A rendered dendrite, a cubic metal crystal with a satin finish, on a dark background: six main arms along the axes of a cube, each lined with rows of side branches, the longest carrying smaller branches of their own.

Phase-field · WebGPU

Watch metal freeze.

A phase-field solidification lab, live in your browser. Grow dendrites, pour alloys, read the grains.

Growth

It grows in branches.

A metal crystal freezing out of its melt does not stay a ball. It sends arms out along the directions its lattice prefers.

Branching

Arms grow on arms.

Side arms sprout along each main arm, and smaller arms branch off the side arms, all along the same cube axes.

Cooling

Then it cools.

The render stops growing here. In a real casting the arms keep thickening and coarsening while melt remains.

The whole crystal

One seed, one crystal.

Every arm grew from the first speck, and all of them share one lattice.

The instrument

Grow your own.

The instrument solves the phase-field equations on your GPU. Change the melt and the branches change.

Open the instrument

Skip to the instrument

A six-armed crystal seen through the ORIENT lens: one grain, one color

One casting · ten lenses

02 / 10

ORIENT

Polarized light: every grain shows in its own color.

A field of white-hot steel dendrites solidifying

Melt types

01 / 04

Steel

It pours white-hot, the brightest melt in the instrument.

A six-armed dendrite growing in the volumetric 3D solver, raymarched

The third dimension

TRUE 3D

A cubic crystal grows six arms, not four. In the instrument you can section the volume, x-ray it for porosity and export it as an STL.

Aluminum dissolves 1.65 wt% silicon and no more. Past that line the casting is two phases and this solver grows one, so the app names the silicon it will not grow rather than drawing both.

Liquidus depressionΔT_L = Σ m_ic_i, two mixes

A356 + TiB · Q ≈ 71 K44.7 K

Al–1Zn · Q ≈ 1 K1.6 K

The bars are liquidus depressions, not grain counts; an earlier grain-count comparison here was withdrawn, and the science page has the record.

Alloy composer

A356 + TiB

Add elements to a base metal by weight. The composer reports the liquidus shift, Q and where the mix sits on its phase diagram.

Al base + Si 7.0 wt% + Mg 0.35 wt% + Ti 0.12 wt%

growth restriction factor Q: 71K
the pour: Si 7.0wt%
equilibrium leaves: (Al) + (Si)

Pour this alloy Mix your own

The science

No scripts. No particles.

The crystal and the heat around it are two coupled fields, solved cell by cell on your GPU. Pour an alloy and a third field, the solute, joins them.

Read the science Open the instrument

phase field φ: τ ∂φ/∂t = ∇·(ε²∇φ) + φ(1−φ)(φ−½+m)
heat T: ∂T/∂t = ∇²T + K ∂φ/∂t
phase-field model: Kobayashi (1993), anisotropic
alloy: Warren–Boettinger, dilute
grain size: ASTM E112
emergent: CET, recalescence, twin competition