A COMPARISON BETWEEN
PRECIPITATION PHENOMENA
IN BULK AND EVAPORATED
GOLD-NICKEL ALLOYS
A. A. DE KEIJZER
A COMPARISON BETWEEN PRECIPITATION PHENOMENA IN BULK AND EVAPORATED GOLD-NICKEL ALLOYS
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•• { fA COMPARISON BETWEEN
PRECIPITATION PHENOMENA
IN BULK AND EVAPORATED
GOLD-NICKEL ALLOYS
PROEFSCHRIFT
TER VEBKRIJGING VAN DE GRAAD VAN DOCTOR I N DB
TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL DELFT OP GEZAG VAN D E RECTOR MAGNIFICUS
DR. IR. C. J . D. M. VERHAGEN, HOOGLERAAR I N DE AFDELING DER TECHNISCHE NATUURKUNDE,
VOOR EEN COMMISSIE UIT DE SENAAT TE VERDEDIGEN OP WOENSDAG 17 J U N I 1 9 7 0 TE 1 6 UUR
DOOR
ABRAHAM ADRIAAN DE KEIJZER
SCHEIKrrNDIO INGBNIEUB QEBOREX TE MIDDELBUBQ
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fc 1970 H E N K E 8 - H 0 L L A N D N.V. - HAARLEMDit proefschrift is goedgekeurd door de promotor
Aan mijn ouders Aan Marijke, Martijn en Hu^o
I wish to thank those members of the staff of the Laboratory of Metallurgy who gave their assistance in the preparation of this thesis.
CONTENTS
page
1. INTRODUCTION 9 2. DISCUSSION OF PREVIOUS WORK
A) The Au-Ni system 11 B) Discontinuoua precipitation 17
3. ORIENTATION RELATIONS DURING PRECIPITATION I N A
GOLD-NICKEL ALLOY 27 4. T H I N METAL FILMS P R E P A R E D BY EVAPORATION 45
5. PRECIPITATION PHENOMENA I N EVAPORATED Au-Ni FILMS
CONTAMINATED W I T H CARBON 59 6. PRECIPITATION PHENOMENA IN " B U L K " Au-Ni ALLOYS
CONTAMINATED W I T H CARBON 79
7. SUMMARY 98 8. SAMENVATTING 101
CHAPTER 1
INTRODUCTION
Gold and nickel are mutual soluble above ' ^ 812° C. At lower temper-atures the Au-Ni system has a miscibility gap (fig. 1). Homogeneous alloys can be retained a t roomtemperature by quenching alloys from temper-atures in the solid solution region. In this way it is possible to measure several properties of the homogeneous alloys, for instance: hardness, lattice-parameters, electrical resistance, magnetic properties, etc.
If homogeneous alloys («) are annealed a t temperatures above 400° C they decompose into a goldrich («i)- and a nickelrich («2) phase for compo-sitions lying inside the miscibility gap. This decomposition, which we will call "high temperature precipitation", can be described as discontinuous
precipitation: the ai/(X2 phases, nucleated at grain boundaries, grow into
the matrix as lamellar crystals (duplex structures or "cells"). No compo-sition differences occur in the matrix ahead of these growing (%i/«2 cells. Although the Au-Ni system has been subject of many investigations, i t
1800 1600 2 1 4 0 0 e t 1200 1000 800 600 4 0 0 200 0 20 40 60 80 100 atomic percent Ni
Fig. 1. Au-Ni equilibrium diagram, spinodal and miscibility gap. miscibility gap according to HANSEN (1958); chemical spinodal calculated from thermo-dynamic d a t a ; coherent miscibility gap determined by KIMBALL and COHEN (1969); 0000 coherent spinodal according to WOODILLA and AVERBACH (1968); • • • • coherent spinodal according to GOLDINO and Moss (1967) (after KIMBALL
10
is as yet not possible to describe the "high temperature precipitation" by means of modern theories on discontinuous precipitation owing to the lack of sufficient experimental details.
If homogeneous Au-Ni alloys are annealed at temperatures below '^.' 300° C, a "low temperature precipitation" takes place. Probably nickel-rich clusters are formed in this temperature range. This type of precipi-tation is observed only in goldrich alloys. Details of the process are difficult to investigate because the precipitation rate becomes very slow when quenched-in vacancies have disappeared into sinks (dislocation loops, grain boundaries, etc.). For this reason it is not certain t h a t this process is a spinodal decomposition as has been suggested by some authors. I t is also unknown whether there is a transition stage between the low temper-ature precipitation and the main (discontinuous) reaction.
In this thesis we have paid attention only to the "high temperature precipitation". Our aim was to get more information about the growth of the /xil(X2 duplex structures by means of X-ray diffraction techniques and electron transmission microscopy. To this end we prepared a Au-40 at. % Ni monocrystal which was decomposed at ~ ' 600° C. An orientation-relation between the (Xi/«2 phases and the matrix was established and data could be obtained of the geometry of the «i/«2 lamellae (chapter 3). Because partly decomposed Au-Ni alloys are difficult to prepare into a suitable thickness for investigation by electron microscopy, we could not obtain detailed information of the boundary between the «i/«2 regions and the matrix. Series of experiments were carried out to investigate the suitability of evaporated thin films to study details of discontinuous precipitation reactions. I t appeared t h a t these films are very sensitive to contamination and decompose mostly by a continuous precipitation process. Isolated nickelrich particles were formed. The matrix composition changed continuously during growth of these particles. The reason for this phenomenon might be t h a t small amounts of carbon are dissolved in the films during annealing in vacuum. Discontinuous precipitation could be observed only if extreme care was taken to avoid carbon con-tamination. This was accomplished by evaporating and annealing the Au-Ni films in ultrahighvacuum of about 10~® Torr (chapter 5).
Finally the influence of carbon was studied on the precipitation kinetics in "bulk" Au-Ni alloys. I t could be established t h a t also in bulk alloys discontinuous precipitation is hindered by carbon. The precipitation rate is less than in pure Au-Ni alloys and three dimensional growth of ai/a2 lamellae is impeded (chapter 6).
The experiments and results described in the chapters 3, 5 and 6 have been published in the Proc. Kon. Ned. Akad. Wet. Amsterdam B febr., apr. and June (1970) respectively.
CHAPTER 2
DISCUSSION OF P R E V I O U S W O R K A. T H E Au-Ni SYSTEM
High temperature precipitation
K O S T E R and DANNÖHL published in 1936 results of a comprehensive study of the precipitation phenomena in Au-Ni alloys. They determined the lattice parameters of the quenched alloys, the composition of the equilibrium phases, the electrical conductivity, magnetic properties and hardness at several temperatures. They found t h a t the composition of the supersaturated solid solution remained constant during the formation of the equilibrium phases «i and «2. I t appeared t h a t the «i and at phases nucleated at grain boundaries and were growing as lamellar structures into the matrix (fig. 2). U N D E R W O O D (1954) re-examined the precipitation behaviour of Au-Ni alloys. He measured the electrical resistance, rate of growth and rate of nucleation of several alloy compositions and tried to interpret the obtained results with the current theories on nucleation and grain growth. The rate of growth appeared to have a maximum at temperatures of about 600° C for most of the alloys (fig. 3). The rate of nucleation had a maximum a t 550° C. From his findings the author con-cluded t h a t the spinodal theory of BORELIUS (1937) cannot be valid for the Au-Ni system.
The time dependence of the rate of nucleation has also been determined for two adjacent grains and for their mutual grain boundaries. AVRAMI'S
matrix
grain boundary
Fig. 2. ai/«2 lamellar structure ("cell") nucleated at a grain boundary, growing into the matrix (schematically). 5r = growth direction of the (xijoii lamellae. «1 =
12 900 O ö 800 o ei 700 a E *- 600 A 5 0 0 4 0 0 -300 1
- /
-1 -1/ /
( ^
hK-/ B 1 1 A
J j ^ - ^
^ + T ' X ^ 4 0 0 -s,^^ \ [ ; ] ^ - 200 ^ lOO-' ^ ^ _ ^ ^ ^ - 5 0 • 10-—-^ 1 1 1 • i 1 ^ 1 0 - ^ ^ qo:::::^4ÖÖ70\v ^ ^ ^/J^i^;^
\ ' c 1 1 1 10\
x\\"
^y\
^ - ^ \l
1 1 20 4 0 6 0 composition (at°/oNi)-8 0 100
Fig. 3. Contoiu-s of equal growth rates, superimposed on the Au-Ni phase diagram according to UNDERWOOD (1954). 4 = miscibility gap; S = maximum growth r a t e ; (C = maximum initial ZIFB of quenched alloys). The numbers in the figure indicate
growth rates x 10^ mm/sec.
concept of pre-existing germ nuclei in the untransformed matrix or grain boundary, accounts qualitatively for the sharp rise to an early peak in the nucleation rate curves. The linear growth rate (at the early reaction times) indicates t h a t the initial transformation product can be considered to consist of small hemispheres growing out from the grain boundary in three dimensions. No difference in growth rate was found for nuclei into one or the other grain.
The transformation can be described by the rate expression: (1) or in linear form:
d±
dt K-{l-f)-t^ (2) wherelog ^In j-^j = log ^ ^ ^ + (m + 1) log <
/ = fraction of the matrix being transformed i L = r a t e constant
t = time
m + 1 = 1 means one dimensional growth m + 1 = 2 means two dimensional growth m + 1 = 3 means three dimensional growth
If the course of the transformation vs. time is plotted in a linear form, the slopes of the resulting straight lines indicate an average value of two.
13
The reason must be t h a t a t later times the impinged nodules advance toward the grain centers on essentially a plane front. Besides nucleation of «1 and «2 at grain boundaries. U N D E R W O O D observed nodular precipi-tation in the grains, especially in large grains and a t higher temperatures. Probably the nodules are formed at cracks and holes inside the grains. Twin boundaries are quite common in Au-Ni alloys but appeared not to be preferred sites for nucleation. The author did not perform experiments to detect a possible orientationrelationship between the (Xi/(X2 phases and the matrix grains in which they were growing. K O S T E R and S C H N E I D E R (1937) took Debye-Scherrer photographs of a partly decomposed Au-70 a t . % Ni alloy. The reflections of the goldrich- and nickelrich phases were lines of continuous density. From this finding they concluded t h a t the
ixijocz phases were randomly oriented. FLANDERS and SCHOENING (1961) measured magnetic properties of partly decomposed monocrystals Au-24.8 a t . % Ni. They could interpret the magnetic torque curves by assuming t h a t the nickelrich particles were elongated in <111> matrix directions. The crystallographic orientation of the particles changed from randomness after short anneals to some alignment after long anneals. Laue and oscil-lation X-ray photographs showed t h a t an appreciable amount of the goldrich phase was oriented in relation to the parent crystal. The [100] direction of a goldrich crystallite was found to be parallel to any one of the <100> directions of the parent phase. The question whether the gold-rich crystallites were randomly rotated around this [100] direction could not be answered because of contradictory evidence obtained from different specimens. As to the nickelrich phase, on some photographs a very small amount of preferred orientation could be detected; it was, however, too faint to be interpreted. The authors explained these results by the difference in lattice parameters of the different phases. For a solid solution con-taining 25 a t . % Ni and for the resulting goldrich- and nickelrich phases (decomposition temperature 400° C) the lattice parameters are 3.968 A, 4.026 A and 3.530 A respectively. Hence it may be expected t h a t the nickelrich phase breaks away from the parent crystal very early in its development *) and t h a t the goldrich phase keeps a certain degree of orientation in relation to the parent phase.
In later experiments SCHOENING and FLANDERS (1962) were able to obtain nickelrich particles of about 300-1000 A in thickness and an average length to width ratio of two to three, by preferentially etching of a decomposed Au-24.8 a t . % Ni crystal (annealed a t 400° C). This result complicated the interpretation of previous measurements of mag-netic properties of a decomposed alloy, because several particles were larger t h a n the critical single domain size and are not only elongated b u t also plate-like shaped. The authors postponed the discussion of the
mag-*) This explanation is contradictory to the results of the magnetic measurements mentioned before.
14
netic results until not only the size and shape, but also the orientation of the precipitates had been observed directly by thin film experiments.
Low temperature precipitation
SIVERTSEN and W E R T (1959) reported an additional stage of precipi-tation, which was found to occur at relatively low temperatures for the Au-Ni system ( < 2 2 5 ° C ) . I t was completed in less than 1/10,000 of the time required for the main phase reaction. This was deduced from the change of the electrical resistance and the volume of quenched Au-30 a t . % Ni alloys which were annealed at temperatures < 225° C. A maximum in the resistance occurred after about 15 min at 150° C (r^ 2 min at 210° C). The final value of the resistance was lower than t h a t of quenched alloys. The variations were largest for specimens which were quenched from high temperatures.
If a specimen annealed at 150° C was further annealed at 315° C, the electrical resistance increased again, and regained the value of an as-quenched alloy. This process, called reversion, was thought to be caused by chemical or size instability at higher temperatures of structures formed at temperatures < 225° C. The authors suggested two possibilities for this low temperature precipitate: the one is t h a t vacancies retained upon quenching are rearranged at the annealing temperatures, the other is true clustering of atoms. However, if a specimen reversed at 315° C was further annealed at 150° C, re-precipitation occurred, although at a much slower rate. For this reason the low temperature precipitate seems more likely to be a clustering of atoms. The vacancies are only rate controlling the process.
GIBALA (1964) showed t h a t the relative magnitude and rate of precipi-tation decreased with increasing nickel content. For alloys with more t h a n 50 a t . % Ni the reaction was extremely slow.
SIVERTSEN and SUNDAHL (1961) studied the phenomenon by means of X-ray diffraction techniques. From these measurements the authors postulated t h a t excess quenched-in vacancies coagulate into platelets on the {111} planes; the vacancy clusters collapse and give rise to the for-mation of tetrahedral stackingfaults where nickel atoms tend to segregate. FuKANO (1961) observed low temperature precipitation in thin evaporated Au-20 a t . % Ni films. Upon ageing for 2 hours at 165° C satellite peaks appeared along (lOO) directions on the low angle side of the matrix diffraction spots. The satellites disappeared upon ageing at 250-300° C and were interpreted as due to a modulated pre-precipitation structure with a period of about 70 A in <100> directions.
K I M B A L L (1966) and (1969) re-examined the low temperature precipi-tation, to investigate whether the process could be described as spinodal decomposition. No conclusive evidence for or against spinodal decompo-sition was found. Most probably nickelrich precipitates are formed which are coherent with the matrix.
15
CAHN (1961) and (1962) has shown t h a t spinodal decomposition should be suppressed in a binary alloy system if the lattice parameter is not constant across the phase diagram. The author predicted the coherent spinodal suppression for the Au-Ni system to be of the order of 2000° C. GoLDiNG and Moss (1967) recalculated the coherent spinodal by using measured entropy and elastic data. According to these authors the coherent spinodal has a maximum for alloys of about 40 at. % Ni a t /-^ 0° C. This result is shown in fig. 1 together with experimental data of K I M B A L L (1969) and WOODILLA and AVERBACH (1968).
Thermodynamic properties
The large size difference between gold and nickel atoms causes con-siderable changes in the electronic orbitals on solid solution formation ( F L I N N , AVERBACH and COHEN (1954)). The net effect appears to be a "loosening" of the lattice as evidenced by the positive deviation of the lattice parameters from Vegard's law (ELLWOOD and BAGLEY (1951-52), D A Y (1961), and CRAWLEY and FABIAN (1966)). The activity coefficients of gold and nickel do not vary with composition in a simple manner. They show a large positive deviation from Raoult's law (SEIGLE, COHEN and AVERBACH (1952), D A Y and H U L T G R E N (1962), and SELLARS and MAAK (1966)). The entropy of mixing is much larger than the ideal one. The excess entropy is attributed to an increase in vibrational entropy resulting from the heat capacity of the alloys being larger t h a n the average heat capacity of the component metals. The positive enthalpies of mixing are thought to be due to the lattice distortion, resulting from size difference between the gold and nickel atoms. From this latter result one should expect, according to the quasi-chemical theory, t h a t there is in the solid solution region preference for like bonds (formation of nickelrich- and goldrich clusters). However, diffuse X-ray scattering, measured by F L I N N , AVERBACH and COHEN (1953) and (1954), offered evidence t h a t short range order, rather t h a n clustering exists in homogeneous Au-Ni alloys. The authors explained this result by assuming t h a t strain energy is less in the case of ordering t h a n in the case of clustering. MUNSTER and SAGBL (1958) repeated these measurements. They measured at much smaller angles (30' instead of 5°) and found tendency for like bonds in the solid solution (clustering!). These contradictory results lead NAGORSEN and AVERBACH (1961) to measure again the diffuse scattering at small angles. I t was now found t h a t the very pronounced small angle scattering was almost identical t o the scattering produced b y rolled foils of pure gold. Therefore these authors concluded t h a t the small angle scattering found with the alloys was not associated with atomic arrangements but with double Bragg reflections. Finally Moss (1966), measuring the profiles of (200) and (400) reflections of Au-40 a t . % Ni alloys quenched from the solid solution region to room temperature, concluded anew t h a t there seems to be preference for like bonds, although the author was not quite
16
sure t h a t no decomposition of the crystal had occurred during the quench. The problem whether clustering or ordering of atoms exists in the solid Au-Ni solutions is not unambigiously solved as yet. Therefore it is not possible (from these arguments) to say with certainty whether or not the quasi-chemical theory fails in the case of Au-Ni alloys.
Diffusion in the Au-Ni system
Measurements on the rate of selfdiffusion of gold in Au-Ni alloys were performed by K U R T Z , AVERBACH and COHEN (1955). The selfdiffusion of nickel in Au-Ni and interdiffusion in this system was measured by R E Y -NOLDS, AVERBACH and COHEN (1957). The selfdiffusion-coefficients Z)*, and Z)2„ exhibit a smoothly varying dependence on composition, without any anomalies due t o thermodynamic properties of the system and do not differ more t h a n a factor of 2 over most of the composition range. Hence, a pronounced Kirkendall effect should not be expected in the Au-Ni system.
The interdiffusion can be described readily by the Darken equation:
5=ta.i.;. + ....i>s,)(i + i i ^ ;
D = interdiffusion-coefficient D* = selfdiffusion-coefficient
/NI = activity-coefficient of nickel
^Ni = fraction of nickel in a Au-Ni alloy
The interdiffusion rate becomes quite low for alloy compositions of about 80 a t . % Ni. This must be caused by the thermodynamic factor:
' , d\n / N ]
) d In a^Ni
which becomes '~-'0.1 in this composition range. This points to a low driving force for interdiffusion.
CHATTBRJEE and FABIAN (1968) measured lattice and grain boundary diffusion of gold in nickel. Values of the activation energy Q and the pre-exponentional factor Do are:
Qi = 55 ±2 kcal/mole A , =0^02 ± 0.005 cm2/sec
^6 = 30 ± 5 kcal/mole Z)o(, = 3.0 ± 0.8 cm2/sec The activation energy for grain boundary diffusion is appreciably lower than for lattice diffusion. That means t h a t grain boundary diffusion is much larger t h a n volume diffusion (^-^ 10^ times at 600° C). The authors did not give any information about the crystallographic configuration of the grain boundary along which the diffusion was measured.
17
can be described by a discontinuous precipitation process but details of the precipitation kinetics are unknown. The "low temperature precipi-tation process" is not quite clear. Fluctuations in composition have been detected but it is not proved t h a t the process can be described by spinodal decomposition.
Diffusion experiments have shown a slow interdiffusion in the nickelrich alloys. Hardly any data are available on grain boundary diffusion. B. DISCONTINUOUS PRECIPITATION
I n the foregoing section, it was pointed out t h a t Au-Ni alloys show discontinuous precipitation phenomena above ' ^ 400° C but t h a t details of the process are unknown. In the following we will outline the most important features of discontinuous precipitation and suggest possible experiments to be carried out which may give more information about the precipitation kinetics in the Au-Ni system.
In a discontinuous precipitation process the homogeneous phase a decomposes into the equilibrium phases «i and «2 from the earliest stages of the process. The ai/a2 phases nucleate mostly a t grain boundaries (fig. 2) and form duplex structures of lamellar crystals (also called "cells"). During the precipitation process these ai/a2 cells grow into the matrix crystals by addition of atoms at the edges of the lamellar crystals. This process is governed by grain boundary diffusion along the boundary be-tween the cells and the matrix. Diffusion in the matrix ahead of the growing cells is negligible in most cases. Hence, the composition of the matrix grains remains constant until the grains are completely trans-formed into ociloc2 cells.
I n this respect discontinuous precipitation differs from continuous pre-cipitation. In the latter process isolated nuclei of the oc2 phase are formed a t grain boundaries or inside the matrix grains. These nuclei grow by addition of solute atoms by means of «o^Mme-diffusion. The matrix compo-sition changes gradually until all the solute atoms are drained. At t h a t moment the depleted matrix has become the equilibrium phase «i.
CHRISTIAN (1965) expects discontinuous precipitation to be important when nucleation is easy, either because of nearly matching structures, or because the supersaturation is large. In dilute solutions with appreciable surface energy between the phases, continuous precipitation is expected to be more important.
According to SMITH (1953), nucleation of (Xi/«2 cells a t grain boundaries may be explained in the following way (illustrated by fig. 4). Cell I nucleates a t grain B. The «i phase (depleted matrix) has the same crystal-lographic orientation of B. Cell I will grow into adjacent grain A and not a t an appreciable rate into B, due to the similar orientation of «i and matrix B. Only between the cell and matrix grain A a grain boundary is present which may act as a short circuit for diffusion. Similarly cell I I , nucleated a t grain A will grow only into grain B. So it seems as if the
18
Fig. 4. Nucleation of lamellar on/aa structures ("cells") at a grain boundary between two crystallites A and B (after SMITH (1953)). The -xi phase (depleted matrix) in cell I has the orientation of crystallite B, the on phase in cell I I t h a t
of crystallite A.
originally straight boundary between A and B becomes curved after pre-cipitation has started.
This process has been extensively studied for Pb-Sn alloys. Recently T u and T U R N B U L L (1969) described for this system the orientationrelation between the oci and «2 lamellae within a cell to be
[001]sn//[110]pb with (010)sn//(lll)pb
As the atomic (010) plane of the tin structure can be regarded as a slightly distorted close packed plane, the orientationrelation between the «1 and «2 phases is one in which the close packed planes and directions of the lead and tin structures are parallel. Occasionally a new tin grain nucleated at a growing edge of a lamella was observed by the authors to be in twin orientation relation with the original lamella.
In an earlier paper, T u and T U R N B U L L (1967) studied the formation of ai/«2 cells in oriented bicrystals of Pb-7 a t . % Sn. They found t h a t changing the tiltangle Ö of the bicrystal resulted in different growth rates of the cells, either growing into crystal A or B (fig. 4) in accordance with the description of the growth as given by SMITH (1953). If the tiltangle 0 (misorientation around <100) axis) was less t h a n 7°, the discontinuous precipitation was replaced by a continuous precipitation. Apparently the grain boundary can no longer support the cellular reaction if 0 is made too small.
Another important phenomenon concerns the spacing S between the lamellae. S appears to be large at low supersaturations and high temper-atures and small at high supersaturations and low tempertemper-atures. Further it appears t h a t in many cases the ai/«2 phases in the cells do not have
19
reached equilibrium composition. Apparently the segregation along the advancing cell-matrix boundary is incomplete. This was deduced from resistometric data (TURNBULL and T R E A F T I S (1955)), from repUca's (Liu and AARONSON (1968)), and from X-ray diffraction measurements (SPEICH (1968)).
Many theories have been proposed to obtain relations between the various quantities defining the process e.g. growth rate G, temperature T, grain boundary diffusion coefficient Z)», lamellar spacing 8, fraction of solute atoms actually precipitated Q, interfacial energy a between the «i/«2 lamellae and the supersaturation {xQ — Xg) of the alloys. CHRISTIAN
(1965) reviewing these theories remarked t h a t "the process is so complex and there are so many unspecified variables, t h a t it may be more in-formative to test experimentally measured growth rates, spacings and diffusion coefficients for self-consistency than to a t t e m p t to predict the growth rates and spacings from first principles". However, to get an im-pression of the difficulties encountered as well in theoretical descriptions, as in experiments to determine the important parameters, we will try to outline some aspects of the current theories. T U R N B U L L (1955) analysed the growth of «i/«2 lamellae in supersaturated Pb-Sn alloys. The author used an expression for the growth rate G derived by Z E N E R (1946) for the growth of pearlite nodulus:
... ^ Xo-Xe 2D
(') ^ = - ^ - ^ where G is the growth rate of the «1/1x2 lamellae, and XQ, Xe are (in the case of Pb-Sn) atomic fractions of tin in the supersaturated alloy and in the matrix of equilibrium composition respectively, Z) is a volume-diffusion coefficient and 8 the spacing between the lamellae. Equation (5) was derived by assuming t h a t the solute atoms reach the lamellae edges by volume diffusion. I t appeared t h a t a growth rate G ^ 10"^ cm/sec and a spacing 8 ^ lO"* cm would require a volume diffusion coefficient
Dv of about 10^10 cm^/sec a t 300° K, which is about 10* times larger t h a n
extrapolated values for Z)„. T U R N B U L L modified Eq. (5) by assuming t h a t the solute atoms drain preferentially along the cell-matrix boundary, according to SMITH (1953). In t h a t case:
(^) ^ = ^ T • ^ ^
where d is the thickness of the cell-matrix boundary (2-4 A), and D^ is a boundary diffusion coefficient. To account for the observed rate of cell growth: Db «» 10~^ to 10~' cm^/sec, which is the right order of magnitude for grain boundary diffusion a t 300° K.
Z E N E R (1946) proposed t h a t the spacing 8 will take on the value t h a t maximizes G. He showed t h a t the growth rate is a maximum when
one-20
half of the driving free energy is tied up in ai/«2 interfaces. From this result T U R N B U L L deduced the relation between 8 and the supersaturation ratio Xojxe to be
(7) S = ^"^
kT In (xo/Xe)
where a is interfacial energy, v is the volume of a tin atom and k is the Boltzmann constant. T U R N B U L L found his results only consistent with the
functional relation between the interlamellar spacing and supersaturation
ratio as predicted by Eq. (7). However, the values of 8 required to satisfy the equation quantitatively are about 100 times smaller t h a n observed. According to CAHN (1959) the discrepancy between experiment and theory is the result of confusing minimum spacing with minimum pre-cipitate thickness. The chemical potential Afi = RT In Xejxo (for dilute so-lutions) is related to the minimum permissible radius of curvature at the tip of the lamellae and hence related to the minimum precipitate thickness. I t is AFo (free energy change when one mole of alloy is decomposed into the equilibrium phases) which is related to the minimum spacing. For ideal solutions:
(8) AFo^NkTfxolog"^ + ( l _ ^ o ) l o g L - ^ \
If XQ — Xe<^Xe, AFo varies as (xo — Xg)^ whereas A/i varies as {xo — Xe). Correcting the results of T U R N B U L L (1955), CAHN (1959) found a dis-crepancy of 3 to 8 instead of 100 between measured and calculated spacings. CAHN (1959) refined the theory of discontinuous precipitation in an ap-preciable way. The essential part of his theory is t h a t if diffusion is limited to the advancing cell boundary, the lamellae of the cells cannot reach equilibrium composition at any non-zero growth rate. For this reason the growth rate of the cells can no longer be determined by the diffusion rates alone. I t is assumed t h a t the cell boundary moves with a velocity proportional to the net free energy decrease, taking into account the incompleteness of segregation as well as the creation of lamellae surfaces. The growth rate G is given by
(9) G=~'M-AF where AF is the net free energy change, M (the proportionality factor) is an average boundary mobility. If segregation is incomplete, only a fraction P oi AFo will be gained by precipitation; according to Z E N E R (1946) 2aVI8 is the dissipated energy into grain boundaries ( F = molar volume of the alloy), hence
21
If the lamellar spacing is so small t h a t all the possible free energy change is converted into surface energy, AF = 0 and G = 0. In t h a t case (P assumed to be 1) the minimum spacing is
As was mentioned before, according to Z E N E R (1946) maximum growth rate occurs if the spacing 8 is twice this minimum spacing So- If P < 1 the spacing will be correspondingly larger by 1/P.
Since the growth rate influences the degree of segregation, there are three unknowns G, P and 8 and only two equations (9) and (10). To solve this problem CAHN assumed t h a t the spacing which the system chooses is t h a t which maximizes the decrease in free energy AF. Because of Eq. (9) this is also the spacing which maximizes the growth rate G.
For his further calculations CAHN (1959) made the following simplifying assumptions:
1) the advancing boundary is plane (illustrated by fig. 5),
2) no diffusion occurs except in a boundary layer of thickness d\ the diffusion coefficient Db is independent of concentration and è is so small t h a t there is no concentration gradient across the thickness of the boundary layer,
3) the system has reached steady state i.e. the concentration in the advancing slab is stationary. The diffusion equation may then be written as
(12) Db-Ö-^ +G-{xo-x„) = 0
where a;o = matrix concentration, Xb and Xp are concentrations in the boundary and the «i lamella, Z is a distance along the boundary normal to the lamellae (see fig. 5)
Xb and Xp are functions of Z, which means t h a t the lamellae vary in
concentration across their thickness (indicated by region I in fig. 5), 4) Xb and Xp are related by some simple equation Xp = k-Xb ( i < l ) , 5) at the interface between the lamellae the (Xi/(X2 phases have equilibrium
concentration Xg,
6) the alloy of composition xo is considered to be only slightly super-saturated. In t h a t case the spacing 8x^ (width) can be neglected with respect to t h a t of the «i phase Soc^^.
With these assumptions CAHN derived Xp as function of Z. From this result an expression could be found for the fraction Q of the minor com-ponent precipitated:
(13) e=Atanh'-^
22 where
(14) k-G-8^
Db-d
This factor oc is t h e key parameter describing the precipitation process. For example, if a = 1 about 92 % of solute atoms is precipitated into «2 lamellae and 8 % is left in the xi lamellae. The latter p a r t of the solute atoms m a y reach the «2 platelets by volume diffusion, which means t h a t the platelets attain equilibrium concentration Xe (region I I in fig. 5) a certain time t (sec) after their formation. Because the cell-matrix boundary is advancing with G cm/sec, region I I (fig. 5) is located d cm behind t h e boundary, where d = G-t. If ZlPo can be assumed to vary with composition as (xo — Xe)^ the fraction P of zlPo realized due to incomplete segregation is
(15) t a n h matrix (XQ) A sech2 —-2 —-2 - ^ Z (Xo) db.l.
I /b I
Fig. 5. Cross section of a oci/aa lamellar structure as in fig. 2. a i = depleted matrix, «2 = precipitated solute atoms. 5r = growth direction of the <xija-i lamellae. d.b.l.= diffuse boimdary layer between the matrix and the lamellae. ó = thickness of the boxmdary layer. /S'=lamellar spacing (in the case of small supersaturation, the width of the «2 lamellae can be neglected with respect to t h a t of the on lamellae). .2 = distance along the boundary normal to the lamellae, xo, Xb, a;j, = concentration of solute atoms in the matrix, the boundary and the «i-lamella respectively. Xe=equilibrium concentration of solute atoms in the «i phase. / = concentration of solute atoms as function of Z in the xi lamellae close to the boundary layer due to grain boundary diffusion, / ƒ = concentration of solute atoms as function of .Z in the «i lamellae a t a distance d from the boundary. The concentration of solute atoms in this part of the «i lamella has reached the equilibrium value Xe
23
The fraction R oi AFo converted t o surface free energy due t o grain boundaries between the «i/«2 lamellae is
^^^^ ^=-S=-SAK
I t is derived by CAHN t h a t R is given also b ydP
(17)
R=-2a-y-d(x
R can have any value from 0 (infinite spacing) t o 0.49.
(P — R) is the fraction of zlPo available to exert pressure on the boundary, which leads to an expression for the growth rate
(18) G=-{P-R)-M-AFo To check Eq. (18) with experiments, CAHN used values of growth rates in the Au-Ni system measured by U N D E R W O O D (1954) (see fig. 3). Cell growth in this system is assumed t o be a low-mobility high-diffusivity extreme. I n this case (« being small) (P — R) is approximately constant and the growth rate will be proportional t o AFo or t o the square of the supersaturation. For example a t 700° C a growth rate of 100 A/sec is found for an alloy composition of 41.5 a t . % Ni (called xioo) and 500 A/sec for 49.75 a t . % Ni (called a;5oo). The equilibrium composition a t 700° C i s 33.25 a t . % Ni (xe). That means t h a t
a;5oo—a^e 16.5 _ a;ioo-a;e 8.25
which should be equal t o l/500/[^100 = 2.2, a rather good agreement. This can also be checked a t the nickelrich side of the phase diagram and a t different temperatures (see fig. 3). Values for (x5oo — Xe)l(xioo — Xe) are found:
4.1, 2.0, 2.6, 1.8, 3.3 and 3.0.
Although the pretty large scatter, CAHN assumed these values to be in accordance with predictions from Eq. (18).
A better check of Eq. (18) would be obtained if txijoiz cell growth is studied in bicrystals. The variation of growth rate, spacing and fraction precipitated can be measured as function of tiltangle 6 while AFo remains constant. Such experiments have been performed by Liu and AARONSON (1968) with Pb-Sn bicrystals. I t appeared t h a t values of boundary diffusi-vities could be obtained in reasonable agreement with tracer diffusion measurements. To this end G, 8 and Q were determined at several temper-atures and tiltangles. Data of the latter parameter were deduced from replica's. Values of R were ranging from 0.36-0.49 based on the experi-mental data and equation (17). From this result a much too high value
24
of a was calculated (--^ 2000 ergs/cm^). An independent determination of
R was made from the estimate t h a t a= 125 ergs/cm^ and Eq. (16), giving R fv 0.02. With such a small proportion of AFo being used for interfacial
energy, the basic assumption t h a t 8 is "chosen" so as to maximize AF seems most unlikely to be correct.
Also S P E I C H (1968) criticized CAHN'S theory, because growth rates of ai/a2 cells in the system Fe-Zn did not fit Eq. (9). S P E I C H could describe his results only by assuming t h a t the growth rate G is proportional to
(AF)^. With this assumption SPEICH obtained somewhat different equa-tions relating G, P , R, M and
ZlPo-Recently H I L L E R T (1969) pointed out t h a t TURNBULL (1955) and CAHN (1959) neglected to consider the force actually pulling the grain boundary. According to H I L L E R T this force can be described by
(19) P' = AFmlVm
where AFm is the net free energy decrease accompanying the decompo-sition and Vm is the molar volume of the new phase. To quote the author: "without this force, which has been overlooked in previous theories of discontinuous precipitation, this process may not be possible". Taking into account free energy losses due to diffusion inside the interface, and not neglecting the spacing (or width) of the «2 lamellae with respect to t h a t of the «i lamellae, H I L L E R T derived
(20) 8^, • ^°
T(Xü-Xef
T{Xo~Xe){Xoi2-Xe)
(22) G ^ {Xo-Xef.
Such a strong variation of the growth rate with supersaturation (Eq. (22)) seems not to be in agreement with data of growth rates in the Au-Ni system as were mentioned before (see also fig. 3).
Different sets of equations have been derived by PBTERMANN and HoRNBOGEN (1968), SHAPIRO and K I R K A L D Y (1968), and by AARONSON and L I U (1968). The agreement between the various theories is not large. However, the theoretical approach has made clear t h a t in order to describe discontinuous precipitation, data of several parameters defining the process must be known, e.g. growth rates, spacings (or width), amount of segre-gation (composition of the ai/a2 lamellae), interfacial energies and grain boundary diffusivities. Whereas the latter parameter depends very much on the type of grain boundary between the ai/a2 cells and the matrix, growth rates of differently oriented cells in one and the same specimen will not be the same.
25
In this thesis we have examined discontinuous precipitation reactions in the Au-Ni system by means of X-ray difiraction techniques and electron transmission microscopy, in order to get information about the growth and geometry of ai/a2 cells.
The Au-Ni system was chosen because it is one of the most simple systems and the matrix as well as both the ai/«2 product phases have the same crystallographic structure (face centered cubic).
From our measurements it could be deduced t h a t in Au-Ni monocrystals growth competition occurs between cells with a different growth rate. After a relatively short time only fast growing cells are growing into the matrix grains. The «i/«2 phases in these cells have a specific orientation with respect to the matrix, giving a cell-matrix boundary of high diffusivity. The ai/(X2 phases do not form plates as shown in fig. 2, but are growing as needles with a high length to width ratio. The spacing is very much dependent on the temperature, but is in all cases small, varying between 0.05-1 fx.
That means t h a t it will be very difficult to get information about the composition of the ai/a2 lamellae. An analytical technique has to be applied, for example micro-X-ray-analysis. However, the instruments at present available are not able to analyse details of 0.1-0.5 fx. We do not believe t h a t reliable data can be obtained from replica's (Liu and AARON-SON (1968)). Mostly the spacings of the lamellae are not very unique and the width of the lamellae cannot be determined accurately. The same criticism holds for the determination of the amount of segregation by means of resistometric techniques or X-ray diffraction. The former tech-nique is too indirect, the latter gives more information about the regions in which composition differences are reduced by volume diffusion (region I I in fig. 5), t h a n about regions near to the cell-matrix boundaries. Perhaps it is possible to obtain information on this point by micro-Kossel diffraction patterns.
As was mentioned in chapter I (introduction) we have investigated the suitability of thin evaporated films to study details of discontinuous precipitation phenomena. I t has turned out t h a t thin Au-Ni films are very sensitive to contamination. Discontinuous precipitation is observed only if extreme care is taken to keep the films free of impurities. Especially Au-50 a t . % Ni alloy films showed some peculiar phenomena due to carbon contamination: on the one hand, precipitation of nickelrich precipitates at temperatures above the solvus temperature of the pure Au-Ni system and on the other hand, a t lower temperatures continuous precipitation instead of a discontinuous mode of decomposition.
A comparison has been made with bulk Au-Ni alloys contaminated with carbon. I t appears t h a t carbon has a retarding influence on the discontinuous precipitation reaction and changes the growth kinetics of the ai/(X2 lamellae. To describe these phenomena quantitatively data must be known concerning the influence of carbon on grain boundary diffusion
26
and interfacial energies. The phenomenological descriptions given in this thesis m a y be a starting point to perform these experiments.
R E F E R E N C E S
AARONSON, H . I. and Y. C. Liu, Scripta Met. 2, 1 (1968). BORELIUS, G . , Ann. Physik. 28, 507 (1937).
CAHN, J . W., Acta Met. 7, 18 (1959), ibid. 9, 795 (1961), ibid. 10, 179 (1962). CHATTERJBE, A . and D. J . FABIAN, J . Inst. Metals 96, 186 (1968).
CHRISTIAN, J . W., Transformation in metals and alloys. Pergamon Press, London, 456 (1965).
CRAWLEY, A. F . and D. J . FABIAN, J . Inst. Metals 94, 39 (1966). DAY, G . F . , J . Inst. Metals 89, 296 (1961).
and R. HULTGREN, J . Phys. Chem. 66, 1532 (1962).
ELLWOOD, E . C . and K. Q. BAGLEY, J . Inst. Metals 80, 617 (1951-1952). FLANDERS, P . J . F . and F . R. L. SCHOENING, J . Appl. Phys. S 32, 344S (1961). F L I N N , P. A., B. L. AVERBACH and M. COHEN, Acta Met. 1, 664 (1953), ibid. 2,
92 (1954).
FuKANo, Y., J . Phys. Soc. Japan 16, 1195 (1961). GIBALA, R . , Trans. Met. Soc. AIME 230, 255 (1964). GoLDiNG, B . and S. C. Moss, Acta Met. 15, 1239 (1967).
HANSEN, M . , Constitution of binary alloys. McGraw-Hill Book Comp., Inc. 220 (1958). HILLERT, M . , The mechanism of phase transformations in crystalline solids, Inst.
Metals Monograph 33, 231 (1969).
KIMBALL, O . F . , Thesis, Northwestern University (1966).
and J . B . COHEN, Trans. Met. Soc. AIME 245, 661 (1969). KOSTER, W . and W. DANNÖHL, Z . Metallk. 28, 248 (1936).
and A. SCHNEIDER, Z . Metallk. 29, 103 (1937).
KURTZ, A. D., B. L. AVERBACH and M. COHEN, Acta Met. 3, 442 (1955). L I U , Y . C . and H. I. AARONSON, Acta Met. 15, 1343 (1968).
MOSS, 8., Local atomic arrangements studied by x-ray diffraction. J . B. COHEN and J . E. HILLIARD eds., Gordon and Breach Sci. Publ. New York 106 (1966).
MUNSTER, A. and K. SAGBL, Naturw. 45, 462 (1958).
NAGORSEN, G . and B. L. AVERBACH, J . Appl. Phys. 32, 688 (1961). PBTERMANN, J . and E. HORNBOGBN, Z . Metallk. 59, 814 (1968).
REYNOLDS, J . E., B. L. AVERBACH and M. COHEN, Acta Met. 5, 29 (1957). SCHOENING, F . R . L . and P . J . FLANDERS, Phil. Mag. 7, 1069 (1962). SEIGLE, L . L . , M . COHEN and B. L. AVERBACH, J. Metals 4, 1320 (1952). SELLARS, C . M . and F . MAAK, Trans. Met. Soc. AIME, 236, 457 (1966). SHAPIRO, J . M. and J . S. KIRKALDY, Acta Met. 16, 579 and 1239 (1968). SIVERTSEN, J . M. and C. W E R T , Acta Met. 7, 275 (1959).
and R. C. SUNDAHL, Acta Met. 9, 162 (1961). SMITH, C . S., Trans. A.S.M. 45, 533 (1953).
SPEICH, G . R . , Trans. Met. Soc. AIME, 242, 1359 (1968). Tu, K. N. and D. TURNBULL, Acta Met. 15, 1317 (1967)
, Acta Met. 17, 1263 (1969). TURNBULL, D . , Acta Met. 3, 55 (1955).
and H. N. TRBAFTIS, Acta Met. 3, 43 (1955). UNDERWOOD, E . E . , Thesis M.I.T. (1954).
WOODILLA, J . E. and B . L. AVBRBACH, Acta Met. 16, 255 (1968). ZBNBR, C , Trans. Am. Inst. Min. (Metall) Engrs. 167, 550 (1946).
CHAPTER 3
O R I E N T A T I O N R E L A T I O N S D U R I N G P R E C I P I T A T I O N I N A GOLD-NICKEL ALLOY i)
8umraary
On decomposition of a monocrystalline Au-40.4 a t . % Ni alloy at 608° C, it is found t h a t the goldrich phase (ai) and the nickelrich phase («2) are oriented in relation to the matrix according:
(110)[001]a,/«/(lll)[lIO]matrU which comprises in fact twelve different variants.
The «1 and «2 phases grow as duplex structures ("cells") in all the twelve orien-tations. In each particular cell, the ai and «a phases are parallel oriented. The lamellae seem to be elongated in <H1> directions of the matrix, which is a <110> direction of the orientation of the lamellae (in the above variant [110]).
From electronmicroscope images it is deduced t h a t the nickelrich phase consists of needles with a large length to width ratio ( > 20). Twin formation in the cells is assumed to be produced by internal stresses due to the precipitation process and is not an important mechanism for changing the growth direction of the cells.
§ 1. INTRODUCTION
If a supersaturated alloy decomposes into two phases «i and «2 by a discontinuous precipitation process, nuclei of the «i/a2 phases are formed, mostly at grainboundaries. The transformed regions of the ocijaz phases form duplex structm-es ("cells") of lamellar crystals of the ai and «2 phases. The cells grow hemispherically into the matrix grains. The compo-sition of the matrix does not change during the growth of the «1/1x2 lamellae.
The precipitation process is very rapid, due to diffusion shortcircuits formed by the cell-matrix boundary. Volume diffusion in the matrix ahead of the growing cells can be neglected in most cases.
The growth process of the (x\j(X2 regions is dependent on several factors, such as the diffusioncoefficient Dt along the cell-matrix boundary, the supersaturation of the alloy, the temperature, and the interfacial energy
a between the otijoiz lamellae. This dependence has been treated
theoreti-cally by several workers, for example TURNBULL (1955), CAHN (1959),
H I L L E R T (1969).
The Pb-Sn system is undoubtedly the best studied of all systems showing discontinuous precipitation reactions. Experiments have been carried out 1) The contents of this chapter were carried out in cooperation with C. DB GROOT.
28
with bicrystals, in order to study nucleation and growth of cells at differ-ent tiltboundaries (Tu and T U R N B U L L (1967), Liu and AARONSON (1968)).
I t was possible to measure the growth rate, the spacing between the «1 and «2 lamellae and the amount of segregation during the growth of the cells, as function of tiltangle, temperature and supersaturation ratio. Theoretical conclusions could be checked with the experimental data, but it appeared t h a t the agreement between theory and experiments was not satisfactory on all points. The theory has to be refined and at the same time experiments have to be set up to get more accurate data.
1600 1400 1 2 0 0
t
1000 U 8 00 0) D [? 600 0) CL E 4 0 0 ^ " " 0 20 40 60 80 100 Atomic per cent NickelFig. 1. Gold-Nickel phase diagram (HANSEN (1958)).
The Au-Ni system seems an attractive system for studying discontinuous precipitation phenomena. According to the phase diagram (fig. 1), gold and nickel are mutual soluble above 812° C. Below this temperature the matrix decomposes into two phases «i and <X2, which have the same crystal structure. Although it has been known for a long time t h a t Au-Ni alloys decompose by a discontinuous process at temperatures above 400° C
( K O S T E R and D A N N Ö H L (1936), U N D E R W O O D (1954)), not much details
concerning the way the process takes place, are given by these investi-gations. To obtain more information about the precipitation phenomena, we studied the formation of the (Xi/«2 phases in a Au-40.4 at. % Ni mono-crystal at about 600° C (actually 608° C).
29
K O S T E R and SCHNEIDER (1937) deduced from Debye-Scherrer X-ray photographs t h a t the ocijoct cells, which appeared to form at the surface of a decomposing Au-Ni monocrystal, were randomly nucleated.
To interpret magnetic measurements on partly decomposed Au-Ni monocrystals, F L A N D E R S and SCHOENING (1961) supposed the nickelrich particles of the (Xi/a2 cells to be elongated in <(111> matrix directions. X-ray measurements however, failed to establish a possible orientation of the ai/«2 cells in relation to the matrix. The [100] direction of a goldrich crystallite was found to be parallel to any one of the <(100) directions of the parent phase. The question whether the goldrich crystallites were randomly rotated around this [100] direction could not be answered. The reflections of the nickelrich phase were too weak to be interpreted.
By selective etching the decomposed Au-Ni crystal, SCHOENING and F L A N D E R S (1962) isolated elongated nickelrich particles, but it was im-possible to conclude from this experiment t h a t these particles were grown perpendicular to {111} matrix planes.
If ocifaz cells are randomly nucleated at the surface of a decomposing Au-Ni monocrystal, the resulting cell-matrix boundaries may be of all possible types: There can be boundaries with low diffusibility (such as low angle boundaries) and boundaries with a high diffusibility. During decomposition it is thus possible t h a t growth selection will occur between the different cells. At a later stage of the decomposition process only fast growing cells will transform the matrix.
If this were the case, one might expect t h a t it would result in a definite crystallographic relationship between these cells and the matrix. I t seemed of interest to us whether this is actually the case; and if possible to obtain more information about the boundary between the fast growing cells and the matrix.
Experimental results
§ 2. PREPARATION o r Au-Ni MONOCRYSTALS
The monocrystal we used in our experiment was a Au-40.4 a t . % Ni alloy (size about 5 mm. length and a diameter of 0.5 mm.). I t was prepared some years ago in this laboratory by H. L. M. P I J N E N B U R G in the following way. Gold and nickel were melted in an alumina crucible under argon atmosphere. Nickel (99.998 wt.%) was obtained from Johnson and Matthey Ltd. London; gold (99.9 w t . % ) from Drijfhout & Zn., Amsterdam. When the temperature of the melt was lowered to about 1100° C, an alumina-pipe (I.D. 0.5 mm.) was dipped into the melt, while the other side was connected to a vacuumchamber (pressure 600 Torr). By means of the vacuum a part of the Au-Ni melt was sucked into the pipe to a height of about 12 cm. A part of 10 cm. of the pipe was heated to 850° C, to avoid precipitation of the alloy. Details of the experimental arrangement are given in fig. 2.
30
Immediately after sucking, the pipe + alloy was quenched in water. The thinwalled pipe was removed by carefully breaking the thin alumina wall. The Au-Ni alloy was etched in aqua regia. At the upper end of the "wire" small crystals were formed; in the middle, single crystals were grown of 1-3 cm. length. Rotation photographs with CuKa radiation
Fig. 2. Apparatus (schematically) for making Au-Ni monocrystals. 1) Au-Ni melt, 2) alumina crucible, 3) graphite block, 4) high frequency coil, 5) alumina pipe (at one side connected to a vacuumchamber), 6) oven (850° C), 7) quartz tube,
8) inlet and outlet of purified argon.
showed a sharp resolution of the (422)Kai, ^oit doublet, at the calculated diffraction angle for an alloy of the composition 40.4 a t . % Ni. In the following experiments we used a crystal with <110> about 17° from the wire axis.
§ 3. ANNEALING OF THE CRYSTAL AT 608° C AND X - R A Y DIFFRACTION STUDIES
The monocrystal Au-40.4 a t . % Ni was annealed in a small vacuum-oven a t 608° C. Nucleation of the «i/a2 cells did not start all over the surface, unless the monocrystal was slightly rubbed with emery paper (400) before heat treatment. After 17j min. a t 608° C the (Xijoct cells were grown over a distance of about 140-150 ^ into the matrix (fig. 3). This corresponds to a growth rate of 1.4x10-* mm/sec, in agreement with the results obtained by U N D E R W O O D (1954).
Fig. 3. Partly decomposed Au-40.4 a t . % Ni monocrystal, after being heated 17 J min. at 608° C. In the center of the photograph the still untransformed matrix
is visible. Plane of cutting / (110) matrix.
Fig. 4. X-ray photograph of the partly decomposed specimen of fig. 3, after removal of 20 ,« of the surface. During exposure of the film, the specimen was not
Fig. 8. Details of the oii/a2 structure. Plane of cutting / (110) matrix. Indicated are original matrix directions.
Fig. 13. ( I l l ) and (200) reflections of a nearly monocrystalline Au-60 a t . % Ni alloy, on a Debye-Scherrer X-ray photograph. The specimen was rotated during
exposure of the film. a) homogeneous alloy.
b) partly decomposed alloy. The reflections of the «i and «a phases are of homo-geneous intensity.
a) bright field image (with 100 kV eloc- b) dark field image with (111)J^^: goldrich trons). phase bright on the photograph.
c) dark field image with ( l l l ) ^ ^ : nickel- d) electrondifïraction image, (indicesrefer rich lamellae bright on the photograph. to the «i/aa structure).
Fig. 9. Nickelrich and goldrich lamellae formed in a Au-40 a t . % Ni foil at 600° C. Plane of the specimen ~'(112).
(a)
(b)
a) bright field image b) electrondiffraction image
(Twa(j = twins of the «i phase TW(X3=twins of the -xa phase) c) stereographic projection
corre-sponding to b)
• • poles of the on/'xz lamellae A D poles of twins in the
gold-rieh phase.
Fig. 10. oiija2 lamellae formed in a Au-40 a t . % Ni alloy at 600° C. Twins are visible in the goldrich phase. The plane of the foil intersects the cell structure about 10 degrees off (110)cii/a2
31
X-ray diffraction of the specimen as such showed no, or only a very faint orientation of the oci and txz phases. Because of the limited pene-tration depth of the CUK„ radiation into a Au-40.4 a t . % Ni alloy, the X-ray diffraction pattern refers only t o the surface. I t is possible t h a t a t the surface nucleation of cells has been random, because the surface of the crystal was "damaged" by rubbing before heat treatment. In fact, already after about 10 ,« of the surface layer was removed by electro-chemical polishing i), an orientation of the «i and «2 phases was visible on the X-ray photograph. After removing another 10 /j. the photograph shown in fig. 4 was obtained. A marked orientation of the cxij<x2 phases can be deduced from the intensity maxima on the (111) and (200) re-flections of the goldrich («i) phase. The nickelrich («2) phase rere-flections are only very weak, but are on all photographs at the same positions on the Debye-Scherrer rings as the goldrich phase («i) reflections.
To improve resolution we measured the orientation of the «i phase in relation to the matrix, on a Siemens texture goniometer. In the an-nealed condition (fig. 3) no matrix reflections will be detectable on the X-ray pattern, or a t the texture goniometer, as the matrix is completely screened by the surrounding ai/a2 layer. Therefore we " m a r k e d " the specimen with a flat side (parallel to the wire axis) at one end when it was still in the homogeneous state.
Measuring the crystal orientation with respect to the flat side, it was possible t o correlate the «i/a2 orientations after the heat treatment with t h a t of the original matrix crystal.
Measurements of the (100), (111) and (110) pole densities of the gold-rich phase gave the results shown in fig. 5 in stereographic projection, in relation to the matrix.
Analysing the pole-figures, it appears t h a t the maxima in the densities of all the three poles lie close to the following relationship between the «1 phase and the matrix:
(110)j/(lll)matrlx and [001]«,//[lT0]„atrlx
This means twelve possible orientations. For example (110)(x,//(lll)matrix comprises three orientations with:
[001]^,//[lT0]™trix [001]J/[T01]niatrix and
[00l]„.//[0Tl]„,atrix
The same holds for the three remaining octahedral planes.
1) Composition of the electropolishing bath: 67.5 g potassium-cyanide, 15 g potaasium-sodium-tartrate, 15 gpotassium-ferrocyanide, 2.5 ml ammoniumhydroxide, 22.5 g phosphoric acid (solid) in 1000 ml water. Temp, of the bath 60° C. (MCTEGART (1959^).
a) (100) poles a) (100) poles
b) ( H I ) poles b) ( H I ) poles
c) (HO) poles c) (110) poles
Fig. 5. Pole densities of the goldrich Fig. 6. Stereographic projection of the phase. • • indicate the original matrix twelve variants of the goldrich phase orientation: (11 1)OT/plane of projection. (oti) orientation corresponding to (110) [ 0 0 1 ] « / ( 1 1 1 ) [ 1 T 0 ] T O . Matrix orientation ( l l l ) / p l a n e of projection.
33
The corresponding "theoretical" relationships are shown in the stereo-graphic projections fig. 6a, b and c.
Fig. 7a shows for (100) and (110) the superposition of experimental and the so called "theoretical" pole figures.
A somewhat better agreement between the pole charts and the stereo-graphic projection is found, when (650)(x, and (560)^^ are taken parallel to the {111} matrix planes. This means a tilt of ± 5 degrees with respect to (110)a,//(lll)matrix. Especially the correspondence between the (100) poles close to the equator of the projection becomes slightly better. This holds also for the "star-like" regions in the (110) projection (fig. 7b).
N O T E : I n comparing pole densities measured with the texture goniometer, with "theoretically" predicted pole figures, one has to keep in mind t h a t not all the predicted poles need to be present. One of the reasons is t h a t sometimes
re-a) (110)[001]«/(111)[1101
(560)a \ ^ ('^^'^>"»' together with [001]a/[H0]m.
Fig. 7. Comparison of the (100) and (110) pole densities with two possible orien-tationrelations between the goldrich phase and the matrix.
34
flections are screened by absorption of the specimen. Whether actually the relation :
[m>C S ^(^^i)'"^'--"' """"^ [ooi]«/[iTo]„aü-ix
is closer to the true orientationrelationship than the "simpler" relation mentioned before, we cannot say. To decide this, the reflections of the ai phase must be sharper than in our case. At the moment both orientationrelationships seem to be possible. Because they do not differ very much, we adhere in this paper to the relation:
(110)[001]«/(lll)[lT0]„»trlx
Because the nickelrich phase (aj) reflections were always parallel to the goldrich phase reflections, this orientationrelationship is also valid for the «2 phase.
§ 4. OPTICAL MICROSCOPY
The stereographic projection does not give any information about the dimensions and growth directions of the ai/a2 lamellae.
Cutting the partially decomposed Au-Ni crystal along a (110) matrix plane (that is almost perpendicular to the length direction of the specimen (fig. 3)), and etching with aqua regia, showed elongated ai/a2 lamellae lying more or less in <111> matrix directions (fig. 8; magnification was originally - ^ 3000 x ).
Following the same procedure the crystal was examined on a cut along a (111) matrix plane. In this case the lamellae were very short and hardly visible. From these findings one might conclude (although with a high degree of uncertainty) t h a t the lamellae are elongated in <111) matrix directions. This result is in accordance with the suggestion made by F L A N D E R S and SCHOENING (1961). When the particles have the shape of needles, or small platelets (SCHOENING and FLANDERS (1962)), with the length direction perpendicular to the ( H I ) matrix planes, only short lamellae will be visible on a specimen surface parallel to (111) matrix.
I n an effort to get information about a possible crystallographic charac-ter of the cell-matrix boundary, a number of cuts were made parallel to (110) matrix. Metallographic examination of the polished and etched surfaces gave the impression t h a t the ai/a2 cell-matrix boundaries cut the surface along <112) matrix directions. These can be intersections of the surface by {111} matrix planes. If this is true, the cell-matrix boundary is formed by {111} matrix planes and {110} ai/a2 planes. However the cell-matrix boundary intersections with a polished (110) matrix surface are very often without any particular direction, from which it must be concluded t h a t the boundary is probably of a crystallographic nature only on a very small scale.
§ 5. ELECTRON MICROSCOPY AND ELECTRON DIFFRACTION
Additional information about the ai/a2 lamellar structure can be ob-tained from electronmicroscope transmission images. Because the partly decomposed cylindrical Au-Ni monocrystal (diameter 0.5 mm.) did not have a very suitable shape to prepare thin foils, we cold-rolled a Au-40
35
a t . % Ni alloy to foils of a thickness of about 100 ^. Small disks (diameter 3 mm.) were made of the foils by means of a punching machine. The disks were homogenized by heating at 850° C in a vacuumoven during one hour and quenched to room temperature. After heating the disks 7J min. at 600° C and quenching to room temperature, the disks were electropolished. For this purpose we used a P.T.F.E. specimen holder described by D E W E Y and L E W I S (1963). The electrolytic solution (compo-sition see § 3) was circulated and directed to the disks by means of small stainless steel tubes, to avoid gas bubble formation on the specimen. Homogeneous alloys were easy to polish; partly decomposed alloys on the contrary polished in an uneven way. We did not succeed in polishing the oiiloc2 cells and the matrix at equal rate. When the lamellar ai/(X2 structure was polished to a suitable thickness, the adjacent matrix crystal was already dissolved. We could therefore obtain only information about the «i/a2 cell structure and not establish the orientationrelation of the cells with the matrix, or study the cell-matrix boundary.
I t is of course possible t h a t the cells observed in the thin foils are not the fast growing cells t h a t we observed in the interior of a Au-Ni mono-crystal. We do not expect however t h a t the cell structures will be very much different.
A typical example of the ai/a2 cell structure in the decomposed foils can be seen in the photographs of fig. 9. From the electrondiffraction pattern fig. 9d it is clear t h a t the «i and «2 phases are crystallographically parallel oriented: Every reflection due to the goldrich (ai) phase is ac-companied by a reflection of the nickelrich («2) phase with the same Miller indices.
Dimensions and boundaries of the «i/a2 lamellae
The lamellae appear to be very long compared to their thickness. On fig. 9 nickelrich lamellae can be seen of about 2 fi, with a thickness of 300-500 A.
The length direction of the lamellae is < 110), in accordance with findings from optical microscopy of a decomposed monocrystal (§ 4) (elongation of lamellea in < n i ) matrix corresponds to <110) of the«i/a2 cell orientation).
Sometimes a length direction <112> is found (fig. 10). We do not know whether these <112) lamellae belong to the fast growing cells of which the orientationrelation with the matrix was analysed in the monocrystal (§ 3). Also these lamellae have a length of more than 2 ^ .
If 'the foil intersects the cell in such a way t h a t the <110) or <(112> directions of the lamellae do not lie in the plane of the foil, the length of the lamellae diminishes rapidly with the intersection angle. For example the nickelrich lamellae in fig. 10 are only about 0.5 fi in length; the foil intersects the lamellae at an angle of about 10° with < n 2 > . We conclude from this and many other photographs t h a t the nickelrich lamellae have a needle-like shape. The needles (with length direction (110> or <112>
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of the ai/a2 cell orientation) are more or less embedded at random in the goldrich phase. The length of the lamellae is mostly >2 [i. The cross dimensions are about 300-1000 A.
I t is difficult to analyse the nature of the boundaries between the «i and (X2 phases from electron transmission images; on the one hand because the thickness of the foils is not uniform and on the other hand because it cannot be concluded from electron diffraction patterns what is exactly the intersection angle of the foil with the «i/«2 cell structure. When the boundaries between the a i and «2 phases appear to be sharp on the transmission images, one might conclude t h a t the boundary is perpen-dicular to the surface of the foil. If fringes are seen along the boundary, one must analyse the inclination of the boundary with respect to the foil surface, from the width of the fringe region and the estimated thickness of the foil (mostly not more than about 700 A if images can be made of the goldrich alloys). However fringes can change in appearance due to change in foil thickness, or by a change in the intersection of the cell with the plane of the foil. For example the nickelrich lamellae (fig. 9b) show sharp boundaries (probably {111} planes) and boundaries with fringes (see arrows). If we estimate the foil thickness to be 500-700 A and the width of the fringe region about 350 A, the boundary is inclined 35°-27° to the surface of the foil. The boundary can be of the type {110}. Occasionally an intersection has been made nearly perpendicular to the length direction of the lamellae, from which it could be analysed t h a t also {100} boundaries are formed. Therefore we have the impression t h a t the boundaries between the «i and 1x2 phases prefer planes of the type { H I } , {110}, and {100}. Some possible shapes of the nickelrich lamellae are drawn in fig. 11. In fig. 11a, a (111) matrix is thought to be parallel to the plane of drawing and parallel to a (110) (Xijoa plane (although this need not to be the actual cell-matrix boundary (§ 4)), together with [001]a,/a2/y[110]ni. In fig. l i b the nickelrich needles are drawn in perspective view.
8pacings of the ai/(X2 lamellae
The spacing between the goldrich- and nickelrich lamellae is not very constant, even on one and the same photograph (fig. 9c). This seems to be caused mainly by the fact t h a t the nickelrich lamellae are not regularly spaced in the goldrich phase. The spacing of the goldrich phase /S^^ was estimated to be about 1700-2000 A. The width of the nickelrich phase
8^^ cannot be neglected in this case of a Au-40 at. % Ni alloy which was
decomposed at 600° C. An appreciable amount of the nickelrich phase is formed. The width, or spacing of the nickelrich phase 8,^^ is about 300-400 A.
The spacings are very sensitive to a change in the decomposition temper-a t u r e : temper-at 500° C: 8^^ is ~ 550 A temper-and S„, ~ 150 A.
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Fig. 11. Possible configurations of nickelrich phase needles in an orientation related to the matrix: (110)[001](x,/aj/'(lll)[110]m. Planes indicated by the numbers are (llO)^^,. Needles 1-6 belong to only one variant of the orientationrelation. a) nickelrich needles with [110] perpendicular to (111) matrix. The plane of drawing
is parallel to (111) matrix.
b) nickelrich needles in perspective view.
Composition of the /xijoct lamellae
A very important factor in the theory of discontinuous precipitation
(CAHN (1959), H I L L E R T (1969)) is the fraction of the solute atoms which is actually precipitated. If the segregation of the solute atoms during growth of the oci/at lamellae by grainboundary diffusion is not complete, the «1 phase will not have reached equilibrium composition. Afterwards segregation can be made complete only by volume diffusion in the ai/a2 cell.
In this connection it is interesting to analyse whether the goldrich phase (fig. 9b and 9d) has reached equilibrium composition. If we assume t h a t the nickelrich phase (the minor component) has reached equilibrium composition (about 95 at. % Ni a t 600° C) as given by the phase diagram (fig. 1), we can calculate the composition of the goldrich phase from the diffraction pattern (fig. 9d). For the calculation given in the tables 1 and 2, use was made of the relation:
where 2 L-X = D(HIiL)-d(HKL)
i n e f f e c t i v e distance of the specimen to the film (mm.)
