Lilienfeld 1925 Split the Support Transversely

# Split the Support Transversely: A Controlled Fracture, Not a Break

Step 1 chose glass specifically because it stays electrically invisible and withstands the device's bias — properties that have nothing to do with how predictably that same glass actually fractures. Splitting the block transversely is not a matter of applying enough force somewhere and hoping the crack lands in a useful place; glass is brittle enough that an uncontrolled fracture propagates wherever the geometry and internal flaws happen to concentrate stress, which is rarely the single straight line this step actually needs. The real content of this step is forcing that fracture to occur exactly where the control electrode will later need to sit, by deliberately lowering the stress required to crack the glass at one specific transverse line, well below what it would take to crack it anywhere else.

## 1. A Flaw Lowers the Stress a Crack Needs to Grow

Griffith's fracture criterion describes exactly why a deliberately introduced flaw — a scribed line across the intended split — makes fracture easier at that location than anywhere else on the same block. The stress intensity at the tip of any flaw of length $a$ under an applied stress $\sigma$ is:

where $Y$ is a geometric factor depending on the flaw's shape. A crack only propagates once $K_I$ reaches the glass's own critical fracture toughness, $K_{IC}$ — and because $K_I$ grows with $\sqrt{a}$, a scribed flaw deliberately made longer than any naturally occurring surface defect elsewhere on the block reaches that critical value at a far lower applied stress than an unscribed region would. This is the entire mechanism behind scoring glass before breaking it: not weakening the material in some vague sense, but placing one specific location so far ahead of every other point on the block in its race toward $K_{IC}$ that the fracture has nowhere else to go.

## 2. Real Diagram: One Flaw Wins the Race to Critical Stress Intensity

## 3. The Resulting Surface Has to Be Flat Enough to Seat the Foil Later

A controlled fracture along the right line is only half the requirement — the two resulting faces also have to be flat and matched closely enough that Step 3's foil sits with uniform contact when the block is reassembled, rather than bridging a gap at some points and crushing against a high spot at others. Treating the fracture surface's own deviation from a true flat plane as the limiting factor, a workable criterion is that this deviation stay small relative to the foil itself:

A fracture driven by a single, dominant stress-intensity flaw tends to propagate along a cleaner, flatter plane than one left to find its own path through whichever natural flaws happen to be present — which is a second, independent reason the scribe-and-fracture approach in Section 1 matters here: it is not only about choosing where the glass breaks, but about the surface quality that choice happens to produce as a side effect, one that Step 3 and Step 4 depend on without ever controlling it directly themselves.

## Real Diagram: Why the Scribe Reaches the Threshold First

## Split the Support Transversely's Place in the Process Lineage

Split the Support Transversely follows Step 1, Prepare the Insulating Support, which selected and verified the glass block this step now deliberately fractures; it precedes Step 3, Insert Thin Aluminum Foil, which needs the flat, correctly located gap this fracture creates in order to seat the control electrode at all. It is the second step of this concept's construction sequence and the first point where the glass's mechanical behavior, rather than its electrical properties, becomes the active concern — a controlled brittle fracture standing in for what could otherwise just as easily have been an uncontrolled, useless break.