- 1+h), n i s the number of steps, y0 , y 1 , ... , Yn are the values of the functionsor
We divided the integration range in n=4m steps (h) ; other step sizes are also possible.
The gradient dx/dNb at a certain Nb is calculated with the derivative of the polynomial:
y = dNb/dx = a 1+2a 2x+3a3x2+ ... +nanxn-l.
The POLCOEF procedure belonging to the ORTHOPOL proce-dure uses the coefficients of the polynomial.
vm is calculated with the formula vm= A+BxNb·
This formula is used because the concentratien in a binary system can always be divided into steps where Vm is nearly linear. But other functions are also possible and usable.
ê!:~E-~
Using plot procedures, a graph of the polynomial through the corrected points (crosses) is drawn.
A few more details of the program are given in the flow diagram of Fig. 3.3
26
[START)
+
/Reading of the Nb's r which the Dv has to calculated
+
at be
Calculation of Kn's Initialisation of lower and upper integral totals
+
(Reading of time and number of curves For each curve Do A For each Nb Do C
0
[Nb in region of this +yes curve\ Interpolation of x(Nf) between x[1]
and x [m+
Calculation of integrals x~x(Nb)+ lower integral x::l:x(Nb)+ upper integralI
0
(~eading
of A,B, number of points (m) , data points+
Correcting data points and platting of corrected points
+
Polynomial curve fitting of corrected points and data points Platting curve
t
For each Nb Do B Calculation of d~ffusion coefficient no no fNb in region )---\above this curvet
yes ICalculation of Ilower integral
ICalculation of upper integral
Add integral(s) to lower and upper integral totals
Fig. 3.3 Flow diagram of the computer program
3.2 The ratio of the intrinsic diffusion coefficients Eq. (15) is used for the calculation of the ratio Db/Da.
x When
J
-oo Nb-Nbl -=:.._-=_,dx vm is denoted by A II
we can write:
( 1 8)
If pure metals are used as starting materials, eq.(18) yields:
A
. B
( 1 9)Eq. (18) enables us to see easily where the Kirkendall interface must lie, depending on whether only the A or B atoms move. From eq. (19) i t is clear that the interface lies at the B-side if only B atoms move, and at the A-side if only A atoms move. If we have, for example, a couple consisting of the pure roetal A and an alloy of the composition AB, sa that Nb1
=
1 and Nb2=
~, eq.(18)is transformed into:
(20)
In eq. (20) neither the numerator nor the denominator can be negative. Sa 0 < A/B < 2. The ratio A/B can have
values between 0 and 2 only. Sa i t is clear that the Kirkendall interface lies at the A-side if only the A-atoms move, and if only the B-atoms move the position of the interface corresponds to B
=
~A.C H A P T E R 4
CONSTITUTION OF THE Mo-Ni, Mo-Fe AND Mo-Co SYSTEMS AND PROPERTIES OF THEIR PHASES
4.1 The eguilibrium diagram of the Mo-Ni system and the structure of the various phases
Casselton and Hume-Rothery22 have determined the whole
diagram (see Fig. 7.19). The determinations were carried out by means of a combination of thermal analysis,
microscopie, and X-ray methods.
~h~_§2~!9_§Q1~~!Q~-Q~-~!_!~-~Q
The solubility of ~i in Mo is very slight; at most 1.8 at% Ni at 1362 C.
~h~-~=J~2~!lEh~~~
The homogeneity range is about 2-3 at% and is centred round 50.8 at% Ni according to Pearson23 and round
47 at% Ni according to Casselton et al.22
The o-phase has a pseudo-tet~agonal unit cell with a= b = 9.108 and c = 8.852 Ä and contains 56 atoms per unit cell. However, the structure is orthohombic and the
. 2 2 2 2~r25
space group ~s P 1 1 1 • ~h~-r=J~Q~!~lEh~§~
The homogeneity range is very narrow, probably less than 1 at%. The phase has an orthorhombic Cu Ti type of
structure with the parameters a = 5.064
R,
b = 4.244R
and c = 4.448R.
The phase contains 2atoms per unit cell. The space group is Pmmn26~h~-~=J~Q~!~lEh~§~
Casselton et al. did not succeed in obtaining a comple-tely homogeneaus alloy. The composition is in the range
of 80.5-81.0 at% Ni. Harker27 found that this phase has
a tetragonal structure with a = 5.731 and c
=
3.571R,
and showed that the tegragonal cell could be regarded as a superlattice of the f.c.c. solid salution of Mo in Ni. Casselton et al.22 found a tetragonal structure witha = 5.683 and c = 3.592
R.
According to Guthrie and Stansbury2e MoNi4 is b.c. tetra-gonal with a= 5.727 and c = 3.566
R
with space groupI 4/m.
!h~_§Q~!9_êQ!~~!Q~-Q~-~Q_!n_N!
The maximum solubility is 28.4 at% Mo at 1318°c.
Casselton et al.22 give also the lattice parameters as
Alloys were prepared by sintering powders at 1250°C. at% Mo 0 17.1 22.5 24.0 27.0 Table 4.1 a in
R
3.5238 3. 5917 3.6179 3.6263 3.6373Vlasova 29 , Spruiell 30 and Gordon Le Fevre31 have studied
the intermediate structures, formed during the conversion of solid solutions into MoNi4 • The solid salution
exhibits a tendency towards clustering, even at very low concentrations of Mo, which is typical of the ordered phase formed at higher Mo concentration.
Saburi et al. 32 reported that alloys containing more than 20 at% Mo, when quenched from the high-temperature a-solid salution region, and subsequently annealed below the periteetic temperature (865°C), do not decompose into 8-MoNi4 and y-MoNi3 only, but at the beginning of the
decomposition a Pt2Mo type superlattice (possibly
orde-red Ni2Mo) is also formed.
4.2 The equilibrium diagram of the Mo-Fe system and the structure of the various phases
The diagram given by Hansen33 is essentially basedon
work published befare 1930. In 1967 Sinha, Buckley and Hume-Rothery34 determined a part of the phase diagram, namely the iron-rich side, up to 40 at% Mo (see Fig. 8.11).
~h§_§Q!i9_êQ!~~iQ~-Q~-E~-i~-~Q
The solid solubility of Fe in Mo was established by lattice 8arameter measurements 35 . At 1100, 1200, 1300 and 1400 C the solubility is 4.5, 6.0, 7.9 and 11.0 at% Fe respectively.
~h~-<I=I?hèê~
The formula of the o-phase at the Mo-side is considered to be FeMo. The ether two boundaries are not exactly known. The phase is s~able in the temperature range between 1180 and 1540 C. The structure is tetragonal; a= 9.188 and c = 4.812
R,
30 atoms per cell.The space group is P42/mnm36 .
Wilsen and Spooner 37 confirmed this structure, and calculated the parameters a = 9.218 and c
=
4.813R.
~h~-~=1[~2~Q~li?hèë~The composition of the -phase has a concentratien range
thus be Fe3Mo2 • The crystal structure, however, is based
on the A7B6 type structure and is analogous to Fe7W6 and
Co7Mo6 and therefore called ~.
The lattice parameters of the phase only determined for the Fe-rich side, are: for the rhombohedral cel!
a= 9.001 Rand a= 30°38.6', containing 13 atoms per cel!, and for the corresponding hexagonal cel! a= 4.754 and c = 25.716 R3~, ~ontaining 39 atoms per cel!.
The space group is R3m. Th5 periteetic temperature for the formation of ~ is 1370 c.
~g~-~:E~~~~
Sinha et al.3~ have found a new phase, containing aboub 62.6 at% Fe. The phase is stable between 1245 and 1488 c. On cooling below 1245°C the R-phase decomposes only very slowly and very long annealing times are required to complete the decompositiQn.
The space group is c;i-R3 and contains 53 atoms per unit cel!. The lattice para~eter for the rhombohedral cel! is a= 9.016
X
and a= 74 27.8'. For the correspondinghexagonal cel! ~he lattice parameters would be a = 10.910 and c
=
19.354 Ä.~hê-~èYêê:2hèêê_~:irê~~QL
Zaletaeva et al38 claims to have isolated the compound
Fe2Mo from 0.1C-16Cr-25Ni-6Mo steel by electrolytic
separation and found i t to be isostructural with Fe2W.
This was confirmed by Elliot39 •
Sinha et al.34 , however, found that the À-phase has a hexagonal MgZn2-type structure with 12 atoms per cel!. For an alloy containing 66.7 at% Fe, the lattice para-meters are: a= 4.745 and c
=
7.734 R. The formation ofthe phase is very slow. None of the other investigators have found this phase.
!h~_§Q1!Q_§Q!~!!Q~-Q~-~Q_!~_[ê
Hansen33 reports a maximum solubility of Mo in Fe of
26 at% at 1450°C.
The vertex of the Ó-loop was found to !ie at about 1.6 at% Mo at 1150 C.
4.3 The equilibrium diagram of the Mo-Co system and the structure of the various phases
Quinn and Hume-Rothery40 determined the diagram in 1963
except for the a/S Co transformation (see Fig. 9.14). The structure ofa-Co is f.c.c. and S-Co has the close-packed hexagonal structure. The alloys were prepared from powders which were pressed into smal! bars, and these were subsequently sintered in hydrogen. After annealing and quenching, the alloys were examined 30 microscopically and by X-ray diffraction.
!h~_§Q1~Q_§Q1~~!Q~-Q~_ÇQ_!~-~Q
Quinn et al.40 found the solub~lity of Co in Mo at the periteebic temperature of 1620 C to beat most 11.5 at%. At 1250 C the solubility was about 2 at% Co.
!h§_~:JÇQ2~Q~l2h~§~
The Mo-rich boundary of the O-phase lies between 63 and 64 at% Mo and is almast vertical. It decomposes eutec-toidally at 1250°C. Forsyth and d'Alta da Veiga41 found
that the a-phase is tetrag~nal with lattice parameters a = 9.2287 and c = 4.8269 Ä. The unit cel! contains 30 atoms and the space group is P42/mnm.
!h~_g=JÇQz~QilQh~~~
This phase extends from 54.5 to 49.5 at% Co at 1335°C. With decreasing temperature the homogeneity range narrows on the Co-rich side. According to Forsyth and d'Alta da Veiga42 the ~-phase (containing 46.15 at% Mo) has th5 rhombohedral Fe7W6 structure with a = 8.970
g,
a = 30 47', 13 atoms per unit cel! and space group R3m, or for the ~orresponding hexagonal cel! a= 4.762 and c = 25.615 Ä.
!h§_~:JÇQl~Ql2h~§~
This phase is formed below 1030°C by a peritectoid reaction between the ~- and the 8-phases and possesses a narrow composition ran1e. In an alloy containing 75 at% Co, d'Alta da Veiga4 found that the K-phase
possesses the hexagonal Ni3Sn-type structure with
a= 5.1245, c = 4.1125 and c/a = 0.8025 and 2 atoms per unit cel!. The space group is P63/mmc. This is a
super-lattice of the close-packed hexagonal structure with a doubled a-spacing and a halved axial ratio.
!h§_~:JÇQ1~Qll2h~§~
This phase has been found by Quinn et al.40 and is not included in Hansen's33 diagram. The 9-phase has roughly
the composition Co9Mo2 and is related to the close-packed hexagonal structure. The diffraction lines of an alloy containing 18 at% Mo were indexed by Quinn et al~0 as fitting a hexagonal cell with a = 2.5973, c = 4.2123
~ and c/a = 1.6218 at 1100°C.
The 8-phase is formed peritectoidally at 1200°C by reaction between the ~-phase and a-co and decomposes eutectoidally at 1080°c.
The solid salution of Mo in Co
----
-
---Quinn et al.40 observed that this solid salut ion when quenched from the f.c.c. area always partly transfarms into the close-packed hexagonal structure. The maximum
C H A P T E R 5
DIPFUSION IN THE Mo-Ni, Mo-Fe AND Mo-Co SYSTEMS
5.1 Diffusion in the Mo-Ni system
Davin et al.44 investiga5ed the interditfusion of Mo and Ni between 1000 and 1300 C, using Ni-Mo91.3Ni diffusion couples. (Designations like Mo91.3Ni will be used
throughout this thesis to denote a Mo-Ni alloy contai-ning 91.3 at% Ni.)
The concentratien vs. penetratien curves were established by an electron microprobe. The diffusion coefficients were calculated by Grube's method. For Q and D0 , 64.4 kcal/mole and 0.853 cm2/sec, respectively, were found. Swalin et al.45 have also investigated the interdit-fusion of Mo and Ni, employing Ni-Mo99.07Ni difinterdit-fusion coup6es. The temperature interval they used was 1150 to 1425
c.
The concentratien in the diffusion zone was determined chemically by means of sectien analysis. The diffusion coefficients were also calculated by Grube's method, and from these Q was found to equal2
68.9 kcal/mole and D0 3.0 cm /sec.
While the results of Davin et al.44and Swalin et al.45 are in reasonably good agreement with each ether( there is a great discrepancy with the results of Budde 6 • He calculated for the activatien energy a value of 50.8 kcal/mole and for the frequency factor a value of 0.0314 cm2/sec. He used diffusion couples of the type
Ni-Mg79.2Ni and annealing4tem~er~t~fe~ of 11f0 and 1290 C. Kalinovich et al. '4 ' ' ' 1 ' 21 have investigated the diffusion of Ni and Mo in a number of Mo-Ni alloy~ in an electric field (Table 5.1). They used Ni63 and Mo 9 radio-active isotopes. Direct current heated the specimen and induced an electric field. From a great number of experimental values D were calcu-lated. In all cases log D vs. 1/T plots were straight lines so that Q and Do could be calculated.
The diffusion coefticients of Mo in Ni were determined by Bgrisov et al. at temperatures between 900 and 1200 C. Ni was electroplated with radio-active Mo. No marked boundary diffusion was observed. The found Q
=
51 kcal/mole and D0=
1.6x10-3 cm2/sec.The same authors55 studied the diffusion of Ni in Mo. Mo slices were chemically plated with radio-active Ni. 32 Diffusion annealing was performed at temperatures between
Table 5.1
Ac ti vation energies and frequency factors for Ni and Mo ditfusion
in a number of Mo-Ni aZZoys in an electric field
Alloy Ni ditfusion Mo diffusion T 0
c
Ref0 Do Q Do Ni 60.5 9.96 47 Mo92Ni 56.4 2.55 54.9 1. 31 1000-1400 48 Mo80Ni 48.8 0.1 9 50.3 0.25 950-1300 49,50 Mo84Ni 52.2 0.63 54.6 1 . 30 950-1300 51,52 Mo77Ni 47.4 0.12 49.5 0.20 1100-1300 53 Mo82Ni 50.4 0.34 52.2 0.45 950-1400 47
900 and 1200°C. Diffusion coefficients were determined by the technique of removing thin layers (2-10 w) and measuring the residual integral activity of the specimen. For the Ni diffusion in Mo, Q was calculated to be
85 kcal/male and D0 62 cm2/sec.
Hashimoto and Tanuma56 have investigated recently the
mutual diffusion welding of Mo using intermediate mate-rial, such as Ni and Fe.
Belgw 900°C Ni appears to be more suitable than Fe. From 900 C the strength of the joint decreased with increasing welding temperature because gf the formation of an inter-metallic compound. Above 900 C Fe is preferable.
5.2 Diffusion in the Mo-Fe system
Krishtal et al.57 have investigated the interditfusion
of Mo and Fe in a d6ffusion couple consisting of the pure metals at 1250 C and after annealing for 10h. The ditfusion zone is 350w + 20w and the diffusion coeffi-cient of Mo in Fe was found to be 6.6x10-9 cm2/sec.
Borisov et al.58 studied the diffusion of Mo in pure Fe
and in an Mo99.3Fe alloy. The specimens were poly-crystalline with a grain size of approximately 5-10 wm. The radio-active isotape Mo99 was used, being
electro-plated on the surface. The diffusion coefficients were determined in two ways, viz. by the absorption method and by layer-wise analysis. The latter method yielded mean coefficients (Dm) which characterised the total flow in the volume and grain boundaries. In the absorp-tion method both the bulk and the boundary diffusion were determined separately. The results are summarised
34
Table 5.2
The aativation energies and frequenay factors of the diJfusion of Mo99 in pure Fe and in an Fe-Mo alloy,
using two different measuring methods
Methad Q kcal/male ~0 cm2!_sec Remarks
Layer-wise 49.0 0.3 Dm in pure Fe
Absarptien 73.0 7.8 x 1 0 3
Dvol i.n pure Fe Layer-wise 64.0 2.24 x 1 0 2 Dm in Fe-Mo alloy
1 0 4
Absarptien 75.0 1 . 3 x Dvol in Fe-Mo alloy The temperature range was 750 to 900°C. The mean acti-vation energy determined by layer-wise analysis is seen to be lower than the corresponding energy for pure volume diffusion. This is due to the influence of grain boundaries, which is much less in the Fe-Mo alloy. Pivot et al.59 studied the diffusion between Fe and
Fe 15-20 wt% Mo alloys consisting of a(solid salution of Mo in Fe) and ~(Fe7Mo6). The penetratien curves were determined with a microprobe. The activatien energy was calculated to be 60.0 kcal/male and the frequency factor 10 cm2/sec for the a-solid solution.
Rawlings and Newey60 investigated the system using Fe-Mo
~!;!~s!~~ ~~~~~~!d !~et~~~~;:~u;:~eb:~~~:~i~~~
1
~n~r~~05°C.
They were examined with a mieroprobe (see Table 5.3) and a micro-hardness analyser. The hardness of the R- and ~-phases were 955 and 1054 kg/mm2 Hv· The authors do nat mention the solid solutions.Table 5.3
Phases identi fied in the diitusion couples (Rawlings et al. )
(the aompositions of the phases are only averages)
Treatment R-phase d Jl-phase d o-phase d at% Fe ].lm at% Fe )llTl at% Fe )lffi
192 days 800°C 60.0 6 81 days 900°C 57.2 11 12 days 1125°C 61 . 0 47 6~ days 1255°C 63.0 1 0 60.5 1 0 + 3 6 days 1320°C 69.4 10 58.4 15 + 3
H
day 1405°C 62.3 3 50.3 5+ present, but the layer was toa thin to allow proper determination of the concentration.
Seebold and Birks61 have annealed a Fe-Mo sandwich couple
at 1100°C for 66h and examined i t with a microprobe. A 30 ~m thick diffusion zone with the composition 37-39 at% Mo (~-phase) was found to be present. The Fe-~ inter-face showed a continuous crack. The investigators con-cluded that no solid solutions were formed in the couple.
5.3 Diffusion in the Mo-Co system
Interdiffusion coefficients for mutual diffusion of Co and Mo were already determined in 1955 by B~ron and Lambert62 at 900, 11go, 1275, 1500 and 1700
c.
For runsat 900, 100 and 1275 C, Co-Mo couples were prepared by inserting a Co rod into a hollow Mo cylinder and the thickness of the diffusion layers was determined as a function of the time. The diffusion coefficients were determined, using the formula B2
=
4Dt, where B is thewidth of the diffusion zone. For runs at 1500 and 1700°C, the inner rod consisted of an ~1loy of Mo + 3.42 wt% Co. The couples were heated for 95h in an H2 atmosphere.
The penetratien curves were determined by means of
chemical analysis of machined chips of 250 ~m thickness. In these cases the Boltzmann-Matano method was used for calculation of the diffusion coefficient. Byron et al. derived an activatien energy of 34.8 kcal/mole, and a frequency factor of 2.82x10-6 cm2/sec.
Davin et al.44 have studied the interdiffusion of Mo and
Co also gsing Co-Mo90.2Co diffusion couples between 1000 and 1300 C. Values of 62.8 kcal/mole for the activatien energy and 0.231 cm2/sec for the frequency factor were
found.
For the diffusion of Co in Mo (Mo was electroplated with radio-active Co) at temperatures between 1000 and 1300°C Borisov et al. 55 calculated Q to be 77.5 kcal/mole and
D0 6 cm2/sec.
36
C H A P T E R 6
EXPERIMENTAL PROCEDURES
6.1 Introduetion
In principle the experimental procedure was as fellows: (a) Preparatien of diffusion couples of pure metals or
alloys.
(b) Annealing at a certain temperature.
(c) Metallographic preparatien for investigation purposes.
(d) Continuatien of annealing, if necessary. 6.2 Preparatien of the diffusion couples
A large number of different diffusion couples were pre-pared. In fact, in a number of cases sandwich couples consisting of three different materials were prepared, e.g. Mo-Mo62.0Ni-Ni. Often two-phase alloys were used, because the single-phase alloys were mostly very brittle and difficult to handle, e.g. the 8-phase, and the ~
phases in the Mo-Fe and Mo-Co systems.
In Tables 6.1 and 6.2 details are given about the purity of the metals used. The carbon present in Ni (MRC1) caused the hardness to increase from 175 to 270 kg/mmz. Annealing has a very great influence upon the hardness. No significant difference in diffusion behaviour between the nickel supplied by Halewood or (MRC2) was noticed.
Table 6.1
Vickers micro-hardness of the starting materials; load 50g Me tal Ni (MRC1) Ni (MRC2) Ni(halewood) Ni (MRC1) Ni(MRC2) Mo(Drijfhout) Fe (MRC) Co(MRC) Co(IviRC) Treatment as received as received as receiged 89h 1300
c
89h 1300°C as received as received as received melted !!v kg/mmz 271 175 177 11 8 11 6 304 208 218y 218àà the identations have peculiar shapes.
Table 6.2
Typiaal analysis of the pure metals in ppm by weight
Element
c
Mg Al Sis
Ca Mn Fe Ni Cu Pb 0 N H Be Cr Co Mo Ag p Ta Snw
V Ti Zn Zr DR Ni (Hal) 1l 50 < 2 25 < 7 < 8 <30 bal 6 <40 <70 <40 3 <30 Hal Balewood DH Drijfhout Ni (MRC2) 50 5 <10 5 bal <15 20 < 5 1 2 10 Ni (MRC1) ik 600 15 45 45 250 bal 1 0 150 2 Mo (DH) 50 100 30 2 3 bal 200 Fe (MRC) 30 < 5 <10 35 30 < 5 20 bal 1 0 40 <10 78 < 3 < 2 < 5 1 0 10 <50 20 <10 <40 <10 <10 <10 <10 Co (MRC) 40 2 3 <10 < 8 <10 3 400 120 1 0 < 1 balik perforrned by Analytical Laboratory, N.V. Philips, Eindhoven, Netherlands
DR distillation residues
The binary alloys were prepared by are rnelting Mo and either Ni (Hal or MRC2), or Fe or Co in the proper
weight ratio and in an argon atrnosphere. Each sample was rernelted five tirnes in order to obtain the desired
hornogeneity. The loss of weight was less than 0.2 wt%. Portions of 5 to 7g were melted. In larger portions (10g)
of an alloy of 5 to 7g each were remelted in the same furnace in a special mould to obtain a bar of 10 mm in diameter. Each bar was annealed in a silica capsule for some period of time and at a certain temperature depen-ding on the temperatures at which the alloy was used as starting material in diffusion couples. Each bar was sawn into 1-2 mm thick slices, using a 1 mm carborondum or a diamond blade, dependent on the nature of the mate-rial. After this, the slices were ground on wet silicon carbide papers of various grades, the finest being 600. Polishing after grinding caused no significant difference in the diffusion behaviour. After thorough degreasing, the slices of the couple constituents were subjected to a sli~ht pressure, and spot-welded in a vacuum of
1x1o- Torr. Electron probe micro-analysis of the
asbounded specimens showed interditfusion due to this bonding treatment to be insignificant.
The diffusion couples were annealed at temperatures be-tween 800 and 1300°C in silica capsules in a vacuum of
10-2 mm Hg. The temperatures were measured by means of
a Pt-Pt (10 % Rh) thermocouple with an accuracy of~ 2°C
and recorded continually. After the heat treatment the
specimen was rapidly cocled (Ni-Mo system) or quenched
by dropping the capsule into water and immediately
breaking i t (Fe-Mo and Co-Mo systems). The couple was mounted in epoxy resin. A cross-sectien of the diffusion zone, sufficiently remote from the edge to eliminate the effects of surface diffusion, was ground and polished in
a plane parallel to the direction of diffusion using
0.05 ~m Al203 on a soft cloth. The samples were washed
and etched in a mixture of equal volume of concentrated
HN03 , H~SO~ and H3PO in order to make visible the phase
beundarles for metaliographic analysis. To reveal the boundary Co-a solid salution in the Co-Mo system, the couple was first etched in a mixture of concentrated
HN03 with water 1:1.
6.3 Microscopie examinatien
Microscopie examinatien of the diffusion layer and
measurement of the layer thickness were carried out with
a Reichert Neepan microscope using a calibrated filar
micrometer eyepiece. By this methad information was
obtained regarding the number of phases in the couple
and thei r layer thicknesses in dependenee of time and
temperature.
Very aften the marker interface was also visible in the
microscope and the position of i t was measured.
6.4 Mieroprobe analysis
For determining concentratien versus penetratien profiles an AEI-SEM IIA electron probe micro-analyser was used. The X-ray intensities obtained with the mieroprobe have to be converted into concentratien units. Normally, one of the various theoretically based correction procedures is used. The conversion into concentratien units can also be carried out by using calibration standards63 • Up to now i t is generally accepted that only single-phase standards can be used to set up a calibration curve, but as shown by Bastin, Heijwegen, Van Loo and Rieck64 , poly-phase alloys can also be employed as standards, provided that some conditions (see below) are fulfilled. The main reasen why standards are used is the reliability of the methad and its independenee of possible instrument error. The systems which have been investigated in our labora-toryare Ti-Ni65 , Ti-Al66, Ti-Cu, Mo-Ni, Mo-Fe and Mo-Co.
We shall mention here the results of the last three systems.
In all cases the Ziebold-Ogilvie relation63 is shown to be valid:
where:
(21)
the relative intensity
IA/I~
X-ray intensity of component A from a certain area of an alloy A-B
X-ray intensity of component A from an equally large area of the pure reference metal A
weight fraction of component A in the alloy A-B MB
a constant equal to aA . ~ , where aA is a con-stant and MB and MA are th~ atomie we1ghts of the
elements B and A, respectively
male fraction of the component A iri an alloy A-B
The constants aA and AA should be dependent only on the
alloy system and the eperating condit ions for the
ana-lysis.
A great number of standards have been used. Only a minority were purely single-phase alloys. Whether poly-phase alloys are suitable as standards or not, depends
(a) the alloys have to be macroscopically homogeneous, i.e. any cross-sectien has to be representative of the whole sample,
(b) microscopically, i.e. the grain size of the various phases has to be smaller than a certain value which is determined by (i) the measuring method, and (ii) the curvature of the calibration curve.
The region from which the X-rays originate may be a small area around the electron beam, focussed upon the samples (point measurement) , or a square of variable size over which the electron beam is scanned (scan measurement). If polyphase alloys are investigated, i t will be clear that point measurements will not work be-cause of the tremendous number that is necessary to give a reliable average result. Therefore, scan measurements have to be performed.
In fact, a calibration curve is required only to verify the validity of the Ziebold-Ogilvie relation. After this verification we can calculate the concentrations using this relation.
The alloys were melted as described in sectien 6.2. They were prepared for mieroprobe investigation by in-serting them in conducting resin and grinding up to 600 grit silicon carbide paper, followed by polishing. The alloys were not etched. In order to determine the value of KA, a representative value of IA for the alloy surface was obtained by scanning 30-100 different squares and counting the pulses of element A radiation for 10 seconds. Befere and after the measurement, 10 squares of equal size of the pure roetal A were examined under the same conditions. The size of the scanned areas (100x 100 ~m to 25x25 ~m) was adapted to the microstructure of the alloy and the choice of the accelerating voltage. The results for our systems and eperating conditions are shown in Table 6.3 and in the Figures 6.1 (a, band c).
When recording the penetratien curve in a diffusion couple, point measurements were carried out under the same eperating conditions as in the calibration mea-surements. The steps in which the diffusion couple was movedunder the electron beam were at least 2.5 ~m. The movement was parallel to the direction of the diffusion, and the interface in the couple was oriented parallel to the X-ray take-off path in orde~ to avoid absorption effects. Owing to several edge ,,ffects, however, the concentratien at the interface could not be determined accurately within a distance of about 2 ~m of the phase 40 interfaces (see also Chapter 7).
0.8 K 1 0.6 0.4 0.2 0.80 K 10.60 0.40 0.20 I I I Mo-Ni ~ 0.80
/:
/
Mo-Fe ;" K/?
I
I
0.60 /../
.Mo OAO~
.
Ni
1
"1
20 40 60 ---at%Ni 80 100 • Co,25Kv o Co,30Kv/
'
• Fe,20Kv 0.20 o Fe,JOKv 20 40 60 80 100 --at% Fe Fig. 6.1 20 40 60 - - a t%Co80 100 Calibration curves for the various systems
Table 6.3
Survey of the aalibration data in Mo-Ni, Mo-Fe and Mo-Co systems.
The X-ray take-off angZe is 22.5°; the probe current is 0.2 WA.
Number of
System standard Radiation Crystal KV ~A ~A alloys Mo-:tH 13 Ni Ka LiF 30 1 . 7 4 1. 06 7 MoL a Mica 30 1 .1 5 1 . 8 8 Mo-F'e 1 0 Fe Ka LiF 20 1 • 81 1 • 05 6 Fe Ka LiF 30 2.04 1 .1 9 Mo-Co 11 Co Ka LiF 25 1. 78 1 . 09 4 Co Ka LiF 30 1 . 89 1.16 41
