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Experimental demonstration of sustained entirely detached growth in the vertical directional solidification (VDS) configuration under terrestrial gravity: A dynamic capillary-gravity stability criterion of entirely detached solidification for the long length

This paper experimentally demonstrates that sustained entirely detached growth of antimony-based semiconductor crystals can be achieved under terrestrial gravity in a vertical directional solidification configuration using conical-bottom quartz ampoules, which stabilize the crystal-ampoule gap and improve crystallization quality by suppressing wall-induced defects.

Original authors: Dattatray Gadkari

Published 2026-07-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Dattatray Gadkari

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to grow a perfect, giant ice cube inside a glass jar. Usually, as the water freezes, it sticks to the glass walls. This causes the ice to crack, get messy, or grow unevenly because it's being squeezed and scratched by the jar. Scientists have long dreamed of growing crystals (like the special materials used in infrared cameras and lasers) without them ever touching the container walls. It's like trying to bake a cake that never touches the pan.

For a long time, people thought this "floating" growth was only possible in space, where gravity doesn't pull the liquid down. Or, they thought it only happened for a tiny moment before the crystal crashed back into the wall.

But here is the twist: A researcher named Dattatray Gadkari has shown that you can actually do this right here on Earth, under normal gravity, and keep it going for a long time.

The Magic Trick: A Special Oven and a Cone

Gadkari didn't use a spaceship or a magic wand. He used a custom-built oven (called a Vertical Directional Solidification furnace) and a very specific glass tube (a quartz ampoule) with a cone-shaped bottom.

Think of the oven like a giant, vertical thermometer that is hottest in the middle (around 1000°C), cooler at the top (500°C), and coolest at the bottom (200–300°C). This isn't a straight line of heat; it's a bumpy, wavy temperature landscape.

Inside this oven, he put a glass tube filled with melted semiconductor materials (mostly antimony-based, like Indium Antimonide or Gallium Antimonide). He cooled the tube slowly, moving it down through the heat zones.

The "Floating" Crystal

As the material cooled, something amazing happened. Instead of sticking to the glass, the solid crystal started to pull away from the walls, leaving a tiny, invisible gap of liquid between the crystal and the glass.

Imagine a swimmer in a pool who, instead of touching the side, manages to stay perfectly centered in the water, with a thin layer of water separating them from the pool wall all the way up. That is what happened here. The crystal grew upward, defying gravity, while staying completely detached from the glass tube.

This wasn't a short trick. The crystal stayed detached for a long stretch—between 40 and 75 mm in length. The gap between the crystal and the wall was incredibly small, ranging from 30 to 275 micrometers (that's thinner than a human hair!), but it stayed open and stable the whole time.

Why Didn't It Crash? The "Tug-of-War"

You might wonder: "Why didn't gravity just smash the crystal back into the wall?"

The paper explains that it's a delicate tug-of-war.

Gravity is trying to pull the heavy liquid down, which would squash the crystal against the glass.
Surface Tension (the "skin" of the liquid) is trying to hold the liquid in a curved shape, keeping the crystal away from the wall.

In most normal setups, gravity wins, and the crystal sticks. But Gadkari found a "sweet spot" where these two forces balance perfectly. He calls this the Gadkari Stability Criterion.

He discovered that if a specific number (let's call it Sigma, Σ) is between 0.60 and 0.65, the crystal stays floating.

If the number is below 0.60, the surface tension is too weak, and the crystal sticks to the wall.
If the number is above 0.65, the forces get too wobbly, and the gap collapses or becomes unstable.
But right in that narrow 0.60 to 0.65 zone? The crystal floats happily, growing long and straight without ever touching the glass.

What This Means for the Crystal

Because the crystal never touched the glass, it didn't get scratched or stressed. The paper reports that these "floating" crystals turned out to be much better quality. They had fewer cracks, fewer defects, and were more uniform than crystals grown the old way (where they stick to the wall).

What This Is NOT

It's important to know what this experiment didn't do:

It didn't use space or microgravity. It worked right here on Earth with normal gravity.
It didn't use magnets to float the liquid (like in some other experiments).
It wasn't just a tiny, split-second event. It was sustained growth over a long distance.
It wasn't a "floating zone" where the whole liquid is suspended in air. The liquid at the top was still touching the glass; only the solid crystal part was floating away from the wall.

The Bottom Line

Gadkari's work suggests that by carefully designing the shape of the glass tube (a cone at the bottom) and controlling the temperature in a very specific, non-linear way, we can create a "dynamic capillary stabilization." This is a fancy way of saying the heat and the liquid's surface tension work together to keep the crystal suspended in mid-air inside the tube.

The paper doesn't claim this solves every problem in crystal growth, but it provides strong experimental proof that sustained, entirely detached growth is possible on Earth for these specific materials, provided you stay within that narrow stability window of 0.60 < Σ < 0.65. It's a new way to grow high-quality crystals without the usual headaches of them sticking to their containers.

Technical Summary: Experimental Demonstration of Sustained Entirely Detached Growth in Vertical Directional Solidification (VDS) Under Terrestrial Gravity

Problem Statement
Directional solidification systems have long sought to utilize detached and dewetted growth phenomena to reduce crystal–ampoule interaction, thereby minimizing thermo-mechanical stress, suppressing wall-induced cracking, and improving interface regularity. While detached growth has been successfully demonstrated in microgravity environments and as partial or localized dewetting under terrestrial conditions, sustained, entirely detached growth over extended lengths under 1g (terrestrial gravity) remains insufficiently understood and experimentally elusive. Under Earth's gravity, hydrostatic loading, wetting instability, meniscus collapse, and reattachment tendencies typically destabilize long-duration crystal separation. Conventional models based on static dewetting or constitutional detachment often fail to explain long-scale, continuous separation against gravity without external mechanical separation or levitation.

Methodology
The study employed a custom-designed, single-zone Vertical Directional Solidification (VDS) furnace operating under terrestrial gravity. Key experimental components included:

Furnace Configuration: An indigenously developed single-zone furnace with a unique, highly nonlinear asymmetric thermal profile. The temperature distribution features a lower cooling zone (200–300°C), a central high-temperature zone (~~1000°C), and an upper zone (~~500°C). This architecture generates coupled axial and radial thermal gradients.
Ampoule Geometry: Sealed quartz ampoules with a conical-bottom geometry (apex angles of 45–75°) were used to facilitate self-oriented seed formation. The ampoules contained high-purity Sb-based semiconductor systems (InSb, GaSb, and InGaSb alloys) with various dopants (Te, Bi, Se, Mn, Mg).
Process Parameters: Growth was conducted with melt-column heights of 40–75 mm, crystal radii of 5–12 mm, and axial thermal gradients ranging from 10 to 32°C/cm. Translation speeds were maintained between 2–5 mm/h.
Experimental Scope: Over eighty growth runs were systematically analyzed to examine detached-gap evolution, interface morphology, and crystallization characteristics.

Key Contributions

Experimental Demonstration of Sustained Detachment: The paper reports the first experimental realization of sustained, entirely detached growth over lengths of 40–75 mm under terrestrial gravity without mechanical separation or microgravity conditions. The crystals remained continuously separated from the ampoule wall by a stable annular gap of 30–275 µm throughout the solidification process.
Dynamic Capillary-Stabilization Mechanism: The authors propose that this phenomenon is not a static dewetting event but a dynamically stabilized nonequilibrium state. The stability is governed by a coupled interaction of capillary pressure, hydrostatic force balance, thermocapillary redistribution, and the specific nonlinear thermal architecture of the VDS furnace.
The Gadkari Stability Criterion (GSC): A dimensionless stability parameter, $\Sigma$ , was derived and experimentally validated to define the stability window for detached growth. The parameter represents the ratio of destabilizing hydrostatic forces to stabilizing capillary forces:
$\Sigma = \frac{\rho g h r_g}{\gamma \cos \theta}$
Where $\rho$ $ρ$ is melt density, $g$ $g$ is gravity, $h$ $h$ is melt-column height, $r_g$ $r_{g}$ is the detached-gap width, $\gamma$ $γ$ is surface tension, and $\theta$ $θ$ is the wetting angle.
- Stable Regime: The paper identifies a narrow stability window where $0.60 < \Sigma < 0.65$ . Within this range, capillary pressure dynamically balances hydrostatic loading, sustaining the detached state.
- Instability Regimes: $\Sigma < 0.60$ leads to attached growth (gap collapse), while $\Sigma > 0.65$ results in gap destabilization and oscillatory reattachment.
Differentiation from Existing Models: The work distinguishes the VDS process from conventional Bridgman growth (continuous wall contact), static dewetting models (localized, near-equilibrium), and microgravity floating growth (levitation-based). The VDS process achieves detachment through thermal-gradient-driven dynamic stabilization while maintaining continuous melt feeding via wall contact of the liquid phase above the interface.

Results

Gap Stability: Experimental measurements confirmed that stable detached growth occurs only when the radial meniscus-gap width remains finite, nearly constant, and spatially stable along the growth axis. Gap widths varied between 30 and 275 µm, remaining stable despite crystal lengths up to 75 mm.
Crystal Quality: Detached crystals exhibited smooth external surfaces with significantly reduced wall-adhesion marks. Characterization data (Tables 1 and 2) indicated reduced dislocation densities (e.g., $0.62 \times 10^3$ cm $^{-2}$ for InSb) and improved structural uniformity compared to conventional attached growth.
Thermal Architecture Role: The nonlinear thermal profile was found to be critical. It induced thermocapillary convection and interface-curvature redistribution near the three-phase boundary, which dynamically stabilized the meniscus and prevented collapse.
Reproducibility: The detached configuration was reproducibly achieved across more than 80 runs with various Sb-based compositions, confirming that the phenomenon is intrinsically linked to the VDS thermal architecture rather than accidental dewetting.

Significance
The paper claims to establish a new framework for long-scale contactless bulk crystal growth under terrestrial gravity. By demonstrating that entirely detached growth can be sustained without microgravity or mechanical separation, the work challenges the conventional view that hydrostatic forces inevitably preclude long-duration detachment on Earth. The proposed dynamic capillary stabilization mechanism and the Gadkari Stability Criterion provide a theoretical and experimental basis for optimizing crystal growth conditions to minimize defects and stress. The authors assert that this process represents a distinct category of thermally stabilized annular detached directional solidification, offering a pathway to produce high-quality semiconductor substrates with reduced thermomechanical constraints.