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Diffraction and microscopy studies of the atomic structure of grain boundaries
Ultramicroscopy North-Holland,
14 (1984) 11-26 Amsterdam
DIFFRACTION BOUNDARIES P. LAMARRE, Department Received
AND MICROSCOPY
F. SCHMUCKLE,
of Materials 11 January
11
STUDIES
OF THE ATOMIC
K. SICKAFUS
Science and Engineering,
STRUCTURE
OF GRAIN
and S.L. SASS
Cornell University, Ithaca, New York 14853, USA
1984; received in final form 13 February
1984; presented
at Workshop
January
1984
The structure of grain boundaries and the influence of solute segregation on boundary structure were studied using diffraction and microscopy techniques. The determination of the projected atomic structure of a large angle [OOl] twist boundary by use of X-ray diffraction techniques was demonstrated. Using an electron diffraction technique it was shown that the local change in plane spacing at a large angle [OOl] twist boundary was dependent on the type of bond (ionic, metallic, covalent) in the material. It was shown that solute segregation causes a major change in the dislocation content of a small angle [OOl] twist boundary in Fe containing a small amount of Au. These observations are evidence for the occurrence of a two-dimensional phase transformation in the grain boundary. As a result of these studies, generalizations were made concerning the structure of large-angle twist boundaries and the influence of bond type on boundary structure.
1. Introduction In recent years a considerable amount of detailed information has been obtained about the structure of grain boundaries by the use of electron microscopy, electron diffraction, X-ray diffraction and computer modeling techniques. Many questions about grain boundary structure still remain to be answered. This paper will discuss some of the important questions that still remain and then describe experiments that attempt to provide answers. 1.1. What is the atomic grain boundaries?
structure
of large-angle
One of the important justifications for studies of grain boundary structure is that through knowledge of their structure it should be possible to understand how boundaries influence properties. As the first step in this process it is necessary to obtain detailed information on the atomic structure of grain boundaries. The boundaries that are good candidates for studies that can provide such information are tilt boundaries, using high resolution electron microscopy techniques [l], and twist
boundaries, using X-ray diffraction techniques. In section 2 of this paper the recent results [2] of an X-ray diffraction study of the projected atomic structure of a large angle [OOl] twist boundary in Au will be examined. 1.2. What is the influence of material and bond type on grain boundary structure? Computer modeling calculations of boundary structure in fee metals predict that the atomic structure should be influenced by the metal in which the boundary is present [3]. Recent observations show that the structures of the same boundary in Au and Ag are quite similar [4], in sharp disagreement with this prediction. The reasons for this disagreement are not understood at present. It seems reasonable to also predict that when the type of bonding in the material changes (e.g., from ionic, to metallic, to covalent) the grain boundary structure should change in a characteristic manner. In order to obtain information on the influence of bond type on boundary structure, the local variation in plane spacing normal to the same type boundary in materials with largely ionic, metallic and covalent type bonding was determined. The
0304-3991/84/$03.00 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
results of this study will be discussed of this paper. 1.3. What is the influence grain boundary structure?
in section
of solute segregation
3
on
It is frequently observed that solute atoms segregate to grain boundaries in alloy systems where there is limited solubility in the solid solution [5]. Auger spectroscopy has shown the presence of typically up to a monolayer of solute at internal interfaces in such systems where equilibrium segregation is important [6]. The practical consequence of such segregation is frequently the embrittlement of the grain boundary region, making it susceptible to fracture at relatively low stresses [7]. It is of considerable interest to learn how the presence of the solute changes the mechanical properties of the boundary. Is the solute changing the chemical bonding across the interface as suggested by Messmer and Briant [8], or is it changing the atomic structure, or perhaps both? In section 4 of this paper the question of whether the presence of solute at the boundary influences the structure of the boundary is addressed.
2. The projected atomic structure of the I= (8 = 36.9”) [OOl] twist boundary in gold 121 2.1. Introduction
5*
to diffraction from grain bounduries
In order to better understand the details of the experimental results of this section, it is useful to first examine the reciprocal lattice associated with the grain boundary. All of the X-ray diffraction observations were made on manufactured bicrystals (see ref. [9] for details), one of which is shown schematically with a small-angle twist boundary at its midplane in fig. la. The reciprocal lattice of this boundary is shown schematically in fig. lb, where the H and K axes lie parallel to the boundary, and the L axis is normal to the boundary plane. The reciprocal lattice is that of the coincidence site lattice (CSL) of the boundary (see ref. [9]). The periodic strain field associated with the * z‘ is the reciprocal
of the density
of coincidence
sites.
Fig. 1. (a) Bicrystal containing a small-angle [OOI] twit boundary with misorientation 0 at its midplane. (b) Schematic three-dimensional reciprocal lattice for the grain boundary m
(a).
grain boundary gives rise to extra reflections, which are shown in the form of reciprocal lattice rods (relrods) since the boundary is not periodic along the z-direction. Reflection intensities in the L = 0 plane are related to the structure of the boundary projected onto the boundary plane while the length of the relrods is related to the boundary thickness. The structural information discussed in this section comes from measurements made on the structure factors in the L = 0 plane (F,,,,,) while the information discussed in section 3 comes from the relrod profiles along the L direction. Since the amount of material at a grain boundary is quite small (equivalent to approximately one monolayer [lo]) the diffraction intensity is also quite low. In order to be able to detect scattering from the boundary region in a reasonable length of time, it is necessary to use high intensity X-ray sources. In previous work on high-angle twist boundaries in Au [9], when using a rotating anode X-ray generator operating at 9 to 10 kW, X-ray film exposures of 100 h were re-
P. Lamarre
et al. / Atomic
structure
of the unit cell
When determining the structure of a periodic object the first step is to determine the dimensions of the unit cell. In grain boundary studies performed on manufactured bicrystal specimens, the unit cell is that of the CSL which is expected to be fixed by the choice of the misorientation axis and angle, and the boundary plane. The second step is to determine the symmetry elements of the unit cell. Figs. 2a and 2b show top and side views, respectively, of the unit cell of the Z = 5 [OOl] twist boundary, with 2 atomic planes above and below the boundary plane. The structuree shown is
Ave
L
Unrelaxed
LO201
a
.
15
Iroo11
0
b
0.
0
.
*
13
in the coincidence site lattice (CSL) configuration; that is, the two crystals are not translated away from the coincidence position for fee structures. Following Bristowe and Cracker [ll], it is seen that this unit cell has the symmetry elements shown in fig. 2c. Any translation of one crystal with respect to the other, which is not a vector of the DSC lattice [12], will change the symmetry associated with the boundary structure. Figs. 2d and 2e show the symmetry elements of two high symmetry translated states characterized by DSC translations D,/2 and (0, + D,)/2, where D, and D2 are the orthogonal DSC basis vectors in the plane of the boundary [ll]). Other translations are possible, and for these cases the number of symmetry elements decreases. The symmetry of the unit cell can be determined from the experimentally observed structure factor rules. The structure factor rules for the three translation states shown in figs. 2c-2e) are given in table 1. A complication in this analysis arises for the D,/2 translation state, where the actual boundary structure could consist of a mixture of domains with the same translation state.
quired to obtain the desired diffraction patterns. Using synchrotron radiation for the same diffraction geometry, an exposure of a few hours was required to obtain diffraction patterns similar to those produced with the rotating anode generator. The X-ray diffraction experiments were carried out at the Cornell High Energy Synchrotron Source (CHESS). 2.2. The symmetry
of gram boundaries
0
0
B 0
*
.
+
AA 0
’ .
Ave
[200]
Perpendicular
n
In
the
Fig. 2. (a) Schematic
diagram of the unrelaxed
P = 5 primitive CSL unit cell projected
grain
and (e) (Dl + Dz)/2
translation
[OOl] twist boundaries
onto the grain boundary
shown. The symmetry
in fee crystals.
elements
grain
Four-fold
-
the same unit cell with two planes above and below the boundary
to
Two-fold
0
boundary
boundary axis axis
plane
Two-fold
his
Two-fold
screw
axis
plane. (b) Side view of
of (c) CSL, (d) D, /2
translation,
Table
1
Diffraction
symmetry
and structure
IFnKi.I= IFiriiz = lFm,I F l,M, = 0 if H is odd
factor
selection
rules
= IFHKLI = IFHKT.I = IFKHLI
FCj,, = 0 if K is odd n, /2
structure
IFIIKI.I = I~~~7.1= l5~i.l
= IFMKLI = I6,~r.l f IFKH/.I
FOKU = 0 if K is odd (D, + D,)/2
structure
IFHK,.I = I&XL No structure
= I~~KLI = IFHKLI = IF,,,zI = IFKH~ I
factor forbidden
reflections
but different orientations. For example, in different areas of the boundary the translation can be either D,/2 or D,/2, yielding two domains. In this case the scattering from the two domains will average together in such a way that there are no longer structure-factor-forbidden reflections and more symmetry is shown in the diffraction pattern than actually exists in any particular domain. The distinguishing difference between the CSL and all other configurations lies in those structure factor selection rules which are related to the presence of two-fold screw axes. For the CSL structure, F,,,, (H = odd) and FoKo (K = odd) must be zero, whereas for the (D, + D,)/2 translation or for a mixture of domains with D,/2 and D/2 translations, intensity can be present at these positions. The observations of Budai, Bristowe and Sass [2] shown in fig. 3 are consistent with the 2‘ = 5 unit cell being in the CSL configuration (untranslated state). The space group of this structure is P42;2 [13]. 2.3. The number
of independent
atoms
in the unit
cell
Once the symmetry has been established the next step is to determine the minimum number of atoms whose positions must be located in order to completely characterize the unit cell contents. By examination of fig. 2a it is seen that there are 5 atoms per plane, with the X. y positions off one atom per plane (at either l/2, l/2 or 0, 0) fixed by the translation state of the boundary. The remaining four atoms in the plane are symmetry-
related by the 4-fold axis. Thus it is necessary to locate 2 atoms per plane in order to locate all the atoms in the plane. If only the X, y positions are to be determined, then it is necessary to locate 1 atom per plane in order to locate all the atoms in the plane. It is also seen that the atoms in the upper and lower crystals are related by the two-fold screw axes lying in the interface plane. What this means is, if it is assumed that the grain boundary is 4 atomic layers thick, then in order to determine the atomic structure projected onto the boundary plane, it is necessary to determine the X, _pcoordinates of only 2 atoms (marked A, B in fig. 2a). Most of the experimental observations are in the L = 0 plane (see fig. 3) which contains information only on the x, y coordinates. Thus the study here is concerned with determining the projected boundary structure. The assumption that significant atomic displacements for a 2 = 5 boundary are limited to a region which is only 4 atomic layers thick (- 0.8 nm for Au) is based on both experimental and theoretical considerations. The thickness of the strained region for a 2 = 377 (0 = 23.8”) twist boundary in gold was experimentally determined to be - 0.8 nm [14]. The intensity profiles for relrods for a 2 = 5 (0 = 36.9O ) boundary were qualitatively observed to be broader, implying a smaller thickness for the strained region. For the B = 23.8’ case, the boundary thickness was in good agreement with the O-lattice spacing, d,, of 0.7 nm. This agreement is consistent with St. Venant’s principle [15]. For the 2 = 5 boundary, the O-lattice spacing is only 0.456 nm and a-narrower boundary region is expected. If the stresses decrease exponentially as exp( - 2rz/d,) [15], then the displacements at a distance z, corresponding to the third plane from the boundary, would be a factor of 275 times smaller than the displacements in the first plane. Thus the assumption that significant relaxations are restricted to a four-layer region in the vicinity of the boundary plane is quite reasonable. 2.4. The atomic positions
in the unit cell.
Following upon the conclusions of the previous section, the determination of the projected 2 = 5
P. Lamarre et al. / Atomic structure of grain boundaries
5
I=
5-
OBSERVATIONS
n
FCC
0
STRONG
15
6= 36.9”
REFLECTION 240,
GB
n
4202
4 -
0
MEDIUM
0
WEAK
A
ABSENT
GB GB
0
/ 3 -
0
0
n
A
A
4002 w
0
A
/ /
K 2 -
/
0
/
A
1 -
/
110,
n
&_A_-_---_
0 t
L
zoo*
m
A
’
-
_
-a
_
_
n
-“;“1_ _ _ _;;;F_+ 3i02
I
I
,
I
0
1
2
3
4
in the HKO
reciprocal
5
I
I
6
7
H Fig. 3. X-ray diffraction
observations
lattice plane for the Au I=
boundary structure proceeds by the standard reliability factor approach that has been used for crystal structure determinations [16]. In this method the x and y coordinates for the two independent atoms labelled A and B in fig. 2a are scanned in small increments over an area covering the range of atomic displacements which generate all possible grain boundary configurations. For each configuration the magnitudes of the structure factors are calculated and compared to the experimentally observed structure factors using the definition of the reliability factor, R, given below:
i where 5”” is the observed structure factor jth reflection, F,Ca’ the calculated structure
of the factor
5 [OOl] twist boundary.
of the jth reflection, and WI a weighting factor (0 < w, < 1). The set of xA, yA, xri, y, coordinates which leads to the smallest value for R provides the best fit to the diffraction observations. Thus the determination of the 2 = 5 structure becomes a search for minimum values for the function R(x,, y,, xr_,, ye). The observations in fig. 3 were put into a quantitative form for use in the reliability factor analysis (see table 1 of ref. [2]). The structure in fig. 4 which is based on the unit cell in fig. 2a was determined to have the smallest R. Examination of fig. 4 reveals several interesting points about the structure. Note that the displacement associated with atom A (first plane from the boundary) is much larger than the displacement associated with atom B (second plane from boundary). This rapid decrease in magnitude for the atomic displacements in planes away from the boundary is as expected for a large-angle boundary (see section 2.3). In order to understand the origin
B-----------q 9
I I
d
I
aa+-
I
i+
I I I
P A
P
I
4
4
A--w
I
I
1
9B
I O1 I
0
displacements associated with the structure generated by the diffraction analysis can be gained by examining fig. 5a, which shows six unrelaxed unit cells containing only the atoms in the first planes above and below the boundary. As mentioned earlier, the displacement of any “white” atom depends on a balance between the repulsive forces of the nearby “black” atoms and the restoring
I
d
a
I
.---_--_-.---------A--______&
&_-_-_-____-&
I
Fig. 4. Atomic displacements for the projected 2’= 5 CSL unit cell. This structure had the smallest R ( = 0.15).
IO
A
I I
*O I
IO
A
I I
of the displacements, consider the forces acting on atom A. The atoms in the lower crystal act to hold atom A in its undisplaced position in order to preserve fee stacking. The atoms in the upper crystal act to displace atom A, with the nearest atoms having the largest effect. In the unrelaxed configuration, atoms A and A, are 23% closer than the nearest neighbor distance in a perfect fee crystal. Thus the observation that in this structure these atoms move apart is physically quite reasonable. Examination of the boundary structure shows that it exhibits symmetry-related displacements which can be interpreted as local rotations about points of good match (called O-elements [12]). The degree of rotation is large ( - 20’ ). At this point, it is important to attempt to understand the 2 = 5 boundary structure in terms of more general physical concepts which may be applicable to other boundaries. The existence of rotational type displacements in grain boundaries was first recognized in connection with low-angle twist boundaries [17]. Here, the observed structure can be interpreted as local rotations about O-elements, of approximately 8/2, which produces large areas of near perfect crystal separated by narrow regions of misfit (lattice screw dislocations). Clearly if local rotations of about o/2 are to occur in large-angle boundaries then large atomic displacements must be involved. Such displacements were not found to occur in the X = 5 computer simulations [2] but are a result of the diffraction analysis, as can be seen in fig. 4. Further insight into the unique nature of the
O I
.I
0
A
0
O
1
I
IO ./
A
0
O1 A 0 0. ~________~________._-------A Unrelaxed
0
A
O1
I I
*O
.O
0
01 I
I I
I
IO I A A
.I
0
01
I I
I A
Ai
0
01 A A I I 0 I 0 ~--------~------_-*--------~ IO I A I I I
.O I
IO A
0
./ 01
A
b ~---__+-t-----+-t-----O--t
6 I I
A
A
h
& I
A
A
A
+
A
I
A
~~~~~~~~~~$__~~~_~__$__~___~_~~
0
I I
0 I
IA
A
0
O VA0
A
b O VA0
A
I
I
I
A A I I ~~~~~~___~__~_~~~_~~~~~~~~~~
I
O A
A
’
6 I
Relaxed
Unrelaxed
Fig. 5. (a) Projected unrelaxed z‘= 5 CSL unit cells contalmng only the atoms in the first planes above and below the grain boundary. (b) Projected relaxed E= 5 CSL unit cells determined by the diffraction analysis. (c) Illustrating the atomic configuration in the vicinity of a unit cell corner.
P. Lamarre
et al. / Atomic structure
force of the “white” single crystal. Fig. 5b shows the structure determined by the diffraction analysis. The “white” atoms are located approximately on the edges of the CSL unit cell, positions of special symmetry. It can be seen that the magnitudes of the displacements are such as to maximize the distance between the “white” and “black” atoms. In fig. 5c the situation in the vicinity of a unit cell corner in figs. 5a and 5b is shown but now with the 2nd, 4th, 6th, etc. planes above the boundary indicated by a black circle l and the lst, 3rd, 5th, etc. planes below the boundary indicated by a white diamond 0. Here it is seen that the 0 atom in the 1st plane below the boundary has by the arrow) in a rotated by - 8/2 (indicated clockwise sense to a position which is approximately on the unit cell edge. It is clear that the displaced 0 atom is in the position of the median fee unit cell between the upper and lower crystals. Thus the diffraction structure conforms to the originally recognized in low angle concept, boundaries, that defines the interface as separate patches of median fee structure. It is interesting that examination of the structure of the 2 = 13 boundary determined by Bristowe and Sass [3] (fig. 4c of their paper) shows the presence of the same local structure, since atoms above and below the boundary plane rotate about O-elements by an angle of - 8/2. As a logical extension of these results, it is tempting to generalize the presence of patches of median fee structure to all high angle [OOl] twist boundaries. 2.5. Conclusions (1) X-ray diffraction techniques can be used to obtain information on the detailed atomic structure of large angle grain boundaries. In particular it is possible to determine (a) the symmetry and, from this, the translation state of the boundary structure, and (b) the projected atomic structure. (2) The 2 = 5 (B = 36.9O) [OOl] twist boundary in Au was shown to be in the untranslated (coincidence) configuration, by a determination of the boundary symmetry. (3) The projected structure of the 2 = 5 boundary consists of groups of atoms which have
of grain boundaries
17
undergone large rotations about regions of good match (O-elements) in the planes immediately adjacent to the boundary. The structure is made up of separate patches of median fee structure. A similar atomic configuration is present in the 2 = 13 (6 = 22.6’) boundary. It is suggested that large rotations about O-elements to produce median fee regions occur in all large angle [OOl] twist boundaries.
3. The influence of bond type on the structure of grain boundaries As a means of studying the influence of bond type on grain boundary structure, it was decided to examine the behavior of the atomic plane spacing along the direction normal to the boundary plane. A new electron diffraction technique was used to study the local variation in plane spacing in the vicinity of the same [OOl] twist boundary in NiO (ionic bonding), Au (metallic bonding) and Ge (covalent bonding). This new diffraction approach [18] will now be described. 3.1. Thin crystal model as the basis of a diffraction technique for detecting the change in plane spacing normal to a twist boundary In fig. 6a a bicrystal is shown with the grain boundary represented as a thin crystal with thickness t. The present treatment will deal with a [OOl] twist boundary in a fee structure (for convenience in discussion) and for this case (002) planes with spacing a, are parallel to the boundary in both crystals. In the interface region the plane spacing is ab, and it will be assumed that a,, > a,,,. In reciprocal space an extra reflection is expected from the thin boundary region, as shown in fig. 6b. Particular attention is paid to the L-direction normal to the boundary passing through 000, since for this case, the diffraction intensity is influenced only by the component along L of the displacement of the atoms in the vicinity of the boundary. The extra grain boundary reflection is elongated because the boundary region is thin, and is displaced away from the superimposed 002,,, fee reflections toward 000, since l/a, > l/a,. Thus
Real
Rectprocal
Space
l.i
of reflections This will no& for simplicity, treated as a spacing. The versely related relrod.
Space
Crystal
along the L-direction through 000. be done in the present paper, where. the grain boundary region will be thin crystal with a uniform plane thickness, t, of the boundary is into the length of the grain boundary
Grain boundary
3.2. Experimentul
technique und results
am
b
Fig. 6. (a) Bicrystal containing
grain boundary
at its midplane.
The spacing of the atomic planes parallel to the boundary
is (I,,,
In crystals 1 and 2. The plane spacing in the grain boundary assumed
to be a different
direction
in reciprocal
constant
value u,,. (b)
The
is
OOL
space due to the bicrystal in (a).
according to the thin crystal model, the plane region can be despacing ah in the boundary termined by examining the interface edge-on in the electron microscope, and measuring the position of the grain boundary reflection relative to the fee reflection. It is expected that u,, will not be constant, but vary along the n-direction, since the displacement field associated with a grain boundary is predicted to fall off exponentially with distance from the boundary plane [15]. It may be possible to determine this variation, u,,( II ). by analysis of observations on the systematic row
Fig. 7. [Ool] twist boundary
(0 = 22 o ), (a) Boundary
inclined
- 30°
In order to determine the position of the extra reflection described in fig. 6b. it is necessary to examine edge-on [OOl] twist boundaries in the electron microscope. The procedures to produce these specimens are described elsewhere. and will be only briefly summarized here. Specimens containing a [OOl] twist boundary in the edge-on orientation in Au were produced by epitaxial growth on a NaCl substrate containing an edge-on [OOl] twist boundary, which was obtained by hot pressing together two cleaved NaCl single crystals [18]. Bicrystals containing a [OOl] twist boundary in NiO were produced by hot pressing together two cleaved NiO single crystals at the desired misorientation [19]. A slab containing the edge-on boundary was then cut from this bicrystal with a diamond saw and ion thinned to produce a specimen suitable for electron microscopy. A typical [OOI] (8 = 22’ ) twist boundary in NiO is shown in fig. 7. Bicrystals containing a [OOl] twist boundary in Ge were grown from the melt using two preori-
to the incident
beam. (b) Same boundary
viewed edge-on
P. Lumarre et al. / Atomic structure of grain boundaries
ented seed crystals. The electron microscopy specimen was obtained in the same manner as for NiO. The experiment described in section 3.1 involves the detection of weak grain boundary reflections which are in the vicinity of matrix reflections of the type OOL. To make the required observations it is necessary to tilt the Ewald sphere by small increments, in order to explore the region in the vicinity of the matrix reflections. The geometry of the experiment in reciprocal space is shown in fig. 8a and the resultant diffraction patterns in the vicinity of the superimposed 002,,, reflections for three different orientations of the Ewald sphere are illustrated schematically in figs. 8b-8d. Diffraction patterns were taken using a Siemens IO2 electron microscope operated at 125 kV, with a well-defocused second condenser lens and exposure times of 30 to 900 s. The orientation of the Ewald sphere was changed in small steps (0.1’ -0.25 ’ ) by varying the direction of the incident electron beam using the dark-field beam deflection coils. Figs. 9a-9f show six diffraction patterns from a long series taken in the vicinity of the 002 reflection, from the grain boundary in NiO. Fig. 9c clearly shows a streak which is displaced away from the 002 reflection toward 000. The tilt
I
‘b)k)(d)
0
Ill
0:2
000
L
Incident beam direction
I I
(b)
I
of - 3/4O from fig. 9c to fig. 9f is sufficient to cause the streak to disappear. The displacement of the streak toward 000 indicates that there is an increase of the (002) plane spacing in the vicinity of the [OOl] twist boundary in NiO. Fig. 9c is characteristic of the observations in this series. Similar experiments were performed on the same type twist boundary in Au and Ge, with a characteristic diffraction pattern for each material shown in fig. 10, together with fig. 9c from NiO. Comparison of the three diffraction patterns in figs. lOa-10c shows a considerably different behavior of the boundary streak for each material. The large displacement toward 000 observed for NiO in fig. 10a corresponds to a large increase in the (002) plane spacing at the [OOl] twist boundary. The small displacement towards 000 observed for Au in fig. lob also corresponds to an increase in (002) plane spacing at the [OOlJ boundary, but with a smaller magnitude than in NiO. The streak is longer in NiO than in Au, which suggests that the NiO boundary is thinner than the Au boundary. Finally, the very small displacement of the streak away from 000 for the Ge boundary in fig. 10~ corresponds to a small decrease in the (002) plane spacing at the [OOl] boundary [28]. The shortness of the streak in fig. 10~ compared to those in figs. 10a and lob indicates that the boundary in Ge is wider than in either NiO or Au. The diffraction observations indicate that there is an expansion in the vicinity of the [OOl] boundary in NiO and Au, while in Ge there may be a small contraction. 3.3. Discussion
(dl L
Fig. 8. (a) Diffraction geometry in the vicinity of the 002 region of reciprocal space. (b)-(d) Schematic diffraction patterns corresponding to the different orientations of the Ewald sphere in (a). The grain boundary relrod is broadened out normal to the foil surface as is the 002 reflection. The boundary relrod is of much lower intensity and thus is detected over a smaller range of orientations than is the 002 reflection.
19
and conclusions
If these observations are considered to be representative of the effect of bonding on boundary structure, then they can be used to make general statements about the structure of grain boundaries. Thus, along the direction normal to the grain boundary it is expected that for materials with (1) ionic bonding there will be a large expansion, (2) metallic bonding there may be a small expansion, and (3) covalent bonding there will be a very small contraction. In addition, it appears that a boundary in a material with covalent bonding is thicker than a boundary in a material with metallic bonding, which is thicker than a boundary in a material with ionic bonding.
Fig. 9. Electron diffraction patterns from a long series taken on the 22’ in steps of - 1 o in going from (a) to (f).
twist boundary
shown in fig. 7. The beam orit :nta
P. Lamarre et al. / Atomic structure of grain boundaries
21
MO
Fig. 10. Electron
diffraction
patterns
in (a) NiO, (b) Au and (c) Ge.
showing the characteristic
grain boundary
diffraction
streaks
from the same [OOI] twist boundary
P. Lamarre et al. / Atomic structure of pun
22
It remains
now to understand
the general
be-
epitaxial
havior in terms of the type of bonding. Why IS the change in plane spacing in ionic materials so large,
ing
concentrated
(001)
materials
and an expansion,
it is so small, spread out and possibly
contraction?
Perhaps
plain
large
is the
materials of NiO
contain
expansion
both
Ni2+
behavior
for
in certain
will be first
boundaries ions,
to an increase
This prediction modeling
ions with like
neighbors.
in the (002)
is in agreement
calculations
that a large increase
When
plane spacing.
with the computer
of Wolf
[20],
in the (002)
relatively
bonding, open
traction
such as Ge,
crystal
does occur,
structure.
perhaps
this
repulsion,
which
tend
is
temperature.
chosen
NaCl
and
If a slight
conat the
further work is needed to improve
structure
tion, diffraction servations
between
and type of bonding.
calculations
are needed
grain
In addi-
and quantitative
ob-
to help with the interpreta-
tion of these diffraction
sintering
same
NaF
were
the specimens was
of annealing,
in H,O
which
102 electron
to
and then
segregation.
dissolved
ating at 125 kV or a JEM scope operating
used
single crystals
bicrystals
two
misori-
for 24 h at each
procedure
Au*
by sinter-
have been
to give extensive
- 100 nm thick
The
leaving
were examined microscope
200CX
electron
opermicro-
at 200 kV.
4.2. Experimental Fig.
lla
effects.
results
shows
the [OOl] twist boundary
pro-
duced from pure Fe and a square network of dislocations which are aligned along (110) directions is clearly visible. Figs. lib and llc show
Fe-O.l8at%
boundary
which
During
either in a Siemens
density.
of the relation
crystals
The
containing
atmosphere
with the final temperature
350°C
observations
the understanding
a hydrogen
Fe-O.lElat%
grain boundary Ge has found a local atomic configuration which can lead to an increase in its Clearly
bicrystal
was produced
were held at 450, 400 and 350°C
strong
to have a
it is because
The
show
plane spacing
expected at [OOl] twist boundaries in NiO. At the other extreme, materials with directional
it is
under
ented by 8 = lS”.
bicrystals
02-
plane of a [OOl]
of NaF.
Fe single
and
there will be a strong Coulombic
leading
in
together
produce
regions
nearest
a
to ex-
layer
the [OOl] twist boundary
Since the (002) planes
that across the interface
twist boundary, signs
the easiest
with ionic bonding.
expected
occurs
while in covalent
houndurr~.~
[OOl]
network lla.
boundary Au
boundary (110)
taken on two different
twist
alloy
with
lla.
Fig.
in fig.
of dislocations directions,
Moire
from
a similar lib
which
similar
fringes
regions of the
produced shows
the
a square
are aligned
to that observed
are frequently
cially in those regions
the
8 as
along in fig.
present,
espe-
where the two crystals
did
not sinter together, however the (110) dislocation network is still clearly visible in fig. llb. Fig. llc 4. The boundary
influence structure
4.1. Experimental
of solute
segregation
on grain
I211 approach
In order to be able to study the effects of solute segregation on grain boundary structure, it is necessary to examine the structure of the same boundary both in the absence and the presence of solute. This is best accomplished by manufacturing [OOl] twist boundaries using the hot pressing technique first used by Schober and Balluffi [22] to produce Au bicrystals. As the first step, 50 nm thick (001) single crystal films of Fe were produced by epitaxial growth on cleaved NaCl single crystals which were covered by a 50 nm thick
shows
another
boundary
region
in which
of
the
a different
Fe-O.l8at%Au structure
is ob-
served; that is, a square network of dislocations which are aligned along (100) directions. It will be demonstrated that the (100) network results from the segregation of Au to the twist grain boundary. The Burgers vectors, b, of the dislocations in the network in figs. lb and lc were determined by measuring the dislocation spacing, d, and the misorientation angle, 8, associated with the twist boundary, and then ]b]/d. A complication the shortest * Composition spectroscopy.
using Frank’s formula, 0 = in this analysis arises when
allowed b does not lie in the plane of determined
using
Rutherford
backscattering
P. Lamarre et al. / Atomic structure of grain boundaries
Fig. 11. Transmission electron micrographs of 0 z l.S” [OOl] twist boundary Fe-O.lSat%Au; (a) and (c) are two different regions of the same boundary.
the
twist
boundary.
The
shortest
structure
is fa(lll),
boundary
plane. In situations
component
which
is not
b in the bee in the (001)
such as this it is the
of the b along the dislocation
line, 6,,
which is used in Frank’s formula. In this manner it was shown that the Burgers vectors of the (100) network in fig. llc are ~~(100) type, while the b, of the (110) network in fig. llb is consistent with Burger vectors of the type ta(ll1). In order to determine if the two different
net-
works
23
viewed at normal incidence
observed
in the
in: (a) Fe and (b). (c)
Fe-O.l8at%Au
alloy
are
associated examined
with different amounts of Au, they were with the microanalytical capability of
the
2OOCX,
JEM
using
energy-dispersive
X-ray
spectrometry. It is worthwhile pointing out that if all of the Au contained in the single crystals above and below the grain boundary were located in the same (001) plane, there would be - l$ monolayers of Au present. The electron beam samples a volume of material
containing
the single
crystals
above
and below the boundary boundary
region.
spectrum
from
grain boundary
plane as well as the grain
Fig. 12a shows a typical the region
containing
the
plane,
X-ray
using
Rutherford
(110)
(RBS).
The RBS
cates
network of dislocations as in fig. Ilb. X-ray peaks from Au, Si and Al are clearly observed. Fig. 12b
the bicrystal
spectrum
in the vicinity
shows a typical X-ray spectrum from the region containing the (100) network of dislocations as in
plane, with lesser amounts
fig. 11~. Again,
FeeO.l8at%Au
are clearly
X-ray
observed.
also observed
12b were taken ness
The
from Au, Si and Al
Si and Al peaks
from the “pure”
no Au was detected. trolled
peaks
The spectra
under
conditions
to be as similar is the same
as possible.
for both
Thus a comparison
were
Fe bicrystals,
sets
while
in figs. 12a and
for
that were con-
surfaces.
boundary [23]),
Since
The foil thick-
boundary
concentrated
at the two
the
alloy
( - O.l4at%Au
at 5OO’C
was carefully
examined
of second
at the midplane remaining
tion
of Au associated
example,
the Au segregation
is seen that the Au peak from the region contain-
boundary
is equivalent
ing
would be - l/4
the
(100)
network
of dislocations
is larger
than the Au peak from the region containing (110) network of dislocations. It is found typically
the amount
ing the (100) greater
than
the that
of Au in the volume contain-
network the
is at least a factor
amount
of Au
containing the (110) network. In order to obtain information tion of the Au along
the direction
(1 IO>
DISLOCATION NETWORK
in the
solution,
much
than
and the
of the bicrystal. in the solid solu0.18
at%.
If.
to the surfaces
to 1 monolayer,
monolayer
which corresponds
of two
information
volume
the boundary diameter.
remaining
plane
The RBS
It clearly
from would
for and
then there in the solid
to a Au composition
on the composition
such a profile
to the
less
and
since after
technique profile
a region
normal
to
- 0.5 mm in
be desirable
from a region hundred
of
provides
to have
nanometers
or less in diameter.
I
3
NETWORK
Si Al I
I
Energy
particles
of - 0.04 at%, much less than the composition
AuM,
X-ray
will be
the phase boundary.
on the distribunormal
phase
of Au to the outer surfaces
boundary
the Au concentration
It
of
of the two phase
in this system
peaks should give a measure of the relative amounts regions.
composition
the grain boundary
the segregation
of the area under the same Au
con-
of the grain
is in the vicinity
the presence
grain
indi-
is largely
none were seen. This is not surprising
of observations.
with the two different
spectroscopy
in fig. 13 clearly
that the Au in the bicrystal
centrated outer
was examined
backscattering
(keV)
X-ray
Energy
Fig. 12. The low energy portion of the energy-dispersive X-ray spectra from regions the (110) network of dislocations; (b) the (100) network of dislocations.
(keV) of boundary
in Fe-O.18
at%Au which show: (a)
P. Lamarre et al. / Atomic structure of grain boundaries
I 1.0
0 0.5
i
, 15
I^h 2.5
20
Backscattered
Energy
3.0
2.70
2.65
(MeV)
Backscattered
2.75 Energy
(MeV)
Fig. 13. (a) Rutherford backscattering spectrum from the Fe-0.18atSAu bicrystal which is shown schematically. spectrum from (a), on which is indicated the origin of the Au signal from the bicrystal.
phase
4.3. Discussion
region
(see
microstructure
fig. 2 of ref.
observed
correspond to a two phase boundary (with the (110)
has limited
each being a separate
solubility
in the host material. Fe-Au
this paper. The occurrence the grain
boundary
measurements. the formation the Fe-Au small
of solute segregation
at
has been confirmed
It can be concluded, of the (100)
by RBS
therefore,
dislocation
twist boundary.
displayed dislocation
that
network
microanalytical
in fig. 12 taken
in combination
in fig. 11 indicate
network
becomes
respect to the (110) dislocation amount of Au at the boundary
that the
favored
network increases.
in
at the
The
with the observations (100)
in
alloy is due to Au segregation
angle
results
This is
alloy discussed
with as the These
observations have clearly demonstrated that solute segregation has a strong influence on the dislocation structure of a small angle twist boundary. It may also be concluded that the change in the character of the dislocation network indicates that a two-dimensional
phase
transformation
brought
explanation crostructure,
At present
the bicrystal
the (100)
are inho-
network is stable, while in
the region with low Au concentration,
the (110)
is stable. Regardless
of which explanation
the observations
in fig. 11 are evidence
is correct, for
a second
in Au, and in the region with high Au
concentration network
the
could
be put forth for this mithe original single crystal
films used to manufacture mogeneous
Thus
and llc
Au
mixture in the grain and (100) networks
phase).
can also whereby
[25]).
in figs. llb
It is generally accepted that solute segregation to grain boundaries is extensive when the solute the case for the Fe-rich
(b) The enlarged
the occurrence
of a two-dimensional
phase
transformation. Much work remains to be done in order to fully understand
these
experimental
results.
It is im-
portant to decide whether the observations in figs. llb and llc represent a two phase mixture. it may be possible to answer this question by studying how the relative areas of the two different networks change when the average Au concentration is increased.
It is also of interest to ask whether the
about by an increasing amount of solute has occurred in the grain boundary. Such transformations have already been observed on single crystal
change in grain boundary structure is influenced by the r&orientation angle 8. Both of these questions are concerned with the determination of the
surfaces [24]. Hart [25] discussed for the case of a grain boundary
phase diagram of a grain boundary, the details of which were discussed in a recent paper by Cahn [26]. Analogous studies to determine the phase
amounts
of solute
such a possibility where increasing
take the boundary
into a two
diagrams
of
surfaces
have
recent
years
[24,27].
cerned
with
where
located.
It can be speculated
the
dislocation
transmission interesting network
electron
carried
questions
Au segregation
is con-
the
dedicated
microscope
Au
of Au causes a
dislocations.
are concerned
Ad-
with whether
the
the grain boundary,
and
dislocations
embrittlement
it is reasonable
whether
with increasing
Finally,
the change
Fe-P.
in boundary
to
structure
amount of solute seen in the Fe-Au
Work
is in progress
to answer
these
questions.
in the dislocation
structure
of the
grain boundary from that present in pure Fe. (2) The change in dislocation structure with increasing occurrence formation
amount of
a
of solute
is evidence
two-dimensional
phase
for the trans-
in the grain boundary.
111A. 121 J.
Bourret
and
P.D. Bristowe
Budai.
in this paper using dif-
fraction techniques to study grain boundary structures in Au was supported by the National Science under
grant
DMR-79-16331
and its
predecessors. The work on NiO and the segregation studies in Fe-Au were supported by the Department of Energy under Contract No. DEAC02-81-ER10956. The use of the central research facilities of the Materials Science Center, the Rutherford backscattering facility of Professor J.W. Mayer and the Cornell High Energy Synchrotron Source are gratefully acknowledged. The NiO single crystals
were grown in the laboratory
of Dr.
Phil.
Mag.
A39
405.
(197’))
and S.L. Saw
Acta Met. 31 (19X3)
[31 P.D. Bristowe and S.L. Sas\. Acta Met. 2X (19X0) 575. A.M. Donald and S.L. Sabs.. Scripta Met. I41 J. Budai. (1982)
16
393.
J. Physique 36 (1975) C4-117. [51 E.D. Hondros. Trans. AIME 161 H.L. Marcus and P.W. Palmberg,
245 (1969)
1 bb4. 171 J.R. Low, Jr.. D.F. Stein. Trans. AIME 242 (1968)
A.M.
Turkalo
D.Y. Guan
Crystal II-21W. Bollmann, (Springer, New York,
Acta
W. Gaudig
C‘rocker.
Schwarvz
Defects
and
and
and
New
and
and S.L. Sass,
Liou
D. Wolf,
Advan.
P. Royen (1955)
[24] [25]
and and
E.W.
Hart,
Phil.
A40 (1979)
Flow
111 Crystals
From
Msg.
Materi-
21 (1970)
Met.
17 (19X3)
in: Surfaces
New
and
Interfaces
Materials
York,
1OY. 1141. Science
1981).
to be published. Scripta
Balluffi,
H. Reinhardt,
Scripta
[27] J.M.
Blakely
(American
caused
Sot.
1977).
Systems,
Met.
Phil.
18 (19X4)
Msg.
Z. Anorg.
N. Perdereau
Cahn,
show
Roy.
Mag.
Diffraction
Peterson,
R.W.
Phil.
Scripta
Ceram..
Trans.
20 (1969)
Allgem.
lb5. 511.
C‘hem. 281
and
J. Oudar.
2 (1968)
179.
Surface
Sci. 36
225.
[26] J.W.
[28] Note
Interfaces
18.
Y. Berthier. (1973)
Balluffi.
and S.L. Sass.
[22] T. Schober
Crystalline
Plastic
York,
Vol. 14 (Plenum.
1211 K. Sickafus [23]
N.L.
A3X (197X)
p. 74.
and Ceramic-Metal
Research, [20]
R.W.
and
457
725.
Mag. 34 (1976)
Mag.
Phil.
1953)
[18]
K.-Y.
Phil.
S.L. Sass.
[17] T. Schober P. Lamarre
30 (19X2)
A39 (1979)
and
J.B. Cohen,
Press,
LaForce.
1970).
Dislocationa [151 A.H. Cottrell. (Oxford University Press,
1161 L.H.
Met.
Mag.
and W. Bollmann, [I31 R.C. Pond London 292 (1979) 449. [I41 J. Budai. 757.
R.P.
and S.L. Sass. Phil.
and A.G.
Briatowe
and
14.
and C.L. Brlant, [Xl R.P. Messmer and S.L. Sass. Phil. [91 W. Gaudig
in Ceramic
Foundation
J. Desaeaux.
699.
[19]
described
with the assistance
419.
als (Academic
Acknowledgements The research
was produced
Laboratory.
References
1111 P.D. 487.
(1) The segregation of Au to a small angle [OOl] twist boundary in an Fe-rich Fe-Au alloy causes a change
National
of Dr. W. Skrotzki.
l1U W. Gaudig, 923.
4.4. Conclusions
major
at Argonne
The Ge bicrystal
in the
system also occurs in other systems such as Fe-Sn and
Peterson
It is also
if it does, the role of the ~(100) inquire
N.L.
scanning
to have lower en-
of 1 u( 111)
process.
is
may have suffi-
this question.
dislocations
embrittles
in
that the Au decorates
to ask why the presence of ~(100)
out
question
boundary
A
to answer
ergy than a network ditional
A further in the
cores.
cient resolution
been
added that
Met.
J. Physique and Society in small
by plane
to the boundary.
H.V.
43 (1982)
for Metals, proof:
Interracial
1979)
Detailed
displacements rumpling
Cb-199.
Thapliyal.
Segregation
p. 137.
diffraction of this
or segregation
as well as a decrease
calculations
type
could
of point in plane
also
be
defects
spacing.
14 (1984) 11-26 Amsterdam
DIFFRACTION BOUNDARIES P. LAMARRE, Department Received
AND MICROSCOPY
F. SCHMUCKLE,
of Materials 11 January
11
STUDIES
OF THE ATOMIC
K. SICKAFUS
Science and Engineering,
STRUCTURE
OF GRAIN
and S.L. SASS
Cornell University, Ithaca, New York 14853, USA
1984; received in final form 13 February
1984; presented
at Workshop
January
1984
The structure of grain boundaries and the influence of solute segregation on boundary structure were studied using diffraction and microscopy techniques. The determination of the projected atomic structure of a large angle [OOl] twist boundary by use of X-ray diffraction techniques was demonstrated. Using an electron diffraction technique it was shown that the local change in plane spacing at a large angle [OOl] twist boundary was dependent on the type of bond (ionic, metallic, covalent) in the material. It was shown that solute segregation causes a major change in the dislocation content of a small angle [OOl] twist boundary in Fe containing a small amount of Au. These observations are evidence for the occurrence of a two-dimensional phase transformation in the grain boundary. As a result of these studies, generalizations were made concerning the structure of large-angle twist boundaries and the influence of bond type on boundary structure.
1. Introduction In recent years a considerable amount of detailed information has been obtained about the structure of grain boundaries by the use of electron microscopy, electron diffraction, X-ray diffraction and computer modeling techniques. Many questions about grain boundary structure still remain to be answered. This paper will discuss some of the important questions that still remain and then describe experiments that attempt to provide answers. 1.1. What is the atomic grain boundaries?
structure
of large-angle
One of the important justifications for studies of grain boundary structure is that through knowledge of their structure it should be possible to understand how boundaries influence properties. As the first step in this process it is necessary to obtain detailed information on the atomic structure of grain boundaries. The boundaries that are good candidates for studies that can provide such information are tilt boundaries, using high resolution electron microscopy techniques [l], and twist
boundaries, using X-ray diffraction techniques. In section 2 of this paper the recent results [2] of an X-ray diffraction study of the projected atomic structure of a large angle [OOl] twist boundary in Au will be examined. 1.2. What is the influence of material and bond type on grain boundary structure? Computer modeling calculations of boundary structure in fee metals predict that the atomic structure should be influenced by the metal in which the boundary is present [3]. Recent observations show that the structures of the same boundary in Au and Ag are quite similar [4], in sharp disagreement with this prediction. The reasons for this disagreement are not understood at present. It seems reasonable to also predict that when the type of bonding in the material changes (e.g., from ionic, to metallic, to covalent) the grain boundary structure should change in a characteristic manner. In order to obtain information on the influence of bond type on boundary structure, the local variation in plane spacing normal to the same type boundary in materials with largely ionic, metallic and covalent type bonding was determined. The
0304-3991/84/$03.00 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
results of this study will be discussed of this paper. 1.3. What is the influence grain boundary structure?
in section
of solute segregation
3
on
It is frequently observed that solute atoms segregate to grain boundaries in alloy systems where there is limited solubility in the solid solution [5]. Auger spectroscopy has shown the presence of typically up to a monolayer of solute at internal interfaces in such systems where equilibrium segregation is important [6]. The practical consequence of such segregation is frequently the embrittlement of the grain boundary region, making it susceptible to fracture at relatively low stresses [7]. It is of considerable interest to learn how the presence of the solute changes the mechanical properties of the boundary. Is the solute changing the chemical bonding across the interface as suggested by Messmer and Briant [8], or is it changing the atomic structure, or perhaps both? In section 4 of this paper the question of whether the presence of solute at the boundary influences the structure of the boundary is addressed.
2. The projected atomic structure of the I= (8 = 36.9”) [OOl] twist boundary in gold 121 2.1. Introduction
5*
to diffraction from grain bounduries
In order to better understand the details of the experimental results of this section, it is useful to first examine the reciprocal lattice associated with the grain boundary. All of the X-ray diffraction observations were made on manufactured bicrystals (see ref. [9] for details), one of which is shown schematically with a small-angle twist boundary at its midplane in fig. la. The reciprocal lattice of this boundary is shown schematically in fig. lb, where the H and K axes lie parallel to the boundary, and the L axis is normal to the boundary plane. The reciprocal lattice is that of the coincidence site lattice (CSL) of the boundary (see ref. [9]). The periodic strain field associated with the * z‘ is the reciprocal
of the density
of coincidence
sites.
Fig. 1. (a) Bicrystal containing a small-angle [OOI] twit boundary with misorientation 0 at its midplane. (b) Schematic three-dimensional reciprocal lattice for the grain boundary m
(a).
grain boundary gives rise to extra reflections, which are shown in the form of reciprocal lattice rods (relrods) since the boundary is not periodic along the z-direction. Reflection intensities in the L = 0 plane are related to the structure of the boundary projected onto the boundary plane while the length of the relrods is related to the boundary thickness. The structural information discussed in this section comes from measurements made on the structure factors in the L = 0 plane (F,,,,,) while the information discussed in section 3 comes from the relrod profiles along the L direction. Since the amount of material at a grain boundary is quite small (equivalent to approximately one monolayer [lo]) the diffraction intensity is also quite low. In order to be able to detect scattering from the boundary region in a reasonable length of time, it is necessary to use high intensity X-ray sources. In previous work on high-angle twist boundaries in Au [9], when using a rotating anode X-ray generator operating at 9 to 10 kW, X-ray film exposures of 100 h were re-
P. Lamarre
et al. / Atomic
structure
of the unit cell
When determining the structure of a periodic object the first step is to determine the dimensions of the unit cell. In grain boundary studies performed on manufactured bicrystal specimens, the unit cell is that of the CSL which is expected to be fixed by the choice of the misorientation axis and angle, and the boundary plane. The second step is to determine the symmetry elements of the unit cell. Figs. 2a and 2b show top and side views, respectively, of the unit cell of the Z = 5 [OOl] twist boundary, with 2 atomic planes above and below the boundary plane. The structuree shown is
Ave
L
Unrelaxed
LO201
a
.
15
Iroo11
0
b
0.
0
.
*
13
in the coincidence site lattice (CSL) configuration; that is, the two crystals are not translated away from the coincidence position for fee structures. Following Bristowe and Cracker [ll], it is seen that this unit cell has the symmetry elements shown in fig. 2c. Any translation of one crystal with respect to the other, which is not a vector of the DSC lattice [12], will change the symmetry associated with the boundary structure. Figs. 2d and 2e show the symmetry elements of two high symmetry translated states characterized by DSC translations D,/2 and (0, + D,)/2, where D, and D2 are the orthogonal DSC basis vectors in the plane of the boundary [ll]). Other translations are possible, and for these cases the number of symmetry elements decreases. The symmetry of the unit cell can be determined from the experimentally observed structure factor rules. The structure factor rules for the three translation states shown in figs. 2c-2e) are given in table 1. A complication in this analysis arises for the D,/2 translation state, where the actual boundary structure could consist of a mixture of domains with the same translation state.
quired to obtain the desired diffraction patterns. Using synchrotron radiation for the same diffraction geometry, an exposure of a few hours was required to obtain diffraction patterns similar to those produced with the rotating anode generator. The X-ray diffraction experiments were carried out at the Cornell High Energy Synchrotron Source (CHESS). 2.2. The symmetry
of gram boundaries
0
0
B 0
*
.
+
AA 0
’ .
Ave
[200]
Perpendicular
n
In
the
Fig. 2. (a) Schematic
diagram of the unrelaxed
P = 5 primitive CSL unit cell projected
grain
and (e) (Dl + Dz)/2
translation
[OOl] twist boundaries
onto the grain boundary
shown. The symmetry
in fee crystals.
elements
grain
Four-fold
-
the same unit cell with two planes above and below the boundary
to
Two-fold
0
boundary
boundary axis axis
plane
Two-fold
his
Two-fold
screw
axis
plane. (b) Side view of
of (c) CSL, (d) D, /2
translation,
Table
1
Diffraction
symmetry
and structure
IFnKi.I= IFiriiz = lFm,I F l,M, = 0 if H is odd
factor
selection
rules
= IFHKLI = IFHKT.I = IFKHLI
FCj,, = 0 if K is odd n, /2
structure
IFIIKI.I = I~~~7.1= l5~i.l
= IFMKLI = I6,~r.l f IFKH/.I
FOKU = 0 if K is odd (D, + D,)/2
structure
IFHK,.I = I&XL No structure
= I~~KLI = IFHKLI = IF,,,zI = IFKH~ I
factor forbidden
reflections
but different orientations. For example, in different areas of the boundary the translation can be either D,/2 or D,/2, yielding two domains. In this case the scattering from the two domains will average together in such a way that there are no longer structure-factor-forbidden reflections and more symmetry is shown in the diffraction pattern than actually exists in any particular domain. The distinguishing difference between the CSL and all other configurations lies in those structure factor selection rules which are related to the presence of two-fold screw axes. For the CSL structure, F,,,, (H = odd) and FoKo (K = odd) must be zero, whereas for the (D, + D,)/2 translation or for a mixture of domains with D,/2 and D/2 translations, intensity can be present at these positions. The observations of Budai, Bristowe and Sass [2] shown in fig. 3 are consistent with the 2‘ = 5 unit cell being in the CSL configuration (untranslated state). The space group of this structure is P42;2 [13]. 2.3. The number
of independent
atoms
in the unit
cell
Once the symmetry has been established the next step is to determine the minimum number of atoms whose positions must be located in order to completely characterize the unit cell contents. By examination of fig. 2a it is seen that there are 5 atoms per plane, with the X. y positions off one atom per plane (at either l/2, l/2 or 0, 0) fixed by the translation state of the boundary. The remaining four atoms in the plane are symmetry-
related by the 4-fold axis. Thus it is necessary to locate 2 atoms per plane in order to locate all the atoms in the plane. If only the X, y positions are to be determined, then it is necessary to locate 1 atom per plane in order to locate all the atoms in the plane. It is also seen that the atoms in the upper and lower crystals are related by the two-fold screw axes lying in the interface plane. What this means is, if it is assumed that the grain boundary is 4 atomic layers thick, then in order to determine the atomic structure projected onto the boundary plane, it is necessary to determine the X, _pcoordinates of only 2 atoms (marked A, B in fig. 2a). Most of the experimental observations are in the L = 0 plane (see fig. 3) which contains information only on the x, y coordinates. Thus the study here is concerned with determining the projected boundary structure. The assumption that significant atomic displacements for a 2 = 5 boundary are limited to a region which is only 4 atomic layers thick (- 0.8 nm for Au) is based on both experimental and theoretical considerations. The thickness of the strained region for a 2 = 377 (0 = 23.8”) twist boundary in gold was experimentally determined to be - 0.8 nm [14]. The intensity profiles for relrods for a 2 = 5 (0 = 36.9O ) boundary were qualitatively observed to be broader, implying a smaller thickness for the strained region. For the B = 23.8’ case, the boundary thickness was in good agreement with the O-lattice spacing, d,, of 0.7 nm. This agreement is consistent with St. Venant’s principle [15]. For the 2 = 5 boundary, the O-lattice spacing is only 0.456 nm and a-narrower boundary region is expected. If the stresses decrease exponentially as exp( - 2rz/d,) [15], then the displacements at a distance z, corresponding to the third plane from the boundary, would be a factor of 275 times smaller than the displacements in the first plane. Thus the assumption that significant relaxations are restricted to a four-layer region in the vicinity of the boundary plane is quite reasonable. 2.4. The atomic positions
in the unit cell.
Following upon the conclusions of the previous section, the determination of the projected 2 = 5
P. Lamarre et al. / Atomic structure of grain boundaries
5
I=
5-
OBSERVATIONS
n
FCC
0
STRONG
15
6= 36.9”
REFLECTION 240,
GB
n
4202
4 -
0
MEDIUM
0
WEAK
A
ABSENT
GB GB
0
/ 3 -
0
0
n
A
A
4002 w
0
A
/ /
K 2 -
/
0
/
A
1 -
/
110,
n
&_A_-_---_
0 t
L
zoo*
m
A
’
-
_
-a
_
_
n
-“;“1_ _ _ _;;;F_+ 3i02
I
I
,
I
0
1
2
3
4
in the HKO
reciprocal
5
I
I
6
7
H Fig. 3. X-ray diffraction
observations
lattice plane for the Au I=
boundary structure proceeds by the standard reliability factor approach that has been used for crystal structure determinations [16]. In this method the x and y coordinates for the two independent atoms labelled A and B in fig. 2a are scanned in small increments over an area covering the range of atomic displacements which generate all possible grain boundary configurations. For each configuration the magnitudes of the structure factors are calculated and compared to the experimentally observed structure factors using the definition of the reliability factor, R, given below:
i where 5”” is the observed structure factor jth reflection, F,Ca’ the calculated structure
of the factor
5 [OOl] twist boundary.
of the jth reflection, and WI a weighting factor (0 < w, < 1). The set of xA, yA, xri, y, coordinates which leads to the smallest value for R provides the best fit to the diffraction observations. Thus the determination of the 2 = 5 structure becomes a search for minimum values for the function R(x,, y,, xr_,, ye). The observations in fig. 3 were put into a quantitative form for use in the reliability factor analysis (see table 1 of ref. [2]). The structure in fig. 4 which is based on the unit cell in fig. 2a was determined to have the smallest R. Examination of fig. 4 reveals several interesting points about the structure. Note that the displacement associated with atom A (first plane from the boundary) is much larger than the displacement associated with atom B (second plane from boundary). This rapid decrease in magnitude for the atomic displacements in planes away from the boundary is as expected for a large-angle boundary (see section 2.3). In order to understand the origin
B-----------q 9
I I
d
I
aa+-
I
i+
I I I
P A
P
I
4
4
A--w
I
I
1
9B
I O1 I
0
displacements associated with the structure generated by the diffraction analysis can be gained by examining fig. 5a, which shows six unrelaxed unit cells containing only the atoms in the first planes above and below the boundary. As mentioned earlier, the displacement of any “white” atom depends on a balance between the repulsive forces of the nearby “black” atoms and the restoring
I
d
a
I
.---_--_-.---------A--______&
&_-_-_-____-&
I
Fig. 4. Atomic displacements for the projected 2’= 5 CSL unit cell. This structure had the smallest R ( = 0.15).
IO
A
I I
*O I
IO
A
I I
of the displacements, consider the forces acting on atom A. The atoms in the lower crystal act to hold atom A in its undisplaced position in order to preserve fee stacking. The atoms in the upper crystal act to displace atom A, with the nearest atoms having the largest effect. In the unrelaxed configuration, atoms A and A, are 23% closer than the nearest neighbor distance in a perfect fee crystal. Thus the observation that in this structure these atoms move apart is physically quite reasonable. Examination of the boundary structure shows that it exhibits symmetry-related displacements which can be interpreted as local rotations about points of good match (called O-elements [12]). The degree of rotation is large ( - 20’ ). At this point, it is important to attempt to understand the 2 = 5 boundary structure in terms of more general physical concepts which may be applicable to other boundaries. The existence of rotational type displacements in grain boundaries was first recognized in connection with low-angle twist boundaries [17]. Here, the observed structure can be interpreted as local rotations about O-elements, of approximately 8/2, which produces large areas of near perfect crystal separated by narrow regions of misfit (lattice screw dislocations). Clearly if local rotations of about o/2 are to occur in large-angle boundaries then large atomic displacements must be involved. Such displacements were not found to occur in the X = 5 computer simulations [2] but are a result of the diffraction analysis, as can be seen in fig. 4. Further insight into the unique nature of the
O I
.I
0
A
0
O
1
I
IO ./
A
0
O1 A 0 0. ~________~________._-------A Unrelaxed
0
A
O1
I I
*O
.O
0
01 I
I I
I
IO I A A
.I
0
01
I I
I A
Ai
0
01 A A I I 0 I 0 ~--------~------_-*--------~ IO I A I I I
.O I
IO A
0
./ 01
A
b ~---__+-t-----+-t-----O--t
6 I I
A
A
h
& I
A
A
A
+
A
I
A
~~~~~~~~~~$__~~~_~__$__~___~_~~
0
I I
0 I
IA
A
0
O VA0
A
b O VA0
A
I
I
I
A A I I ~~~~~~___~__~_~~~_~~~~~~~~~~
I
O A
A
’
6 I
Relaxed
Unrelaxed
Fig. 5. (a) Projected unrelaxed z‘= 5 CSL unit cells contalmng only the atoms in the first planes above and below the grain boundary. (b) Projected relaxed E= 5 CSL unit cells determined by the diffraction analysis. (c) Illustrating the atomic configuration in the vicinity of a unit cell corner.
P. Lamarre
et al. / Atomic structure
force of the “white” single crystal. Fig. 5b shows the structure determined by the diffraction analysis. The “white” atoms are located approximately on the edges of the CSL unit cell, positions of special symmetry. It can be seen that the magnitudes of the displacements are such as to maximize the distance between the “white” and “black” atoms. In fig. 5c the situation in the vicinity of a unit cell corner in figs. 5a and 5b is shown but now with the 2nd, 4th, 6th, etc. planes above the boundary indicated by a black circle l and the lst, 3rd, 5th, etc. planes below the boundary indicated by a white diamond 0. Here it is seen that the 0 atom in the 1st plane below the boundary has by the arrow) in a rotated by - 8/2 (indicated clockwise sense to a position which is approximately on the unit cell edge. It is clear that the displaced 0 atom is in the position of the median fee unit cell between the upper and lower crystals. Thus the diffraction structure conforms to the originally recognized in low angle concept, boundaries, that defines the interface as separate patches of median fee structure. It is interesting that examination of the structure of the 2 = 13 boundary determined by Bristowe and Sass [3] (fig. 4c of their paper) shows the presence of the same local structure, since atoms above and below the boundary plane rotate about O-elements by an angle of - 8/2. As a logical extension of these results, it is tempting to generalize the presence of patches of median fee structure to all high angle [OOl] twist boundaries. 2.5. Conclusions (1) X-ray diffraction techniques can be used to obtain information on the detailed atomic structure of large angle grain boundaries. In particular it is possible to determine (a) the symmetry and, from this, the translation state of the boundary structure, and (b) the projected atomic structure. (2) The 2 = 5 (B = 36.9O) [OOl] twist boundary in Au was shown to be in the untranslated (coincidence) configuration, by a determination of the boundary symmetry. (3) The projected structure of the 2 = 5 boundary consists of groups of atoms which have
of grain boundaries
17
undergone large rotations about regions of good match (O-elements) in the planes immediately adjacent to the boundary. The structure is made up of separate patches of median fee structure. A similar atomic configuration is present in the 2 = 13 (6 = 22.6’) boundary. It is suggested that large rotations about O-elements to produce median fee regions occur in all large angle [OOl] twist boundaries.
3. The influence of bond type on the structure of grain boundaries As a means of studying the influence of bond type on grain boundary structure, it was decided to examine the behavior of the atomic plane spacing along the direction normal to the boundary plane. A new electron diffraction technique was used to study the local variation in plane spacing in the vicinity of the same [OOl] twist boundary in NiO (ionic bonding), Au (metallic bonding) and Ge (covalent bonding). This new diffraction approach [18] will now be described. 3.1. Thin crystal model as the basis of a diffraction technique for detecting the change in plane spacing normal to a twist boundary In fig. 6a a bicrystal is shown with the grain boundary represented as a thin crystal with thickness t. The present treatment will deal with a [OOl] twist boundary in a fee structure (for convenience in discussion) and for this case (002) planes with spacing a, are parallel to the boundary in both crystals. In the interface region the plane spacing is ab, and it will be assumed that a,, > a,,,. In reciprocal space an extra reflection is expected from the thin boundary region, as shown in fig. 6b. Particular attention is paid to the L-direction normal to the boundary passing through 000, since for this case, the diffraction intensity is influenced only by the component along L of the displacement of the atoms in the vicinity of the boundary. The extra grain boundary reflection is elongated because the boundary region is thin, and is displaced away from the superimposed 002,,, fee reflections toward 000, since l/a, > l/a,. Thus
Real
Rectprocal
Space
l.i
of reflections This will no& for simplicity, treated as a spacing. The versely related relrod.
Space
Crystal
along the L-direction through 000. be done in the present paper, where. the grain boundary region will be thin crystal with a uniform plane thickness, t, of the boundary is into the length of the grain boundary
Grain boundary
3.2. Experimentul
technique und results
am
b
Fig. 6. (a) Bicrystal containing
grain boundary
at its midplane.
The spacing of the atomic planes parallel to the boundary
is (I,,,
In crystals 1 and 2. The plane spacing in the grain boundary assumed
to be a different
direction
in reciprocal
constant
value u,,. (b)
The
is
OOL
space due to the bicrystal in (a).
according to the thin crystal model, the plane region can be despacing ah in the boundary termined by examining the interface edge-on in the electron microscope, and measuring the position of the grain boundary reflection relative to the fee reflection. It is expected that u,, will not be constant, but vary along the n-direction, since the displacement field associated with a grain boundary is predicted to fall off exponentially with distance from the boundary plane [15]. It may be possible to determine this variation, u,,( II ). by analysis of observations on the systematic row
Fig. 7. [Ool] twist boundary
(0 = 22 o ), (a) Boundary
inclined
- 30°
In order to determine the position of the extra reflection described in fig. 6b. it is necessary to examine edge-on [OOl] twist boundaries in the electron microscope. The procedures to produce these specimens are described elsewhere. and will be only briefly summarized here. Specimens containing a [OOl] twist boundary in the edge-on orientation in Au were produced by epitaxial growth on a NaCl substrate containing an edge-on [OOl] twist boundary, which was obtained by hot pressing together two cleaved NaCl single crystals [18]. Bicrystals containing a [OOl] twist boundary in NiO were produced by hot pressing together two cleaved NiO single crystals at the desired misorientation [19]. A slab containing the edge-on boundary was then cut from this bicrystal with a diamond saw and ion thinned to produce a specimen suitable for electron microscopy. A typical [OOI] (8 = 22’ ) twist boundary in NiO is shown in fig. 7. Bicrystals containing a [OOl] twist boundary in Ge were grown from the melt using two preori-
to the incident
beam. (b) Same boundary
viewed edge-on
P. Lumarre et al. / Atomic structure of grain boundaries
ented seed crystals. The electron microscopy specimen was obtained in the same manner as for NiO. The experiment described in section 3.1 involves the detection of weak grain boundary reflections which are in the vicinity of matrix reflections of the type OOL. To make the required observations it is necessary to tilt the Ewald sphere by small increments, in order to explore the region in the vicinity of the matrix reflections. The geometry of the experiment in reciprocal space is shown in fig. 8a and the resultant diffraction patterns in the vicinity of the superimposed 002,,, reflections for three different orientations of the Ewald sphere are illustrated schematically in figs. 8b-8d. Diffraction patterns were taken using a Siemens IO2 electron microscope operated at 125 kV, with a well-defocused second condenser lens and exposure times of 30 to 900 s. The orientation of the Ewald sphere was changed in small steps (0.1’ -0.25 ’ ) by varying the direction of the incident electron beam using the dark-field beam deflection coils. Figs. 9a-9f show six diffraction patterns from a long series taken in the vicinity of the 002 reflection, from the grain boundary in NiO. Fig. 9c clearly shows a streak which is displaced away from the 002 reflection toward 000. The tilt
I
‘b)k)(d)
0
Ill
0:2
000
L
Incident beam direction
I I
(b)
I
of - 3/4O from fig. 9c to fig. 9f is sufficient to cause the streak to disappear. The displacement of the streak toward 000 indicates that there is an increase of the (002) plane spacing in the vicinity of the [OOl] twist boundary in NiO. Fig. 9c is characteristic of the observations in this series. Similar experiments were performed on the same type twist boundary in Au and Ge, with a characteristic diffraction pattern for each material shown in fig. 10, together with fig. 9c from NiO. Comparison of the three diffraction patterns in figs. lOa-10c shows a considerably different behavior of the boundary streak for each material. The large displacement toward 000 observed for NiO in fig. 10a corresponds to a large increase in the (002) plane spacing at the [OOl] twist boundary. The small displacement towards 000 observed for Au in fig. lob also corresponds to an increase in (002) plane spacing at the [OOlJ boundary, but with a smaller magnitude than in NiO. The streak is longer in NiO than in Au, which suggests that the NiO boundary is thinner than the Au boundary. Finally, the very small displacement of the streak away from 000 for the Ge boundary in fig. 10~ corresponds to a small decrease in the (002) plane spacing at the [OOl] boundary [28]. The shortness of the streak in fig. 10~ compared to those in figs. 10a and lob indicates that the boundary in Ge is wider than in either NiO or Au. The diffraction observations indicate that there is an expansion in the vicinity of the [OOl] boundary in NiO and Au, while in Ge there may be a small contraction. 3.3. Discussion
(dl L
Fig. 8. (a) Diffraction geometry in the vicinity of the 002 region of reciprocal space. (b)-(d) Schematic diffraction patterns corresponding to the different orientations of the Ewald sphere in (a). The grain boundary relrod is broadened out normal to the foil surface as is the 002 reflection. The boundary relrod is of much lower intensity and thus is detected over a smaller range of orientations than is the 002 reflection.
19
and conclusions
If these observations are considered to be representative of the effect of bonding on boundary structure, then they can be used to make general statements about the structure of grain boundaries. Thus, along the direction normal to the grain boundary it is expected that for materials with (1) ionic bonding there will be a large expansion, (2) metallic bonding there may be a small expansion, and (3) covalent bonding there will be a very small contraction. In addition, it appears that a boundary in a material with covalent bonding is thicker than a boundary in a material with metallic bonding, which is thicker than a boundary in a material with ionic bonding.
Fig. 9. Electron diffraction patterns from a long series taken on the 22’ in steps of - 1 o in going from (a) to (f).
twist boundary
shown in fig. 7. The beam orit :nta
P. Lamarre et al. / Atomic structure of grain boundaries
21
MO
Fig. 10. Electron
diffraction
patterns
in (a) NiO, (b) Au and (c) Ge.
showing the characteristic
grain boundary
diffraction
streaks
from the same [OOI] twist boundary
P. Lamarre et al. / Atomic structure of pun
22
It remains
now to understand
the general
be-
epitaxial
havior in terms of the type of bonding. Why IS the change in plane spacing in ionic materials so large,
ing
concentrated
(001)
materials
and an expansion,
it is so small, spread out and possibly
contraction?
Perhaps
plain
large
is the
materials of NiO
contain
expansion
both
Ni2+
behavior
for
in certain
will be first
boundaries ions,
to an increase
This prediction modeling
ions with like
neighbors.
in the (002)
is in agreement
calculations
that a large increase
When
plane spacing.
with the computer
of Wolf
[20],
in the (002)
relatively
bonding, open
traction
such as Ge,
crystal
does occur,
structure.
perhaps
this
repulsion,
which
tend
is
temperature.
chosen
NaCl
and
If a slight
conat the
further work is needed to improve
structure
tion, diffraction servations
between
and type of bonding.
calculations
are needed
grain
In addi-
and quantitative
ob-
to help with the interpreta-
tion of these diffraction
sintering
same
NaF
were
the specimens was
of annealing,
in H,O
which
102 electron
to
and then
segregation.
dissolved
ating at 125 kV or a JEM scope operating
used
single crystals
bicrystals
two
misori-
for 24 h at each
procedure
Au*
by sinter-
have been
to give extensive
- 100 nm thick
The
leaving
were examined microscope
200CX
electron
opermicro-
at 200 kV.
4.2. Experimental Fig.
lla
effects.
results
shows
the [OOl] twist boundary
pro-
duced from pure Fe and a square network of dislocations which are aligned along (110) directions is clearly visible. Figs. lib and llc show
Fe-O.l8at%
boundary
which
During
either in a Siemens
density.
of the relation
crystals
The
containing
atmosphere
with the final temperature
350°C
observations
the understanding
a hydrogen
Fe-O.lElat%
grain boundary Ge has found a local atomic configuration which can lead to an increase in its Clearly
bicrystal
was produced
were held at 450, 400 and 350°C
strong
to have a
it is because
The
show
plane spacing
expected at [OOl] twist boundaries in NiO. At the other extreme, materials with directional
it is
under
ented by 8 = lS”.
bicrystals
02-
plane of a [OOl]
of NaF.
Fe single
and
there will be a strong Coulombic
leading
in
together
produce
regions
nearest
a
to ex-
layer
the [OOl] twist boundary
Since the (002) planes
that across the interface
twist boundary, signs
the easiest
with ionic bonding.
expected
occurs
while in covalent
houndurr~.~
[OOl]
network lla.
boundary Au
boundary (110)
taken on two different
twist
alloy
with
lla.
Fig.
in fig.
of dislocations directions,
Moire
from
a similar lib
which
similar
fringes
regions of the
produced shows
the
a square
are aligned
to that observed
are frequently
cially in those regions
the
8 as
along in fig.
present,
espe-
where the two crystals
did
not sinter together, however the (110) dislocation network is still clearly visible in fig. llb. Fig. llc 4. The boundary
influence structure
4.1. Experimental
of solute
segregation
on grain
I211 approach
In order to be able to study the effects of solute segregation on grain boundary structure, it is necessary to examine the structure of the same boundary both in the absence and the presence of solute. This is best accomplished by manufacturing [OOl] twist boundaries using the hot pressing technique first used by Schober and Balluffi [22] to produce Au bicrystals. As the first step, 50 nm thick (001) single crystal films of Fe were produced by epitaxial growth on cleaved NaCl single crystals which were covered by a 50 nm thick
shows
another
boundary
region
in which
of
the
a different
Fe-O.l8at%Au structure
is ob-
served; that is, a square network of dislocations which are aligned along (100) directions. It will be demonstrated that the (100) network results from the segregation of Au to the twist grain boundary. The Burgers vectors, b, of the dislocations in the network in figs. lb and lc were determined by measuring the dislocation spacing, d, and the misorientation angle, 8, associated with the twist boundary, and then ]b]/d. A complication the shortest * Composition spectroscopy.
using Frank’s formula, 0 = in this analysis arises when
allowed b does not lie in the plane of determined
using
Rutherford
backscattering
P. Lamarre et al. / Atomic structure of grain boundaries
Fig. 11. Transmission electron micrographs of 0 z l.S” [OOl] twist boundary Fe-O.lSat%Au; (a) and (c) are two different regions of the same boundary.
the
twist
boundary.
The
shortest
structure
is fa(lll),
boundary
plane. In situations
component
which
is not
b in the bee in the (001)
such as this it is the
of the b along the dislocation
line, 6,,
which is used in Frank’s formula. In this manner it was shown that the Burgers vectors of the (100) network in fig. llc are ~~(100) type, while the b, of the (110) network in fig. llb is consistent with Burger vectors of the type ta(ll1). In order to determine if the two different
net-
works
23
viewed at normal incidence
observed
in the
in: (a) Fe and (b). (c)
Fe-O.l8at%Au
alloy
are
associated examined
with different amounts of Au, they were with the microanalytical capability of
the
2OOCX,
JEM
using
energy-dispersive
X-ray
spectrometry. It is worthwhile pointing out that if all of the Au contained in the single crystals above and below the grain boundary were located in the same (001) plane, there would be - l$ monolayers of Au present. The electron beam samples a volume of material
containing
the single
crystals
above
and below the boundary boundary
region.
spectrum
from
grain boundary
plane as well as the grain
Fig. 12a shows a typical the region
containing
the
plane,
X-ray
using
Rutherford
(110)
(RBS).
The RBS
cates
network of dislocations as in fig. Ilb. X-ray peaks from Au, Si and Al are clearly observed. Fig. 12b
the bicrystal
spectrum
in the vicinity
shows a typical X-ray spectrum from the region containing the (100) network of dislocations as in
plane, with lesser amounts
fig. 11~. Again,
FeeO.l8at%Au
are clearly
X-ray
observed.
also observed
12b were taken ness
The
from Au, Si and Al
Si and Al peaks
from the “pure”
no Au was detected. trolled
peaks
The spectra
under
conditions
to be as similar is the same
as possible.
for both
Thus a comparison
were
Fe bicrystals,
sets
while
in figs. 12a and
for
that were con-
surfaces.
boundary [23]),
Since
The foil thick-
boundary
concentrated
at the two
the
alloy
( - O.l4at%Au
at 5OO’C
was carefully
examined
of second
at the midplane remaining
tion
of Au associated
example,
the Au segregation
is seen that the Au peak from the region contain-
boundary
is equivalent
ing
would be - l/4
the
(100)
network
of dislocations
is larger
than the Au peak from the region containing (110) network of dislocations. It is found typically
the amount
ing the (100) greater
than
the that
of Au in the volume contain-
network the
is at least a factor
amount
of Au
containing the (110) network. In order to obtain information tion of the Au along
the direction
(1 IO>
DISLOCATION NETWORK
in the
solution,
much
than
and the
of the bicrystal. in the solid solu0.18
at%.
If.
to the surfaces
to 1 monolayer,
monolayer
which corresponds
of two
information
volume
the boundary diameter.
remaining
plane
The RBS
It clearly
from would
for and
then there in the solid
to a Au composition
on the composition
such a profile
to the
less
and
since after
technique profile
a region
normal
to
- 0.5 mm in
be desirable
from a region hundred
of
provides
to have
nanometers
or less in diameter.
I
3
NETWORK
Si Al I
I
Energy
particles
of - 0.04 at%, much less than the composition
AuM,
X-ray
will be
the phase boundary.
on the distribunormal
phase
of Au to the outer surfaces
boundary
the Au concentration
It
of
of the two phase
in this system
peaks should give a measure of the relative amounts regions.
composition
the grain boundary
the segregation
of the area under the same Au
con-
of the grain
is in the vicinity
the presence
grain
indi-
is largely
none were seen. This is not surprising
of observations.
with the two different
spectroscopy
in fig. 13 clearly
that the Au in the bicrystal
centrated outer
was examined
backscattering
(keV)
X-ray
Energy
Fig. 12. The low energy portion of the energy-dispersive X-ray spectra from regions the (110) network of dislocations; (b) the (100) network of dislocations.
(keV) of boundary
in Fe-O.18
at%Au which show: (a)
P. Lamarre et al. / Atomic structure of grain boundaries
I 1.0
0 0.5
i
, 15
I^h 2.5
20
Backscattered
Energy
3.0
2.70
2.65
(MeV)
Backscattered
2.75 Energy
(MeV)
Fig. 13. (a) Rutherford backscattering spectrum from the Fe-0.18atSAu bicrystal which is shown schematically. spectrum from (a), on which is indicated the origin of the Au signal from the bicrystal.
phase
4.3. Discussion
region
(see
microstructure
fig. 2 of ref.
observed
correspond to a two phase boundary (with the (110)
has limited
each being a separate
solubility
in the host material. Fe-Au
this paper. The occurrence the grain
boundary
measurements. the formation the Fe-Au small
of solute segregation
at
has been confirmed
It can be concluded, of the (100)
by RBS
therefore,
dislocation
twist boundary.
displayed dislocation
that
network
microanalytical
in fig. 12 taken
in combination
in fig. 11 indicate
network
becomes
respect to the (110) dislocation amount of Au at the boundary
that the
favored
network increases.
in
at the
The
with the observations (100)
in
alloy is due to Au segregation
angle
results
This is
alloy discussed
with as the These
observations have clearly demonstrated that solute segregation has a strong influence on the dislocation structure of a small angle twist boundary. It may also be concluded that the change in the character of the dislocation network indicates that a two-dimensional
phase
transformation
brought
explanation crostructure,
At present
the bicrystal
the (100)
are inho-
network is stable, while in
the region with low Au concentration,
the (110)
is stable. Regardless
of which explanation
the observations
in fig. 11 are evidence
is correct, for
a second
in Au, and in the region with high Au
concentration network
the
could
be put forth for this mithe original single crystal
films used to manufacture mogeneous
Thus
and llc
Au
mixture in the grain and (100) networks
phase).
can also whereby
[25]).
in figs. llb
It is generally accepted that solute segregation to grain boundaries is extensive when the solute the case for the Fe-rich
(b) The enlarged
the occurrence
of a two-dimensional
phase
transformation. Much work remains to be done in order to fully understand
these
experimental
results.
It is im-
portant to decide whether the observations in figs. llb and llc represent a two phase mixture. it may be possible to answer this question by studying how the relative areas of the two different networks change when the average Au concentration is increased.
It is also of interest to ask whether the
about by an increasing amount of solute has occurred in the grain boundary. Such transformations have already been observed on single crystal
change in grain boundary structure is influenced by the r&orientation angle 8. Both of these questions are concerned with the determination of the
surfaces [24]. Hart [25] discussed for the case of a grain boundary
phase diagram of a grain boundary, the details of which were discussed in a recent paper by Cahn [26]. Analogous studies to determine the phase
amounts
of solute
such a possibility where increasing
take the boundary
into a two
diagrams
of
surfaces
have
recent
years
[24,27].
cerned
with
where
located.
It can be speculated
the
dislocation
transmission interesting network
electron
carried
questions
Au segregation
is con-
the
dedicated
microscope
Au
of Au causes a
dislocations.
are concerned
Ad-
with whether
the
the grain boundary,
and
dislocations
embrittlement
it is reasonable
whether
with increasing
Finally,
the change
Fe-P.
in boundary
to
structure
amount of solute seen in the Fe-Au
Work
is in progress
to answer
these
questions.
in the dislocation
structure
of the
grain boundary from that present in pure Fe. (2) The change in dislocation structure with increasing occurrence formation
amount of
a
of solute
is evidence
two-dimensional
phase
for the trans-
in the grain boundary.
111A. 121 J.
Bourret
and
P.D. Bristowe
Budai.
in this paper using dif-
fraction techniques to study grain boundary structures in Au was supported by the National Science under
grant
DMR-79-16331
and its
predecessors. The work on NiO and the segregation studies in Fe-Au were supported by the Department of Energy under Contract No. DEAC02-81-ER10956. The use of the central research facilities of the Materials Science Center, the Rutherford backscattering facility of Professor J.W. Mayer and the Cornell High Energy Synchrotron Source are gratefully acknowledged. The NiO single crystals
were grown in the laboratory
of Dr.
Phil.
Mag.
A39
405.
(197’))
and S.L. Saw
Acta Met. 31 (19X3)
[31 P.D. Bristowe and S.L. Sas\. Acta Met. 2X (19X0) 575. A.M. Donald and S.L. Sabs.. Scripta Met. I41 J. Budai. (1982)
16
393.
J. Physique 36 (1975) C4-117. [51 E.D. Hondros. Trans. AIME 161 H.L. Marcus and P.W. Palmberg,
245 (1969)
1 bb4. 171 J.R. Low, Jr.. D.F. Stein. Trans. AIME 242 (1968)
A.M.
Turkalo
D.Y. Guan
Crystal II-21W. Bollmann, (Springer, New York,
Acta
W. Gaudig
C‘rocker.
Schwarvz
Defects
and
and
and
New
and
and S.L. Sass,
Liou
D. Wolf,
Advan.
P. Royen (1955)
[24] [25]
and and
E.W.
Hart,
Phil.
A40 (1979)
Flow
111 Crystals
From
Msg.
Materi-
21 (1970)
Met.
17 (19X3)
in: Surfaces
New
and
Interfaces
Materials
York,
1OY. 1141. Science
1981).
to be published. Scripta
Balluffi,
H. Reinhardt,
Scripta
[27] J.M.
Blakely
(American
caused
Sot.
1977).
Systems,
Met.
Phil.
18 (19X4)
Msg.
Z. Anorg.
N. Perdereau
Cahn,
show
Roy.
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Diffraction
Peterson,
R.W.
Phil.
Scripta
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20 (1969)
Allgem.
lb5. 511.
C‘hem. 281
and
J. Oudar.
2 (1968)
179.
Surface
Sci. 36
225.
[26] J.W.
[28] Note
Interfaces
18.
Y. Berthier. (1973)
Balluffi.
and S.L. Sass.
[22] T. Schober
Crystalline
Plastic
York,
Vol. 14 (Plenum.
1211 K. Sickafus [23]
N.L.
A3X (197X)
p. 74.
and Ceramic-Metal
Research, [20]
R.W.
and
457
725.
Mag. 34 (1976)
Mag.
Phil.
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[18]
K.-Y.
Phil.
S.L. Sass.
[17] T. Schober P. Lamarre
30 (19X2)
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J.B. Cohen,
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Dislocationa [151 A.H. Cottrell. (Oxford University Press,
1161 L.H.
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and W. Bollmann, [I31 R.C. Pond London 292 (1979) 449. [I41 J. Budai. 757.
R.P.
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and A.G.
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Acknowledgements The research
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(1) The segregation of Au to a small angle [OOl] twist boundary in an Fe-rich Fe-Au alloy causes a change
National
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l1U W. Gaudig, 923.
4.4. Conclusions
major
at Argonne
The Ge bicrystal
in the
system also occurs in other systems such as Fe-Sn and
Peterson
It is also
if it does, the role of the ~(100) inquire
N.L.
scanning
to have lower en-
of 1 u( 111)
process.
is
may have suffi-
this question.
dislocations
embrittles
in
that the Au decorates
to ask why the presence of ~(100)
out
question
boundary
A
to answer
ergy than a network ditional
A further in the
cores.
cient resolution
been
added that
Met.
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by plane
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H.V.
43 (1982)
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Interracial
1979)
Detailed
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Cb-199.
Thapliyal.
Segregation
p. 137.
diffraction of this
or segregation
as well as a decrease
calculations
type
could
of point in plane
also
be
defects
spacing.