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The Dislocation: Edge, Screw, and Mixed

A perfect crystal should be ludicrously strong, yet a copper wire bends in your fingers. The reason is a one-dimensional flaw — the dislocation — that lets a crystal shear one row of atoms at a time. Meet its two pure forms, the edge and the screw, the mixed dislocations in between, and the iron rule that a dislocation line can never simply stop inside a crystal.

The strength paradox

In the last rung you met the zero-dimensional flaws — the point defects, a missing atom here, a stranger squeezed in there. Now we step up one dimension, to a defect that runs as a LINE through the crystal, and it turns out to be the most consequential imperfection in all of materials science. To see why, start with a paradox. Take a flawless crystal and ask how hard you must push to make one whole plane of atoms slide bodily over the plane beneath it. You are fighting every bond across that plane at the same instant, and the arithmetic is brutal: the theoretical shear strength works out to roughly a tenth of the shear modulus G. For copper (G is about 48 GPa) that predicts yielding near 8 GPa.

Now measure it for real. A soft, well-annealed copper single crystal begins to yield at a shear stress of about 1 MPa — not 8 GPa. That is a shortfall of thousands. Real metals are not a touch weaker than the perfect-lattice estimate; they are one to four orders of magnitude weaker, and softer the purer and better-annealed they are. Something must let a crystal shear WITHOUT snapping every bond on the plane at once. That something is the dislocation: a line defect along which the crystal is already caught half-slipped, so that shearing the whole plane costs only the small price of walking the line across it, one row of bonds at a time.

The edge dislocation: an extra half-plane

The easiest dislocation to picture is the edge dislocation. Imagine a perfect stack of atomic planes, then jam one extra HALF-plane of atoms into the top half of the crystal, like slipping a spare card halfway into a deck. The rows above must crowd together to make room (they are in compression); the rows below spread apart to close the gap (tension). The interesting thing is not the half-plane itself but its bottom EDGE — the line, buried deep in good crystal, where the extra plane runs out. That line is the dislocation line, and the thin tube of badly-strained, mis-bonded atoms around it is the dislocation core. Crystallographers draw the whole affair with an upside-down 'T', the symbol ⊥: its stem is the extra half-plane, its foot rests on the plane the dislocation will later slide along.

EDGE DISLOCATION  (an extra half-plane of atoms, viewed end-on)

    o   o   o   o   o   o   o
    o   o   o   o   o   o   o     above:  rows CROWDED  (compression)
    o   o   o   |   o   o   o
    o   o   o   |   o   o   o      |  = the extra half-plane
    o   o   o   T   o   o   o      T  = the core (its bottom edge)
    o   o    o     o    o   o
    o   o     o       o    o      below:  rows SPREAD   (tension)
    o   o      o        o   o
   ---------------- slip plane ----------------

   * the dislocation LINE runs straight INTO the page, along the T
   * b (Burgers vector) = one atom-spacing, lying IN the page and
     PERPENDICULAR to the line   --->   (this is EDGE character)
An edge dislocation seen end-on: an extra half-plane wedged in from above crowds the rows over it and spreads those below. Its buried bottom edge is the dislocation line (into the page); the Burgers vector b lies across that line.

How much slip does this one line carry, and in which direction? All of that is captured by a single vector, the Burgers vector b. You measure it by walking a closed loop of atom-to-atom steps around the line and seeing by how much the loop fails to close — the Burgers circuit, which is the whole subject of the next guide. For now, hold just one fact: for an edge dislocation, b is PERPENDICULAR to the dislocation line, and it points along a close-packed row by exactly one atomic spacing. That right angle between the line and its Burgers vector is the signature of pure edge character.

The screw dislocation: a spiral ramp

The second pure form is stranger, and worth picturing slowly. Take a block of crystal, imagine slicing halfway through it on a flat cut, then shove the two lips of the cut past each other by one atomic spacing in a direction PARALLEL to the cut's leading edge — and reweld. There is no extra half-plane anywhere. Instead the once-flat atomic planes are now joined into a single continuous helical ramp, exactly like the spiral ramp of a multi-storey car park that fuses 'floor 3' and 'floor 4' into one unbroken sloping surface. Walk a full loop around the central line and you climb up (or down) by one plane. That central line is a screw dislocation, and the helix is why it is named after a screw thread.

Run the same Burgers-circuit measurement around a screw and you meet its defining contrast with the edge: here the Burgers vector b lies PARALLEL to the dislocation line, not across it. Edge and screw are the two clean extremes — b perpendicular to the line, or b along it — and they behave quite differently. An edge carries that compression-above, tension-below asymmetry; a screw's distortion is a pure twist, with no extra plane and no crowding, which is exactly why (as guide 3 will show) a screw can transfer its glide onto more than one plane while an edge is confined to a single one.

Mixed dislocations, and the line that cannot just stop

Real dislocations are almost never purely edge or purely screw. Picture a dislocation as a curved line — very often a closed loop — threading through the crystal. Here is the key constraint that ties everything together: the Burgers vector b is the SAME everywhere along that one line. It is a property of the line as a whole, fixed once and for all — but the line's DIRECTION is free to wander. Where the line runs perpendicular to b it is locally edge; where it runs parallel to b it is locally screw; and everywhere in between it is a mixed dislocation, part edge and part screw in a smoothly varying blend. A single circular loop with one fixed b is therefore pure edge at two points, pure screw at two points, and mixed all the way round the rest — edge and screw are not two different objects but two views of the same thing.

This constant-b rule has a beautiful consequence: a dislocation line can never simply stop dead in the middle of a perfect crystal. If it did, you could draw a Burgers circuit that wraps the line on one side of the endpoint and misses it on the other, demanding that the crystal be both slipped and not slipped along the very same cut — a contradiction. So a dislocation line must do one of exactly three things: close back on itself in a loop, run out to a free surface or a grain boundary, or meet other dislocations at a node, where their Burgers vectors balance like electric currents at a junction (this is Frank's node rule). A tangled crystal is therefore a single CONNECTED network of line, never a scatter of loose ends.

How it moves — and why that makes metals soft

Now we can dissolve the paradox we opened with. Under a shear stress a dislocation does not snap a whole plane of bonds; it glides, and at any instant only the single row of bonds right at its core swaps partners. Think of dragging a heavy rug across a floor. Haul the whole rug and you fight friction under its entire area at once — that is the perfect-crystal price. Instead, kick a small ruck, a wrinkle, into one end and walk that ruck across the rug; at each moment only the little buckle is moving, yet by the time it reaches the far end the whole rug has shifted by the width of the ruck. A gliding edge dislocation is that travelling ruck — and a caterpillar humping a single fold along its body is the very same trick in the animal kingdom.

  1. A shear stress pushes the atoms just above the slip plane sideways against those just below.
  2. Rather than every bond across the plane breaking together, only the one row of bonds at the dislocation core stretches and snaps.
  3. The extra half-plane instead bonds to the next plane over; the former neighbour is left behind as the new half-plane.
  4. The dislocation line has advanced by exactly one Burgers vector along its slip plane — a tiny, cheap step — and the whole process repeats.
  5. When the line finally reaches a free surface, the top half of the crystal has slipped over the bottom by one atomic spacing, leaving a visible step.

A dislocation glides most easily on the crystal's most widely-spaced, densely-packed planes and along its close-packed directions; that pairing of a slip plane with a slip direction is a slip system. In face-centred-cubic metals like copper it is the {111} planes and <110> directions — twelve equivalent systems — which is precisely why FCC metals are so ductile. And this is the honest headline of the whole rung: because gliding dislocations let a crystal shear one row at a time, real metals fall far below their theoretical strength, and it is only because these lines glide that metals can be forged, rolled and drawn at all. The rest of this rung fills in the picture — guide 2 measures b with the Burgers circuit; guide 3 turns glide into the full story of slip and strength; guide 4 works out the stress field, the line energy (which grows as b squared), and the Peierls stress of lattice friction a dislocation must beat to move; and guide 5 splits a dislocation into partials bounding a stacking fault, and shows how a Frank-Read source breeds the fresh line that keeps a crystal deforming.