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5.4 Partial Dislocations and Stacking Faults

5.4.1 Stacking Faults and Close Packed Lattices

	Let's consider a close packedlattice, and look at the close packed planes.
		In a simple model usingperfect spheres we have the following situation:
		We take the blue atoms as the base planefor what we are going to built on it, we will call it the "". The next layer will have the center of the atomsright over the depressions of the -plane; it could be either the - or - configuration. Here the pink layer is in the "" position If you pick the - configuration (and whatever you pick at thisstage, we can always call it theB - configuration), the third layer caneither be directly over the - plane andthen is also an - plane (shown for oneatom), or in the - configuration. If you chose ""; you obtain thehexagonal close packedlattice (hcp), if you chose "", you get theface centered cubic lattice(fcc) You can't have it both ways. If you start in the position somewhere (in the picture thegreen atoms) and on the positionsomewhere else (light blue), you will get a problem as soon as the two layersmeet. For varieties sake, and to be able todistinguish the layers better, the bottom layer here is in dark blue.
	The stacking sequences of the twoclose-packed lattices therefore are
		fcc:...
		hcp:...
	Looking at this sequences incross-section is a bit more involved; it is best done in a<110> projectionof thefcc lattice
					Planes with the same letter are on lines perpendicular to the{111} planes, as indicated by thin black lines.
					The projection of the elementary cell is shown with lines.
					We now remove of ahorizontal{111} plane - e.g. by agglomeration of vacancies on thatplane - it shall be a-plane here.
					Now and- planes become neighbors and relax into theconfiguration shown.
					We produced astacking fault because the stacking sequence.. has been changed to the faulty sequence... The stacking fault is between the large letters.
					Stacking faults by themselves are simpletwo-dimensional defects. They carry a certainstacking fault energyγ; very roughly around a few100mJ/m2.
					The disc of vacancies obviously is bordered by an. What is the Burgers vector of thisdislocation? We shall see farther down.
	If we do not condense on a plane, but fill in a disc ofagglomerated, we obtain thefollowing structure
					The stacking sequence...again is faulty; itis now... . The stacking fault is between the large letters.
					This is a than the one from above.
					For historical reasons, we call the stacking fault produced byvacancy agglomeration "intrinsicstacking fault" and the stacking fault produced by interstitialagglomeration "extrinsic stackingfault".
					The extrinsic stacking fault also seems to be bordered by anedge dislocation. Again, what is the Burgers vector?
	In order to determine the Burgersvector of the apparent dislocations bordering the stacking faults, we must do aBurgers circuit use the Volterradefinition. For this we must first be clear about the directions in the chosenprojection. This is shown below.
		in the<110> projection shown for the elementary cell traced out on the right or above Traces of the (color-coded) (right angle to direction) in the<110> projection and the elementary cell.
	From a Burgers circuit or from aVoltaterra cut, we obtain the same result (Try it! It is easier in this case tohop from atom to atom (instead from lattice point to lattice point); start atthe stacking fault).
		The Burgers vector of thesedislocations isb = ± a/3 <111>  -! Donot, at this point, forget thedistinction betweenlattice and crystal!
		Dislocations with Burgers vectors ofthis type are calledpartialdislocations, or more correctly, partial dislocations, or simplyFrank dislocations.
	This brings us to a generaldefinition:Dislocations with Burgers vector that are translation vectors of the lattice are called. They must bynecessity border a two-dimensional defect, usually a stacking fault.
			This can be verified with theVolterra construction if weadd one element: Make a cut in a{111} plane and shift bya/3<111> perpendicular to the plane. The element added is that wenow include shift vectors that aretranslation vectors of the, butvectors between of the.
			Partial Burgers vectors and stacking faults thusmay exist if the packing of atoms defining the crystal has additionalsymmetries not found in the lattice. Checkthis advancedmodule for an elaboration.
			As stated in thedefinition of the Volterracut-shift-weld procedure, you now must add or remove material. The total effectis the creation of a Frank partial along the cut line and, by necessity, astacking fault on the cut part of the{111} plane.
	We also see now that the primarydefects which are generated by the agglomeration of intrinsic point defects infcc lattices are small "stackingfault loops".

	Now we may ask a question: Can weproduce stacking faults? Indeed, we may - use theVolterra definition to seehow:
		Make a cut on a{111} plane, e.g. between theA- andB-plane.
		Move theB-plane so it is nowin aC-position. No material must be removed or added.
		Weld together: You now have thestacking sequenceABCACABCA... instead ofABCABCA.., i.e. youproduced the stacking sequence of an stacking fault.
	The vector of the shift must be theBurgers vector of the partial dislocation resulting from this operation as theboundary of the intrinsic stacking fault. This shift vector can be seen byprojecting the elementary cell on the close packed{111} plane where wedid the cut.
		The displacement vectors for producing stacking faults with the Volterra construction. We have all vectors pointing from one "dent" to a neighboring one. The directions in the{111} plane. If you superimpose the two red circles, you have the projection shown on the left.  Each one of the red vectors would move a{111} plane from an A-position to aB position (marked by a green dot).
		The relevant displacement vectors areof the typeb = a/6<112>. (Check it! It's good exercise forgetting used to lattice projections). Dislocations with this kind of Burgersvector are calledpartial dislocations, Shockleydislocations, or simplyShockleypartials.
		In our<110> projection, Shockley and Frank partials look like this(after a picture from "Hull and Bacon"). The pictures aredrawn in a slightly different style, to make things a bit more complicated (getused to it!)
		You can't quite see the Shockleydislocation? Well, neither can I. But it is time to get used to the fact thatnot all dislocations are edge dislocation, clearly visible in schematicdrawings. We will encounter dislocations that are far weirder and almostimpossible to "see" in a drawing, or hard to draw at all. Butnevertheless they exist, possess a stress- and strain field described by theformulas from before, and are just thereal world inside crystals.
	By now you are wondering if thesepartial dislocations are an invention of bored professors? They are more or less the kind of dislocations that really existinfcc crystals (and some others)!
		The reason for this is that perfectsdislocations (with a Burgers vector of the typea/2<110>, i.e. alattice translation vector) will. This is one kind of a possible reactioninvolving partial dislocations, which we are going to study in the nextsubchapter.

© H. Föll