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I - o U1 o O O" O" Nheterogeneous nucleation in
magnesium-zinc alloys
BIBLIOTHEEK TU Delft P 1952 7166 651150heterogeneous nucleation in
magnesium-zinc alloys
PROEFSCHRIFT
ter verkrijging van de graad van doctor in de technische wetenschappen aan de Teclmische Hogeschool Delft, op gezag van de rector mag-nificus Prof.dr.ir. H. van BekkuJii, voor een commissie aangewezen door het college van dekanen, te verdedigen op dinsdag 4 mei 197b te 14.00 uur
door
Jacobus van Liere
metaalkundig ingenicur geboren te Borssele
Academic Service - Den Haag ^^,^^"\
1976 _ | ( ^ (
Prof. dr. ir. B. Okkerse Prof. dr. ir. F.J. Kievits
kan
z i j n p i o e t s c h r i f t . Voor dt expcriiiicntcle Iiulp lu i h e t verv tardigen en onderzoeken van de legei mgen worden met n>ime II. M e i n i a n , L . ^ . J . van \ e l z e n , T h . J . van \ e l z e n en d i . i i . LI. Uemei genoeiitd, De t h e o r e t i s c h e beschouwingen en beiekeningen in hoofdstuk 5 zouden onjiiogelijk z i j n geweest zonder de h u l p v in i i . 1. katgeniian. lie stimulerende d i s c u s s i c s van onze gez.uiielnke a i b e i d met d r . I). Kuivbv\ijk en p i o t . d r . i i . J.A. Steketee \vab voor ons een g r o t e s t e u n . De verzoigmg \ a n t o t o ' s ,
f i g u r e n , typeuerk en l a y - o u t was in de u i t s t e k e n d e handen van J.L.M. J a c o b s e , L). van S l m g e r l a n d en mevr. L, l i k e n a a r . Voor de k o r r e k t i e van de Kngelse t e k s t dank ik mevr. l.achters voor de zorg en tocwijding waaniiee ze zich \ a n h a a r taak gekvveten h e e l t . IJe gczamclijke inspanning r e s u l t e e r d e in d i t p r o e f s c h r i f t waarin z i j , welke m e t met n.uiie z i j n gcnoemd, door mij in gedachten worden gememoreerd.
i)it p r o e f s c h r i f t kw iiii mede t o t stand door g e l d e l i j k e s t e u n van de s t i c h t i n g Z.h.O. welke een s t u d i e i e i s naai U n i v e i s i t e i t e n in tanada en de \crenigde S t a t e n mogelijk maakte.
contents
1 Introduction
A review of literature
2.1 The magnesium-zinc equilibrium diagram 3 2.2 The aging sequence in magnesium-zinc alloys 7 2.3 Heterogeneous nucleation sites for the g' phase 14
2.4 Nucleation on dislocations 19
2.5 Literature 24
Experimental 28
3.1 Alloy composition and specimen preparation 28 3.2 The production and shearing of single crystals 31
3.3 Analyses of the nucleation phenomena 38
3.4 Literature 41
Experimental results 42
4.1 Quenching from different atmospheres 42 4.2 Precipitation of B' on (0001)<1120> dislocations 47
4.3 Precipitation of B' on {10Tl}<1120> dislocations 52 4.4 Precipitation of 6' on {10T0}<1120> dislocations 53 4.5 Precipitation of 6' on {1122}<1123> dislocations 55
4.6 Precipitation on jogged dislocations 59 4.7 Heterogeneous precipitation just below the
solubility line 63 4.8 The effect of quenching or deformation on the
kinetics of aging 64 4.9 Literature . 66
5.1 Introduction 67 5.2 The effect of the pre-selected shape 68
5.3 The strain energy of an incoherent ellipsoidal
nucleus 75 5.4 The interaction energy of an incoherent
ellip-soidal nucleus on a screw dislocation 77
5.5 Results and discussion 82
5.6 Literature 88
Discussion of the results 89
6.1 Ouenching from different atmospheres 89
6.2 Nucleation on dislocations 92 6.3 Some final considerations 103
6.4 Literature 106
Samenvatting 107
Summary 110
List of symbols 113
1
1 introduction
Magnesium-based magnesium-zinc alloys are used commercially in various fields. In the aeronautics field they are used for helicop-ter skins, undercarriage legs, floorings etc. They are also employed in the manufacture of military equipment and for several other ap-plications for which a medium strength or high strength to weight alloy is required. The alloys used can be divided into cast and
wrought alloys. Cast alloys in cuirent use contain 5 or 61 zinc,
wrought alloys in current use contain 1 , 3 or 6°6 zinc. In most cases 0.5°6 zirconium is added for grain refinement.
In alloys containing more than 31 zinc precipitation hardening is the most important strengthening mechanism. The improvement of mechanical properties by precipitation hardening is attributed to the Precipitation of an intermetallic phase B'- This phase is not the equilibrium phase but a transition phase with the structure and properties of the Laves phase MgZn^. The shape and orientation of this phase have been the object of several studies.
Important parameters in the precipitation hardening process are the volume fraction and the density and distribution of the hardening precipitates. It is known that during deformation the slip disloca-tions bow between the hardening precipitates instead of shearing them. This means that the average inter-particle spacing is a par-ticularly important parameter. Is has been observed that the inter-particle spacing is influenced by heterogeneous nucleation of the hardening precipitate, according to the type, number and distribu-tion of the heterogeneous nucleadistribu-tion sites.
In this thesis the heterogeneous nucleation of the hardening phase on dislocations is investigated. As the hardening phase occurs in two different shapes with different orientations with respect to the matrix, this aspect is treated first. It is seen in the wider context of the precipitation sequence.
X Unless otherwise stated alt aonaentrations are expressed in
2
A review of possible nucleation sites is given and the nucleation on dislocations is discussed. After a description of the experimen-tal procedure the results are presented. In an attempt to under-stand the results more quantitatively a model was developed which sheds some light on the main factors of heterogeneous nucleation. The model is not able to explain all experimental results, but it does contribute to a better qualitative understanding of the parameters which play an important role in the nucleation process. The thesis is concluded by a discussion of results.
2 a review of literature
This chapter contains a review of relevant literature. First several versions of the equilibrium diagram are presented. The pre-cipitation sequence is then described in detail and the conflicting results obtained by different authors are discussed. A^ter conclu-ding that the hardening phase nucleates also heterogenecmsly, the possible nucleation sites are considered. The chapter ends with a review of several theories on heterogeneous nucleation.
2.1 T h e n a g n e s i u m - z i n c equilibrium d i a g r a m
Magnesium and zinc are both hexagonal metals. The solid solu-bility both of zinc in magnesium and of magnesium in zinc is limited, however. One of the reasons for the limited solubility is the dif-ference in atomic size (approx. 15°o). The solid solubility of zinc in magnesium as shown in ligure 2.1 is based on the X-ray data given by Schmid and Seliger (1932) and Park and Wyman (1957). The data for the solidus line are from Park and Wyman.
600 500 400 300 200 100 y /
./ /
/ /
/ /
/ 7
/ /
/
; • :x^^^
x^^
/-r^^^^^''^
weight per ee 40 6 0 1 K , , , 1 1 , , nt zinc eo , 1Figure 2.1 The solid solubility of zinc in magnesium, based on X-ray data of Schmid and Seliger
(x) (1932) and of Park and Wyman (o) (1957) .
02 04 06 OB 10 12 U 16 IB 20 22 24 26 26 3%
4
The central region of the equilibrium diagram is rather com-plex owing to the occurrence of an intermetallic compound MgyZn,, which is only stable in a small temperature interval. Below approx. 300 C eutectoidic decomposition of Mg^Zn.. occurs. According to Laves (1939) and Koster (19S0) this decomposition can be described as
Mg^Zn^ ^ a(Mg) + Mg2Zn2,
whereas according to Anderko (1957) it can be described as
r4gyZn, •+ a(Mg) + MgZn.
This decomposition is important since it leads to an equilibrium diagram in which the magnesium solid solution is either in equili-brium with MgjiZn, or with MgZn. Raynor (1959) assumes that MgZn is also unstable at lower temperatures, giving rise to eutectoidic decomposition at 290 C
MgZn -> a(Mg) + Mg^Zn,.
At least four different versions of the central region of the equilibrium diagram can be found. The most important versions are shown schematically in Figure 2.2. In our opinion Raynor's version is the most appropriate for reasons to be discussed later (Section 2.2)
The difficulty in determining the correct equilibrium diagram arises from the large number of nearly equal lattice spacings deter-mined by X-ray diffraction analysis of the phases Mg^Zn,, MgZn and Mg^Zn,. The lattice spacings of the last two phases, as determined by different authors, are shown in Table 2.1.
The reflections which make it possible to distinguish between MgZn and Mg_Zn_ are all very weak. Strong reflections corresponding to a spacing such as 2.23 A are found in both inter-metallics.
5
Table 2.1: The lattice spacings of MgZn and Mg Zn as determined by different authors. Lattice spacings below 4 A corresponding to weak reflections and lattice spacings below 2 A are not shown.
Anderko 1957 0 * d(A) I* 12.42 m 7.54 mw 7.30 m 5.97 w 4.97 w 4.78 vw 4.32 mw 4.22 ms 4.01 w 2.45 ms 2.39 s 2.33 ms 2.23 vs 2.16 m 2.05 s MgZn Clark 0
d(A)
12.9 7.5 6.4 6.0 5.0 4.85 4.40 4.28 4.07 2.47 2.34 2.31 2.25 2.23 2.16 2.05 and Rhines 1957VI,
43 438
25 20 13 13 50 13 31 63 63 100 38 43 50 Anderko 1957d(X)
4.76 4.59 4.26 4.14 4.01 2.47 2.33:
2.23 2.20 2.18 I*w
mww
m
vw ms ms ms s ms Mg ,Zn. Clark and 0 d(A) 15 13.0 10.9 6.3 5.4 5.2 4.90 4.73 4.69 4.38 4.23 4.09 3.99 2.50 2.36 .2.35 2.25 2.23 2.20 2.16 1957 Rliinesi / i ,
6 6 64
4 4 25 50 50 38 75 256
63 75 75 75 100 100 75 Gallot 1966 0 d(A) 14 12.86 10.65 7.02 6.79 6.46 6.34 5.32 5.15 4.89 4.70 4.66 4.40 4.33 4.29 4.23 4.10 4.00 X visually estimated6
Q. E *- 290 E330: ^
Mg Mg7Zn3 L a v e s ( 1 9 3 9 ) MgZn p Z n Mg2Zn3 MgZn2 Mg Mg7Zn3 K o s t e r (1950) MgZn p-Zn Mg2Zn3 MgZn2 -340 290 Mg Mg7Zn3 MgZn ^ Zn Mg MgYZn3 MgZn | — Z n Anderko (1957) ^^^MgZnz I ^ > ^ ° ^ ^^^^^^ ^^^M?Zn2Figure 2.2 Four versions of the magnesium side of the Mg-Zn equilibrium diagram.
a) Laves (1939) b) Koster (1950) c) Anderko (1957) d) Raynor (1959)
The structure of the MgZn phase was determined by Tarschisch (1933) as hexagonal with a = 5.33 A and c = 17.6 A , but his results have since been criticized by various authors. This ambiguity has no consequences for this thesis.
The structure of the '^IgZn, phase is well known. ^IgZn, has a
7
The unit cell contains four molecules with atoms at the following positions (Figure 2.3):
,, .1 2 , ,2 1 -. ,2 1 1 , ,1 2 1 .
Mg (3,3,v),(3,3,v),(3,3,2 - V),(3,3,2 - v)
Zn^^^ (0,0,0),(0,0,1)
1 _ _ ' _ _ _ _
^"(b) •^"'^"'4^' (2u,u,^), (u,u,-^-), (u,2u,^), (2u,u,^), (u,u,^),
U = - 0.170 V :: 0.062
Figure 2.3 The MgZn unit cell; the positions of the magnesium and zinc atoms are indicated by open and closed circles respectively.
o
Mg•
ZnThe structure of the Mg^Zn, phase was determined by Gallot ^ -" o o (1970) as triclinic with parameters a = 13.18 A, b = 14.51 A,
c = 5.25 A, a = 97.17°, B = 95.68° and y = 76.79°.
2.2 T h e a g i n g s e q u e n c e i n m a g n e s i u m - z i n c a l l o y s
The aging sequence in t h e magnesium-zinc system appears t o be r a t h e r complex. There i s much confusion i n t h e l i t e r a t u r e , e s -n e c i a l l y with regard t o G.P. zo-ne formatio-n a-nd t h e formatio-n of t h e e a u i l i b r i u m p h a s e . A review of t h e p r e c i p i t a t i o n sequences p r o -Dosed by d i f f e r e n t a u t h o r s i s given in Table 2 . 2 .
Table 2,2 The precipitation sequence in Mg-Zn alloys. Presence, shape and orientation are indicated.
Year Authors
1959 Sturkey and Clark 1)
G.P. zone formation Intermediate phase
6, (MgZn2) Equilibrium Phase S (MgZn) 1962 Murakami 2) G.P. plate_ //{1010} ne edle 1966 Gallot 3)
1971 Mima and Tanaka 4) G.P.
plate //{lOTi} B' (MgZn2) needle [1120]e!//[0001]Mg [0001]B^//<n20>Mg S, (MgZn2) needle B; (MgZn2) plate (0001)By/(0001)Mg [1120]By/[10T0]Mg B (Mg2Zn3) conpressed needles [001]6//[0001]Mg or [001]B//<0lT0>Mg and [100:B//<4229>Mg B (MgZn) plate 1973 Takahashi 5) 1) 21 •il 4) '•^ i l l o y T l l o y l l l o > I l l o y T l l O \ MR-Zn Mg-Zn M6-Zn Mg-Zn Mg-Zn S aged between S aged between 6 aged between •1 aged between 4 aged between 149 70 50 60 Rr -260°C 170°C 2™"C 200"C 140°( G.P.I plate //{1120} G.P.II oblate spheroid on (0001) u&pd B] (MgZn2) n e e d l e i2n]B;//[oogi]Mg inn %f)lc lf!.'hniquci elci-tron diffrdction
Liiic-tcthnique, electron miLrostopy Various X-ray diffraction techniques tTlorimetru measurements, Dchye-Sherrer sm.iI 1-anglc X-nv stattcrinj;
"00011 B]//<1120>Mg
B'2 (>igZn2)
n e e d l e
9
G.P. zone formationThe first author i\fho claimed to have detected G.P. zones was Murakami (1962). Using Laue X-ray diffraction of single crystals he showed that age hardening in the temperature range of 70-100 C is caused by the formation of G.P. zones on {1010} planes. In 1965 Clark suggested that differences in response to age hardening at 70-100 C compared with aging at 149 C should be attributed to G.P. zone formation. These G.P. zones could not be resolved by transmis-sion electron microscopy and could not be detected by electron dif-fraction. Gallot (1966), using several X-ray diffraction techniques on Mg-Zn 6 single crystals, found no indication of G.P. zone forma-tion. Streaks observed after aging at temperatures between 50 C and 250 C were attributed to the intermediate phase B' instead of to G.P. zone formation. These streaks always occurcd simultaneously with the B' spots, even after aging at 50 C. Consequently Gallot attributed them to B'. Mima and Tanaka (1971) reported that in single crystals of Mg-Zn 4 aged at 70°C plate-like G.P. zones were formed on the {1011} planes. Direct confirmation of G.P. zones by electron microscopic observations was not obtained, however. The presence of G.P. zones was postulated on the basis of calorimetric measurements. Absorption of heat was observed prior to the evolution of heat due to the precipitation of the transition phase 6'. In addition to G.P. zone formation a pre-B' phase was postulated from the same measure-ments. These authors did not indicate any crystallographic
diffe-rences between the G.P. zones and the pre-6' phase. At 60°C and below they assumed the presence of G.P. zones of different shapes. Takahashi (1973) also adopted this view. By means of small-angle X-ray scattering he postulated two types of G.P. zones: a plate-shaped G.P. zone (G.P.I) parallel to {1120} Mg at temperatures below 60 C and an oblate spheroid (G.P.2) on the basal plane of the matrix at temperatures betvi/een 60 C and 80°C.
10
The intermed.iate phase B'
In contrast to the confusion associated with the detection of G.P. zones, there is much more agreement concerning the intermediate phase. Sturkey and Clark (1959) concluded from electron diffraction patterns that the intermediate phase has the composition and struc-ture of the Laves phase .MgZn^. The needle shape of this phase was first determined by Murakami (1962) and later confirmed by Clark (1965). Gallot (1964) carefully examined Mg-Zn 6 single crystals by employing the Weissenberg teclinique and using Mo-Ka radiation. He confirmed the results which Sturkey and Clark obtained from electron diffraction. All spots situated on streaks through (OOOt) Mg could be indexed as spots of the intermediate phase B' (MgZn^) with
lat-9 o
tice parameters a = 5.20 A and c = 8.57 A. The orientation relation
was * —
[1120] B' // [0001] Mg [0001] B' // <1120> Mg.
This means that there are in fact three families of B' precipitates. The needles are all parallel to [0001] Mg and thus perpendicular to the basal plane. A (1010) Mg reciprocal lattice plane, deduced from Gallot's orientations, is shoisn in Figure 2.4 together with a diffrac-tion pattern of a crystal in the corresponding orientadiffrac-tion. The posi-tions and spacings of the diffraction spots measured from optically scanned diffraction patterns are in reasonable agreement with Gallot's observations.
The 6' phase is needle-shaped and Clark (1965) measured length to width ratios of up to forty. The unusual length of the B' needles was rationalized on the basis of differences in growth rate of the interface in different directions in the matrix. The a-axis of B' grows parallel to the c-axis of the magnesium matrix. Since the spacings along the a-axis of B' closely match the c-axis of the alloy matrix, the B' /matrix interface in that direction is assumed to be a well-ordered dislocation boundary. Thus during the early stages of precipitation B' adopts the form of a needle, after which the point effect of diffusion at the tip of the needle promotes continued lengthening.
Figure 2.4 A(iolo) Mg reciprocal lattice plane deduced from
Gallot's orientation relationship for the B' needle in
magnesium-zinc alloys. The diffraction pattern with the corresponding zone-axis was taken from a Mg-Zn 3.5 alloy aged at 180°C for 70 hours.
12
In a later publication Gallot (1965) reported the appearance of diffraction spots between the magnesium (OOOt) layers after longer aging times. Again these spots had to be indexed as B'
(MgZn^), however this B' phase had a different orientation and shape. Gallot found
(0001) 6' // (0001) Mg
[1120] B' // [inTO] Mg.
The shape of the particles of this phase, determined from electron micrographs, was plate-like. The plates were parallel to the basal plane. Gallot called the needle shape of B' the B^ phase and the plate shape of B' the Bo phase.
The matrix and BA precipitate both have hexagonal lattices and a common [0001] zone axis. The overlapping lattices with dif-ferent lattice spacings give rise to Moire fringes which can best be observed in foils with approx. [0001] zone axis and a strong {1oTo}reflection operating. This is sho\\m in Figure 2.5.
Figure 2.5 Bp precipitates showing Moire fringes due to the overlapping lattices of matrix and precipitate.
The Moire fringes have spacings of approx. 40 A, corresponding to (1010),
Mg 2.78 A and d^;
(1120) 2.60 A, which is in agreement with
Gal lot's results.
Mima and Tanaka (1970) observed the same plate-shaped phase but they assumed that this was the equilibrium precipitate MgZn.
Takahashi (1973) confirmed that different shapes of the intermediate phase occur during aging. From X-ray diffraction patterns he deduced that the BA phase is needle-shaped, the needle being perpendicular to the {1010} planes. We could not confirm this observation.
The equilibrium phase S
For certain technical applications the composition, shape, orientation, etc. of the equilibrium phase are less important, especially as far as the mechanical properties are concerned. From the theoretical point of view it is interesting to consider the complete sequence. The composition of the equilibrium phase, ds found by various authors, is either MgZn or Mg^Zn,. The most extensive investigation was described by Gallot (1£66). Gallot defined two families of 6 precipitates (Mg^Zn,) with different shapes and different orientation relations with regard to the matrix.
The first family of 6, causing the appearance of diffraction spots in the (OOOt) reciprocal lattice planes, consists of thick rods parallel to [0001] Mg, with
o The spacing of (0001) Mg and (001) B is almost equal (5.2 A ) .
The second family of B precipitates causes the appearance of diffraction spots in three families of reciprocal lattice planes which are parallel to the directions <1120> Mg and [0001] Mg. Some of these precipitates are rod-shaped, but the rods arc more compressed. Finally the rods become plate-shaped. Ihe orientation relationships found were
[001] B // •-OlTO> Mg and probably
[100] B // <4229> Mg.
Summarizing this review of literature it can be concluded that the different authors are at variance with each other concerning the presence, shape and orientation of the G.P. zones. The authors who
'observed' G.P. zones differ as to the orientation of the zones and their shape.
The occurence of two different shapes of an intermediate phase in one alloy is quite remarkable. The results obtained by Gallot appear to be reliable as far as the orientation relations and the morphology are concerned.
The most extensive investigation into the composition, orien-tation and shape of the equilibrium phase is also by Gallot. The results which he obtained are most convincing and confirm Raynor's version (Section 2.1) of the equilibrium diagram at relatively low temperatures.
2.3 H e t e r o g e n e o u s n u c l e a t i o n sites for t h e B' phase
Tlie hardening phase is sl, the needle-shaped precipitates
being perpendicular to the basal plane. Fully hardened alloys con-tain predominantly 6' and occasionally B, and B precipitates (Chun and Byrne 1969; van Liere 1970). In the overaged condition the number of B precipitates increases and the number of Bl and B^ precipitates decreases.
15
This means that the strength of magnesium-zinc alloys is mainly
dependent on the dispersion of B\- As is the case with most
transi-tion phases B' nucleates in preference heterogeneously and conse-quently the dispersion of B, is a function of the number of hete-rogeneous nucleation sites. Both Clark (1965) and Gallot (1966) mention dislocations as nucleation sites for the B] needles. Clark assumes that vacancy condensation 'debris' will also act as hete-rogeneous nucleation sites. Important factors in the hetehete-rogeneous nucleation process of a particular precipitating phase are the Burgers vector and the line direction of the nucleation agent. The characteristics of dislocations and dislocation loops will be dis-cussed first, after which the nucleation on dislocations will be considered.
Burgers vectors in H.C.P. magnesium alloys
In order to classify the orientations of the possible Burgers vectors in H.C.P. metals Berghezan, Fourdeux and Amelinckx (1961)
introduced a graphical representation (Figure 2.6) which is similar to that given by Thomson (1953) for F.C.C. metals.
The following dislocation types can be distinguished: a) perfect dislocations with Burgers vectors in the basal plane
represented bv the vectors AB, BC and AC; the magnitude of the Burgers vectors is ^ <1120>;
b) perfect dislocations with Burgers vectors perpendicular to the basal plane represented by the vector ST; the magnitude of the Burgers vector is [0001];
c) imperfect dislocations (Shockley partials) with Burgers vectors in the basal plane represented by the vectors Aa, Bcr, and Ca; the magnitude of the Burgers vectors is -y <10T0>;
d) imperfect dislocations with Burgers vector perpendicular to the basal plane represented by the vector aS; the magnitude of the
Burgers vector is -~ [0001];
e) imperfect dislocations represented by the vectors AS, BS, etc; the magnitude of the Burgers vectors is T- < 2 0 2 3 > ;
f) perfect dislocations with Burgers vectors in the second order pyramidal planes represented by the vectors BE, CE, etc; the magnitude of the Burgers vectors is ^ <1123>.
Slip systems in magnesium and its alloys
The normal slip system at room temperature is the basal slip system (0001)<1120>. The dislocations can dissociate into partials,
for example
AB = Aa + oB.
The spacing of the partials in magnesium is very small since the stacking fault energy is relatively high {estimates vary from 125 erg/cm^ (Hales 1968) to 280-300 erg/cm^ (Harris 1965, Hillairet 1970)}. If for some reason basal slip is restricted undissociated screw dislocations in the basal plane can cross-slip either in a pyramidal plane or in a prismatic plane. The slip systems
(0001) [2TT0], (0111) [2110] and (0110) [ZTTO] are indicated in Figure 2.7.
17
Figure 2.7 a) The slip systems of the type (0001) [2llo], (Olll) [2U0] and (oflO) [2ll0]
b) the slip system (1122) [1123].
By applying suitable shear stresses (Section 3.2) it is possible to introduce dislocations in any one of the slip systems discussed above. It is also possible to introduce dislocations in second order pyramidal planes of the {1122} type by activating the
{1122} <1123> slip system. The critical resolved shear stress in various magnesium-zinc alloys at different temperatures is indicated in Table A (See .^pendix).
Vacancy loops and interstitial loops
After quenching pure magnesium from high temperatures it has been observed that vacancies present in supersaturated solution preci-pitate as plate-like cavities in certain lattice planes. In extremely pure magnesium (impurity content less then 1 ppm) the vacancies condensate in second order prismatic planes of the {1120} type
(Hillairet 1970). The Burgers vector associated with these loops is 1 <1120>.
In magnesium with a slightly higher impurity content (<30 ppm) the vacancies precipitate as plate-like cavities in the basal plane
(Harris and Masters 1965, Lally and Partridge 1965, Hillairet 1970). Nearly all these loops contained stacking faults, but occasionally some unfaulted loops were observed. The unfaulted loops had the Burgers vector [0001], the faulted loops had the Burgers vector r <2023>.
6
In addition to vacancy loops interstitial loops have also been observed. Harris (1965) assumes that as a result of contraction stresses around impurity particles numerous prismatic loops are punched out. The punched-out loops were observed to glide or to shrink by climb until they disappeared at elevated temperatures. Lally and Partridge observed faulted vacancy loops after quenching from dry argon atmospheres and interstitial loops after quenching from moist argon atmospheres. The interstitial loops were punched out from heavily deformed areas in the material. The rows of loops were all aligned along <1120>directions. The Burgers vector of each loop was of the •=<1120> type and most of the loops were found to be situated in the {1120} planes. Glissile interstitial loops with 3<1120> Burgers vector situated in {1120} planes and produced by prismatic punching have already been described (Partridge 1962). Lally and Partridge explain this observation by assuming that after quenching from moist argon atmospheres hydrogen precipitates at sites
suitable for the recombination of [H] to H-. fi hydrogen pressure builds
up, which is sufficient to nucleate interstitial dislocation loops and to deform the material.
All the results described above were obtained with unalloyed magnesium. For magnesium alloys no extensive investigations of the type discussed above are knoim to this author. Vydyanath (1968) deduced the presence of dislocation rings in ^lg-Zn 3 from a slow change in electrical resistivity during aging, but no evidence
19 2.4 N u c l e a t i o n on d i s l o c a t i o n s
It is well known that dislocations act as nucleation sites and affect the precipitation process. The shape, size, orientation etc. of the precipitates can be modified by their presence. The stress field of the dislocation reduces the activation energy for the nucleation of the new phase and modifies the diffusion process, thereby changing the kinetics of the nucleation and growth of the precipitate. Recent reviews have been given by Larche (1975) and Russell (1976).
The change in free energy due to the formation of a nucleus on a dislocation is given by
AF = AF + AF + AF + A F , + A F . ,
V s E d 1
where AF is the volume free energy, AF is the interfacial free energy, AF is the strain energy of the nucleus, AF, is the strain energy of the dislocation in the nucleus volume and AF. is the interaction energy of the nucleus and the dislocation. Nucleation on dislocations is a very complicated process, since the various energy terms involved and the geometrical factors such as the shape and orientation of the growing nucleus, b and u of the dislocation, are interrelated and dependent on the elastic and structural pro-perties of both the matrix and the nucleus. Consequently, in order to develop quantitative models certain assumptions have to be made for the purpose of simplification . All these models have in common the fact that bulk pronerties are apnlied to the growing nucleus and that they are based on continuum theory, so that no orientation relationship can be considered. The various models are based on different assumptions concerning the coherency between nucleus and matrix, the presence of strain energy and the method of selecting the shape of the nucleus.
Vv'ithin the scope of this thesis we shall briefly discuss the quantitative models by Cahn (1957) and Gomez-Ramirez (1971) and we shall consider the empirical rule formulated by Nicholson (1963, 1967, 1970), which relates qualitatively the shape and lattice orientation of a precipitate to the type of dislocation.
20
Cahn's model for nucleation on dislocations
Cahn (1957) considers a cylindrical nucleus around the core of a dislocation. The nucleus is assumed to be incoherent with the matrix and to have the same specific volume as the matrix. Then the free energy per unit length for a cylinder of radius r consists only of the strain energy of the dislocation, the volume free energy and the surface free energy:
AF(r) = - A In r - irr^f + 2TrYr + C , (1)
2 2 where A = yb /47r(1-v) for an edge dislocation, and A = yb /4ir for
a screw dislocation, u is the shear modulus, v is the Poisson con-stant, f is the volume free energy of formation of a new phase, Y is the interfacial free energy of the boundary, C- is a constant representing the core energy of the dislocation and b is the magni-tude of the Burgers vector.
The first two terms of equation(1) favour nucleation, the third term opposes it. AF(r) has under certain conditions a minimum and a maximimi, which can be obtained from
dAF(r) A A ^ T T J- ri^
— g ^ = 0 = - - + 2irY - 2Trfr. (2)
From (2) we find:
r = | j [1 + /i-2 Af/iTY^].
2
If 2Af/TrY = a<1 there exist a minimum and a maximum of AF(r). The
minimum value of AF(r) occurs for r= r =-jr [1 - /1-a], which is the
radius of a metastable cylinder of the new phase around the dislo-cation. Fluctuations which thicken the new phase locally require an increase in free energy until the volume energy exceeds all other energy terms and growth occurs. The problem is to determine the shape and size of that fluctuation which requires the minimum energy rise in order to attain the critical size.
21
If the radius r of the nucleus is a function of the distance z along the dislocation line, the total free energy change due to a local fluctuation in diameter of the cylinder can be described
AF = i [- A m ^ + 2^Y(r A + r'2 - r ^ ) - ^l{?-x]^\d.z, (3)
o
where r' = dr/dz.
AF is a function of the size and shape of the nucleus. In the saddle point of the function the value of AF is called AF^. In order to calculate the size and shape of the nucleus in the saddle point Cahn applies the Euler-Lagrange equation on the integral:
r- ^ - g = C2 , 3r'
g is the integrand and C, is a constant. where
" ^ 1
Taking r/r = 1 + y, z/r = x and 1-a = B it can be shown that
af = £=^^-^. ^4)
where
q = ' - ^ • (5)
1 +
2
in(l+y) + (-y^)y(y+2) - C2(l+y)If r = r and T — = 0 then q = 1 and Co = 0. o dz ^ 2
Substituting (4) in (3) one obtains the following expression for AF*
[IlZ /rT^]dy, (6)
o
where q(e) = 1. The nucleus size and shape for different values of f and typical values of b, y, and Y are shown in Figure 5.1 (Chapter 5)
The heterogeneous nucleation model of Gomez-Ramirez
Gomez-Ramirez (1971) proposed a model for the nucleation on dislocations in which the elastic distortions caused by the diffe-rence in specific volume of the two phases in the elastic field of the dislocation were taken into account. He considers an infinite homogeneous medium containing a straight dislocation. In order to calculate the interaction energ)' of an incoherent nucleus of volume V and a dislocation line Gomez-Ramirez applies a set of hypothetical operations originally suggested by Eshelby (1957) for a solid-solid transformation in a homogeneous isotropic medium. An essential con-dition is that the elastic constants are the same for parent and product phase.
The volume V around a dislocation is removed from the matrix. Surface tractions of equal magnitude and opposite sign arc applied to both the surface of the hole left in the matrix and the surface of the volujne V. After removal of the surface tractions the volume is allowed to transform stress-free. This assumption is unrealistic since the line segment of the dislocation is still present in the volume removed. If this complication is ignored and Eshelby's treatment is completed, the calculations result in an expression for the interaction energy associated with the formation of the nucleus on the dislocation. In this model the interaction energy is dependent on the shape of the nucleus and is zero for symmetrical nuclei and for screw dislocations. After obtaining a general ex-pression for the free energy of formation of a nucleus he numeri-cally calculated AF^ for different values of f, b, y and a set of pre-selected shapes. The results indicate that the size parameter is critical in determining the nucleation barrier, while the shape parameter has a relatively small influence when Y is a constant.
The empirical nucleation rule
In quantitative models the lattice orientation relationship between nucleus and matrix has to be ignored. For those cases in which a lattice orientation relationship is observed an empirical
rule has been developed in order to explain the nucleation phenomena Qualitatively. The rule is based on the assumptions that the nucleus is structurally similar to the precipitate and that the strain around a nucleus can in principle be deduced from the lattice orientation relationship of the precipitate. The rule was deduced from observa-tions of coarsened precipitates which had nucleated selectively on dislocations. It was found that a given dislocation does not provide an equally effective nucleation site for each precipitate which has a definite lattice orientation relationship to the matrix.
Nicholson (1963, 1967, 1970) states that only those precipi-tates are found to nucleate the misfit vector of which has a compo-nent in the direction of the Burgers vector of the dislocation. The nucleation of nrecipitates tends to occur on those segments of the dislocation which lie in the relevant 'habit' plane of the precipitate. The reason for this behaviour is found in the reduc-tion of the strain energy of the precipitate in the strain field of the dislocation. The largest reduction in strain energy occurs if the precipitate and the dislocation are oriented in such a way that the misfit vector of the precipitate and the Burgers vector of the dislocation are parallel.
Illustrations of the principle described above can be found in the systems Al-Cu, Fe-N and Al-Cu-Mg. In the Al-Cu system (Thomas 1956) the e' phase is plate-shaped. Its habit plane is parallel to the {100} planes and the phase is assumed to be coherent across the
(100) interface. The misfit in the direction perpendicular to the habit plane is 30°s. On dislocations with Burgers vector -|[110] e' precipitates parallel to (100) and (010), the e' parallel to (001)
is not present. On helical dislocations with Burgers vector o-[110] the precipitates nucleate on those line segments which lie in the relevant (100) plane.
In the Fe-N system (Fischer 1962) the plate-shaped a" (Fe„N) has a misfit geometry similar to 8' in Al-Cu. It nucleates only on those dislocations lying in a (100) plane. The same result was fotmd for jogged dislocations having a line segment in the relevant (100) plane.
A more detailed picture is obtained from the precipitation of the equilibrium S phase in the Al-Cu-Mg system (Ifeatherly 1968). The S phase is lath-shaped, the axis of the lath being parallel to the <100> directions of the aluminium matrix. The cross-section of the lath is rectangular, with the edges parallel to the {021} planes. Considering the misfit surface of the S precipitate it appears that the largest misfit lies in a direction normal to the broad face of the lath whereas the lattice misfit along the lath is very small. Since for each [100] direction there are four orientations of the lath, there are twelve habit planes. It was observed that only one lath direction nucleates on any one dislocation. This means that only four of the twelve lath variants may have nucleated. On prismatic dislocation loops it was found that only two of the four variants had nucleated and these were the ones where the normal to the broad face of the lath is most nearly parallel to the Burgers vector of the dis-location. This illustrates the selectivity of nucleation on disloca-tions for the observadisloca-tions described. In our opinion, however, the number of observations is still too limited to formulate a rule which is able to explain all nucleation phenomena observed.
2.5 L i t e r a t u r e
- Anderko, K.P., E.J. Klimek, D.W. Levison and W. Rostoker Trans. Amer. Soc. Metal. 1957, 49, 778.
- Berghezan, A.A. Fourdeux and S. Amelinckx Acta Met. 9, 1961, p.464.
- Bemolde, M. , J. Gallot and R. Graf C.R. Acad. Sc. Paris, 1967 t. 264 Serie C 1458.
- Cahn, J.W. Acta Met. 1957, 5, 169.
- Clark, J.B. and F.N. Rhines Trans. AIME 1957, 209, 425.
- Chun, J.S. and J.G. Byrne Journal of Materials Science 4, 1969, p. 861.
- Eshelby, J.D. Proc. Roy. Soc. 1957, A 241, 376. - Fisher, R.M. Thesis Cambridge University 1962.
- Gallot, J., K. Lai, R. Graf and A. Guinier C.R. Acad. Sci. 1964, 258, 2818.
- Gallot, J. and R. Graf Bull. Soc. Franc. Miner. Crist.
1965, 88, 149.
- Gallot, J. and R. Graf C.R. Acad. Soc. 1965, 261, 728.
- Gallot, J. and R. Graf C.R. Acad. Soc. 1966, 262, 1219
- Gallot, J. These, Faculte des Sciences de I'Universite de Rouen, Rouen 1966.
- Gallot, J. Private communication 1970 .
- Gomez-Ramirez, R. Ph.D. Thesis Stanford University 1971.
- Gomez-Ramirez, R. and G.M. Pound Metall. Trans. 1973, 4, 1563.
- Hales, R., R.E. Smallman and P.S. Dobson Proc. Roy. Soc. A 307, 1968, p. 71/81.
- Harris, J.E. and B.C. Masters Proc. Roy. Soc. A 1966, 292, 240.
- Hillairet, J., C. Mairly, J. Espinasse et V. Levy Acta Met. 18, 1970, p. 1285.
- Koster, W. Zeitschrift fur Metallkunde 1950, 41, 37.
- Lally, J.S. and P.C. Partridge Phil. Mag. 13, 1968, p. 9.
- Larche, F. to be published.
- Laves, F. Naturwissenschaften 1939, 26, 454.
- Liere, J. van Afstudeerverslag T.H. Delft 1970.
- Mima, G. and Y. Tanaka Trans. J.I.M. 12, 1971, p. 71.
- Mima, G. and Y. Tanaka Trans. J.I.^1. 1, 1971, p. 323.
- ^''isra, S., R. Narayana, G.M.K. Sarma Trans. Indian Institute of Metals 20, 1967, p. 239/240.
- Murakami, Y., 0. Kawano and H. Tamura Kyoto University, Memoirs of the Faculty of Engineering 23, 1962, p. 1281.
- Naryana, R.L., S a m a , G.M.K. and S. Misro Trans. Indian Inst. Metals 1967, 12, 239.
- Nicholson, R.B. and A. Kelly Progress in Materials Science
1963, 10, 149.
- Nicholson, R.B. in Electron Microscopy and Strength of Crystals edited by G. Thomas and J. Washburn Interscience l\iblicers London, 1963 p. 861.
- Nicholson, R.B. Phase Transformations, American Society for Metals 1970 Metals Park London p. 269.
- Park, J.J. and L.L. Wyman WADC Techn. Rept. 57-504 oct 1957.
- Partridge, P.C. C.E.G.B. Berkeley Nuclear Lab. Rep. (RD/B/N.35) 1962.
- Raynor, G.V. The Physical tetallurgy of Magnesium and Its Alloys Pergamon Press London 1959.
- Russell, K.C. to be published 1976.
- Schmid, E. and H. Seliger Zeitschrift fiir Electrochemie 1932, 37, 455.
- Seitz, F. Imperfections in Nearly Perfect Crystals 1952 (John Wiley) New-York and London, 47.
- Sturkey, L. and J.B. Clark J. Inst. Metals 19 , 88, 177.
- Takahashi, T., Y. Kojima and K. Takanishi J. Japanese Institute of Light Metals 23, 1973, p. 376/382.
- Thomas, G. and J. Nutting Symposiimi on the Mechanisme of Phase Transformation in Solids, London 1956, p. 18.
- Thomson, N. Proc. Phys. Soc. London 1952, B66, 481.
- Vydyanath, H.R., D.H. Sastry and K.I. Vasu Phys. Stat. Sol. 29, 1968, p. K 137.
- Weatherly, G.C. and R.B. Nicholson Phil. Mag. 1968, 17, 801.
28
3 experimental
In this chapter the alloy composition and specimen preparation are discussed. The quenching and aging procedure of the
magnesium-zinc specimens of various compositions is described and the limitations of studying heterogeneous nucleation phenomena in polyarystalline specimens is considered. The techniques for preparing single crystals are then discussed and the growth, orientation determination and shearing of the single crystals are described. Finally, there follows a method for the analysis of characterisation of dislocations in various slip systems.
3.1 A l l o y c o m p o s i t i o n and s p e c i m e n p r e p a r a t i o n
Magnesium and magnesium-zinc alloys were prepared from high purity components. Magnesium of 99.8?) purity was obtained from Norsk Hydro A.S. (Norway); zinc of 99.99°s purity was obtained from Preussag A.G. (W. Germany). The results of neutron activation ana-lysis of the impurities in both coiiponents are given in Table 3.1.
Table 3.1 Analysis of magnesium and zinc used for alloy preparation during this investigation. The concentrations of the
impurities are expressed in ppm with a relative accuracy of 5% (< = the detection limit) .
Al Cu Fe Mn Ti Zn Mg
Mg 58 <500 350 <50 <2500 250
Zn 17 <70 80 <4 <200 - <3000
Magnesium was melted in a carbon crucible by means of indirect high frequency induction heating. In order to avoid contamination the melt was kept in a purified argon/SO, atmosphere. After melting z m c was alloyed m the desired quantity, a i m i n g ana casting tooK place without disturbing the protecting atmosphere. The results of neutron activation analysis of the alloys obtained in this way are shov/n in Table 3.2.
Table 3.2 Analysis of magnesium and magnesium-zinc alloys used in this investigation. The concentrations of the impurities are expressed in weight-percentage with a relative aoauraay of 5%. A: B: C: D: E: Mg Mg-Zn 2.0 Mg-Zn 3.5 Mg-Zn 5.5 Mg-Zn 7.5 Fe 0.10 0.10 0.10 0.07 0.09 Cu 0.04 0.04 0.04 0.08 0.05 Na 0.05 0.06 0.05 0.05 0.04 Mn 0.03 0.02 0.02 0.03 0.02 Al 0.02 0.02 0.01 0.02 0.01 Zn
-2.04 3.78 5.40 7.30The alloys were homogenised by a two step homogenisation treatment. The first homogenisation temperature was 340 C, approx. 4 C below the melting point of the Mg-Mg^Zn, eutectic. After 24 hours at 340 C the decomposition of the eutectic had sufficiently proceeded to prevent remelting of the segregated zinc when the temperature was raised. The second homogenisation temperature was between 344 C and 480 C, depending on the alloy composition. The homogenisation treat-ment was terminated after 48 hours. The ingots were then planed and hot-rolled at suitable temperatures. The thickness was gradually reduced from 7 mm to 1.5 mm. X-ray micro-analysis showed that the variation in zinc composition was less then 0.10°6.
From each alloy a number of strips was used for the prepara-tion of tensile bars and hardness specimens. Flat tensile bars were cut from the strips in longitudinal direction. The bars were 90x3x1.5 mm in size and were drawn in an 'Instron' tensile testing machine under closely controlled conditions. Hardness specimens
10 x 10 x 1.5 mm were cut from the strips and mechanically polished, with 1/4 vm diamond powder. For the micro-Vickers hardness
(200 g/20 sec), the average value of 20 measurements with a'Leitz' duramet hardness tester, was taken. The grain size of all specimens was kept under continuous control in order to avoid erroneous inter-pretation of differences in mechanical properties.
30
The remaining strips were cold-rolled to the desired thickness of 0.5 mm. Specimens 3 mm in diameter were punched and recrystallised at approx. 20 C below the solidus line. The discs were chemically
polished in a solution of S% HNO, in ethyl alcohol, then rinsed in
methyl alcohol and dried.
All specimens were placed in pyrex tubes, which were evacuated to 3 10 Torr and then filled with either purified argon or hydrogen to a pressure of 700 Torr. The pyrex tubes were sealed-off and annealed in a vertical tube furnace. The pure magnesium specimens were annealed for one hour at 550 C, the magnesium alloys at 550 C, 480 C, 420 C and 344 C respectively before quenching in ice-brine (0 C ) . On contact with the brine the pyrex tube cracked and the specimens shot rapidly through the liquid. From dummy experiments the cooling rate of the discs was roughly estimated to be 16000 C/sec.
Some of the discs were electrochemically polished in a 'Tenupol' polishing apparatus. The polishing conditions were: voltage 11.7 V; temperature - 5 C; polishing bath: 601 destilled water, 35°4 methyl
alcohol, 5% nitric acid. Before the hole appeared the disc was
transfered from the 'Tenupol' to a chemical polishing bath consis-ting of 5°i nitric acid in 1:1 methyl/ethyl alcohol. After the hole appeared the disc was rinsed in purified methyl alcohol and dried between sheets of filter paper.
The remaining specimens received an aging treatment, which was in some cases preceded by a slight deformation. The specimens of alloy C (Mg-Zn 3.5) were aged at 180 C for 5 hours. More concentrated magnesium-zinc alloys (D-E) were isothermally aged at 180 C for 2.5 and 1 hours respectively in order to allow comparison of similar struc-tures. Several specimens of alloy C received an aging treatment at other temperatures,namely 120°C, 150°C, 210°C and 240°C. The aging times for these temperatures were determined from a relation given by Mima and Tanaka (1971) for the initial hardness and resistivity rise in Mg-Zn 4. The aging treatment was carried out in air in a 'Heraeus RT 360' oven. The temperature of the oven was controlled to + 1 C. After aging the specimens received the same polishing procedure as above.
31
All specimens were examined in a 'Philips W 300' Electron
Microscope, operating at 100 kV. The structures observed were analysed and photographically recorded. In a few cases the discs were heated in situ so that structural changes could be followed. Special attention was given to the heterogeneous nucleation of precipitates on different types of dislocations. The Burgers vector b and line direction u were determined and the relation between b. u and the morphology of nucleated precipitates was investigated. This relation could be easily obtained for dislocations in the basal plane. Deformed polycrystalline specimens always contain
(0001)<1120> dislocations, since the critical shear stress for this slip system is very small compared with the critical shear stresses for other slip systems. Deformation of polycrystalline specimens at elevated temperatures (above 225 C) introduces other types of dis-locations, for example {1oTl}<1120> disdis-locations, whereas
{10T0}<1120> and {1122}<1123> dislocations were rarely observed. These last mentioned dislocations are only occasionally present in heavily deformed material. The dislocation density is then so large that electron micrographic analysis of nucleation phenomena is al-most impossible. For this reason it was decided to shear single crystals of Mg-Zn 3.5 under controlled conditions.
3.2 T h e p r o d u c t i o n and shearing of s i n g l e c r y s t a l s
The preparation of single crystals of magnesium-based alloys by means of the Bridgeman technique v/as described by Akhtar (1972) and van der Plancken (1974); single crystal preparation by means of recrystallisation was described by Gallot (1966). In this inves-tigation rod-shaped single crystals, 3 mm in diameter, were prepared using the modified Bridgeman technique described by Weiner (1974). As starting material this technique requires polycrystalline rods with a composition equal to the desired composition of the single crystals.
The rods with a diameter of 2.9 mm were turned from alloys prepared from the pure components as described in Section 3.1. The rods were slightly etched in diluted nitric acid prior to remelting.
The single crystals were grown in a cylindrical carbon crucible with a sharply tapered bottom in order to obtain a good starting point for single nucleation. The crucible was annealed at approx.
1500 C in vacuum in order to relase internal stresses and to diminish the quantity of dissolved gases. After annealing the crucible was reamed to obtain a straight cylindrical hole 3 mm in diameter.
The single crystals were grown in a vacuum of approx. 10 Torr. In order to minimize evaporation of both the magnesium and zinc, the top of the crucible was covered with a plug. The temperature of the melt was approx. 700 C and the grovrth velocity was 6 cm/hour. At this velocity single crystals could be grown without excessive evaporation of magnesium and zinc.
The single crystals obtained were about 4-7 cm long. As the surface was contaminated with carbon it was chemically polished in a dilute solution of nitric acid in alcohol. Metallographic sec-tioning showed in addition to the presence of sub-boundaries a regular segregation pattern, as shown in Figure 3.1a. The single crystals were homogenised in sealed-off Pyrex tubes evacuated at a pressure of 3 10 Torr. The tubes were heated in a circulating air furnace at approx. 20 C below the solidus line. Homogenisation for 7 days was sufficient to reduce the number of sub-boundaries and to eliminate the segregation pattern. Figure 3.1b shows the microstruc-ture of a Mg-Zn 3.5 alloy after homogenisation for 7 days at 520 C.
After homogenisation the orientation of the single crystals was determined by the transmission Laue method. It is then possible to shear the single crystals along a selected slip system, intro-ducing in this way dislocations of the desired type.
The single crystal was mounted in a cylindrical specimen hol-der, the axis of the rod being parallel to one edge of the square film.
33
Figure 2.1 The microstructure of a Mg-Zn 3.5 single crystal before and after homogenisation.
a) A cross-section of the single crystal rod with a regular micro-segregation pattern and the presence of sub-boundaries. b) The microstructure after homogenisation for 7 days at 520 C.
From a Laue transmission picture a stereographic projection was made on a plane perpendicular to the incident X-ray beam. The diffraction spots were indexed with the aid of computer drawn stereographic pro-jections. A slip plane suitable for shearing in the apparatus to be described below was now selected. The selection of a slip system was restricted by the maximum tilt angle (37 ) of the specimen holder. By rotating and tilting the crystal the pole of the selected slip plane was brought to the north pole of the stereographic projection. The slip plane lies then in the horizontal plane. In the stereographic projection the slip direction is now found on the equator. IVhen the specimen is brought into shear position by tilting 90 forwards, the slip direction is found on the basic circle. The sequence of Laue pictures and their corresponding stereographic projections is shown in Figure 3.2.
In general the selected slip direction deviates from the fixed shear direction of the apparatus. For this reason the crystal must be rotated in its slip plane.
34
(a)
35
Figure 2.2 A sequence of Laue pictures and their corresponding
stereographic projections.
a) After mounting in the specimen holder.
b) After 17° rotation and 5 tilt to verify the pattern indexing
(010 projection).
c) After 101° rotation and 36 tilt to take the pole of the selected
slip plane (basal plane) almost to the north pole.
36
A cylindrical 'cuff was pushed over the crystal and the spe-cimen holder. This cuff has at one end an inclined plane, the incli-nation corresponding to the angle between the slip plane and the rod cross-section. The cuff was mounted m such a way that the selec-ted slip plane and the inclined plane of the cuff were parallel.
The shearing took place in an apparatus originally designed by Lebbink (1951) and recently modified. Details of the experimental arrangement are given in Figure 3.3.
1. Gear box 6. Spring load 11. Specimen holder 2. Motor 7. Shear block 12. Cuff
3. Worm wheel 8. Displacement transducers 13. Single crystal rod 4. Screiv spindle 9. Adjustable 'Syndanyo' disc 14. Up-down switch 5. Bar guide 10. Heaters , 15. Main switch
Figure 3.3 Details of the shear apparatus, originally designed by Lebbink (1951) and recently modified.
Two shear blocks were used for shearing, one fixed, the other mobile. In each block a disc was inserted which could rotate in the shear plane. Each disc had a hole with a diameter corresponding to the external diameter of the cylindrical cuff. The holes were milled at an angle corresponding to the angle between the slip plane and the cross-section of the single crystal rod. The crystal, with its slip plane fixed by the inclined cuff, was mounted in such a way that the slip plane was parallel to the shear plane. By rotating the disc through the angle between the selected slip direction and the fixed shear direction, the selected slip direction was made parallel to the shear direction of the apparatus.
The specimens were sheared at room temperature or at tempera-tures of approx. 250 C. Owing to the low critical resolved shear stress the basal slip system could be activated at room temperature; the other slip systems had to be activated at an elevated tempera-ture. The elevated temperature was obtained using two small resistance furnaces, heating the specimen holder and the ends of the single crys-tal rod at 450 C. The heat was conducted through the rod to the shear zone in the crystal. In order to restrict thermal leakage in the shear apparatus, the discs were made from 'Syndanyo', a material with a very small thermal conductivity coefficient.
The shear stresses and shear strains were measured by means of two calibrated 'Hewlett-Packard' displacement transducers type 7 DCDT-100 and recorded by a 'Moseley' X-Y recorder model 7001 AM.
The shear strain was restricted to approx. 3°«. This corresponds to a shear of about 0.1 mm. The dislocation density found in the material
7 2 after shearing was about 10 /cm .
3.3 A n a l y s i s of the n u c l e a t i o n p h e n o m e n a
After shearing, discs 3 mm in diameter and 0.5 mm thick were cut from the shear zone in the single crystal rod by means of spark erosion. The discs were annealed for several minutes at 480 C and quenched in water. Immediately after quenching the specimens were aged for 5 hours at 180 C. The specimens were electrochemically polished as described above and examined in the electron microscope. The 'decorated' dislocations were selected and their bright field and dark field images together with the corresponding diffraction patterns recorded.
Although the slip system to be investigated was pre-selected by means of single crystal shear, a check was always made to see whether the dislocations observed were of the type expected. For this reason the Burgers vector b of the dislocation and the dislocation line direction u were determined. From these two parameters the slip plane, the slip system and the character of the dislocation line can be deduced.
In order to determine the line direction u the procedure described by Head and collaborators (1973) was followed. In this method the images of the line defect in at least two beam directions have to be recorded. The best results are obtained if the two projected directions differ markedly. In each recorded image the specific diffraction vector g is indicated together with a vector from another diffraction spot. This vector serves to determine the correct sense of the projected line direction with respect to the diffraction vector g. The angle between g and the projection of u is measured and marked on each image. The true crystallographic direction of u must now be deter-mined using a stereographic net. In an arbitrary stereographic projection the great circles corresponding to the zone-axis of each image are drawn.
iii
Figure 3.4 An illustration of the method of Head and collaborators (1973) to determine the line direction u from electron macrographs in at least two beam directions.
For each case the projected direction of u is marked at the corres-ponding angle from the diffraction vector in the correct sense. The true direction of u lies in the plane containing the beam direc-tion and the projecdirec-tion of u in that beam direcdirec-tion. This plane can be constructed for each beam direction by drawing the great circle containing the projected direction of u and the beam direction. The intersection of these great circles determines the direction u of the dislocation. The procedure is illustrated in Figure 3.4. When the Burgers vector b and the line direction u do not coincide, the slip plane can be determined. From the line direction the line length L of the dislocation can be determined and the number of precipitates per unit length calculated.
41
3.^ Literature- Akhtar, A. and E. Teghtsoonian, Phil. Mag. 1972, 4, 897.
- Gallot, J. These, Faculte des Sciences de I'Universite de Rouen, Rouen 1966.
- Head, A.K., P. Humble, L.M. Clarebrough, A.J. Morton and C.F. Forwood Confuted Electron Micrographs and Defect Identification.
North Holland Publishing Company Amsterdam 1973.
- Lebbink, F. and W.G. Burgers. Selected Topics in X-ray Crystallo-graphy North Holland Publishing Company Amsterdam 1951.
- Mima, G. and Y. Tanaka, Trans. J.I.M. 1971, 12, 71.
- Plancken, F. van der. Private communication.
4 experimental results
This chapter deals with the structures which are found in mag-nesium and magmag-nesium-zinc alloys after quenching from different at-mospheres. After annealing in situ to record the successive stages in
the aging process, different nucleation sites showed different beha-viour. This nucleation behaviour was extensively analysed in poly-crystalline material. The nucleation of 3-,' and Bl on basal disloca-tions was studied in alloys of various composidisloca-tions aged at 180 C, whereas the influence of the aging temperature was studied in an alloy containing 3.5% zinc. A relationship was established between the supersaturation of zinc and the product b.u for the nucleation of Bl and 6'- Ihe nucleation of B | and 6 ' on other types of
disloca-1 2 1 2
tions was analysed in single crystalline material with approx. 3. 57o zinc. These dislocations were generated in the following slip systems: pyramidal slip, prismatic slip and second order pyramidal slip.
Finally, some experimental results concerning the kinetics of aging are presented.
4 . 1 O u e n c h i n g f r o m d i f f e r e n t a t m o s p h e r e s
The magnesium d i s c s ( m a t e r i a l A) quenched from a p u r i f i e d argon atmosphere i n i c e - b r i n e c o n t a i n e d only a few quenched-in d i s l o c a t i o n s . No d i s l o c a t i o n loops could be d e t e c t e d . The absence of vacancy loops i s not t h e r e s u l t of a too slow quenching r a t e . After quenching pure magnesium (99.99!.) under t h e same c o n d i t i o n s we o b t a i n e d s i m i l a r r e -s u l t -s a-s r e p o r t e d by H i l l a i r e t (1970), which i n d i c a t e -s t h a t the quenching r a t e was s u f f i c i e n t l y h i g h .
When t h e magnesium d i s c s were quenched from a hydrogen atmos-phere t h e s t r u c t u r e observed in both m a t e r i a l s d i f f e r e d markedly
from, t h e s t r u c t u r e found a f t e r quenchin? from an argon atmosphere. D i s l o c a t i o n - r i c h a r e a s , more or l e s s s p h e r i c a l in shape and approx. 0.3 ym i n d i a m e t e r , were observed (Figure 4 . 1 ) . The d e n s i t y of t h e s e
1 2 - 3
a r e a s v/as about 10 cm. , t h e d i s l o c a t i o n density i n t h e areas was of t h e order of 10 -10 cm .
43
From these heavily deformed areas loops had been punched which were nresumably interstitial. The number of loops in a row decreased with increasing impurity content. The rows of loops are often tapered.
The Burgers vector of the loops was determined to be -^<^^20>•, the
glide directions corresnond to <1120> directions.
Figure 4.1 Magnesium (material A) quenched from a hydrogen atmosphere at 550 C in ice-brine. Loops, presumably interstitial, are punched out from the heavily deformed areas in the three glide directions in the basal plane.
zone axis = {011\ = [J273]
foil plane = flslnj 4<n<6 The magnesium-zinc alloys (materials B - E) contained similar heavily deformed areas after quenching from a hydrogen atmosphere. However, in these specimens no rows of dislocation rings punched out from the heavily deformed areas were observed. All the areas disap-peared quickly after a very short annealing treatment at 180 C. In the age-hardening alloys (alloys C and D) their original location is easily traced back, owing to the large number of precipitates which have nucleated within the deformed zone.
44
Alloy C, containing quenched-m dislocations and areas with high dislocation density, was annealed in situ at 180 C. The dis-location-rich areas disappeared within a minute. After about fif-teen minutes of aging precipitates started to appear. It can be seen from Figure 4.2a-c that the precipitates appear preferentially at those sites where a dislocation was present at the start of the aging -nrocess. For example, the helical dislocations reduce their line energy by decreasing their line length, but the original
heli-Figure 4.2 Mg-Zn 3.5 (alloy C), quenched from a hydrogen atmosphere in ice-brine.
a) The structure observed immediately after quenching.
b) The structure after aging in situ at 180 C during 5 minutes. c) The structure after aging in situ at 180 C during 60 minutes.
zone axis [112] = [1102] foil plane (llOn) 2<n<3
0.5 vm
45 (b)
i
##•
' , - •
(o)4
4 *
cal patterns are maintained by the precipitates. This observation indicates that the nucleation of the precipitates does not take place during the quench but in the first period of the aging treatment, since we must assume that the process of spiralization takes place after the quench. In addition to the dislocation lines the foil surfaces are also heterogeneous nucleation sites. This gives rise to the appearance of surface precipitates which unfortunately inter-fere with the observations in the 'bulk'.
After aging for five hours at 180 C the bulk has the structure shown in Figure 4.3. The two phases B,' and Bo have nucleated on the dislocation lines. It can be seen that some dislocations act as nuc-leation sites for the needle-shaped B' precipitate, while others act as nucleation sites for the plate-shaped B' precipitate. This pheno-menon is discussed in greater detail in the next sections.
f
*
#
r
a^pP
/'
^ 1— O.E/
/
mFigure 4.2 Mg-Zn 3.5 (alloy C), quenched from a hydrogen atmosphere in ice-brine and aged for 5 hours at 180 C. Heterogeneous nucleation
47
4.2 P r e c i p i t a t i o n of B' on ( 0 0 n i ) < 1 1 2 0 > d i s l o c a t i o n s
4 . 2 a A g i n g of Mg-Zn 3 . 5 a t 180°C
Of t h e four s l i p systems discussed before (Section 2 . 3 ) , t h e p r e c i p i t a t i o n of s ' on (0001)<1120> i s most e a s i l y examined,since a f t e r a s l i g h t deformation of a p o l y c r i s t a l l i n e specimen most d i s -l o c a t i o n s a r e of t h i s t y p e . A s y s t e m a t i c a n a -l y s i s of many a-lmost s t r a i g h t d i s l o c a t i o n s a f t e r f i v e hours aging leads t o t h e conclusion t h a t B\ had mainly n u c l e a t e d on (0001)<1120> screw d i s l o c a t i o n s , whereas Bo had mainly n u c l e a t e d on (0001)<1120> edge d i s l o c a t i o n s . D i s -l o c a t i o n s for which t h e ang-le p between Burgers v e c t o r b and -l i n e d i r e c t i o n u i s between 35 and 55 c o n t a i n both B] and Bo p r e c i p i -t a -t e s (Figure 4 . 4 ) .
p ; .
K
n e e d l e - s h a p e d p ' ( p ! , )
s c r e w d i s l o c a t i o n edge d i s l o c a t i o n
Figure 4.4 The relation for the nucleation of B' on (0001)<1120> dislocations found in Mg-Zn 3.5 after aging at 180 C, p is the angle between the Burgers vector b and the line direction u.
fhis relationship could be confirmed by the analysis of curved dis-locations in the basal plane, for which p changed continuously from 0 to 90°.
48
Basal dislocations present at the start of the aging process act in the way described as heterogeneous nucleation sites for the 6' and Bo precipitates. It does not appear to be important whether or not the dislocation line moves away from its initial position during the aging process.
Supporting evidence for this nucleation behaviour is obtained from the following observations. Small-angle twist boundaries in the c-plane, consisting of screw dislocations with Burgers vectors v<1120>, act as nucleation sites for the B] precipitates. As shown
m Figure 4.5, this effect gives rise to a very regular precipitate distribution.
49
«
" ^Ik
i ' ^^
t 1
t % kt
J 0 5 m * .. *" •« 1 * 1Figure 4.5 A twist boundary in the basal plane. The screw disloca-tions act as nucleation sites for the B'-i precipitates. The needle axis of Bl is perpendicular to the image plane.
zone axis [001] = [0001] foil plane (0001)
Small-angle tilt boundaries, consisting of edge dislocations in the basal plane with Burgers vector ^[1120] are occupied by the plate-shaped Bo precipitates, as illustrated in Figure 4.6.
The density (number of precipitates per centimeter dislocation line)
of B] precipitates on (0001)<1120> dislocations of predominantly screw
5 -1
character was about 3 10 cm ; the density of Bo precipitates on (0001)<1120> dislocations of predominantly edge character was about 2 10^ c m " \
